Ultrafast Optical Control over Hot Electron Dynamics in
Nanoplasmonic Systems
byJacob Pettine
B.S., University of Colorado Boulder, 2013

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Department of Physics
2020

Committee Members:
David Nesbitt, Chair
Markus Raschke
Margaret Murnane
Andreas Becker
Gordana Dukovic

ProQuest Number: 28156452

All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent on the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,a note will indicate the deletion.

ProQuest 28156452
Published by ProQuest LLC ( 2020 ). Copyright of the Dissertation is held by the Author.
All Rights Reserved.
This work is protected against unauthorized copying under Title 17, United States CodeMicroform Edition © ProQuest LLC.
ProQuest LLC
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346

ii
Pettine, Jacob (Ph.D., Physics)
Ultrafast Optical Control over Hot Electron Dynamics in Nanoplasmonic Systems
Thesis directed by Prof. David Nesbitt

Nanoscale metal systems support strong light-matter interactions known as plasmons,
which generate high densities of high-energy (“hot”) electrons. These hot electrons can be
harvested by surrounding molecules or semiconductors, or emitted into free space, with eachpossibility representing a broad set of applications, including next-generation solar energy
conversion and storage, novel biological therapies, and ultrafast nanoscale electronics. The
full realization and optimization of many of these applications, however, will require a detailed understanding of where hot electrons are excited, how fast and far they travel, andwhat directions they travel in—i.e. their spatial, temporal, and momentum distributions.
In this thesis, new methods are introduced for measuring, modeling, and even optically controlling nanoplasmonic hot electron distributions on femtosecond timescales, using a unique
single-particle, angle-resolved nonlinear photoemission spectroscopy technique with a highlytunable ultrafast visible laser system. These experiments are both complemented and driven
by the parallel development of a simple new theoretical framework for predictively modeling nanoplasmonic hot electron distributions and dynamics. A variety of nanoparticle
geometries are investigated to reveal an equally wide variety of behaviors, from the simple
directional photoemission properties of complex defects to the strikingly complex and often
counter-intuitive photoemission properties of simple nanorods and spherical nanoparticles.

Dedication

To my wife, Janet, my parents, Holly, Chris, and Patty, and my grandparents, Bea,
Al, and Helen, for the examples they all set with their strengths of character and for theirunconditional support.

iv

Acknowledgements

I would first like to thank my family and friends for their years of support, patience, andinterest. One of the great joys of my PhD has been sharing the excitement and demystifying
the experience of laboratory life with others. For directly shaping and sharing in thatlaboratory life, I would like to thank my friends and colleagues in the Nesbitt Lab, Tim,
Mikhail, Hsuan-Lei, Andrea, Brian, David, Kirstin, Andy, Mia, Dan, Abhigyan, Ya-Chu,and Candice, with special thanks my adviser, David Nesbitt, for his insightful guidanceand emphasis on the importance of community in science. I would also like to thank myundergraduate adviser, Dana Anderson, for his continued guidance. I’m very grateful tothe phenomenal technical and administrative staff within JILA, including David, Mark,
Corey, J.R., Jim, James, Carl, Terry, Hans, Kim, Todd, Beth, Julie, David, Kim, Agnieszka,
Maryly, Cindy, Steven, Rebecca, Brian, Jennifer, Randall, Daniel, Karen, and Jason, as
well as Garry in MCDB. I would further like to thank my collaborators, Catherine Murphy
and Sean Meyer at the University of Illinois Urbana-Champaign, as well as Teri Odom
and Priscilla Choo at Northwestern University. The opportunity to work with exceptional
scientists both within and outside of the local CU Boulder community was a true highlightof my PhD. I also gratefully acknowledge the AFOSR, the NSF Physics Frontier Center, andthe NSF Graduate Research Fellowship Program for funding this work. Finally, I would liketo thank my wife, Janet, for reminding me to also live a full life outside of the lab.

Contents

Chapter
1 Introduction1

1.1

Nanoplasmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.2

Dynamics in Nanoplasmonic Systems . . . . . . . . . . . . . . . . . . . . . .

9

1.3

Hot Carrier Science and Applications . . . . . . . . . . . . . . . . . . . . . .

10

1.3.1

Photocatalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.3.2

Photodetection and Photovoltaics . . . . . . . . . . . . . . . . . . . .

12

1.3.3

Photocathodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

1.4

Volume- and Surface-Mediated Photoelectric Effects . . . . . . . . . . . . . .

14

1.5

Angle-Resolved Photoemission Measurements . . . . . . . . . . . . . . . . .

16

1.6

Ultrafast Nanoscale Photocurrent Control . . . . . . . . . . . . . . . . . . .

18

2 Experimental Methods

20

2.1

Scanning Photoelectron Imaging Microscopy . . . . . . . . . . . . . . . . . .

21

2.2

Ultrafast Laser and Optics Systems . . . . . . . . . . . . . . . . . . . . . . .

22

2.2.1

Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.2.2

Dispersion Compensation . . . . . . . . . . . . . . . . . . . . . . . .

24

2.2.3

Pulse Characterization . . . . . . . . . . . . . . . . . . . . . . . . . .

27

2.3

Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

2.4

Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

vi
2.5

Surface Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2.6

Scanning Sample Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.7

2D Velocity Map Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

2.8

3D Velocity Map Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

2.9

Femtosecond Pump-Probe Studies . . . . . . . . . . . . . . . . . . . . . . . .

42

2.10 System Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

3 Theoretical Methods
3.1

3.2

3.3

3.4

3.5

3.6

44

Analytic Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.1.1

Sphere and Ellipsoid Electrostatics . . . . . . . . . . . . . . . . . . .

44

3.1.2

Mie Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

3.1.3

Hybridization Theory . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

Finite Element Electrodynamics Simulation . . . . . . . . . . . . . . . . . .

50

3.2.1

Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . .

50

3.2.2

Cross-Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Thermalization Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.3.1

Femtosecond Electron Thermalization . . . . . . . . . . . . . . . . . .

56

3.3.2

Picosecond Lattice Thermalization . . . . . . . . . . . . . . . . . . .

58

3.3.3

Two-Temperature Model . . . . . . . . . . . . . . . . . . . . . . . . .

58

Electron Emission Mechanisms. . . . . . . . . . . . . . . . . . . . . . . . .

59

3.4.1

Thermionic Emission . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.4.2

Multiphoton Photoemission (MPPE) . . . . . . . . . . . . . . . . . .

61

3.4.3

Optical Field Emission (OFE) . . . . . . . . . . . . . . . . . . . . . .

62

Multiphoton Photoemission Theory . . . . . . . . . . . . . . . . . . . . . . .

63

3.5.1

Volume Monte Carlo Modeling. . . . . . . . . . . . . . . . . . . . .

64

3.5.2

Surface Photoemission Theory . . . . . . . . . . . . . . . . . . . . . .

67

3D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

vii
3.6.1

BASEX Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

3.6.2

Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

4 Volume Photoemission from Thin Gold Film

74

4.1

Three-Step Photoemission Modeling . . . . . . . . . . . . . . . . . . . . . . .

74

4.2

Au Film Velocity Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

4.3

Interband vs. Intraband Photoexcitation . . . . . . . . . . . . . . . . . . . .

82

4.4

VMI Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

4.5

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

5 Optical Photocurrent Control with Nanoshells and Nanostars

92

5.1

Gold Nanoshells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2

Directional Photoemission from Nanoshell Defect Hot Spots . . . . . . . . . 102

5.3

Ultrafast Nanostar Photocathodes . . . . . . . . . . . . . . . . . . . . . . . . 115
5.3.1

Nanostar Plasmon Resonances . . . . . . . . . . . . . . . . . . . . . . 117

5.3.2

Single-Tip Photoemission Properties . . . . . . . . . . . . . . . . . . 122

5.3.3

Polarization- and Frequency-Controlled Directional Photoemission . . 135

5.3.4

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6 Volume vs. Surface Multiphoton Photoemission
6.1

93

143

Gold Nanorods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.1.1

Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

6.1.2

Nanorod SPR Properties . . . . . . . . . . . . . . . . . . . . . . . . . 147

6.2

Volume-Mediated Nanorod MPPE . . . . . . . . . . . . . . . . . . . . . . . . 149

6.3

Detuning into the Surface-Mediated Regime . . . . . . . . . . . . . . . . . . 157

6.4

General Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

6.5

Regulating Photocurrents with Mesoporous Silica Coatings . . . . . . . . . . 175

6.6

Continuous Angular Control over Nanoshell Photoemission . . . . . . . . . . 176

viii
7 Ultrafast Time-Resolved Velocity Map Imaging

186

7.1

Femtosecond Pump-Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

7.2

Time-Resolved Velocity Map Imaging . . . . . . . . . . . . . . . . . . . . . . 191

7.3

7.2.1

Fermi Liquid Theory Behavior . . . . . . . . . . . . . . . . . . . . . . 193

7.2.2

Hot Electron Decay Processes . . . . . . . . . . . . . . . . . . . . . . 195

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

8 Summary and Outlook

202

Bibliography

205

Appendix
A Laser Shutter and Piezo Driver Circuit Diagrams

223

Figures

Figure1.1

Plasmon resonances modes for bulk, surface, and nanolocalized systems . . .

7

2.1

Overview of the SPIM apparatus and example SPIM scan . . . . . . . . . .

23

2.2

Frequency-resolved optical gating characterization of Ti:sapphire pulses . . .

28

2.3

Vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.4

Photograph of the ample stage . . . . . . . . . . . . . . . . . . . . . . . . . .

36

2.5

Velocity map imaging lens and simulated trajectories . . . . . . . . . . . . .

38

2.6

Photograph of the velocity map imaging system . . . . . . . . . . . . . . . .

41

2.7

Scheme for 3D velocity map imaging data collection . . . . . . . . . . . . . .

41

3.1

Cross-sections calculated via FEM field solutions in COMSOL for a gold
nanorod in water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

54

Two-temperature model evolution of the electron and lattice temperatures fora gold nanorod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.3

Monte Carlo surface and volume meshes . . . . . . . . . . . . . . . . . . . .

66

3.4

Surface photoemission simulation geometry . . . . . . . . . . . . . . . . . . .

71

4.1

Illustration of the ballistic three-step photoemission process . . . . . . . . . .

79

4.2

Gold film VMI series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

4.3

Gold film intensity-dependence process order characterization. . . . . . . .

83

4.4

Gold film photoemission spectrum . . . . . . . . . . . . . . . . . . . . . . . .

87

x
4.5

Velocity map imaging calibration . . . . . . . . . . . . . . . . . . . . . . . .

89

5.1

Nanoshell TEMs and representative dark-field scattering spectrum . . . . . .

93

5.2

Calculated and measured nanoshell cross-sections, field enhancements, andphotoemission spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

5.3

Nanoshell intensity-dependence process order characterization . . . . . . . .

97

5.4

Nanoshell VMI series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

5.5

Directional photoemission from a single Au nanoshell . . . . . . . . . . . . . 104

5.6

Nanoshell photoemissivity and directionality statistics . . . . . . . . . . . . . 106

5.7

Confirmation that all nanoshell photoemission takes place in the perturbative
multiphoton regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.8

Polarization-controlled directional 3PPE from a single nanoshell with multiple
hot spots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.9

Example nanoshell SEMs showing defects correlated with directional emission 112

5.10 Nanoshell finite element simulations . . . . . . . . . . . . . . . . . . . . . . . 114
5.11 Single-nanostar plasmon resonance excitation and photoelectron velocity mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.12 anostar statistical characterization via electron microscopy . . . . . . . . . . 120
5.13 Characterization of single-tip multiphoton photoemission . . . . . . . . . . . 124
5.14 Single-tip directional velocity distributions . . . . . . . . . . . . . . . . . . . 125
5.15 Nanostar finite element simulations . . . . . . . . . . . . . . . . . . . . . . . 127
5.16 Representative nanostar electron sea and lattice heating . . . . . . . . . . . . 129
5.17 Experimental and reconstructed nanostar velocity distributions . . . . . . . . 131
5.18 Nanostar photoemission time traces . . . . . . . . . . . . . . . . . . . . . . . 132
5.19 Nanostar photoemissivity and limitations due to melting . . . . . . . . . . . 134
5.20 Nanostar multi-tip excitation and selectivity . . . . . . . . . . . . . . . . . . 136
5.21 Frequency-controlled directional photoemission from a single nanostar . . . . 139

xi
5.22 Polarization-controlled directional photoemission from a single nanostar . . . 140
6.1

Characterization of nanorod surface plasmon resonance photoemission properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

6.2

Nanorod TEMs, dimension statistics, and UV-vis spectra . . . . . . . . . . . 150

6.3

Photoemission characteristics of the nanorod samples . . . . . . . . . . . . . 150

6.4

Nanorod VMIs for different diameters and ligands . . . . . . . . . . . . . . . 151

6.5

Volume photoemission distributions as a function of nanorod aspect ratio . . 153

6.6

Nanorod intensity-dependence process order summary . . . . . . . . . . . . . 154

6.7

Calculated angular contrast values for nanorods of different diameters andaspect ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

6.8

Finite element simulations of nanorod surface and volume plasmonic fieldenhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.9

Surface photocurrent and internal quantum efficiency maps for resonantlyexcited nanorods of different aspect ratios . . . . . . . . . . . . . . . . . . . 162

6.10 Transition from nanorod volume to surface photoemission with red detuning

164

6.11 Photoemission angular contrast as a function of relative and absolute energy
detuning from nanorod SPRs . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.12 Red-detuned nanorod intensity-dependence . . . . . . . . . . . . . . . . . . . 165
6.13 Two-temperature model of electron and lattice heating for a gold nanorod . 167
6.14 Nanorod volume and surface photoemission time traces . . . . . . . . . . . . 167
6.15 Nanorod surface emission changes over time . . . . . . . . . . . . . . . . . . 168
6.16 Effects of screening, S/V ratio, and nanoparticle geometry (curvature) on
surface and volume contributions . . . . . . . . . . . . . . . . . . . . . . . . 172
6.17 Slices of plasmonic field enhancements for various nanoparticle geometries . . 173
6.18 Gold nanosphere and nanoshell characterization . . . . . . . . . . . . . . . . 178

xii
6.19 Photoemission properties of the representative correlated nanoshpheres andnanoshells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.20 Simulated nanosphere and nanoshell volume and surface plasmonic fields andcorresponding photoemission distributions . . . . . . . . . . . . . . . . . . . 182
6.21 Continuous polarization-controlled nanoshell photoemission rotation over thefull azimuthal range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.1

Nanorod pump-probe intensity- and polarization-dependence . . . . . . . . . 189

7.2

Nanorod pump-probe time delay scans . . . . . . . . . . . . . . . . . . . . . 190

7.3

Angle-integrated 3D-reconstructed kinetic energy spectra for a gold nanorod

7.4

Energy-dependent hot electron lifetimes in a single gold nanorod . . . . . . . 194

7.5

Various hot electron decay pathways . . . . . . . . . . . . . . . . . . . . . . 196

7.6

Effect of pump beam intensity on measured average hot electron decay time

192

198

Chapter 1
Introduction

Plasmonic science has experienced strong exponential growth in recent decades,[23]driven by applications such as surface-enhanced Raman scattering[71] (SERS) and sensing.[103]The dramatic increase in interest has been sustained by an increasing variety of precisionsynthetic[41, 113, 124] and fabrication[39, 206] methods, along with novel applications inareas such as solar energy harvesting,[30, 83] metamaterials,[132, 194] lasers,[194] quantum
nanophotonics,[50] biological therapies,[157, 13] and ultrafast electron sources.[162, 126] Central to all of these applications is the simple concept of conduction electrons collectively“sloshing” back and forth in a nanoscale metal container (nanoparticle). For certain metals(e.g. Au, Ag, Cu, Al) this resonant oscillation can be very strong and can occur in thevisible spectral range, with resonance properties tabulated for a variety of materials.[18] As
charge carriers (electrons and holes) build up on the nanoscale surfaces of high and highlyvarying curvature, they generate strong evanescent electric near-fields that may represent
10-fold or higher enhancements over the incident optical excitation fields. The strong plasmonic optic field density can subsequently excite high densities of hot charge carriers within
the nanoscale volumes, which can be collected/emitted into the surrounding medium (e.g.
molecules, semiconductors, or free space) or may decay into phonons to generate high thermal energy densities.[69] The resonance properties of nanoplasmonic particles/structures, thecorresponding spatiotemporal energy (re)distribution in these systems, and their resonancepositions depend strongly on the particle material, shape, and surrounding medium.[111]2
The present work focuses both on photonic (plasmonic) and electronic (hot carrier)processes in nanoplasmonic systems, with a strong emphasis on the hot carrier dynamics that occur on tens of femtosecond timescales. These processes are central to hot carrier science and technology, which is a field in and of itself with important implications
for next-generation solar photovoltaics,[30] chemical conversion and energy storage,[31, 6]
photodetectors,[22] ultrafast electron imaging/diffraction,[127] x-ray laser sources,[138, 75]
and terahertz nanoelectronics.[89, 173] All of these applications rely on the efficient generation and transfer/emission of hot carriers by shining coherent (laser) or incoherent (e.g.
solar) light on nanoplasmonic structures. Ultimately, the efficacy of these technologies willclearly depend on how well the hot carrier excitation processes and subsequent dynamics areunderstood.
Much of the physics central to hot carrier science (particularly with semiconductor
or vacuum collection media) has already been developed in the photoemission literaturefrom the past century, with particularly strong progress in the 1960s [17] and the 1970s[114, 48] on the volume- and surface-mediated photoeletric effects,[189] as will be discussed
in much greater detail in Section 1.4, Chapter 3, and subsequent chapters. However, evenfor macroscopic crystalline solids, the full (one-step) quantum theory of photoexcitation andemission is often intractable, forcing practitioners to rely on phenomenological (three-step)models,[78] to be discussed later. The uniquely strong, nanolocalized field enhancements andnanoscale curvatures of nanoplasmonic systems present further challenges for theoreticallymodeling electronic photoexcitation and emission. Moreover, visible plasmonic excitation
frequencies (∼1.5–2 eV) require multiphoton absorption to overcome the work function ofplasmonic metals (e.g. φAu ≈ 5 eV) and the band structure of gold, for instance, permits
few to no direct/vertical/interband transitions above the vacuum level, instead promoting avariety of coherent vs. incoherent and volume vs. surface excitation pathways.
To understand nanoplasmonic hot carrier dynamics in detail—with the ultimate goalsof predictive modeling, tailored particle/structure design, and optical control over hot elec-

3tron emission dynamics—six–seven degrees of freedom must be experimentally resolved:
two–three spatial degrees of freedom, three momentum degrees of freedom, and the temporal evolution of the hot carrier excitation and emission distributions. Spin or carrier
charge can also become important in various applications (e.g. photocatalysis), althoughwill likely be more readily encoded in any experimental/theory that captures many or allof the above six–seven degrees of freedom.[169] Thus, the most definitive experiments will
include some combination of nanoscale spatial resolution, angle-resolved momentum resolution, and femto/attosecond temporal resolution. While a number of high-quality nanometerfemtosecond space-time-resolved photoemission studies are underway,[34] understanding of
the essential momentum degrees of freedom is still nascent for nanoplasmonic hot electron
science. The new experimental insights and theoretical models introduced here are therefore
largely the result of building up a new technique for a better understanding of the momentum
degrees of freedom of hot electrons emitted from single supported nanoparticles.
Following a general overview in the present chapter and detailed summaries of theexperimental (Chapter 2) and theoretical (Chapter 3) methods utilized and developed forthis work, this thesis will evolve chronologically from initial nanoplasmonic velocity mapping
studies in Chapter 4, to capabilities for ultrafast photocurrent control via selective nanoshelland nanostar surface hot spot emission in Chapter 5, to fully distinguishing and modeling volume vs. surface photoexcitation/emission via gold nanorods in Chapter 6. Finally,
Chapter 7 will address current efforts combining femtosecond pump-probe and 3D velocity
mapping, with a look at future directions in Chapter 8.
Some initial notes on nomenclature that will be relevant throughout the thesis:
 The terms photoemission and photocurrent will be used interchangeably, although

they normatively represent the difference between emission into the vacuum andemission into a surrounding collection material (e.g. a semiconductor). Such terms
may also be applied to charge transfer to a molecular adsorbate. The essential fea-

4tures of the excitation and emission/transfer are largely the same, and it is primarily
these features that are investigated herein.
 The terms nanoparticle vs. nanostructure typically denote synthetic particles vs.

fabricated (nanolithographic) structures, respectively, although the distinction isneither fundamental nor particularly distinct for some hybrid methods (e.g. ablative
nanoparticle generation or chemical nanostructure growth). Nanoparticles are typically synthesized in solution and thus tend to have stabilizing ligands, while nanostructures are typically fabricated via electron beam lithography or other nanolithography methods (e.g. nanosphere lithography) and are thus ligand-free. Nanoparticles
are often (though not always) monocrystalline, while nanostructures are often polycrystalline. Only synthetic, ligand-stabilized nanoparticles are discussed here, but
the supported nanoparticles and nanostructures are often treated interchangeably inthe literature (and rightly so), so long as the particle geometry and relevant environmental effects (e.g. ligands, substrate) are accounted for accordingly. Both terms
will thus be used to denote nanoplasmonic systems. It shall be shown that, barring
damping effects over time due to conversion into an amorphous carbon layer,[183]ligands have negligible observable effect on the hot electron dynamics and the measured photoemission distributions.
1.1

Nanoplasmonics
Plasmonic nanoparticles are metal (e.g. Au, Ag, Cu, Al) nanoparticles hosting acollective conduction electron oscillation known as a localized surface plasmon resonance(SPR). Conduction electrons in metals are delocalized/itinerant, which in a ballistic picturemeans that they are free to move around with respect to the positive ion metal lattice. Thissystem is therefore a plasma with mobile negative charge carriers (electrons) and a static
positive ion background. In the free electron limit, such systems are known as Drude or5free-electron metals, with plasma frequency (see discussion below)sne e 2
ωp =
,
0 me

(1.1)

while in other cases material dispersion can be accounted for via effective mass me → m∗e .
The plasma frequency represents the fundamental optical response time of the metal. Foran approximate toy model, taking a cubic volume element, V , and displacing the conduction
electrons density ne by a small amount δx leads to depolarization field between the two
sheets of charge Edep = ene /0 δx, neglecting fringe effects. Note that 0 is used instead of 
because the process under examination is the screening itself (with d-band screening effects
neglected). Thus, the depolarization force on a displaced charge is
Fdep = −eEdep
=−

e2 ne
δx
0

(1.2)

= −me ωp2 δx,
which is harmonic with plasma frequency given by Eq. 1.1.
The full optical response of the material is encoded in the complex dielectric function,
which is isomorphic (contains the same information and bijectively maps onto) the complex
refractive index, susceptibility, and polarizability. The optical response can be derived via
the Lorentz oscillator model,[81]me x00 (t) + γx0 (t) + me ω02 x(t) = −eE(t)(1.3)

with harmonic field E(t) = E0 e−iωt and damping rate γ. For x(t) = Ae−iωt , the dipole
moment for N electrons is given byp(t) = −N ex(t)
1
e2
E.
=
2
me ω0 − ω 2 − iγω(1.4)

The dielectric function, /0 = 1 + χ(1) is therefore given by
(ω)
ne2 X
fj
=1+
,
2
0
0 me j ωj − ω 2 − iωγj

(1.5)

6
where fj is the oscillator strength for a resonance andP

j fj = 1 (Thomas-Reiche-Kuhn sumrule). Approximating a free-electron metal or, correspondingly, taking the optical frequency
ω to be much greater than the largest system resonance, ωj,max , Eq. 1.5 reduces to thewell-known Drude model,[81, 115]
ωp2
(ω)
=1− 2
.
0
ω + iγω(1.6)

At this point, the phenomenological γ term is often modified for d-band effects or surface
collisional effects via simple Mattheissen’s rule summation over the relevant damping rates.
For ω  γ, Eq. 1.6 takes the simple form for the real part,ωp2
1 (ω)= 1 − 2,
0
ω

(1.7)

ωp2 γ
2 (ω)
= 3 ,
0
ω

(1.8)

and imaginary part,of the dielectric function. Neglecting the imaginary part, it is seen that that the metal ishighly reflective with no propagating field for ω < ωp (negative  and thus purely imaginary√refractive index, n = ) and exponential/evanescent skin depth, with no absorption if2 = 0—i.e. strictly no damping and thus infinite conductivity. For ω > ωp , the metal
becomes perfectly transmissive (positive  and thus purely real refractive index). Nonnegligible γ and thus 2 contributes to absorption and thus effectively blurs this transition.
Thus, metals become highly transparent in the UV, while the ionosphere plasma frequency
is around 10 MHz, for example.
Bulk plasmon resonances (along with traveling and localized surface plasmons to be
discussed) are bosonic quasiparticle excitations of the conduction electron plasma (Fig. 1.1a).
The bulk plasmons are longitudinal charge density oscillations, which therefore cannot be
excited optically, but may be excited via electron beams (e.g. in energy loss spectroscopy)
or via high-energy (often >5 eV) photoelectrons. The introduction of an interface to a bulk
system leads to the possibility of surface-localized charge density oscillations coupled to optical fields, known as surface plasmon polaritons (Fig. 1.1b). As with bulk plasmons, these7

Figure 1.1: Plasmon resonance modes for bulk, surface, and nanolocalized systems. (a) Bulk
material and corresponding bulk plasmon oscillation. (b) Surface interface with grating(e.g.), roughness-, or prism-launched traveling surface plasmon polariton mode. (c) Nanoparticle with dipolar surface plasmon resonance shown.

8
traveling polaritons have well-defined momenta, which are greater than the corresponding
electromagnetic field momenta. Thus, surface plasmon polariton excitation requires some
additional mechanism for momentum conservation such as a higher-index (e.g. glass prism)
coupler to launch a plasmon on the other side of a metal film, or a surface grating.[155]Finally, one can treat a flat film as the surface of an infinitely large sphere and then shrink
down the sphere to the nanoscale. As the sphere shrinks down past the scale of the optical excitation wavelength, the traveling polariton mode resolves into a linear combination ofmultipolar oscillations and momentum is no longer a good quantum number. These multipolar oscillations are known as localized surface plasmon resonances, which will be abbreviatedhere simply as “SPRs”. Most of the studies to be discussed will be in the dipolar/quasistatic regime (R  λ) (Fig. 1.1c), although quadrupolar resonances will occasionally beconsidered and the full multipolar Mie theory will be discussed in Section 3.1.2.
Localized SPRs dephase due to lifetime (T1 ) and pure dephasing (T2∗ ) contributions on∼10 fs timescales, with the total dephasing rate (T2 ) given by Matthiessen’s rule,
1
1
1
=
+ ∗.
T2
2T1 T2(1.9)

The factor of two difference is simply due to intensity (T1 ) vs. field (T2∗ ) dependence. Lifetime mechanisms include radiative damping into photonic modes and nonradiative damping into hot electron-hole excitations. Pure dephasing mechanisms include bulk electronphonon and electron-surface scattering (particularly for small particles < 20 nm) during
plasmon oscillations,[111] which serves as a ballistic interpretation for the essentially elastic
energy redistribution that can take place during collective conduction electron motion. The
homogeneously-broadened plasmon extinction linewidth is determined by T2 . For very small
particles (< 100 nm) under visible excitation, the nonradiative energy pathways (σabs ) are
typically dominant over the radiative pathways (σsca ). As an interesting consequence, manysmall particles with the same volume as one large particle can absorb energy more efficiently.
When combined with the larger hot carrier escape efficiencies for the shorter path lengths,

9smaller particles are often ideal for hot carrier technologies. Such hot carrier excitation andsubsequent dynamics will be discussed briefly in the next section and in detail in Chapter 3.
1.2

Dynamics in Nanoplasmonic Systems
Following plasmon decay into electron-hole excitations on ∼10 fs timescales, metallic

screening eliminates the correlation between the opposite charges and yields free carrierson ∼1 fs timescales. Via the optical absorption at visible plasmonic frequencies (1–4 eV),
the free carriers have energies much greater than kT (0.025 eV at room temperature), andare thus considered “hot” electrons and holes. Depending on the excitation energy (seeFermi Liquid Theory in Section 3.3.1), the hot electrons undergo both inelastic (hot-cold
electron-electron) and essentially elastic (electron-phonon) collisions on ∼30 fs timescales.
Electrons lose half of their energy on average to a single electron-electron collision[159] anda nascent hot electron probability distribution (following instantaneous excitation; i.e. theimpulse response or Green’s function) will thermalize relatively quickly within a few hundred
femtoseconds.[69] By contrast, the elastic electron-phonon collisions incur minimal energy
loss per collision (on the order of 10 meV[4]), which leads to longer, few-picosecond timescales
for hot electron-lattice thermalization.[69] Since the temperature-dependent electron heat
capacity is over an order of magnitude smaller than the lattice heat capacity, for instance, ingold (see Section 3.3.2), the peak hot electron temperatures are often an order of magnitude
or so higher than peak lattice temperatures, which will have interesting implications for hot
electron emission dynamics, as discussed in Section 3.4. In the nonradiative decay chain,
therefore, the optical energy goes from plasmon excitations (∼10 fs) to nascent hot carriers(∼10–100 fs) to thermalized hot carriers (∼0.1–1 ps) to thermalized lattice phonons (∼1–100ps) to environmental heating (>100 ps). Nascent hot electron distributions from intraband
excitation (i.e. not d-band excitations just above the Fermi level[216]) contain the largest
number of high-energy (> 1 eV) hot electrons, useful for many applications, which thus sets
the relevant collection timescale around 10–100 fs following excitation.

10
Each step of this energy cascade has a broad set of corresponding applications. On
the photonic timescale of the plasmon oscillation (∼10 fs), elastic photon scattering into
dipolar or higher-order oscillation radiation patterns can be utilized for “optical antenna”
applications, including phased arrays.[210] The strong plasmonic field enhancements can also
be exploited for resonance-enhanced elastic or Raman scattering of nearby molecules.[71, 199]
Additionally, the high nanoscale photon densities can also be used for light trapping inphotovoltaic systems,[7] as well as sensing the environment via resonance shifts, scattering, or
fluorescent signatures.[103] Electronic timescales of ∼10–100 fs will be the primary focus here,with applications in photocatalysis,[182, 214, 6, 55] photovoltaics/photodetection,[30, 23,187] and photocathodes,[39, 127, 170, 99, 217] corresponding to electron transfer, injection,or emission into nearby molecules, semiconductor, or free space, respectively. These processes
and applications will be discussed in greater detail in the next section. On picosecond andlonger timescales, coherent acoustic modes can be utilized for nanoscale actuation,[195] while
incoherent heating can be utilized for enhanced catalysis,[32] and targeted cancer ablation
therapy.[157]
1.3

Hot Carrier Science and Applications
As mentioned in the previous section, plasmonic hot carriers are utilized for myriad

applications and now represent a major emphasis of plasmonics research. While a few important applications such as photocatalysis, photovoltaics, and photocathodes will be describedin further detail here, it should be recognized that the underlying physics for all of thesesystems is qualitatively similar. As will be discussed in Section 1.4 and Chapter 3, hot carriers can either be ballistically transferred following excitation within the nanoparticle into
whichever collection medium is present, else they can be excited directly at the metal-medium
interface. While different collection media (e.g. molecules, semiconductor, or vacuum) will
influence the surface barrier and/or surface state properties and thus quantitatively affectthe absolute and relative (surface vs. volume) cross-sections, many qualitative features of

11
the semi-classical or quantum hot carrier dynamics remain the same across all processes.

1.3.1

Photocatalysis

Photocatalysis is perhaps the largest sector of nanoplasmonic hot carrier science, with
important opportunities for enhanced catalytic efficiencies and bond selectivities comparedwith typical thermally-activated processes.[32, 6] While a wide variety of hot-carrier-driven
catalytic processes have been studied, two areas of particular interest are H2 O[212, 201] andCO2 [198, 160] reduction for solar fuel production/storage and closure of the carbon cycle.
The simple idea is that high densities of hot electrons and holes excited within individual
nanoparticles can be transferred to surface molecules, with high overall interaction surface areas for nanoparticle colloids/ensembles. In some competition with the terminology from photoexcitation literature, charge transfer is categorized into “direct” excitation/transfer intoa surface-hybridized admolecule/metal state or “indirect” excitation in the metal nanoparticle followed by ballistic transfer to the admolecule.[6] This qualitatively maps onto the
distinction between surface vs. volume photoexcitation to be discussed in the Section 1.4.
Direct excitation may have the advantage of additional energy specificity,[55] while indirect/ballistic transfer would be less discriminating with respect to adsorbed states due tothe excited Fermi-Dirac hot carrier distributions. Various semiconductor (e.g. TiO2 ) Schottky barrier energy “filters”, however, can be employed both to promote charge separationand provide some control over the hot carrier energy distribution that participates in thechemical processes,[125, 123] e.g. by only collecting the highest-energy electrons and holes.
Indeed, a promising area for nanocatalysis includes nonuniform coatings of electron andhole “filter” materials, along with additional catalytic material coatings (e.g. Pt nanoparticles) such that invidual nanoparticles serve both as the anode and cathode with strong
charge separation and sensitivities to both electron and hole reactions (also to ensure propercharge neutralizaton).[125, 201] In this direction, one also encounters opportunities for fewnanometer-scale site-selective catalysis, either via nanoparticle design[165] or by active opti-

12
cal control over the hot spot regions of highest hot carrier density and transfer efficiency.[31]This leads to intriguing new capabilities for optimization and ultrafast (possibly even coherent) control over chemical reactions. Such work, however, will require a thorough understanding of hot electron distributions and dynamics, toward which this thesis is directed.

1.3.2

Photodetection and Photovoltaics

Two other related areas of high interest in hot carrier science are next-generation
photodetectors[95, 23] and photovoltaics,[30] both involving excited charge transfer to a surrounding semiconductor medium, such as TiO2 . So long as the carriers can be efficiently
transferred over the Schottky barrier,[131] such applications can benefit from broadband
plasmonic ensembles, heterostructures, or arrays that absorb nearly all of the incident radiation in the solar energy range. Both photodetectors and photovoltaics would benefit fromenhanced broadband sensitivity, while photodetectors could also be designed with sensitivity to frequency and/or polarization (e.g. via spatially-varying nanostructure arrays[95])for direct spectroscopic and polarimetric readout. Indirect vs. direct charge transfer pathways are also crucial to these systems.[202] A detailed understanding of volume and surface
photoexcitation/injection pathways will allow for geometry-optimized nanostructures for thehighest collection efficiencies within the short hot carrier lifetimes. In other words, designing
metal nanostructures in which most hot carriers are either excited directly at the metalsemiconductor interface or are within an inelastic mean free path of the interface (with theappropriate directionality for efficient transfer) will require a detailed understanding of hot
carrier excitation mechanisms, spatial distributions, momentum distributions, and temporal
decay dynamics. While the results described herein are for multiphoton excitation/emission
into the vacuum, the general insights apply equally to the single-photon regime, as well as
to other surrounding media, such as semiconductors.

13
1.3.3

Photocathodes

The most direct set of applications of the present work are those involving ultrafast
photocathodes,[99] i.e. the generation of spatially and temporally coherent electron pulses
in free space for use in femtosecond transmission electron microscopy,[211, 49] point projection microscopy,[154, 127] diffraction,[211, 127, 66, 191] x-ray generation,[150, 75, 138]
rectified optical signal detection,[152, 90, 206, 89, 219] lightwave electronics and attosecond
streaking measurements.[99] Whereas conventional flat surface photocathodes have spatial
coherence limited by the mesoscale focal spot of the triggering laser,[3] leading to corresponding limited focusability and image blurring, chemically-etched gold and tungsten nanotips
have emerged[76, 162, 130] as a highly-coherent photocathode with point-like spatially emission for high beam coherence. Not only are tip dimensions typically smaller than a few
tens of nanometers, but the effective source size of electrons emitted from a hemispherical
tip can be smaller still.[43] State-of-the-art etched nanotips have indeed been shown to yieldelectron beams with spatial coherence only an order of magnitude above the quantum uncertainty limit, with femtosecond temporal coherence.[49] However, although the large shafts ofetched nanotips lead to ready manipulation and positioning in many photocathode systems(including with respect to a surrounding electrodes for beam focusing and other manipulation) such systems are incompatible with nanoscale and/or on-chip configurations. Suchnanoelectronic and on-chip electron beam probing applications are nascent, but will require
carefully-controlled, fully nanoscale cathodes.
It will be shown in detail in Chapter 5 that gold nanostars with ultra-sharp (3.4 nm) tip
radii serve as exceptional nanoscale counterparts to etched nanotips, with multiple tips andresonances for optically-controlled switching/steering of the directional emission and beamcoherence properties approaching those of the etched nanotip beams. Such nanoparticles
or comparable nanostructures could be readily integrated into existing on-chip nanoscale
circuits, as demonstrated recently for THz nanoelectronics.[89, 219] Furthermore, the per-

14
turbative rather than strong-field emission properties are examined herein for these systems
in order to achieve minimal energy spread (and thus optimal temporal coherence) as well as
to mitigate heating.
1.4

Volume- and Surface-Mediated Photoelectric Effects
Following the work of Hertz, Einstein, and others around the turn of the twentieth cen-tury in explaining the photoelectric effect from an energy conservation standpoint, leading toa watershed in quantum mechanics, the question of momentum conservation was pending amore detailed development of the energy structure of solids. Despite the simplicity of Fowler
theory and its success in predicting near-threshold photoemission efficiency curves,[52] theactual photoexcitation mechanisms were not addressed, although the theory invoked thenotion that all of the excitation kinetic energy should go into the surface-normal velocity
coordinate and thus implied a surface-mediated excitation mechanism. The surface vs. volume/bulk photoemission dichotomy for momentum conservation in photoexcitation/emission
was introduced around the same time by Tamm and Schubin.[186] While the elucidationand theoretical treatments of various photoemission mechanisms has substantially evolved
over the years, the fundamental volume vs. surface dichotomy has remained intact. Thesemechanisms will now be defined, with details of their corresponding spatial and momentum
distributions in nanoplasmonic systems described in later chapters.
Volume excitation mechanisms are those that do not require the presence of a surface, in which momentum is conserved during photoexcitation via direct lattice-mediatedor indirect phonon-, defect/impurity-, or electron-mediated excitations. The presence of anearby surface is merely a practical necessity to observe subsequent photoemission. Volume
emission contributions depend on |E| and are related to the A · ∇ term in the light-matterinteraction Hamiltonian (in the velocity gauge) in addition to third-body scattering terms.
Such excitations are completely dominant, for instance, in studies of flat gold film excited
via normally-incident laser light (thus the surface-normal field |E⊥ | ≈ 0).[145] While un-15derstanding the precise volume excitation amplitudes for the various coherent (via virtualstates) and incoherent (via intermediate state population) multiphoton excitation pathways
remains a challenging problem, it has been argued that plasmon-mediated multiphoton excitation is typically a coherent process.[121, 63] Nonetheless, the absence of direct/interband
excitations from the Fermi level to above the vacuum level for the current photon energy
range (1.2–1.8 eV) indicates that at least one phonon or other indirect scattering event musttake place during coherent multiphoton excitation to populate the final state. For instance,a coherent four-photon excitation above the vacuum level will require a final phonon scattering event.[145] Most of the presentation herein remains agnostic to the precise volume
mechanism(s), as these do not meaningfully influence the analysis or conclusions but instead remain an interesting problem for further resolution on nanoplasmonic hot electron
dynamics.
Surface excitation mechanisms, by contrast, are those that rely on momentum nonconservation due to translational symmetry breaking at the surface potential barrier, i.e.
from strongly spatially-varying fields or wavefunctions. These contributions depend on |E⊥ |and are related to both the A · ∇ term (e.g. due to evanescent external electron wavefunction or surface states) and ∇ · A (due to surface field variation) terms in the lightmatter interaction Hamiltonian.[57] While the ∇ · A term is now often referred to as the“surface effect” in itself,[78] the original surface photoeffect theories only considered theA · ∇ term,[57] which should be considered for surface processes as well. Surface excitations
are dominant, for instance, for gold nanostars with sharp tips and therefore extra-strong
surface hot spots,[144] along with a variety of other systems in the multiphoton intensity
regime.[180, 118] Surface-like tunneling emission is a given for strong field processes.[106] In
the modeling to be presented in Chapter 3, coherent multiphoton surface-mediated excitation are considered,[144, 203] with the predominant excitation density occurring just outside
the surface in the few-Å region of overlapping plasmonic field and external electron density.
Some ambiguity can begin to occur in very small (< 20 nm) nanosystems with ge-

16ometric confinement becoming prominent,[117, 128] although such effects could still betreated within the surface vs. volume framework (i.e. treating it as diffuse volume-like
excitation[117]). Some ambiguity may also exist with surface-phonon-mediated excitation or
excitation from surface states. Taking surface states as an example: Surface states are clearlya surface-like feature, but they contribute some generic charge density within the volume
that could be excited in a volume-like manner, i.e. depending on |E| rather than |E⊥ | with
momentum conserved via volume-like phonon scattering. However, the intrinsic momentum
non-conservation due to the highly-varying spatial fields along the surface direction can be
expected to lead to much higher cross-sections for a direct surface-mediated excitation, i.e.
depending on |E⊥ | with momentum conserved via “surface scattering”. Thus, in practice,surface states should lead to predominantly surface-mediated emission as defined above (although these are not expected to contribute appreciably in any of the present studies). This
also highlights that the surface and volume processes are not defined by a particular lengthscale (e.g. electron scattering length or optical skin depth) but rather by the fundamental
mechanisms for momentum conservation in the optical excitation matrix elements.
1.5

Angle-Resolved Photoemission Measurements
Even without angular resolution, photoemission spectroscopy of single plasmonic nanopar-

ticles can provide a wide range of information on the plasmon resonances, multiphoton excitation processes, and total photoemission cross-sections.[171, 172, 65, 64, 62, 12] By varying
the visible excitation laser intensity and measuring the total photoemission rate, one can determine the multiphoton process order via power-law fit (nPPE ∝ I n ) or observe deviations
from this behavior due to thermionic or strong-field emission.[75] By varying polarizationand frequency, one can map out nanoparticle resonances in 2D optical parameter space,[144]which can be particularly rich for complex, multi-resonant geometries. The photoemission
rate is extremely sensitive to the field enhancement, with |E/E0 | = 10 leading to a 106 -foldincrease in the photoemission rate for a 3-photon process. Far-field polarization-, frequency-,

17
and intensity-dependent studies can therefore serve to map out the near-field plasmonic hot
spots and some details of the hot electron dynamics/distributions, particularly when thenanoparticle geometry is subsequently correlated with electron microscopy and, perhaps,
simulated via electromagnetic finite element or finite difference numerical methods.
The introduction of photoelectron velocity resolution provides substantial additional insight into the near-field hot electron dynamics. The implementation of velocity map imaging(VMI) to be introduced here for studying surfaces and supported nanoparticles is motivatedby the enormously successful application of the technique in molecular spectroscopy anddynamics,[178, 197] while also drawing inspiration from angle-resolved photoemission spectroscopy (ARPES) on surfaces. A number of ARPES techniques have been established over
the years, including what may be considered “conventional” ARPES using a hemispherical analyzer,[35, 196] more recent angle-resolved time-of-flight (AR-ToF) setups using adelay line detector for concurrent 3D detection,[196, 70, 36] and momentum imaging using a
PEEM column and two hemispherical analyzers.[98] Time-, position-, and 1D energy-resolved
PEEM also provides impressive capabilities for studying single-nanoparticle plasmonics andelectron dynamics,[15, 161] and nanoARPES techniques are emerging for simultaneously
high spatial and angular resolution.[163] All of these techniques offer different advantages,
but only recently have two techniques been developed for angle-resolved, resonantly-excited
single-nanoparticle photoemission spectroscopy studies at UV–visible–NIR frequencies: atime-of-flight momentum-resolving electron microscope (ToF k-PEEM)[106] and the scanning photoemission spectroscopy technique using VMI to be discussed herein.[145] With thelatter technique, some of the most important experimental capabilities for comprehensive
angle- and momentum-resolved photoelectron studies of single nanoparticles are demonstrated using the relatively simple, cost-effective, and versatile scanning photoemission microscopy/spectroscopy system. Some goals for these studies include (i) the measurementof low-energy (near threshold) photoelectrons produced via nonlinear emission following
visible-photon plasmonic excitation, (ii) efficient and reproducible access to large numbers

18of addressable nanoparticles for correlated studies and statistics, and (iii) the ability to collect and characterize photoemission from the full 2π upper-half-space solid angle withoutsample manipulation (i.e., tilting). Also of crucial importance are high photoelectron collection efficiencies, such that nanoparticles may be investigated with low integrated pulse
energies (which for femtosecond pulses may nevertheless correspond to high peak intensities) to minimize heating, melting, and ponderomotive forces, thereby permitting focus onphotoemission processes relevant under truly perturbative laser intensity conditions. This
technique is described in detail in Chapter 2.
1.6

Ultrafast Nanoscale Photocurrent Control
The primary goal of this research is to demonstrate new capabilities for measuring,predictively modeling, and ultimately optically controlling nanoscale photocurrents on ultrafast (i.e. femtosecond, approaching attosecond) timescales. Experimental angle-resolved
photoelectron spectroscopy studies will prove essential for developing simple yet accurate
models for femtosecond hot electron dynamics. These models can then be utilized to predict
hot electron spatial and momentum distributions (and temporal dynamics) in arbitrarily
complex nanoparticle geometries. In demonstrating these capabilities, a variety of opticalphotocurrent control mechanisms will be uncovered. In particular, control over hot carrier photocurrents can be achieved via (i) optically selecting plasmon resonance modes andtheir corresponding surface field distributions (hot spots) and volume field distributions, (ii)optical control over the surface vs. volume cross-sections, and (iii) with synthetically- or
lithographically-controlled nanoparticle coatings. Methods (i) and (ii) will be addressed indetail for various nanoparticle and hot spot geometries, while upcoming results via method(iii) will be presented as well.
With applications in ultrafast information processing (preserving Moore’s law by going
faster as we approach fundamental size limtations), ultrafast nanoelectronics,[89, 173] femtosecond electron spectromicroscopy,[127] and coherent control over nanoscale chemistry[31,1955] in mind, detailed nanometer/femtosecond spatiotemporal photocurrent control is highly
desireable. However, controlling photocurrents has remained surprisingly challenging, withthe primary demonstrations thus far requiring specialized materials and/or strong, highlytailored optical fields. Photocurrent polarity, for example, has been controlled via the circular
photogalvanic effect in topological insulator systems,[119] carrier-envelope-phase sensitivity in dielectrics exposed to strong optical fields,[167] and perturbative[179] or strong-field
quantum pathway interference in graphene.[73] Some level of angular control has also been
demonstrated with etched nanotip (Au or W) emitters.[136, 204] By comparison, plasmonic
nanodevices provide two essential benefits: (i) Versatility, with extensive angular control on
few-femtosecond (or faster) timescales and few-nanometer spatial scales, along with (ii) simplicity, utilizing available nanofabrication/synthetic techniques and standard tabletop laser
technologies for optical current control that can be readily integrated into a wide variety ofexisting nanocatalytic, photovoltaic, or nanoelectronic systems.

Chapter 2
Experimental Methods

The next generation of hot carrier devices, such as photocathodes, targeted drug delivery agents, photodetectors, and photocatalysts for solar fuel production, will require a higher
level of design and control over the nanoscale, femtosecond hot carrier charge transfer andemission. Presently, most hot carrier applications simply take advantage of the high carrier
densities excited within nanoplasmonic systems, with little regard for where the electrons
are excited (spatially) and where they go from there (temporal dynamics and momentum
distributions). Although a number of techniques have emerged to address these questions
via nanoscale hot electron spatial mapping,[40, 165, 74] only recently have studies begun
to directly address the critical momentum degrees of freedom.[106, 107] As a consequence,
there remains a significant gap in understanding, optimizing, and actively controlling hot
carrier excitation and emission dynamics.
Toward this end, a unique photoelectron spectroscopy system has been built up to
study photoemission from individual nanoparticles as a function of input laser frequency,
polarization, intensity, and femtosecond pump-probe time delay. Furthermore, using a simple three-electode electrostatic lens system in a velocity map imaging configuration[44] and a
spatially-resolved electron detector, the photoelectrons are collected with 2D (vx , vy ) angularresolution. With picosecond time-of-flight resolution, vz can also be measured to acquire thefull 3D photoelectron velocity distribution.[109] When correlated with scanning electron micrographs, finite element electrodynamics simulations, and 3D photoemission modeling, such

21
measurements provide a wealth of information on the spatial and momentum distributionsof hot electrons excited in various nanoplasmonic geometries. Recent studies have begun toelucidate these hot electron distributions and dynamics, but capabilities for the predictive
theoretical modeling and design of next-generation nanoplasmonic systems will require more
extensive experiment-theory comparisons. Theoretical methods are addressed in Chapter 3,
while the present chapter provides a detailed description of our unique single-nanoparticle,
angle-resolved photoelectron spectroscopy technique.
2.1

Scanning Photoelectron Imaging Microscopy
Scanning photoemission microscopy involves raster scanning a sample stage over a(diffraction-limited) laser spot and collecting the emitted photoelectrons as a function of position. In this way, individual nanoscale objects can be located and studied as a function oflaser parameters such as polarization, frequency, and intensity. By combining such capabilities with velocity-resolved photoelectron detection, a substantial amount of information on
near-field electron excitation and emission dynamics can be directly measured and/or reconstructed. We refer to this technique as scanning photoelectron imaging microscopy (SPIM),
encompassing the scanning microscopy technique as well as the photoelectron velocity map
imaging (VMI) collection scheme, discussed in detail below. By further correlating the
SPIM measurements with scanning electron microscopy (SEM) or atomic force microscopy(AFM), along with correlated electromagnetic simulations, many details of the hot electron
excitation/emission distributions and dynamics in nanoscale systems are revealed.
The SPIM system is illustrated in Fig. 2.1. While this unique and relatively simple configuration for photoelectron spectroscopy is primed for new insights into nanoscale
systems, thin films, 2D materials, and perhaps eventually single molecules, the focus here
is on the photoemission properties and hot electron dynamics of plasmonic nanoparticles.
Due to their strong nanolocalized field enhancements, plasmonic metal nanoparticles thatfill only a small fraction of the diffraction-limited laser spot can still dominate the photoe-

22
mission by orders of magnitude over the conductive substrate (e.g. ITO) background. Thisis illustrated in the example SPIM scan of gold nanoshells in Fig. 2.1, which demonstrates
the high signal-to-background, along with the spatial mapping resolution, which is actually
sub-diffraction-limited due to the n-th order multiphoton excitation (with spot diameter√λ/(2NA n)).
2.2

Ultrafast Laser and Optics Systems

2.2.1

Laser System

The highly-tunable ultrafast laser system consists foremost of a modelocked Ti:sapphireoscillator (KMLabs Swift) running at 75 MHz and generating ∼40 fs pulses with up to∼1.75 W of average output power. Modelocking is passively achieved via Kerr lensing
in a “soft aperture” configuration (i.e. where the cavity loss for the continuous wave vsmodelocked/pulsed mode is determined by the cavity optics rather than an additional hard
aperture). The gain bandwidth of the Ti:sapphire crystal and the adjustable dispersion characteristics of the cavity allow for tuning between 675–980 nm. Four piezo-motor-controlled
degrees of freedom are present for tuning the cavity dispersion: (i) dispersing prism insertion, (ii) collimation prism insertion, (iii) tuning slit position, and (iv) tuning slit width. By
adjusting all four degrees of freedom, the oscillating mode can be tuned over the full range
while maintaining similar pulse duration via appropriate bandwidth settings. A calibration
file is generated manually and the values are interpolated for automated tuning over the fullrange. The cavity air is purged (primarily of water) via circulation through both desiccant
and molecular sieve (Drierite), with regular replacement or desiccant regeneration multiple
times a year required to maintain < 1% cavity humidity, particularly if the cavity is opened
frequently for alignment. The humidity is monitored via a wireless sensor and low humidity
is essential to stable operation at the furthest near-IR settings (> 925 nm). Even so, thecavity always remains highly unstable in the 930-950 nm range due to residual water vapor

23

Figure 2.1: Overview of the SPIM apparatus and example SPIM scan. Photoelectron counts
are collected as a function of sample position as the stage is raster scanned in the xy plane.
While the illustration shows the pump-probe capabilities, the example scan and most studies
presented herein are performed with single-color multiphoton excitation. Signal-integrated
SPIM intensity maps allow for single-particle identification, as shown for gold nanoshells on
ITO with excitation at ~ω = 2 eV (620 nm). The 335(12) nm FWHM measured in the singleparticle subscan agrees well with expectation of√340 nm, determined via convolution of thediffraction-limited
laser spot size, 620 nm/2NA 3, with the 164 nm particle diameter, with√a factor of 3 in the denominator to account for the three-photon photoemission process.

24
and strong absorption by a vibrational overtone or combination band thereof.
The Ti:sapphire cavity is operated with either a 10% or 20% output coupling (OC)mirror, which must be manually exchanged. The 10% OC leads to less loss and therefore
greater tunability over the full cavity range, but with less overall output power (< 1 W
with 8–8.5 W pump power for stable operation). The 10% OC is therefore utilized whenusing the oscillator fundamental itself, i.e. when operating in the 675–980 nm tuning range.
By contrast, the 20% OC leads to more cavity loss and less stability/tunability (typically∼750–850 nm) but much higher output powers (up to ∼1.75 W with 9.5–10 W pump power)
for subsequently pumping the second harmonic generation (SHG) and optical parametricoscillator (OPO).
Both SHG (χ(2) (2ω = ω + ω)) and subsequent OPO (via difference frequency generation, χ(2) (ωsignal = ωpump − ωidler )) are generated with beta barium borate (BBO) crystals.
Commensurate with the oscillator tuning range, the SHG is tunable between ∼350–490
nm, with typical conversion efficiency around 30% and peak powers greater than 650 mW
achieved at 400 nm for 1.75 W fundamental power (20% OC). When pumped with >600mW of SHG power at 400 nm, the OPO is tunable between 520–780 nm with output powers
above 100 mW across much of the range. Thus, between the SHG, OPO, and fundamental
outputs, the laser system is widely tunable across the entire visible range, while also reaching
into the UV and near-IR.
2.2.2

Dispersion Compensation

Consider a narrow-band optical pulse traveling through a dispersive medium, withlinewidth small enough that the wavevector (k(ω) = 2πn(ω)/λ for real/dispersive refractive
index component n(ω)) can be reasonably expanded about some center frequency, ω0 :k(ω) = k(ω0 + δω)≈ k(ω0 ) + k 0 (ω)

1δω + k 00 (ω) δω 2 + . . . ,
2
ω0
ω0

(2.1)

25
in which
ω0,
vp (ω0 )1
k 0 (ω) =,vg (ω0 )ω0k(ω0 ) =vg0 (ω)k 00 (ω)=ω0ω0vg (ω0 )2

,

(2.2)

where vp = ω/k = c/n is the phase velocity and vg = dω/dk is the group velocity. The zerothorder term is therefore simply the overall phase lag due to traveling in a medium. The firstorder term accounts for the group (pulse envelope) velocity through the medium, leading toa carrier-envelope offset phase. The second-order term accounts for the dispersion in groupvelocities for different carrier frequencies; i.e., if one imagines that the pulse is composedof many different sub-pulses with different carrier frequencies, these will spread out in afrequency-dependent dispersive medium (leading to pulse broadening and chirping). This is
known as group velocity dispersion (GVD) and is the primary mechanism for femtosecond
pulse broadening in materials. Higher-order terms will have additional pulse broadening
and nonlinear chirping effects. Note that all of these effects are linear optical effects—i.e.
depending on refractive index n(ω) (isomorphic with χ(1) (ω) when including the imaginarypart) and independent of the field strength. Second- and higher-order dispersion are merely
terms in the Taylor expansion of n(ω). This linearity is indeed crucial for pulse dispersion
compensation, to be discussed.
The respective effects of each of these terms become clearer by writing out the electricfield in terms of its Fourier transform:
ZẼ(ω)e−iωt dωZ−iω0 t=e|Ẽ|eik(ω0 +δω)z e−iδωt d(δω)
Z
1 00
2
0
i(k0 z−ω0 t)=e|Ẽ|ei(k (ω)|ω0 δω+ 2 k (ω)|ω0 δω +...)z e−iδωt dδω,E(t) =(2.3)

26
which has been separated into the carrier frequency (the exponential term out front) andthe pulse envelope (the Fourier integral). The offset between the carrier (traveling at vp (ω0 ))and the envelope (traveling at vg (ω0 )) is known as the carrier-envelope offset (CEO) phase,
described by the first-order dispersion term. This is seen more clearly by rearranging Eq.
2.3:
i(k0 z−ω0 t)

Z|Ẽ|ei(k (ω)|ω0 δω+ 2 k (ω)|ω0 δω +...)z e−iδωt dδωZ|Ẽ|ei( 2 k (ω)|ω0 δω +...)z e−iδω(t−k (ω)|ω0 z) dδω,

(2.4)φCEO = ω0 k 0 (ω)|ω0 z.

(2.5)

E(t) = ei(k0 z−ω0 t)

=e

0

1 00

1 00

2

2

0

such that t → t − k 0 (ω)|ω0 z, and

The GVD of a material is an intrinsic physical property, typically reported in unitsof fs2 /mm, and for many glasses in the visible range is around 100 fs2 /mm. Group delay
dispersion (GDD) is simply the GVD multiplied by the length of the material, and is therefore
an extrinsic property with units of fs2 . Upon solving the inverse Fourier transform in Eq. 2.4,
one finds that the pulse broadening effect is described (for a Gaussian, BW-limited pulse)
by
∆tf =

q
∆t2i + 16(ln 2)2 GDD2
∆ti

.

(2.6)

Higher-order terms such as third-order dispersion (TOD) lead to additional (asymmetric)
pulse broadening, nonlinear pulse chirp, etc. These higher-order terms are typically determined via numerical pulse propagation modeling.
Except in regions of anomalous dispersion near a resonance, GVD in glass is positive;e.g. +45 fs/mm2 in fused silica. Thus, to compensate for material GVD, some negative GVD
elements must be introduced into the system, such as chirped mirrors, diffraction gratings,
or prisms. Given that GVD is still a linear optical process, dispersion compensation can be
performed anywhere in the system, including before or after the positive GVD elements, or27
anywhere between. Overshooting with too much negative GVD leads to the same detrimental effects on pulse durations as positive GVD, readily seen as ∆tf depends only on GDD2
in Eq. 2.6. It is thus often necessary—particularly in systems with frequency-tunable pulses
or variable material path lengths—to introduce a tunable negative GVD dispersion compensating element. This is achieved here using an ultrafast prism pair with a retro-mirror—i.e.
a “prism compressor”. In this configuration the laser pulse is dispersed by the first prism,
collimated by the second prism, then returns via retroreflection to be focused by the second prism and re-collimated by the first prism. A slight downward angle is imposed so thereturn beam can be picked off by a half mirror. While positive GVD leads to a positive
chirp with lower/redder frequencies at the front of the pulse, negative GVD of this prism
system is achieved via configuring the prisms for longer total optical path length for longer
wavelengths. While blue frequencies refract more from the first prism and ultimately travel
longer distances in air, the red frequencies travel much longer distances within the secondR
prism, leading to an overall longer optical path length ( ndl) for the redder frequencies andthus negative GDD.

2.2.3

Pulse Characterization

Pulse characterization is achieved by the typical means, including intensity autocorrelation and frequency-resolved optical gating (FROG),[188] which split the beam, vary thetime delay between the two pulses, send them into a BBO crystal, and measure the output
SHG power or power spectrum, respectively. While the intensity auto-correlation simply
measures the symmetrized pulse intensity, FROG provides enough information to also retrieve the phase information and thereby reconstruct the electric field. As shown via the
FROG trace in Fig. 2.2, the output pulses from the Ti:sapphire laser under typical operating conditions are measured to be ∼50 fs, in reasonable agreement with the predictedbandwidth-limited pulse duration of ∼40 fs.
More importantly, to characterize the pulses at the sample and optimize the relevant

28

Figure 2.2: (a) FROG trace of a typical Ti:sapphire output pulse train. (b) Pulse intensityand phase retrieved from the FROG trace, with a Gaussian fit FWHM of 52 fs.

dispersion compensation, the built-in autocorrelation or cross-correlation capabilities of thenonlinear photoemission signals are exploited. As described in Section 2.9, an automatedstepper motor translation stage in the SHG path is used to control the delay between pulses
with ∼1 fs precision. First, the SHG pulse is split—one along the delay stage path and theother along a separate path—and recombined prior to the sample, i.e. in a Mach-Zehnderinterferometer configuration. The 1 + 1 pump-probe photoemission signal is measured asa function of delay time, thus yielding an intensity autocorrelation. Assuming an instantaneous response time for the sample, the pulse width is thus simply the autocorrelation√
FWHM/ 2. The known SHG pulse duration is then used to measured the OPO or oscillator pulse durations via cross-correlation 1 + 10 pump-probe measurements. Note that thesystem is not suitably stable to resolve the interference fringes, and thus the auto- and crosscorrelations are phase-averaged. However, with additional fine (piezo-actuated) stabilization,
future phase-resolved interferogram measurements may be readily achieved.[143]

29
2.3

Vacuum System
The SPIM vacuum system is illustrated and shown schematically in Fig. 2.3. The

system consists of a lower chamber (∼90 L) which contains everything aside from the detector, including four unprotected flat silver mirrors redirecting the laser through the reflective
microscope objective (Ealing 25-0548) onto the scanning sample stage, three quartered piezoelectric posts for fine positioning/scanning, the overall sample positioning block holding thestage and objective, three coarse positioning piezomotors (New Focus Picomotor 8302), thethree VMI electrostatic lens electrodes, the µ-metal shield, and a nest of wiring. This lower
chamber is pumped by two turbomolecular pumps (TI: Pfeiffer TMU 261, T2: Pfeiffer TMU
071 P) for a total pumping speed of 260 l/s, neglecting conductance limitations of the systemgeometry. Both of these turbos are backed by a single dual-stage rotary vane pump (Leybold D16A). The typical base pressure of the lower chamber, measured via ion gauge withthe gate valve to the upper chamber closed, is 4×10−7 Torr. In case of power failure, theturbos turn off and remain off, while the rotary vane turns back on when power is restored.
To prevent oil backstreaming from the rotary vane pump in case of power failure, a relay
interlock is set to close a pneumatic auto-off safety valve (Kurt J. Lesker ASVQF25-120A),
such that when the power returns to the rotary vane it will be pumping on ambient througha highly conductance-limited channel (thus limiting the gas load) rather than directly on thechamber without the turbos on. A zeolite molecular sieve further prevents any backstreamed
oil from creeping into the foreline or system, which is occasionally baked and regenerated insitu with the rotary vane pump on and the foreline valve closed.
The upper chamber (∼10 L) contains the microchannel plate (MCP) detector (BeamImaging Solutions, BOS-75 with OPT01 (Chevron)), which is highly sensitive to oil andwater vapor contamination and must be kept below 2×10−6 Torr during operation to prevent
shorting and MCP damage. Prolonged storage below the room-temperature water vapor
pressure (∼ 15 Torr) is recommended, along with extended pumping and a slow voltage

30
ramp-up cycle (see user manual) prior to subsequent operation. To maintain a high level ofcleanliness in this chamber, a gate valve is situated between the lower and upper chambersthat remains closed except when operating. The upper chamber has a dedicated turbo (T3:
Hi-Pace 80, 67 l/s) with a dedicated oil-free diaphragm backing pump (Pfeiffer MVP 0402). With the gate valve closed, typical upper chamber pressures are around 2×10−7 Torr
and around 3×10−7 Torr with the gate valve open. These nominal pressures can be achieved
within 2–3 hours of pumping down the system from ambient (e.g. after sample replacement),
although minimum operating pressures < 1 × 10−6 Torr can usually be achieved within 1–1.5
hours of pumping down, so long as the chamber was only opened briefly for sample exchange.
For a future improvement, it would be prudent to install an additional gate valve on thechamber-side of the upper turbo, thereby allowing for high-vacuum storage, currently limitedby the few-Torr backing pressure of the diaphragm pump.
2.4

Sample Preparation
Samples for correlated photoelectron spectroscopy studies must be both (i) largely

transparent across the visible excitation range and (ii) Ohmic with suitably low resistancefor nanoparticle reneutralization between photoemission events. While glass coverslips withthin (∼10 nm) metal films, such as Au or Pt, have been utilized successfully, similarly thintransparent conductive oxide films tend to have particularly high transmission (∼90%) acrossthe visible range and particularly low photoemission cross-sections for minimal backgroundsignal. Indium tin oxide (ITO) on glass is the most widely-manufactured substrate and iscommonly utilized for supported photoemission studies.[64, 75, 106] Borosilicate coverslips(170 µm thick) with 10 nm ITO films are prepared commercially by Thin Film Devices,
Inc. via sputtering deposition in a large (6×6 ft) chamber for optimal homogeneity, with
an ultimate RMS area roughness < 1 nm, sheet resistance around 1 kΩ/, work function
φITO ≈ 4.2 eV, and background levels that are typically multiple orders of magnitude lower
than plasmonic nanoparticle photoemission signals.[64]31

Figure 2.3: (a) Illustration of the vacuum system chambers and turbo pumps (T1-3). (b)Schematic version with all valve, gauge, and pump model numbers.

32
Correlated particle location (“registration”) is achieved by depositing an alphanumericAu grid on top of the ITO via negative photomask lithography. The grid is generated using
negative UV photoresist with an uncoated copper TEM grid (LF-400) as the mask. A 5
nm Ti adhesion layer is deposited onto the exposed ITO regions prior to the 50 nm Au
layer via e-beam evaporation. Following overnight resist removal via acetone soaking andgentle acetone-soaked cotton-tipped applicator removal of any lingering Au leaflets within the
narrow grid regions, the ITO substrate sheet resistances and photoemission properties within
SPIM remain unchanged from non-gridded samples. However, one or two instances occurred
when using expired and perhaps over-baked resist in which the samples came out with ∼5fold higher sheet resistances and ∼3-fold lower photoemissivities in SPIM, potentially due
to residual resist.
Aqueous nanoparticle dispersions (synthesized commercially or via academic collaborators) are deposited onto registered ITO substrates via spin coating a 30–50 µL aliquot
at 1500 rpm, following the appropriate dilution. With some variation due to nanoparticle
size and stabilizing ligand effects (e.g. concentration-dependent micelle formation), concentrations of 3×1010 NP/mL (50 pM) are often optimal. These concentrations yield typical
coverages of 0.05 nanoparticles/µm2 , or 20 particles in a 20 × 20 µm2 scan area on average. Such coverages are ideal for efficient particle location and characterization via SPIM
scans, while ensuring negligible probability of two particles overlapping within the same
diffraction-limited excitation region. The full, typical deposition procedure is: 10 s vortex,
30 s sonication, 10 s vortex, dilute, 10 s vortex, dynamic 1500 rpm deposition onto a freshly
UV-ozone-cleaned ITO substrate and drying via a 5 min spin. The UV-ozone cleaning of the
ITO substrate for > 10 min (often > 30 min) up to deposition is essential for improving wetting by removing residual hydrocarbons. Dynamic spin coating is preferred to static drop
casting as it prevents particle diffusion over the substrate, which can lead to aggregation
during deposition.
For high-resolution TEM sample characterization, nanoparticle dispersions are drop-

33
cast onto carbon-coated TEM grids. Concentrations are adjusted for suitable coverages, but
given the much broader range of acceptable coverages, full-concentration samples often yieldsuitable results with 5–10 min deposition times. A TEM-grid sample holder compatible with
the VMI lens system has been implemented for correlated SPIM-TEM studies, but this is
generally more challenging and the carbon substrate substantially damps the plasmon resonance. In most cases, nanoparticles cannot be resolved in SPIM above the background levels.
New configurations such as ITO-coated SiN grids have been attempted, but grid damage during the coating process led to null results. Thus, capabilities for correlated TEM studies arelimited to total count rate studies with no velocity resolution. However, opportunities exist
in the future for very high-resolution (including potentially atomically-resolved TEM imaging) correlated angle-resolved photoelectron spectroscopy studies by finding a novel TEM
grid configuration that is suitably robust.
2.5

Surface Cleaning
An important experimental “cleaning” protocol for achieving high-quality velocity

maps is now briefly discussed. Essentially all nanoparticle velocity maps initially reveala predominantly isotropic distribution peaking strongly at zero transverse momentum (seeSection 5.1), which can be ascribed to inelastic scattering processes during photoemission.
This occurs regardless of the cleaning method employed prior to loading the sample into thevacuum system (e.g. UV-ozone exposure, plasma cleaning, and/or solvent rinsing). Sucheffects are observed for all nanoparticles and most surfaces studied, and are attributed tobrief (∼10 min) ambient air exposure between sample cleaning and loading into the vacuum chamber. However, as with similar demonstrations by the El-Sayed group with regard
to Au-thiol ligand removal,[82] brief exposure of nanoparticle samples to second harmoniclight (here ∼1 GW/cm2 at 400 nm for ∼1 s, under high vacuum conditions) can serve to
break surface bonds or remove surface adlayers, presumably due to hot electron transfer.
In our VMI apparatus, this appears to eliminate the isotropically-scattered photoemission

34
contribution near zero energy, thereby revealing the anisotropic photoemission distributionsof primary fundamental interest, as demonstrated for gold nanoshells in Section 5.1. Most
importantly, this procedure only eliminates the inelastically-scattered central peak near zeroenergy and has no observable effect on the underlying photoemission behavior, with the same
directionality of the photoemission observed before and after 400 nm light exposure. Furthermore, this in vacuo laser cleaning is highly reproducible, yielding qualitatively identicalresults for every nanoshell studied and upon multiple venting/pumping cycles for the same
nanoparticle. It can also be performed quickly and efficiently using the scanning stage toclean dozens of nanoshells in a target area prior to study.
While the precise scattering mechanisms remain unknown, the interaction appears tobe primarily with an air (i.e., water) adlayer on the nanoparticle/ligand surface, evidenced
by repeated cleaning → air exposure → cleaning studies of the sample nanoparticles. No
additional changes are observed in the photoelectron momentum distributions for longer
exposures or higher intensities, indicating that photoelectron scattering effects have been
largely eliminated. Finally, this cleaning effect is only observed for ∼3.1 eV (400 nm) or
higher-energy photons, with no significant effect evident even with higher intensities of themost energetic optical parametric oscillator output (∼2.3 eV photons). While further studies
to explore the precise photoelectron-adlayer interactions would be warranted and interestingin themselves, here the cleaning remains a well-converged heuristic that eliminates unwanted
post-emission inelastic scattering effects.
2.6

Scanning Sample Stage
While the tunable ultrafast excitation laser system and velocity-resolved detection

system are essential to the work in this thesis, the custom scanning stage represents theheart of the SPIM system. The stage itself is custom-machined from copper with a removablecentral copper sample holder piece (Fig. 2.4), which can be selected for ITO-coated coverslips
or TEM grids. ITO coverslips are positioned over the large hole in the stage for optical access35
and held down by a piece of copper shim with a large central hole for electron emission withminimal field distortion. The shim also establishes electrical contact between the sample
stage and the sample ITO layer, and is held in place by a set of finger springs. With the
TEM grid holder, the grid merely rests in a 3 mm alignment recess with no shim or otherholder on top to prevent field distortion for velocity map imaging. A more conventional
TEM grid holder arm that severely distorts the electrostatic lens field is also available andcan be utilized for TEM-correlated non-velocity-resolved studies. In velocity map imaging
studies, the entire sample stage acts as the repeller electrode and is held at large negative
voltages (typically −4500 V).
The sample stage rests above the microscope objective on three ruby positioning balls
held by three quartered piezoelectric posts for fine ±20 µm xy scanning. The stage position isthen controlled via applying voltages determined via the PID scanning software (see Section2.10) through NI DAQ voltage output cards to be amplified via the piezo driver circuit (seeAppendix) and applied to the appropriate post segments. Two small (∼1 cm2 ), electricallyisolated copper plates on the +y and −x sides of the sample stage couple to two nearby
capacitive sensors (∼1 mm gap at rest position) to read out the sample stage position for
closed-loop positioning. The closed-loop scanning calibration is performed by imaging thephotoemission from the C-flat substrate with a regular array of holes. Piezo calibration
factors are adjusted to ensure the proper scan size, angle, and to eliminate distortion.
2.7

2D Velocity Map Imaging
Photoelectrons are mapped as a function of transverse (vx , vy ) initial velocity ontotransverse (x, y) final position on a spatially-resolved phosphor-MCP detection system. Velocity map imaging was originally introduced by Eppink and Parker in 1997[44] to overcome
the limitations of grid electrodes in molecular photoionization studies.[27] In particular, electrodes with a wire grid/mesh were originally utilized to produce a nearly-uniform electricfield, thereby mapping initial transverse velocity onto spatial detector position in a simple

36

Figure 2.4: Copper sample stage with hole for optical access, shim to hold down and electrically contact ITO sample coverslip, and xy closed-loop positioning capacitive sensor plates.

37
manner. However, large excitation volumes (due to overlap of laser focal spot with molecularbeam) in the tens of micron range or larger served to blur the final distributions. Furthermore, the grids led to charge collection and reduced collection efficiency, while also causing
field distortions that led to further blurring of the final images. Eppink and Parker discoveredthat by instead using three electrodes (a repeller, extractor, and ground) with the extractor
and ground electrodes having two central holes, enough degrees of freedom were present togenerate a high-quality electrostatic lens for linear velocity-to-position mapping. Moreover,the lensing led to a novel property of the mapping being sensitive only to initial velocity
rather than position, thereby reducing blurring due to the excitation volume, eliminating
blurring due to mesh-related field distortion, and also eliminating photoion/photoelectron
attenuation due to collection by the grid.
Here, the reduction in spatial blurring is not such an issue due to the nanoscale origin—however, it does allow for compensation of any offset from the electrostatic lens axis (i.e.
imperfect laser-electrode alignment) that is bound to occur. The velocity map imaging
electrostatic lens configuration is shown in Figs. 2.5 and 2.6, with the copper sample stage
held at −4500 V serving as the repeller electrode, the copper extractor electrode (∼1.8 cm
hole diameter) placed 1 cm above the sample stage is held at −3700 V, and the groundelectrode (∼3.2 cm hole diameter) is placed 1 cm above that. Beginning just above theground electrode, a µ-metal shield runs the length of the flight tube (∼59 cm) to eliminate
spatial drift due to the geomagnetic field. The voltages are applied via a single 5 kV power
supply (SRS P350) and adjusted via a voltage divider between plates. The extractor-torepeller voltage ratio of 0.82 is maintained for optimal focusing at the detector, while theoverall voltage is adjusted to change the magnification. To prevent event overlap, countingmode studies are often conducted at −500 V repeller voltage, for example. Distortions
due to photoelectron proximity with the electrodes can occur for lower voltages (higher
magnification) and must be treated with care if performing velocity mapping studies underthese conditions.

38

Figure 2.5: Simulation of electron trajectories and VMI equipotentials using SIMION 8.0,
with equipotential lines displayed in 500 V increments and all distances to scale. A uniformly
increasing transverse velocity ∆vρ = 0.44 nm/fs, with outermost trajectories corresponding
to 21 me vρ2 = 5.0 eV) leads to a uniformly increasing radial displacement on the detector,
increment d = 8.82 mm, which is constant within the 32 µm detector resolution limit (MCP
pore pitch). This linear mapping is insensitive to vz due to the strong immersive acceleration
field at the sample (∼1 kV/cm): the same linear mapping is achieved within instrument
resolution for 21 me vz2 = 0 (black/left trajectories) and 21 me vz2 = 10 eV(blue/right trajectories).

39
The accelerated photoelectrons are focused onto a microchannel plate (MCP detector),
where each 25 µm channel (32 µm pitch) acts as a continuous dynode electron multiplier.
With a standard voltage of 0.9–1 kV applied across both of the two MCP plates arranged
in a Chevron configuration (total 1.8–2 kV voltage differential), a single electron event ismultiplied up to ∼ 107 electrons with a log-normal distribution. Matched plates cut fromthe same die are utilized for optimal resistance (10 MΩ and 10.5 MΩ measured for theupper and lower plates, respectively) and gain matching. An external voltage divider canbe utilized to control the plate biasing, but in this matched case the plates themselves serveas the voltage divider. A −40 V bias is applied to the front plate to reject slow electrons
and thereby reduce background counts due to externally-generated events or backscattered
events generated when photoelectrons impinge on the front plate area rather than in a pore.
This noticeably reduces the background level by ∼50% while maintaining the same signal
levels (a mere 40 V barrier will not block the 4.5 kV-accelerated photoelectrons). Due to thespatial correlation with the voltage connector wires, the primary source of such avoidable
background counts appears to be electrons generated via field emission from hot spots on
the bare connector wires.
The ∼ 107 electrons leaving a single MCP pore (assuming good chevron pore alignment) are accelerated further onto the phosphor screen via a 3 kV differential between thephosphor and top MCP plate. This acceleration improves phosphorescence signal while
preventing space-charge blooming of the electron clouds, to ensure the smallest spot sizes
possible on the phosphor and thereby limiting event overlap on the camera. Spot sizes
are measured to be around 500 µm, which indicates room for improvement compared withcommercially-specified spot sizes of ∼200 µm. The 3+ keV electrons impinging on the P-47
(Y2 SiO5 :Ce3+ ) phosphor plate (400 nm peak emission wavelength, 55 ns decay time, 0.06
photons/eV/electron quantum yields) generate photons that are collected by a CCD camera
positioned outside of the vacuum system, imaging the phosphor screen through the phosphorcoated glass vacuum window (see Beam Imaging Solutions BOS-75 assembly). The events

40
are centroided and coordinates compiled over tens of minutes to general 2D velocity maps
with 105 counts or more. Pixel-to-velocity calibration is achieved via two methods: (i) fitting
experimental Au film Fermi edges as a function of excitation photon energy, and (ii) SIMION
electron trajectory simulations. SIMION was also employed to determine/verify the optimal
extractor/repeller focusing conditions and is quite accurate for an accurate system model,
as evidenced by agreement between the experimental and simulated calibration factors tobetter than 5% (Section 4.4).
2.8

3D Velocity Map Imaging
To extend the 2D velocity map imaging capabilities to full 3D angle-resolved pho-toelectron velocity mapping, the photoelectron time-of-flight can be measured. This is asignificant challenge, however, due to the mere 200–300 ps time-of-flight spreads for a ∼1 eV electron beam kinetic energy spread, as timing resolution must be a few tens of picoseconds. This can be achieved via delay line detectors,[193] but Wen Li and coworkers
have recently demonstrated simple methods for converting 2D VMI to 3D VMI systems byinstead simply reading out the transient MCP currents and sampling the event pulses with
an ultrafast (>2 GHz) digitizer.[104, 105, 109, 46, 45] While their methods utilize a regeneratively amplified (∼1 kHz) laser that triggers both the camera and digitizer collection, the75 MHz collection rate utilized here requires a different method. The scheme is shown in
Fig. 2.7, where the digitizer is instead triggered only when an event occurs via the MCP
pulse, with another digitizer channel reading in the relevant laser pulse data. Both MCP
and laser pulse peaks are fit down to the digitizer jitter level (a few tens of ps) to achieve∼30 ps TOF timing. This is sufficient to resolve the vz distribution.
Camera and digitizer events are correlated by their overall timestamps. For thesestudies, a faster 520 fps CMOS camera has been implemented to enable higher count rates.
While multiple events in a single image can be correlated to the digitizer pulses via amplitude,
for now the studies are performed in the regime with fewer than one event per frame on

41

Figure 2.6: Velocity map imaging system, showing reflective microscope objective and scanning sample stage (repeller electrode).

Figure 2.7: Scheme for 3D velocity map imaging data collection.

42
average to avoid ambiguity (i.e., incorrectly assigned camera-digitizer event correlation).
Frame rates that are 25-fold higher thus help to compensate for these limited signal rates.
2.9

Femtosecond Pump-Probe Studies
Pump-probe studies to be discussed in Chapter 7 are achieved by placing a motorized

linear delay stage (Newport UTS150CC, ESP301 Motion Controller) with a retro-mirror
pair in the SHG beam path for ∼1 femtosecond timing accuracy. The position is not phasestabilized via fast piezo-based PID interometry, so the pump-probe studies are all phaseintegrated, i.e. only the intensity envelope is resolved with no/minimal interference fringes.
Beam sample alignment is achieved approximately via markers on the back-reflection CCD
television monitor, while careful alignment is achieved by particle location in SPIM scansat both colors. Relative pump-probe timing alignment is controlled via the automated andmultiple manual delay stages in the beam paths, first using a fast photodiode to achievecoarse overlap, then running pump-probe delay scans to locate the signal peak. Further
details will be described in Chapter 7.
2.10

System Control
The SPIM system is controlled by a software suite written in LabWindows/CVI, i.e.

the National Instruments C Language integrated development environment with integrated
graphical user interface functionality and ready implementation of the full national instruments hardware/software suite. The primary “SPIM.exe” program has purview over everything from the camera, digitizer, power supplies/voltages, and laser shutter, to the scanning/positioning functionality. This program is connected to the “PiezoPID.exe” positioning
program via DataSocket Server, as well as the delay stage positioning software. All physicalinput/output (e.g. system control and data acquisitions) aside from commercial camera anddigitizer hardware is handled by two NI DAQ cards, models PCI-6221 and PCI-6703, housedin BNC breakout boxes. The VMI detection camera is implemented in the control suite via

43
the GenICam camera API standard, while the digitizer is run via its own custom C API.
Both camera and digitizer are run on seperate threads, generated automatically via API
event-driven callback functions.
Essentially all data analysis is performed in a MATLAB AppDesigner-generated program, “VMI Aanlysis Suite”, which includes VMI visualization, angular and radial distribution analysis, time series analysis, 3D visualization and routines, as well as all simulation
routines for Monte Carlo and quantum photoemission calculations. The simulation routines
simply take data exported directly from COMSOL Multiphysics as inputs.
The KMLabs laser system is controlled on a seperate, dedicated computer by commercial “KMCtrl.exe” software package for adjusting prism and slit positions (along withcalibration, spectrometer readout, etc.). The OPO control software has been customized forready tunability and PID-driven wavelength locking.

Chapter 3
Theoretical Methods

A significant element in this thesis is the development and implementation of simple
theoretical methods for calculating nanoplasmonic 3D photoelectron distributions. A fairamount of real estate will therefore be devoted in this chapter to expounding on thesemethods.
3.1

Analytic Electrodynamics
Analyticity in electrodynamics simulations requires a high degree of nanoparticle sym-

metry. Most plasmonic field distributions will be calculated numerically, which can be done
for arbitrary nanoparticle geometries. However, some simple analytic geometries will first be
examined to understand some essential features of the plasmon modes. Detailed derivations
for spheres, ellipsoids, and Mie theory are presented in Bohren and Huffman,[20] while someessential features will be highlighted here.

3.1.1

Sphere and Ellipsoid Electrostatics

Nanoparticles much smaller than the wavelength of an applied optical field can betreated as if exposed to a constant electric field. This is known as the quasi-static or dipole
approximation. The harmonic time dependence is then readily included as the sum or integral
over harmonic modes, so long as the fastest frequency component remains in the quasi-static
regime. This is a good approximation for nanoparticles with < 100 nm dimensions under45
resonant visible and near-IR excitation (400–1000 nm wavelength). The electrostatics ofspheres and ellipsoids are presented in detail in various textbooks,[20, 177] but some key
features of the derivations and results will be discussed here. These features will provide
important context in which to understand the plasmonic behaviors of various spherical (e.g.
nanospheres and nanoshells) and prolate (e.g. nanorods and nanostar arms) geometries tobe discussed later on.
The electric field inside of an uncharged metal nanosphere immersed in a uniformbackground field, E0 = E0 x̂, can be determined by solving the Laplace equation in sphericalcoordinates subject to the appropriate boundary conditions.[81] The result is a constantinternal field,
Ein =

30
E0 x̂,
(ω) + 20(3.1)

and a dipolar external field at the nanosphere surface,
Eout = E0 x̂ +(ω) − 20(3E0 n̂ − E0 x̂),(ω) + 20(3.2)

where n̂ is the surface normal. Evidently, there is a resonance at (ω) = −20 , which is known
as the Fröhlich condition. Since (ω) = 1 (ω) + i2 (ω) is a complex quantity, the imaginary
component must be small for strong resonance. For noble metals such as gold, silver, theresonance has a high Q factor and occurs in the visible spectral range, as described in the“periodic table of plasmonics”.[18] One often approximates 2 ≈ 0 and 1 via the Drude
model[81] as1 (ω)/0 = 1 − ωp2 /ω 2 ,(3.3)

where ωp = (ne2 /0 me )1/2 is the bulk plasma frequency, n being the electron number density.
Plugging this into Eq. 3.1, one finds that the Fröhlich condition is satisfied at localized SPR
frequency
ωpωSPR = √ .
3

(3.4)

For gold nanospheres, Eq. 3.4 yields a resonance around 5.2 eV. The actual resonanceoccurs around 2.4 eV (520 nm), which is significantly different than the Drude model due to46
d -band contributions to the dielectric function, where the gold 5d -band lies approximately
2 eV below the Fermi level.
It will be of particular interest to determine surface- versus volume-mediated photoemission contributions, which will depend on the ratio of surface to volume fields. From Eqs.
3.1 and 3.2, this ratio is given for the surface point along the polarization axis (n̂ = x̂) by
Ein
(ω)
=
.
Eout
0

(3.5)

This could also be determined immediately by considering the boundary condition for thenormal component of the displacement field, which must be continuous across an interface
with no free charge,
D in · n̂ = D out · n̂.

(3.6)

At the “tip” along the laser polarization axis, where both internal and external fields arenormal to the surface, this leads immediately to Eq. 3.5. It can be seen that the plasmon resonance, ∝ ((ω) + 20 )−1 drops out of Eq. 3.5, such that the ratio of surface to volume fields
only depends upon the material dielectric function for spheres and more generally for ellipsoids, which also have uniform internal fields and corresponding dipolar surface charge/field
distributions.
The derivation here in the quasi-static regime suggests that the SPR does not depend
upon the size of the sphere. As will be shown in the next section, deviations begin to occur
for larger particles (> 100 nm), with additional dipolar dynamic depolarization contributions and higher-order multipolar contributions. For particles much smaller than the elastic(phonon scattering) mean free path of ∼30 nm in Au,[4] an additional surface scattering
contribution becomes prominent in influencing the plasmon dephasing time (Section 1.1).
In general, the SPR frequency depends upon the nanoparticle size, geometry, material (via(ω)), and the surrounding medium (0 → m (ω)).
Understanding the effects of nanoparticle geometry on plasmonic field distributions
and corresponding photoemission distributions will be the primary objective of this thesis.

47
The geometry influences the manner in which charges build up on nanoscale curved surfaces
and their Coulombic interactions. Many such effects can be illustrated by the behaviors of
ellipsoidal nanoparticles, which can also be treated analytically. The discussion here shallagain be restricted to ellipsoids with all dimensions much smaller than the optical wavelength,
thus permitting the quasi-static approximation. In this case, the Laplace equation must be
solved in ellipsoidal coordinates with the scalar potential expanded in ellipsoidal harmonics.
This problem has been solved in detail in a number of textbooks, including Bohren andHuffman[20] and Stratton.[177] For a general ellipsoid (principal semi-axes a > b > c), theinternal electric field is given by
Ein,i =

1
E0,i ,
1 + Li ( − m )(3.7)

where Li is the “depolarization factor” along one of the principal semi-axes, i = a, b, c,
abc
Li =
2m

Z ∞

ds

0

(s + i2 )((s + a2 )(s + b2 )(s + c2 ))1/2

.

(3.8)

Now specializing a bit to the particularly relevant case of a prolate spheroid (ellipsoid of
revolution with a > b = c), the tip field due to E0 = Ea polarized along principal axis a
is readily determined by the boundary condition on the surface-normal component of thedisplacement field (Eq. 3.6) to be
Etip =

1
E0 .
m 1 + La ( − m )(3.9)

Thus the external-to-internal tip ratio is the same as Eq. 3.5, as it must be by boundary
conditions.
More interesting is the absolute tip field enhancement, which is given from Eq. 3.9 by
Etip /E0 . As described by Liao and Wokaun,[108] the result can be written as the sum of therelative ellipsoid field and E0 as
Etip =(1 − m La )( − m )E0 + E0 .
1 + La ( − m )(3.10)

48
This can be further rewritten as
Etip = γEdip + E0 ,(3.11)

into a resonant dipolar field that encodes the plasmonic contribution,µ − m2 b2
Edip = 2 3 =E0
2a
3 a 1 − La ( − m )(3.12)

and a purely geometrical enhancement factor,γ=

3 a2(1 − m La ).
2 b2(3.13)

This geometric enhancement compared with the dipolar field is known as the “lightning rod
effect”, with γ > 1 along the a axis of a prolate spheroid, and γ = 1 for a sphere. For a 3:1
prolate spheroid, for instance (similar to nanorod geometries to be studied), γ = 12 is alreadya whopping geometrical tip field enhancement, on top of the plasmonic field enhancement.
The simple physical picture behind this lightning rod enhancement is that more electrons
can pack into regions with higher curvature due to the asymmetric forces on the charges
from the material vs. environment directions (e.g. charge A in the medium can move closer
to charge B at a nanotip because no charges lie beyond charge B in the vacuum to pushback), as is well known in electrostatics. Such strongly electric-field-enhanced “hot spots”
at sharp nanoparticle tips are an important feature for many nanoplasmonic applications—particularly nonlinear applications such as surface-enhanced Raman scattering (SERS), withsignal ∝ |E/E0 |4 , and multiphoton photoemission studies, with signal ∝ |E/E0 |8 being
common (i.e., in the 4-photon photoemission regime).

3.1.2

Mie Theory

For larger nanoparticles (> 100 nm) approaching a significant fraction of the visible
excitation wavelength scale, the dipolar approximation of a uniform electric field acrossthe particle is no longer adequate and higher-order multipolar oscillation modes become

49significant. From the other direction, taking an extended metal surface and shrinking it down
to the nanoscale, one finds that traveling surface plasmon polariton modes with well-defined
momentum begin to resolve into multipolar oscillation modes for which momentum is nolonger a good quantum number, i.e. “localized” surface plasmon oscillations. The solution
to Maxwell’s equations for light scattering off of large metal spheres was first treated by
Gustav Mie in 1908. The derivation, based upon expansion in vector spherical harmonics, isreproduced in detail in various texts, including Bohren and Huffman.[20] While quadrupolar
modes become relevant in some of the studies to be discussed, another important result of
Mie theory is the expansion of the dipolar term with respect to the size parameter, x = ka
where k is the optical wavenumber and a is the sphere radius. As shown in Meier[120]and summarized by Maier[115] (not to be confused), the dipolar polarizability begins todisplay substantial contributions from radiative damping and an effect known as dynamic
depolarization—i.e. the retardation of the polarization field due to the finite speed of light.
These terms lead to plasmon broadening and red-shifting, independent of interactions withhigher-order multipolar oscillations.

3.1.3

Hybridization Theory

When multiple plasmon modes interact strongly due to Coulomb interactions between
the surface charges, it may become necessary to rediagonalize into a more appropriate basis.
This “strong coupling” effect must be accounted for in studies of gold nanoshells (withinteracting core/shell modes) and gold nanostars (with interacting arm modes), for instance.
The typical approach to describing such effects in plasmonic systems is by hybridization
theory, which was developed by Prodan, Nordlander, and coworkers in the early 2000s[151]in a treatment that directly parallels molecular orbital theory. For example, the dipolar√
oscillations of the gold nanoshell outer sphere (radius R2 , resonance at ωp / 3) and innerpcore void (radius R1 , resonance at 2/3ωp ) couple to generate nanoshell dipolar modes at

50
frequencies[151]


2
ω±
=

ωp2

2

1±

1
3

s
1+8



R1
R2

3


.

(3.14)The lower-energy ω− “bonding” mode corresponds to inner and outer oscillations being inphase, whereas for the higher-energy ω+ “anti-bonding” mode they are π out of phase. The
ω− mode has a large dipolar moment and is thus “bright”, while the ω+ mode is “dark” andhas a very small optical excitation cross-section. Similar considerations exist for higher-ordermultipolar moments and other nanoplasmonic geometries, although both hybridized modes
may maintain a non-negligible optical excitation cross-section.
3.2

Finite Element Electrodynamics Simulation
Even barring substrate effects, most nanoparticle geometries are too complicated (i.e.

have insufficient symmetry) to be treated analytically. A variety of numerical methods forsolving Maxwell’s equations, including the discrete dipole approximation (DDA),[205] theboundary element method (BEM), the finite difference time domain (FDTD) method, andthe finite element method (FEM).[85] Here, FEM is employed to capitalize on a number ofadvantages discussed below (along with the simple, pragmatic advantage of software license
availability).

3.2.1

Finite Element Method

The finite element method (FEM) is a numerical technique for solving differential
equations, particularly useful for complicated domain geometries and inhomogeneous media.
Although finite element, finite difference, and other methods are commonly and effectively
used to simulate nanoplasmonic electromagnetic fields, the main difference is that FEM takes
advantage of the weak formalism (see below) for solving partial differential equations (i.e.,weighted integral with one derivative shifted over to the weighting function), which decreases
the differential order and relaxes the continuity requirements on the approximate solutions.

51
Finite difference methods (e.g. FDTD), on the other hand, solve the differential equations
directly in their strong form and are thus generally not as versatile with complex geometries
and physical boundary systems. This is often evidenced by strong noisy spikes in FDTD
solutions around nanoparticle surface boundaries. Such effects may be overcome or excused
when investigating linear processes, but are intolerable when simulating surface-mediatedmultiphoton photoemission (to be discussed in Section 3.5.2), which is proportional to thesurface field to the 2n power (e.g. E 8 for 4-photon photoemission) and thus greatly amplifies
any numerical noise. COMSOL Multiphysics (a portmanteau of COMputational-SOLver)is the popular finite element analysis software package utilized for all electromagnetic field
simulations in this thesis. Multiphysics refers to the ability to simultaneously solve multiple
coupled sets of PDEs, including for stress/strain, electromagnetics, fluid mechanics, and heatflow.
To understand the weak form of a PDE, begin with a generic (just linear, for now)differential equation in domain Ω (boundary δΩ):L̂(n) u(x) − f (x) = 0,

(3.15)

where L̂(n) is some nth -order differential operator and u(x) is the desired solution. The
appropriate number of boundary conditions is assumed. Eq. 3.15 is known as the strong
form of the differential equation as the nth -order derivative must exist (i.e. the function must
be continuous to the (n − 1)th -order). Taking the weighted integral with arbitrary weightfunction, ωi (x), leads to the weighted-integral form of the differential equation:Zωi (L̂(n) u(x) − f (x))dx = 0.

(3.16)Ω

Now integration by parts relieves u(x) of one differential order and places it on the weightfunction:ωi (L̂

(n−1)

Z
−

u(x))
δΩ

(n−1)

∂x ωi (L̂ΩZu(x))dx −ωi f (x)dx = 0.

(3.17)Ω(This is playing somewhat fast and loose with the nature of the differential operator; if it hasa zeroth-order term, this must be separated out explicitly.) This is known as the weak form

52of the PDE. The weight function, ωi can be readily chosen to be continuous to first order,
and to have a simple derivative, which we’ll ultimately use to solve the integrals directly andobtain a linear algebraic set of equations. As it stands, Eq. 3.17 still represents an exact
formulation of the problem, for arbitrary weight function.
To make the problem tractable and numerically soluble, the domain is discretized into
a set of N nodes. The function is then expanded in a basis set,u(x) ≈

X

cj φj (x).

(3.18)N

The basis functions φj (x) are typically chosen to be hat/triangle/tent functions centered onnode i and going to zero at the nearest-neighbor nodes. The approximation indicated in Eq.
3.18 is due to the incompleteness of the basis functions. Since the weak form holds for any
weighting function, a convenient choice is ωi = φi (Galerkin method). The integrals in Eq.
3.17 can then be solved in a relatively straightforward fashion for each i and j, and are only
nonzero for j = i, i ± 1. The net result is a set of linear algebraic equations which can besummarize in matrix form as
Ac = b,(3.19)

in which A is known as the “stiffness matrix” and is a sparse, tridiagonal matrix. Inverting
A via efficient algorithms for sparse matrices and solving for the ci ’s leads to an approximate
solution (Eq. 3.18) to the differential equation. At each step of the iterative matrix solver,
the error of the i-th step is determined via
Error(i) =|b − Ax(i) |,|b|(3.20)

where b and A are already known. The goal of the iterative solver is to iterate until thiserror is below some tolerance, e.g. 10−3 . The actual discretization process generates an ndimensional mesh, which may consist of triangular/quadrilateral or analogous higher-orderelements. The preferred element type and meshing method (e.g., structured, unstructured,or hybrid) depends on the problem geometry and parameters.

53
A final important consideration for electrodynamics simulations is to truncate thedomain using absorbing boundary conditions. To avoid spurious reflections at the domainboundaries, perfectly matched layers (PMLs)are often implemented.[16] This is achievedby analytic continuation of the relevant propagation coordinate into the complex plane,x → x + ωi f (x) for some chosen decay function f (x), such that the plane waves are dampedaskeikx → eikx e− ω f (x) ,(3.21)

which yields frequency-independent attenuation (for dispersionless k = nω/c) that has beenshown to be reflectionless for normal-incidence waves[16] and still minimal reflection at all
but the steepest off-normal angles.

3.2.2

Cross-Sections

Scattering, absorption, and extinction are calculated in multiple non-redundant ways,
including via heat dissipation, incident/scattered flux, the optical theorem, and linear combinations thereof. All of the results are within a few percent, verifying the accuracy of thecalculations. While methods exist for calculating the scattering cross-sections of supported
nanoparticles, scattering is only considered here for nanoparticles embedded in homogeneous
media as the absorption cross-section and corresponding heating is the primary quantity ofinterest for photoemission studies. In the following equations, E = E 0 + E rel , where E
is the total electric field, E 0 is the incident electric field, and E rel is the relative field due
to interactions with the nanoparticle, which is equal to the scattered field in the far-fielddomain (r  λ  D for particle dimension D).
The absorption cross-section is given by the total power dissipation over the nanoparticle volume, V ,1
σabs =I0

Z
Ploss dV,

(3.22)

V

where, by Ohm’s law, Ploss = J · E. Alternatively, the absorption is given by the net inward

54

Figure 3.1: Cross-sections calculated via FEM field solutions in COMSOL for a 9×31 nm
gold nanorod in water. (a) Absorption, (b) scattering, and (c) extinction cross-sections
calculated via the different methods described in the text, all displaying either perfect orstrong agreement.

55
flux across a boundary surface surrounding the nanoparticle, δΩ,1
σabs = −I0

Z
E × H · dS,(3.23)

δΩor byσabs = σext − σscat ,(3.24)For the example of a nanorod in water, all three methods are found to yield identical results
Fig. 3.1a. The scattering cross-section is given by the net far-field scattered flux across asurrounding boundary surface,1
σscat =I0

Z
E rel × H rel · dSFF ,(3.25)

δΩFFor via Eq. 3.24 if the other two quantities are known. In COMSOL, the far-field fields canbe realized either with a large domain and far-away boundary surface, or by implementing
the Stratton-Chu far-field formulation. All three methods for determining the scatteringcross-section agree to within a few percent Fig. 3.1b. Finally, the extinction cross-section isdetermined either by Eq. 3.24 or by the optical theorem, which relates the imaginary partof the forward scattering amplitude f (0) to the total extinction via
σext =

4π
Im{f (0)}k(3.26)

Both methods for determining σext agree to within negligible error Fig. 3.1c.
3.3

Thermalization Kinetics
Localized plasmon modes are bosonic quasiparticle excitations with dephasing times

typically < 10 fs, partially due to lifetime decay into electron-hole excitations (note that
due to metallic screening, such electron-hole pair excitations decorrelate within a few femtoseconds, leading to individual/uncorrelated hot carriers). These hot carriers thermalize
via scattering with cold (Fermi sea) carriers on tens of femtosecond timescales, which subsequently thermalize with the lattice phonon bath on few picosecond timescales.[69] Depending

56
upon the timescale and physical quantities of interest, such thermalization kinetics may bemodeled by different means, including isolating the femtosecond electron-electron thermalization and considering energy-depending in/out-filling effects (particularly via Fermi liquid
theory).

3.3.1

Femtosecond Electron Thermalization

Electron-phonon scattering mean free paths in gold of ∼30 nm around the Fermi level
correspond to ∼30 fs scattering times, but due to the nearly elastic ∼10 meV energy loss
per collision it takes many collisions for the electrons to effectively transfer energy into thelattice. Thus, on the few-hundred femtosecond timescales or faster, the electron kinetics canbe modeled independent from the lattice. The energy deposited into the electron bath by afemtosecond laser pulse with intensity profile I0 (t) is given by
Ce (Te )dTe= I0 (t)σabs .
dt(3.27)The temperature-dependent electron heat capacity is given via the Sommerfeld model[4] asCe (Te ) =2Te ne
π 2 kBV ≈ 1.5 × 10−19 J/K,
2EF

(3.28)

for nanoparticle volume V = 104 nm3 , gold electron density ne ≈ 5.9 × 1028 m−3 , Fermi
energy EF = 5.53 eV, and using Te = 300 K for the estimated value. Integrating Eq. 3.27
leads tos
Te (t) =T02 +4EF σabs2
π 2 kBne V

Z t

I0 (t0 )dt0 ,(3.29)−∞

where taking t → ∞ yields an expression for the max electron temperature reached in termsof the total pulse fluence. A typical electron temperature evolution for a 100 fs pulse, peak
I0 = 108 W/cm2 , σabs = 104 nm2 , and V = 104 nm3 is shown in Fig. 3.2, leading to a pulseaveraged temperature of 1000 K at the laser pulse peak and a peak temperature of 1500 K,
with a much more modest peak lattice temperature of 350 K. These short timescale kinetics are particularly important when determining an effective, pulse-averaged temperature in

57
photoemission spectra (approximately the temperature at the pulse peak) and when considering possibilities for thermionic emission from a highly heated electron gas—see Section
3.4.1 for further details.
The model in Eq. 3.27 assumes that the pulse energy is immediately transferred intoa thermalized excited electron distribution. However, it is clear that electrons will first be
excited to a nascent non-thermal distribution (essentially a small fraction of the groundstate Fermi-Dirac distribution excited up to EF + ~ω) which then internally thermalizes
via hot-cold electron-electron scattering on tens of femtosecond timescales. These dynamics
effectively delay the temperature increase by a few tens of femtoseconds and are accounted
for via Fermi liquid theory. The term “Fermi liquid theory” actually refers to a broader
framework for analyzing metal conduction excitations as quasiparticles, but in this context
it is specifically used in reference to the τe−e ∝ (E − EF )2 hot electron (quasiparticle)
lifetimes.[111] This is a simple result of Fermi’s Golden Rule when assuming a uniform joint
density of states and excitation matrix elements around the Fermi level—i.e. hot electronsin collision with cold electrons have a phase space proportional to (E − EF ) to decay into,
while cold electrons have the same phase space factor they can be excited from, such thatthe hot electron decay rate goes as the square of the excitation energy. This well-known
result can be encoded into the dynamics by modifying Eq. 3.27 as follows:dTe=
Ce (Te )
dt

Z ~ω
0

fna (t, δE)δE
d(δE),
τFLT (δE)(3.30)

where δE = (E − EF )2 and τFLT (δE) = a(δE/EF )2 with a determined experimentally.
The nascent excited distribution, fna , only loses population and can thus be solved forindependently via
dfna (t, δE)
1
I0 (t)σabs=−
fna (t, δE) +fna (0, δE).
dt
τFLT (δE)~ω(3.31)

58
3.3.2

Picosecond Lattice Thermalization

On tens of picosecond timescales after most of the absorbed pulse energy has beentransferred to the lattice, but before energy is transferred to the environment on 100 ps tonanosecond timescales, the peak lattice temperature can be simply approximated via
Tl =Fpulse σabs
Cl(3.32)

for total pulse fluence Fpulse and lattice heat capacity
Cl = cl ρV ≈ 2.5 × 10−17 J/K.

(3.33)In Eq. 3.33, for gold, the specific heat capacity cl = 129 JK−1 kg−1 , mass density ρ = 19.32
kg/m3 , and nanoparticle volume V = 104 is utilized for the approximate heat capacity. Since
the lattice heat capacity (Eq. 3.33) is over two orders of magnitude larger than the roomtemperature electron heat capacity (Eq. 3.28), the peak lattice temperature (on tends ofpicosecond timescales) is much greater than the peak electron temperature (on hundreds offemtosecond timescales), as seen in Fig. 3.2. Note that this does not scale proportionately
with the relative heat capacities due to the Te dependence of Ce (Te )—i.e. the Te increaseis about an order of magnitude greater than Tl rather than two order of magnitude since
Ce itself increases by about an order of magnitude during electron heating. These simple
calculations of peak lattice temperature are important for determining nanoparticle melting
thresholds for pulsed laser excitation.
3.3.3

Two-Temperature Model

Finally, to fully model the electron and lattice temperature evolution, including intermediate (few picosecond) timescales, the two-temperature model is utilized.[69] The kinetic
equations becomedTe= −g(Te − Tl ) + I0 (t)σabs
dt
dTl
Cl
= g(Te − Tl ),dt

Ce (Te )(3.34)(3.35)

59
where g ≈ 2 × 10−7 W/K is the electron-phonon coupling constant.[69, 47] The full electron
and lattice temperature evolution for the same parameter set as above is shown in Fig. 3.2.
Eq. 3.34 could additionally be modified to account for Fermi liquid theory dynamics as
described above.
3.4

Electron Emission Mechanisms
Electron emission from metals is often separated into three primary categories: thermionicemission due to heating of the conduction electron gas, perturbative multiphoton photoemission (MPPE), and strong-field optical field emission (OFE). Note that MPPE includes
single-photon emission—i.e. the conventional photoelectric effect. The distinction between
these three processes is not so clear-cut, however, as MPPE and OFE are limiting casesof the same surface photoemission physics[203] and thermionic emission is the zeroth-orderterm in the multiphoton perturbative expansion. In practice, many processes are categorized as thermally-enhanced MPPE or OFE (e.g. W or LaB6 electron microscopy emitter
tips)—particularly when the effect is significant enough for a given MPPE application tolower the process order by one—or photofield emission, in which multiphoton absorption
promotes electrons to higher energies with a smaller subsequent tunnel barrier. While weemphasize emission into vacuum, analogous processes can occur for other collection media,
including semiconductors or molecular layers.

3.4.1

Thermionic Emission

Thermionic emission occurs for metals above absolute zero due to the thermal tailof the Fermi-Dirac conduction electron distribution. Assuming the metal is held at a constant temperature, the thermionic current per area is given by the Richardson-Dushman
equation[4]−φJ = cAT 2 e kB T ,(3.36)

60

Figure 3.2: Two-temperature model evolution of the electron and lattice temperatures fora 20 nm diameter, 60 nm length gold nanorod for a 100 fs pulse, peak I0 = 108 W/cm2 ,σabs = 104 nm2 , and V = 104 nm3 .

61
in which φ is the work function and where the Richardson constant,24πeme kBA=
= 1.2 × 106 Am−2 K−2 ,3h(3.37)

is modified by some constant c ≈ 0.5 that depends on surface reflections and other detailsof the surface and emission. Setting aside such details, Eq. 3.36 is readily derived byintegrating over the fraction of the Fermi-Dirac conduction electron velocity distribution
with sufficient surface-directed kinetic energy to overcome the work function. While thiscurrent is only strictly zero at absolute zero temperature, it remains quite negligible inphotoemission experiments for electron gas temperatures less than a few thousand kelvin.
3.4.2

Multiphoton Photoemission (MPPE)

Excluding the zeroth-order thermionic term, the multiphoton photoemission expansion
determined via time-dependent perturbation theory can be written in general form as
MPPE =∞X

σnPPE I0n ,(3.38)

n=1

in which the dependence on the laser polarization and frequency is left implicit. While
I0 is merely the input field intensity at the local surface or volume region of interest andis therefore often known, the σnPPE are quite complicated and encode all of the relevant
plasmonic field enhancement effects, surface vs. volume effects, laser parameter dependencies(i.e. polarization and frequency), coherent vs. incoherent excitation pathways, etc. The
primary objective of this thesis, therefore, is to determine these nonlinear coefficients bothexperimentally and theoretically with as much generality as possible. Some of the relevant
theoretical considerations will be addressed in Section3.5, with combined experimental andtheoretical insights in the remaining chapters. While all of the experimental investigations
are necessarily in 2PPE or higher regimes to overcome the 4–5 eV metal work functions withvisible photon energies, the physics will be made as general as possible and therefore apply
to the linear regime as well (most relevant to photovoltaic and photocatalytic collection via
semiconductors and molecules, respectively).

62
3.4.3

Optical Field Emission (OFE)

For strong optical fields approaching the surface atomic fields of ∼10 V/nm, conduction
electrons can tunnel through the triangular barrier either directly from the ground state(OFE), with thermal assistance (“thermally-assisted” OFE), or following below-threshold
multiphoton absorption (“photofield” emission). Considering only typical OFE, tunneling
emission occurs in the strong-field, low-frequency limit where the optical phase is longer
than the electron “tunneling time”. By contrast, MPPE occurs in the weak-field, highfrequency perturbative regime. These regimes are commonly and conveniently distinguishedby a single, dimensionless quantity known as the Keldysh parameter,[91]
γ=

ω
ω
st

=

φ
,
2Up

(3.39)√
where ω is the optical frequency, ωt = eE/ 2me φ is the tunneling frequency under surface
electric field E (including plasmonic enhancement), φ is the work function, andUp =e2 E 24me ω 2(3.40)

is the ponderomotive energy. Conditions for which γ > 2 lead to MPPE, while γ 6 1 lead toOFE. In particular, the transition is found to occur within the 1 < γ < 2 range.[75] Even in
the MPPE and transitional regimes, post-emission classical dynamics due to ponderomotive
acceleration in strongly spatially varying and decaying plasmonic fields can be important andmay be accounted for by simulating the classical trajectories via the simpleman model.[39]
While OFE requires strong optical intensities around ∼ 1013 W/cm2 (corresponding
to electric fields of ∼10 V/nm), typical nanoparticle surface plasmonic field enhancement
factors of 10–30 significantly reduce the laser intensity requirements, leading to OFE for
more readily achievable input intensities in the range of a tens of GW/cm2 .[75, 106] Thelarge currents and narrow angular emission distributions from nanoplasmonic tips and othersystems make the OFE regime appealing for a variety of nascent applications, including

63
optical phase detection,[164, 152] x-ray free electron laser (XFEL) sources,[150, 75] andelectron imaging and diffraction.[127, 66, 126] However, the intensity must be managed
carefully in such systems to balance strong OFE with space-charge effects, along with strong
heating and possible melting. Such effects are negligible in MPPE applications. Furthermore,
the photoelectron kinetic energy spread in MPPE is typically < 1–2 eV and can be madequite narrow near threshold,[3] compared with > 10 eV spreads typical in OFE.[39] For highresolution diffraction and other applications, therefore, MPPE (with possible post-emission
acceleration) may be more appealing. All studies described herein are performed within the
MPPE regime.
3.5

Multiphoton Photoemission Theory
Photoelectric effect experiments and theory in the late 19th century and early 20th

century heralded the quantum revolution. Such progress was related only to the energy
conservation aspect of the photoelectric effect, however, as the nascent quantum theory
wasn’t sufficiently sophisticated to understand features relevant for momentum conservation. It wasn’t until the work of Bloch, Sommerfeld, and others in the 1920s in developing
an understanding of the quantum electronic structure of solids that notions of momentum
conservation arose.[186]Due to the negligible linear momenta of the incoming photons compared with the outgoing electrons in the visible-frequency photoelectric effect, momentum conservation demands
electron scattering with a massive third body during photoexcitation and emission. Photoemission via volume excitation is dominated by scattering with the periodic lattice potential
when the transition is energetically allowed, but visible plasmonic excitation is often below
the relevant interband threshold and instead involves interactions with phonons, defects,
impurities, or other electrons. By contrast, surface photoexcitation and emission pathways
arise due to the translational symmetry breaking at an interface and thus involve scattering with the surface potential barrier, including contributions from the electromagnetic field

64
variation, localized surface states, and the evanescent external decay of internally-delocalized
Bloch wavefunctions.[57] For nanoscale systems with . 20 nm dimensions, intraband excitation mediated by geometrical confinement can also become significant.[117, 24, 128]

3.5.1

Volume Monte Carlo ModelingVolume (multiphoton) photoemission is modeled within the phenomenological, ballistic three-step framework developed by Berglund and Spicer in 1964.[17] Although phenomenological, the three-step model was placed on firm theoretical footing by Feibelman
and Eastman,[48] and others (see, e.g., Hufner[78]) via comparison with a formal one-stepFermi’s Golden Rule treatment. In the three-step framework, electrons (i) are optically excited into a higher-energy eigenstate of the material, (ii) travel ballistically to the surface
with an exponential survival probability due to inelastic scattering (λinel ≈ 5 nm at EF + 5 eV
in gold[88, 102]) along the way, and (iii) transmitted into the vacuum (or other surrounding
collection medium, such as semiconductor or surface adsorbate layer) with finite probability
if they have sufficient normal momentum to overcome the surface potential barrier. For astep potential barrier, the transmission function increases gradually above threshold and isgiven by[56]Tstep (kz ) =4~kz pz,~kz + pz

(3.41)

where ~kz is the internal surface-normal momentum and pz is the external surface-normal
momentum, related via energy conservation by~2 kz2p2= z + EF + φ,2me
2me

(3.42)

for surface barrier height EF +φ. By contrast, the transmission function for a smooth barrierdue, for instance, to an unscreened image force, is approximately a unit step function[56]
 2 2

~ kz
Tsmooth (kz ) ≈ θ− EF − φ θ(kz )2me(3.43)= θ(pz ).

65
To account for all hot electron trajectories over a nanoparticle volume within thethree-step photoemission framework, a Monte Carlo numerical integration routine is implemented. Whereas direct integration is computationally intensive, wasteful for highly
spatially-nonuniform nonlinear excitation, and also requires care with the internal-to-external
phase space Jacobian transformation, the Monte Carlo method is efficient and encodes all
Jacobian effects automatically. Varying degrees of sophistication have been implemented inprevious Monte Carlo hot electron transport/emission calculations, including emphasis on
surface-scattering[19] or on volume scattering determined via ab initio theory.[31, 84] None ofthese previous calculations have emphasized full momentum resolution, however, only total
incident counts or internal quantum efficiencies. Here, the elements that are most importantfor full 3D velocity resolution and nonuniform spatial excitation (i.e. utilizing near-fields determined via finite element simulation) with inelastic mean free paths smaller than particle
dimensions (thus neglecting minor surface scattering effects) are implemented. Approximations of constant joint density of states and constant excitation matrix elements are madefor the coherent nonlinear excitations, such that the ground state Fermi-Dirac distribution ispreserved for the nascently-excited hot electrons. Furthermore, the approximation is madethat the hot electrons are excited isotropically, which is realistic for phonon-mediated multiphoton excitation that effectively randomizes the final hot electron momenta.
The Monte Carlo routine is represented in Fig. 3.3. A weighted random selection of
a nanoparticle volume point is performed with nonlinear field enhancement weight factor|E/E0 |2n determined via finite element simulation. To avoid volume discretization error, wethen perform a random displacement (∆r) within the volume associated with each mesh vertex. An angle is then selected at random and the momentum is randomly selected, weighted
by the excited Fermi-Dirac distribution. Next, the surface vertex closest in angle is determined and the corresponding distance and surface normal (n̂surf ) are used to determine
scattering and transmission probabilities, respectively. Given the small amount of excess
kinetic energy (∼1 eV) relative to the work function (∼4.25 eV), hot electrons that un-

66

Figure 3.3: Depiction of the surface and volume mesh vertices utilized in the Monte Carlomodeling. Each surface vertex corresponds to a ∼1 nm2 area with nearly constant surface
normal (n̂surf ). Each volume vertex corresponds to a ∼1 nm3 volume with an electric fieldenhancement determined via finite element modeling. To avoid any discretization effects,
the excitation coordinates are randomly perturbed by ∆r within the volume associated witha randomly-selected (nonlinear field-weighted) mesh vertex.

67
dergo even a single inelastic scattering event with a cold electron lose half of their energy
on average[159] and are therefore typically unable to escape and may be neglected. The
possibility of surviving a single scattering event via the triangular final energy distributionsof electrons determined by Ritchie and Ashley[159] is accounted for, including exchange effects, but the emission contribution of these scattered electrons is negligible. The mean freepath for elastic scattering (∼30 nm) is much larger than the inelastic mean free path (∼5nm) and therefore safely neglected as well. In cases where it is deemed necessary-—i.e. forlower-energy excitations escaping over a low-energy Schottky barrier-—the effects of inelastic
and elastic scattering can be readily included in this simple Monte Carlo algorithm. Thismethod can also be modified to allow for geometries with concave features (and therefore selfintersecting trajectories), but the simple convex modeling covers many essential geometries,
including spheres, rods, cubes, triangles, etc.

3.5.2

Surface Photoemission Theory

While a number of photoemission theories exist for metal surfaces,[116, 114, 208, 203,
135] the recent Green’s function perturbation theory analysis by Yalunin and coworkers[203]provides a particularly versatile framework for multiphoton photoemission, along with ponderomotive effects and the extension into the OFE regime. Furthermore, the theory accounts
for essential backscattering effects and quantum amplitude interference between the direct
and backscattered outgoing waves. This theory is therefore selected and implemented tomodel surface-mediated multiphoton photoemission velocity distributions for coherent excitation at a metal-vacuum interface, modified into a two-step process to account for the highgradient evanescent surface plasmonic fields. In the first step, free-electron initial states are
excited into field-dressed final states (Volkov states) with the ponderomotive quiver energy
appearing in the energy conservation equation,p2~2 k 2+ n~ω =+ Up + EF + φ
2me
2me(3.44)

68
in which ~k is the initial state momentum and p is the final state drift momentum. In
the second step, as the electron leaves the evanescent surface plasmon field region, theponderomotive energy is fully converted into kinetic energy corresponding to the surfacenormal momentum. The differential multiphoton photocurrent is given byX
d3 JMPPE
2~kz=
Pn (kz )2 k 2 /2m −E )/k T
3
(~
e
F
B
dkx dky dkz(2π) me n>n e+1(3.45)minwhich is the collision rate of Fermi sea electrons on the surface potential barrier, scaled by
the dimensionless excitation and emission probability, Pn (kz ), and summed over all allowed
multiphoton process orders as determined by energy conservation.
The photoemission rate can be written in terms of external momentum via the coordinate transformation~kx = px ,~ky = py ,~2 kz22me+ n~ω =

p2z
2me

(3.46)+ Up + EF + φ.

The Jacobian determinant is |d3 k/d3 p| = pz (~4 kz ) and the photoemission probability is thus
given in external momentum coordinates by
2 X
pz
d3 JMPPE= 3
Pn (kz (pz )),2 /2m +U +φ−n~ω)/kT(pep
dpx dpy dpz
h me n e+1(3.47)

in which all process orders may contribute to a final momentum state at finite temperature due to the exponential Fermi-Dirac tail, though most processes are negligible at room
temperature except the dominant multiphoton order dictated by energy conservation. For
completeness, the photoemission probability derived by Yalunin and coworkers via Green’s
function solution to the time-dependent Schrödinger equation[203] is given here in terms of

69
external coordinates as
q
p2z
2
~ 2m
+ Up + φ + EF − n~ω2e√Pn (kz (pz )) =In (pz ) + Rn(1) Rn(2) In (−pz ) ,2me (EF + φ)pz!
Z 2π sp2mepz
p2z
In (pz ) =+√− 2Up eiS(q) dq,~ω − Up −
h 0
2me
2me
r
Up
pz Up
cos(q) −sin(2q),S(q) = nq + 2
~ω me
2~ω
q
p2z
pz
+ Up + EF + φ − √2m
2m
e
e
(1)
Rn = − q 2
,
pz
p
z
√
+ Up + EF + φ + 2me
2me
r !
Up
p
z
Rn(2) = J0 −4.
~ω me(3.48)The integral terms In (±pz ) represent the outward- and backward-moving excited waves
outside of the medium. The reflection coefficients on the backward-moving wave account for(1)

rescattering on the surface potential barrier, where Rn is the reflection coefficient for a step(2)down potential (height EF + φ) and Rn accounts for the effect of the oscillating triangularbarrier in the applied optical field. Interference between the direct and rescattered waves canhave significant effects on the final emission amplitude, as discussed in detail by Yalunin andcoworkers.[203] Finally, we include the ponderomotive energy transfer in the present case ofan evanescent plasmonic field via the coordinate transformation p2z /2me → p2z /2me − Up .
To calculate the full 3D photoelectron velocity distribution for a given nanoparticle, thephotoemission contributions from each surface area element are calculated using the surface
field enhancements determined via finite element simulation. The photoemission distribution
is calculated with respect to each surface normal (p̂z,rel ) and rotated into the global frame (p̂z )via Cartesian rotation matrices. Only a single rotation about axis p̂z × p̂z,rel is required for
azimuthally-isotropic distributions. A sample uniform surface mesh and nonlinear surfacenormal field enhancement distribution is shown in Fig. 3.4. It should finally be noted thatgeometries with concave surface regions may allow for the intersection of emitted electrons
with other surfaces of the emitter geometry. These effects are not presently accounted for,70
although they should be negligible for the tip-like emission described in the present work.
3.6

3D Reconstruction
While time-of-flight photoelectron resolution is being implemented for direct 3D pho-toelectron velocity mapping, all measurements shown herein are 2D (vx , vy ), vz -integrated
velocity maps. Many features of interest will be directly evident in these distributions, although in some cases it will be beneficial or necessary to reconstruct the full 3D distributions.
There are essentially two routes to such reconstruction: (1) When the functional form of the
3D distribution is known (e.g. ∼ cos(θ) surface photoemission), the 2D velocity map can be
fit to the projection of this distribution. (2) If some minimal symmetry condition is present
in the photoelectron velocity distribution, such symmtery can compensate for the information lost in the projection and numerical reconstruction methods can be applied (Sections
3.6.1 and 3.6.2). The minimal symmetry condition in the velocity map imaging configuration
is for the photoelectron velocity distribution to have an axis of cylindrical symmetry parallelto the detection plane, i.e. perpendicular to the vz projection axis. While method (1) will
be discussed in Chapter 4 in the context of thin film photoemission, some methods of type(2) will be addressed here.

3.6.1

BASEX Algorithm

The vz projection (forward Abel transform) in velocity map imaging (VMI) experiments
is given byZ ∞P (vx , vy ) =f (vx , vy , vz )dvz ,(3.49)−∞

for an initial 3D distribution f (vx , vy , vz ). This projection/transform can be reversed for
3D distributions with cylindrical symmetry along an axis parallel to the detector—i.e.
f (vx , vy , vz ) = f˜(vr , vx ) for x-axis cylindrical symmetry—using various inverse Abel transform methods. Here the basis set expansion (BASEX) algorithm of Dribinski et al.[42] is71

Figure 3.4: Surface photoemission simulation geometry. Example nanostar surface meshand nonlinear field enhancement distribution utilized in theoretical 3D photoemission calculations. Multiphoton photoemission distributions are calculated with respect to the surface
normal for each nanostar surface area element (e.g. shaded patch), corresponding to eachtriangular mesh vertex at which the surface field enhancements are calculated.

72
implemented, using the nearly-Gaussian basis set from the original paper with σ = 1 px and a
regularization parameter value of q =10. The transform is carried out efficiently via matrix
inversion and multiplication in MATLAB, yielding the original 3D photoelectron velocity
distribution so long as the cylindrical symmetry assumption is valid, otherwise yielding anapproximation to the original distribution.
The essential idea of the method is to fit the projected distribution (P ) to the projections of Gaussian-like basis functions to reconstruct the original cylindrically-symmetricimage space distribution. By cylindrical symmetry, Im(x, y) = Im(x, ρ) for radial vector ρin cylindrical coordinates. The data matrix form of Im(x, y) is thus denoted as Im. The fit
in this analytic treatment corresponds to a linear operation (using the notation of Dribinski
et al.[42] unless otherwise specified),
Im = Z T CZ,(3.50)
T

2

−1

T

T −1

C = (XX + q I) XP Z (ZZ ) ,where C is the fit coefficient matrix for the projected Gaussian basis functions, X is the
projection-space basis, Z is the image-space basis, q is the regularization parameter toprevent over-fitting to noise, and I is the identity matrix. Eq. 3.50 reduces to
Im = Z T (XX T + q 2 I)−1 XP ,(3.51)

such that the transform matrix is Z T (XX T + q 2 I)−1 X. The basis matrices Z and X
depend only on the image size and Gaussian width parameter, σ, and are thus calculated
once and utilized for all calculations. For further details, the reader is referred to the original
work of Dribinski and coworkers.[42]3.6.2

Other Methods

Other methods for reconstruction include the Hankel transform method and polar onion
peeling methods.[197] While the brute-force Hankel method can lead to noisy results in thepresence of noisy inputs and problems with divergences,[197] the polar onion peeling method

73
presents an interesting alternative for metal film photoemission. The method effectively
deconvolves the vz degree of freedom by progressively peeling away radial projections of the
3D distribution. For ∼ cos(θ) surface photoemission, the projection is a constant value out
to the Fermi level, which leads to particularly straightforward implementations (e.g. for Au
film), as shown by Ye and Küpper.[207] This serves as a particularly nice alternative method
to the direct fitting method presented in Section 4.1 for reconstruction of film photoemission
distributions.

Chapter 4
Volume Photoemission from Thin Gold Film

Before examining the photoemission behaviors of nanoscale particles, some generalfeatures of multiphoton photoemission from a typical plasmonic metal (gold) are investigated,while simultaneously calibrating the velocity mapping system. In particular, flat gold films
are prepared commercially (PHASIS) via sputter deposition of 10 nm polycrystalline Au
film on a 2 nm Ti adhesion layer on a borosilicate coverslip. The adhesion layer and careful
sputtering procedure ensure flat gold films (< 1 nm RMS surface roughness) without theisland formation commonly observed for < 100 nm Au films deposited directly on glass.
The samples are stored in N2 -purged containers prior to usage and the the sample area isrefreshed for each experimental measurement to prevent any laser-induced adlayer buildupfrom affecting the velocity distributions. For example, a central inelastic scattering peak
can “grow in” under typical exposure to peak intensities of ∼0.1 GW/cm2 over the courseof 10–20 minutes, although the precise cause of this remains unknown. The majority of thischapter is taken from recent work on Au film.[145]4.1

Three-Step Photoemission Modeling
The majority of VMI applications take advantage of the high level of spatial symmetryoffered by atomic and molecular photoelectron/photoion velocity distributions in the gas
phase, specifically perfect cylindrical symmetry with respect to an axis parallel to the planeof detection. Under these conditions, the full 3D photoelectron/photoion velocity distribu-

75
tions can be efficiently recovered from the 2D VMI projections using inverse Abel transform
algorithms.[197, 5] Unfortunately, photoemission from surfaces and supported nanoparticles
may not exhibit the requisite spatial symmetry necessary to infer the vz projections directly(although this shall be examined in subsequent chapters). The ultimate solution has been
to implement fast timing on the electron arrivals and thereby measure the full 3D velocity
distributions directly (Section 2.8).[109] However, provided one has a sufficiently accurate
and physically justified model (vide infra), it is also possible to directly fit the 2D photoelectron projections and thereby infer the full 3D velocity distributions. A simple photoemission
model below, with the fitting method demonstrated for Au films.
It should first be clarified that PES methods in the low-energy (visible) regime essential for studying nanoplasmonic phenomena provide qualitatively different insights compared with UV or x-ray PES studies. For example, the band structure of gold[156] makes
evident that the visible OPO photons (~ω < 2.4 eV) employed herein have insufficient energy to promote direct/vertical transitions (in which total momentum is conserved modulo
the reciprocal lattice vector) from below the Fermi level to states above the vacuum level(Evac −EF ≈ 5 eV). To achieve momentum conservation in an indirect/nonvertical photoexcitation process within the volume of the material (bulk-mediated photoemission), an electron
must necessarily undergo a collision with a third body such as a photon, lattice defect, or
impurity center.[94] Alternatively, the necessary momentum during photoexcitation can beprovided by a collision with the surface potential barrier (surface-mediated photoemission).
In this case, the photoemission signal depends only upon the surface-normal component of
the electric field due to the well-defined direction of the surface potential gradient (∇V )contributing to the transition matrix element.[114] Such surface contributions are expected
to be quite minimal for the smooth Au films studied here (∼1 nm RMS surface roughness,characterized via AFM), since the surface-normal electric field component is small for light
excitation at normal incidence. In contrast, such surface-mediated photoemission effects will
be shown to play a more important role for nanoplasmonic geometries such as nanostars

76(Chapter 5), with strong and sharp tip hot spots, with plasmon-enhanced optical fields thatare both concentrated at the surface and pointed primarily along the surface normal.
To model photoemission following bulk-mediated excitation in the Au film and Au
nanoshells, we treat the emission process within the framework of a ballistic three-step picture(see Fig. 4.1),[17] in which the electrons (i) are excited within the volume of the material, (ii)travel ballistically to the interface with the possibility of scattering along the way, and (iii)
escape (“refract”) into the vacuum if there is sufficient momentum normal to the surface toovercome the work function barrier. Such a three-step model has been the most commonlyused method for predicting and interpreting photoemission spectra since its developmentin 1964 by Berglund and Spicer.[17] This three-step model is phenomenologically simple
by nature but nonetheless can provide important physical insight into the photoemission
process due to the same underlying Fermi golden rule formalism with the rigorous (but often
intractable) quantum-mechanical one-step model.[48, 78] Most importantly, since the result
is independent of the specific excitation mechanism, the same model can be applicable toa large variety of processes, such as linear photoemission, multiphoton photoemission, andthermionic emission.
The final velocity distribution of the ejected photoelectrons (fout (v)) can be predictedfrom the velocity distribution inside the metal (fin (v 0 )), based on the knowledge of the inelastic scattering probability, S(v 0 ), the surface barrier transmission function, T (v 0 ), and theJacobian transformation between the internal (primed) and external (unprimed) coordinatesthat accounts for the momentum loss and corresponding refraction at the surface barrier.
Conservation of particle number for electrons with sufficient perpendicular velocity to escape, dNout (v) = S(v 0 )T (v 0 )dNin (v 0 ), leads to a direct relation between the internal (fin ) andexternal (fout ) velocity distributions
2

0

0

0

02

0

fout (v)v sin(θ)dvdθdφ = S(v )T (v )fin (v )v sin(θ )∂(v 0 , θ0 , φ0 ))dvdθdφ ,∂(v, θ, φ)

where |∂(v 0 , θ0 , φ0 ))/∂(v, θ, φ)| is the determinant of the Jacobian matrix.

(4.1)

77
For a surface normal in the ẑ direction, the photoelectron transmission function is given
by
0

0

0



T (v ) = T (v , θ ) = Θ1 ∗ 022 0m v cos (θ )/Φ − 1
2 e

(4.2)

in which Θ is the Heaviside step function, m∗e is the electron effective mass, and Φ is thesurface potential barrier measured with respect to the bottom of the conduction band, as
shown in Fig. 4.1. This form of the transmission function simply assumes that the electrons
will escape with unity probability if they have sufficient kinetic energy associated with theperpendicular momentum component to overcome the surface barrier ( 21 m∗e v 0 cos(θ0 ) > Φ)or will otherwise be reflected. The effective mass accounts for the fact that the excitedelectrons are actually quasiparticle excitations in a strongly interacting (Coulombic) manybody system, which may be regarded as a free particle with an adjusted mass. Henceforth,however, it will be approximated that m∗e ≈ me for the nearly free electrons in the gold
conduction band. The velocity-dependent inelastic scattering probability is determined byintegrating the velocity and depth-dependent scattering probability,S̃(v 0 , z 0 ) =1 − z0 /λcos(θ0 )
inel
,
e
τ

(4.3)

over all z 0 = [0, τ ], where τ is the gold thickness (10 nm for the Au film), and λinel ≈ 5
nm is the inelastic mean free path for hot electrons near the photoemission threshold (∼5eV).[88, 102] For λinel  τ , the depth-averaged inelastic scattering probability takes on thelimiting form, S(v 0 ) = S(θ0 ) ≈ λinel cos(θ0 )/τ .
Finally, the Jacobian transformation requires a well-defined relationship between theinternal and external variables. Energy conservation yields the relation, 21 me v 2 = 12 me v 02 −Φ,
while conservation of parallel momentum requires that v sin(θ) = v 0 sin(θ0 ) and φ = φ0 since
there is no azimuthal dependence to the transmission through a smooth surface barrier.
These results can be combined to rewrite Re. 4.1 explicitly as
fout (v) ≈λinel  me 1/2
fin (v 0 (v))v cos(θ),
τ
eΦ

(4.4)

78
where λinel is taken as a constant over the narrow energy range of near-threshold electrons,
and the transmission step function limits the applicable domain of Eq. 4.4 to the upper-halfspace, θ 6 π/2. Note that if the internal distribution is isotropic (i.e., fin (v 0 ) = fin (v 0 )), theexternal distribution for near-threshold photoemission is predicted to vary with the typicalcos(θ) angular distribution, with an additional sin(θ) term from the spherical Jacobian factor.
From detailed balance conditions, this would be consistent with angle-independent, unity
sticking coefficients for electrons impinging on the Au surface from the vacuum. It is noted
for later analysis of curved nanoparticle surfaces that the angle θ in Eq. 4.4 is defined withrespect to the surface normal of each emitting area element. Using the simple relationshipbetween fin and fout in Eq. 4.4, the details of the internal excited electron distributions invarious systems can now be explored via velocity map imaging experiments. This will bedemonstrated next for Au film, the results from which will then provide a useful context fornanoparticle VMI investigations.
4.2

Au Film Velocity Mapping
A representative sample of 5 velocity map images (VMIs) measured on Au film isdisplayed in Fig. 4.2a, taken from 16 total measurements at different OPO photon energies
between 1.63 and 2.25 eV. These VMIs represent vz -integrated projections of the full 3D
photoelectron velocity distributions, where the initial transverse speed (vρ = (vx2 + vy2 )1/2 ) is
linearly mapped onto the corresponding radial position on the detector. Several features ofthe velocity distributions are immediately evident in the log-scale VMIs, such as the sharp
circular edges corresponding to photoemission of electrons from the Fermi level in the metal,
clearly extending outward with increasing photon energy (1.80, 1.90, 2.00, 2.10 eV) due tothe increasing energy above the vacuum level. Note, however, that this smooth trend isbroken by a dramatic contraction that occurs between 2.1 and 2.25 eV photon energy, whichcorresponds to the sharp transition between the 3PPE and 2PPE regimes, also identified
in the intensity-dependence studies in Fig. 4.3. For these normalized VMIs (105 electrons

79

Figure 4.1: Illustration of the ballistic photoemission process. Internal variables are denotedwith primes, and the external variables are unprimed (see text for details of the three-stepmodel).

80
per image), this contraction occurs when 2~ω becomes comparable to the work function
and near-threshold (and thus lower velocity) 2PPE electrons become the dominant sourceof signal.
Another striking aspect of the VMI data for Au film in Fig. 4.2a is the high degreeof azimuthal symmetry in the ejected electrons, which from Eq. 4.4 would be consistent,
for example, with a spherically-symmetric photoelectron distribution excited within the Au
film. It is worth noting that this is not an obvious result, since for transitions with linearlypolarized light, anisotropy in the momenta might have been expected due to the polarization
dependence of the transition matrix elements Mi,f ∝ hf |A · p| ii, where A is the electromagnetic vector potential, and p = i~∇ is the momentum operator.[78] However, the band
structure of gold requires transitions at visible frequencies to be nonvertical/indirect (evenfor two- or three-photon excitation), in which case the requisite scattering with phonons orlattice impurities randomizes the electron velocity vectors during excitation. It is therefore
reasonable to approximate the hot electron internal excited velocity distributions as isotropic,
as strongly corroborated by the azimuthal symmetry in the Au film VMI data. This provides additional symmetry constraints and simplifies the inversion procedure to determine
the scalar electron speed distributions by analyzing the radial dependence of the velocity
map images.
Angularly averaged VMI radial distributions are presented in Fig. 4.2b, where angularaveraging involves summing all electron events that fall within a certain radial bin (bin width= 1 pixel) and dividing by the corresponding cylindrical phase space factor, 2πvρ . Thus,
the distributions in Fig. 4.2b must be multiplied by 2πvρ to obtain the total count rate ata particular vρ . Based on the three-step photoemission model (Eq. 4.4), least-squares fits
to the radial distributions in Fig. 4.2b can be used to determine the emitted photoelectron
speed distribution and the corresponding internal hot electron speed distributions inside theAu film. To reproduce the experimental loss of vz information due to the projection onto thedetector, the full 3D photoelectron velocity distribution described by Eq. 4.4 is transformed

81

Figure 4.2: (a) Log-scale velocity map images measured on gold film for a series of photon
energies and linear polarization, count-normalized to 105 electrons per image, with the speed
corresponding to electrons emitted from the Fermi level (vF ) indicated with a dashed line
based on fits. (b) Angularly averaged radial distributions, shown with fits to the threestep photoemission model (solid black lines). The dashed black lines are the fits with thed-band contribution subtracted out, and the shaded areas therefore correspond to the dband contribution at each photon energy. The noise floor is characterized with the laser
blocked and is included in the fits. (c) Depiction of the possible routes for multiphoton
excitation, with a simplified band structure for the purpose of demonstration, along withthe corresponding density of states distributions. Arrows in parentheses indicate possible
phonon-mediated transitions necessary to conserve momentum.

82
into cylindrical coordinates and integrated over vz ,Z ∞fout (vρ , vz )dvz ,VMI(vρ ) = A

(4.5)

0

in which fout (vρ , vz ) is the emitted photoelectron distribution function in cylindrical coordinates, with the z axis orthogonal to the substrate and detection planes. Since fout (v) ∝fin (v 0 (v))vz (Eq. 4.4), the observed radial VMI distributions can then be least-squares fit toa sufficiently physically motivated and parametrized expression for fin via Eq. 4.5.
4.3

Interband vs. Intraband Photoexcitation
The internal distribution of hot electrons (fin ) is generated by the promotion of the

Fermi-Dirac conduction electron distribution to energies above the vacuum level via multiphoton absorption, as depicted in Fig. 4.2c. Any energy dependence of the Au joint densityof states (JDOS) and transition matrix elements between the initial and final states willalter the excited distributions relative to the initial distributions, but these quantities canbe approximated as constant in gold over the narrow range of photon energies studied here.
For indirect (e.g. phonon-assisted) volume excitation mechanisms, MPPE may proceed via
a single phonon-assisted multiphoton absorption step coupled through virtual intermediate
states or multiple phonon-assisted absorption steps with hot electron population also generated in intermediate eigenstates of the system below the vacuum level. As an additional
consideration for photon energies approaching 2 eV, direct 5d-6sp interband transitions also
become possible.[156] Due to the weak interatomic overlap between tightly bound 5d orbitals,
these 5d bands in gold have relatively flat dispersion curves compared with that of the 6sp
conduction band, leading to a large additional DOS at energies > 2 eV below the Fermi
level. These interband transitions are quite strong, as evidenced by the strong yellow colorof gold.[153] Following direct one-photon absorption from a 5d-band state to a 6sp-bandstate above the Fermi level, the electrons can then be indirectly excited above the vacuum
level via subsequent multiphoton absorption (Fig. 4.2c), which again requires a collision

83

Figure 4.3: Multiphoton photoemission process orders are determined for gold film by measuring the photoemission signal as a function of peak laser intensity for a series of photon
energies. The process order is the number of photons an electron must absorb to overcome
the work function, where “effective” non-integer process orders are due to contributions
from both the two-photon (I 2 ) and three-photon (I 3 ) processes. Examples of the intensitydependent plots are provided in the figure insets for photon energies at 1.9 eV (3PPE, solidred) and 3.1 eV (2PPE, solid blue).

84
with a phonon or lattice impurity for momentum conservation.
The combination of intraband and interband multiphoton excitation pathways can bemodeled via a sum of (i) a pure Fermi-Dirac term for electrons originating in the conduc(FD)tion band (fin) and (ii) an exponentially decaying term that approximates the d-band(d)contribution to the JDOS (fin ). This approximation appears to be justified by previous
XPS measurements of the conduction and 5d-band DOS of gold.[175] Within the three-stepmodel, energy redistribution due to inelastic scattering is calculated to be negligible for thenear-threshold electrons studied herein (free electron kinetic energies 61 eV), since very
few electrons are able to escape after even a single inelastic collision.[17] The net speed
distribution for electrons excited in the Au film is therefore(FD)

fin (v 0 ) = fin
(FD)

fin

(d)

(d)

(v 0 ) + Ad fin (v 0 ),

1

02

2

(v 0 ) = (e( 2 me (v −vF )−n~ω)/kTe + 1)−1 ,
1

02

(4.6)

2

fin (v 0 ) = e−βd ( 2 me (v −vF )−n~ω) ,where the internal electron velocity in the gold (v 0 ) is related to the external velocity inthe vacuum (v) by conservation of energy: 21 me v 02 = 12 me (v 2 + vF2 ) + φAu . By Eq. 4.6, Eq.
4.5, and Eq. 4.4, the angularly-averaged velocity distributions determined from the VMIs
can then be fit with parameters A (total amplitude), Ad (relative d-band contribution), βd(effective exponential decay constant for d-band DOS), kTe (conduction electron Fermi-Diractemperature), and vF (Fermi velocity). To minimize parameter correlation, Ad , βd , and kTe
are globally constrained across the speed distribution fits for the 16 different excitation
photon energies. The dominant process order, n, is known and held fixed for each photon
energy. The resulting fits are shown in Fig. 4.2b, which clearly capture both the independentand global behaviors of the distributions quite well. Note, in particular, the increasing
importance of the d-band contributions for higher photon energies, particularly > 1.8 eV, aswell as the dramatic contraction of the Fermi edge due to the onset of 2-photon photoemission
channel above 2.1 eV.

85
As a brief interlude, it should be noted that the measured velocity distributions are
actually in camera pixel units, which must therefore be calibrated. This is simultaneously
achieved via these fit distributions, as addressed in the next section, resulting in a calibration
factor that is utilized for the remainder of this section. The globally-fit Fermi-Dirac electron
temperature is found to be Te = 450 ± 50 K (± standard error). This fairly modest increase
above room temperature can be attributed to electron heating that occurs during a laser
pulse, with equal or higher electron temperatures >500 K demonstrated previously for 30 nm
thick Au film and similar absorbed pulse fluences (∼200 µJ/cm2 ).[47] The relative d-band
amplitude fits globally to Ad = 0.06 ± 0.01, and the exponential constant approximating thed-band DOS is globally fit to βd = 4.2 ± 0.2 eV−1 , which nicely reproduces the approximate
DOS of gold determined via XPS experiments.[175]For an even clearer parsing of the 3PPE, d-band 3PPE, and 2PPE contributions to Au
thin film photoemission, the overall signals have been measured as a function of OPO photon
energy, as reported in Fig. 4.4. On a logarithmic scale, the total MPPE spectrum shows adramatic increase in the photoemission rate (over four orders of magnitude) with increasing
photon energy between 1.63 and 2.33 eV, at constant intensity. This, in turn, reflects theincreasing electron DOS that can be excited above the vacuum level with increasing photon energy, especially once n~ω is large enough to promote 3PPE from the d-band states
and 2PPE from the occupied conduction band states. The MPPE curve in Fig. 4.4 is fit
by integrating the ejected photoelectron distribution over all velocities and employing theparameters determined in the VMI fits. The fits reproduce the behavior well with only the
2PPE and 3PPE amplitude parameters floated, for which the steep onset of 2PPE between
2.1 and 2.2 eV photon energies is in excellent agreement with the abrupt transition in powerlaw slopes demonstrated in Fig. 4.3. The fit amplitude of the 2PPE term is nearly four ordersof magnitude greater than that of the 3PPE term, which illustrates how lower-order processes
in the perturbative MPPE expansion become dominant once energetically above threshold.
It is clear that the 2PPE signals (once energetically accessible) should eventually become

86stronger than the d-band contributions with increasing OPO photon energy, as the d-band
emission is still a 3-photon (interband absorption + intraband 2PPE) process and therefore
involves an additional transition matrix element with respect to any 2-photon process. As
expected, however, the d-band signal (i.e., the difference between the solid and dashed lines
in Fig. 4.4) does become much stronger than 3PPE from the conduction band for photon energies >1.9 eV. Despite a few approximations, the excellent agreement between least-squares
fits and photoemission data for both the VMIs at many different photon energies (Fig. 4.2a)and the integrated distribution (Fig. 4.4) indicates that the ballistic three-step model withd-band contributions captures much of the essential physics underlying MPPE from thin Au
films.
4.4

VMI Calibration
Velocity map images are read out as counts per camera pixel. The origin and the veloc-

ity calibration factor must therefore be determined in order to analyze these distributions.
The origin is simply determined via Gaussian center fit of the highly-centralized photoemission distribution from a nearby spot on the ITO at 400 nm (2-photon) excitation. The
calibration factor is more challenging, and would ideally be determined by measuring photoelectron emission from discrete energy lines in a molecular system.[178] While a noble gas
flow source may be implemented in future with the laser focal spot shifted just above the ITO
sample coverslip to stimulate gas-phase emission, this is currently not available. Instead, allelectrons are photoemitted from solids with no discrete energy lines (note also that no surface states are probed given the surface-parallel polarization). Instead, therefore, the Fermiedge represents the most dramatic feature in the photoemission distributions, whch may
therefore be fit as a function of photon energy to calibrate the system. The photoelectron
kinetic energies corresponding to the Fermi level in the material (∝ vF2 ) have been plotted asa function of multiphoton excitation energy in Fig. 4.5. Note the strong linear proportionality, confirming simple expectations from the photoelectric effect that the maximum kinetic

87

Figure 4.4: Gold film MPPE spectrum measured with a constant effective (i.e., pulse-widthcorrected) input intensity at each OPO photon energy. The spectrum is fit using the ballistic
photoemission model integrated over all photoelectron velocities. To achieve the 5 ordersof magnitude in dynamic range without event overlap on the CCD and corresponding event
loss at high count rates, the intensity is decreased for photon energies >2.2 eV, and themeasured signal scaled back up accordingly. While changing the intensity will affect therelative amplitude between the 2PPE and 3PPE contributions, care is taken to avoid any
effects on the spectrum by performing this operation far enough away from the transition
region (2PPE is already dominant at 2.2 eV).

88energies increase with total photon energy, with the intercept yielding the work function,
φAu = 4.46 ± 0.05 eV. This value is lower than observed for atomically clean, single-crystal
gold surfaces[122] (∼ 5.1 eV) but consistent with measurements of polycrystalline gold surfaces exposed to ambient air/water vapor.[51] This decrease in work function with ambient
exposure arises from a molecular adlayer (e.g. water), which can suppress the inherent dipole
layer at the metal surface and decrease the corresponding potential barrier.[87] The slope in
Fig. 4.5 provides an important experimental calibration, yielding a pixel-to-speed conversion
factor of γ = 4150 ± 40 m/s/px, which is within 5% of the value simulated using SIMION(4240 m/s/px). This value will is utilized for all subsequent studies.
4.5

Discussion
Sensitive detection and analysis of multiphoton photoelectrons as a function of angle

and speed has been demonstrated using the SPIM technique on smooth, extended Au thinfilms. The 2D transverse velocity map data has been fit in the framework of a ballistic, threestep photoemission model to recover the vz information and thereby the full 3D photoelectron
velocity distribution. This analysis strongly suggests that the hot electron distribution in
the Au film is excited isotropically as well as that the electrons are excited with sufficientperpendicular momentum to overcome the surface potential barrier and leave the surface ina cos(θ) external angular distribution, due to the loss of momentum normal to the surface
and the corresponding Jacobian transformation between internal and external coordinates.
Furthermore, the final electron speed distributions are reproduced well by a simple sum of (i)a Fermi-Dirac distribution for the conduction electrons and (ii) an exponential decay in DOS
for the d-band electrons. Along with insights into the electronic properties of thin Au films,
which provide an essential context for subsequent Au nanoparticle studies, two important
observations about the SPIM surface VMI technique are summarized below.
First of all, multiphoton PES in the visible-photon energy range provides fundamentally different information than single-photon UV or x-ray PES, which are commonly used

89

Figure 4.5: Summary of fit results for gold film VMIs, showing the kinetic energy for electrons
originating at the Fermi level (∝ vF2 ) versus the total energy for an n-photon process. Theintercept yields a work function of 4.46(5) eV, and the slope, 20,400(350) px2 /eV, corresponds
to a velocity calibration factor γ = 4150(40) m/s/px . The simulation (dashed line) is from
SIMION -calculated trajectories and the slope is within 5% of the experimental value.

90
for measuring valence band structure and core/valence DOS, respectively. This is because
visible excitations above the vacuum level in noble metals involve nonvertical/indirect transitions and therefore require collisions with a phonon, lattice defect, impurity center, or thesurface during excitation to conserve momentum. Implications of this indirect excitation
mechanism have been demonstrated by the Au film studies, Fig. 4.2, including isotropic excitation and the strong, vertical interband excitation of d-band electrons compared with theweaker, nonvertical intraband excitation of conduction electrons. Furthermore, in multiphoton excitation processes, electrons must couple through real or virtual intermediate states
before escaping. Multiphoton techniques (e.g., time-resolved 2PPE) can therefore provide
information on the unoccupied states below the vacuum level and are particularly useful formeasuring hot electron dynamics in femtosecond pump-probe studies.[14, 143, 218] Properties such as the lifetimes and decay pathways of excited electron distributions in these intermediate states are especially important for plasmonic applications that rely on hot electron
extraction, such as photodetection,[22] photocatalysis,[110] and solar energy conversion.[30]Second, determination of the work function to within ∼50 meV is possible even in theabsence of any narrow spectral features due to the steepness of the Fermi edge, which ispreserved by the high-quality linear VMI mapping of transverse velocity onto radial detector
position. This ∼50 meV precision approaches that of common photoemission and Kelvinprobe work function measurements, which have typical uncertainties ranging from 10 to 50
meV,[38] although the accuracy has not been characterized here via other work function
measurements. While this aspect of the experimental technique still has room for optimization, the fundamental instrument energy resolution is calculated to be better than 10 meV
at 1 eV photoelectron kinetic energy (or 1%) for the voltages/magnification utilized, limited
primarily by the MCP pore spacing and ultrashort pulse bandwidth. This could in principle
be further improved for low-energy electrons by increasing the magnification and/or MCP
size or decreasing the pore size/pitch. It should finally be emphasized that these SPIM studies benefit significantly from continuous OPO tunability over the full visible spectrum, which

91
provides a crucial additional spectral dimension and the ability to characterize photoelectron
velocity distributions as a function of photon energy.

Chapter 5
Optical Photocurrent Control with Nanoshells and Nanostars

Now that the performance of the SPIM system and studies of thin gold film on flatglass have been studied in detail, a natural step into the nanoscale domain is to study
thin gold film on nanoscale curved glass—i.e. gold/silica nanoshells. It will be shownthat many nanoshells display crevice defect hot spots that lead to highly-spatially-localized
and thus highly-directional photoemission. This provides an opportunity to demonstratepolarization-controlled hot spot selectivity and photoemission angular control for nanoshells
with multiple defects. However, the precise near-field photoemission mechanisms from concave, uncontrolled hot spots are not so clear. For further clarity and control, we thus
study gold nanostars and demonstrate both polarization- and frequency-controlled emission
from well-controlled, sharp convex tip hot spots. The nanostars behave as multi-tip photocathodes and provide an unprecedented level of optical control for current generation,
switching/modulation, and even pseudo-continuous beam steering. These results and associated theoretical methods for simulating surface-mediated photoemission from arbitrary
gold nanoparticles provide crucial insights for similar light-matter transducers to be incorporated in THz nanoelectronics and novel on-chip electron beam sources, circuits, and novel
quantum probe modalities. The majority of this chapter is taken from recent work on Au
nanostars[144] and Au nanoshells.[145, 146]

93

Figure 5.1: (a) Transmission electron micrograph of three nanoshells supported on a carbon film, with high-magnification images demonstrating various gold shell surface roughness
features. (b) Representative single nanoshell scattering spectrum measured via dark-fieldmicroscopy (DFM), for a nanoshell supported on an ITO/glass substrate.

5.1Gold Nanoshells
For the present experiments, commercially available Au shell/silica core nanoparticles

with lipoic acid ligands (nanoComposix Inc., Rcore = 60 nm and Rtotal = 82 nm) are spincoated onto a 10 nm ITO-coated glass coverslip with an Au registration grid for correlated
studies. High-resolution TEM micrographs of nanoshells deposited on a carbon film areshown in Fig. 5.1a. Although the geometric cross section of a single nanoshell represents
only a relatively small fraction of the laser focal illumination area (10% at 650 nm), thecombination of strong plasmonic near-field enhancements and the |E|2n photoemission sensitivity result in nanoshell emission rates several orders of magnitude higher than the ITO
background, as previously demonstrated for Au nanoshells[62] and nanorods.[65, 64] Since
the localized surface plasmon resonance (LSPR) plays such a dominant role in the photoemission dynamics for these nanoparticles, it is worth first presenting a brief characterization of
the plasmonic properties of the nanoshells via both optical and photoemission measurements(along with theoretical expectations) and comparing these with Au film.
Dipolar and quadrupolar nanoshell scattering properties are characterized via darkfield microscopy (DFM), with a single-nanoshell scattering spectrum shown in Fig. 5.1b. As

94described elsewhere,[64] the DFM setup is separate from the SPIM system and consists ofwhite light from a tungsten/halogen lamp focused onto the sample via a dark-field condenser
lens. Scattered light is collected via a microscope objective on the opposite side of the sample and imaged onto an electron-multiplying CCD (Princeton Instruments Cascade II) via
a spectrometer (Acton SpectraPro 150, 150 grooves/mm grating). The spectrographs fromindividual nanoparticles are background-corrected and scaled to correct for spectral nonuniformity of the light source, the system transmission function, and the camera sensitivity
curve. Unless otherwise indicated, nanoshells in these SPIM experiments are excited with
100–200 fs pulsed light at ~ω = 1.9 eV (650 nm), which is strongly coupled to the dipolar
SPR.
Experimental UV-vis extinction data for an ensemble aqueous nanoshell solution arecompared with the COMSOL finite element method (FEM) and Mie theory calculations[140]for isolated (non-aggregated, uncoupled) nanoshells in water (Fig. 5.1a). The dominant lowenergy extinction peak can be readily identified in Mie and finite element method (FEM)
calculations as the dipolar SPR scattering component, while the smaller peak to the blue
is quadrupolar SPR absorption. These calculations are based on the measured core radiusof 60(6) nm (1σ standard deviation) and an outer radius of 82(12) nm, as characterized via
TEM of 100 nanoshells. Radii are calculated from the particle areas after thresholding TEM
images, thereby averaging over any bumps on the shell surfaces. The shell layer is modeledusing the bulk dielectric function of Au,[86] with the silica and water refractive indices set to1.45 and 1.33, respectively. The Mie and FEM theoretical results in Fig. 5.1a are in excellent
agreement with one another, but clearly blue-shifted by ∼0.1 eV with respect to the UV-vis
measurements. Due to the strong sensitivity of the nanoshell SPR to shell thickness, there
are a number of factors that could be contributing to this disagreement, such as surface
roughness, nonconcentric core offsets,[134, 80] or the environment effect of surface ligands.
Similar offsets observed previously for gold nanoshells were attributed to ∼4 nm surface
roughness on both the interior and exterior surfaces of the Au shell layer.[133]95

Figure 5.2: (a) UV-vis data compared with FEM and Mie theory calculations, all normalized
to the dipolar scattering peak. The calculations use the average core radius R1 = 60(6)nm and average outer radius R2 = 82(12) nm. (b) Linear absorption cross section andnear-field enhancement calculated via FEM (top) and experimental MPPE spectrum for arepresentative gold nanoshell with the gold film spectrum shown for comparison (bottom).

96
Mie theory is applicable for spherical particles but is not readily extended to supported
nanoparticles. However, FEM calculations are highly versatile with respect to complex
geometries[85] and are therefore used to calculate the absorption cross section and near-fieldenhancement spectrum for a supported nanoshell, as shown in Fig. 5.2b. The supported
nanoshell dipolar LSPR is predicted to be blue-shifted from the aqueous value (1.65 → 1.85eV) due to the smaller effective refractive index of the vacuum/substrate environment.[92]The electronic band structure properties of the Au shell layers are expected to be much thesame as Au film, and the photoemission proceeds via MPPE with the crossover from 3PPE
to 2PPE occurring around ~ω ≈ 2.15 eV for both systems (Figs. 4.3 and 5.3). This strongly
suggests that nanoscale curvature and corresponding plasmonic near-field enhancement effects have the most significant influence on the photoemission properties of Au nanoshells
relative to Au thin film. Simply stated, the plasmon resonance enhances the absorption andphotoemission but also emphasizes any surface effects due to charge localization and the resulting electric-field enhancements at the nanoshell surface. To confirm these expectations,the integrated MPPE spectrum is shown for a single Au nanoshell in Fig. 5.2b, where aphotoemission enhancement of ∼50 compared with the Au thin film signals represents anunmistakable signature of the dipolar plasmon resonance around 1.85 eV. A sharp kink due
to the onset of 2PPE is also observed around 2.1 eV, in good agreement with the intensitydependence results in Fig. 5.3. The nanoshell MPPE spectrum can thus be thought of as ascaled version of the Au thin film spectrum, enhanced by over an order of magnitude by the
dipolar and quadrupolar plasmon resonances.
Turning now to investigations utilizing the SPIM velocity mapping capabilities, a series of VMIs collected at different photon energies is summarized in Fig. 5.4a for a single, representative nanoshell, prior to any cleaning (see Section 2.5). The transition from
3PPE to 2PPE behavior is again clearly evidenced in the velocity distributions by the corresponding dramatic contraction in the Fermi edge that occurs between 2.00 and 2.15 eV,in excellent agreement with both the intensity-dependence results in Fig. 5.3 and the 2PPE

97

Figure 5.3: Multiphoton photoemission process orders are determined for a representative
gold nanoshell by measuring the photoemission signal as a function of peak laser intensity
for a series of photon energies. The process order is the number of photons an electron must
absorb to overcome the work function, where “effective” non-integer process orders are due
to contributions from both the two-photon (I 2 ) and three-photon (I 3 ) processes. Examplesof the intensity-dependent plots are provided in the figure insets for photon energies at 1.9
eV (3PPE, solid red) and 3.1 eV (2PPE, solid blue).

98
onset observed in Fig. 5.2b. A surprising characteristic of these nanoshell VMIs is thehigh degree of azimuthal isotropy, despite linearly polarized excitation light coupling to
the dipolar and quadrupolar SPR modes and the strong anisotropy of the correspondingnear-field enhancements.[134] This will turn out to be due to post-emission photoelectron
inelastic scattering with some air (i.e. water) adlayer on nanoshells that have not yet beencleaned via high-energy photon (3.1 eV SHG beam) exposure. The inelastic scattering effectively randomizes the emitted electron directions. However, as a first attempt at modelingthis scattered behavior, it is assumed that the electrons are emitted uniformly from thenanoshell surface. The three-step photoemission model is again utilized but now with thecos(θ) factor in Eq. 4.4 eliminated to account for uniform emission from the overall sphericalnanoshell geometry. The presence of the substrate can be approximately taken into accountby assuming that all downward-moving electrons are collected by the ITO, which uniformly
scales the photoemission distribution by an overall factor of 0.5. With these additional assumptions, the radial VMI distributions in Fig. 5.4b are least-squares fit using the d-band
parameters determined from the Au film studies. Although the Fermi edges are fit reasonably well with a globally fit Fermi temperature of 430(50) K, it is now clear that the fits
do not even qualitatively capture all of the behavior in the photoemission distributions. In
particular, the large excess signals near zero velocity that constitute as much as 30% of thetotal photoemission count rates are not correctly predicted by the three-step photoemission
model, which does not account for post-emission inelastic scattering. Even so, the work
function of 4.33(10) eV can still be determined with high accuracy as it depends primarily
upon the sharp Fermi edges. This is close to the 4.46(5) eV work function measured on Au
film but lowered by additional considerations such as the spherical particle geometry (whenelectrically grounded),[200] ligand surface dipole effects,[87] and the contact potential with
the ITO substrate.[215]
When one takes into account the linear laser polarization and strong anisotropy ofthe dipolar and quadrupolar LSPR electric near-field distributions, the nearly complete

99

Figure 5.4: (a) Log-scale VMIs measured on a representative gold nanoshell for a series ofphoton energies and linear polarization, count-normalized at 105 electrons per image, withthe speed corresponding to electrons emitted from the Fermi level (vF ) indicated with adashed line based on fits. The axes are now in physical velocity units, using the calibration
factor determined via gold film measurements. (b) Angularly averaged VMI radial distributions are displayed on a logarithmic vertical scale, shown with fits to the three-step model(black) assuming uniform photoemission from all surface areas on the nanoshell.

100
azimuthal symmetry observed in the nanoshell VMI distributions is initially rather surprising.
For example, considering just the dipolar SPR, the near-field enhancements are predicted
to be strongest along the plasmon axis defined by the laser polarization, with maximum
enhancements of |E/E0 | ≈ 8 determined via FEM calculations at the nanoshell surface (~ω =1.9 eV—see Fig. 5.2b), compared with |E|/|E0 | near unity at the surfaces perpendicular tothe plasmon axis. It shall be shown in Section 6.6 that volume-like emission is dominant
for defect-free nanoshell dipolar excitations, but the simple, initial intuition of excitation in
the surface-enhanced regions is first examined here. Most electrons will be excited in theplasmon-enhanced-field regions near the surface of the Au shell, only traveling ∼5 nm in
the gold film before either escaping from the surface or decaying below the vacuum level via
electron-electron scattering.[24, 102] Since these short inelastic mean free paths are very small
compared with the nanoshell dimensions (∼160 nm diameter), photoemission will effectively
be localized to the regions of greatest excitation. The cos(θ) distribution of the emitted
electrons is peaked in the direction normal to each surface area element from which theelectrons escape, such that any anisotropy in the position-space emission distribution should
produce a corresponding anisotropy in velocity space. In the case of dipolar nanoshell surface
emission (which again, turns out not to be the correct explanation, let alone post-emission
scattering effects), one would expect emission peaking along the dipolar plasmon axis. Verymuch contrary to these expectations, there is little anisotropy evident in Au nanoshell VMI
distributions in Fig. 5.4a. Furthermore, neither the process order (2PPE/3PPE), nor the
coupling to different SPR modes (dipolar/quadrupolar) at different photon energies appears
to affect the VMI distribution. Only a change in the energy cutoff corresponding to the
Fermi level inside the metal is evident with increasing photon energy, as clearly displayed inFig. 5.4b.
The possibility that scattering is occurring with the surface ligands (lipoic acid) and/or
an additional molecular adlayer (i.e. due to brief exposure to ambient conditions in sample
preparation) during the photoemission process—effectively randomizing the photoelectron

101velocity directions—will now be explored. As described in Section 2.5, repeated air exposure→ cleaning cycles demonstrate that it is not ligands, but rather some reversible adlayer(e.g. water) that develops upon air exposure. Such an adlayer being responsible for strong
post-emission inelastic scattering explains both the unexpected isotropy in the velocity distribution and the excess electron densities observed near zero transverse speed in the VMI
distributions in Fig. 5.4b. Upon exposure to low doses of second harmonic 400 nm light(∼1 GW/cm2 for ∼1 s at ~ω = 3.1 eV) the peak near zero velocity in the velocity map
and radial distribution disappears. The distribution is still fairly isotropic looking on alogarithmic scale but is no longer centralized near zero kinetic energy, indicating that theinelastic scattering effect has been greatly reduced. It should be noted that the resulting
radial distribution is still not captured well by the isotropic photoemission model. This will
be examined in more detail via full Monte Carlo modeling in Section 3.5.1. Regardless, this“cleaning” effect is highly reproducible over many nanoshells and does not change appreciably upon longer or higher-intensity exposure. This indicates that if surface admolecules
are indeed being cleaned off, all or most have been removed at these exposure levels. Interestingly, an observation of Au-thiol bond cleavage and therefore cleaning of ligands fromgold nanoparticles with 400 nm exposure has been reported previously by El-Sayed andcoworkers and was attributed to hot electron energy transfer into the Au-S ligand bond triggering dissociation.[82] While it is not expected that ligands are being cleaned off here—or ifthey are, they weren’t responsible for scattering in the first place and the removal thus goes
unnoticed—a similar hot-electron-mediated cleaning effect may be occurring that requires
the high-energy SHG photons. Other sample-cleaning techniques (e.g., chemical rinsing,UV/ozone cleaning, plasma cleaning, and heating on a 200 ◦ C hot plate) have also been
attempted prior to loading the nanoshell sample into the vacuum chamber, none of which
produced any observable effect on the nanoshell photoemission distributions. This indicatesthat high densities of hot electrons with sufficiently high energy are essential to the ligand
removal process, or possibly that surface cleaning must take place in vacuum due to fast

102
adlayer deposition under ambient conditions.
One final intriguing observation is that this cleaning effect only occurs with 400 nm
or higher-energy light (as it has also been observed at 350 nm), with exposure to 2.3 eV
OPO photons producing no observable effect. Previous studies have demonstrated strongnanoshell photoemission-dependence on the laser polarization, which was attributed to hot
spot effects arising from few- or even sub-nanometer defects on the nanoshell surface.[62] In
the interest of eliminating possible contributions from defect hot spots in these initial singlenanoparticle VMI studies, it is noted that all nanoshells described so far were chosen thatexhibit less than 10% variations in MPPE signal with laser polarization. By contrast, 90%of the nanoshells display strong polarization dependence due to the presence of defect hot
spots, to be discussed in the next section, while more detailed studies of isotropic nanoshells
and opportunities for full angular photoemission control will be discussed in Section 6.6 once
the notions of volume and surface MPPE have been examined in more detail.
5.2

Directional Photoemission from Nanoshell Defect Hot Spots
The photoemission rate for a typical Au nanoshell is highly sensitive to the laser po-

larization even for normal-incidence light, as shown in Fig. 5.5b and explored previously
in detail.[62] Because the nanoshells observed via TEM and SEM are nominally spherical,
the strong polarization dependence indicates the presence of additional structure such as
bumps and/or pits on the surface of the Au shell, which break the expected azimuthal symmetry of a supported spherical object. Despite the small individual surface areas of these
hot spots relative to the overall nanoshell surface area, it has been shown that plasmonic
field enhancements can grow disproportionately relative to a shrinking emitter area with asharp geometrical feature, thereby enabling even sub-nanometer hot spots to compete withand even dominate the overall photoemissivity.[62] This effect is enhanced even more dramatically in the multiphoton regime, where the photoemission rate is highly nonlinear withrespect to the local electric field, scaling as E 2n for nPPE. Nanometer-scale surface structure

103that could potentially produce these effects is evident in the correlated SEM image in theinset of 5.5a, as well as in the TEM images in Fig. 5.1a. The polarization dependence ofthe photoemission rate shown in Fig. 5.5b is thus fit by a constant term to account for
the underlying isotropic behavior expected for a perfectly smooth nanoshell, which becomes
the dominant behavior around the minimum photoemissivity polarization angle, θmin , anda localized hot spot term proportional to cos6 (θ − θmax ). The latter 2nth-order cosine term
corresponds to the projection of the field along the hot spot axis for a three-photon (2n = 6)
process. Note that even when polarized along θmin , all of the nanoshells are still orders ofmagnitude more photoemissive than the ITO substrate.
Photoemission originating from localized hot spots on the nanoshell surface should beleaving the nanoparticle in a well-defined average direction, corresponding approximately towhichever side of the nanoshell the hot spot is located. The measured photoelectron momentum maps for single nanoshells, as in Fig. 5.5a, confirm the expectation of anisotropic
photoemission, which is indeed strongly directional. Note that all nanoshells have been
SHG-cleaned (see Section 2.5) prior to investigation to eliminate the surface adlayer due
to air exposure and the associated inelastic scattering. Contrary to initial expectations, acomparison of the momentum map with the polarization dependence for the same nanoshell(Figs. 5.5a and 5.5b) reveals that the photoemission is actually strongest in the direction orthogonal to the laser polarization at peak photoemissivity angle, θmax . Moreover, orthogonal
photoemission is observed for the majority of nanoshells, with only ∼10% of the nanoshells
exhibiting a nominally parallel photoemission relative to the laser polarization at θmax (Fig.
5.5a). Although initially surprising, the orthogonal emission from these hot spots is consistent with a “nanocrevice”-type defect geometry that can readily form between the crystal
domains on the polycrystalline shell. At least one of these nanocrevice defects is evident asa dark spot in the micrograph inset in Fig. 5.5a and is also approximately aligned with thepeak photoemission direction. As will be shown in further detail via additional correlated
SEM-SPIM studies, along with finite-element simulations, these nanocrevice regions can be-

104

Figure 5.5: Directional photoemission from a single Au nanoshell, with all measurements
taken at ~ω = 1.9 eV on the dipolar SPR. (a) Photoelectron momentum map for a single
nanoshell at the maximum photoemission polarization, θmax . (Inset: a correlated SEM
image.) (b) Polarization dependence for the same nanoshell, fit to cos2n (θ) (with n = 3) forthe hot spot plus a constant term for the isotropic nanoshell contribution. (c) Momentum
map for the same nanoshell, but now at the minimum photoemission polarization, θmin ,which demonstrates a more nearly isotropic photoemission behavior.

105
come strong hot spots when the laser polarization is orthogonal to the nanocrevice spatial
axis. If the average photoelectron momentum is approximately radially outward from thenanocrevice hot spot region, then the photoemission direction will also be orthogonal to thelaser polarization, as observed.
Additional near-field insight is gained by investigating the statistics of nanoshell pho(n)(n)

toemissivities, σPE (θ) (where nPPE = σPE I n ), over many nanoshells at polarization angles,θmax and θmin . Photoemissivity statistics for 3PPE at ~ω = 1.9 eV are summarized in Fig.
5.6 for 45 individual nanoshells. When combined with correlated momentum maps and SEM
images for each nanoshell, these statistics tell a simple story: A given nanoshell surface may
contain zero, one, or more nanocrevices, any one of which may become a hot spot when the
SPR is driven along the appropriate axis. The maximum nanoshell photoemissivities (atpolarization θmax ) are spread out over more than 3 orders of magnitude due to very sensitive
dependence on the specific crevice geometry and the corresponding near-field enhancement(nPPE ∝ (|E|/|E0 |)2n ). By contrast, the minimum photoemissivities are more strongly clus
−
(n)
W 2
. This indicates that thetered near the smallest values of σPE (θmin ) ≈ 5 × 10−25 es / cm
2
photoemission at polarization θmin may be reaching the lower limit of the defect-free dipolar
SPR enhancement. This picture is corroborated by momentum maps with polarization atθ ≈ θmin , as demonstrated in Fig. 5.5c, which in most cases look quite isotropic despite
strong anisotropy/directionality observed with polarization at θmax . It may be noted thateven the predominantly isotropic momentum distributions still tend to have a slight preference toward the orthogonal emission relative to the laser polarization, which will be exploredin terms of volume photoemission Section 6.6. The total momentum distribution at any laser
polarization angle is simply the linear combination of the θmin and θmax distributions, withthe latter strongly peaking due to scaling by cos2n (θ − θmax ).
To verify that all directional photoemission observed in these experiments is due to
hot spot MPPE enhancement rather than OFE and/or ponderomotive acceleration following emission, photoelectron transverse kinetic energy distributions have been recorded at

106

Figure 5.6: (a) Nanoshell statistics on the average photoemission direction (θPE ) relative toθmax , with θPE determined via Gaussian fit to radially integrated momentum distributions.
(b) Nanoshell photoemissivity statistics at the maximum enhancement polarization, θmax ,and minimum enhancement polarization, θmin , for each nanoshell.

107
multiple different laser intensities and frequencies. The results are presented in Fig. 5.7 fora single nanoshell, in this case one displaying the less typical behavior of peak photoemission(with polarization at θmax ) parallel to the laser polarization axis (Fig. 5.7a). Even for these
uncommon parallel emitters, the intensity- and frequency-dependent behavior demonstrated
in Figs. 5.7b and 5.7c is completely consistent with the more commonly observed perpendicular emitters. Specifically, as the intensity is increased in Fig. 5.7b in uniform steps of
0.2 GW/cm2 at ~ω = 1.90 eV, the total photoemission signal increases as I 3 (as expected
for 3PPE), but the transverse kinetic energy distributions remain largely unchanged. Thisstrongly supports a three-photon photoemission (3PPE) process. Conversely, although ponderomotive acceleration could in principle be taking place following MPPE in strong hot
spot evanescent fields, one would expect the kinetic energy cutoff to increase approximately
linearly with laser intensity,[101] whereas no such change is observed in the kinetic energy
spectra over a 5-fold change in intensity. Furthermore, the Fermi edge drop-off around 1.5 eV
kinetic energy corresponds to the expected value for 3PPE: 3~ω−φ = 5.7−4.2eV = 1.5 eV, inwhich the supported nanoshell work function of ∼4.2 eV was also measured previously.[145]Thus, we can be quite certain of these experiments being in the fully perturbative 3PPE
regime.
For gain further insight into the photoemission dynamics from nanoshell hot spots,
transverse kinetic energy spectra have been measured as a function of laser photon energy,
shown in Fig. 5.7c. These results are perfectly consistent with the MPPE mechanism, with
the Fermi edge expanding outward by ∆n~ω with increasing photon energy and with a clear
transition from the 3PPE regime to the 2PPE occurring between ~ω = 1.90 and 2.20 eV.
This sharp transition is quite strikingly revealed in the inset of Fig. 5.7c, which summarizes
the power-law fits to intensity-dependence studies at a series of laser photon energies (nPPE∝ I n ) and, as expected, displays a precipitous sigmoidal shift in behavior between n = 3
and 2. None of this behavior is expected in an OFE process, nor in a thermionic process.
As a final confirmation of the multiphoton process, the Keldysh parameter (γ, Sec-

108

Figure 5.7: Confirmation that all photoemission takes place in the perturbative multiphoton
regime. (a) Momentum map for a nanoshell/hot spot exhibiting a nearly parallel emission(but the demonstrated behavior is equally valid for the much more common orthogonal
emitters). (b) Angle-integrated transverse kinetic energy spectra as a function of peak pulse
intensity. The dashed line represents the kinetic energy of electrons originating from aroundthe Fermi level within the gold. (c) Angle-integrated transverse kinetic energy spectra fordifferent incident photon energies. (Inset: Summary of laser intensity-dependence measurements, with the process order determined via power-law fit, where nPPE ∝ I n ). The tailevident in the ~ω = 2.20 eV 2PPE distribution is due to a remaining 3PPE contribution,
due to proximity to the 2PPE–3PPE cross-over frequency (~ω = 2.15 eV).

109
tion 3.4.3) provides a convenient single-parameter indicator for MPPE (γ > 1) versus OFE(γ < 1).[91] At the highest peak input intensities at the sample of 1 GW/cm2 (E0 ≈ 0.1
V/nm), for a measured nanoshell work function around 4.2 eV and assuming a large hot spot
E-field enhancement of 50 at ~ω = 1.90 eV, the Keldysh parameter is γ = φ/(2Up = 4.6, witha ponderomotive energy Up = e2 E 2 /(4me ω 2 ) ≈ 0.1 eV. These values indicate that photoemission is occurring in the multiphoton regime with minimal post-emission ponderomotive
acceleration, even under the most extreme hot spot conditions expected in these experiments. In combination with the laser intensity and frequency studies discussed above, thesecalculations confirm unambiguously that the directional photoemission occurs from MPPE
processes, arising from the specific geometries and nano-localized nature of the nanoshell
defect hot spots rather than strong-field acceleration effects.
Unlike surface- or nanotip-based photocathodes, which impose directionality via themacroscopic geometry, the directionality of photoemission from nanoparticles is potentiallymore subtle, versatile, and tunable in nanoshells by choice of different SPR hot spots. This
tunability is clearly demonstrated on a nanoshell that happens to have two hot spots withdifferent θmax but nearly equal photoemission efficiencies, as shown in Fig. 5.8. For such a
(1)

(2)

system, rotation of the laser polarization between θmax and θmax also rotates the photoemission direction by a nearly equivalent angle (in the present case, approximately 90◦ ). Thisillustrates the basic concept for an optically-controlled photocurrent switch, which could be
operated on femtosecond time scales via ultrafast polarization control. Although the occurrence of nearly equivalent hot spots is not common in these nanoshells due to the variabilityof defect geometries and the strong |E/E0 |6 photoemission sensitivity to electric field, thisphotoemission switching behavior is in fact observed for many nanoshells, just with different hot spot photoemissivities. More importantly, this provides a proof-of-concept for how
nanoparticles/nanostructures might be specifically synthesized/fabricated for a near-field
control of photoemission properties. For example, nanoparticles such as nanostars (to be
discussed) or tailored nanolithographic structures[2] could take advantage of this effect in a

110

Figure 5.8: Polarization-controlled directional 3PPE from a single nanoshell with multiple
hot spots of nearly identical photoemissivity, excited at ~ω = 1.9 eV.

far more controlled manner, with multiple strong, tailored hot spots.
As the majority of the nanoshell hot spots exhibit a maximum photoemission orthogonal to the laser polarization direction, we can exploit a combination of SEM and finite
element modeling (FEM) to explore which shell topologies might be most likely to produce
this behavior. Correlated SEM and VMI images of 45 sample nanoshells reveal a common
crevice-type structure corresponding to dark spots on the nanoshell surface (or light spots in
TEM), as highlighted in Fig. 5.9. The peak VMI photoemission direction is correlated with
one of these crevices in approximately 40% of the nanoshells studied. This 40% correlation isentirely reasonable considering that approximately half of the nanoshells would be expected
to have hot spots in the lower hemisphere (not visible in the SEM images), whereas some will
have crevices on the sides of the nanoshells that are less evident in the electron beam imaging. It is thus likely that the observed crevices (or sub-features therein) represent a common
geometry for a highly photoemissive hot spot.[67] Previous studies have indeed highlighted
the nanocrevice geometry as a probable candidate responsible for the extra strong field enhancements observed with nanoshells and rough metal surfaces.[67, 62, 54] It is worth notingthat the crevice locations on the nanoshell in Fig. 5.8 are not evidently aligned with thephotoemission directionality. This falls into the category of nanoshells that do not display

111
clear directional correlations, possibly due to crevices hidden in the lower hemisphere. It isalso possible that the photoemission direction is not perfectly aligned with a crevice evident
in SEM/TEM due to a more complex hot spot geometry. Toward this end, more controlled
studies of phtooemission from well-defined nanostar tip hot spots are explored next.
Different nanometer-scale features could lead to strong hot spots and photoemission
enhancements even within the constraints imposed by these correlated SEM/VMI studies.
To help elucidate these features further, FEM simulations have been utilized to explore theelectric near-field enhancements for a given nanocrevice defect geometry embedded into theside of a nanoshell. Sample surface field enhancements are calculated in COMSOL Multiphysics 5.3 and presented in Figs. 5.10a and 5.10c, where it can be seen that the crevice
becomes a strongly enhanced hot spot when the laser is polarized orthogonal to the crevice
radial vector (Fig. 5.10a), whereas the hot spot exhibits negligible field enhancement forparallel polarization. If we consider a photoemission model that assumes a local photoemissivity dependent on surface E-field enhancement to the order 2n, then a 10-fold E-field hot
spot enhancement for this sample geometry would correspond to a peak 3PPE enhancement(per unit surface area) of ∼ 106 . Using this model as a simple starting point, we integrate thecalculated E-field (raised to the appropriate n = 6 power for 3PPE) over the entire nanoshellsurface. This already predicts an overall 200-fold enhancement of hot spot photoemission
for perpendicular (θmax ) vs. parallel (θmin ) polarization. Furthermore, the FEM near-field
distributions for orthogonal laser polarization in Fig. 5.10a suggest a very simple physicalmechanism for the field enhancements: the crevice behaves like a nanogap or a nanoscalecapacitor with the strongest enhancement occurring at the parallel, closely spaced walls near
the crevice apex. To avoid unphysically small feature sizes in the model that could lead to
singularities in the field enhancements, the smallest radius of curvature in these simulations
is limited to the radius of a single gold atom (∼1.7 Å). Variation in the crevice parameters(e.g. depth and curvature) changes the exact values of field enhancement, but no essential
features of the hot spot behavior. Although such predictions will depend on the precise

112

Figure 5.9: Example SEM and VMI images on single nanoshells that show either (left panel)a clear correlation or (right panel) no correlation between the directional photoemission anda nanoshell surface feature.

113
characterization of the nanocrevice geometry, these model FEM results already rationalize
the many orders of magnitude dynamic range in photoemissivity enhancements observed
experimentally (see Fig. 5.6b).
To model the hot spot photoelectron momentum distributions for the nanocrevice hot
spots without knowledge of the precise crevice geometry, emitted electron trajectories (i.e.
bouncing around in the crevice), or surface vs. volume photoexcitation ratio, a simple radial
emission model is adopted. The photoelectron fluxes from each surface area element are
taken to be proportional to the surface E-field enhancement raised to the 2n = 6 power
appropriate to 3PPE, with these enhancements determined via the previously discussed
FEM results and mapped as a fine, uniform mesh over the entire nanoshell surface. The
momentum distribution from each surface area element is based on a ballistic three-stepmodel,[17] as discussed in Chapter 4Briefly summarized, a Fermi-Dirac speed distribution isassumed inside the nanoshell, with the emitted photoelectron distribution scaled by a p cos(θ)
Jacobian transformation from internal to external coordinates, whereby velocity components
are treated by the usual conservation of energy (i.e. work function) and parallel momentum atthe surface potential barrier. The emission from each nanoshell surface area element is taken
to be centered relative to the radial vector (i.e. outward from the center of the nanoshell),which invokes the simple intuitive idea that once the complicated near-field collision dynamics
within the defect walls have played out, the photoelectrons will be ejected approximately
radially outward from the hot spot region. Such near-field dynamics include diffusion in
the gold before emission and the re-absorption or multiple scattering events that may occur
for many photoelectron trajectories due to concave crevice geometries. The resulting pz integrated (px , py ) momentum maps predicted from this simple physical model are shownin Figs. 5.10b and 5.10d for laser polarization orthogonal (θ ≈ θmax ) and parallel (θ ≈θmin ) to the nanocrevice axis, respectively. The results for orthogonal polarization in Fig.
5.10a reproduce the essential qualitative behavior observed in the experimental distributions,
namely, strong directional photoemission (i) orthogonal to the laser polarization axis and (ii)

114

Figure 5.10: Finite-element simulations (a, c) of the near electric field distribution andcorresponding model velocity map images (b, d) for the calculated electron flux arounda nanoshell with a single nanocrevice are shown for orthogonal (a, b) and parallel (c, d)polarization of the laser relative to the hot spot radial direction. See text for model details.

115
radially away from the crevice geometry. By contrast, for parallel polarization at θmin , thecrevice exhibits E fields unenhanced by any plasmonic effects, resulting in a much weaker(200-fold less) photoemission characterized by a dipolar SPR near-field distribution andwith the peak emission aligned with the laser polarization axis. Interestingly, however, theexperimental photoelectron momentum maps at θ ≈ θmin often also have a tendency toward
orthogonal (but centro-synmmetric) emission (e.g. Fig. 5.5c). Understanding these effects
requires an investigation of the internal nanoshell field distributions and volume-mediatedphotoexcitation/emission mechanisms, to be discussed in Section 6.6.
In summary, transverse (px , py ) photoelectron momentum maps of single Au nanoshells
have been explored to reveal highly directional photoemission distributions in the weakfield MPPE regime. Combined evidence from momentum mapping, laser polarization studies, nanoshell photoemissivity statistics, and correlated SEM imaging suggests that small
crevices in the nanoshell surface play an important role, leading to directional emission andcorroborating previous work revealing the presence of nanoscale hot spots on Au nanoshellsurfaces.[67, 185, 62] For the great majority (90%) of the nanoshells, the photoemission direction is orthogonal to the peak laser polarization axis, indicating that the hot spots are dueto the nanocrevice-type roughness seen under scanning electron microscopy and simulated
via finite-element analysis. Polarization control over the near-field electron photoemission
behavior has been demonstrated for a single nanoshell with dual hot spots, providing a proof
of concept for the engineering of plasmonic nanostructures with selective directional controlof photoemission via laser polarization, which can be rotated on ultrafast time scales.
5.3

Ultrafast Nanostar Photocathodes
With nanostars and other multi-resonant particles, important opportunities for spa-

tiotemporal photocurrent control emerge via frequency- and polarization-selective excitationof different plasmonic hot spots, which are often spatially separated and oriented in different
directions.[77, 194, 68, 174, 146] Electric near-field hot spots have been extensively investi-

116
gated in nanoplasmonic systems, with photoemission electron microscopy (PEEM) studies
establishing the correlation between photoemission and plasmonic hot spots with ∼20 nm
spatial resolution.[77, 8] Furthermore, these techniques have been combined with opticalpulse shaping[21] to achieve coherent control over spatial photoemission distributions on
femtosecond timescales.[2] However, direct observation of the corresponding photoelectron
momentum-space distributions has remained a challenge, requiring angle-resolved photoelectron mapping from single, resonantly-excited nanoparticles. Such capabilities have only
appeared recently[145, 146, 106, 107] as a comprehensive understanding of photocurrent distributions is becoming crucial for the design and implementation of nanocathodes in nascentultrafast nanoelectronics and electron imaging applications. Full photoelectron momentum
and energy characterization has been achieved by Lehr et al. on individual gold nanorods
and bow-tie nanoantennas using time-of-flight momentum PEEM,[106, 107] which serves toclarify nanoplasmonic angular photoemission distributions and phenomena such as the transition into the optical field emission regime. Angular photoelectron mapping and steering
have also been demonstrated for gold[136] and tungsten[204, 11] nanotips, primarily in thefield emission regime. Despite these advances, many important aspects of the nanoplasmonic photoelectron emission mechanism and opportunities for angular control remain tobe elucidated, particularly in the multiphoton regime.
Here, optically-controlled directional multiphoton photoemission from single gold nanostars is demonstrated using 2D photoelectron velocity mapping and 3D reconstruction for
detailed characterization of the angular and energy distributions. These investigations begin
with an examination of the plasmonic properties and directional photoemission from single
nanostar tips resonantly excited using a pulsed femtosecond laser. Individual tips behave
as locally-bright, point-like electron sources with a high degree of spatial coherence. The
selective excitation of different tips is then demonstrated on a single nanostar via optical frequency and polarization control, yielding wide angular switching/steering of the tip-aligned
photoemission currents. Correlated scanning electron microscopy (SEM) and 3D photoemis-

117sion modeling clarify the effects of nanostar tip geometry and plasmonic field enhancements.
As the overall directional effects are not contingent on laser intensity, the present method
for optically controlling photocurrents can be extended from the weak-field (multiphoton)regime into the strong-field (optical field emission) regime. However, weak-field multiphoton
photoemission (MPPE) processes are emphasized here due to the minimal nanostar heating,sub-single-electron femtosecond pulses (∼ 10−5 photoelectrons from each pulse on average)that preclude space-charge effects, and < 1 eV photoelectron kinetic energy spreads for hightemporal coherence. Photocurrent control timescales approaching the attosecond range may
be achievable, fundamentally limited only by the nonlinear photoemission decay associatedwith plasmon dephasing.

5.3.1

Nanostar Plasmon Resonances(The following synthetic procedures were developed by the Teri W. Odom Group andexecuted by Priscilla Choo at Northwestern University.)
Nanostars are synthesized via a seedless growth method, in which (4-(2-hydroxyethyl)1-piperazineethanesulfonic acid) (HEPES) buffer functions both as a nucleation and a shapedirecting agent. A 1 M stock HEPES solution is made by dissolving the buffer salt in Millipore water (18.2 MΩ·cm). The pH of the HEPES solution is measured and adjusted to7.38 using concentrated NaOH solution. Nanostars are synthesized by adding 0.2 mM (final concentration) gold (III) chloride trihydrate (HAuCl4 ) to 110 mM HEPES buffer andvortexing for one minute after HAuCl4 addition. The growth solution is left in dark for 24hours to allow for growth and stabilization. To improve size homogeneity and to achieve thedesired resonances within the tuning range of Ti:sapphire laser, density gradient centrifugation is carried out to sort the nanostars. A continuous linear sucrose gradient is created byusing a custom mixing program of the gradient maker (BioComp Instruments) to mix 50%
and 60% weight-to-volume sucrose solutions at an angle. At this point, 500 µL of 8–10 nM
concentrated nanostar solutions are layered on the top of the prepared gradient and cen-

118
trifuged at 4400 g for 4 hours. The samples are fractionated at intervals of 4 mm from themeniscus (BioComp Instruments) and centrifuged at 15000 rpm for 25 minutes to remove
excess sucrose. Each fraction is then dialyzed in Thermo Fisher 20K Slide-A-Lyzer Dialysis
Cassettes for 24 hours to remove remaining sucrose from the solution. Transmission electron
microscopy images are taken of each fraction to choose the population with desired size andaspect ratio of the branches. Fraction 7 out of 23 is selected for the present studies.
The gold nanostars are synthesized with sharp 3.4 ± 0.4 nm radii tips and the sorting
selects for simple geometries with an average number of three tips lying in the surface plane(Fig. 5.12). Electron micrographs for a selection of representative nanostars are shownin Fig. 5.11a. Plasmonic properties are readily characterized using normal-incidence laser
light for these primarily in-plane geometries, with the nanostars supporting localized surface
plasmon resonances across the near-infrared tuning range of the Ti:sapphire oscillator (700–1000 nm). The resonance properties are characterized for three sample nanostars via spectral(Fig. 5.11c) and polarization dependences (Fig. 5.11d), with the peak polarization indicatedin the correlated SEM insets aligned along a particular tip for each nanostar. In each case, then-photon photoemission (nPPE) rate varies as ΓnPPE ∝ cos2n (θ − θtip ) as the polarization
angle θ is rotated away from the resonant tip, consistent with the field projection onto asingle, well-defined hot spot axis. The essential role of the plasmon resonance in driving thesebehaviors has been established in previous photoemission studies correlated with dark fieldmicroscopy for gold nanorods,[64] confirming the direct relation between surface plasmon(Mie) resonances in linear scattering spectra and the peaks observed in MPPE spectra.
Due to the E 2n ∝ I n electric near-field sensitivity of the n-photon process, nanostars withmultiple similar tips may have only one dominant hot spot (e.g. Star 2). Note, for instance,that a mere 10% difference in field enhancement results in a factor of two difference in the
4PPE rate.
Electrons must absorb multiple visible or near-infrared photons (∼1.5 eV) to overcome
typical metal work functions (∼5 eV) and escape into the vacuum. The total MPPE rate is119

Figure 5.11: Single-nanostar plasmon resonance excitation and photoelectron velocity mapping. (a) Transmission electron micrographs of representative few-arm nanostars (50 nm
scale bar) with insets displaying individual tips (5 nm scale bars). (b) Experimental configuration, in which photoelectrons with initial transverse (vx , vy ) velocity are linearly mapped
onto (x, y) position on the MCP detector. (c) Three example nanostars, each with a single
dominant plasmon resonance mode excited via polarization aligned along the arm axes, as
indicated by the arrows (50 nm scale bars). (d) Polarization-dependent photoemission rate
at peak resonance wavelengths for each of the three stars, characterizing the peak polarization settings. Data is fit to cos2n (θ − θtip ) for multiphoton process order n. (e) Summary ofmultiphoton process orders for plasmon resonance modes on different nanostars, determined
via linear intensity-dependence fits on log-log plots (power-law behavior) as demonstrated
for the three example stars. The resulting process order data is fit to a sigmoidal curvefrom n = 3.01(3) to n = 3.99(4), demonstrating the clear transition from the 3-photon to
the 4-photon regime with decreasing photon energy. Intermediate values between 3 and 4
are effective process orders representing a weighted average of 3-photon and 4-photon contributions. All reported parenthetical values are standard errors of the variance-weighted
nonlinear least squares fits.

120

Figure 5.12: Nanostar statistical characterization via electron microscopy. (a) Example
transmission electron microscopy (TEM) and scanning electron microscopy (SEM) imagesof stars with different numbers of arms, Narms . All SEM micrographs are collected following
exposure to laser intensities of ∼0.1 GW cm−2 or greater in photoemission studies. The lackof observable morphological differences between the unexposed nanostars in TEM images
and the laser-exposed nanostars in SEM images (those with no Pt coating, specifically)
provides strong evidence that no appreciable particle melting occurs during photoemission
studies. For most studies, a 3 nm Pt coating was applied to the nanostars to improve SEM
contrast and thereby clarify the nanostar geometries. All scale bars are 25 nm. (b) Statisticalcharacterization of nanostar dimensions in TEM and SEM (3 nm Pt coating) images. An
approximate 3 nm broadening is evident in all features due to the Pt coating.

121
described by a sum over process orders,ΓMPPE =

X

=

X

ΓnPPE

n

(5.1)
σn (ω, θ)I0n ,n

in which I0 is the input laser intensity and σn (ω, θ) is the nPPE cross-section as a functionof laser frequency and polarization. The plasmonic field enhancement effect is therefore
included within σn (ω, θ). Multiphoton process orders are determined for a random selectionof resonantly-excited nanostars by measuring photoemission rate as a function of peak laser
pulse intensity. The process order summary in Fig. 5.11e reveals a sigmoidal transition from
3PPE to 4PPE centered around 830 nm (1.5 eV), indicating a nanostar tip work functionof φ ≈ 3~ω830 = 4.5 eV at which 3-photon-excited electrons from the Fermi level begin to
overcome the surface potential barrier. Intensity-dependence plots and power-law fits areshown for the three sample nanostars, with the non-integer Star 2 process order (n = 3.6±0.1)
representing weighted contributions from both 3PPE and 4PPE processes. From Eq. 5.1,
the log-log slope isP
σn (ω, θ)I0n n
dlog10 (ΓMPPE )= Pnndlog10 (I0 )n σn (ω, θ)I0
X
wn n,
=

(5.2)

n

which is the weighted average over process orders with weight factors wn = σn (ω, θ) I0n
P/ n σn (ω, θ) I0n representing the relative contributions of each process order, such thatP
n wn = 1. With only 3PPE and 4PPE processes contributing, Eq. 5.2 yields an effective
process order of 3.5 when σ3 (ω, θ) I03 = σ4 (ω, θ) I04 , as is the case at 830 nm in Fig. 5.11e.
It should be noted that peak photocurrents of 108 s−1 during the peak laser pulse intensity
correspond to an average of only 10−5 photoelectrons from each pulse when multiplied by thelaser pulse duration (∼ 10−13 s). With a laser repetition rate of 75 MHz, photoemission rates
greater than 100 s−1 are thus achieved with negligible probability of two electron emission
events occurring within a single laser pulse, thereby precluding any space-charge effects.

122
These measurements verify that all signal is predominantly due to MPPE rather than
optical field emission or thermionic emission for the range of intensities utilized in thesepstudies. For further verification, the Keldysh parameter, γ = φ/2Up , is again used tocharacterize the transition from weak- to strong-field emission,[91] where φ is the work function and Up = e2 E 2 / (4me ω 2 ) is the ponderomotive energy. For peak input pulse intensities
I0 < 3 × 108 W cm−2 and simulated field enhancements |E/E0 | < 100 described below,
Keldysh parameters γ > 3 fall within the MPPE regime and corroborate the measured
intensity dependences.

5.3.2

Single-Tip Photoemission Properties

Selecting Star 1 (Fig. 5.11c and Fig. 5.13a) as a representative single-tip emitter,the characteristic photoelectron velocity distributions were measured and modeled from theresonantly-excited nanostar tip. First, finite element simulations were performed using thenanostar geometry measured via correlated SEM for insight into the plasmonic field enhancements. Nanostar geometries are modeled in SolidWorks 2017 with a 10 nm diameter core andcylindrically-symmetric arms modeled using dimensions (lengths, widths, and angles) fromcorrelated SEM micrographs, minus the 3 nm Pt coating layer applied prior to SEM imaging
for improved contrast (Fig. 5.12). Out-of-plane arms are modeled with shapes/widths determined via TEM statistics (Fig. 5.12) and shorter lengths of ∼25 nm. The tips are modeledwith radii of 3.4 nm based on TEM statistical characterization. A 1 nm HEPES ligand layer
surrounds the nanostar, with the refractive index set to 1.5 based on typical values for similarorganic molecules in the visible range. A small extinction coefficient klig = 0.25 is included
for the ligand layer to account for a consistent red-shift in the experimental versus simulated
absorption spectra. This is not expected for the HEPES itself, but is instead attributed toamorphous carbon buildup that commonly occurs in nanotip systems in the regions of strong
optical field enhancement.[183] Here the carbon buildup may be attributed to photon- or hot
electron-mediated cracking and reorganization of the organic ligands. Consistent application

123
of this small extinction coefficient uniformly improves spectral agreement for all calculations,
possibly accounting for other damping effects not considered in the modeling. The complex
refractive index of the 10 nm ITO film is determined via ellipsometry and the complex refractive index of gold is taken from the literature.[86] Further details of the finite element
modeling are shown in Fig. 5.15 and discussed in Section 3.2. The simulated surface-normal
field distribution in Fig. 5.13b highlights all of the tips in the linear case, with a particularly
strong peak enhancement of |E⊥ /E0 | ≈ 50 at the resonantly-excited tip. This tip becomes
clearly dominant when the field enhancement is raised to the 8th power for the relevant 4PPE
process, with the nonlinear enhancement strongly confined to its apex. Photoemission distributions measured for this hemispherical hot spot geometry may also guide expectations
for convex hot spots in other systems, including etched nanotip photocathodes.[126, 192]
The measured 2D (vz -projected) photoelectron velocity map in Fig. 5.13c shows clear
directionality along the resonant tip axis, as would be predicted for electrons emitted outward
from the field-enhanced surface region. The 3D velocity distribution (Fig. 5.13e) has beenreconstructed using the basis set expansion (BASEX) algorithm,[42] which relies on theapproximation of cylindrical symmetry around the resonant x-axis tip to compensate for
information lost in the vz projection (Section 3.6.1). Tip-aligned directional emission is also
observed for Stars 2 and 3 (Fig. 5.14), which are resonantly excited in the transition regime
and the 3PPE regime, respectively. While both 3PPE and 4PPE processes lead to similarly
tip-aligned photoemission distributions, photon energies just above the 3PPE onset may be
preferred to reduce the kinetic energy spread (Fig. 5.14) for optimal temporal coherence ofthe photoelectron waveform.[3]Photoemission generally proceeds by a combination of volume and surface mechanisms
for momentum conservation[189] (Section 3.5). The directional distributions observed here
indicate the dominant role of surface scattering, in which case the multiphoton excitation
rate depends on the surface-normal electric field,[114, 116, 189] E⊥2n . By contrast, volume
excitation mechanisms depend on internal fields as E 2n (Fig. 5.15) and produce hot electrons

124

Figure 5.13: Characterization of single-tip multiphoton photoemission. (a) Scanning electron micrograph of a representative single-tip emitter (Star 1). The tips appear broader
than in transmission electron micrographs and nanostar statistics due to a 3 nm Pt film
deposited prior to electron imaging to improve sample conductivity and image quality. Thisadded thickness is therefore subtracted from the measured nanostar dimensions for modeling and simulation. Scale bar: 50 nm. (b) Modeled nanostar geometry with calculated
linear and 8th-order (4-photon) surface-normal electric field enhancements. All measurements and calculations are performed on-resonance at 900 nm and 0◦ polarization. The
ITO-coated substrate and HEPES ligands (not shown) are included in the field calculations.
(c) Experimental and (d) theoretical velocity map images of the vz -projected photoelectron
distribution. (e) Reconstructed experimental and (f) theoretical 3D velocity distributions,
showing iso-probability surfaces at 75%, 50%, and 25% maximum along with the overall vz
projections. (g) Angular distributions and (h) electron kinetic energy distributions determined from xy slices of the 3D experimental and theoretical distributions.

125

Figure 5.14: Single-tip directional velocity distributions. (a) Velocity maps of the threesample stars in the 4PPE regime (Star 1), transition regime (Star 2), and the 3PPE regime(Star 3). The emission is aligned with the resonant tip in each case. All scale bars are 50 nm.
(b) Corresponding electron kinetic energy distributions determined from 3D reconstructions,demonstrating a narrowing in the distribution near the onset of the 3PPE regime (e.g. Star
2).

126
throughout the nanostar that would escape from various surfaces around the tips and body,leading to largely isotropic rather than directional velocity distributions. The present theoretical investigations are therefore restricted to surface-mediated MPPE, which is further
supported by the tip-localized photoemission observed in nanostar PEEM studies.[77]Calculations based on the coherent surface MPPE theory developed by Yalunin etal.[203] were carried out to determine photoemission rates and velocity distributions fromeach nanostar surface area element, using the full SEM-correlated nanostar geometry andsimulated plasmonic fields shown in Fig. 5.13b, with a fine surface mesh shown in Fig.
5.15. To calculate the full 3D photoelectron velocity distribution for a given nanostar,
the photoemission contributions from each surface area element are calculated using thesurface field enhancements determined via finite element simulation. The photoemission
distribution is calculated with respect to each surface normal (p̂z,rel ) and rotated into theglobal frame (p̂z ) via Cartesian rotation matrices. Only a single rotation about axis p̂z ×
p̂z,rel is required for azimuthally-isotropic per-area emission distributions. A sample uniform
surface mesh and nonlinear surface-normal field enhancement distribution is shown in Fig.
5.15, along with additional details of the finite element domain. It should be noted thatgeometries with concave surface regions (including nanostars) may allow for the intersectionof emitted electrons with other surfaces of the emitter geometry. These effects are notpresently accounted for, although they should be negligible for the tip-like emission describedin the present work.
Empirical values are utilized for all surface MPPE model inputs, with the exceptionof the pulse-averaged Fermi-Dirac electron temperature, which is calculated at 2500 K via
a two-temperature model, shown in Fig. 5.16, with a linear nanostar absorption crosssection of 104 nm2 determined via the finite element simulations. The emission process ateach nanostar surface area element consists of a heated Fermi gas impinging on the surface
barrier and becoming excited via coherent multiphoton absorption into external Volkov (fielddressed) states. The outgoing photocurrent includes direct and surface-rescattered quantum

127

Figure 5.15: Nanostar finite element simulations. (a) Uniform nanostar surface mesh andcross-section demonstrating the typical domain and meshing. (b) Volume and surface fieldenhancements calculated for the resonantly-excited nanostar (900 nm, 0◦ ). The 8th-orderfield enhancement for the 4PPE process leads to a highly-localized surface field enhancement at the tip (leading to tip-aligned directional emission), but a more spread-out volume
field enhancement that would produce more isotropic emission if volume-mediated MPPE
processes were dominant. (c) Domain slices showing the field enhancement with a different
color map for additional clarity.

128
amplitudes. Optical field penetration into the gold is neglected and all excitation therefore
occurs from the external evanescent component of the initial free electron wavefunctions,which accounts for momentum non-conservation at the surface barrier. Due to the shortdecay length of the external electron wavefunction (∼2 Å) and the small quiver amplitudeof the emitted electrons (∼1.5 Å) relative to the plasmonic field decay length (∼1.5 nm),the external field is approximated to be uniform in calculating the emission amplitude. The
evanescent plasmonic field then ponderomotively accelerates the emitted electrons outward
from the surface, uniformly shifting the kinetic energy distribution by Up . This is simply
accounted for in the modeling via the coordinate transformation p2z /2me → p2z /2me − Up .
The ponderomotive energy Up = E 2 e2 / (4me ω 2 ) = I0 |E/E0 |2 e2 / (2cε0 me ω 2 ) for the present
input intensity (I0 = 2 × 108 W cm−2 ) and calculated tip field enhancement (|E/E0 | = 50) is
only 0.03 eV. Though only a minor contribution in the present studies, the ponderomotiveenergy scales linearly with the input intensity and quadratically with the field enhancement
and thus may become important in other similar systems.
Theoretical 2D (Fig. 5.13d) and 3D (Fig. 5.13f) distributions reiterate and confirm
the tip-aligned directionality, with good agreement in the photoelectron angular (Fig. 5.13g)
and kinetic energy (Fig. 5.13h) distributions. The slight downward directionality in thetheoretical 3D distribution is due to the ITO image charge field, which skews the tip fieldenhancement toward the substrate (Fig. 5.17). However, the otherwise strong agreement
between experimental and theoretical distributions indicates that such substrate symmetrybreaking effects are minor. With regard to substrate effects, it is worth mentioning thepossibility of gap resonances occurring in nanoscale junctions between nanoparticles andconducting substrates separated by an organic molecular layer such as the ∼1 nm HEPES
ligand layer on the nanostars, as observed previously with Au nanospheres separated froman Au film substrate by an organic spacer layer.[166] While no direct evidence of a gap
resonance effect is observed in the present experiments nor in the finite element simulations(Fig. 5.15), due primarily to the in-plane resonance excitation with in-plane polarized light,

129

Figure 5.16: Representative nanostar electron sea and lattice heating. (a) Electron temperature calculated via the two-temperature model with the parameters utilized for Star 1
measurements and determined via simulations: peak input intensity 2 × 108 W/cm−2 , 200
fs pulse duration, nanostar volume of 104 nm3 , and a linear absorption cross-section of 104
nm2 . The effective temperature measured in MPPE experiments can be expected to beapproximately the temperature at the pulse peak, i.e. ∼2500 K. Due to similar excitation
conditions, cross-sections, and volumes for the nanostars studied, this temperature is utilized
in all photoemission calculations described in the main text. (b) Evolution of electron andlattice temperatures calculated via the two-temperature model. Peak lattice temperaturesless than 500 K are too low to induce nanostar melting.

130such effects can be difficult to accurately account for in the simulations as they depend
sensitively on the details of the nanostar-substrate interface, which is not directly observe.
Although the near-field contributions to photoemission dynamics and distributions
have been investigated in detail in order to gain general insights for arbitrary emitter geometries, the nanostar tips studied here are among the sharpest nanoplasmonic geometries
available and for most purposes can be treated as point-like electron sources. Electrons may
therefore be emitted into a broad angular distribution (Fig. 5.13g) but still retain a highdegree of spatial coherence, determined by the small source radius (3.4 nm) and photoelectron angular uncertainty (∼70◦ ). The transverse spatial coherence is often characterized
via the normalized root-mean-square beam emittance, a conserved phase space quantity inaberration-free systems defined by εrms = βγL σr σθ at the beam waist,[158] in which β = v/c
for average photoelectron velocity v, γL is the Lorentz factor, σr is the transverse spatial
uncertainty, and σθ is the angular uncertainty. Since a beam waist is located at the source,
the emittance is approximated via the tip radius (σr = 3.4 nm), angular emission uncertainty (σθ = 70◦ = 1220 mrad—Fig. 5.13g), and average velocity (v/c = 0.0014), as 5.9
nm·mrad. This serves as an upper limit, as the effective source size is determined by tracing
electron trajectories back to the center of the hemispherical tip.[43] Even as an upper limit,
this nanostar tip MPPE beam emittance is approaching values achieved on pulsed nanotip
sources (around 1.7 nm·mrad) in the linear photoemission regime,[49] which, in turn, areonly an order of magnitude higher than the uncertainty limit of εrms = ~/ (2me c) = 0.19
nm·mrad.
Single nanostar tips also remain stable emission sources in the present intensity range
during hours of measurements, including at least half an hour of continuous exposure whilecollecting velocity maps, as demonstrated in Fig. 5.18. Only modest lattice heating of∆T ≈ 200 K is calculated during a laser pulse (Figs. 5.16 and 5.19) with 13 ns between
pulses sufficient for equilibration back to room temperature. The high degree of stability
and spatial coherence enables ultrafast point-projection[127, 126, 191] and diffractive[66,131Figure 5.17: Experimental and reconstructed velocity distributions. Comparison between
experimental and reconstructed photoelectron velocity projections for Star 1, along withslices through the reconstructed and theoretical 3D distributions. The reconstruction is ingood agreement with the experimental velocity map image. The theoretical calculations
are also in good agreement with the reconstructed/experimental distributions, aside from aslight skew toward the surface (−z direction) in the xy slice due to the induced ITO substrate
image charge oscillation.

132

Figure 5.18: Nanostar photoemission time traces. Average photoemission rate (as opposedto peak rate) as a function of time measured for six nanostar emitters. Each star is asingle-tip emitter with well-defined photoemission directionality, as has been demonstrated
for representative Stars 1–3. Each time trace therefore represents photoemission from asingle nanostar tip. Due to the nonlinear process (MPPE ∝ E 6 or E 8 ), small fluctuationsin the near-electric-field at the tip (±10%) readily lead to the observed signal fluctuations,although the cause of such near-field fluctuations is not currently known. The average laser
power is stable to < 2% during measurements.

133
127, 191] imaging of nearby nanoscale objects following possible electron beam manipulationsuch as acceleration or collimation via nanoengineered electron optics.[61] For higher opticalintensities, a variety of new physical behaviors emerge in the strong fields and gradients atpoint-like nanotips,[99] including the onset of tunneling emission and subsequent quiver or
sub-cycle dynamics.[72] Such effects are negligible in the present multiphoton photoemission
studies, but the theory readily extends into intermediate- and strong-field regimes[203] andthe influence of strongly-varying plasmonic fields on the photoelectron trajectories can be
included in the manner demonstrated by Dombi et al.[39] when necessary.
The temporal coherence is primarily limited by the photoelectron kinetic energy spread,leading to longitudinal dispersion that is most prominent immediately following emission(prior to acceleration in the electrostatic lens), when the average electron kinetic energy
is comparable to the spread in the energy distribution. A full width at half maximum
kinetic energy spread around 0.8 eV is observed for the characteristic nanostar tip MPPE
distribution measured in Fig. 5.13h. This is a substantial improvement over typical kinetic
energy spreads > 10 eV in the optical field emission regime[100, 39] and can be improved
further by carefully matching the n-photon energy to the work function.[3]Limits on the achievable photoemission currents from gold nanostars and other plasmonic nanoparticles are imposed either by space-charge effects or by particle melting athigh excitation pulse energies. As shown in Fig. 5.19, nanostar melting is expected to occur at photocurrents less than 1 electron/pulse, which precludes any space-charge effects.
These melting limits are not approached in the present studies, which are therefore far fromthe regime in which space-charge effects become important. Photocurrents exceeding 100
electrons emitted in a femtosecond pulse have, however, been demonstrated for patternedgold nanorods10, in which case space-charge limitations do become important. The peak
photocurrents reported in Fig. 5.19 are calculated using the surface MPPE theory. The
peak nanostar lattice temperatures (see Section 3.3.2) are calculated simply from the bulk
heat capacity of gold, a typical nanostar volume of 104 nm3 , and simulated linear absorption

134

Figure 5.19: Nanostar photoemissivity and limitations due to melting. (a) The photocurrent
is calculated using the surface photoemission theory as a function of pulse duration andinput pulse intensity, assuming 750 nm excitation (3PPE in weak-field regime), 4.5 eV work
function, average nanostar volume of 104 nm3 , linear absorption cross-section of 104 nm2 andtip field enhancement factor of 50 from simulations. The dashed line represents the upper
limit on pulse energy (intensity × duration) at which the onset of particle melting will occur
at or around the melting temperature of bulk gold (1337 K). (b) The corresponding maximum
photocurrent is plotted as a function of pulse duration for different possible nanostar melting
temperatures, as particle melting typically occurs at lower temperatures due to the highfraction of more weakly-bound surface atoms.

135cross-section of 104 nm2 . The bulk gold melting temperature (1337 K) serves as an upper
limit on the nanostar melting temperature, although nanostar melting is likely to occur at
lower temperatures due to the high nanoparticle surface-to-volume ratio and more weaklybound surface atoms. It is evident that higher intensities can be utilized with shorter pulse
durations due to the trade-off between linear absorption and third-order photoemission crosssections, but the effective photoemission order and the maximum achievable photocurrent
begin to level off at shorter pulse durations as the Keldysh parameter drops below unity andinto the optical field emission regime.

5.3.3

Polarization- and Frequency-Controlled Directional Photoemission

Building on previous investigations of selective nanostar tip excitation,[77] the excitation of in-plane tips with in-plane polarization control in the present studies provides aparticularly clear mapping between optical parameters and tip hot spots. While the presenceof many tips and the effect of near-field tip-tip coupling[68] can lead to complicated opticalparameter mappings in some cases, the simple, typical nanostar behaviors are emphasized
here and selective tip excitation is demonstrated by independently tuning frequency andpolarization. Multiple tips are involved in both plasmon resonance modes for the four-tip
nanostar in Fig. 5.20a, but simulations in Fig. 5.20b reveal that only one tip hot spot isdominant for each mode. Spectra and polarization plots show two distinct plasmon peaks
at nearly-orthogonal peak polarization angles, with the photoemission rate at either peakshowing minimal contributions from the other. Entirely frequency-controlled tip selectivity
can thus be achieved for an isotropic polarization state (circular or unpolarized) or for a linear polarization state oriented between the two resonance modes. The frequency sensitivity
depends on the spectral peak widths, relative amplitudes, and separation.
An intermediate laser frequency setting exists between the spectral peaks at which
both plasmon modes are equally excited at their respective linear polarization angles. This isdemonstrated by the four-lobed polarization dependence measured between the resonances at

136

Figure 5.20: Multi-tip excitation and selectivity. (a) Experimental slices through the opticalfrequency and linear polarization parameter space, with photoemission peaks at (795 nm,
90◦ ) and (860 nm, 15◦ ). At either spectral peak, the laser polarization dependence shows
minimal signature of the other resonance, while between resonances (835 nm) the four-lobed
behavior shows equal contributions from both resonance modes. The peak polarization axes
are indicated in the correlated SEM insets for each resonance, as determined via nonlinear
cosine fits shown in the polarization plots (50 nm scale bar). (b) Theoretical surface multiphoton photoemission rates for the correlated nanostar geometry. Aside from a small blue
shift, peaks at (785 nm, 90◦ ) and (830 nm, 15◦ ) are in good agreement with the experimental
results. All four tips are modeled with the same radius (3.4 nm), but photocurrent density
maps demonstrate single-tip excitations at the resonance conditions due to the specific plasmonic mode structure. Measurements and calculations are performed at 1 × 108 W/cm−2
peak input intensity.

137
835 nm in Fig. 5.20a and reiterated by the calculations in Fig. 5.20b for the correlated nanostar geometry. At the intermediate frequency, the linear polarization angle may thus be tuned
to select between the two resonance modes and corresponding tip hot spots, demonstrating
polarization-controlled selective tip excitation. The relative mode strength (i.e. relative
lobe amplitude in the polarization plots) can be continuously adjusted via frequency tuning.
Overall, the two-dimensional optical parameter space sampled in Fig. 5.20 is described by the
(n)

(n)

nPPE photoemission cross-section, σn (ω, θ) = A1 (ω) cos2n (θ − θ1 )+A2 (ω) cos2n (θ − θ2 ),
(n)

(n)

in which A1 (ω) and A2 (ω) are the n-photon spectra of the two plasmon resonance modes.
In addition to the strong theoretical agreement with the observed spectral and polarization
behaviors (Fig. 5.20b), MPPE rates are calculated to within an order of magnitude ofthe experimental measurements by integrating the theoretical current density, JMPPE , overthe nanostar surface, accounting for both 3PPE and 4PPE contributions. Reserving otheraspects of the theory, this level of quantitative agreement corresponds to calculated fields
within 50% of the experimental values for a 3PPE process (∝ E 6 ), which is relatively strong
agreement considering the sensitivity of the field enhancements to the precise tip radius,
the charge distribution during plasmon oscillation (i.e. the overall nanostar geometry), andthe surface dielectric environment due to the HEPES surface ligands. Note that while thespectra of the nanostar in Fig. 5.20 happen to coincide with the 3PPE-to-4PPE cross-overaround 830 nm (Fig. 5.11e), the observed behaviors are a general feature of multi-resonancegeometries and are also demonstrated in the next section with a nanostar studied entirelyin the 3PPE regime.
The nanostar in Fig. 5.21a displays simple multi-resonance behavior, with a higherenergy (blue) dipolar resonance mode aligned with the shorter tip and a lower-energy (red)dipolar resonance mode aligned with the longer tip. These two tips are approximately orthogonal and can be individually addressed, as established in the polarization dependence at
different excitation frequencies (Fig. 5.21b). By instead maintaining circular polarization,
tip selectivity can be achieved with frequency tuning alone, as discussed with the previous

138
nanostar and further demonstrated here via MPPE simulations (Fig. 5.21c). Velocity distributions measured (Fig. 5.21d) and calculated (Fig. 5.21e) at each frequency are directionallyaligned with the corresponding resonant tip axis and photoemission directionality is rotatedby a full 90◦ upon frequency-controlled switching between tips. The average electron kinetic
energy decreases with excitation frequency by conservation of energy. When both tip modes
are excited at intermediate frequencies (e.g. Fig. 5.21c, 775 nm), the resulting velocity distribution is simply a linear combination of the individual tip angular distributions. Thus, thislinear combination allows for a continuous steering of the average emission angle, although
the total angular distribution is broadened by arising from two separate point-like sources.
Polarization-controlled directional emission is presented in Fig. 5.22 for the same
nanostar as in Fig. 5.21, but exclusively at the intermediate frequency setting at which bothtips are equally resonantly enhanced. Simulations demonstrate switching of photoemissive
regions between the two tip hot spots as the linear polarization is rotated out of alignment
with one mode and into alignment with the other (Fig. 5.22a). The photoemission directionality is rotated by 90◦ (Figs. 5.22b and 5.22c) in the same manner observed via frequency
control, due to the same underlying process of selective hot spot excitation. Intermediate
polarizations again result in a linear combination of the two tip angular distributions, withthe relative weights determined by the polarization dependence (Fig. 5.22a). Although fullpolarization contrast is demonstrated by complete alignment along either tip mode, the polarization plot indicates that much less angular tuning is necessary to strongly favor one
tip over the other due to the cos6 (θ − θtip ) polarization sensitivity for each plasmon mode.
Strong tip selectivity can be achieved with a 90:10 emission ratio by only ±10◦ tuning awayfrom the intermediate polarization, at which the emission ratio is 50:50. Therefore, as a benefit of the MPPE nonlinearity, photoemission directionality can be rotated by 90◦ with only
∼20◦ polarization rotation. This fine degree of tip discrimination also indicates possibilities
for utilizing higher tip densities for a more continuous control of angular photoemission.

139

Figure 5.21: Frequency-controlled directional photoemission. (a) Correlated nanostar scanning electron micrograph with the shorter and longer resonant tips at 50◦ and 315◦ , respectively (50 nm scale bar). (b) Experimental polarization dependence for frequency at the
short-tip resonance (725 nm, blue), between resonances (775 nm, orange), and at the long-tip
resonance (825 nm, red) with nonlinear cosine fits for the 3-photon process. (c) Calculated
multiphoton surface current distribution at different frequencies, showing the transition from
one tip hot spot to the other with circular polarization. (d) Experimental and (e), theoreticalvz -projected velocity maps on and between the two resonances using circular polarization.
Vectors indicate the peak directions determined by Gaussian fits around the peaks of theangular distributions. Peak photoemission angles range from 55◦ (50◦ ) at 725 nm to 325◦(315◦ ) at 825 nm for the experimental (theoretical) velocity distributions, i.e. a 90◦ photoemission rotation. The vector magnitude represents the speed (vF ) of photoelectrons excitedfrom the Fermi level, which decreases with decreasing photon energy by energy conservation,1
m v 2 = n~ω − φ, with tip work function φ = 4.5 eV and n = 3 in this excitation energy
2 e F
range (~ω = 1.5–1.7 eV). The Fermi velocity does not coincide with the apparent edge ofthe 825 nm (red) distribution due to the velocity dependence of the photoemission amplitude, which leads to deviations from a simple Fermi-Dirac distribution (particularly nearzero velocity) and shifts the effective edge outward relative to vF for near-threshold photon
energies.

140

Figure 5.22: Polarization-controlled directional photoemission. (a) Experimental nanostar
polarization dependence at 775 nm with nearly equal contributions from both nanostar
tip resonances. Tip hot spots are selected by rotating linear polarization while keeping
frequency constant, as demonstrated in the calculations on and between the resonances. (b)Experimental and (c) theoretical vz -projected velocity maps for the different polarizations atconstant frequency. Vectors indicate the peak directions determined by Gaussian fits aroundthe peaks of the angular distributions. Peak photoemission angles range from 55◦ (50◦ ) at
50◦ linear polarization aligned along the short tip to 310◦ (315◦ ) at 315◦ linear polarizationaligned along the long tip, for the experimental (theoretical) velocity distributions. The
vector magnitude represents the velocity of photoelectrons excited from the Fermi level (vF ),which remains constant for all distributions due to the fixed excitation frequency.

141
5.3.4

Discussion

Preliminary photoemission directional control capabilities have been demonstrated forgold nanoshells via polarization-sensitive defect hot spot excitation. With gold nanostars,
highly versatile photoemission switching/steering has been demonstrated by independently
tuning one of two optical degrees of freedom (frequency or linear polarization), leaving theother available for modifying the control characteristics. For example, polarization can beutilized for tip selection and corresponding manipulation of angular currents, while frequency
can be simultaneously utilized to control the electron kinetic energy distributions and relative tip photoemission enhancement. Such possibilities illustrate how techniques developed
for coherent control over nanoplasmonic hot spots using femtosecond optical amplitude, frequency (phase), and polarization shaping[2, 176] can be directly applied to photocurrent
degrees of freedom. The photoemission switching timescale is fundamentally limited by theplasmon dephasing (T2 ) time and by the optical cycle of the excitation laser field, which defines the fastest timescale on which polarization and frequency can be manipulated. Due tothe E 2n process nonlinearity, the nPPE current decays 2n-times faster than the plasmonic
field, which typically dephases in 10 fs or less.[64, 69] Thus, the 3PPE and 4PPE decay
times are comparable to the 1–3 fs optical cycles for visible and near-infrared frequencies.
This suggests that spatiotemporal control over hot spot excitation and directional current
generation may be achieved on timescales approaching the attosecond range, even in the
weak-field MPPE intensity regime.
Gold nanostars behave as prototypical nanoplasmonic cathodes, with the multi-tip geometries shown to provide direct maps between laser parameters and excitation of different
hot spots. Individual tip hot spots have been extensively characterized for sample nanostars
via polarization and spectral studies, correlated SEM imaging, and finite element simulations. Angle-resolved photoelectron velocity measurements demonstrate corresponding frequency and polarization control over photoemission current direction, with all experiments

142
corroborated by 3D surface-mediated photoemission calculations that can be carried out forarbitrary nanoplasmonic geometries. Although volume-mediated excitation processes mustalso be considered in general, the observed directionality and agreement between experimentand theory strongly underscores the dominant role of surface-mediated MPPE at the sharp
nanostar tips. The results presented here highlight opportunities for implementing designer
plasmonic nanoparticles and nanostructures as all-optical photocurrent control elements in avariety of applications, including femtosecond electron imaging and diffraction, polarizationsensitive photodetection, site-selective photocatalysis, and terahertz nanoelectronics.

Chapter 6
Volume vs. Surface Multiphoton Photoemission

The relatively low-energy visible resonances and extraordinary optical field concentration in nanoplasmonic systems has served to revitalize the century-old problem[186] of
distinguishing between (i) electron excitation throughout the volume of the material, followed by ballistic transport and escape, versus (ii) excitation and emission directly at thesurface (Section 1.4).[189] Understanding these mechanisms will unlock opportunities fornanoscale control over hot carriers in emerging plasmonic photocatalytic, photovoltaic, andnanocathode applications (see Section 1.3), among others.
At the heart of this issue is the negligible linear momenta of the incoming photons
compared with the outgoing electrons. Momentum conservation thus demands electron
scattering with a massive third body during photoexcitation and emission. Photoemission
via volume excitation is dominated by scattering with the periodic lattice potential whensuch a transition is energetically allowed, but visible plasmonic excitation is often below
the relevant interband threshold and instead requires scattering with phonons, defects, impurities, or other electrons.[114, 142] These mechanisms depend on the total electric field,|E|2n , for n-photon processes. By contrast, surface photoexcitation and emission pathways
arise due to the translational symmetry breaking at an interface and thus involve scattering with the surface potential barrier, including contributions from the electromagnetic field
variation, localized surface states, and the evanescent external decay of internally-delocalized
Bloch wavefunctions.[57] All of these mechanisms depend on the surface-normal electric field,

144|E⊥ |2n . For nanoscale systems with . 20 nm dimensions, intraband excitation mediated bygeometrical confinement can also become significant.[117, 24, 128] Although ambiguities canarise in categorizing surface vs. volume processes in some systems, the highly-localized
surface fields are quite distinct from the diffuse volume fields and corresponding excitation
mechanisms/distributions in most nanoplasmonic systems. Further details on the surface
vs. volume photoexcitation/emission paradigm, including excitation matrix elements andpossible coherent vs. incoherent multiphoton pathways, can be found in Section 1.4.
Given the strong and highly-spatially-varying electric field enhancements in nanoplasmonic systems, volume vs. surface photoexcitation will often lead to disparate spatial andangular photocurrent distributions, which can be harnessed in plasmonic hot carrier devices.
Hot carrier catalysts, for instance, already exhibit high reaction efficiencies and productspecificity compared with thermally-activated processes,[31, 6] as demonstrated via CO2
conversion[213] and H2 O splitting[59, 201] for solar fuel production. However, further enhancements in catalytic activity and device functionality can be achieved by controlling the
hot carrier spatial and momentum degrees of freedom to compliment anisotropic coatings[96,125, 201, 25] or even to introduce nanometer site selectivity.[32, 165] Similar opportunities exist in broadband photodetection[95, 22] and solar energy conversion.[30, 202] While internal
hot electron emission at metal-molecule[59] or metal-semiconductor[189, 125, 201] interfaces
is often classified as either “direct” excitation at the surface or “indirect” transfer following
volume excitation,[31, 6, 142, 202] these map directly onto the distinction between surface
and volume mechanisms in external (metal-vacuum) photoemission. A deeper understanding and control of volume vs. surface effects is therefore essential to optimizing hot carrier
device performance, regardless of the application or collection medium. The majority of thischapter has been taken from recent work on Au nanorods[148] and Au nanoshells.[147]

145
6.1

Gold Nanorods
The primary focus of this chapter is to distinguish volume vs. surface photoemis-

sion pathways in plasmonic nanoparticles by their dramatically different photoelectron momentum distributions. It will first be shown that resonant longitudinal excitation of gold
nanorods leads to transverse (orthogonal/side) MPPE distributions due to the dominanceof volume excitation mechanisms. A novel transition from volume (transverse/side) to surface (longitudinal/tip) MPPE will then be demonstrated, which occurs with red detuning of
the excitation laser as a result of the enhanced metallic screening of internal electric fields
at lower frequencies. Detailed modeling of the volume and surface photoemission distributions reproduces all of these effects and allows for the quantitative distinction between the
MPPE cross-sections. Most importantly, it is demonstrated that the relative surface vs.
volume MPPE depends primarily on plasmonic field enhancements, which can be simulated
via classical finite element, finite difference, or other methods. Although measurements are
performed in the 2-, 3-, and 4-photon regimes to overcome the ∼4.25 eV gold nanoparticle
work function with visible excitation frequencies, the analysis and conclusions are generalwith respect to process order and should therefore remain valid down to the linear regime
for 1-photon applications. Finally, these results allow for the introduction of general designprinciples for engineering volume and surface processes and thereby controlling hot electron
excitation and emission distributions in designer nanoplasmonic systems.

6.1.1

Synthesis(The following synthetic procedures were developed by the Catherine J. Murphy Groupand executed by Sean M. Meyer at the University of Illinois Urbana-Champaign.)
Nanospheres of 70 nm diameter are synthesized based on the method of Perrault etal..[141] A solution of 12 nm spherical gold seeds is prepared by quickly injecting 1 wt%
sodium citrate to a boiling aqueous solution of 0.5 mM HAuCl4 under vigorous stirring.

146
After 5 minutes, a ruby red color is seen, and the heat is turned off and the solution allowed
to cool naturally to room temperature on the hot plate. Without any purification, 9.6 mL ofwater is mixed with 100 µL of 1 wt% HAuCl4 in a 20 mL glass vial and kept under continuous
stirring at room temperature with a Teflon-coated stir bar. Quickly, 25 µL of 1 wt% sodium
citrate and 115 µL of seed solution were added followed by a rapid injection of 100 µL of
0.03 M hydroquinone. After 20 minutes of stirring, the stir bar is removed, and the particles
are centrifuged once at 1000 rcf for 15 minutes and dispersed into 1 mL water. This 1 mLof particle solution is quickly injected into 9 mL of 10 mM CTAB (cetyltrimethylammonium
bromide) and mixed gently overnight. The following morning, the particles are subjected to
two rounds of centrifugation at 1000 rcf for 15 minutes followed by redispersion in 5 mL of
1 mM CTAB.
Nanorods with aspect ratios (L/D) from 1.5–3 are synthesized using the seed-mediatedgrowth method of Liz-Marzan and coworkers.[58] Small nanorod seeds are prepared in highquality and used as the seeds to grow larger, monodisperse nanorods with the correct size andwidth. It is recommended, due to the length of the procedure, to refer to the original article
for a complete understanding of the synthesis. Briefly, a CTAB and 1-decanol mixture ismade and used to prepare small spherical seeds, then carefully in another binary surfactant
solution they are introduced with more gold, silver, and acid to grow small nanorods for use
in the growth of larger particles. Then, another similar growth solution containing silver,
gold, hydrochloric acid, weak reducing agent, and seeds at a precise concentration is mixed
and allowed to grow overnight. For the L/D = 1.5 nanorods, 45 µL 0.01 M AgNO3 and55 µL of seeds are used with 500 µL 0.1 M hydroquinone in the absence of any additionalacid. For the L/D = 2.5 nanorods 200 µL of 0.01 M AgNO3 , 50 µL of 1 M HCl, 80 µL
if 0.1 M ascorbic acid, and 55 µL seeds were added. The nanorods are then subjected tocentrifugation two times at 2000 rcf for 20 minutes and dispersed in 1 mM CTAB after 3+hours of growth at 27 ◦ C.
Nanorods with L/D = 3–5 are prepared, with variations, from the method of Zubarev

147
et al.[190] The first step is to make small CTAB-capped gold seeds of 1–2 nm. This is achievedby adding 0.46 mL of a basic sodium borohydride solution (prepared by adding 46 mg of
sodium borohydride directly to 10 mL ice-cold 0.01 M sodium hydroxide and diluting thissolution 10-fold with 0.01 M sodium hydroxide) under vigorous stirring to a solution of 9.5
mL 0.1 M CTAB and 0.5 mL 0.01 M HAuCl4 . After allowing an hour for the excess sodium
borohydride to decompose, growth solutions are prepared. Growth solutions are preparedby mixing the following reagents as listed in order of 9.5 mL of 0.1 M CTAB, 0.5 mL of 0.01
M HAuCl4 , varying amounts of 0.1 M AgNO3 (10–40 µL), 0.5 mL of 0.1 M hydroquinone,
and a varying seed amount (90 µL seeds for L/D = 3–4.5 and 40 µL for larger aspect ratio).
The particles are kept at room temperature overnight and grown to completion. The nextday, each tube is then subjected to centrifugation two times at 2000 rcf for 20 minutes andthe nanorods are dispersed in 1 mM CTAB after 3+ hours of growth at 27 ◦ C.

6.1.2

Nanorod SPR Properties

Strong electric near-field enhancements are generated at the tips of gold nanorods
where conduction electrons collectively pile up during longitudinal localized surface plasmon
resonance (SPR) oscillations. At the same time, appreciable field enhancements are also
generated within the metal volume. High densities of hot carriers may therefore be excitedat nanorod tips via surface excitation mechanisms or inside the nanorod via volume excitation mechanisms. The corresponding photoemission pathways are illustrated in Fig. 6.1a,along with the scanning photoelectron imaging microscopy (SPIM) experimental configuration. Different photoemission angular distributions are expected for the two mechanisms,[9]depending upon the nanoparticle geometry and the electric near-field distribution of theexcited plasmon mode. This provides a direct means of identifying volume and surface photoemission contributions via single-particle, angle-resolved photoelectron velocity mapping.
Photoemission spectra are shown in Fig. 6.1b for nanorods of similar diameter, D =21 ± 4 nm (Fig. 6.2), but different lengths and thus aspect ratios (L/D), illustrating

148

Figure 6.1: Characterization of nanorod surface plasmon resonance photoemission properties. (a) Configuration of scanning photoelectron imaging microscopy experiments, illustrating volume and surface emission from an illuminated gold nanorod (with a quarter section
removed to show the volume excitation). (b) Multiphoton photoemission spectra measured
for nanorods of various aspect ratios, fit to nonlinear Lorentzian profiles. (c) Signal dependence on linear laser polarization in the azimuthal (xy) plane, fit to cos2n (θ − θrod and shownwith scanning electron micrographs of the correlated nanorods (L/D = 1.5, 2PPE; L/D = 4.5, 4PPE), where laser polarization θ = 0◦ is along the x axis.
(d) Photoelectron velocity map collected at the longitudinal resonance of the correlated
L/D = 3.2 nanorod in the inset, exhibiting transverse photoemission. (e) Summary ofphotoemission directionality for all nanorods of various aspect ratios and spatial orientations,with transverse peak photoemission observed in every case. Data colors (here and elsewhere)
are mapped to the corresponding wavelength. Scale bars: 20 nm.

149
the anticipated linear increase of SPR wavelength with nanorod aspect ratio[112, 168] for
L/D & 2 as summarized in Fig. 6.3. For the gold nanorod work function around 4.25
eV, electrons must absorb multiple photons to overcome the surface potential barrier, withnanorod resonances ranging from 950 nm (1.3 eV photon energy, n = 4 photons) at L/D =5 down to the spherical limit of 540 nm (2.3 eV photon energy, n = 2 photons) at L/D =1. Measurements of the photoemission dependence on linear laser polarization (angle θ)in the azimuthal plane (Fig. 6.1c) show clearly-defined longitudinal resonances along thelong nanorod axes, noticeably narrowing in the 4-photon regime (L/D ≈ 4.5) relative tothe 2-photon regime (L/D ≈ 1.5) due to the nPPE∝ E 2n cos2n (θ − θrod ) dependence of the
field projection along the nanorod axis. Pulse durations around 150 fs, pulse peak intensitiesof 108 W cm−2 , and calculated nanorod extinction cross-sections around 10−10 cm−2 leadto the excitation of nearly 104 plasmons/pulse, which is much larger than the 2–4 quantaoccasionally absorbed toward MPPE (one MPPE event every ∼ 105 pulses, with a 75 MHz
laser repetition rate), thus justifying a classical treatment of the plasmonic fields.
6.2

Volume-Mediated Nanorod MPPE
While longitudinal electron emission outward from the highly field-enhanced nanorod

tips has been observed in the strong-field tunneling[74, 152] and transitional regimes,[106] itis surprisingly observed here that weak-field MPPE is predominantly transverse (orthogonal)
to the resonantly-excited longitudinal nanorod axis, as demonstrated in Fig. 6.1d. In otherwords, electrons are evidently emitted from the sides rather than the tips of the nanorods.
This transverse photoemission is observed for every nanorod investigated (Fig. 6.1e), irrespective of aspect ratio (L/D = 1.5–5), surface ligands (Fig. 6.4), size (D = 10–40 nm,
Fig. 6.4), or corresponding size-dependent differences in faceting.[137] Electron thermalization effects during the pulse duration are accounted for via two-temperature modeling[69] asdiscussed in detail in Section 3.3.3. Intensity-dependence studies (to be discussed further)also demonstrate negligible thermionic or thermally-assisted emission effects. Furthermore,

150

Figure 6.2: Transmission electron micrographs and dimensional statistics of synthesized
CTAB-coated nanorod samples, with aspect ratios ranging from 1 (spheres) to 5. The
spheres are larger to ensure sufficient signal-to-background in photoemission measurements.
Corresponding UV-Vis spectra for aqueous dispersions show longitudinal surface plasmon
resonance peaks ranging from 550–980 nm, with transverse surface plasmon resonance peaks
at 510 nm.

Figure 6.3: Photoemission characteristics of the nanorod samples. (a) Surface plasmon resonances measured via multiphoton photoemission as a function of nanorod aspect ratio. The
black line is a linear least squares fit. (b) n-photon photoemission cross-sections determined
as a function of nanorod aspect ratio via intensity-dependence studies.

151

Figure 6.4: Velocity map images collected for CTAB-coated nanorods of 10 nm, 20 nm, 40 nm
diameters with similar aspect ratios and longitudinal surface plasmon resonance frequencies.
The rightmost panel shows the velocity map for a 20 nm diameter nanorod coated in HDT
ligands, which have a covalent Au-thiol bond rather than an ionic CTA-bromide bond.

measurements with dispersion-compensated 40–50 fs pulses yield the same transverse MPPE
distributions. Such observations provide a strong initial indication that the transverse photoemission arises due to volume-mediated hot electron MPPE for the nanorod geometry.
In such a mechanism, one expects hot electrons excited throughout the nanorod to escapeballistically from the cylindrical body with a predominantly transverse distribution and fromthe hemispherical tips with a nearly isotropic distribution. As a starting point, if uniform
excitation throughout the nanorod volume and a short inelastic mean free path (λinel  D)are assumed, the relative side versus tip contributions can be approximately estimated by
the ratio of corresponding surface areas, which works out to be Sside /Stip = L/D − 1. It istherefore expected that the photoemission distribution will become isotropic as L/D → 1(Sside  Stip ) or to become increasingly dominated by transverse contributions as L/D → ∞(Sside  Stip ).
To show definitively that the photoemitted electrons primarily originate within thevolume of the resonantly-excited nanorods, photoemission distributions are measured as afunction of nanorod aspect ratio. As expected, the 2D velocity maps in Fig. 6.5a demonstrate that the photoemission angular distributions become more isotropic with decreasing
aspect ratio and completely isotropic in the spherical limit. The radially-integrated angular152
distributions in Fig. 6.5c can be characterized by an angular contrast, AC, defined asAC =hk countsi − h⊥countsi
hk countsi + h⊥countsi(6.1)

where the brackets denote averaging (within ±2◦ ) over the two longitudinal (0◦ and 180◦ ) andtransverse (90◦ and 270◦ ) directions on the 2D velocity maps. This definition of the angularcontrast provides a model-independent metric of how transverse (AC → −1) or longitudinal(AC → +1) a given distribution is. Angular contrast values are summarized as a functionof aspect ratio in Fig. 6.5e, where AC clearly becomes more negative (transverse) as thenanorod aspect ratio increases, and goes to 0 in the isotropic spherical limit, as expected forthe volume photoemission mechanism. Note that the angular contrast and the photoemission
mechanisms described here are not to be confused with molecular photoionization and thecorresponding anisotropy parameter, β.[178]
A summary of nonlinear process order, n (where nPPE ∝ I0n ), from intensity-dependence
measurements performed on resonance for each nanorod studied is shown in Fig. 6.5d andelaborated in Fig. 6.6. The results show a clear sequential transition from 2PPE to 3PPE to
4PPE with increasing SPR wavelength and linearly-correlated increasing aspect ratio (Fig.
6.1b and Fig. 6.3). The well-defined integer process orders and transitions verify that thepresent studies are performed in the perturbative MPPE regime rather than the optical fieldemission or thermionic regimes (Section 3.4). Non-integer process orders in the transition
regions arise naturally in the power-law fits and reflect the weighted sum of the two contributing process orders.[144] It is also noted that no sudden changes in photoemission angular
distributions or corresponding angular contrast values are observed in the transition regions
between process orders. The physics is qualitatively the same at all nonlinear orders studied
herein (n = 2–4), simply with a different total excitation energy n~ω and nonlinear absorption cross-sections. It is thus anticipated that the present observations can be extrapolated
from the multiphoton regimes down to the linear emission regime for systems with lower hot
electron emission barriers, including metal-semiconductor and metal-molecule junctions.

153

Figure 6.5: Volume photoemission distributions as a function of aspect ratio. (a) Correlated
electron micrographs and velocity maps for a series of nanorods excited at their longitudinalsurface plasmon resonances (SPRs), down to the spherical limit. Nanospheres of larger
D = 70 nm were studied compared with nanorods (D = 20 nm) for sufficient signal levels,
but this is neither expected nor observed to affect their photoemission properties. Scalebars: 50 nm. (b) Velocity distributions for the same nanorods as in (a), modeled using
the ballistic (3-step) Monte Carlo theory. (c) Radially-integrated angular distributions fromthe velocity maps in (a) with transverse (⊥) and longitudinal (k) directions indicated and 0◦
along the x (i.e. vx ) polarization axis. (d) Process order summary of n-photon photoemission
measured via power-law intensity-dependence fits (Fig. 6.6—error bars are standard errorsof the fits) for all investigated nanorods for longitudinal SPR excitation, shown with overallsigmoidal fits. The SPR wavelength axis is linearly-mapped (except around L/D = 1) tothe aspect ratio (Fig. 6.3). (e) Photoemission angular contrast of all investigated nanorods
for longitudinal SPR excitation, becoming more negative (transverse) with increasing aspectratio and isotropic in the spherical limit. Ballistic Monte Carlo theory curves shown foruniform and nonuniform (finite-element-simulated) internal fields. The error bounds shownfor the simulated fields case assume an inelastic mean free path between 7 nm (top) and 5
nm (bottom), with the primary curve calculated at 6 nm.

154

Figure 6.6: Intensity-dependence process order summary with example single-nanorod data
and fits for n = 2–4. All measurements are performed at the nanorod longitudinal surface
plasmon resonance.

155
To understand the volume MPPE distributions in further detail, a Monte Carlo algorithm is implemented within a ballistic, three-step photoemission model.[17] While this is
described in Section 3.5.1, it is presented briefly here. In this model, electrons are first excited
to randomly-selected vector momenta (thus approximating isotropic phonon-mediated multiphoton excitation), with Fermi-Dirac weighting, from points selected randomly throughout
the nanorod volume. The volume element selection probability is weighted by the nonlinear
internal field enhancement (|E/E0 |2n ) determined via electrodynamic finite element simulations with the ligands and substrate accounted for. For supported nanorod and nanospheresimulations, a 1.5 nm CTAB (cetyltrimethylammonium bromide) ligand layer surrounding
the particles is included in the simulations, along with an additional 0.5 nm gap between theligand layer and the substrate to avoid extra-narrow domain regions. Overall, the rectangulardomain consists of the glass substrate with a 10 nm ITO film, the vacuum superstrate, thegold nanoparticle with ligand layer, and a perfectly-matched layer surrounding the domain
to prevent field reflection at the domain boundaries. The effect of the transparent conducting
substrate image charge oscillation is to enhance the field on the lower half of the nanorod,
as accounted for in the Monte Carlo and surface MPPE modeling, respectively. Nanorods
are modeled as perfect cylinders with hemispherical end caps, with diameter D and total
tip-to-tip length L. Triangular surface and tetrahedral volume meshing were constructedwith near-uniform element size across the nanoparticle surface and volume, with the element
side length (2 nm) selected to be much smaller than the nanoparticle dimensions and any
electric field variation on the surface or within the volume. This is particularly essential,
as the same mesh and calculated field values at the vertices are subsequently utilized forboth volume and surface photoemission modeling. The optical constants of gold are takenfrom the literature[86] and determined for the ITO film via ellipsometry. Optical constants
nlig = 1.5 and klig = 0.25 for the CTAB ligand layer, where the small extinction coefficientaccounts for the presence of amorphous carbon due to the hot-electron-driven conversion of
the organic ligands. Further discussion of this conversion process and nanorod photoemission

156
stability can be found below.
The calculated pulse-averaged electron temperature of 1000 K (via two-temperaturemodeling; see Section 3.3.3) is utilized for the excited Fermi-Dirac distribution to accountfor minor effects of electron heating during the pulse duration. The hot electrons then travelballistically over some distance (d) to the surface with an exponential survival probability for
inelastic hot-cold electron-electron scattering, e−d/λinel . The inelastic mean free path, λinel ≈6 nm, is approximately constant over the narrow threshold energy range of interest[24, 88]
and the possibility of electrons surviving a single inelastic scattering event with sufficient
momentum to subsequently escape is accounted for, although this contribution is found to be
negligible. Finally, hot electrons that reach the surface are transmitted into the surrounding
medium with unity probability if they have sufficient surface-normal momentum to overcome
the surface potential barrier and are otherwise reflected and lost. Trajectories following
surface reflection could be readily incorporated into the modeling and may be relevant forparticle dimensions similar to or less than the inelastic mean free path,[28, 19] but are safely
neglected here as λinel  D and L. Quantum barrier reflections corresponding to a sharp
barrier (barrier width much smaller than the hot electron wavelength for near-thresholdemission[56]) are also modeled in comparison with the smooth barrier limit (e.g. due to image
potential and/or ligand effects) and the corresponding transmission unit step function[189,56], yielding little effect on the resulting distributions. The effect of “refraction” at thesurface barrier due to perpendicular momentum loss and parallel momentum conservation is
fully accounted for within the simulations. While other integration methods have been used
to solve for the spatial distributions of emitted hot electrons,[28, 79] the Monte Carlo method
provides a computationally efficient means of integrating over all hot electron trajectories
for arbitrary nanoparticle geometries.[31, 19, 84] Further details of the ballistic Monte Carlo
method are described in Section 3.5.1.
The calculated Monte Carlo velocity maps in Fig. 6.5b and AC values in Fig. 6.5e
recapitulate the experimental angular distributions reasonably well. Simulated AC values

157
for different nanorod diameters are also shown in Fig. 6.7. Small longitudinal surface
photoemission contributions are likely the cause of the slightly less negative experimental
angular contrast values compared with the calculations, as examined in the next section.
Except for near the Fermi edge, which is in good agreement due to the experimental determination of the 4.25 ± 0.1 eV work function from the process order transitions (Fig.
6.5d) and from the velocity maps, the radial dependence of the photoemission distribution
is evidently not reproduced as well by the approximation of constant joint density of statesand energy-independent excitation matrix elements utilized in the Monte Carlo modeling.
Further details of the nascent hot electron distribution could be incorporated into the modeling, but this would require a significantly more detailed ab initio treatment of the material
band structure and a variety of multiphoton volume excitation channels, including direct
versus indirect (phonon-mediated) transitions in coherent and incoherent channels. Suchab initio calculations have been demonstrated by Narang and colleagues for two-photon
excitation[129] but are beyond the scope of the present work.
6.3

Detuning into the Surface-Mediated Regime
For further insight into the roles of both volume and surface photoemission processes,

the electric near-field distributions are simulated as a function of excitation frequency (andthus detuning from SPR) in Fig. 6.8a. Unlike the well-known uniform internal fields for
ellipsoids,[177] internal fields for nanorods are stronger near the center due to a hemisphericalsurface charge distribution at the tips (dipolar in the spherical limit) with field vectors that
destructively cancel within the tip regions but add constructively near the nanorod center.
Such central concentration of the field distributions leads to more centralized excitationof hot electrons, which subsequently escape predominantly from the sides of the nanorods
rather than the tips due to the limiting inelastic mean free path. This results in morenegative (transverse) angular contrast values compared with uniform excitation throughout
the nanorod body, as seen by comparing the theoretical curves in Fig. 6.5e. This is a

158

Figure 6.7: Calculated angular contrast (AC) values for nanorods of different diameters andaspect ratios, using the nonlinear field distributions calculated via finite element modeling.
As the nanorod radius becomes comparable to the inelastic mean free path (∼5 nm here)
more electrons can escape from the entire nanorod surface, including the hemispherical tips.
This leads to a more isotropic emission distribution and less negative (less transverse) AC
values. The uniform field curve only depends on the relative side vs. tip surface areas, which
depends only on the aspect ratio and is constant with diameter.

159
very different phenomenon from centralized heating effects that have been observed due tohigher electron kinetic energy in the center of the nanorod during plasmon oscillations,[74]as thermal effects are negligible in these relatively low-intensity (I0 ≈ 0.05–0.1 GW cm−2 )perturbative studies.
While the overall field enhancement is strongest on the plasmon resonance, the relative surface field contribution increases with red detuning due to enhanced screening of theinternal fields at lower frequencies by the conduction electrons. The ratio of these nonlinear
surface and volume field enhancement integrals (proportional to the nonlinear photoemission(nPPE)

cross-section ratio, σS(nPPE)/σV) is summarized for different aspect ratios in Fig. 6.8b.

The total multiphoton photoemission rate can be written as
MPPE =XσSnPPE (ω) + σSnPPE (ω) I0n ,

(6.2)

n

where the surface and volume nPPE cross-sections are given by(n)(n)
σSnPPE (ω) = cS (ω)ηS (ω)

Z|E⊥ (r, ω)/E0 |2n dS,(6.3)|E(r, ω)/E0 |2n dV,

(6.4)

and
(n)
(n)
σVnPPE (ω) = cV (ω)ηV (ω)(n)

respectively. The cS
(n)

Z

(n)

and cV factors are the surface and volume nonlinear absorption(n)densities and ηS and ηV are the emission quantum yields for a given process order. Strictly
speaking, the volume emission quantum yield in Eq. 6.4 is actually a volume-averaged
quantity,(n)ηV (ω) =R(n)ηV (r, ω) |E(r, ω)|2n dV,
R|E(r, ω)|2n dV(6.5)

which therefore depends on the geometry and can be determined via ballistic Monte Carlomodeling using the simulated fields.

(n)Typical values for ηV

for nanorods are between

0.1% and 1%, as quantified via full nanorod surface maps in Fig. 6.9, although this depends strongly on the frequency[52] and may also be substantially enhanced by surface

160

Figure 6.8: Finite element simulations of surface and volume plasmonic field enhancements.
(a) Volume (|E/E0 |) and surface (|E⊥ /E0 |) field enhancement maps for L/D = 3 nanorod
viewed in the xy plane (ligand layer and ITO substrate accounted for but not shown). Volume
fields are dominant at higher excitation energies (e.g. SPR + 0.3 eV) while surface fields
are dominant at lower excitation energies (e.g. SPR − 0.3 eV). (b) Ratio of the nonlinear
surface field integral to the nonlinear volume field integral for a series of nanorod aspectratios across the n = 2–4 spectral regions. Points indicate the calculated surface plasmon
resonance wavelengths. The fluctuations in the 2PPE regime are primarily due to the onsetof 5d-band absorption and dispersion.

161
(n)

roughness.[60] By comparison, ηS only depends on generic properties of a locally-flat metalvacuum surface potential barrier and is therefore not geometry-specific. As a result, the only
geometry-specific quantities are the field enhancement integrals in Eqs. 6.3 and 6.4 (which(n)encode the plasmonic response of the system) and ηV , which can be determined via finite(n) (n)(n)element and Monte Carlo modeling, respectively. The remaining cS ηS and cV values areproperties only of the material and/or nanoparticle-vacuum interface. Thus, if these mate(n)(n)

rial quantities can be characterized experimentally, then σS and σV are fully determined,
permitting the surface and volume contributions to be predicted for arbitrary nanoscale oreven macroscopic geometries.
(n)

Toward the goal of determining σS(n)and σV separately, photoelectron velocity map-ping is utilized to distinguish the volume and surface distributions. Considering the dramaticchange in the relative nonlinear surface vs. volume field enhancements with detuning (seeFig. 6.8b, the photoemission is expected to transition from the transverse volume-dominateddistribution (AC < 0) always observed around the SPR to a longitudinal surface-dominateddistribution (AC > 0) with only modest red detuning. This is precisely what is observed inFig. 6.10a, with the angular contrast summarized in Fig. 6.10c becoming positive around∆~ω ≈ −0.25 eV detuning. Unlike transverse volume emission, the longitudinal surface
emission is often asymmetric due to amplification of any tip field asymmetry (i.e. due toslight tip curvature differences) by the nonlinear process. For example, a 10% differencein the tip fields results in a factor of two difference in 4PPE rates (∝ |E/E0 |8 ). To takesuch asymmetry into account, the angular contrast values are obtained by averaging overboth longitudinal directions (Eq. 6.1). The measured angular contrast values for 9 sample
nanorods resonant between 700–800 nm (L/D = 2.5–3.5) are summarized in Fig. 6.10c,
which all display very similar behaviors with detuning. Notably, the range of detuning values crossing AC = 0 is about a factor of three narrower than the spread in absolute energies
arising from the spread in the SPR energies due to sample heterogeneity, as shown in Fig.
6.11. With respect to detuning from the surface plasmon resonance, all curves in Fig. 6.11a

162

Figure 6.9: Surface photocurrent (JnPPE ) and internal quantum efficiency maps forresonantly-excited nanorods with aspect ratio L/D = 5 (top), 3 (middle), and 1 (bottom),determined via Monte Carlo volume photoemission simulations. Each rod is resonant in adifferent nonlinear regime. (Left) The surface current proportional to the total number of escaped electrons from each surface area element, which shows that most electrons are excitednear the center of the nanorod in the centralized field-enhanced region, subsequently escaping mostly from the nearby surfaces (as limited by inelastic scattering). (Right) The internal
quantum efficiency is taken to be a discrete value for each area element, with the total given
by surface-averaged value. The L/D = 5 and 3 rods have similar maximum electron kinetic
energies (n~ω − φ) of ∼0.8 eV at resonance and therefore have similar quantum efficiencies.
The excess electron kinetic energy is much smaller (∼0.2 eV) in the sphere case for the 540
nm resonance and 2-photon photoemission, such that the escape quantum efficiency is aboutfour times smaller. Such frequency dependence is described by Fowler theory (1) (with thefrequency dependence trivially extended into the n-photon regime via ~ω → n~ω).

163
are nearly overlapped. However, the spread in the curves with respect to absolute excitationenergy (Fig. 6.11b) is as broad as the spread in resonances. Thus, it is clear that the transition is not due to an absolute energy effect such as the transition from 3PPE to 4PPE (withthis line indicated in Fig. 6.11b). Furthermore, intensity-dependence measurements verify
that the surface emission at −0.4 eV red detuning remains in the multiphoton regime rather
than the strong-field regime (Fig. 6.12). Higher input intensities are utilized at −0.4 eV red
detuning (I0 ≈ 2 GW cm−2 versus 0.05 GW cm−2 on resonance), but this simply maintains
similar signal levels by compensating for the drop in the plasmonic field enhancement off
resonance.
Under the present weak-field input intensities, nanorod heating is negligible (∼30 K
lattice temperature increase, Fig. 6.13) and thus there is no possibility of melting. To
verify that nanorods remain stable emitters during these studies, we demonstrate three
typical time traces in Fig. 6.14 for nanorods excited on resonance and at red detuning. The
volume emission on resonance is clearly very stable, while surface emission at red detuning
can be quite spiky, if fundamentally still fairly stable. The cause of the spikes is unknown,
though may be attributed to single-atom displacement (so-called “picocavity”) effects, whichtransiently create a factor of ∼4 larger field in a sub-nanometer region.[26] For the 4PPE
process, the 4-fold increase in |E/E0 | leads to a 105 -fold increase in |E/E0 |8 , which can thus
have noticeable effects despite the miniscule single-atom area. The surface signal fluctuations
may alternatively be attributed to ligand rearrangement and corresponding sudden changes
in the surface dielectric environment. In any case, the volume emission is insensitive tosuch effects and thus remains quite stable. Looking with velocity resolution, it is found thatwhile volume photoemission distributions remain quite stable/unchanged after prolonged
nanorod exposure, surface distributions tend to change a bit after ∼1 hour of continuous
exposure (Fig. 6.15). This is attributed to the well-known buildup of amorphous carbon
in the strongly field-enhanced tip regions,[183] in this case attributed to the cracking andrearrangement of surface ligands. The nonuniform amorphous carbon leads to varying near-

164

Figure 6.10: Transition from volume to surface photoemission with red detuning. (a) Experimental and (b) theoretical velocity maps at various detunings from the SPR of the correlated
example nanorod, showing the transition from volume (transverse) to surface (longitudinal)
photoemission. (c) Summary of angular photoemission contrast values for 9 nanorods, withdata points for the example rod in (a) and the theoretical curve from (b). All nanorods display consistent behavior and transition from the volume regime (shaded, AC < 0) into thesurface regime (AC > 0) around −0.25 eV detuning. (d) Relative volume and surface contributions determined from the fit of a(n) in (c). (e) Volume and surface nPPE cross-sections
for the example nanorod in (a).

165

Figure 6.11: Demonstrating that the transition from volume to surface photoemission atlower excitation frequencies is not due to an absolute energy effect, but rather a detuning
effect. (Left) Angular contrast versus detuning from the surface plasmon resonance, as also
shown in the main text. All curves for 9 nanorods have similar trends and overlap quite
well. The spread in detuning values crossing into the surface regime AC = 0 is a factor ofthree smaller than the spread of surface plasmon resonance values. (Right) Angular contrast
versus absolute excitation photon energy, showing a much broader spread dictated entirelyby the spread in SPRs of the 9 nanorods.

Figure 6.12: (Left) 3PPE intensity dependence for an example nanorod (L/D ≈ 3) excited onresonance, versus (Right) the 4PPE intensity dependence. Red-detuned emission therefore
remains in the multiphoton regime, as expected.

166
field enhancements and corresponding surface photoemission distributions, while potentiallyalso increasing scattering and therefore leading to more diffuse distributions.
To help theoretically characterize the relative surface and volume contributions to theobserved photoelectron distributions, the 3D photoemission distributions (and 2D projections) are modeled for each mechanism, taking the correlated nanorod geometry into account(Fig. 6.10b). Volume photoemission distributions are again modeled via the ballistic Monte
Carlo method, while the surface MPPE theory developed by Yalunin and coworkers[203] isimplemented to model the surface distributions. The implementation of this surface MPPE
theory to arbitrary nanoparticle systems is described in Section 3.5.2. In all experiments
and theory, the 3D photoelectron velocity distributions are projected/integrated over thevz degree of freedom, leading to the 2D (vx , vy ) velocity maps. The 3D distributions arecalculated explicitly, while the experimental 3D distributions could be recovered via inverse
Abel transform [42] by assuming cylindrically-symmetric photoemission distributions about
the nanorod long axis, as demonstrated in Chapter 5 for gold nanostars but not performed
here.
(nPPE)The relative weighting between calculated surface and volume contributions, σS(nPPE)σV/, depends on the ratio of the field integrals (Fig. 6.8b) as well as the primarily

material-specific (geometry-independent) coefficients in Eqs. 6.3 and 6.4. By working in thethreshold photoemission regime with excess photoelectron kinetic energies < 2 eV and approximating a constant density of states and excitation matrix elements in this narrow energy
range, the frequency dependence of both surface and volume coefficients can be expected to
(n)

(n)

(n)

(n)

obey Fowler’s law,[52] cS (ω)ηS (ω) ∝ cV (ω)ηV (ω) ∝ (n~ω − φ)2 , thus canceling out in(nPPE)

the σS(nPPE)/σV(nPPE)

ratio. As a result, all of the frequency dependence in σS(nPPE)/σVis contained within the ratio of the nonlinear field integrals, scaled by a single frequencyindependent prefactor
a

(n)

=

(n)

(n)

(n)

(n)

cS (ω)ηS (ω)
cV (ω)ηV (ω)

.

(6.6)

167

Figure 6.13: Two-temperature model of electron and lattice heating for a D = 20 nm,
L/D = 3 nanorod. The peak lattice temperature increase is ∼30 K, while the conduction
electrons have a pulse-averaged temperature of ∼1000 K (at the pulse peak) and reach an
overall peak temperature of 1500 K a couple hundred femtoseconds following excitation,
before thermalizing with the lattice on a few-picosecond timescale.

Figure 6.14: Volume (left) and surface (right) MPPE time traces for three typical nanorods.

168

Figure 6.15: Typical changes observed in the surface MPPE velocity distributions following∼1 hour of continuous laser exposure at typical intensities. All three L/D ≈ 4 nanorods
shown here are excited at 975 nm (≈ SP R− 0.2 eV) in the 4PPE regime, with angular contrast AC ≈ 0. Due to the limited detuning from resonance (∼0.2 eV), the distributions still
have a notable transverse component superposed with the asymmetric longitudinal surface
emission.

169
Thus, the role of experiment in determining the surface and volume photoemission contributions has been reduced to determination of this single a(n) parameter for a given processorder, n.
Weighting the modeled surface and volume photoemission distributions by the field
integral ratio from Fig. 6.8b, it is found that a(3) ≈ 7.5 pm (±50%) yields the best agreementwith the experimental angular contrast as a function of detuning (Fig. 6.10c). The relative
surface and volume contributions are now quantified, as shown in Fig. 6.10d, which indicatesthat volume processes account for 90% of the total photoemission on resonance. As suggested
earlier, the 10% surface contribution on resonance accounts for the slightly less negative (lesstransverse) experimental angular contrast values in Fig. 6.5e relative to the purely volume(nPPE)

Monte Carlo theory. With σS(nPPE)/σV(nPPE)

now determined and σS(nPPE)

+ σV

known

(nPPE)

directly from the total experimentally-measured photoemission rates (Eq. 6.2), σS(nPPE)σVandcan be determined independently, as summarized in Fig. 6.10e for the representative(nPPE)

nanorod. It is noted that σS(nPPE)and σVare only directly determined in the 3PPE

range. While explicit a(n) values for other process orders could be determined via additional
detuning studies, this investigation instead simply relies on the approximate continuity in(nPPE)

experimental σS(nPPE)/σVvalues (i.e. no sudden changes observed with detuning) fromthe L/D ≈ 3 nanorod detuning studies in Fig. 6.10 to extend the 3-photon results into theadjacent 2- and 4-photon ranges. With the aid of finite element and Monte Carlo modelingof the geometry-specific quantities (field integrals and escape efficiencies, respectively), this
now allows one, in principle, to quantitatively predict the volume vs. surface photoemission
behaviors for arbitrary gold nanoparticle geometries.
6.4

General Design Principles
It has been shown that the plasmonic field enhancements are of primary importancein determining the relative surface and volume contributions to electron emission. With a(3)and therefore the material-specific properties in Eqs. 6.3 and 6.4 determined from detuning170
experiments, the effects of optical parameters and nanoparticle geometry on the relative
contributions of surface and volume photoemission can now be quantitatively estimated, including the effects of (i) material screening, (ii) geometric surface-to-volume (S/V ) ratio, and(iii) nanoparticle shape/curvature. In particular, it is demonstrated that optical parameters
influence the relative surface versus volume contributions primarily via frequency-dependent
screening, while the nanoparticle shape controls the plasmonic field distribution at constantexcitation frequency. Direct results from the 3PPE range (Fig. 6.10) are again extended into
(nPPE)

the 2PPE and 4PPE ranges by approximate continuity in σS(nPPE)/σV, although this will

negligibly affect the principles and conclusions discussed.
First, the effects of frequency-dependent screening and the plasmon resonance (Fig.
6.16a) on the surface vs. volume photoemission contributions are considered. Specifically,(nPPE)

the plasmonic field enhancements and resulting σS(nPPE)/σVratios are simulated forligand-free nanorods in vacuum, for a series of aspect ratios (Fig. 6.16a). In this purely vacuum environment, the surface field enhancements are more prominent and longer nanorods
are predicted to be surface emitters on resonance, unlike the ligand-coated, ITO-supported
nanorods studied experimentally. For nanospheres in the electrostatic approximation andE 0 = E0 x̂, the Laplace equation yields a constant internal field (Section 3.1.1)
E in =

30
E0 x̂.
(ω) + 20(6.7)

As discussed in Section 3.1.1, the external-to-internal electric field ratio at the tip is given
simply by
Etip (ω)
(ω)=.
Ein (ω)0(6.8)

The crucial result is that the plasmonic resonance term, ∝ ( (ω) + 20 )−1 , drops out of
the field ratio in Eq. 6.8 entirely, leaving only with the screening effects described by themetal dielectric function,  (ω). Furthermore, the same cancellation of the surface and volume plasmonic field enhancements occurs in the full nonlinear field integrals, leading to(nPPE)σS(nPPE)/σV∝ | (ω) /0 |2n , as shown in Fig. 6.16a. It is thus concluded that the dra-

171
matic increase in surface over volume photoemission at longer wavelengths can be simply
attributed to enhanced metallic screening of internal fields. At a constant excitation wave(nPPE)

length, the progressive overall drop in σS(nPPE)/σVwith increasing nanorod aspect ratioin Fig. 6.16a is due to details of the nanorod geometry and plasmonic field distributions.
Next,the effects of nanoparticle scale (Fig. 6.16b) on the surface vs. volume photoemission contributions are considered. The importance of the geometric S/V ratio has
been emphasized in other investigations,[59] but it remained unclear whether this was truly
the decisive factor, in general, due to the previous lack of direct mechanistic insight into
the surface and volume excitation processes. Here, we effectively isolate the effect of S/Vratio by investigating nanorods with the same aspect ratio but different diameters, as inFig. 6.16b. By maintaining the same shape, the field enhancement distributions and SPRs
remain approximately constant with size, while the S/V ratio changes by three-fold, from
0.44 nm−1 (D = 10 nm) to 0.15 nm−1 (D = 30 nm). This factor of three is already rela(nPPE)

tively minor compared to the orders-of-magnitude changes in σS(nPPE)/σVwith modest

detuning and the similarly strong shape-dependent effects to be discussed next. Moreover, a(n)commensurate change in the volume emission efficiency with nanoparticle size, 1/ηV ∝ D,
(nPPE)

effectively cancels the S/V ∝ D−1 contribution to σS(nPPE)/σV. This occurs for larger

particles (D  λinel ) as the fraction of hot electrons excited within the escape depth fromthe surface (∼ λinel ) to the total number of electrons excited throughout the nanoparticle
approaches the geometric S/V ratio,[189] such that the escape efficiency scales as S/V (i.e.
n)(nPPE)

ηV ∝ D−1 ). Thus, σS(nPPE)/σVremains remarkably constant with nanoparticle scale atfixed excitation frequency, as shown in Fig. 6.16b. It is not until particle dimensions becomecomparable to or smaller than the hot electron inelastic mean free path that the S/V ∝ D−1(nPPE)

scaling begins to take over.[189] This σS(nPPE)/σV∝ D−1 regime may nonetheless be rel-evant for low-energy hot electron catalysis (e.g. λinel ≈ 40 nm for gold at ∼1.5 eV excitationenergy) with small nanoparticles (D < 30 nm).
Finally, the effects of nanoparticle shape (Fig. 6.16c) on the surface vs. volume pho-

172

Figure 6.16: Effects of screening, S/V ratio, and nanoparticle geometry (curvature) on
surface and volume contributions. This set of simulations is performed in vacuum (no ligands
or substrate). Shading indicates the volume-dominated regime. (a) Surface/volume nPPE
cross-section ratio determined quantitatively from detuning studies (Fig. 4) for L/D = 1–5
nanorods. Points indicate plasmon resonance wavelength. The dashed curve is the scaled
dielectric function of gold, which determines the frequency dependence of the surface/volume
cross-section ratios. (b) Cross-section ratio for L/D = 4 nanorod for D = 10–30 nm, withzoomed-in inset. (c) Cross-section ratio for bipyramid, nanorod, and dumbbell, all withsimilar resonance, S/V ratio (to within 10%), and total V (to within 30%).

173

Figure 6.17: Slices of plasmonic field enhancements for bipyramid, nanorod, and dumbbell
geometries with the corresponding surface-normal tip enhancements and total volume center
enhancements noted. All geometries are simulated in a vacuum environment with no surface
ligands.

toemission contributions are considered. While the effect of nanoparticle size/scale has been(nPPE)

shown to be generally minor, the nanoparticle shape strongly influences σS(nPPE)/σVvia

the plasmonic field distributions. Sharp convex features, for instance, can lead to more
dramatic surface field enhancements due to the lightning rod effect,[108, 99] whereas flator concave features can shift emphasis to the volume fields. Thus, we attempt to isolate
the effects of nanoparticle curvature by comparing particles of different shapes but similar
SPR, S/V ratio, and total volume (see Fig. 6.16c). Sharper-tipped geometries, such as
bipyramids, have more concentrated surface field enhancements and more diffuse volume
enhancements (Fig. 6.17), leading to an enhanced surface photoemission contribution. Thisis corroborated by observations of tip-localized photoemission from silver bipyramids,[118]and gold nanostars,[144, 77] and etched gold nanotips.[99] Conversely, more concave geometries such as dumbbells display much weaker surface fields and stronger relative interior
field enhancements (Fig. 6.17), leading to a dramatically enhanced volume photoemission
contribution.
(n)Interestingly, the effect of shape on internal quantum efficiency, ηV , is typically negli(3)gible. For example, ηV = 0.27% for the L/D = 4 resonantly-excited nanorod in Fig. 6.16c,

174
(3)

while ηV = 0.32% for the dumbbell excited at nearly the same SPR frequency. The strong(nPPE)

influence of nanoparticle shape on σS(nPPE)/σV

therefore arises from the shape-dependent

distribution and concentration of plasmonic fields, rather than the volume escape efficiency.
This has two significant benefits for designer plasmonic devices: (i) the plasmonic fields
can be readily simulated by a variety of classical methods (e.g. finite element simulation),and (ii) a further degree of optical control—beyond frequency-dependent screening—canbe readily exerted by coupling to different plasmon resonance modes via laser polarizationand frequency. Different plasmon resonance modes will display different volume and surface
field distributions, which has been utilized, for instance, to control photocurrents from gold
nanostars with multiple tip hot spots associated with different plasmon modes.[144, 77]In summary, the essential roles of nanoscopic volume vs. surface photoexcitation
mechanisms in nanoplasmonic hot electron emission have been demonstrated, along withcorresponding opportunities for designing and optically controlling hot electron spatial andmomentum distributions. Volume excitation, which is dominant for nanorods excited attheir longitudinal resonances, leads to hot electrons excited predominantly near the centerof the nanorods in the centralized field-enhanced region, which subsequently escape fromthe nearby side surfaces in a transverse momentum distribution. However, red detuning of
the excitation frequency strongly de-emphasizes the volume fields due to enhanced metallic
screening, instead promoting hot electron excitation directly at the tip surfaces. The surfaceexcited electrons are preferentially emitted longitudinally along the nanorod axis and therefore exhibit completely different spatial and momentum distributions compared with thevolume-excited hot electrons. Both processes are shown to be important in nanoplasmonic
systems and must be accounted for in general. We have demonstrated that comprehensive
volume (ballistic Monte Carlo) and surface (fully quantum) MPPE theory can be used tomodel these behaviors, but more importantly that the plasmonic field enhancement distribu(n)tions (rather than the geometric S/V ratio or internal quantum efficiency, ηV ) are criticalin controlling the surface vs. volume excitation. After characterizing the material-specific175(nonlinear) absorbances, it was shown that the surface vs. volume photoemission propertiesof arbitrary gold geometries can be predicted simply via classical electrodynamics simulations. This introduces exciting opportunities for the design of hot electron catalysis andnanoelectronic devices, in which the geometry can be optimized to control plasmon mode
structure and corresponding surface vs. volume distributions. Hot electron spatiotemporal
distributions may then be controlled on nanometer spatial scales and femtosecond timescales
via ultrafast optical frequency and polarization manipulation.[2, 144, 146]
6.5

Regulating Photocurrents with Mesoporous Silica Coatings
Another opportunity for controlling both volume and surface photocurrents, or com-plementing control schemes discussed herein, is to block emission from certain nanoparticle
regions via anisotropic SiO2 coatings. This effort is presently underway and is therefore
only mentioned briefly as promising results emerge. While initial indications of insulating
silica coatings blocking hot electron emission have been demonstrated,[184] this has now
been shown unambiguously via SPIM photoemission studies, with the relevant transmission
dynamics characterized. In particular, nanorods have been coated with both dense silica andmesoporous silica. “Mesoporous” silica actually has nanoscale pores of few-nanometer diameters that displace the surface ligands as the stabilizing agent on gold nanorods.[1, 53] Hot
electrons excited in the gold nanorods travel through silica with few-nanometer inelastic mean
free path, and thus photocurrents are substantially attenuated via dense silica, by orders ofmagnitude for relatively thin (∼10 nm) silica coatings. Substantial attenuation also occurs
through mesoporous silica, although the dynamics do not appear to be single-exponential
and drop off much more slowly with coating thickness. This can be interpreted via a simple geometrical model in which hot electrons escape through the nanoscale porous channels
that randomly form over the surface. As mesoporous silica can be nonuniformly coated on
the nanorod tips, body, or otherwise, this provides an additional method for tailoring hot
electron emission distributions, which can compliment nanoparticle geometric and optical

176
control schemes discussed here with nanostars, nanorods, and nanoshells. These studies will
illustrate both specific routes for such control, but also general opportunities for applying
nonuniform insulating coatings to influence nanoplasmonic hot carrier photocurrents.
6.6

Continuous Angular Control over Nanoshell Photoemission
Emerging capabilities for ultrafast photocurrent control typically rely on tuning opticalpolarization and/or frequency to selectively excite one or more discrete hot spots defined by
the particle geometry. By contrast, a unique case will now be introduced in which hot electron excitation and emission distributions can instead be continuously controlled via linear
laser polarization in the azimuthal plane of a gold nanoshell supported on a substrate. In
this configuration, it is the laser field that breaks the azimuthal symmetry of the supported
nanoshell and determines the plasmonic field distribution. Using angle-resolved photoelectron velocity map imaging, it is found that the hot electrons are predominantly emitted
orthogonal to the nanoshell dipolar surface plasmon resonance axis defined by the laser polarization. Furthermore, such anisotropic emission is only observed for nanoshells, while solid
gold nanospheres are found to be isotropic emitters. All of these effects are recapitulated
via simulation of the plasmonic electric field distributions within the nanoparticle volume
and ballistic Monte Carlo modeling of the hot electron dynamics. These results demonstrate a highly predictive level of understanding of the underlying physics and possibilities
for ultrafast spatiotemporal control over hot carrier dynamics.
The unique photoemission properties of gold nanoshells are clarified by comparison withgold nanospheres. Gold nanospheres (Fig. 6.18a) are purchased commercially (Nanopartz
Inc.) with citrate ligands and average diameter 100 ± 4 nm (1σ standard deviation) characterized via transmission electron microscopy (TEM). Gold nanoshells (Fig. 6.18b) are alsopurchased commercially (nanoComposix) with lipoic acid ligands, total diameter 147 ± 5
nm, and silica core diameter 118 ± 4 nm characterized via TEM. While the nanosphere
dipolar SPR position around 560 nm (Fig. 6.18c) is relatively insensitive to size, a well-

177
known special property of gold nanoshells is the sensitive dependence of the SPR position
on core/shell aspect ratio.[133, 93] In this case, the gold nanoshells have a typical dipolar
SPR around 675 nm when supported on the ITO-coated glass substrate in vacuum or air,as demonstrated by the single-particle scattering spectrum in Fig. 6.18d. The multiphoton
photoemission (MPPE) properties of gold nanoshells have been characterized in detail in
Chapter 5, including a work function around 4.3 eV and a corresponding transition between
the 2-photon photoemission (2PPE) and 3-photon photoemission (3PPE) regimes occurringaround 2.15 eV excitation photon energy (580 nm). The nanospheres and nanoshells arestudied on resonance in the 2PPE and 3PPE regimes, respectively, but we shall show thatthe excitation/emission properties depend primarily on the plasmonic field distributions,such that the angular photoemission behaviors do not fundamentally depend on processorder. Therefore, the results presented here should be equally applicable down to the linear (1-photon) regime for lower-threshold-energy metal-semiconductor Schottky barriers or
metal-molecule junctions.
While defect hot spots can be present on spherical nanoparticle surfaces and lead tostrongly polarization-sensitive signals,[62] directional photoemission,[146] and exceptionallyhigh surface-enhanced Raman scattering,[185, 67] we focus on defect-free nanospheres andnanoshells with minimal MPPE variation as a function of azimuthal linear polarization,
demonstrated in Figs. 6.19a and 6.19b for the same particles as in Figs. 6.18c and 6.18d.
The particles are therefore highly spherical, as any plasmonic field enhancements variation
due to geometric anisotropy would be strongly amplified by the nonlinear photoemission
process (nPPE ∝ |E/E0 |2n ). Any anisotropy to be observed in the hot electron emission
distributions can therefore primarily be attributed to symmetry breaking via the linear laser
polarization and the corresponding nanosphere and nanoshell plasmonic field enhancement
distributions. Furthermore, since the laser polarization only defines an axis rather than aspecific direction, the projected (2D) photoelectron velocity distributions are expected toremain centrosymmetric.

178

Figure 6.18: Gold nanosphere and nanoshell characterization. (a) Nanosphere and (b)nanoshell transmission electron micrographs. (c) Nanosphere and (d) nanoshell singleparticle dark field scattering spectra showing the dipolar surface plasmon resonance peaks,
with correlated scanning electron micrographs in the insets (scale bars: 100 nm). These
two representative particles are utilized for subsequent correlated photoemission studies andsimulations.

179
Photoelectron velocity maps in Figs. 6.19c and 6.19d for the representative nanosphereand nanoshell, respectively, show distinctly different behaviors. In particular, the nanospheredistribution is azimuthally isotropic while the nanoshell distribution is notably anisotropic
with stronger photoemission orthogonal to the laser polarization axis. In both cases, thedecrease in photoelectron counts near the center of the distributions is due to a surfacenormal velocity weighting factor in the photoemission speed distribution (Section 3.5.2),
which leads to a decrease in signal near the center of the 3D distributions that persists in the
2D projections, as will be reproduced in simulations. As expected, the anisotropic nanoshell
photoemission distribution remains centrosymmetric.
To quantify the anisotropy, the angular contrast, AC, of the radially-integrated 2D
angular distributions is again utilized (Eq. 6.1). Recall that the value of AC approaches+1 for highly longitudinal MPPE (parallel to the laser polarization axis) and −1 for highly
transverse MPPE (orthogonal to the laser polarization axis). This simple quantification of
the anisotropy is agnostic to any particular set of basis functions (e.g. Legendre polynomials)
and should not be confused with the anisotropy parameter (β) in molecular photoionization
studies,[178] as the nanoparticle photoemission distributions depend on the details of theplasmonic field distributions and hot electron emission dynamics. The nature of such distributions will instead be elucidated via simulations. The isotropic nature of the nanospherephotoemission observed in Fig. 6.19c (AC ≈ 0), which has also been discussed in detail in
Section 6.2, arises from the uniform dipolar field excited within a spherical conductor (Fig.
6.20a) and a volume-mediated photoexcitation/emission mechanism. Such volume MPPE
mechanisms, along with the rather more interesting plasmonic field distributions within gold
nanoshells that lead to the transverse photoemission observed in Fig. 6.19d (AC = −0.18),
will now be discussed in detail. By comparing experimental MPPE velocity distributions
with simulated surface vs. volume MPPE distributions, it shall be shown that volume mechanisms are unambiguously dominant in these studies.
Volume xy slices are shown in Figs. 6.20a and 6.20b for the two geometries (accounting

180

Figure 6.19: Photoemission properties of the representative correlated nanoparticles from
Fig. 1. (a) Nanosphere and (b) nanoshell total MPPE rates as a function of linear laser
polarization angle at peak input intensity I0 = 0.5 GW/cm2 in both cases. Both particles arehighly isotropic, displaying . 10% signal variation with laser polarization. The solid lines are
the average MPPE rates as a reference. (c) Nanosphere photoelectron velocity map, showing
largely isotropic photoemission (AC ≈ 0) in the 2PPE regime. (d) Nanoshell photoelectron
velocity map, showing predominantly transverse photoemission (AC < 0) relative to thepolarization-defined dipolar SPR oscillation along the x axis.

181
for the ITO substrate in the simulations). The internal field distribution is highly isotropic
for the nanosphere dipolar resonance. By contrast, the nanoshell internal field distribution is
anisotropic and favors the shell regions transverse to the laser polarization and corresponding
dipolar SPR axis. This is explained by the fact that the excited “bright” nanoshell dipolar
mode (Section 3.1.3) consists of the core (i.e. gold void) dipolar oscillation in phase with theshell dipolar oscillation,[93, 151] as illustrated by the charge distribution in Fig. 6.20b. For
this oscillation mode, the fields due to like charges destructively cancel for shell regions inclose proximity to the polarization axis, while the fields arising from opposite charges further
away from this axis around the transverse shell regions add constructively.
Isotropic internal sphere distributions vs. transverse internal shell distributions lead toisotropic vs. transverse hot electron excitation and emission, explaining the observed photoelectron velocity distributions. However, to further elucidate these dynamics, the ballistic
Monte Carlo photoemission model is utilized (Section 3.5.1). Briefly, the uniform nanoparticle volume and surface meshes from finite element simulations are utilized to discretize
the computational domain. Hot electrons are excited within a randomly-selected (but E 2n weighted) volume element into a randomly selected (Fermi-Dirac-weighted) k vector, basedon an assumption of uniform density of states and excitation matrix elements around thegold Fermi level. Hot electrons reach the surface with an exponential survival probability (6nm inelastic mean free path around 4.5 eV excitation energy[88, 24]) and are transmittedwith unit probability if they have sufficient surface-normal momentum to overcome the surface potential barrier, which is a suitable approximation assuming a smooth image potential
barrier.[189] All downward-moving photoelectron are neglected by approximating them tobe perfectly collected by the ITO substrate. Although the theoretical radial distributions
require further modeling beyond the simple approximations of uniform density of states andtransition matrix elements employed in this Monte Carlo modeling (i.e. first principles electronic structure theory[24, 129]), many of the essential features are already well reproduced.
The calculated volume-mediated photoemission distributions in Figs. 6.20c and 6.20d

182

Figure 6.20: Simulated volume and surface plasmonic fields and corresponding photoemission
distributions, with the laser polarized along the x axis. (a) Nanosphere and (b) nanoshell xy
volume slices showing the simulated field enhancement distributions, with the corresponding volume-mediated photoemission distributions in (c) and (d), respectively, calculated via
Monte Carlo MPPE modeling. As observed experimentally, the nanosphere distribution isisotropic (AC = 0), while the nanoshell distribution is peaked transverse to the laser polarization axis (AC < 0). (e) Nanosphere and (f) nanoshell surface-normal field enhancement
distributions, with the corresponding surface-mediated photoemission distributions in (g)and (h), respectively, calculated via quantum MPPE modeling. In both cases, the surfacemediated photoemission is peaked along the laser polarization axis (AC > 0).

183
reiterate the essential behaviors observed in the experimental distributions (Figs. 6.19c and6.19d)—i.e. isotropic nanosphere emission and transverse nanoshell emission. For comparison, the simulated surface field distributions are shown in Figs. 6.20e and 6.20f alongwith the corresponding longitudinal dipolar photoemission distributions calculated by implementing the surface-mediated MPPE theory of Yalunin and coworkers[203] for arbitrary
nanoscale geometries, as described in Section 3.5.2. Such longitudinal photoemission distributions (AC & +0.3) are completely different from the observed nanosphere (AC ≈ 0) andnanoshell (AC ≈ −0.2) distributions, confirming that volume rather than surface photoemission processes are dominant in these studies.
Now that the transverse nanoshell emission distributions are understood via the internal plasmonic field distributions and ballistic hot electron dynamics, it is shown that the angular distribution can be rotated continuously by the laser polarization. Unlike other demonstrations of photocurrent control where the nanoparticle geometry imposes its anisotropy on
the hot electron emission distributions (e.g. nanostars, nanoshell defects, nanorods), thenanoshell emission anisotropy is completely determined by the linear laser polarization axis
and can thus be continuously rotated in the azimuthal plane for the normal-incidence light(Fig. 6.21). Setting aside substrate effects, the 3D distributions corresponding to the 2D
projections in Fig. 6.21 are approximately cylindrically symmetric about the laser polarization axis, such that the hot electrons are emitted from the top of the nanoshell (and bottom,
if reflected rather than collected by the ITO) as well as from the sides, all transverse to
the laser polarization. Thus, rather than localized hot spot emission, the photoelectrons
originate throughout the gold shell volume. Nonetheless, the plasmonic volume fields andcorresponding hot electron distributions can still be controlled to a high degree via the opticalexcitation parameters, as demonstrated by the continuous polarization-dependent angularcontrol. In general, the spatial resolution for controlling such volume processes is defined by
the inelastic mean free path.
These results illustrate new capabilities for continuous photocurrent control as op-

184

Figure 6.21: Continuous polarization-controlled nanoshell photoemission rotation over thefull azimuthal range. Experimental (top) and theoretical (bottom) photoelectron velocity
distributions for the representative correlated nanoshell, at a series of linear laser polarizations. The experimental (theoretical) peak photoemission axes are along 87◦ (90◦ ), 41◦ (45◦ ),−3◦ (0◦ ), and −45◦ (−45◦ ), as determined via approximate sinusoidal fits. The peak photoemission is therefore transverse/orthogonal to the laser polarization axis, with constantAC ≈ −0.2 in each case.

185
posed to discrete hot spot selectivity, along with the essential role of volume excitation insome nanoplasmonic systems and simple methods for predicting the photoemission distributions via classical plasmonic field simulations and ballistic Monte Carlo modelling. Whileit has clearly been shown that volume MPPE mechanisms are predominant in the isotropic
nanoshell data herein, surface MPPE mechanisms would lead to similar opportunities forcontinuous angular control over photoemission from nanoshells as well as nanospheres (Fig.
6.20). Furthermore, at higher laser intensities, strong-field processes would yield surface
emission along the dipolar SPR axis, similar to demonstrations with gold nanorods[74, 106]and dielectric nanospheres.[181] Furthermore, while we only study the gold nanoshell dipolar SPR here, the quadrupolar resonance mode has a different internal field distribution andwill thus produce different hot electron spatial and momentum distributions. This provides
both a frequency as well as a polarization “control knob” in these nanoplasmonic systems
for ultrafast manipulation of hot electron spatial and momentum distributions.
To summarize this section, it has been shown that gold nanoshells are volume photoemitters when excited at their dipolar SPRs, yielding transverse anisotropic photoemission distributions relative to the linear laser polarization axis. The anisotropic photoemission
can be continuously rotated in the azimuthal laser polarization plane due to the sphericalsymmetry of the nanoshell, demonstrating new opportunities for optical control over hot
electron photocurrents and/or charge injection into nearby molecules for plasmonic photocatalysis. These results compliment other emerging capabilities for designing and actively
controlling nanoscale hot carrier dynamics via plasmonic hot spot selectivity or anisotropic
nanoparticle coatings. In the present case, since polarization can be rotated/shaped on femtosecond timescales, these results represent another step toward coherent photochemistry,
spatiotemporal electron waveform control for imaging, and ultrafast nanoelectronics.

Chapter 7
Ultrafast Time-Resolved Velocity Map Imaging

The ultrafast dynamics of nanoplasmonic hot carriers have been previously investigated
via optical measurements[69, 10] and by photoemission measurements.[15] Optical measurements may be simultaneously sensitive to both hot carrier and lattice thermalization processes, providing a broad view of dynamics in the nanoparticle following laser excitation.
These techniques, however, yield limited information on hot electron-electron thermalizationand cannot directly resolve dynamical lifetimes as a function of excitation energy. Without
energy resolution, these experiments can only assign a single-exponential decay time to thehighly energy-dependent, many-exponential decay dynamics of the hot carriers, with theslowly-decaying hot carriers at the lowest excitation energies therefore disporportionately
emphasized. Furthermore, these low-energy (“warm”) carriers are of limited importance to
hot carrier devices due to their inability to overcome surface barriers or activation energies. Unlike optical measurements, photoemission techniques can readily incorporate energy
resolution for a more detailed view of femtosecond hot carrier dynamics.[14] Furthermore,
photoemission techniques specifically probe the initial hot carrier thermalization step withlimited sensitivity to the subsequent energy cascade, which can be a feature for these studies.
Although optical studies of dynamics in single metal nanoparticles have become morecommon in the past couple decades,[139, 37, 209, 10, 33] few pump-probe photoemission
dynamics studies with single-nanoparticle resolution on femtosecond hot electron dynamics
have been performed to date. Single-particle studies are essential to obtaining the most187
relevant, detailed understanding on nanoparticle properties, and now set the benchmarksthat guide nanoparticle design. This not only eliminates inhomogeneous broadening that
plagues all ensemble measurements, but also has the potential to reveal new insights thatwould otherwise be averaged over or concealed. Clearly, single particle studies are also
necessary for angle-resolved velocity resolution.
The essential goal is to understand how fast hot electrons in the relevant excitationenergy range (for emission/collection/injection/transfer) decay, and by what mechanisms.
This will yield fundamental insight into hot carrier dynamics, while also providing practical guiding principles for designing nanoparticle geometries to promote efficient escape in
the locations/directions desired. This serves to compliment the angle-resolved photoemission measurements and modeling in previous chapters, now directly resolving the relevant
dynamical lifetimes and corresponding energy-dependent inelastic mean free path, rather
than relying on bulk gold quantities. To learn as much as possible about the dynamics
relevant to all hot carrier applications, therefore, time- and energy-resolved photoemission
measurements are performed here on single gold nanorods.
7.1

Femtosecond Pump-Probe
Single gold nanorods (L/D ≈ 4, D = 10 nm) are studied via pump-probe excitation,with the pump-probe time delay controlled with femtosecond resolution by means of a translation stage in the pump beam path (Section 2.9). With a clear pump-probe signal peakobserved in the time delay scan, it is first necessary to verify the process taking place during
pump-probe illumination of the nanorods, whether a simple two-photon pump-probe process
or a more complicated higher-order process. To this end, pump-probe intensity-dependence
measurements are performed on an individual nanorod (Fig. 7.1a), in which the pump orprobe beam intensity is held fixed while the other is varied. The linear proportionality ofsignal to intensity obsered in each case indeed describes a simple 1 + 10 pump-probe photoemission process, where the prime simply denotes the different photon energy. Linear

188
polarization dependence studies on the same representative nanorod are shown in Fig. 7.1b,
demonstrating that the single-color (pump) multiphoton photoemission (MPPE) signal isenhanced by orders of magnitude when the pump polarization is aligned along the resonant
longitudinal plasmon axis. Perhaps more suprising is that this is the case for the probe-only(400 nm) polarization dependence as well, despite being closer in energy to the transverse
plasmon resonance (∼ 500 nm). The implication is that the pump and probe beams must
both be aligned along the longitudinal rod axis for appreciable pump-probe signal, which
unfortunately precludes the ability to perform cross-polarized studies to avoid any coherent artifact effects,[143] to be discussed later. Additionally, these polarization behaviors
establish that effectively all interactions are plasmon-mediated, with no observable contribution from direct absorption. If direct absorption had any appreciable effect, there would
be non-negligible signal for polarization along the transverse plasmon axis.
By varying the time delay between the pump and probe pulses, hot electron dynamics
following plasmonic excitation can be temporally resolved. For Gaussian laser pulses, thecross-correlation between the pump and probe pulses will also be Gaussian and represents
the instrument response function (IRF), assuming an instantaneous system response. If the
response of the system is not effectively instantaneous, due to hot carrier dynamics thatpersist on timescales approaching or exceeding (i.e. not much less than) the IRF width, thenthe pump-probe cross-correlation will instead represent the IRF convolved with the impulse
response of the system. An example impulse response due to a 30 fs exponential decay
process is shown in Fig. 7.2a. So far without energy resolution, this effective exponential
decay time represents the average lifetime of hot electrons over the relevant excitation energy
range (∼1–2 eV). Furthermore, both the forward process (pump before probe) and reverse
process (probe before pump) must be accounted for, which is why any dynamics in a singlecolor pump-probe experiment result in symmetric broadening of the IRF.[14] In two-color
experiments, however, the forward and reverse processes are fundamentally different, andthe cross-correlation will generally be asymmetric. It will be shown that the hot electron

189

Figure 7.1: (a) Pump-probe intensity-dependence measurements, demonstrating the 1 +1’ excitation. (b) Individual pump and probe azimuthal polarization-dependent MPPE signals. (c) Incoherent pump-probe photoemission pathway through population of intermediate
states.

190

Figure 7.2: Pump-probe time delay scans. (a) Instrument response function measured on the
ITO substrate, with an example nanoparticle impulse response (dashed line), the convolutionof which yields (b) the nanoparticle delay scan with ∼35 fs forward decay time.

lifetimes drop off precipitously with excitation energy, such that probe-excited hot electrons(3.1 eV) will decay much more quickly than pump-excited hot electrons (1.8 eV) and thereverse decay will be essentially negligible.
The ITO substrate is utilized to measure the system IRF. A cross-correlation measurement on the ITO substrate, shown in Fig. 7.2a, appears highly symmetric and is fit wellby a single Gaussian peak. The high degree of symmetry in Fig. 7.2a indicates that either(i) no dynamics are taking place in the ITO on timescales greater than the lower resolvable
limit of ∼15 fs, or (ii) dynamics are taking place nearly symmetrically for the forward andreverse processes. It is also possible that (iii) asymmetric pump or probe pulse shapes are
effectively compensating for the dynamics and thereby masking them—but it is much lesslikely that this would happen to be the case. This will be ruled out completely in futurestudies on Pd films, known to have negligible hot carrier lifetimes.[14] As noted above, case(ii) can be ruled out given the very different photon energies involved: In the reverse process
the 3.1 eV probe beam generates a highly-excited hot electron distribution, of which only
the hottest can energetically be photoejected by the pump beam. From previous studies infilms it is known that highly excited electrons in the 3 eV excitation energy range decay very

191
quickly, on timescales of a few femtoseconds.[88, 102, 24] Although no studies have been
performed on ITO, these same studies on various metal films yield lifetimes of ¡ 10 fs evenfor excitation in the forward-process pump energy range, and therefore case (i) is most likely.
In either case, this cross-correlation on ITO sets an upper bound on the width of the IRF,
and from the preceding considerations would at most lead to a modest systematic decreasein any decay times measured for hot electrons in gold nanorods.
With the preliminaries established, dynamics are now investigated in gold nanorods.
The cross-correlation of a single nanorod shown in Fig. 7.2b deviates notably from theIRF, being both wider and clearly asymmetric, with a tail-off toward positive time delays.
As a guide to the eye, the best Gaussian fit is also shown in Fig. 7.2b, which overshootsat negative time delays and undershoots appreciably at positive delays – consistent witha forward exponential decay process. While a Gaussian clearly does not capture the true
behavior, the convolution of the two functions in Fig. 7.2a, with the IRF fixed and theexponential decay left floating, fits the data well. The exponential time constant extracted
from the fit in Fig. 7.2b is 35 fs. The timescale of this decay is similar to that of hotelectron lifetimes measured in gold films for the same 1–2 eV excitation energy range.[14]It should again be noted that this single-exponential fit is merely an approximate averageof the energy-dependent (and process-dependent) decay lifetimes. While these measured
decay times represent some combination of hot electron lifetimes (T1 ) for incoherent pumpprobe excitation (i.e. populating intermediate states) and plasmon dephasing times (T2 )for coherent excitation, the measured 35 fs decay times are much longer than the < 10 fs
plasmon dephasing times and can therefore be confidently assigned to hot electron lifetimes.
7.2

Time-Resolved Velocity Map Imaging
Combining time and energy resolution for a more complete characterization of the hot

electron dynamics, 2D velocity maps are measured as a function of pump-probe time delay.
Approximating cylindrically-symmetric photoemission about the nanorod long axis, the 3D

192

Figure 7.3: Angle-integrated 3D-reconstructed kinetic energy spectrum for a gold nanorodon (red; pump-probe) and off (black; background) the pump-probe delay peak. Pump-probe
nanorod 2D velocity distributions are similar to those shown previously in Chapter 6 forsingle-color MPPE and are thus not shown here. The gradual Fermi edge indicates anelevated electron temperature around 2000 K.

193
distributions are reconstructed via the BASEX inverse Abel transform algorithm (Section
3.6.1). Kinetic energy distributions are then determined by integrating over the angular
distribution, as shown in Figs. 7.3 and 7.4a. The pump-probe signal in Fig. 7.4a is shown
decreasing from its optimal value at a +30 fs delay to the non-pump-probe background
distribution at large positive time delays. An example energy slice at 0.5 eV above thevacuum level is demonstrated in Fig. 7.4b. By fitting the cross-correlation at each energy bin
to an exponential decay, the hot electron lifetimes are determined as a function of excitationenergy (Fig. 7.4c). The results appear linear on a log-log scale, indicating a power-law
behavior in the probed energy range, where a power-law fit yields an inverse quadratic
dependence of the lifetime on the excitation energy in the excitation energy range observed,
with good agreement over four different rod measurements. A simple physical model for thisbehavior, along with the implications for hot electron dynamics, are considered in the next
section.

7.2.1

Fermi Liquid Theory Behavior

A simple physical model for the observed inverse-quadratic dependence of the hot
electron lifetimes on excitation energy is due to Fermi’s Golden Rule. The derivation itself isstraightforward, and is discussed in a number of places.[14] The essential idea is illustrated
in Fig. 7.5a, in which a hot electron with energy E has a number of states proportional toE−EF (Fermi level EF ) available to decay into during an inelastic electron-electron scattering
event. This proportionality relies on the joint density of states (DOS) being approximately
constant in this excitation range, and also requires that the number of filled hot electronstates is much smaller than the number of available states, or that the filling of hot electronstates is also approximately constant in this energy region. These approximations will be
examined below. Conversely, the number of cold Fermi sea electrons that can be excited
above the Fermi level during the inelastic collision is also proportional to E − EF , under thesame assumptions. Therefore, making a final approximation of constant transition dipole

194

Figure 7.4: Energy-dependent hot electron lifetimes in a single gold nanorod. (a)Background-subtracted kinetic energy spectra as a function of pump-probe delay time. (b)Pump-probe delay scan at energy slice indicated in (a). (c) Summary of fit decay times asa function of excitation energy, shown on a log-log plot with a power-law fit yielding clear
inverse quadratic Fermi liquid theory behavior in this excitation energy range.

195
matrix element for all of the excitations, then Fermi’s Golden Rule yields[111]1τe−e∝ (E − EF )2 .

(7.1)

The last assumption is known as the random-k approximation, which has been shown to be
in good agreement with more detailed calculations.[218] The assumption of a constant DOS
within the pump photon energy to either side of the Fermi level is quite reasonable for thegold 6sp band.[29]7.2.2

Hot Electron Decay Processes

While the simple Fermi liquid theory lifetime behavior provides strong evidence for a
predominant hot-cold electron-electron scattering decay channel (also well-known to be thepredominant hot carrier decay channel in many metal systems [14]), other processes may
contribute to the hot electron lifetimes and should be examined. Alternate depopulation
channels include inelastic scattering between two hot electrons (Fig. 7.5b), electron-phonon
scattering (Fig. 7.5c), and charge transfer to the ITO (Fig. 7.5d). These channels modify
the hot electron lifetime in a straightforward manner via Mattheissen’s rule:
1
1
1
1
1
=
+
+
+
,
T1
τe−e τITO τe−ph τe−e,hot(7.2)

where τITO represents a spatially-averaged charge transfer lifetime from nanorod to ITO,
τe−ph is the electron-phonon scattering time, and τe−e,hot is the scattering time for two hotelectrons, all as a function of energy. If additional population of an excited state occurs
subsequent to the pump excitation (i.e. via in-filling from higher excited states), the population dynamics of that energy level can no longer be modeled by such a simple exponential
decay and the full kinetics must be accounted for. Auger effects that have previously been
observed to affect lifetimes in bulk gold[14] are due to excitation of d-band holes, which does
not occur here due to a pump photon energy (1.8 eV) that is just below the d-band thresholdenergy of gold (Chapter 4). The various population and depopulation processes will now be
considered, with additional experimental evidence to indicate the importance of each.

196

Figure 7.5: Various hot electron decay pathways. (a) Hot-cold electron-electron inelastic
scattering, (b) hot-hot electron-electron scattering, (c) electron-phonon scattering, and (d)charge transfer to the ITO substrate.

197
Scattering between two hot electrons (Fig. 7.5b) is generally not considered due to thelow density of hot electrons excited relative to cold electron bath. However, in nanoscaleparticles with exceedingly high absorption cross-sections due to plasmon-mediated excitation,
hot electrons can begin to make up a significant fraction of the relevant conduction band
population. In particular, finite element calculations of gold nanorods supported on ITO
yield peak absorption cross-sections around 2 × 10−10 cm2 at the plasmon resonance. For
peak pulse intensities around 100 MW/cm2 , corresponding to 2 × 1013 photons/pulse/cm2
at the pump photon energy, around 4 × 103 hot electrons are excited with each pump pulse.
From bulk gold densities and a valency of one electron per atom, the 10×40 nm nanorods
have approximately 1.5 × 105 conduction electrons, of which about a third are within apump photon energy of the Fermi level. With hot electrons therefore approaching 10% of
the relevant electron population for scattering, electron-electron scattering between two hotelectrons should be taken into consideration. The signature for this second-order kinetic
process is a decay rate that depends upon the hot electron population, and the significanceof this mechanism is therefore testable by measuring lifetime as a function of pump beam
intensity. Such a measurement is shown in Fig. 7.6 for a single nanorod, which reveals thatno statistically-significant shift in the average hot electron lifetime occurs with increasing
pump intensity. Furthermore, the energy dependence expected of this process would be(E − EF )−1 instead of the observed (E − EF )−2 , based on similar considerations as with hotcold electron-electron scattering, but in this case the second hot electron that gets excitedduring scattering originates from anywhere between EF and (EF + hνpump ) regardless of theother hot electron’s energy. Therefore, the second factor of E − EF is replaced by a constantfactor, hνpump . From both of these experimental observations it is evident that, despite thepossibly large densities of hot electrons excited in a nanorod, the inelastic scattering between
two hot electrons still does not contribute appreciably to the population dynamics.
Electron-phonon scattering (Fig. 7.5c) occurs on ∼30 fs timescales comparable toelectron-electron scattering[4] but is considered quasi-elastic, because on average it only

198

Figure 7.6: Effect of pump beam intensity (and thus hot carrier population and heating) on
measured average hot electron decay time. No effect is observed within the experimental
uncertainty.

199
decreases the hot electron excitation energy by 10 meV of so. This is less than the experimental energy resolution and therefore multiple electron-phonon scattering events mustoccur to constitute an effective change in population for a given energy level. Furthermore,
the electron-phonon scattering cross-section depends only weakly on energy, such that all
but the highest excited energy levels would be repopulated via electron-phonon cascading at
approximately the same rate that they are depopulated, effectively nullifying contributions
to the lifetime. The lifetime energy-dependence results in Fig. 7.4c confirm experimentallythat electron-phonon scattering has little effect on the lifetimes, else an energy-independent
contribution and therefore deviations from the Fermi liquid theory behavior would be expected.
In previous studies of Ag metal nanostructures on graphite,[149] charge transfer between the particle and the substrate (Fig. 7.5d) was found to have a substantial effect on hot
electron lifetimes. Charge may either be transferred to or from the substrate, although themuch stronger absorption and higher densities of hot electrons in the metal nanoparticles
would strongly push the equilibrium in favor of transfer to to substrate. The magnitude andenergy-dependence of charge transfer is determined by the shape of the tunnel barrier between the nanorods and the ITO, which is due to the organic CTAB spacer layer. Although
the shape of the tunnel barrier is not precisely known, there is little expectation that it would
yield an (E − EF )−2 tunneling probability rather than the exponential tunelling energy dependence for an energy-independent barrier width. Therefore, again invoking the observed
inverse-quadratic energy dependence of the lifetimes, it is unlikely that charge transfer isaffecting the hot electron dynamics. While this is evidently a negligible effect in the present
studies, promoting charge transfer from nanoparticles to a substrate or surrounding semiconductor medium is of substantial interest for photovoltaics and photodetection. Thus, these
sorts of studies hold promise for identifying and optimizing such dynamics in systems withstronger transfer characteristics.
Having already discussed the lack of hot electron cascading effects (in-filling of lower

200
energy levels) due to electron-phonon scattering, along with inelastic electron-electron scattering between two hot electrons, any remaining cascading effects are attributed to inelastic
electron-electron scattering between hot and cold electrons. Assuming constant DOS andtransition dipole matrix element, hot electrons lose half of their excitation energy to anelectron-electron scattering event on average,[159] and therefore only states near or less thanhalf of the maximum excitation energy (hνpump ) will be affected by cascading.[97] Considering the nanorod work function of ∼4.3 eV and the probe photon energy of 3.1 eV, only
electrons with (E − EF ) & hνpump /2 = 0.9 eV are probed in these experiments, and therefore
the cascade process should only play a minor role in the measured lifetimes of the lowestenergy hot electrons probed. In the lifetime energy-dependence measurements this would
manifest as a small curl-up at lower energies, which is not observed in Fig. 7.4c.
7.3

Discussion
Having excluded all other population and depopulation processes, it would appear

that the primary mechanism for hot electron decay in the probed excitation energy range
is indeed hot-cold electron-electron scattering, described via Fermi liquid theory. Auger
effects are precluded by the fact that the maximum hot carrier energies (i.e. pump photon
energies), are insufficient to promote 5d-band electrons above the Fermi level, which requires∼2 eV, and indeed full energy transfer in this manner is unlikely. It is also found that little
additional excited population is generated in the probed energy range following the pumpexcitation, and therefore the measured hot electron lifetimes directly reflect τe−e rather than
any additional in-filling kinetics in the energy range of interest. While these studies do notreach all the way down to the Fermi level, the 1–2 eV excitation range studied is particularly
relevant for photocatalysis and photovoltaics, in which such energies are required for the
hot electrons to overcome the Schottky barrier or transfer into an admolecular energy level.
Correspondingly, the hot electron lifetimes have been directly fit (rather than compared withmodels) and shown to have a very precise inverse-quadratic dependence on the excitation

201
energy, which is predicted by simple Fermi’s Golden Rule arguments. These results provide
enticing indications of opportunities for full time-resolved 3D velocity mapping capabilities
for detailed characterization of hot electron dynamics in complicated nanoplasmonic andother nanoscale geometries.

Chapter 8
Summary and Outlook

A new set of experimental and theoretical methods have been built up for studying
femtosecond hot electron dynamics in nanoplasmonic systems. A variety of nanoscale geometries have been studied—including thin gold film along, gold nanospheres, nanoshells,
nanorods, and nanostars—all revealing new fundamental insights and opportunities for predictively modeling and optically controlling naonscale photocurrents for a wide variety of
hot carrier scientific and technological applications. While gold was the primary material
investigated, it merely served as a convenient noble metal testbed with negligible oxidation
upon air exposure and strong plasmonic resonance properties (along with plentiful options
on nanoparticle geometries). The experimental observations and theoretical methods are
general with respect to material, and can be readily extended to other plasmonic metals or,some cases, even non-plasmonic systems.
Novel capabilities for angle-resolved photoemission resolution of single, immobilized
nanoparticles have led to important insights on volume vs. surface photoemission mechanisms (with plenty of exciting territory remaining to be covered in this realm), photoemission
blocking with insulating coatings (e.g. mesoporous silica), and the detailed photoemission
distributions from general hot spot geometries (e.g. hemispherical tips), which are applicable to numerous other systems, including etched nanotip photocathodes. Perhaps themost important role of these experiments has been to corroborate and drive the development of a simple, comprehensive theoretical framework both volume and surface photoex-

203
citation/emission dynamics via semi-classical Monte Carlo and fully quantum multiphoton
photoemission modeling, respectively. While some developments in the Monte Carlo andother methods were developed “from scratch”, much of the theoretical framework was basedon the work of others and nearly a century of developments in photoemission theory. The
strange and exciting reality is that, even for bulk/film systems, the photoelectric effect is still
not completely understood. The unique features of nanoplasmonic systems open up an evenricher variety of competing photoemission pathways that sustain the challenge of developing
a comprehensive model for all photoemission, particularly when resolved on femtosecond andattosecond timescales. The modest contribution here is to provide a reasonable theoreticalframework that (i) captures many of the essential features of these dynamics, (ii) uses methods that are accessible to the typical experimentalist in the field, and (iii) is simple/generalenough to allow for ready modification with more detailed ab initio theory or experimental
phenomenological parameters.
Having just implemented full 3D velocity mapping capabilities and having yet to fully
utilize the pump-probe capabilities, many exciting studies lie just ahead on the SPIM worldline. A few promising next steps include: Either 2D or 3D angle-resolved photoemisison studies of naonparticles (e.g. gold

nanorods) with anisotropic insulating coatings (e.g. mesoporous SiO2 ), demonstrating new capabilities for photocurrent control. (Work coming out shortly demonstrating the current regulating effects of isotropic coatings, along with initial demonstrations of anisotropy due to coating defects.)
 Studies on nanolithographic structures for detailed geometric control and opportuni-

ties for nanoscale electrode engineering, two-slit diffraction demonstrations, or othergeometries for nanoelectronics or frequency/polarization-resolved photodetection.
 More detailed time-resolved studies on a variety of nanoparticle geometries, materi-als, and environments, using 3D VMI to directly determine the radial distributions

204
without relying on symmetry and 3D reconstruction. Detailed investigations of theeffects of surface collisions, charge transfer at various interfaces, nonlocality, and theeffect of surface-like dielectric function deviations for very small particles.
 Careful 3D velocity-resolved studies on various geometries to refine volume vs. sur-face photoemission models.
 Pushing into the strong-field regime for novel time- and 3D angle-resolved charac-terization of these systems.
These and other directions (such as novel alloy, 2D, and quantum materials) all represent
exciting and relatively low-barrier future research paths.

Bibliography[1] N. S. Abadeer, M. R. Brennan, W. L. Wilson, and C. J. Murphy. Distance and plasmon
wavelength dependent fluorescence of molecules bound to silica-coated gold nanorods.
ACS Nano, 8(8):8392–8406, 2014.
[2] M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, S. Cunovic, F. Dimler, A. Fischer,W. Pfeiffer, M. Rohmer, C. Schneider, F. Steeb, C. Strüber, and D. V. Voronine. Spatiotemporal control of nanooptical excitations. Proceedings of the National Academyof Sciences of the United States of America, 107(12):5329–5333, 2010.
[3] M. Aidelsburger, F. O. Kirchner, F. Krausz, and P. Baum. Single-electron pulses forultrafast diffraction. Proceedings of the National Academy of Sciences of the UnitedStates of America, 107(46):19714–19719, 2010.
[4] N.W. Ashcroft and N.D. Mermin. Solid State Physics. Saunders College, Philadelphia,
1976.
[5] M. N. R. Ashfold, N. H. Nahler, A. J. Orr-Ewing, O. P. J. Vieuxmaire, R. L. Toomes,
T. N. Kitsopoulos, I. A. Garcia, D. A. Chestakov, S. M. Wu, and D. H. Parker. Imaging
the dynamics of gas phase reactions. Physical Chemistry Chemical Physics, 8(1):26–53,
2006.
[6] U. Aslam, V. G. Rao, S. Chavez, and S. Linic. Catalytic conversion of solar to chemicalenergy on plasmonic metal nanostructures. Nature Catalysis, 1(9):656–665, 2018.
[7] H. A. Atwater and A. Polman. Plasmonics for improved photovoltaic devices. Nature
Materials, 9(3):205–213, 2010.
[8] C. Awada, T. Popescu, L. Douillard, F. Charra, A. Perron, H. Yockell-Lelievre, A. L.
Baudrion, P. M. Adam, and R. Bachelot. Selective excitation of plasmon resonancesof single Au triangles by polarization-dependent light excitation. Journal of Physical
Chemistry C, 116(27):14591–14598, 2012.
[9] V. E. Babicheva, S. V. Zhukovsky, R. S. Ikhsanov, I. E. Protsenko, I. V. Smetanin,
and A. Uskov. Hot electron photoemission from plasmonic nanostructures: The roleof surface photoemission and transition absorption. ACS Photonics, 2(8):1039–1048,
2015.

206
[10] H. Baida, D. Mongin, D. Christofilos, G. Bachelier, A. Crut, P. Maioli, N. Del Fatti,
and F. Vallee. Ultrafast nonlinear optical response of a single gold nanorod near its
surface plasmon resonance. Physical Review Letters, 107(5):057402, 2011.
[11] A. R. Bainbridge and W. A. Bryan. Velocity map imaging of femtosecond laser induced
photoelectron emission from metal nanotips. New Journal of Physics, 16:103031, 2014.
[12] T. A. Baker, A. Grubisic, and D. J. Nesbitt. Plasmon mediated multiphoton photoemission microscopy of Au nanoholes and nanohole dimers. Journal of Physical
Chemistry C, 118(13):6959–6971, 2014.
[13] A. Barhoumi, R. Huschka, R. Bardhan, M. W. Knight, and N. J. Halas. Light-induced
release of dna from plasmon-resonant nanoparticles: Towards light-controlled genetherapy. Chemical Physics Letters, 482(4-6):171–179, 2009.
[14] M. Bauer, A. Marienfeld, and M. Aeschlimann. Hot electron lifetimes in metals probed
by time-resolved two-photon photoemission. Progress in Surface Science, 90(3):319–
376, 2015.
[15] D. Bayer, C. Wiemann, O. Gaier, M. Bauer, and M. Aeschlimann. Time-resolved
2ppe and time-resolved peem as a probe of lsp’s in silver nanoparticles. Journal of
Nanomaterials, 2008.
[16] J. P. Berenger. A perfectly matched layer for the absorption of electromagnetic-waves.
Journal of Computational Physics, 114(2):185–200, 1994.
[17] C. N. Berglund and W. E. Spicer. Photoemission studies of copper and silver: Theory.
Physical Review A, 136(4a):1030–1044, 1964.
[18] M. G. Blaber, M. D. Arnold, and M. J. Ford. A review of the optical properties ofalloys and intermetallics for plasmonics. Journal of Physics-Condensed Matter, 22(14),2010.
[19] E. Blandre, D. Jalas, A. Y. Petrov, and M. Eich. Limit of efficiency of generation of
hot electrons in metals and their injection inside a semiconductor using a semiclassicalapproach. ACS Photonics, 5(9):3613–3620, 2018.
[20] Craig F. Bohren and Donald R. Huffman. Absorption and scattering of light by small
particles. Wiley, New York, 1983.
[21] T. Brixner and G. Gerber. Femtosecond polarization pulse shaping. Optics Letters,
26(8):557–559, 2001.
[22] M. L. Brongersma. Introductory lecture: nanoplasmonics. Faraday Discussions, 178:9–
36, 2015.
[23] M. L. Brongersma, N. J. Halas, and P. Nordlander. Plasmon-induced hot carrier scienceand technology. Nature Nanotechnology, 10(1):25–34, 2015.

207[24] A. M. Brown, R. Sundararaman, P. Narang, W. A. Goddard, and H. A. Atwater.
Nonradiative plasmon decay and hot carrier dynamics: Effects of phonons, surfaces,
and geometry. ACS Nano, 10(1):957–966, 2016.
[25] N. D. Burrows, A. M. Vartanian, N. S. Abadeer, E. M. Grzincic, L. M. Jacob, W. N.
Lin, J. Li, J. M. Dennison, J. G. Hinman, and C. J. Murphy. Anisotropic nanoparticles
and anisotropic surface chemistry. Journal of Physical Chemistry Letters, 7(4):632–
641, 2016.
[26] C. Carnegie, J. Griffiths, B. de Nijs, C. Readman, R. Chikkaraddy, W. M. Deacon,
Y. Zhang, I. Szabo, E. Rosta, J. Aizpurua, and J. J. Baumberg. Room-temperature
optical picocavities below 1 nm3 accessing single-atom geometries. Journal of Physical
Chemistry Letters, 9(24):7146–7151, 2018.
[27] D. W. Chandler and P. L. Houston. Two-dimensional imaging of state-selected photodissociation products detected by multiphoton ionization. Journal of Chemical
Physics, 87(2):1445–1447, 1987.
[28] Q. Y. Chen and C. W. Bates. Geometrical factors in enhanced photoyield from small
metal particles. Physical Review Letters, 57(21):2737–2740, 1986.
[29] N. E. Christensen and B. O. Seraphin. Relativistic band calculation and optical properties of gold. Physical Review B-Solid State, 4(10):3321, 1971.
[30] C. Clavero. Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices. Nature Photonics, 8(2):95–103,
2014.
[31] E. Cortes. Efficiency and bond selectivity in plasmon-induced photochemistry.
Advanced Optical Materials, 5(15):1700191, 2017.
[32] E. Cortes, W. Xie, J. Cambiasso, A. S. Jermyn, R. Sundararaman, P. Narang,
S. Schlucker, and S. A. Maier. Plasmonic hot electron transport drives nano-localizedchemistry. Nature Communications, 8:14880, 2017.
[33] A. Crut, P. Maioli, N. Del Fatti, and F. Vallee. Optical absorption and scattering
spectroscopies of single nano-objects. Chemical Society Reviews, 43(11):3921–3956,
2014.
[34] Maciej Dabrowski, Yanan Dai, and Hrvoje Petek. Ultrafast photoemission electron
microscopy: Imaging plasmons in space and time. Chemical Reviews, 120(13):6247–
6287, 2020.
[35] A. Damascelli. Probing the electronic structure of complex systems by ARPES. Physica
Scripta, T109:61–74, 2004.

208[36] A. Damm, J. Gudde, P. Feulner, A. Czasch, O. Jagutzki, H. Schmidt-Bocking, andU. Hofer. Application of a time-of-flight spectrometer with delay-line detector for timeand angle-resolved two-photon photoemission. Journal of Electron Spectroscopy and
Related Phenomena, 202:74–80, 2015.
[37] N. Del Fatti, D. Christofilos, and F. Vallee. Optical response of a single gold nanoparticle. Gold Bulletin, 41(2):147–158, 2008.
[38] G. N. Derry, M. E. Kern, and E. H. Worth. Recommended values of clean metal surface
work functions. Journal of Vacuum Science and Technology A, 33(6):060801, 2015.
[39] P. Dombi, A. Hörl, P. Rácz, I. Márton, A. Trügler, J. R. Krenn, and U. Hohenester. Ultrafast strong-field photoemission from plasmonic nanoparticles. Nano Letters,
13(2):674–678, 2013.
[40] L. Douillard and F. Charra. Photoemission electron microscopy, a tool for plasmonics.
Journal of Electron Spectroscopy and Related Phenomena, 189:24–29, 2013.
[41] E. C. Dreaden, A. M. Alkilany, X. H. Huang, C. J. Murphy, and M. A. El-Sayed. The
golden age: Gold nanoparticles for biomedicine. Chemical Society Reviews, 41(7):2740–
2779, 2012.
[42] V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler. Reconstruction ofabel-transformable images: The gaussian basis-set expansion Abel transform method.
Review of Scientific Instruments, 73(7):2634–2642, 2002.
[43] D. Ehberger, J. Hammer, M. Eisele, M. Krüger, J. Noe, A. Högele, and P. Hommelhoff.
Highly coherent electron beam from a laser-triggered tungsten needle tip. PhysicalReview Letters, 114(22):227601, 2015.
[44] A. T. J. B. Eppink and D. H. Parker. Velocity map imaging of ions and electrons using
electrostatic lenses: Application in photoelectron and photofragment ion imaging ofmolecular oxygen. Review of Scientific Instruments, 68(9):3477–3484, 1997.
[45] L. Fan, S. K. Lee, P. Y. Chen, and W. Li. Observation of nanosecond hot carrier decay
in graphene. J Phys Chem Lett, pages 1485–1490, 2018.
[46] L. Fan, S. K. Lee, Y. J. Tu, B. Mignolet, D. Couch, K. Dorney, Q. Nguyen,
L. Wooldridge, M. Murnane, F. Remacle, H. B. Schlegel, and W. Li. A new electron-ion
coincidence 3D momentum-imaging method and its application in probing strong field
dynamics of 2-phenylethyl-N, N-dimethylamine. Journal of Chemical Physics, 147(1),2017.
[47] W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor. Electron thermalization in gold.
Physical Review B, 46(20):13592–13595, 1992.
[48] P. J. Feibelman and D. E. Eastman. Photoemission spectroscopy - correspondence
between quantum-theory and experimental phenomenology. Physical Review B,
10(12):4932–4947, 1974.

209[49] A. Feist, N. Bach, N. R. da Silva, T. Danz, M. Möller, K. E. Priebe, T. Domröse, J. G.
Gatzmann, S. Rost, J. Schauss, S. Strauch, R. Bormann, M. Sivis, S. Schäfer, and
C. Ropers. Ultrafast transmission electron microscopy using a laser-driven field emitter:
Femtosecond resolution with a high coherence electron beam. Ultramicroscopy, 176:63–
73, 2017.
[50] J. M. Fitzgerald, P. Narang, R. V. Craster, S. A. Maier, and V. Giannini. Quantum
plasmonics. Proceedings of the Ieee, 104(12):2307–2322, 2016.
[51] V. S. Fomenko and G. V. Samsonov. Handbook of Thermionic Properties: Electronic
Work Functions and Richardson Constants of Elements and Compounds. Springer US,
Boston, MA, 1966.
[52] R. H. Fowler. The analysis of photoelectric sensitivity curves for clean metals at various
temperatures. Physical Review, 38(1):45–56, 1931.
[53] Z. Gao, N. D. Burrows, N. A. Valley, S. Egger, G. C. Schatz, C. J. Murphy, andC. L. Haynes. In solution SERS sensing using mesoporous silica-coated gold nanorods.
Analyst, 141(24):6604–6604, 2016.
[54] F. J. Garcı́a-Vidal and J. B. Pendry. Collective theory for surface enhanced Raman
scattering. Physical Review Letters, 77(6):1163–1166, 1996.
[55] J. Gargiulo, R. Berte, Y. Li, S. A. Maier, and E. Cortes. From optical to chemical hot
spots in plasmonics. Accounts of Chemical Research, 52(9):2525–2535, 2019.
[56] P. L. Garrido, S. Goldstein, J. Lukkarinen, and R. Tumulka. Paradoxical reflection inquantum mechanics. American Journal of Physics, 79(12):1218–1231, 2011.
[57] M.L. Glasser and A. Bagchi. Theories of photoemission from metal surfaces. Progressin Surface Science, 7(3):113–148, 1976.
[58] G. Gonzalez-Rubio, V. Kumar, P. Llombart, P. Diaz-Nunez, E. Bladt, T. Altantzis,
S. Bals, O. Pena-Rodriguez, E. G. Noya, L. G. MacDowell, A. Guerrero-Martinez,
and L. M. Liz-Marzan. Disconnecting symmetry breaking from seeded growth for the
reproducible synthesis of high quality gold nanorods. ACS Nano, 13(4):4424–4435,
2019.
[59] M. Graf, D. Jalas, J. Weissmuller, A. Y. Petrov, and M. Eich. Surface-to-volume ratio
drives photoelelectron injection from nanoscale gold into electrolyte. ACS Catalysis,9(4):3366–3374, 2019.
[60] M. Grajower, U. Levy, and J. B. Khurgin. The role of surface roughness in plasmonicassisted internal photoemission schottky photodetectors. ACS Photonics, 5(10):4030–
4036, 2018.
[61] W. S. Graves, F. X. Kärtner, D. E. Moncton, and P. Piot. Intense superradiant x raysfrom a compact source using a nanocathode array and emittance exchange. PhysicalReview Letters, 108(26):263904, 2012.

210[62] A. Grubisic, S. Mukherjee, N. Halas, and D. J. Nesbitt. Anomalously strong electric
near-field enhancements at defect sites on Au nanoshells observed by ultrafast scanningphotoemission imaging microscopy. Journal of Physical Chemistry C, 117(44):22545–
22559, 2013.
[63] A. Grubisic, E. Ringe, C. M. Cobley, Y. N. Xia, L. D. Marks, R. P. Van Duyne,
and D. J. Nesbitt. Plasmonic near-electric field enhancement effects in ultrafast photoelectron emission: Correlated spatial and laser polarization microscopy studies ofindividual Ag nanocubes. Nano Letters, 12(9):4823–4829, 2012.
[64] A. Grubisic, V. Schweikhard, T. A. Baker, and D. J. Nesbitt. Coherent multiphoton
photoelectron emission from single Au nanorods: The critical role of plasmonic electric
near-field enhancement. ACS Nano, 7(1):87–99, 2013.
[65] A. Grubisic, V. Schweikhard, T. A. Baker, and D. J. Nesbitt. Multiphoton photoelectron emission microscopy of single Au nanorods: Combined experimental andtheoretical study of rod morphology and dielectric environment on localized surface
plasmon resonances. Physical Chemistry Chemical Physics, 15(26):10616–10627, 2013.
[66] M. Gulde, S. Schweda, G. Storeck, M. Maiti, H. K. Yu, A. M. Wodtke, S. Schäfer,
and C. Ropers. Ultrafast low-energy electron diffraction in transmission resolves polymer/graphene superstructure dynamics. Science, 345(6193):200–204, 2014.
[67] E. Hao, S. Y. Li, R. C. Bailey, S. L. Zou, G. C. Schatz, and J. T. Hupp. Opticalproperties of metal nanoshells. Journal of Physical Chemistry B, 108(4):1224–1229,
2004.
[68] F. Hao, C. L. Nehl, J. H. Hafner, and P. Nordlander. Plasmon resonances of a gold
nanostar. Nano Letters, 7(3):729–732, 2007.
[69] G. V. Hartland. Optical studies of dynamics in noble metal nanostructures. Chemical
Reviews, 111(6):3858–3887, 2011.
[70] M. Hattass, T. Jalowy, A. Czasch, T. Weber, T. Jahnke, S. Schossler, L. P. Schmidt,
O. Jagutzki, R. Dorner, and H. Schmidt-Bocking. A 2 pi spectrometer for electronelectron coincidence studies on surfaces. Review of Scientific Instruments, 75(7):2373–
2378, 2004.
[71] C. L. Haynes, A. D. McFarland, and R. P. Van Duyne. Surface-enhanced Raman
spectroscopy. Analytical Chemistry, 77(17):338a–346a, 2005.
[72] G. Herink, D. R. Solli, M. Gulde, and C. Ropers. Field-driven photoemission fromnanostructures quenches the quiver motion. Nature, 483(7388):190–193, 2012.
[73] T. Higuchi, C. Heide, K. Ullmann, H. B. Weber, and P. Hommelhoff. Light-field-driven
currents in graphene. Nature, 550(7675):224, 2017.

211[74] R. G. Hobbs, W. P. Putnam, A. Fallahi, Y. Yang, F. X. Kärtner, and K. K. Berggren.
Mapping photoemission and hot-electron emission from plasmonic nanoantennas. Nano
Letters, 17(10):6069–6076, 2017.
[75] R. G. Hobbs, Y. Yang, A. Fallahi, P. D. Keathley, E. De Leo, F. X. Kärtner, W. S.
Graves, and K. K. Berggren. High-yield, ultrafast, surface plasmon-enhanced, Au
nanorod optical field electron emitter arrays. ACS Nano, 8(11):11474–11482, 2014.
[76] P. Hommelhoff, C. Kealhofer, and M. A. Kasevich. Ultrafast electron pulses from atungsten tip triggered by low-power femtosecond laser pulses. Physical Review Letters,
97(24):247402, 2006.
[77] C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and
F. Charra. Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars. Nano Letters, 11(2):402–407, 2011.
[78] S. Hufner. Photoelectron Spectroscopy: Principles and Applications. Springer-Verlag,
Berlin, 3 edition, 2003.
[79] R. S. Ikhsanov, A. V. Novitsky, I. E. Protsenko, and A. V. Uskov. Bulk photoemission
from plasmonic nanoantennas of different shapes. Journal of Physical Chemistry C,
122(22):11985–11992, 2018.
[80] J. B. Jackson and N. J. Halas. Surface-enhanced Raman scattering on tunable plasmonic nanoparticle substrates. Proceedings of the National Academy of Sciences of
the United States of America, 101(52):17930–17935, 2004.
[81] J.D. Jackson. Classical electrodynamics. Wiley, New York, 3rd edition, 1998.
[82] P. K. Jain, W. Qian, and M. A. El-Sayed. Ultrafast cooling of photoexcited electrons
in gold nanoparticle-thiolated dna conjugates involves the dissociation of the gold-thiolbond. Journal of the American Chemical Society, 128(7):2426–2433, 2006.
[83] Y. H. Jang, Y. J. Jang, S. Kim, L. N. Quan, K. Chung, and D. H. Kim. Plasmonic solar
cells: From rational design to mechanism overview. Chemical Reviews, 116(24):14982–
15034, 2016.
[84] A. S. Jermyn, G. Tagliabue, H. A. Atwater, W. A. Goddard, P. Narang, and R. Sundararaman. Transport of hot carriers in plasmonic nanostructures. Physical Review
Materials, 3(7):075201, 2019.
[85] J.-M. Jin. Theory and computation of electromagnetic fields. Wiley, Hoboken, N.J.,
2010.
[86] P. B. Johnson and R. W. Christy. Optical constants of noble metals. Physical Review
B, 6(12):4370–4379, 1972.
[87] A. Kahn. Fermi level, work function and vacuum level. Materials Horizons, 3(1):7–10,
2016.

212
[88] H. Kanter. Slow-electron mean free paths in aluminum, silver, and gold. PhysicalReview B-Solid State, 1(2):522–536, 1970.
[89] C. Karnetzky, P. Zimmermann, C. Trummer, C. D. Sierra, M. Wörle, R. Kienberger,
and A. Holleitner. Towards femtosecond on-chip electronics based on plasmonic hot
electron nano-emitters. Nature Communications, 9:2471, 2018.
[90] P. D. Keathley, W. P. Putnam, P. Vasireddy, R. G. Hobbs, Y. Yang, K. K. Berggren,and F. X. Kartner. Vanishing carrier-envelope-phase-sensitive response in optical-field
photoemission from plasmonic nanoantennas. Nature Physics, 15(11):1128, 2019.
[91] L. V. Keldysh. Ionization in the field of a strong electromagnetic wave. Sov. Phys.
JETP-USSR, 20(5):1307–1314, 1965.
[92] K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz. The optical properties ofmetal nanoparticles: The influence of size, shape, and dielectric environment. Journalof Physical Chemistry B, 107(3):668–677, 2003.
[93] A. S. Kirakosyan, M. I. Stockman, and T. V. Shahbazyan. Surface plasmon lifetimein metal nanoshells. Physical Review B, 94(15):155429, 2016.
[94] C. Kittel. Introduction to Solid State Physics. Wiley, New York, 7th edition, 1996.
[95] M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas. Photodetection with active
optical antennas. Science, 332(6030):702–704, 2011.
[96] M. W. Knight, Y. M. Wang, A. S. Urban, A. Sobhani, B. Y. Zheng, P. Nordlander,and N. J. Halas. Embedding plasmonic nanostructure diodes enhances hot electron
emission. Nano Letters, 13(4):1687–1692, 2013.
[97] E. Knoesel, A. Hotzel, T. Hertel, M. Wolf, and G. Ertl. Dynamics of photoexcitedelectrons in metals studied with time-resolved two-photon photoemission. Surface
Science, 368:76–81, 1996.
[98] B. Kromker, M. Escher, D. Funnemann, D. Hartung, H. Engelhard, and J. Kirschner.
Development of a momentum microscope for time resolved band structure imaging.
Review of Scientific Instruments, 79(5):053702, 2008.
[99] M. Krüger, C. Lemell, G. Wachter, J. Burgdörfer, and P. Hommelhoff. Attosecond
physics phenomena at nanometric tips. Journal of Physics B-Atomic Molecular andOptical Physics, 51(17):172001, 2018.
[100] M. Krüger, M. Schenk, and P. Hommelhoff. Attosecond control of electrons emitted
from a nanoscale metal tip. Nature, 475(7354):78–81, 2011.
[101] J. Kupersztych, P. Monchicourt, and M. Raynaud. Ponderomotive acceleration of photoelectrons in surface-plasmon-assisted multiphoton photoelectric emission. PhysicalReview Letters, 86(22):5180–5183, 2001.

213[102] F. Ladstadter, U. Hohenester, P. Puschnig, and C. Ambrosch-Draxl. First-principles
calculation of hot-electron scattering in metals. Physical Review B, 70(23):235125,
2004.
[103] J. Langer, S. M. Novikov, and L. M. Liz-Marzan. Sensing using plasmonic nanostructures and nanoparticles. Nanotechnology, 26(32), 2015.
[104] S. K. Lee, F. Cudry, Y. F. Lin, S. Lingenfelter, A. H. Winney, L. Fan, and W. Li.
Coincidence ion imaging with a fast frame camera. Review of Scientific Instruments,
85(12):123303, 2014.
[105] S. K. Lee, Y. F. Lin, S. Lingenfelter, L. Fan, A. H. Winney, and W. Li. Communication:
Time- and space-sliced velocity map electron imaging. Journal of Chemical Physics,
141(22):221101, 2014.
[106] M. Lehr, B. Foerster, M. Schmitt, K. Krüger, C. Sönnichsen, G. Schönhense, and
H. J. Elmers. Momentum distribution of electrons emitted from resonantly excited
individual gold nanorods. Nano Letters, 17(11):6606–6612, 2017.
[107] Martin Lehr, Karina Bley, Nicolas Vogel, Bärbel Rethfeld, Gerd Schönhense, andHans-Joachim Elmers. Evidence of spatially inhomogeneous electron temperature in aresonantly excited array of bow-tie nanoantennas. Journal of Physical Chemistry C,
123(19):12429–12436, 2019.
[108] P. F. Liao and A. Wokaun. Lightning rod effect in surface enhanced Raman scattering.
Journal of Chemical Physics, 76(1):751–752, 1982.
[109] Y. F. Lin, S. K. Lee, P. Adhikari, T. Herath, S. Lingenfelter, A. H. Winney, and W. Li.
Note: An improved 3D imaging system for electron-electron coincidence measurements.
Review of Scientific Instruments, 86(9):096110, 2015.
[110] S. Linic, U. Aslam, C. Boerigter, and M. Morabito. Photochemical transformations on
plasmonic metal nanoparticles. Nature Materials, 14(6):567–576, 2015.
[111] S. Link and M. A. El-Sayed. Shape and size dependence of radiative, non-radiativeand photothermal properties of gold nanocrystals. International Reviews in Physical
Chemistry, 19(3):409–453, 2000.
[112] S. Link, M. B. Mohamed, and M. A. El-Sayed. Simulation of the optical absorption
spectra of gold nanorods as a function of their aspect ratio and the effect of the medium
dielectric constant. Journal of Physical Chemistry B, 103(16):3073–3077, 1999.
[113] S. E. Lohse and C. J. Murphy. The quest for shape control: A history of gold nanorod
synthesis. Chemistry of Materials, 25(8):1250–1261, 2013.
[114] G. D. Mahan. Theory of photoemission in simple metals.
2(11):4334–4350, 1970.

Physical Review B,

214[115] S.A. Maier. Plasmonics: Fundamentals and Applications. Springer, New York, 1stedition, 2007.
[116] R. E. B. Makinson. The surface photoelectric effect. Physical Review, 75(12):1908–
1911, 1949.
[117] A. Manjavacas, J. G. Liu, V. Kulkarni, and P. Nordlander. Plasmon-induced hot
carriers in metallic nanoparticles. ACS Nano, 8(8):7630–7638, 2014.
[118] E. Marsell, A. Losquin, R. Svard, M. Miranda, C. Guo, A. Harth, E. Lorek, J. Mauritsson, C. L. Arnold, H. X. Xu, A. L’Huillier, and A. Mikkelsen. Nanoscale imagingof local few-femtosecond near-field dynamics within a single plasmonic nanoantenna.
Nano Letters, 15(10):6601–6608, 2015.
[119] J. W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, and N. Gedik. Control over
topological insulator photocurrents with light polarization. Nature Nanotechnology,
7(2):96–100, 2012.
[120] M. Meier and A. Wokaun. Enhanced fields on large metal particles - dynamic depolarization. Optics Letters, 8(11):581–583, 1983.
[121] M. Merschdorf, W. Pfeiffer, A. Thon, S. Voll, and G. Gerber. Photoemission frommultiply excited surface plasmons in Ag nanoparticles. Applied Physics A-Materials
Science & Processing, 71(5):547–552, 2000.
[122] H. B. Michaelson. Work function of elements and its periodicity. Journal of Applied
Physics, 48(11):4729–4733, 1977.
[123] M. Moskovits.
The case for plasmon-derived hot carrier devices.
Nanotechnology, 10(1), 2015.

Nature[124] N. E. Motl, A. F. Smith, C. J. DeSantis, and S. E. Skrabalak. Engineering plasmonic
metal colloids through composition and structural design. Chemical Society Reviews,
43(11):3823–3834, 2014.
[125] S. Mubeen, J. Lee, N. Singh, S. Kramer, G. D. Stucky, and M. Moskovits. An autonomous photosynthetic device in which all charge carriers derive from surface plasmons. Nature Nanotechnology, 8(4):247–251, 2013.
[126] M. Müller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer. Nanofocused
plasmon-driven sub-10 fs electron point source. ACS Photonics, 3(4):611–619, 2016.
[127] M. Müller, A. Paarmann, and R. Ernstorfer. Femtosecond electrons probing currents
and atomic structure in nanomaterials. Nature Communications, 5:5292, 2014.
[128] P. Narang, R. Sundararaman, and H. A. Atwater. Plasmonic hot carrier dynamics insolid-state and chemical systems for energy conversion. Nanophotonics, 5(1):96–111,
2016.

215
[129] P. Narang, R. Sundararaman, A. S. Jermyn, W. A. Goddard, and H. A. Atwater.
Cubic nonlinearity driven up-conversion in high-field plasmonic hot carrier systems.
Journal of Physical Chemistry C, 120(37):21056–21062, 2016.
[130] C. C. Neacsu, S. Berweger, R. L. Olmon, L. V. Saraf, C. Ropers, and M. B. Raschke.
Near-field localization in plasmonic superfocusing: A nanoemitter on a tip. Nano
Letters, 10(2):592–596, 2010.
[131] C. Ng, J. J. Cadusch, S. Dligatch, A. Roberts, T. J. Davis, P. Mulvaney, and D. E.
Gomez. Hot carrier extraction with plasmonic broadband absorbers. ACS Nano,
10(4):4704–4711, 2016.
[132] X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev. Ultra-thin, planar, babinetinverted plasmonic metalenses. Light-Science & Applications, 2, 2013.
[133] S. J. Oldenburg, R. D. Averitt, S. L. Westcott, and N. J. Halas. Nanoengineering of
optical resonances. Chemical Physics Letters, 288(2):243–247, 1998.
[134] C. Oubre and P. Nordlander. Optical properties of metallodielectric nanostructures calculated using the finite difference time domain method. Journal of Physical ChemistryB, 108(46):17740–17747, 2004.
[135] M. Pant and L. K. Ang. Ultrafast laser-induced electron emission from multiphoton
to optical tunneling. Physical Review B, 86(4), 2012.
[136] D. J. Park, B. Piglosiewicz, S. Schmidt, H. Kollmann, M. Mascheck, and C. Lienau.
Strong field acceleration and steering of ultrafast electron pulses from a sharp metallic
nanotip. Physical Review Letters, 109(24):244803, 2012.
[137] K. Park, L. F. Drummy, R. C. Wadams, H. Koerner, D. Nepal, L. Fabris, and R. A.
Vaia. Growth mechanism of gold nanorods. Chemistry of Materials, 25(4):555–563,
2013.
[138] C. Pellegrini, A. Marinelli, and S. Reiche. The physics of x-ray free-electron lasers.
Reviews of Modern Physics, 88(1):015006, 2016.
[139] M. Pelton, M. Z. Liu, S. Park, N. F. Scherer, and P. Guyot-Sionnest. Ultrafast resonant optical scattering from single gold nanorods: Large nonlinearities and plasmon
saturation. Physical Review B, 73(15), 2006.
[140] O. Pena and U. Pal. Scattering of electromagnetic radiation by a multilayered sphere.
Computer Physics Communications, 180(11):2348–2354, 2009.
[141] S. D. Perrault and W. C. W. Chan. Synthesis and surface modification of highly
monodispersed, spherical gold nanoparticles of 50-200 nm. Journal of the American
Chemical Society, 131(47):17042–17043, 2009.
[142] H. Petek. Photoexcitation of adsorbates on metal surfaces: One-step or three-step.
Journal of Chemical Physics, 137(9):091704, 2012.

216[143] H. Petek and S. Ogawa. Femtosecond time-resolved two-photon photoemission studiesof electron dynamics in metals. Progress in Surface Science, 56(4):239–310, 1997.
[144] J. Pettine, P. Choo, F. Medeghini, T. W. Odom, and D. J. Nesbitt. Plasmonic nanostar
photocathodes for optically-controlled directional currents. Nature Communications,
11:1367, 2020.
[145] J. Pettine, A. Grubisic, and D. J. Nesbitt. Angle- and momentum-resolved photoelectron velocity map imaging studies of thin Au film and single supported Au nanoshells.
Journal of Physical Chemistry C, 122(7):3970–3984, 2018.
[146] J. Pettine, A. Grubisic, and D. J. Nesbitt. Polarization-controlled directional multiphoton photoemission from hot spots on single Au nanoshells. Journal of Physical
Chemistry C, 122(26):14805–14813, 2018.
[147] J. Pettine, A. Marton Menendez, and D. J. Nesbitt. Continuous angular control overanisotropic photoemission from isotropic gold nanoshells. The Journal of Chemical
Physics, 153(10):101101, 2020.
[148] J. Pettine, S.M. Meyer, F. Medeghini, C. J. Murphy, and D. J. Nesbitt. Controlling
hot electron spatial and momentum distributions in nanoplasmonic systems: Volume
versus surface effects. arXiv:2007.07308, 2020.
[149] W. Pfeiffer, C. Kennerknecht, and M. Merschdorf. Electron dynamics in supported
metal nanoparticles: relaxation and charge transfer studied by time-resolved photoemission. Applied Physics a-Materials Science & Processing, 78(7):1011–1028, 2004.
[150] A. Polyakov, C. Senft, K. F. Thompson, J. Feng, S. Cabrini, P. J. Schuck, H. A.
Padmore, S. J. Peppernick, and W. P. Hess. Plasmon-enhanced photocathode forhigh brightness and high repetition rate x-ray sources. Physical Review Letters,
110(7):076802, 2013.
[151] E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander. A hybridization model for theplasmon response of complex nanostructures. Science, 302(5644):419–422, 2003.
[152] W. P. Putnam, R. G. Hobbs, P. D. Keathley, K. K. Berggren, and F. X. Kärtner.
Optical-field-controlled photoemission from plasmonic nanoparticles. Nature Physics,
13(4):335–339, 2017.
[153] P. Pyykko and J. P. Desclaux. Relativity and the periodic system of elements. Accountsof Chemical Research, 12(8):276–281, 1979.
[154] E. Quinonez, J. Handali, and B. Barwick. Femtosecond photoelectron point projection
microscope. Review of Scientific Instruments, 84(10), 2013.
[155] H. Raether. Surface-plasmons on smooth and rough surfaces and on gratings. Springer
Tracts in Modern Physics, 111, 1988.

217[156] T. Rangel, D. Kecik, P. E. Trevisanutto, G. M. Rignanese, H. Van Swygenhoven, and
V. Olevano. Band structure of gold from many-body perturbation theory. PhysicalReview B, 86(12):125125, 2012.
[157] A. R. Rastinehad, H. Anastos, E. Wajswol, J. S. Winoker, J. P. Sfakianos, S. K.
Doppalapudi, M. R. Carrick, C. J. Knauer, B. Taouli, S. C. Lewis, A. K. Tewari, J. A.
Schwartz, S. E. Canfield, A. K. George, J. L. West, and N. J. Halas. Gold nanoshelllocalized photothermal ablation of prostate tumors in a clinical pilot device study.
Proceedings of the National Academy of Sciences of the United States of America,
116(37):18590–18596, 2019.
[158] M. Reiser. Theory and Design of Charged Particle Beams. WILEY-VCH Verlag GmbH& Co. KGaA, Weinheim, 2008.
[159] R. H. Ritchie and J. C. Ashley. Interaction of hot electrons with a free electron gas.
Journal of Physics and Chemistry of Solids, 26(12):1689, 1965.
[160] H. Robatjazi, H. Q. Zhao, D. F. Swearer, N. J. Hogan, L. N. Zhou, A. Alabastri, M. J.
McClain, P. Nordlander, and N. J. Halas. Plasmon-induced selective carbon dioxide
conversion on earth-abundant aluminum-cuprous oxide antenna-reactor nanoparticles.
Nature Communications, 8, 2017.
[161] M. Rohmer, M. Bauer, T. Leissner, C. Schneider, A. Fischer, G. NiednerSchatteburg, B. von Issendorff, and M. Aeschlimann. Time-resolved photoelectron
nano-spectroscopy of individual silver particles: Perspectives and limitations. Physica
Status Solidi B: Basic Research, 247(5):1132–1138, 2010.
[162] C. Ropers, D. R. Solli, C. P. Schulz, C. Lienau, and T. Elsaesser. Localized multiphoton
emission of femtosecond electron pulses from metal nanotips. Physical Review Letters,
98(4):043907, 2007.
[163] E. Rotenberg and A. Bostwick. microARPES and nanoARPES at diffraction-limited
light sources: opportunities and performance gains. Journal of Synchrotron Radiation,
21:1048–1056, 2014.
[164] T. Rybka, M. Ludwig, M. F. Schmalz, V. Knittel, D. Brida, and A. Leitenstorfer.
Sub-cycle optical phase control of nanotunnelling in the single-electron regime. Nature
Photonics, 10(10):667–670, 2016.
[165] J. B. Sambur, T. Y. Chen, E. Choudhary, G. Q. Chen, E. J. Nissen, E. M. Thomas,
N. M. Zou, and P. Chen. Sub-particle reaction and photocurrent mapping to optimize
catalyst-modified photoanodes. Nature, 530:77–93, 2016.
[166] F. Schertz, M. Schmelzeisen, M. Kreiter, H. J. Elmers, and G. Schönhense. Field
emission of electrons generated by the near field of strongly coupled plasmons. PhysicalReview Letters, 108(23):237602, 2012.

218[167] A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Muhlbrandt,
M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz. Optical-field-induced current
in dielectrics. Nature, 493(7430):70–74, 2013.
[168] A. L. Schmucker, N. Harris, M. J. Banholzer, M. G. Blaber, K. D. Osberg, G. C. Schatz,
and C. A. Mirkin. Correlating nanorod structure with experimentally measured andtheoretically predicted surface plasmon resonance. ACS Nano, 4(9):5453–5463, 2010.
[169] G. Schonhense, K. Medjanik, S. Chernov, D. Kutnyakhov, O. Fedchenko, M. Ellguth,
D. Vasilyev, A. Zaporozhchenko-Zymakova, D. Panzer, A. Oelsner, C. Tusche,
B. Schonhense, J. Braun, J. Minar, H. Ebert, J. Viefhaus, W. Wurth, and H. J.
Elmers. Spin-filtered time-of-flight k-space microscopy of Ir - towards the “complete”
photoemission experiment. Ultramicroscopy, 183:19–29, 2017.
[170] B. Schröder, M. Sivis, R. Bormann, S. Schäfer, and C. Ropers. An ultrafast nanotip
electron gun triggered by grating-coupled surface plasmons. Applied Physics Letters,
107(23):231105, 2015.
[171] V. Schweikhard, A. Grubisic, T. A. Baker, and D. J. Nesbitt. Multiphoton scanning photoionization imaging microscopy for single-particle studies of plasmonic metalnanostructures. Journal of Physical Chemistry C, 115(1):83–91, 2011.
[172] V. Schweikhard, A. Grubisic, T. A. Baker, I. Thomann, and D. J. Nesbitt. Polarizationdependent scanning photoionization microscopy: Ultrafast plasmon-mediated electron
ejection dynamics in single Au nanorods. ACS Nano, 5(5):3724–3735, 2011.
[173] K. Sengupta, T. Nagatsuma, and D. M. Mittleman. Terahertz integrated electronicand hybrid electronic-photonic systems. Nature Electronics, 1(12):622–635, 2018.
[174] M. Sivis, N. Pazos-Perez, R. W. Yu, R. Alvarez-Puebla, F. J. Garcı́a de Abajo, and
C. Ropers. Continuous-wave multiphoton photoemission from plasmonic nanostars.
Communications Physics, 1, 2018.
[175] N. V. Smith. Photoemission spectra and band structures of d-band metals 3 - modelband calculations on Rh, Pd, Ag, Ir, Pt, and Au. Physical Review B, 9(4):1365–1376,
1974.
[176] M. I. Stockman. Nanoplasmonics: past, present, and glimpse into future. Optics
Express, 19(22):22029–22106, 2011.
[177] J.A. Stratton. Electromagnetic Theory. International Series in Physics. McGraw-Hill,
Inc., New York, London, 1st edition, 1941.
[178] A.G. Suits and R.E. Continetti. Imaging in Chemical Dynamics. ACS Symposium Series. American Chemical Society: Distributed by Oxford University Press, Washington,
DC, 2001.

219[179] D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B.
Norris. Coherent control of ballistic photocurrents in multilayer epitaxial grapheneusing quantum interference. Nano Letters, 10(4):1293–1296, 2010.
[180] Q. Sun, H. Yu, K. Ueno, A. Kubo, Y. Matsuo, and H. Misawa. Dissecting the fewfemtosecond dephasing time of dipole and quadrupole modes in gold nanoparticles
using polarized photoemission electron microscopy. ACS Nano, 10(3):3835–3842, 2016.
[181] F. Sussmann, L. Seiffert, S. Zherebtsov, V. Mondes, J. Stierle, M. Arbeiter, J. Plenge,
P. Rupp, C. Peltz, A. Kessel, S. A. Trushin, B. Ahn, D. Kim, C. Graf, E. Rühl, M. F.
Kling, and T. Fennel. Field propagation-induced directionality of carrier-envelope
phase-controlled photoemission from nanospheres. Nature Communications, 6:7944,
2015.
[182] D. F. Swearer, R. K. Leary, R. Newell, S. Yazdi, H. Robatjazi, Y. Zhang, D. Renard,
P. Nordlander, P. A. Midgley, N. J. Halas, and E. Ringe. Transition-metal decorated
aluminum nanocrystals. ACS Nano, 11(10):10281–10288, 2017.
[183] J. Szczerbinski, L. Gyr, J. Kaeslin, and R. Zenobi. Plasmon-driven photocatalysis leads
to products known from e-beam and x-ray-induced surface chemistry. Nano Letters,
18(11):6740–6749, 2018.
[184] N. Takeyasu, K. Yamaguchi, R. Kagawa, T. Kaneta, F. Benz, M. Fujii, and J. J.
Baumberg. Blocking hot electron emission by SiO2 coating plasmonic nanostructures.
Journal of Physical Chemistry C, 121(34):18795–18799, 2017.
[185] C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane,
T. R. Huser, P. Nordlander, and N. J. Halas. Surface-enhanced Raman scatteringfrom individual Au nanoparticles and nanoparticle dimer substrates. Nano Letters,
5(8):1569–1574, 2005.
[186] I. Tamm and S. Schubin. On the theory of the photoelectric effect in metals. Zeitschrift
Fur Physik, 68(1-2):97–113, 1931.
[187] M. Tanzid, A. Ahmadivand, R. M. Zhang, B. Cerjan, A. Sobhani, S. Yazdi, P. Nordlander, and N. J. Halas. Combining plasmonic hot carrier generation with free carrier absorption for high-performance near-infrared silicon-based photodetection. ACS
Photonics, 5(9):3472–3477, 2018.
[188] R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A.
Richman, and D. J. Kane. Measuring ultrashort laser pulses in the time-frequency
domain using frequency-resolved optical gating. Review of Scientific Instruments,
68(9):3277–3295, 1997.
[189] A. V. Uskov, I. E. Protsenko, R. S. Ikhsanov, V. E. Babicheva, S. V. Zhukovsky,
A. V. Lavrinenko, E. P. O’Reilly, and H. X. Xu. Internal photoemission from plasmonic nanoparticles: Comparison between surface and volume photoelectric effects.
Nanoscale, 6(9):4716–4727, 2014.

220[190] L. Vigderman and E. R. Zubarev. High-yield synthesis of gold nanorods with longitudinal spr peak greater than 1200 nm using hydroquinone as a reducing agent. Chemistryof Materials, 25(8):1450–1457, 2013.
[191] S. Vogelgesang, G. Storeck, J. G. Horstmann, T. Diekmann, M. Sivis, S. Schramm,
K. Rossnagel, S. Schäfer, and C. Ropers. Phase ordering of charge density waves traced
by ultrafast low-energy electron diffraction. Nature Physics, 14:184–191, 2017.
[192] J. Vogelsang, J. Robin, B. J. Nagy, P. Dombi, D. Rosenkranz, M. Schiek, P. Groß,and C. Lienau. Ultrafast electron emission from a sharp metal nanotaper driven by
adiabatic nanofocusing of surface plasmons. Nano Letters, 15(7):4685–4691, 2015.
[193] A. Vredenborg, W. G. Roeterdink, and M. H. M. Janssen. A photoelectron-photoion
coincidence imaging apparatus for femtosecond time-resolved molecular dynamics withelectron time-of-flight resolution of σ =18 ps and energy resolution δE/E =3.5%. Rev.
Sci. Instrum., 79(6):063108, 2008.
[194] D. Q. Wang, A. K. Yang, W. J. Wang, Y. Hua, R. D. Schaller, G. C. Schatz, and T. W.
Odom. Band-edge engineering for controlled multi-modal nanolasing in plasmonicsuperlattices. Nature Nanotechnology, 12(9):889–895, 2017.
[195] J. Z. Wang, K. Yu, Y. Yang, G. V. Hartland, J. E. Sader, and G. P. Wang. Strong vibrational coupling in room temperature plasmonic resonators. Nature Communications,10, 2019.
[196] B. Wannberg. Electron optics development for photo-electron spectrometers. Nuclear
Instruments and Methods in Physics Research Section A, 601(1-2):182–194, 2009.
[197] B.J. Whitaker. Imaging in Molecular Dynamics: Technology and Applications. Cambridge University Press, Cambridge ; New York, 2003.
[198] J. L. White, M. F. Baruch, J. E. Pander, Y. Hu, I. C. Fortmeyer, J. E. Park, T. Zhang,
K. Liao, J. Gu, Y. Yan, T. W. Shaw, E. Abelev, and A. B. Bocarsly. Light-driven heterogeneous reduction of carbon dioxide: Photocatalysts and photoelectrodes. Chemical
Reviews, 115(23):12888–12935, 2015.
[199] K. A. Willets. Super-resolution imaging of SERS hot spots. Chemical Society Reviews,
43(11):3854–3864, 2014.
[200] D. M. Wood. Classical size dependence of the work function of small metallic spheres.
Physical Review Letters, 46(11):749–749, 1981.
[201] B. H. Wu, D. Y. Liu, S. Mubeen, T. T. Chuong, M. Moskovits, and G. D. Stucky.
Anisotropic growth of TiO2 onto gold nanorods for plasmon-enhanced hydrogen production from water reduction. Journal of the American Chemical Society, 138(4):1114–
1117, 2016.

221[202] K. Wu, J. Chen, J. R. McBride, and T. Lian. Efficient hot-electron transfer by aplasmon-induced interfacial charge-transfer transition. Science, 349(6248):632–635,
2015.
[203] S. V. Yalunin, M. Gulde, and C. Ropers. Strong-field photoemission from surfaces:
Theoretical approaches. Physical Review B, 84(19):195426, 2011.
[204] H. Yanagisawa, C. Hafner, P. Doná, M. Klöckner, D. Leuenberger, T. Greber, J. Osterwalder, and M. Hengsberger. Laser-induced field emission from a tungsten tip: Opticalcontrol of emission sites and the emission process. Physical Review B, 81(11):115429,
2010.
[205] W. H. Yang, G. C. Schatz, and R. P. Van Duyne. Discrete dipole approximation for
calculating extinction and Raman intensities for small particles with arbitrary shapes.
Journal of Chemical Physics, 103(3):869–875, 1995.
[206] Y. J. Yang, M. Turchetti, P. Vasireddy, W. P. Putnam, O. Karnbach, A. Nardi, F. X.
Kartner, K. K. Berggren, and P. D. Keathley. Light phase detection with on-chippetahertz electronic networks. Nature Communications, 11(1), 2020.
[207] H. Ye, S. Trippel, M. Di Fraia, A. Fallahi, O.D. Mücke, F.X. Kärtner, and J. Küpper.
Velocity-map imaging for emittance characterization of multiphoton electron emission
from a gold surface. Physical Review Applied, page arXiv:1707.06472 [Physics], 2018.
[208] G. L. Yudin and M. Y. Ivanov. Nonadiabatic tunnel ionization: Looking inside a laser
cycle. Physical Review A, 64(1), 2001.
[209] M. Zavelani-Rossi, D. Polli, S. Kochtcheev, A. L. Baudrion, J. Beal, V. Kumar,
E. Molotokaite, M. Marangoni, S. Longhi, G. Cerullo, P. M. Adam, and G. Della Valle.
Transient optical response of a single gold nanoantenna: The role of plasmon detuning.
ACS Photonics, 2(4):521–529, 2015.
[210] Y. S. Zeng, S. W. Qu, B. J. Chen, and C. H. Chan. All-plasmonic optical phased array
integrated on a thin-film platform. Scientific Reports, 7, 2017.
[211] A. H. Zewail. 4D ultrafast electron diffraction, crystallography, and microscopy. Annual
Review of Physical Chemistry, 57:65–103, 2006.
[212] P. Zhang, T. Wang, and J. L. Gong. Mechanistic understanding of the plasmonicenhancement for solar water splitting. Advanced Materials, 27(36):5328–5342, 2015.
[213] X. Zhang, X. Q. Li, D. Zhang, N. Q. Su, W. T. Yang, H. O. Everitt, and J. Liu. Product selectivity in plasmonic photocatalysis for carbon dioxide hydrogenation. Nature
Communications, 8:1–9, 2017.
[214] Y. C. Zhang, S. He, W. X. Guo, Y. Hu, J. W. Huang, J. R. Mulcahy, and W. D. Wei.
Surface-plasmon-driven hot electron photochemistry. Chemical Reviews, 118(6):2927–
2954, 2018.

222[215] Y. J. Zhang, O. Pluchery, L. Caillard, A. F. Lamic-Humblot, S. Casale, Y. J. Chaba,and M. Salmeron. Sensing the charge state of single gold nanoparticles via work
function measurements. Nano Letters, 15(1):51–55, 2015.
[216] B. Y. Zheng, H. Q. Zhao, A. Manjavacas, M. McClain, P. Nordlander, and N. J.
Halas. Distinguishing between plasmon-induced and photoexcited carriers in a device
geometry. Nature Communications, 6, 2015.
[217] S. Zhou, K. Chen, M. T. Cole, Z. Li, J. Chen, C. Li, and Q. Dai. Ultrafast field-emission
electron sources based on nanomaterials. Adv Mater, page e1805845, 2019.
[218] V. P. Zhukov and E. V. Chulkov. The femtosecond dynamics of electrons in metals.
Physics-Uspekhi, 52(2):105–136, 2009.
[219] P. Zimmermann, A. Hötger, N. Fernandez, A. Nolinder, K. Müller, J. J. Finley, andA. W. Holleitner. Toward plasmonic tunnel gaps for nanoscale photoemission currents
by on-chip laser ablation. Nano Letters, 19(2):1172–1178, 2019.

Appendix A
Laser Shutter and Piezo Driver Circuit Diagrams

224

225

ND052.sch-1 - Mon Sep 14 10:50:57 2020