Spectroscopy of Electronic States in Organic and Nano-Crystalline Materials Under High
PressurebyJ. Curtis Beimborn II
B.S. Western Carolina University

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 Chemistry
2020
Committee Members:
J. Mathias Weber
Niels Damrauer
Gordana Dukovic
Joel Eaves
Robert Parson
Heather Lewandowski

Beimborn II, J. Curtis (Ph.D., Chemistry, Department of Chemistry)
Spectroscopy of Electronic States in Organic and Nano-Crystalline Materials Under High Pressure
Thesis directed by Professor J. Mathias Weber

Abstract
Semiconductor nanocrystals and organic semiconductors have the potential torevolutionize optoelectronic devices. Both classes of materials have been used in photovoltaic anddisplay technologies and are promising candidates to improve both of these sectors. From aphysical chemistry point of view, they are also intriguing systems to study in order to gain insight
into the fundamental physics of how light interacts with semiconducting materials. Knowledge of
how their crystalline structure and electronic properties are coupled is important from both
fundamental and application perspectives.
This thesis presents the work I have completed on the pressure-response of both inorganic
semiconductor nanocrystals and organic semiconductors using multiple high-pressure generating
apparatus. After a description of the experimental procedures, two chapters focus on the pressureinduced photoluminescence (PL) spectral shifts in perovskite nanocrystals. The PL spectra areused to probe changes in the optical band gap of the perovskites as a function of pressure. The
differences between the behavior of the perovskites CsPbBr3 and CsPbI3 can be traced todifferences in the crystal structure due to the ionic radii of iodide versus bromide. Studies on thesize-dependent pressure-response of CsPbBr3 nanocrystals show that the pressure-induced shift ofspectral features may depend on the degree of quantum confinement in various sizes ofnanocrystals.

ii

The final chapter focuses on an organic semiconductor, rubrene. Rubrene is a material thatpossesses the ability to convert low energy photons into higher energy photons through a process
called triplet-triplet annihilation (TTA) upconversion. Organic upconverting materials generally
require a partner molecule which absorbs the lower energy light (sensitizer). The work in this thesis
on rubrene shows that rubrene ions trapped in the crystal can act as the sensitizing species,
therefore allowing upconversion without an added sensitizer. The TTA process happens throughintermolecular coupling of neighboring molecules, so it should be sensitive to the crystalline
structure. Our results show that the upconversion PL and intrinsic PL in rubrene are quenched byapplied pressure, due to changes in the intermolecular coupling.

iii

For Hannahiv

Acknowledgements
First and foremost, I want to acknowledge and thank my advisor, Professor J. Mathias
Weber. While visiting my family here in Colorado during a spring break in undergrad, roughly
two years before coming to graduate school at CU Boulder, Mathias was kind enough to take thetime to show me around his labs as well as the rest of JILA. This experience solidified my desire
to go to graduate school, and I could not be happier that I was able to complete my PhD in
Mathias’s group. Mathias is not only a brilliant scientist, but he is also an effective group manager.
This is not something to be taken for granted, and I believe our group’s productivity and good
morale are direct results of Mathias’s thoughtful management style. I am excited to continue myfriendship and professional relationship with Mathias as I step into my new role as a professional
research assistant here at JILA.
I have been very fortunate to work with a great group of people here in the Weber group. I
consider everyone who has passed through JILA’s doors during my time here not only as
colleagues, but friends. Michael Thompson and “Xavier” Shuang Xu were here when I first joined
the group and they were very helpful keeping my spirits up during the first few difficult years ofgraduate school. Wyatt Zagorec-Marks joined the group a few years after I did, and has made theselast few years very fun. I really enjoyed working with Wyatt on our publication on rubrene andenjoyed skiing with him on the weekends even more. Our post-doc Leah Dodson and her husband
Thinh have also become close friends of my wife and I, and I thank Leah for all of the careeradvice she has given over the years. I also would like to thank Madison and Rebecca for listening
to me talk about my research and offer new ideas for me to think about. Kenny Wilson and Luke
Walther were undergraduate researchers working with me on my perovskite projects and helpedvimmensely, and for that, I cannot thank them enough. They are both excellent students and evenbetter people and I cannot wait to see what they will do with their futures. Finally, none of thework done in the Weber group would be possible without our funding sources. My work was
specifically funded by the National Science Foundation through the JILA AMO Physics FrontierCenter and the Donors of the American Chemical Society Petroleum Research Fund.
Working in JILA is unlike anywhere else, and the credit for that goes to the JILA staff. As
the first graduate student working on my project, a lot of it had to be built from the ground up andthat would not have been possible without the expertise found in the JILA shops. Over my timehere in JILA, nearly all the staff members have helped me in one way or another, but I must thanksome of them individually for their support of my work. Dave Alchenberger and Mark Carter inthe Keck metrology lab were always able to help me trouble shoot and solve technical problems
related to material properties. Dave also trained me on many of the instruments I used to take data
for this thesis, so I owe him many thanks. Hans Green, James Urich, Kyle Thatcher, Calvin
Schwadron, Todd Asnicar, and Adam Elzey have all invested a lot of time in teaching me newtechniques in the instrument shop and each of them were always there to bounce ideas off of while
I was designing new instrumentation for my experiments. Finally, data cannot be processed oranalyzed without working computers. For that reason, I would like to thank J.R. Raith keeping all
the computers in my lab running smoothly and helping me trouble shoot issues when they arouse.
The Dukovic group here at the University of Colorado also deserves acknowledgement for
their contributions to my work. Before I had access to any powder XRD instruments to analyze
nanocrystal samples, Leah Hall and Pornthip Tongying in the Dukovic group generously took thetime to collect that data for me at the National Renewable Energy Laboratory. Other members ofvi

the Dukovic group were great conversation partners on all things nanoscience, which helped me
grow in my understanding of this field
I would also like to thank two of my undergraduate professors, Scott Huffman and David
Evanoff. Their mentorship during those formative years helped me become the scientist I am
today.
Next, I must acknowledge my family for always being there for me. I am grateful for myparents, James and Gynine Beimborn, I certainly could not have done this without them. They
raised me to persevere through difficult times and instilled in me the interest in science from ayoung age. I would also like to thank my sister Korina for all the support she has given to me. My
grandparents, Nonna, Grandpa, Omi, and Opi have given me much needed moral support
throughout my graduate career.
Finally, and most importantly, I would like to thank my wife, Hannah. She has been an
unwavering source of support and encouragement. She has been there for me through all the
struggles, exhaustion, and late nights collecting data in the lab, while making sure I was keeping
myself happy and healthy. She was able to do all of this while getting a Master’s degree in Speechand Language Pathology, and later on, raising our daughter Iris as the best mom the world has everseen. Hannah, I am so blessed to have you as my life-long best friend and partner.

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Contents

Chapter 1

Introduction ........................................................................................................... 1

1.1

Motivation and Scope ......................................................................................................... 1

1.2

References ........................................................................................................................... 3

Chapter 2

Experimental Methods ......................................................................................... 5

2.1

Overview ............................................................................................................................. 5

2.2

Diamond Anvil Cell ............................................................................................................ 5

2.3

Hydraulic Pressure Generator ............................................................................................. 9

2.4

Upconversion Photoluminescence Spectroscopy ............................................................. 12

2.4.1

Upconversion Photoluminescence Excitation Spectra.............................................. 13

2.4.2

Temperature Dependence of UCPL and PL ............................................................. 15

2.4.3

High-Pressure Upconversion Photoluminescence Excitation Spectra ...................... 16

2.4.4

Pressure-Response of Photoluminescence and Upconversion Photoluminescence.. 17

2.5

Transmission Electron Microscopy .................................................................................. 18

2.6

Powder X-Ray Diffraction ................................................................................................ 18

2.7

References ......................................................................................................................... 19

Chapter 3

Probing the Pressure-Response of Cesium Lead Halide Perovskite

Nanocrystals with Photoluminescence Spectroscopy .............................................................. 20
3.2

Introduction ....................................................................................................................... 20

3.3

Nanocrystal Synthesis ....................................................................................................... 22viii

3.3.1

CsPbI3 Nanocrystal Synthesis via Hot Injection ....................................................... 23

3.3.2

CsPbBr3 Nanocrystal Synthesis ................................................................................ 28

3.3.3

CsPbX3 Nanocrystal Synthesis via Sonication ......................................................... 32

3.4

Photoluminescence Response of CsPbX3 Nanocrystals Under Pressure .......................... 37

3.4.1

Ambient Pressure Phase of CsPbI3 Nanocrystals ...................................................... 38

3.4.2

Pressure Response of CsPbI3 Nanocrystals .............................................................. 39

3.4.3

Pressure Response of CsPbBr3 Nanocrystals............................................................ 41

3.4.4

Pressure-Response of NCs Made from Sonication ................................................... 42

3.5

Pressure-Response Mechanism ......................................................................................... 45

3.6

Conclusions ....................................................................................................................... 47

3.7

References ......................................................................................................................... 48

Chapter 4

Size-Dependence of the Pressure-Response of CsPbBr3 Nanocrystals .......... 56

4.1

Introduction ....................................................................................................................... 56

4.2

CsPbBr3 Nanocrystal Synthesis ........................................................................................ 58

4.2.1

CsPbBr3 Nanocrystal Characterization ..................................................................... 60

4.3

PL Pressure-Response of CsPbBr3 Nanocrystal Samples ................................................. 66

4.4

Conclusion ........................................................................................................................ 72

4.5

References ......................................................................................................................... 73

Chapter 5

Pressure Response of Rubrene Upconversion Photoluminescence ThroughCation and Anion Sensitized Triplet-Triplet Annihilation ..................................................... 82
5.1

Introduction ....................................................................................................................... 82

5.2

Rubrene Crystal Preparation ............................................................................................. 84

5.2.1

Characterization of Rubrene Crystals ....................................................................... 86

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5.3

Upconversion Photoluminescence in Rubrene ................................................................. 88

5.4

Pressure-Response of the Intermediate State .................................................................. 100

5.5

Pressure Quenching of Photoluminescence and Upconversion Photoluminescence ...... 101

5.6

Conclusion ...................................................................................................................... 104

5.7

References ....................................................................................................................... 105

Bibliography…………………………………………………………………………………...112
Appendix…………………………………………………………………………………...…..126x

Tables

Table 5.1: Parameters used in the kinetic model .......................................................................... 98xiFigures

Figure 2.1: (A) cross section of the gas membrane driven diamond anvil cell. Pressurized N2 isconnected to the gas membrane through stainless-steel tubing. As the membrane expands, itapplies pressure to the two diamonds. (B) 3D cross sectional rendering of the diamonds andthe stainless-steel gasket. The sample compartment is illustrated here filled with a green
liquid and a ruby grain for pressure measurement. The laser beam shows the optical access
we have to the sample compartment. (C) Top view of the gas membrane driven diamondanvil cell (diamond top surface shown in blue at the center) showing the three bolts used topre-indent the gaskets and the three positions where the indentation measurements weretaken. ....................................................................................................................................... 6
Figure 2.2: Ruby spectrum with Lorentzian fits of the R1 and R2 peaks for pressure
determination. ......................................................................................................................... 8
Figure 2.3: A simplified schematic of the hydraulic high-pressure generating apparatus. Inset
shows a microscope image of the end of a capillary. The end has been fused closed, andthere is a small air gap within the capillary between the sample fluid and the end. ............. 10
Figure 2.4: (A) A high-pressure plug as purchased (HIP, 100-7XM4) (top) and the modified
high-pressure plug (bottom). (B) The modified high-pressure plug with a capillary epoxied
into it. (C) Capillary showing the full length with high-pressure plug and the window where
the polyimide coating had been removed. ............................................................................ 11
Figure 2.5: Upconversion photoluminescence excitation (UCPLE) spectroscopy setup. ............ 14xii

Figure 2.6: Image of the quartz cuvette in the vacuum chamber. The cuvette could be filled fromthe outside with liquid nitrogen to cool mounted rubrene crystals. The orange vertical line
visible on the outside of the cuvette is a rubrene crystal. ..................................................... 15
Figure 2.7: Setup for collecting UCPLE spectra under pressure in the DAC............................... 16
Figure 2.8: Setup for collection photoluminescence (406 nm excitation) and upconversion
photoluminescence (NIR excitation) spectra under pressure................................................ 18
Figure 3.1: The g-phase perovskite crystal structure, where X is either bromide or iodide anions.
The g-phase crystal structure differs from the a-phase by having Pb-X-Pb angles less than
180°. ...................................................................................................................................... 21
Figure 3.2: Visible absorption (solid) and PL (dashed) spectra of CsPbI3 NCs in hexanes,
prepared using hot injection. ................................................................................................. 24
Figure 3.3: CsPbI3 NC sample size distribution histogram (a) and reference TEM image (b). The
scale bar represents 100 nm. The NCs were synthesized using hot injection....................... 25
Figure 3.4: (a) XRD pattern of CsPbI3 NCs prepared using hot injection. The light gray points are
raw data, the solid red line is a 20-point sliding average. The magenta lines are the expecteddiffraction angles from the orthorhombic perovskite phase, and the blue lines are theexpected diffraction angles for the cubic phase.21 The peak labeled with a * is from left overPbI2 from the synthesis procedure. The peaks labeled with miller indices correspond toreflections from the crystal planes indicated in (b). Sample HRTEM image of a CsPbI3 NC
and its Fourier transform, together with markers of the (020) and (220) planes (b). ........... 27
Figure 3.5: PL of CsPbBr3 NCs in hexanes with 10.9 ± 1.2 nm edge length, prepared by hot
injection................................................................................................................................. 30

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Figure 3.6: Size statistics of the CsPbBr3 NCs prepared using hot injection, with typical TEM
image of the NCs (inset). The scale bar is 20 nm. ................................................................ 31
Figure 3.7: Powder XRD pattern of the CsPbBr3 NCs made with hot injection. The red lines are
the expected pattern for the orthorhombic perovskite structure while the purple lines are theexpected pattern for the cubic perovskite structure. ............................................................. 32
Figure 3.8: Visible absorption (solid) and PL (dashed) of CsPbBr3 (A) and CsPbI3 (B) NCs
prepared using sonication. All spectra are scaled independently. ........................................ 34
Figure 3.9: Particle size distributions for CsPbBr3 (a) and CsPbI3 (b) prepared using sonication.
The scale bars are 100 nm. .................................................................................................... 35
Figure 3.10: HRTEM image of a CsPbBr3 NC prepared using sonication (A) and CsPbI3 NC (B)with lattice spacing. Scale bars are 1 nm. ............................................................................. 37
Figure 3.11: PL spectra of CsPbI3 NCs at different pressures (right). All spectra are scaled to thesame intensity. The ruby fluorescence peaks around 694 nm were deleted from the spectra
for clarity (break in the spectra). The bottom and top traces show the PL spectra at ambientpressure before and after the pressure run. ........................................................................... 40
Figure 3.12: Pressure dependence of PL for CsPbI3 nanocrystals. The band gap energy change isplotted as the deviation of the PL peak at a given pressure from the ambient peak position.
(a) Pressure range below 0.7 GPa. Data points from the hydraulic pressure generator (opensquares) and data taken using the DAC (open circles) from several runs from each setup areshown. The grey lines indicate linear fits of the data in the two regions shown in this panel.
The point at which they cross indicates the pressure where the pressure response changes.
(b) Overview of the entire pressure range up to 2.5 GPa, after which PL was no longer
detected. Data from both the hydraulic pressure generator and the DAC are plotted together,xivand the data were obtained from several pressure runs. Error bars for the PL peak energychange are ±1 meV. .............................................................................................................. 41
Figure 3.13: Pressure dependence of the PL peak for CsPbBr3 nanocrystals. Different symbols
correspond to different pressure runs. Data shown as filled symbols were acquired in the
DAC setup, while data shown as open symbols were taken on the hydraulic setup. No PL
was observed beyond 2.0 GPa. Error bars for PL energy and for pressure in the hydraulicdata sets are smaller than the symbol size. Note that the lowest PL peak energies are slightly
different for runs from different synthetic batches, but the phase change pressure remains
the same. ............................................................................................................................... 42
Figure 3.14: Pressure response of CsPbI3 (A) and CsPbBr3 (B) nanocrystals synthesized with by
the sonication method. The open square data was taken with the hydraulic high-pressure
generator, while the solid squares were taken with the diamond anvil cell. ......................... 44
Figure 3.15: (A) Molecular orbitals generating the VBM. (B) Molecular orbitals generating theCBM (C) Tilting of the octahedra increases the dihedral angle q. ....................................... 46
Figure 4.1: PL spectra of NC size fractions in paraffin oil at ambient pressure. Difference in PL
full width half maximum (FWHM) are due to shorter lifetimes for smaller NCs, not fromsize distributions. .................................................................................................................. 61
Figure 4.2: Size distributions and characteristic sample TEM images of all the NC samples
studied. Each size distribution was obtained by determining the sizes of 150 NCs. ............ 62
Figure 4.3: XRD Analysis of all nanocrystal samples used in our experiments. Part (A) shows
simulations for cubic and orthorhombic structures as a semi-logarithmic plot to accentuate
the low-intensity reflections. The red lines represent the orthorhombic perovskite pattern48
and the violet lines are for the cubic perovskite crystal structure.49 Part (B) shows axv

comparison of experimental XRD data with the simulated patterns (linear scale). Peaks
marked with an asterisk (appearing in some of the samples, most clearly for 5.7 nm and 6.7
nm edge length) are due to residual precursor material. ....................................................... 65
Figure 4.4: PL pressure response of NC samples studied in the present work. Open circles are
raw data coming from at least two high pressure runs for each size, and black squares are
the mean ΔE binned in pressure intervals of 0.2 GPa. The transition pressure is marked withvertical dotted lines with the uncertainty shaded in gray. The uncertainty in pressure foreach data point is ±75 MPa. .................................................................................................. 68
Figure 4.5: The transition pressure at which the PL turns from a red shift to a blue shift as afunction of NC size. This is compared to the transition pressure in bulk CsPbBr3 (dottedline) and the corresponding value reported in Xiao et al.28 for 11.9 nm CsPbBr3 NCs (dashdotted line). ........................................................................................................................... 69
Figure 4.6: The magnitude of the initial pressure coefficient decreases as NC size increases. The
dotted line represents the bulk pressure coefficient reported in Zhang et al.67..................... 71
Figure 4.7: (A) Large NC showing exciton wave function within the bulk of the crystal, which
produces lower coupling to surface states. (B) Small NC showing exciton wavefunction
extending to the surface of the NC, which enhances the coupling to surface states............. 72
Figure 5.1: Rubrene (5,6,11,12-tetraphenyltetracene) molecular structure. ................................. 84
Figure 5.2: Microscope image of a rubrene crystal grown with PVT. ......................................... 86
Figure 5.3: UV-vis absorption of a rubrene crystal grown from PVT. The oscillations on thebaseline beyond 550 nm are interference fringes from an etalon effect between the first andsecond surfaces of the crystal. .............................................................................................. 87xvi

Figure 5.4: Powder XRD of rubrene samples. (A) calculated XRD pattern for triclinic rubrene,(B) calculated XRD pattern for orthorhombic rubrene, (C) crystals grown using PVT, and(D) rubrene powder. Intensity axes are on a logarithmic scale in order to see both the low
and high intensity peaks. ....................................................................................................... 88
Figure 5.5: Bottom panel: solution absorption spectra of the rubrene radical cation (orange line)
and radical anion (blue line); data in the lower panel were adapted from Tagawa and coworkers.42 Top panel: UCPLE spectrum of crystalline rubrene, corrected for a four-photon
process by dividing the raw UCPL intensity by the fluence to the fourth power. The open
circles are individual data points, the black trace is a 20-point-smoothed curve to guide theeye. The red line is the arithmetic product of the absorption spectra of the radical ionsshown in the lower panel. ..................................................................................................... 91
Figure 5.6: Dependence of the UCPL signal intensity on the excitation laser intensity at three
excitation wavelengths. Signals were scaled to compare results from multiple samples.
Open circles are raw data, the blue line is a fit of the laser intensity dependence to theexperimental data. Laser excitation wavelength was set to 769 nm (A), 821 nm (B), and 890
nm (C) to be resonant with the observed transitions in the UCPLE spectrum. The exponents
from the fit of the data are 4.16 ± 0.20 for 769 nm, 4.16 ± 0.22 for 821 nm, and 3.73 ± 0.30
for 890 nm excitation. ........................................................................................................... 93
Figure 5.7: UCPLE spectrum of rubrene powder as received from Sigma Aldrich. Raw data
points are plotted as open circles. The black trace is a 50-point-smoothed curve to guide theeye. ........................................................................................................................................ 94
Figure 5.8: (A) Qualitative reaction diagram showing the recombination of electrons and holes in
the proposed mechanism of UCPL from the excitation of trapped electrons (left) and holesxvii(right) through relaxation processes in the crystal to the generation of a triplet exciton(center). (B) Schematic electron configurations in the reaction mechanism. Ground andexcited state electron configurations of rubrene ions have been determined using TDDFT(see Supporting Information). ............................................................................................... 96
Figure 5.9: Bleaching of UCPL under constant irradiation of 765 nm pulsed radiation operating
at 20 Hz and an average power of 50 mW/cm2. The red dashed line guides the eye to theslow decay of intensity over the course of hours. The vertical blue dashed lines indicate
when the laser was blocked from irradiating the sample. ..................................................... 99
Figure 5.10: UCPLE spectra of rubrene crystals in the DAC. Spectra were recorded at ambient(red data points) and 1.65 GPa (blue data points). The red and blue traces are 300-pointsmoothed curves to guide the eye. ...................................................................................... 100
Figure 5.11: UCPL (purple) and PL (red) quenching under pressure. The relatively large error
bars on the UCPL data come fluctuations in the intensity of the output of the OPO, which
has a large effect on the UCPL, due to the quartic dependence. ........................................ 101
Figure 5.12: Schematic drawing of two rubrene molecules in an orthorhombic crystal. The
molecule on the left shows the p-orbitals of the LUMO, while the molecule on the rightshows the p-orbitals of the HOMO. Decreasing the distance between neighboring molecules
enhances the orbital overlap, increasing the intermolecular electronic coupling. .............. 103

xviii

Chapter 1

1.1

Introduction

Motivation and Scope
Almost every aspect of our modern society is influenced in one way or another byelectronic devices, which rely on the unique properties of semiconductor materials to function.
These unique properties are what allow us to surf the internet on our computers, they produce thebright colors on our cell phone screens, and, very importantly at this point in our history, they canharness the massive amounts of energy that the Earth receives every second from the Sun.
The specific properties of semiconductors that are center stage in this thesis are those
governing how semiconductors absorb and emit light. In general, when light with sufficient energy
impinges on a semiconductor, it can excite an electron across the band gap of the material, leaving
behind a positively charged hole. There are many possible fates for the excited electron and hole,
but there are two that are the most useful. First, the electron and hole can be separated and sent
through a circuit to do work. This is the case for photovoltaics, and there is a massive amount ofwork being done to make this process as efficient as possible. Semiconductor materials with uniqueproperties, some of which are discussed in detail in the following chapters, have the potential to
improve solar cell efficiency. This work is paramount to slow the warming of our planet due to therelease of greenhouse gases into our atmosphere from the burning of fossil fuels. The second fateof the electron and hole we are interested in is when they recombine, reemitting a photon in aprocess called photoluminescence. Studying the photoluminescence of materials has direct
application in light emitting devices such as light emitting diodes. The only difference is that thesedevices use electric current to bring electrons into the conduction band, rather than exciting theelectrons with light.
1

When the physical dimensions of semiconductor crystal are brought down to the nanometerscale, i.e. in a nanocrystal, the electron-hole pair can begin to experience quantum confinement.
This happens when the diameter of the nanocrystal is nearly the same size, or smaller than the
Bohr radius of the bound electron-hole pair, called an exciton. When this happens, the nanocrystals
can be called “quantum dots” and begin to behave less like their bulk sized counterparts, and more
like the hypothetical “particle in a box” taught in every introductory quantum mechanics course.1
Instead of displaying band-like electronic structure like macroscopic solids, they have discreteenergy states. The separation of these energy states is inversely proportional to the square of thequantum dot size. If the quantum dots are photoluminescent, their spectra blue-shift as the size
decreases. Quantum dots are interesting to study from a fundamental perspective due to theirunique quantum behavior, but also have important applications in the fields discussed above.
Organic semiconductors are class of semiconductor materials made from polymers or
crystals where each site is occupied individual molecules. Within organic semiconductors, theacenes are exciting because many of them have the ability to undergo singlet fission and triplettriplet annihilation upconversion. Singlet fission can create double the charge carriers for every
photon absorbed than conventional materials.2 If the efficiency of this process can be optimized,
it could have a profound effect on photovoltaics, increasing the current that can be extracted fromphotovoltaic devices. Triplet-triplet annhilation upconversion can also improve photovoltaic
technology, if sufficiently optimized, by absorbing low energy light that is currently wasted insolar cells and converting it into light with higher energies which the solar cell can make use of.
The unique properties of semiconductors come from the specific building blocks that they
are made from, as well as the crystal structure that the material adopts. For instance, CsPbI3 is asemiconductor material while in the perovskite crystal structure, but an insulator in its

2orthorhombic, non-perovskite phase.3 This drastic change begs the question of how changes to the
crystal structure affect the electronic properties. One can study this by varying the temperature ofa material while probing the desired electronic characteristics, but this method adds or removes
thermal energy, which may introduce effects unrelated to the crystal structure itself. Anothermethod used is changing chemical constituents of the material, forcing a change to the crystal
structure, but it is not immediately clear if any changes observed are due strictly to the modified
crystal structure or to the different chemical identity. Application of high pressures in the GPa
range is a clean way to modify the crystal structure, without introducing unwanted variables. This
allows one to track changes to the electronic properties that are a direct result of changes tointeratomic or, in the case of organic materials, intermolecular distances.
The organization of the rest of the thesis is as follows. In Chapter 2, I will describe how
experiments were performed and what kind of instrumentation was used. Chapters 3 and 4 deal
with the pressure response of perovskites, an exciting semiconducting material with applications
in photovoltaics and display technology. Chapter 3 focuses on the photoluminescence pressure
response of CsPbI3 and CsPbBr3 nanocrystals. In Chapter 4, the size dependence of the pressure
response of CsPbBr3 quantum dots is discussed. Finally, Chapter 5 lays out a mechanism fortriplet-triplet annihilation upconversion in rubrene crystals sensitized by rubrene radical cations
and anions that are trapped in the crystals and discusses pressure-induced changes in the efficiencyof the upconversion process.
1.2

References(1)

Bawendi, M. G.; Steigerwald, M. L.; Brus, L. E. The Quantum Mechanics of Larger
Semiconductor Clusters (“Quantum Dots”). Annu. Rev. Phys. Chem. 1990, 41 (1), 477–496.

(2)

Smith, M. B.; Michl, J. Singlet Fission. Chem. Rev. 2010, 110 (11), 6891–6936.

3

(3)

Lai, M.; Kong, Q.; Bischak, C. G.; Yu, Y.; Dou, L.; Eaton, S. W.; Ginsberg, N. S.; Yang,
P. Structural, Optical, and Electrical Properties of Phase-Controlled Cesium Lead Iodide
Nanowires. Nano Res. 2017, 10, 1107.

4

Chapter 2

2.1

Experimental Methods

Overview
In this chapter, the experimental procedures for the work done in the following chapters

are explained in detail. We used various high-pressure generating techniques (sections 2.2 and 2.3)
in order to study how changes to the crystal structure of different materials affect their electronic
states. To probe these changes, we used photoluminescence and photoluminescence excitation
spectroscopy. The instruments used as well as the preparation steps to characterize our samples
are also described (sections 2.4 – 2.6).
2.2

Diamond Anvil Cell
To produce high pressures to study how the electronic properties of materials are coupled

to the crystal structure, we use a diamond anvil cell. Our diamond anvil cell (DAC) setup is a gas
membrane driven DAC (easyLab Diacell μScopeDAC RT(G), type Ia 16-sided diamond anvils,
base diameter 2.5 mm, culet 0.50 mm, numerical aperture = 0.54) (Figure 2.1) which can producepressures up to tens of GPa. A stainless-steel gasket (type 302 stainless steel, initial thickness 250µm) is needed between the diamonds to form a sample compartment. Blank high-pressure gaskets
must be pre-indented with the diamond anvil cell to a final thickness of 90 - 100 µm before drillingthe sample compartment to ensure proper alignment. A mark was made of the gasket to indicate
its orientation in the DAC. Pre-indentation was done by placing a blank gasket between the
diamonds and closing the DAC. Then the three bolts that hold the DAC together were tightened
until the appropriate thickness was reached (Figure 2.1c). To ensure an even indentation, thethickness of the DAC with the gasket installed was checked at locations a, b, and c shown in Figure52.1c incrementally during the indentation procedure with a micrometer. Once the gaskets werepre-indented, the sample compartment needed to be drilled.

A)

B)

laser

pressurized N2
C)
(a)

(b)
(c)

Figure 2.1: (A) cross section of the gas membrane driven diamond anvil cell. Pressurized N2 isconnected to the gas membrane through stainless-steel tubing. As the membrane expands, it applies
pressure to the two diamonds. (B) 3D cross sectional rendering of the diamonds and the stainlesssteel gasket. The sample compartment is illustrated here filled with a green liquid and a ruby grain
for pressure measurement. The laser beam shows the optical access we have to the sample
compartment. (C) Top view of the gas membrane driven diamond anvil cell (diamond top surface
shown in blue at the center) showing the three bolts used to pre-indent the gaskets and the threepositions where the indentation measurements were taken.

To drill the holes in the gaskets, we used a Nd:YAG laser (Innolas Spitlight 300) operating
at 1064 nm with 5 ns pulse duration at a 20 Hz repetition rate and 3.5 W average power. The laser
beam was routed to a 1 mm aperture and then a 50 mm focal length lens for focusing the beam
onto the gasket. A 532 nm solid state diode pumped laser was aligned to be collinear with the 1064
nm pulsed beam to accurately position the gasket before drilling. Gaskets were mounted on a three-6

axis micrometer translation stage. The holes formed by laser drilling could be made with diametersof 80 µm to 150 µm, by translating the gasket along the propagation axis of the laser beam.
Before each experiment, a small ruby grain was added to the cell along with the sample
and droplet of the high-pressure transducing medium. To measure the pressure during anexperiment, the ruby R1 photoluminescence peak was used as a pressure gauge. This has been
documented in the literature and works by fitting the R1 and R2 lines with Lorentzian profiles (seeFigure 2.2) and using equation 2.1 calculate the pressure.1
𝑃=

𝐴
𝐵+𝐶
𝜆 "#
(exp ,-1 − 0 2 34 − 15
𝐵+𝐶
𝐶
𝜆!

2.1

Where A, B, and C are empirical constants derived from fitting the experimental data. A is equal
to 1820 GPa and B and C are unitless quantities equal to 14, and 7.3 respectively.1 The ruby R1
peak at ambient pressure is l0 and the peak position at elevated pressure is l. This calibration scaleis reported to have a maximum error of ±1% at the low pressures used here.1 Error bars on ourpressure measurements are ±70 MPa which we have estimated from differences in the R1 and R2

7

peak positions from one ruby crystal grain to another due to unique internal strains that exist ineach grain.

Figure 2.2: Ruby spectrum with Lorentzian fits of the R1 and R2 peaks for pressure determination.

During a pressure experiment, the samples were excited using a 406 nm continuous wave
(CW) diode laser at intensities of ca. 0.1 W/cm2 or with a CW 532 nm diode pumped solid statelaser with intensities up to 100 W/cm2. To ensure that the irradiation did not cause significant
heating of the samples, the minimum excitation intensity was used to detect photoluminescence.
DAC spectra were recorded using a Horiba Scientific XploRA Raman microscope (grating with
600 lines/mm, 0.3 nm resolution) or on a fiber coupled spectrometer setup using an Avantes
AvaSpec 2048 fiber optic spectrometer (grating with 300 lines/mm, slit width 50 µm, 2048 pixel
CCD detector array, 2.4 nm resolution). In this setup, the excitation light was focused on the DAC
using an achromatic doublet pair (ThorLabs MAP1030100-A, f1 = 30 mm, f2 = 100 mm) and the8PL was collected on the other side of the DAC in a forward emission geometry with a second
achromatic doublet pair (ThorLabs MAP1030100-A, f1 = 30 mm, f2 = 100 mm). The collected PL
was focused onto a multimode optical fiber (Avantes 400 µm core) using the short focal length of
the achromatic doublet pair.
On the Horiba Scientific XploRA Raman microscope, the ruby photoluminescence wasmeasured using an 1800 lines/mm grating (0.1 nm resolution, slit width 50 µm, 1024 pixel CCD
array). On the fiber optic spectrometer setup, the ruby spectra were recorded with an Avantes 2048
fiber coupled spectrometer (1800 lines/mm grating, 0.1 nm resolution, 2048 pixel CCD array).
PL peak positions were determined by fitting Lorentzians to the measured spectra. The
error associated with this procedure was based on the statistical uncertainty of the fit. After
increasing the pressure between spectra, the system was allowed to equilibrate for 20 minutes
before taking the next data point. This is a needed step because the stainless-steel gasket deforms
plastically rather than elastically, meaning that when pressure is increased on the diamonds, theyslowly deform the metal until equilibrium is reached. We empirically determined that after 20
minutes there are negligible changes to the ruby R1 peak position, and therefore pressure.
2.3

Hydraulic Pressure Generator
A second way to study the pressure response of materials is with a home-built apparatus

that is a hydraulic pressure generating setup (Figure 2.3), modified from a design by Tekmen andco-workers. All components purchased from High Pressure Equipment Company (HIP, Erie,Pennsylvania).2 A hydraulic pressure generator (HIP, 25-5.75-100) capable of producing pressures
as high as 700 MPa pressurized a set of stainless steel tubes filled with ethanol as the pressuretransmitting fluid. This is not nearly as high as the diamond anvil cell, but the pressure generator
allows us to take small steps in pressure, so that we can map out a nearly continuous pressure9response of our materials at these pressures. The pressure was determined using a mechanical highpressure gauge (HIP, 6PG100).

Microscope Objective

365 μmFigure 2.3: A simplified schematic of the hydraulic high-pressure generating apparatus. Inset
shows a microscope image of the end of a capillary. The end has been fused closed, and there is asmall air gap within the capillary between the sample fluid and the end.

Quartz capillaries with an outer diameter of 375 μm and inner diameter of 50 μm (Molex,
TSU050375) were cut into 22 cm long pieces (Figure 2.4). The capillaries come from the
manufacturer coated with an opaque polyimide film so in order to have optical access, a 5 cm
length of polyimide coating was burned off using an oxygen/propane torch. The position of thiswindow on the capillary corresponded to the section that would be underneath the microscope
objective used for sampling PL radiation from the sample when the capillary was coupled to thehigh-pressure tubing (see description of the microscopy setup below). The end of the capillaryfurthest from the window was threaded through a modified pressure plug (HIP, 100-7XM4), into

10

which a 400 μm hole had been drilled and epoxied (Armstrong A-12 Epoxy) into place (Figure2.4). In order to cure the epoxy, the plugs with the capillaries in place were heated at 40° C for 3
hours. The pressure plug could then be coupled to the rest of the apparatus such that the end of thecapillary was in contact with the ethanol in the pressure generating apparatus. After an experiment,
the pressure plugs were removed from the spent capillaries by heating them to 270° C until the
epoxy was burned away. The plugs were then polished in a lathe to ensure good contact to theepoxy for the next experiment.

Figure 2.4: (A) A high-pressure plug as purchased (HIP, 100-7XM4) (top) and the modified highpressure plug (bottom). (B) The modified high-pressure plug with a capillary epoxied into it. (C)Capillary showing the full length with high-pressure plug and the window where the polyimide
coating had been removed.

Samples in hexanes were drawn into the quartz capillaries using capillary action, whilesamples in paraffin oil had to be forced through the capillary using a syringe with a custom adapter
to connect to the high-pressure plug. A small amount of clean paraffin was then drawn into one
end of the capillary with the modified syringe adapter to act as a barrier between the sample andthe ethanol in the high-pressure generating setup. After loading, the free end of the capillary was
fused using an oxygen/propane torch. Fusing the ends of the capillaries must be done by passing
the end of the capillary through the hottest part of the flame for the shortest amount of timepossible. If it is in the flame too long, the hexanes or paraffin oil boil as the glass is fusing, causing
a bubble to form in the capillary wall, significantly compromising its structural integrity.

11Spectroscopy using this setup was done by exciting samples using a 532 nm diode pumped
solid state laser with the confocal microscope or a 375 nm LED (Figure 2.3). Spectra werecollected with the XploRA confocal microscope.
In the hydraulic setup described above, pressurization of glass or quartz capillaries may
result in their destruction. If any gas bubbles are present in the pressure-generator or the steel
tubing, this can result in explosive release of pressure when the capillary breaks, which represents
a hazard to people and equipment. Personal protective equipment must be worn at all times, andpolycarbonate shields installed around the apparatus to block any shards in the event of explosive
failure of a capillary. To ensure there are no gas pockets in the apparatus, ethanol must be flushed
through the whole system every time a new capillary is connected. This will push any air pockets
out with the flushed ethanol.
2.4

Upconversion Photoluminescence Spectroscopy
To produce upconversion photoluminescence in rubrene samples for various experiments,

we used the tunable near infrared (NIR) output of an optical parametric oscillator (OPO) pumped
by a Nd:YAG laser. Two different OPO light sources were used depending on the region of thespectrum scanned. One was a BBO based OPO (GWU premiscan) pumped by the third harmonicof a Nd:YAG laser at 355 nm, the other a KTP based OPO (LaserVision), pumped at by the second
harmonic of a Nd:YAG laser at 532 nm. The output pulse duration in either case was 5 ns with arepetition rate of 20 Hz and average power of 50 mW at the rubrene sample. The peak intensity
per pulse was 1 MW/cm2.
In all three experimental setups described in the following Sections, the OPO output beam
was passed through a combination of a half-wave plate and polarizers (Figure 2.5-Figure 2.8) to
optimize the UCPL signal. A fraction of the beam was picked off with a glass microscope slide12(~8% of the total power) to measure the relative power as a function of OPO frequency. The beam
was then directed to the rubrene sample in one of the configurations described below.
2.4.1

Upconversion Photoluminescence Excitation Spectra
In order to measure where rubrene crystals absorb in the NIR, we used a technique similarin practice to photoluminescence excitation (PLE) spectroscopy3 that we called upconversion
photoluminescence excitation (UCPLE) spectroscopy. To measure a UCPLE spectrum, the output
beam from the OPO setup described above was directed into a vacuum chamber and onto therubrene sample. For measurements that were not done at elevated pressures, the rubrene sample
was mounted on the outside of a quartz cuvette (labeled “L” in Figure 2.5), which could be filledwith liquid nitrogen from the outside of the vacuum chamber for temperature dependent studies.
The vacuum chamber prevented condensation forming on the rubrene when it was at low
temperatures, and it also eliminated the possibility of photooxidation of rubrene.4–6 The vacuum
chamber was pumped to a base pressure ca. 10-2 mbarr with a mechanical pump and inline cold
trap. We used a vacuum chamber in these experiments to determine the UCPLE spectra without
introducing the possibility of photo-oxidation of the rubrene, and to avoid condensing water on
the sample when measuring spectra at 77 K. The frequency of the OPO was tuned while theintensity of the UCPL was measured using a silicon photodiode with an interval of 1 cm-1. The
UCPL spectra were recorded by collecting the output voltage of the photodiode using anoscilloscope was fed to a computer using a LabView program and plotted as a function of OPO
frequency.

13

λ/2 plate

BS

M

Nd:YAG/OPO
polarizer
tunable NIR light-source

BS: microscope slide beam splitter
M: metal mirror
L: liquid N2 dewar
F: 2 x 700 nm short pass filter

power meter

achromatic
doublet pairFvacuum chamberLto pumpoptical fiber

detector

Figure 2.5: Upconversion photoluminescence excitation (UCPLE) spectroscopy setup.

The light incident onto the cuvette was set at an angle of ca. 20° to ensure that no strayreflections of laser light propagated to the detector. To maximize the UCPL signal, we took
advantage of the waveguiding nature of the rubrene crystals and collected the UPCL that wasemitted from the edges of the crystal, with the detection direction grazing the surface of the crystal
mount. If there is self-absorption within the rubrene crystal, this will only introduce a constantoffset across the entire UCPLE spectrum, as only the intensity of the UCPL is measured. The
UCPL was sent through two 700 nm short pass filters (Thorlabs, FESH0700) to remove any stray
NIR laser light. An achromatic doublet pair (ThorLabs MAP1030100-A, f1 = 30 mm, f2 = 100mm) collected the UCPL using the longer focal length and focused it onto an optical fiber (Avantes
400 µm core) which was coupled to a biased silicon photodetector (ThorLabs DET36A2).

14

Figure 2.6: Image of the quartz cuvette in the vacuum chamber. The cuvette could be filled fromthe outside with liquid nitrogen to cool mounted rubrene crystals. The orange vertical line visibleon the outside of the cuvette is a rubrene crystal.

2.4.2

Temperature Dependence of UCPL and PL
To measure the temperature dependence of the UCPL and PL, a K-type thermocouple was

attached to the inside of the cuvette directly behind where the rubrene crystal was mounted (Figure2.5). We measured the temperature dependence of the UCPL by exciting the rubrene crystal ateach NIR absorption feature and the temperature dependence of the PL by exciting with 532 nm
light (doubled ns pusled output of the Nd:YAG). To cool the rubrene crystal down to 77 K, thecuvette was filled with liquid N2. Once the liquid N2 evaporated, the temperature and UCPL or PL
intensity were recorded every 10 seconds until the crystal had warmed up to room temperature15

2.4.3High-Pressure Upconversion Photoluminescence Excitation Spectra
To measure UCPLE spectra under high-pressure, we directed the OPO output beam into

our DAC (Figure 2.7). We loaded the DAC with small rubrene crystal grains made from thephysical vapor deposition, as well as rubrene powders purchased from Sigma Aldrich. The
pressure transducing medium was paraffin oil. A small ruby crystal was included as well to act asa pressure guage. A half wave plate was used to optimize the UCPL signal. The UCPL wascollected in a forward emission geometry due to the limited optical access to the sample inside the
DAC. The two 700 nm short pass filters were able to block all laser light from reaching thedetector, confirmed by using the setup without any rubrene in the DAC. UCPL signal was collected
through an achromatic doublet pair (ThorLabs MAP1030100-A, f1 = 30 mm, f2 = 100 mm) andfocused onto an optical fiber which was coupled to a biased silicon photodetector (ThorLabs
DET36A2). The output of the OPO was scanned over the region of interest and the intensity of the
UCPL was measured at each step with the silicon photodector using an oscilloscope which fed
data to a computer through a LabView program.
λ/2 plateBS

YAG/OPOM

polarizer

DAC

tunable NIR light-source

BS: Microscope Slide Beam Splitter
M: Metal Mirror
DAC: Diamond Anvil Cell
F: 2 x 700 nm Short Pass Filter

power meter
achromatic
doublet pairF
Si photodiodeoptical fiber

Figure 2.7: Setup for collecting UCPLE spectra under pressure in the DAC.

16

2.4.4Pressure-Response of Photoluminescence and Upconversion Photoluminescence
To measure the pressure-response of the PL and the UCPL simultaneously, theexperimental setup in Figure 2.7 was modified as follows. First, instead of measuring the intensityof the UCPL on a photodiode, the UCPL and PL light were sent through the optical fiber into aspectrometer (Figure 2.8). Unlike the experiments described above where only the intensity of the
UCPL or PL were necessary, this enabled us to monitor the UCPL and PL spectra as a function ofpressure. From these spectra, we could extract the integrated intensity as a function of pressure, as
well as determine pressure-induced spectral shifts.
In order to measure PL of rubrene under pressure, a 406 nm laser diode was used for
excitation. PL measurements were done in the forward emission geometry using a 450 nm longpass filter before the achromatic doublet pair to block any transmitted excitation light fromreaching the spectrometer. To accommodate the addition of the diode laser in this geometry, the
UCPL excitation and detection were done in a backward emission configuration with the use of a
780 nm high reflector to guide NIR light into the DAC, but to pass the UCPL light. Two 700 nm
short pass filters were used before the achromatic doublet pair to ensure no NIR excitation lightmade it to the spectrometer. Finally, the power of the diode laser and the OPO were taken
immediately before recording a spectrum (positioned at the dashed boxes in Figure 2.8) so that the
integrated intensity of the spectra could be normalized to laser power.

17406 nm diode laser
HR: 780 nm High Reflector
DAC: Diamond Anvil Cell
F: 2 x 700 nm Short Pass Filter OR 450 nm Long Pass Filter

power meter
DAC

λ/2 plateHR

YAG/OPO
tunable NIR light-source

polarizerF
achromatic
doublet pair

spectrometer

power meter
optical fiber

Figure 2.8: Setup for collection photoluminescence (406 nm excitation) and upconversion
photoluminescence (NIR excitation) spectra under pressure.

2.5

Transmission Electron Microscopy
Transmission electron microscopy (TEM) images were acquired using a FEI Tecnai ST20

and a FEI Tecnai F20 with an accelerating voltage of 200 kV. TEM samples were prepared bydrop casting perovskite NC in a hexanes solutions onto 300 mesh carbon film copper grids(Electron Microscopy Sciences) and allowing the hexanes to evaporate off, leaving only the
nanocrystals suspended on the TEM grid. Illuminating the grid with a 375 nm LED reveals how
much material was deposited onto the TEM grid. It must be even and not excessive, or thenanocrystals will stack, making acquiring useful images impossible.
2.6

Powder X-Ray Diffraction
Samples for powder x-ray diffraction measurements were prepared by drop casting NC

solutions in hexanes onto a silicon low background holder (Bruker Si low background sample
holder). Enough sample was deposited with a thin film of NC material was visible with the naked
eye on the silicon. If there was excess 1-octadecene or other oily substance in the NC solution, a18

droplet of that liquid will form rather than a film. XRD can be done on this droplet, but the signal
to noise is much worse than for the films. Diffraction patterns were measured with a Bruker D8Advance using Cu Kα radiation (λ = 0.1540562 nm) with 4º soller slit pair and a 0.6º divergenceslit. For NC samples, collection times were ~4,000 seconds to acquire good signal to noise ratios.
The powder XRD pattern in section 3.3.1.1 was taken by Leah M. G. Hall on a Rigaku Dmax
diffractometer using a Cu Kα radiation source (λ = 0.1540562 nm) with 0.02° 2θ.
2.7

References(1)

Holzapfel, W. B. Refinement of the Ruby Luminescence Pressure Scale. J. Appl. Phys.
2003, 93, 1813.

(2)

Tekmen, M.; Müller, J. D. High-Pressure Cell for Fluorescence Fluctuation Spectroscopy.
Rev. Sci. Instrum. 2004, 75, 5143.

(3)

Norris, D. J.; Bawendi, M. G. Measurement and Assignment of the Size-Dependent Optical
Spectrum in CdSe Quantum Dots. Phys. Rev. B Condens. Matter Mater. Phys. 1996, 53,
16338.

(4)

Mitrofanov, O.; Kloc, C.; Siegrist, T.; Lang, D. V.; So, W. Y.; Ramirez, A. P. Role ofSynthesis for Oxygen Defect Incorporation in Crystalline Rubrene. Appl. Phys. Lett. 2007,
91 (21).

(5)

Chen, Y.; Lee, B.; Fu, D.; Podzorov, V. The Origin of a 650 Nm Photoluminescence Bandin Rubrene. Adv. Mater. 2011, 23 (45), 5370–5375.

(6)

Ly, J. T.; Lopez, S. A.; Lin, J. B.; Kim, J. J.; Lee, H.; Burnett, E. K.; Zhang, L.; AspuruGuzik, A.; Houk, K. N.; Briseno, A. L. Oxidation of Rubrene, and Implications for Device
Stability. J. Mater. Chem. C 2018, 6 (14), 3757–3761.

19

Chapter 3

Probing the Pressure-Response of Cesium Lead Halide Perovskite

Nanocrystals with Photoluminescence Spectroscopy

This chapter has been adapted with permission from:(a)

Beimborn II, J. C.; Hall, L. M. G.; Tongying, P.; Dukovic, G.; Weber, J. M., “Pressure
Response of Photoluminescence in Cesium Lead Iodide Perovskite Nanocrystals,” J. Phys.
Chem. C, 2018, 122, 20, 11024-11030. DOI: 10.1021/acs.jpcc.8b03280. Copyright 2018
American Chemical Society.

(b)

Beimborn II, J. C.; Walther, L.; Wilson, K.; Weber, J. M., “Size-Dependent PressureResponse of the Photoluminescence of CsPbBr3 Nanocrystals,” J. Phys. Chem. Lett., 2020,
11, 5, 1975-1980. DOI: 10.1021/acs.jpclett.0c00174. Copyright 2020 American Chemical
Society.

3.2

Introduction
Inorganic cesium lead halide perovskites have recently reemerged since their discovery

over half a century ago,1 as materials with not only promising applications, but fascinating
fundamental properties. Following the pioneering work by Protesescu et al. on the synthesis ofperovskite nanocrystals,2 there has been an explosion of interest in the literature. Their
composition-tunable, sharp absorption edges and narrow photoluminescence (PL) spectra makethem excellent candidates to be used for next generation light emitting diode (LED) andphotovoltaics (PV).2–7 Out of the family of CsPbX3 materials, CsPbI3 nanocrystals, with their band
gap at around 1.8 eV, show particular promise for applications in PV devices. For example, a solar
cell using a CsPbI3 nanocrystal film as the absorbing material can reach power conversion20

efficiencies greater than 14%.8 Due to the easily achievable near unity quantum yield of CsPbBr3
NCs,9,10 they are being used to improve various optoelectronic devices such as nano-lasers,11,12
photodetectors,13,14 and using the generated charge carries for photocatalytic reduction of CO2.13,15–
17

Cesium lead halide perovskites belong to the family of ABX3 perovskites. Here A is themonovalent cation Cs+, B is the divalent metal cation Pb2+, and X is a halide. The CsPbX3
perovskite crystal structure is composed of a network of corner-sharing PbX6 octahedra, with theCs+ cations occupying the cavities between the octahedra (Figure 3.1). The perovskite crystal
structure is only stable for a window of ratios of the A, B, and X ionic radii. The Goldschmidt
tolerance factor18 is the most widely used predictor of perovskite stability, however, newer
tolerance factors have been developed using more sophisticated computational tools.19 Smallchanges in the size of the ionic radius of one ion can significantly affect the properties of theperovskite material.

Figure 3.1: The g-phase perovskite crystal structure, where X is either bromide or iodide anions.
The g-phase crystal structure differs from the a-phase by having Pb-X-Pb angles less than 180°.

CsPbX3 halides are much softer than conventional semiconducting materials. CsPbBr3
nanocrystals have a bulk modulus, a measure of the structural response of a material to pressure,21

of 16.9 GPa20 and while the bulk modulus of CsPbI3 has not been experimentally determined yet,calculations estimate it between 16 GPa and 19 GPa.21 These bulk moduli values place CsPbX3
perovskites between soft, molecular crystals, such as tetracene (ca. 9 GPa22), and harder
semiconductor crystals such as CdSe (ca. 53 GPa).23 Given the relatively soft nature of metal
halide perovskites compared to other inorganic materials, it is of interest to explore how highpressure will affect the crystal structure, and to measure how these changes affect the optical gapof these materials. High pressure is a convenient way to modify the structure of a condensed phasesample without increasing thermal energy content by adding heat or changing the chemicalcomposition of the material, facilitating exploration of thermodynamics and structure by changing
a minimum number of variables.
In this chapter, I will present our results on the structural changes that occur in CsPbI3 and
CsPbBr3 perovskite NCs. We used measurements of the optical gap of these materials at elevatedpressures to understand how changes in the crystal structure affect the electronic properties. For
this study, we focused on all inorganic perovskites rather than their organic/inorganic counter parts
to avoid complications the organic A cation could introduce on the pressure dependent effects. The
difference in the ionic radius of the halides is discussed as the major factor contributing to thedifferent pressure-responses of the two materials. I will also compare the results of high-pressure
experiments done on CsPbX3 NCs prepared by two different synthetic procedures.
3.3

Nanocrystal Synthesis
To study the pressure-response of cesium lead halide perovskite NCs, we used various

methods adapted from the existing literature to synthesize CsPbI3 and CsPbBr3 NCs.10,24,25
Conventional hot-injection under inert atmosphere methods were used, which have precise control
over the NC size and size distributions and are the standard for producing high quality samples.

22

We also employed a scalable tip-sonication synthetic method which can produce large amounts ofsample, but with less control over the quality of the final product, to test whether the different
synthesis procedures change any of the NC structural or electronic properties we can measure withhigh-pressure.
3.3.1

CsPbI3 Nanocrystal Synthesis via Hot Injection
The CsPbI3 NC synthesis was adapted from Wang et al.24 A PbI2 solution was prepared byadding 0.18 mmol of PbI2 (Aldrich, 99%), 5.0 mL of 1-octadecene (ODE) (Aldrich, technicalgrade, 90%), 0.5 mL of diisooctylphosphinic acid (DA) (Aldrich, technical grade, ~90%), and 0.5
mL of purified oleylamine (OA) to a round 25 mL bottom flask. The flask was evacuated at 120°C for one hour with vigorous stirring to remove any dissolved water in the solvents.
In a second round-bottom flask, a Cs-DA solution was prepared by adding 0.30 mmol
Cs2CO3 (Aldrich, ReagentPlus, 99%), 5.0 mL of ODE, 0.5 mL of DA, and 0.5 mL of purified OA.
This mixture was kept at 120 °C under vacuum with vigorous stirring until all the Cs2CO3 haddissolved and was then brought to 100 °C under dry nitrogen.
The PbI2 solution was then brought to 140 °C under dry nitrogen. Next, 0.4 mL of theCs2CO3 solution were injected into the PbI2 solution with vigorous stirring. Then, due to theextremely fast nature of this reaction, it must be quenched immediately. This was done bytransferring to a room temperature water bath as quickly as possible, which was within 5 seconds.
The resulting solution was washed by adding excess tert-butanol to precipitate the nanocrystals
from the reaction mixture. This mixture was centrifuged at 6600 g, and the pellet was resuspended
in anhydrous hexanes (Aldrich, ³ 99%) and stored at -21 °C.

23

3.3.1.1 CsPbI3 Nanocrystal Characterization
To characterize our synthesized CsPbI3 samples, we used photoluminescence (PL)spectroscopy, UV-vis absorption spectroscopy, transmission electron microscopy, and powder Xray diffraction. As can be seen in Figure 3.2 the nanocrystals have narrow PL spectra with full
width at half-maximum (FWHM) of 30 nm and sharp band edge absorption.

Figure 3.2: Visible absorption (solid) and PL (dashed) spectra of CsPbI3 NCs in hexanes, preparedusing hot injection.

The CsPbI3 NC samples have a relatively narrow size distribution of 9.8 ± 2.0 nm (Figure3.3) compared to what has been published in the literature up to this point, which is generally
greater than 10% of the average nanocrystal size,3,24 although it is significantly broader than forother quantum dot materials, such as CdSe.26 The reason for the relatively broad size distributionof CsPbX3 NCs lies in the extremely fast kinetics of NC nucleation and growth for this material.21

24

9.8 ± 2.0 nm

Figure 3.3: CsPbI3 NC sample size distribution histogram (a) and reference TEM image (b). The
scale bar represents 100 nm. The NCs were synthesized using hot injection.

The polymorph that CsPbX3 nanocrystals adopt under ambient conditions has been a pointof debate in the literature for some time, as x-ray diffraction (XRD) and high-resolution
transmission electron microscopy (HRTEM) data have been interpreted as evidence for cubic (aphase) as well as orthorhombic (g-phase) perovskite crystal structures (see Section 3.4.1).2,27–29
Powder XRD data indicate that our CsPbI3 NC samples are in the orthorhombic g-phase due to thepresence of peaks between 16° and 28° 2θ. The incorrect assignment of the cubic a-phase that has
been proposed in the literature comes from XRD measurements that did not resolve thesepeaks.21,24,27,29,30 By comparing our experimental XRD data with simulated g-phase and a-phasediffraction patterns (Figure 3.4), it is clear that the data are a closer match to the g-phase. The unit
cell dimensions of our samples are a = 8.6 Å, b = 9.0 Å, and c = 13.1 Å (error bars ± 0.1 Å) which25

are in good agreement with the reported values by Bertolotti et al.29 Using the Scherrer method tocorroborate our TEM size analysis, we found that the crystallite size was 10 ± 2 nm. This value
indeed matches the NC size distribution we obtained from TEM image analysis (Figure 3.3),
indicating that the NCs are single crystalline. Finally, the lattice spacings in the HRTEM imagesof the CsPbI3 NCs are consistent with the orthorhombic g-phase assignment as well (Figure 3.4).

26

(220)
(022)

(020)

a)

Figure 3.4: (a) XRD pattern of CsPbI3 NCs prepared using hot injection. The light gray points are
raw data, the solid red line is a 20-point sliding average. The magenta lines are the expecteddiffraction angles from the orthorhombic perovskite phase, and the blue lines are the expecteddiffraction angles for the cubic phase.21 The peak labeled with a * is from left over PbI2 from thesynthesis procedure. The peaks labeled with miller indices correspond to reflections from thecrystal planes indicated in (b). Sample HRTEM image of a CsPbI3 NC and its Fourier transform,
together with markers of the (020) and (220) planes (b).

27

3.3.2

CsPbBr3 Nanocrystal Synthesis
The CsPbBr3 NCs were synthesized with a method similar to the one used for CsPbI3.

However, it is possible to control the reaction of CsPbBr3 thermodynamically rather thankinetically by controlling the Pb2+:Br- ratio in solution, giving narrow size distributions and more
reproducible results.25,31 In a typical synthesis, 75 mg of PbBr2 (Aldrich, ≥ 98%), 5 mL of 1octadecene (ODE) (Aldrich, technical grade 90%), 0.5 mL of oleic acid (OA) (Aldrich, technicalgrade 90%), and a total of 0.5 mL of OLA and OLA-Br were added to a 25 mL three neck roundbottom flask. In a separate 25 mL round bottom flask, we added 162.5 mg of Cs2CO3 (Aldrich,99%), 9 mL of ODE and 1 mL of OA to make a Cs-oleate solution.
Both flasks were stirred and heated to 120° C under vacuum for 1 hour to de-gas thesolvents. Next, the flask containing the PbBr2 was filled with nitrogen gas and brought to 160° C.
This temperature was chosen to produce nanocrystals with edge sizes on the order of 10 nm tocompare with our CsPbI3 samples.31 The Cs-precursor flask was also filled with nitrogen andallowed to cool to 100° C. Then 0.5 mL of the Cs-oleate solution was swiftly injected into the
PbBr2 containing solution. This reaction mixture was then cooled down to room temperature by
immersing in a room temperature water bath. However, it was not necessary to perform this step
as fast as possible (as in the case of CsPbI3) since the reaction is not kinetically controlled.
To remove as much of the reaction solvents, unreacted precursors, and large aggregates as
possible, 10 mL of anhydrous hexanes (Sigma-Aldrich, mixture of isomers anhydrous ≥ 99%)
were added immediately after the reaction mixture had cooled to room temperature.32 This
colloidally disperses all the CsPbBr3 NCs, but does not disperse or dissolve unreacted precursors
or large CsPbBr3 aggregates. This turbid mixture was centrifuged at 6600 g and the supernatantcontaining the synthesized colloidal NCs was saved. Next, dry nitrogen was blown over the surface

28

of the colloid solution to slowly evaporate off hexanes. Upon sufficient evaporation of hexanes,
the largest NCs began to precipitate out of the colloidal solution, which was characterized by avisual change in the solution from transparent to turbid. This occurs because hexanes are a better
solvent for CsPbBr3 NCs than ODE, in which the synthesis is performed. This turbid solution wasthen centrifuged (6600 g), and the NCs were collected from the resulting pellet and resuspended
in hexanes. This process narrows the size distribution even further by rejecting smaller
nanocrystals.
3.3.2.1 CsPbBr3 Nanocrystal Characterization
As with CsPbI3, we characterized our CsPbBr3 NCs with PL spectroscopy, transmission
electron microscopy, and powder X-ray diffraction. The nanocrystals have narrow PL spectra withfull width at half-maximum (FWHM) of 15 nm, indicating a narrow size distribution (Figure 3.5).

29

Figure 3.5: PL of CsPbBr3 NCs in hexanes with 10.9 ± 1.2 nm edge length, prepared by hot
injection.

We achieved a monodisperse sample with the procedure outlined above with NCs 10.9 ±1.2 nm (Figure 3.6). The standard deviation in the CsPbBr3 was nearly a factor of two smaller thanfor the CsPbI3 NCs. However, the growth kinetics of CsPbBr3 are still fast, preventing even higher
monodispersity achievable in other semiconductor nanomaterials.

30

Figure 3.6: Size statistics of the CsPbBr3 NCs prepared using hot injection, with typical TEM
image of the NCs (inset). The scale bar is 20 nm.

A similar controversy over the crystal structure of CsPbBr3 under ambient conditions aswith CsPbI3 has existed. The CsPbBr3 NCs prepared in the present work were confirmed to be in
the orthorhombic perovskite crystal structure using powder XRD (Figure 3.7). We show calculateddiffraction angles for cubic and orthorhombic crystal structures, and it is clear that ourexperimental data matches the predicted pattern for orthorhombic crystal structure.

31

Figure 3.7: Powder XRD pattern of the CsPbBr3 NCs made with hot injection. The red lines are
the expected pattern for the orthorhombic perovskite structure while the purple lines are theexpected pattern for the cubic perovskite structure.

3.3.3

CsPbX3 Nanocrystal Synthesis via Sonication
Most procedures for synthesizing perovskite NCs require high-temperature injection under

an inert atmosphere.2,33 These methods produce very monodisperse samples with high quantum
yields, but are not easily scalable. Tong et al. published a scalable procedure for synthesizing
monodisperse samples of nanocubes and nanoplatelets of cesium lead halide perovskites (CsPbX3
where X = Cl, Br, or I) in ambient air and without the need for high temperature injection.28 In atypical synthesis, 0.1 mmol of cesium carbonate along with 0.3 mmol of PbX2 (X = Br or I) salts
were added to 10 mL of 1-octadecene with 0.5 mL each of oleylamine and oleic acid. All reagentswere purchased from Sigma Aldrich and used without further purification.

32

This mixture was subjected to 10 minutes of tip ultrasonication at a power of 30 W. During
ultrasonication, the color of the reaction mixture slowly changes from colorless to strongly colored(yellow for X = Br, deep red for X = I), yielding a cloudy suspension that contains both NCs andbulk material. To remove unreacted precursors and bulk material, the suspension was centrifuged
at 6600 g for 10 minutes. The supernatant was discarded, and the pellet was re-suspended inhexanes. This solution was centrifuged again at 2000 rpm for 10 minutes to remove bulk material.
The clear, colored supernatant containing the NCs was saved, and the pellet was discarded. The
clear, colored solution was subsequently centrifuged at higher speeds (>9000 rpm, 20 minutes) tofurther separate nanocrystal size fractions.
3.3.3.1 Characterization of CsPbX3 Nanocrystals from Sonication
The NCs synthesized with sonication have narrow PL spectra with full width at halfmaximum (FWHM) of 15 nm and 35 nm for X = Br and X = I, respectively (Figure 3.8). The PL
spectra match the PL from NCs made with the hot injection method, indicating samples of similar
quality.

33

Figure 3.8: Visible absorption (solid) and PL (dashed) of CsPbBr3 (A) and CsPbI3 (B) NCs
prepared using sonication. All spectra are scaled independently.

The resulting solutions contained monodisperse (8.6 ± 1.8 nm and 4.7 ± 0.5 nm for X = Br
and I, respectively) CsPbX3 NCs (Figure 3.9). The size distributions of the CsPbBr3 is nearly thesame as for the hot injection method after size separation centrifugation. The size statistics for the
CsPbI3 sample made using sonication are dominated by a highly monodisperse majority fractionof small NCs. Interestingly, the PL of the sonicated CsPbI3 sample is not significantly blue shiftedfrom the CsPbI3 hot-injection sample, despite having a smaller average size. This can be explainedby the minority population of large (~10 nm) NCs in the sonicated sample that can be seen in thesize histogram and the TEM image. The smallest nanocrystals likely have significantly lower
quantum yield than the larger NCs, allowing the larger NCs to dominate the PL response, and red
shifting the overall PL peak.21

34

Figure 3.9: Particle size distributions for CsPbBr3 (a) and CsPbI3 (b) prepared using sonication.
The scale bars are 100 nm.

35High resolution transmission electron microscopy (HRTEM) images were taken using a
FEI TALOS F200X CTEM/STEM at 200 keV and used to analyze the NC structure. The latticespacing of the CsPbBr3 and CsPbI3 NCs match the reported values of the orthorhombic perovskite
structure (Figure 3.10).

36

(A)

(B)

Figure 3.10: HRTEM image of a CsPbBr3 NC prepared using sonication (A) and CsPbI3 NC (B)with lattice spacing. Scale bars are 1 nm.

3.4

Photoluminescence Response of CsPbX3 Nanocrystals Under Pressure

37

High pressure techniques have been previously applied to bulk and NC samples of
CsPbBr3,20,34–37 and (CH3NH3)PbX3 (X = Cl, Br, I)24,38–43 as well as to bulk samples of CsPbCl3,35
CH(NH2)2PbI3,44 and the non-perovskite, yellow phase of CsPbI3.45 It is clear from these previous
studies that small differences in the crystal structure of various perovskite materials at ambientpressure can manifest large differences in the pressure response. We use a molecular orbital (MO)picture and a bulk-like band gap picture to interpret our results, as the size of the nanocrystals
results only in weak quantum confinement, and therefore thinking in these terms is appropriate. In
addition, we compare how the ionic radius of the X anion affects the structural properties andpressure response. Finally, we compare and contrast the high-pressure response of NCs
synthesized by two different methods.
3.4.1

Ambient Pressure Phase of CsPbI3 Nanocrystals
Bulk CsPbI3 is metastable in the perovskite crystal structure under ambient conditions, but

is very sensitive to degradation due to moisture.46 Multiple polymorphs exist at ambient pressure
at different temperatures.47 The most stable room temperature phase has a non-perovskite crystal
structure (yellow phase or d-phase).46 Above room temperature, there are three perovskite crystal
structures with different symmetry, denoted a-, b-, and g-CsPbI3 with cubic, tetragonal, andorthorhombic crystal structures respectively.29 The g-CsPbI3 phase is a direct band gap
semiconductor with a band gap around 1.8 eV.3,48
CsPbI3 NCs are also metastable as perovskite structures at ambient temperature, however,are still very sensitive to moisture. The assignment of crystal structure is complicated because thediffraction peaks differentiating the three perovskite structures are weak in intensity. To makematters worse, nanocrystalline twins can exist in a single NC,29 which can lead to destructive
interference of the diffraction signatures characteristic for the orthorhombic lattice. As a result,38

several accounts in the literature describe their samples as cubic, while only recently, others clearly
identify CsPbI3 NCs as orthorhombic.2,21,27–29 However, in agreement with our results (Figure 3.4)
work by Bertolotti et al. and Luther and co-workers has been shown that CsPbI3 NCs are in fact inthe orthorhombic Pnma perovskite crystal structure under ambient conditions (g-phase),21,29 andhave been shown to retain this structure for long periods of time in NC and nanowire
samples.24,47,49
3.4.2

Pressure Response of CsPbI3 Nanocrystals
To prepare a sample for high pressure experiments, the CsPbI3 NCs were dispersed inparaffin, which is hydrostatic up to ca. 3.0 GPa, which is greater than the pressure range studied
in the present work.50 This was accomplished by adding equal amounts of paraffin oil to thesolution of NCs in hexanes, followed by stirring under vacuum to remove the hexanes. The
resulting solutions of NCs in paraffin were saturated.
We measured the pressure dependent shifts of the PL peak of our samples using hydrostaticpressures up to 2.5 GPa. We observed clear qualitative changes in behavior between differentpressure regions. Figure 3.11 shows the PL spectra of CsPbI3 NCs from a typical DAC pressurerun. As the pressure is elevated from ambient, the PL emission peak shifts slightly towards longer
wavelengths, while it shifts to the blue at higher pressures. At ca. 2.3 GPa, PL emission becomesvery weak and finally disappears. Upon return to ambient pressure, the PL emission returns in full,and the peak is observed at the same wavelength as before pressurization.

39

Figure 3.11: PL spectra of CsPbI3 NCs at different pressures (right). All spectra are scaled to thesame intensity. The ruby fluorescence peaks around 694 nm were deleted from the spectra forclarity (break in the spectra). The bottom and top traces show the PL spectra at ambient pressure
before and after the pressure run.

Upon initial compression, the energy of the PL maximum shifts to lower energies nearlylinearly (see Figure 3.12). We can approximately describe this behavior by
𝐸$ = 𝐸! + 𝛼𝑝(3.1)

where E0 is the ambient optical gap, and the pressure coefficient, a, describes the slope dEG/dp.
At low pressures, we find a pressure coefficient a = -14.0 ± 0.6 meV/GPa. Further increase ofpressure eventually leads to a change in the sign of a, resulting in a blue shift of the PL peak40

energy, beginning at ca 0.33 GPa, and continuing up to 2.5 GPa (Figure 3.12). The change in thesign of the pressure coefficient a is not accompanied by an observable drop in PL intensity.

Figure 3.12: Pressure dependence of PL for CsPbI3 nanocrystals. The band gap energy change isplotted as the deviation of the PL peak at a given pressure from the ambient peak position. (a)Pressure range below 0.7 GPa. Data points from the hydraulic pressure generator (open squares)
and data taken using the DAC (open circles) from several runs from each setup are shown. The
grey lines indicate linear fits of the data in the two regions shown in this panel. The point at which
they cross indicates the pressure where the pressure response changes. (b) Overview of the entirepressure range up to 2.5 GPa, after which PL was no longer detected. Data from both the hydraulicpressure generator and the DAC are plotted together, and the data were obtained from several
pressure runs. Error bars for the PL peak energy change are ±1 meV.

3.4.3

Pressure Response of CsPbBr3 Nanocrystals
Figure 3.13 shows the pressure dependence of the PL peak energy Eg of CsPbBr3 NCs

under hydrostatic pressure. Upon initial compression, the energy of the PL maximum shifts tolower energies nearly linearly, and we can approximately describe this behavior by
𝐸$ = 𝐸! + 𝛼𝑝(3.1

where E0 is the ambient band gap, and the pressure coefficient a describes the slope dEG/dp. At
41

low pressures, we find a pressure coefficient a = -34.9 ± 0.8 meV/GPa, which is consistent withliterature values between -35 meV/GPa for bulk samples and -50 meV/GPa for NC samples atsimilar pressures.34,37

Figure 3.13: Pressure dependence of the PL peak for CsPbBr3 nanocrystals. Different symbols
correspond to different pressure runs. Data shown as filled symbols were acquired in the DAC
setup, while data shown as open symbols were taken on the hydraulic setup. No PL was observed
beyond 2.0 GPa. Error bars for PL energy and for pressure in the hydraulic data sets are smaller
than the symbol size. Note that the lowest PL peak energies are slightly different for runs fromdifferent synthetic batches, but the phase change pressure remains the same.
Unlike CsPbI3 NCs, where the change in the sign of a occurs near 0.33 GPa, the transitionpressure for CsPbBr3 much higher, between 1.2 GPa and 1.5 GPa (Figure 3.13).34,37
3.4.4

Pressure-Response of NCs Made from Sonication
NCs made using the scalable sonication method did not show any appreciable differencein the pressure-response of the PL (Figure 3.14). This shows that despite differences in the42nanocrystal growth kinetics between the two methods, the resulting nanocrystals have the samestructural and electronic properties. The pressure coefficient in the red shifting region of the
CsPbBr3 sonicated sample is -35 meV/GPa, which is in great agreement with the pressure
coefficient from hot injection. This implies that this material is insensitive to differences in reaction
conditions. The sonicated CsPbI3 sample did not match the hot-injection method with a = -7.3
meV/GPa. Given the instability of CsPbI3 NCs when exposed to moisture, this could imply adifference between the two samples coming from the sonication method being done under open
air. It could also be due to the fact that the average size of the nanocrystals was smaller than thosemade in the hot-injection method. However, the PL appears to come mostly from the minority
population of large NCs so this cannot account for the difference on its own. Likely, the differencein the slope is a combination of these two variables.

43

(A)

(B)

Figure 3.14: Pressure response of CsPbI3 (A) and CsPbBr3 (B) nanocrystals synthesized with by
the sonication method. The open square data was taken with the hydraulic high-pressure generator,
while the solid squares were taken with the diamond anvil cell.

44

3.5

Pressure-Response Mechanism
To explain the behavior observed in all four of our samples, we consider the three different

ways in which the perovskite crystal structure can respond to application of pressure: bycompression of the MX6 octahedra, by tilting of the octahedra, or by a phase transition into a
different crystal structure.35,51 The behavior of these two materials under pressure was found by
Zou and co-workers using in situ high pressure powder x-ray diffraction and they found that theperovskites are in the g-phase up until the pressure where we see a disappearance in PL, at which
they become amorphous.37,52 In the following, we will discuss how the first two different modesof deformation can be expected to affect the optical gap thinking in terms of band theory and MOtheory.
The band gap of bulk metal halide perovskites is at the G-point for orthorhombic
structures.53 By invoking the symmetry at the G-point, the valence band maximum (VBM) in
CsPbX3 perovskites must be made from the antibonding interaction of Pb 6s and I 5p (Br 4p)
electronic orbitals in CsPbI3 (CsPbBr3) (Figure 3.15),7,53,54 while the density of states at the
conduction band minimum (CBM) is based primarily on the I 5p (Br 4p) orbitals and Pb 6p orbitals(Figure 3.15).7,53–55 While the small dimensions of the NCs do not allow a rigorous use of the bulk
nomenclature for the symmetry points of the Brillouin zone, we expect that the overall characterof the corresponding MO picture will be qualitatively similar.

45

Figure 3.15: (A) Molecular orbitals generating the VBM. (B) Molecular orbitals generating theCBM (C) Tilting of the octahedra increases the dihedral angle q.

Since the VBM at the G-point is dominated by antibonding interactions between the I 5p
(Br 4p) and Pb 6s orbitals, compression of the octahedra will result in a destabilization of the VBM,
pushing it to higher energies (Figure 3.15). The CBM is largely unaffected by octahedroncompression, since the net overlap of the I 5p (Br 4p) and Pb 6p orbitals at the G-point gives the
CBM a net nonbonding character (Figure 3.15), and small changes in the Pb-X distance will not
result in pronounced changes of the CBM energy. Therefore, the mode of deformation
characterized by octahedron compression will result in a narrowing of the band gap and aconcomitant red shift of the PL peak through the destabilization of the VBM, as observed in otherperovskite materials.24,34,37
Tilting of the octahedra (Figure 3.15) as a second mode of deformation will have theopposite effect, allowing for a change in the sign of a without a solid-solid phase transition. As
shown by calculations by Amat et al.,55 deviation of the Pb-X-Pb angle from 180° changes the
mixing of Pb 6p and I 5p (Br 4p) orbitals in the CBM, and diminishes the contributions of Pb
orbitals to the CBM. As a result, the impact of spin-orbit coupling on the CBM energy is lessened,
and the CBM is destabilized. The net effect of tilting is a band gap increase and concomitant blue46

shift of the PL. This result is consistent with the band gap change induced by varying the A cationand the accompanying change in tilt angle q between adjacent octahedra (Figure 3.15).47,55
The above discussion explains the high-pressure behavior for both CsPbBr3 and CsPbI3
NCs. The earlier change in the mode of deformation for CsPbI3 can be qualitatively explained withthe difference in the ionic radii of Br- and I-. Due to the smaller size of the bromide ions, thepressure at which octahedron compression bears a larger energy penalty than octahedron tilting,with the concomitant change in the mode of deformation, happens at a higher pressure than for thesame perovskite crystal structure with iodide ions. The initial slopes of the pressure response also
reflect the differences in sizes of the Br- and I- as the magnitude of the CsPbI3 slope is greater,
since the larger I- is more sensitive to the overlap of the antibonding interactions in the VBM.
3.6

Conclusions
We have studied the structures and pressure response of the PL of CsPbX3 (X = Br, I) NCs.

Qualitatively, both materials behave similarly under applied hydrostatic pressure. Both begin byresponding to the pressure by narrowing of the band gap until undergoing a change in the mode of
deformation that reverses of the sign of dEg/dp, and then continue to blue shift until a second phasetransition causes the PL to disappear. CsPbI3 NCs experience a change in the mode of deformation
at the relatively low pressure of 0.3 GPa, followed by another solid-solid phase transition to a darkphase, which was reversible upon pressure release. In contrast, the change in the mode of
deformation in CsPbBr3 NCs occurred at a much higher pressure of approximately 1.3 GPa. A
second phase transition to a dark phase was also found for CsPbBr3.
We studied the pressure-response of both materials synthesized in two different ways. The
hot injection method produces nanocrystals vary rapidly, with the reaction going to completion in
milliseconds,31 while the sonication method takes minutes to go to completion. Despite the47difference in growth kinetics, the structural and electronic properties of the nanocrystals were
found to be qualitatively the same. This result means that scalable synthetic procedures such assonication can be used to make large quantities of perovskite NCs for various applications.
3.7

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(35)Gesi, K.; Ozawa, K.; Hirotsu, S. Effect of Hydrostatic Pressure on the Structural Phase
Transitions in CsPbCl3 and CsPbBr3. J. Phys. Soc. Jpn. 1975, 38, 463.

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Hirotsu, S.; Harada, J.; Iizumi, M.; Gesi, K. Structural Phase Transitions in CsPbBr3. J.
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Xiao, G.; Cao, Y.; Qi, G.; Wang, L.; Liu, C.; Ma, Z.; Yang, X.; Sui, Y.; Zheng, W.; Zou, B.
Pressure Effects on Structure and Optical Properties in Cesium Lead Bromide Perovskite
Nanocrystals. J. Am. Chem. Soc. 2017, 139, 10087.

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Szafrański, M.; Katrusiak, A. Photovoltaic Hybrid Perovskites Under Pressure. J. Phys.
Chem. Lett. 2017, 8, 2496.

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Xiao, J.; Yang, Y.; Xu, X.; Shi, J.; Zhu, L.; Lv, S.; Wu, H.; Luo, Y.; Li, D.; Meng, Q.
Pressure-Assisted CH3NH3PbI3 Morphology Reconstruction to Improve the High
Performance of Perovskite Solar Cells. J. Mater. Chem. A 2015, 3, 5289.

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Capitani, F.; Marini, C.; Caramazza, S.; Postorino, P.; Garbarino, G.; Hanfland, M.; Pisanu,A.; Quadrelli, P.; Malavasi, L. High-Pressure Behavior of Methylammonium Lead Iodide(MAPbI3) Hybrid Perovskite. J. Appl. Phys. 2016, 119, 185901.

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Matsuishi, K.; Ishihara, T.; Onari, S.; Chang, Y. H.; Park, C. H. Optical Properties andStructural Phase Transitions of Lead-Halide Based Inorganic–Organic 3D and 2D
Perovskite Semiconductors Under High Pressure. Phys. Status Solidi B 2004, 241, 3328.

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Yin, T.; Fang, Y.; Chong, W. K.; Ming, K. T.; Jiang, S.; Li, X.; Kuo, J.-L.; Fang, J.; Sum,
T. C.; White, T. J. High-Pressure-Induced Comminution and Recrystallization of
CH3NH3PbBr3 Nanocrystals as Large Thin Nanoplates. Adv. Mater. 2018, 30, 1705017.

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Jaffe, A.; Lin, Y.; Beavers, C. M.; Voss, J.; Mao, W. L.; Karunadasa, H. I. High-Pressure
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Yuan, G.; Qin, S.; Wu, X.; Ding, H.; Lu, A. Pressure-Induced Phase Transformation of
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Straus, D. B.; Guo, S.; Cava, R. J. Kinetically Stable Single Crystals of Perovskite-Phase
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Stoumpos, C. C.; Kanatzidis, M. G. The Renaissance of Halide Perovskites and Their

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Kondo, S.; Masaki, A.; Saito, T.; Asada, H. Fundamental Optical Absorption of CsPbI3 andCs4PbI6. Solid State Commun. 2002, 124, 211.

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Lai, M.; Kong, Q.; Bischak, C. G.; Yu, Y.; Dou, L.; Eaton, S. W.; Ginsberg, N. S.; Yang,
P. Structural, Optical, and Electrical Properties of Phase-Controlled Cesium Lead Iodide
Nanowires. Nano Res. 2017, 10, 1107.

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Otto, J. W.; Vassiliou, J. K.; Frommeyer, G. Nonhydrostatic Compression of ElasticallyAnisotropic Polycrystals. I. Hydrostatic Limits of 4:1 Methanol-Ethanol and Paraffin Oil.
Compression Elastically Anisotropic Polycrystals. I. Hydrostatic Limits 41 MethanolEthanol Paraffin Oil 1998, 57, 3253.

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Cao, Y.; Qi, G.; Liu, C.; Wang, L.; Ma, Z.; Wang, K.; Du, F.; Xiao, G.; Zou, B. PressureTailored Band Gap Engineering and Structure Evolution of Cubic Cesium Lead Iodide
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Fröhlich, D.; Heidrich, K.; Künzel, H.; Trendel, G.; Treusch, J. Cesium-TrihalogenPlumbates a New Class of Ionic Semiconductors. J. Lumin. 1979, 18, 385.

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55

Chapter 4

Size-Dependence of the Pressure-Response of CsPbBr3 Nanocrystals

This chapter has been adapted with permission from:
Beimborn II, J. C.; Walther, L.; Wilson, K.; Weber, J. M., “Size-Dependent Pressure-Response of
the Photoluminescence of CsPbBr3 Nanocrystals,” J. Phys. Chem. Lett., 2020, 11, 5, 1975-1980.
DOI: 10.1021/acs.jpclett.0c00174. Copyright 2020 American Chemical Society

4.1

Introduction
Semiconductor nanocrystals (NCs) are a unique class of materials due to their size-

dependent properties. The most striking of these is the change in their absorption andphotoluminescence (PL) spectra that can be tuned based on their size when the diameter or edge
length is less than or equal to the material’s bulk Bohr exciton diameter.1–7 As the NC size
decreases below this characteristic length scale, the electron-hole pair (exciton) experiences strong
quantum confinement, which can have a profound effect on the electronic states of the NC.
Concomitantly, crystal momentum k, used to describe the electronic band structure of bulk solidmaterials, is no longer a conserved quantity because momentum is no longer a good quantum
number in a confined system, causing the bulk material’s electronic structure to turn fromcontinuous bands into discrete excitonic states which can be crudely modeled with a particle in athree-dimensional box.8–11 Invoking the particle in a box analogy, as the NC size decreases, theenergy gap of the excitonic state is shifted to higher energies, blue shifting the material’s
absorption and PL spectra.

56

The change in the optical and electronic properties of NCs due to quantum confinement
are not the only size dependent characteristics, as thermodynamic and structural properties oftenchange as a function of NC size as well. In macroscopic bulk materials, the thermodynamic
properties are governed by the vast majority of atoms that are within the bulk volume of the sample,
and surface effects can often be ignored. In NC samples, a large fraction of the total atoms are on
the surface. This surface-to-volume ratio increases as NC size decreases, altering thethermodynamic and structural properties of NCs. For example, changes in the phase transition ofNCs of different sizes can be drastic. In general, the surface energy at constant pressure relaxes in
the liquid phase relative to the solid phase. This drives melting points to lower temperatures forsmaller NCs, as the contribution of the surface energy to the overall internal energy of the NC
grows.12 Similarly, for many NC systems, it has been shown that the pressure at which the NCs
undergo a solid-solid phase transition (at constant temperature) increases as size decreases.13–16
Due to the high surface to volume ratio of NCs, their ambient crystal structure is generally one thatminimizes the surface energy, which promotes the growth of facets with low index surfaces. In
most cases, NCs converted from ambient phases to higher-pressure phases have higher index
surfaces, and therefore greater surface energy.17 As a consequence, it usually takes more pressure
to force smaller NCs to stabilize the increased surface energy of the high-pressure phase.
The size dependent properties of metal halide perovskite (MHP) NCs have recently
attracted attention due to the unique electronic and optical properties of MHPs as well as for theirpotential applications.18–24 For example, the high surface defect tolerance of perovskite NCs allows
photoluminescence (PL) quantum yields up to 90% without any surface modification,6 reaching
100% with only minor post-synthetic treatment.25,26 Similar to other semiconductor NCs, theoptical and structural properties of perovskite NCs depend on their size, changing significantly

57when the diameter or edge length is less than or equal to the material’s bulk Bohr exciton
diameter,1,2,4–7,24 warranting an investigation into the size-dependence of the pressure-response of
the optical gap.
As discussed in section 3.4.1, many MHP NC systems undergo an isostructural solid-solid
phase transition from their ambient orthorhombic perovskite phase (γ-phase) to a second
orthorhombic perovskite phase under hydrostatic pressure.27–32 This isostructural phase transition
manifests itself in a change in the mode of deformation as pressure increases further. Because thecrystal symmetry does not change in an isostructural phase transition, the increase in surface
indices, generally found in high-pressure crystal phases, does not occur. Therefore, it is not at all
clear a priori whether such pressure-induced phase changes follow a similar size dependence asin other materials, or whether MHPs display a qualitatively different behavior.
In this chapter, I will present results on the detailed size dependent pressure-response of
the PL of CsPbBr3 nanocrystals. Studies like this are necessary to understand the interplay ofstructural and electronic properties in MHPs which can in turn help optimize their performance indevices.33–37
4.2

CsPbBr3 Nanocrystal Synthesis
Recent improvements in methods for synthesizing NCs with higher stability and narrower

size distributions7,26,38,39 allow detailed size-dependent experiments for CsPbBr3 NCs. We tuned
the size of the NCs by controlling the Br-:Pb2+ ratio using oleylammonium bromide (OLA-Br).
CsPbBr3 NCs have Br- rich surfaces, so as the Br-:Pb2+ ratio increases, smaller NCs with larger
surface to volume ratios are thermodynamically favored.7,38 This removes the difficulty of trying
to control the NC size through kinetics, which is nearly impossible due to the very fast nucleationand growth kinetics of MHP NCs.7,38 The OLA-Br was synthesized by adding 1 mL of HBr

58

(Sigma-Aldrich, reagent grade 48%) to 10 mL of purified oleylamine (OLA)40 with vigorous
stirring. This must be done slowly, as the reaction is very exothermic.
For the NC synthesis, 75 mg of PbBr2 (Aldrich, ≥ 98%), 5 mL of 1-octadecene (ODE)(Aldrich, technical grade 90%), 0.5 mL of oleic acid (OA) (Aldrich, technical grade 90%), and a
total of 0.5 mL of OLA and OLA-Br were added to a 25 mL three neck round bottom flask. Wechanged the Br-:Pb2+ ratio by adjusting the OLA-Br:OLA ratio while keeping the final volume
consistent across all syntheses.
In a separate 25 mL round bottom flask, we added 162.5 mg of Cs2CO3 (Aldrich, 99%), 9mL of ODE and 1 mL of OA to make Cs-oleate. Both flasks were heated to 120° C under vacuumwith rapid stirring for 1 hour to remove dissolved atmospheric gases. Next, the flask containing
the PbBr2 was filled with nitrogen gas and brought to a temperature between 80° C and 160° C
depending on the desired NC size.7 The lower the temperature, the smaller the final NCs were. The
Cs-precursor flask was also filled with nitrogen and allowed to cool to 100° C. Then 0.5 mL of theCs-oleate solution was drawn into a nitrogen purged syringe through a rubber septum in the roundbottom flask and swiftly injected into the PbBr2 containing solution. This reaction mixture wasthen cooled down to room temperature by immersing in a room temperature water bath. Since NC
size is determined by the Br:Pb ratio rather than by the kinetics of the reaction, it was not necessary
to cool the solution rapidly after adding the Cs-oleate.41
The monodispersity of the crude reaction mixture varied from one reaction to the next, so
in order to increase the monodispersity of NCs, 10 mL of anhydrous hexanes (Sigma-Aldrich,mixture of isomers anhydrous ≥ 99%) were added immediately after the reaction mixture hadcooled to room temperature.26 This disperses all the CsPbBr3 NCs, but does not disperse unreacted
precursors or large CsPbBr3 aggregates. This turbid mixture was centrifuged and the supernatant59containing the synthesized colloidal NCs was saved as the first size fraction. Next, dry nitrogen
was blown over the surface of the colloid to slowly evaporate off hexanes. Hexanes are a better
solvent for CsPbBr3 NCs than ODE, so upon sufficient evaporation of hexanes, the concentrationof ODE reaches a point where largest NCs began to precipitate out of the colloidal solution. This
event causes a sudden visual change in the solution from transparent to turbid. This turbid solution
was then centrifuged, with the first NC size fraction in the pellet and the rest of the colloidal NCs
remaining in the hexanes/ODE solution. This procedure was repeated until there were no hexanes
remaining. NCs from each size fraction were resuspended in anhydrous hexanes forcharacterization. Only the most monodisperse samples were used in high-pressure experiments.
4.2.1

CsPbBr3 Nanocrystal Characterization
Each size fraction of CsPbBr3 NCs was characterized using photoluminescence,transmission electron microscopy, and powder x-ray diffraction. Each size fraction used had brightPL, with monodispersity on par with the best results reported in the literature at this point.24
4.2.1.1 Ambient Photoluminescence
To be consistent with the PL measurements under pressure, the perovskite NCs were
resuspended in the hydrostatic medium, paraffin oil (Fluka Analytical). Paraffin oil is a poor
solvent for the NCs (similar to ODE) so the solutions were very dilute colloids. Solutions were
excited using a continuous wave 406 nm diode laser focused into the cuvette with an intensity of
0.1 W/cm2. The spectra were measured using a fiber optic spectrometer (Avantes AvaSpec-2048,
300 lines/mm, 2.5 nm resolution, Avantes, 400 μm core UV-Vis-NIR fiber). The resulting PL
spectra are displayed in Figure 4.1.

60

Figure 4.1: PL spectra of NC size fractions in paraffin oil at ambient pressure. Difference in PL
full width half maximum (FWHM) are due to shorter lifetimes for smaller NCs, not from size
distributions.

4.2.1.2 Transmission Electron Microscopy
Transmission electron microscopy (TEM) images were acquired using a FEI Tecnai ST20
and a FEI Tecnai F20 with an accelerating voltage of 200 kV. TEM samples were prepared bydrop casting dilute hexanes solutions of NCs onto 300 mesh carbon film copper grids (Electron
Microscopy Sciences) and allowing the hexanes to evaporate. The size analyses for all size samples
are shown in Figure 4.2. All size distributions have ~10% error which is standard for metal halide
perovskite NC samples with the current size selective techniques.24

61

10 nm

count

10 nm

20 nm

20 nm

20 nm

Figure 4.2: Size distributions and characteristic sample TEM images of all the NC samples
studied. Each size distribution was obtained by determining the sizes of 150 NCs.

62

4.2.1.3 Discussion of the Ambient Crystal Structure of CsPbBr3 Perovskite Nanocrystals
Before addressing the PL pressure response in detail, it is necessary to discuss the crystal
structure of CsPbBr3 NCs. As discussed in section 3.4.1, there was disagreement in the literature
over the crystal structure they adopt at ambient temperature and pressure, as early as when cesium
lead halide perovskite NCs were first synthesized.6,42,43 Even in the most recent literature, thisambiguity remains as NCs with different sizes have been reported to have different crystal
structures. Making matters more complicated, according to one report, NCs with about 10 nm edge
length can have a mixture of crystal structures at room temperature and ambient pressure.
Atomically resolved high resolution transmission electron microscopy (HRTEM) of CsPbBr3 NCs
by Brennen et al. revealed that NCs with 5 nm edge length were entirely cubic in crystal structure,even though larger NCs were at least partially orthorhombic.44 For 5 nm nanocrystals (and up toat least 6.5 nm), X-ray diffraction (XRD) patterns suffer from Scherrer broadening that made it
impossible with certain samples to unambiguously distinguish cubic from orthorhombic based on
XRD alone.34,45 Further, there is evidence of the coexistence of tetragonal and orthorhombic crystal
structures in CsPbBr3 NCs at liquid helium temperature, even though the orthorhombic totetragonal phase transition is at 88 °C in bulk CsPbBr3.45,46 The complicated identification of
crystal structure is not unique to MHPs, similar behavior has been observed in oxide perovskites,
where the structure of crystalline domains can vary, even in nanocrystalline samples. For example,
BaTiO3 NCs have a cubic “shell” surrounding a tetragonal “core.”47
4.2.1.4 Powder X-Ray Diffraction
We analyzed our samples by XRD (Figure 4.3) at ambient temperature and pressure. For
sizes ≤ 8 nm, the broadening due to overlap of the large number of diffraction features and Scherrer
broadening make it impossible to make a conclusive assignment. Nevertheless, we do observe63diffraction features for 22° ≤ 2θ ≤ 30° for each size studied here that do not belong in the a-phasepattern, suggesting the γ perovskite crystal structure for all of our samples. The main difference
between the cubic α-phase and the orthorhombic γ-phase is the symmetry reducing tilt of the PbBr6
octahedra. The reduced symmetry of the γ-phase adds diffraction features to the XRD pattern,
often clustered around angles seen in the a-phase pattern; however, it does not remove any of thefeatures associated with the cubic structure. In CsPbI3 NCs, the crystals adopt the γ-phase for all
sizes that have been studied, although the smallest nanocrystals exhibit less of an octahedral tilt
than the larger nanocrystals, decreasing the deviation from a cubic structure.24 The small deviations
from the cubic phase make the diffraction features associated with the orthorhombic phase evenless pronounced. While the assignment of orthorhombic may seem to contradict the HRTEM
results mentioned above, HRTEM is biased toward the structure of the surface, which likely
exhibits even less octahedral tilt (resulting in an essentially cubic character) due to the high surface
tension of NCs.34,47
Taking our data and the recent results by Luther and coworkers on CsPbI3 NCs into
account,24 we assume that the CsPbBr3 NC in the present work are orthorhombic for all sizes dueto the existence of features in the XRD patterns that should not exist if the samples were cubic.
The smallest sizes likely experience less of an octahedral tilt, making them nearly cubic as wasobserved in CsPbI3 NCs.24,34,42–44

64

Figure 4.3: XRD Analysis of all nanocrystal samples used in our experiments. Part (A) shows
simulations for cubic and orthorhombic structures as a semi-logarithmic plot to accentuate the lowintensity reflections. The red lines represent the orthorhombic perovskite pattern48 and the violet
lines are for the cubic perovskite crystal structure.49 Part (B) shows a comparison of experimental
XRD data with the simulated patterns (linear scale). Peaks marked with an asterisk (appearing insome of the samples, most clearly for 5.7 nm and 6.7 nm edge length) are due to residual precursor
material.

65

4.3

PL Pressure-Response of CsPbBr3 Nanocrystal Samples
The pressure induced phase changes in MHPs are conveniently accompanied by changes

in the behavior of the PL under pressure.27,28,32,34 This allows structural information to be studied
by monitoring the PL spectrum of a NC sample as a function of pressure. While in situ XRD isneeded to initially determine the pressure dependent phase behavior of a material, once the PL
response is known it can be used to track the same changes in a given material.34,45,46 This gives us
the ability to understand trends in the size-dependent structural behavior under pressure without
the need to use a synchrotron x-ray source. This approach has been used from the earliest
experiments on the pressure response of semiconductor NCs50 to monitor phase change behavior
in high-pressure experiments, and has more recently also been employed for perovskite NCs inboth high-pressure and temperature dependent experiments.27,28,34
As a simple, phenomenological description of the pressure response, the pressure
dependent change of the PL peak energy from ambient can be written as
Δ𝐸(𝑝) = 𝐸(𝑝! ) + 𝛼(𝑝)𝑝(4.1)

where a is a (pressure dependent) pressure coefficient encoding the shift of the PL peak. As
discussed in section 3.5, a transition pressure has been shown to exist for various MHPs where theresponse of their electronic structure to further pressure increase changes from a red shift to a blue
shift, i.e., where a(p) changes its sign.27–29,51,52 This sign change can be explained by the orbital
contributions to the band structure and by the change in the mode of deformation at the transitionpressure.
In lead halide perovskites, the behavior of the crystal structure under pressure and theaccompanying effect on the electronic structure is well known.27–29,32 For CsPbBr3, the density of66

states at the valence band maximum (VBM) consists of Pb 6s and bromide 4p orbitals with antibonding interaction between the two.27,53–55 The conduction band minimum (CBM) is largely
formed from Pb 6p orbitals and bromide 4p orbitals with non-bonding interactions between
them.27,53–55 As the crystal lattice responds to pressure, the mode of deformation is firstcharacterized by isotropic compression of the PbBr6 octahedra, forcing greater overlap of theantibonding configuration of the Pb 6s and bromide 4p orbitals.20,54,56 The compression of theoctahedra therefore causes an increase the VBM energy, while leaving the CBM largely
unaffected. This causes a decrease of the band gap that manifests itself as a red shift of the PL
peak.
At the transition pressure, the mode of deformation changes concomitant with theaforementioned isostructural phase transition.30 As the pressure is increased further, instead ofcontinued octahedral compression, the octahedra begin to distort and tilt relative to one another,but for CsPbBr3, they preserve the overall orthorhombic crystal symmetry.27,42,43 This octahedral
tilting and deformation diminishes the Pb character of the CBM and with it the stabilization of the
CBM afforded by the spin orbit coupling in the Pb atoms.53,57 Consequently, the CBM energy
increases, while the VBM is mostly unaffected, which results in a blue shift of the PL spectrum.
This change in the sign of the pressure coefficient is a direct result of the change in the mode of
deformation of the crystal lattice and the isostructural phase transition, so it can be used to track
this structural change without using in situ x-ray diffraction measurements.
The transition pressure and the pressure coefficients a for each NC size were found bypressurizing our NC samples in a diamond anvil cell while tracking the PL peak energy (Figure4.4). Finally, the magnitude of the initial pressure coefficient α, which is defined as 𝛼 = 𝑑𝐸/𝑑𝑝,
is relatively constant and close to the reported bulk value for NCs with edge lengths above 7.5 nm,

67

then decreases in magnitude for edge lengths below 7 nm (Figure 4.6). We will discuss these
phenomena as follows by taking into account the surface-to-volume ratio, together with thetransition to the strong confinement regime below 7.5 nm.14,15,17,58,59

Figure 4.4: PL pressure response of NC samples studied in the present work. Open circles are raw
data coming from at least two high pressure runs for each size, and black squares are the mean ΔE
binned in pressure intervals of 0.2 GPa. The transition pressure is marked with vertical dotted lines
with the uncertainty shaded in gray. The uncertainty in pressure for each data point is ±75 MPa.

The transition pressure decreases slightly with decreasing NC size for NCs above 7.5 nm,
exhibits a step-like decrease as edge length decreases below ca. 7.5 nm, and remains at a constantvalue as the size is decreased further (Figure 4.5). For the largest NC samples studied, the transitionpressure is slightly higher than in bulk samples. In contrast with other NC materials, the change inthe mode of deformation at the isostructural phase transition point in MHPs by definition does notchange the lattice indices of their facets.27–29 Without significant surface rearrangement, there is68

probably no large penalty in the surface energy, so the change in the overall internal energy of theNCs at the transition does not increase drastically as the NC size decreases.

Figure 4.5: The transition pressure at which the PL turns from a red shift to a blue shift as afunction of NC size. This is compared to the transition pressure in bulk CsPbBr3 (dotted line) andthe corresponding value reported in Xiao et al.28 for 11.9 nm CsPbBr3 NCs (dash-dotted line).

For the smallest sizes, the fluctuation length scale that can cause an isostructural phasetransition involving a different octahedral tilt could be shorter than for the larger NCs, leading toa phase transition sooner since NCs undergo phase transitions starting from one nucleation sitethat quickly propagates through the rest of the crystal.13,17,50,58,59 Furthermore, low energy Raman
spectroscopy results on CsPbBr3 have shown that local polar fluctuations at room temperaturecause the Cs+ ion to be displaced off center, inducing tilting in the octahedra.60 With a higher
surface-to-volume ratio and the surface acting as a nucleation site, these fluctuations that tilt the69

octahedra on small NCs may be more likely to cause a coherent phase transition at a lower pressure
than in larger NCs, leading to a lower transition pressure.
The transition pressure for NCs with sizes from 5.7 nm to 7.3 nm edge length remains
constant around 0.75 GPa, all of which have physical sizes equal to or smaller than the bulk Bohr
exciton diameter ca. 7.5 nm.46 The consistency in the transition pressure as the size is decreased
below 7.5 nm, may be an indication that crossing over into the strong quantum confinement regime
in the NCs plays a role in the structural transition. Charge carriers form large polarons in CsPbBr3,
distorting the crystal lattice upon photoinduced excitation.61 This distortion can actually cause areversible photoinduced phase transition when 400 nm light excites CsPbBr3 NCs (ca. 11 nm),lasting on the order of 5 ns.62 These NCs undergo an orthorhombic to cubic phase transition, whichhappens because the excitation causes a lattice dilation, subsequently rotating the octahedra so that
the Pb-Br-Pb bond angles increase to 180°. Photoexcitation in the cubic perovskite methyl
ammonium lead iodide (MAPbI3) causes a distortion in the PbI6 octahedra away from the cubic
structure,63 not unlike the distortion found in the high-pressure phase of CsPbBr3 NCs.28 The
photoinduced structural changes are not due to local heating of the sample, but are direct resultsof coupling to phonon modes.62,63 The nanocrystals below 7.5 nm edge length adopt anorthorhombic crystal structure that is already closer to the cubic phase than the larger NCs as
discussed above. Therefore, it is possible that the photoexcitation in these small NCs induces anoctahedral distortion characteristic of the higher-pressure orthorhombic phase. Under hydrostaticpressure, this photoinduced distortion is no longer only metastable, but becomes favored when the
distortion is enough to overcome the barrier of the phase transformation to the high-pressure phase.
This would initiate the band gap widening by decreasing the Pb 6p character in the CBM as thepressure is increased further, changing the sign of α. It is important to note that our PL

70measurements do not provide information about octahedral tilt or distortion at any given pressure,but they can tell us about a change in octahedral tilt or distortion from one pressure to the next,
since an increase in the tilt/distortion causes destabilization of the CBM.
In addition to having a lower transition pressure, NCs below 7.5 nm edge length also showa smaller magnitude of the initial pressure coefficient for the isotropic compression phase (Figure4.6). As nanocrystal size decreases below the bulk Bohr exciton radius, the wavefunction isdelocalized over the entire nanocrystal, coupling the core states to surface polaronic states.64–66

Figure 4.6: The magnitude of the initial pressure coefficient decreases as NC size increases. The
dotted line represents the bulk pressure coefficient reported in Zhang et al.67

The surface polaronic states are below the band gap energy and are less affected byperturbations to the crystal lattice than the core electronic states in NCs are. This would predictthat for NCs in the strong confinement regime, the pressure coefficient measured from tracking
PL would approach zero, as there is a low tunneling barrier to the surface polaronic states due to71the strong coupling (Figure 4.7). This has been experimentally shown for CdSe NCs.66 Likewise,
our data show that CsPbBr3 NCs that are smaller than the bulk Bohr exciton radius experience alarge drop in the magnitude of the pressure coefficient, likely due to the strong coupling to surface
polarons.
A)

B)

Figure 4.7: (A) Large NC showing exciton wave function within the bulk of the crystal, which
produces lower coupling to surface states. (B) Small NC showing exciton wavefunction extending
to the surface of the NC, which enhances the coupling to surface states.

4.4

Conclusion
In summary, we have probed the isostructural phase transition pressures and pressure

coefficients for a range of sizes of CsPbBr3 NCs using PL spectroscopy. Contrary to NC systems
whose pressure induced solid-solid phase transitions involve changing the crystal symmetry, weobserved a reduction in the phase transition pressure as NC size decreases. We explain thisobservation by the fact that the lowest pressure phase transition in perovskite NCs does not leadto the formation of high index facets, so the energy barrier for the phase transition is not drasticallyincreased as NC size decreases. Furthermore, the smaller size of the NCs means that the fluctuation
length scale needed to cause a coherent transition is necessarily smaller than for the larger NCs.
The NCs with the strongest quantum confinement exhibit both a drop in the transition pressure aswell as the magnitude of the pressure coefficient. Both of these effects can be explained by the72complete delocalization of the wavefunction over the whole NC, allowing strong coupling topolaronic states.
4.5

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Chapter 5

Pressure Response of Rubrene Upconversion Photoluminescence ThroughCation and Anion Sensitized Triplet-Triplet Annihilation

This chapter has been adapted with permission from:Spectroscopy of Resonant Intermediate States for Triplet-Triplet Annihilation Upconversion in
Crystalline Rubrene – Radical Ions as Sensitizers, Beimborn II, J. C.; Zagorec-Marks, W.; Weber,J. M., J. Phys. Chem. Lett., 2020, 11, 17, 7212-7217. DOI: 10.1021/acs.jpclett.0c01999. Copyright2020 American Chemical Society

5.1

Introduction
Organic semiconducting materials are much softer than inorganic semiconductors due tothe weak nature of the van der Waals forces that hold the crystal together. This makes pressure an
obvious tool to probe how changes to the intermolecular distances affect the electronic structureof the organic material. A number of organic semiconducting materials have the ability to undergo
single fission (SF) which has potential to improve photovoltaic efficiencies.1 SF takes place whena singlet Frenkel exciton localized on a single molecule can share its energy with a neighboring
ground state molecule, splitting the singlet exciton and creating two triplet excitons.1–3 This is aspin allowed process because the triplet pair, 1(TT) is still a singlet overall.1 There are many factorsthat go into whether or not an organic material will be able to undergo SF, but one importantfeature the material must have is sufficient intermolecular coupling.1,4,5 Efficient SF also requiresthat
𝐸(𝑆% ) − 2𝐸(𝑇% ) ≥ 0

5.1

82

where E(S1) is the energy of the first singlet excited state and E(T1) is the energy of the first triplet
state. For negative energy differences close enough to zero, SF can still happen through thermal
activation.
This phenomenon has gained a lot of interest because it could improve the efficiency oforganic photovoltaics (OPV) devices by creating two excitons from only one absorbed photon.1,4,6
SF can be a faster process than fluorescence in some organic materials, even if thermal activationis required. In rubrene (5,6,11,12-tetraphenyltetracene, see Figure 5.1) crystals, 𝐸(𝑆% ) = 2.23 eV
and 𝐸(𝑇% ) = 1.14 eV, so 𝐸(𝑆% ) − 2𝐸(𝑇% ) = −0.05 eV, which means with thermal activation, SF
should occur.7 The SF rate constant has been measured to be 5 ´ 1010 s-1 when exciting above theband gap (3.12 eV excitation energy, 2.23 eV band gap energy) while the fluorescence rate
constant is only 6.25 ´ 107 s-1,7,8 and SF is responsible for quenching 99.9% of the fluorescence inrubrene crystals.9
The reverse process where two triplet excitons fuse to make one singlet exciton can occur
as well.6,10,11 It happens through the same intermolecular electronic coupling process as SF, but inreverse. Unlike fission, it requires that the two triplet excitons collide for TTA to occur. TTA was
first observed by Parker and co-workers over fifty years ago,12 but has recently regained interest
due to applications in improved OPV efficiency,13–15 medical imaging,16 and photocatalysis.17 The
effects of intermolecular coupling on SF and TTA have been studied extensively in the past bychanging the rates of SF in different polymorphs, by adding different functional groups, or bycovalently bridging dimers.2,3,18–20 By using high-pressure to alter the crystal structure of amaterial, a continuous picture can be built up to how SF or TTA are affected by the pressure
induced changes in intermolecular coupling, rather than the discrete, and perturbative methods
mentioned above.

83

Rubrene has been used widely in UCPL systems in both the solution and solid phase.21–25
It is also an important model system for organic semiconductor crystal materials with high carrier
mobilities, on the order of 1-20 cm2 V-1 s-1.26 Orthorhombic rubrene single crystals can be grownusing sublimation and physical vapor transport27 and are usually needle-like with sizes ranging
from millimeters to centimeters along the elongated crystal axis.28 We recently showed thatrubrene crystals undergo TTA-UCPL using radical ions embedded in the crystal as near-infraredsensitizers. In this chapter, I will explain the mechanism behind radical ion sensitized TTA-UCPL
in rubrene crystals and show through our high-pressure results that TTA is quenched throughcompression of the crystal lattice, and that this also most likely quenches SF by monitoring the PL
intensity of the rubrene.

Figure 5.1: Rubrene (5,6,11,12-tetraphenyltetracene) molecular structure.

5.2

Rubrene Crystal Preparation
Crystals used for UCPL experiments were grown using a procedure for physical vapor

transport (PVT) adapted from Zeng et al.27 For each trial, 20 mg of rubrene powder (Sigma84

Aldrich, sublimed grade, 99.99%) were loaded into a 40 cm long borosilicate glass tube, which
was then placed in a tube furnace. One end of the furnace was connected to an argon tank and flow
controller, and the other end was connected to a mineral oil bubbler to prevent back flow of
atmospheric gases. The argon flow was set at 100 mL/min. The furnace was purged with argon
through the bubbler for ten minutes to ensure that there was no remaining atmospheric oxygen.
After purging, the furnace was set to ramp up the temperature to 290° C over the course of 3 hours.
The temperature was then held at 290° C for 24 hours. After 24 hours, the temperature was allowed
to cool back to room temperature before extracting the crystals. Crystals were generally needlelike (Figure 5.2) with lengths on the long axis between 1 mm and 10 mm, widths ca. 0.5 mm, andthickness ca. 5-10 µm.
Crystals were carefully collected from the borosilicate tube to avoid damaging them. To
this end, an electrostatically charged glass rod inserted into the tube was used to collect the crystals
by electrostatic attraction. Once crystals were removed from the tube, they were placed on either
the outside of a modified quartz cuvette used for the UCPLE and temperature dependence
experiments or on glass microscope slides for other UCPL experiments and characterization. Static
charges in the crystals and on the glass or quartz surfaces were enough to securely hold the crystals
to the quartz cuvette or glass slides. Crystals used in the diamond anvil cell (DAC) needed to besmall enough to fit in the sample compartment in a stainless-steel gasket between the diamonds(see section 2.2 for details) which required carefully breaking off pieces of larger specimens before
inserting them into the gasket hole.

85

Figure 5.2: Microscope image of a rubrene crystal grown with PVT.

5.2.1

Characterization of Rubrene Crystals

5.2.1.1 UV-Vis Absorption
UV-vis absorption spectroscopy was performed on PVT grown rubrene crystals to confirm
there were no impurity absorption features as well as estimate the thickness of the crystal (Figure5.3).27,29–31 We measured the absorbance in transmission mode using a Agilent Cary 5000 UVVis-NIR spectrophotometer by mounting a single rubrene needle-like crystal to a glass slide. The
baseline spectrum was measured through the same glass slide, but next to where the crystal was
mounted. To estimate the thickness, we followed the method by Fillard et al. for calculating film
thickness in an absorbing material. This method takes advantage of the etalon effect between thefirst and second surfaces of the crystal producing interference fringes on the baseline of thespectrum (Figure 5.3, 575 nm – 700 nm).31 Assuming a constant index of refraction for rubrenefrom 600 nm – 700nm of 2.0,32 the spacing of fringes in our sample, gave us an estimated crystal
thickness of 5.3 µm for this specimen.

86

Figure 5.3: UV-vis absorption of a rubrene crystal grown from PVT. The oscillations on thebaseline beyond 550 nm are interference fringes from an etalon effect between the first and second
surfaces of the crystal.

5.2.1.2 Powder X-Ray Diffraction
We used powder x-ray diffraction (Bruker D8 Advance) on as-purchased rubrene powders
and PVT grown crystals (Figure 5.4). In both cases, we placed a few powder grains or crystals
onto a Si low-background holder (Bruker). Both powder and crystal samples have orthorhombic
symmetry and space group Cmca (a = 26.8 Å, b = 7.2 Å, and c = 14.2 Å), consistent with theliterature.29 Some peaks are missing from the crystal sample because of imperfect randomizationof the orientation of the crystals stacking on the sample holder, preventing access to all possible
reflections in the diffractogram. Despite the missing peaks, the reflections present in thediffractogram are a clear match to the orthorhombic powder sample.

87

Figure 5.4: Powder XRD of rubrene samples. (A) calculated XRD pattern for triclinic rubrene,(B) calculated XRD pattern for orthorhombic rubrene, (C) crystals grown using PVT, and (D)rubrene powder. Intensity axes are on a logarithmic scale in order to see both the low and highintensity peaks.

5.3

Upconversion Photoluminescence in Rubrene88

In general, TTA upconversion photoluminescence (UCPL) utilizes a combination of a“sensitizer species”, absorbing longer wavelengths and transferring energy to an “emitter” species,
which emits radiation at shorter wavelengths. The concept has been successfully demonstrated insolutions10,11,23,24,33,34 as well as solid materials.8,22,25,35–39 In order for TTA-UCPL to work in aparticular system, the sensitizer and emitter combination must fulfil several requirements.34 The
sensitizer must be able to undergo efficient intersystem crossing into its triplet state once it has
absorbed a photon, and many sensitizers therefore incorporate heavy metal atoms to increase spin
orbit coupling.40,41 Next, energy must transfer from the sensitizer to the triplet state of the emitter,
requiring a sufficiently long lifetime of the sensitizer triplet state. The emitter triplet state (as an
excited molecule in solution or as a triplet exciton in a crystal) must then diffuse in order to findand interact with another emitter in its triplet state. If the two triplets happen to migrate closeenough, and are in the combined singlet state, 1(TT), they can then combine energy throughintermolecular electronic coupling to bring one molecule to the singlet excited state, S1, leaving
the other in the ground state, S0. The excited singlet molecule can then fluoresce, emitting lightwith a higher energy than was originally absorbed by the sensitizer.
Interestingly, UCPL has been demonstrated in rubrene crystal and powder samples without
any added sensitizing material.8,21,25 Rubrene crystals are able to convert sufficiently intense nearinfrared (NIR) light to visible light matching the fluorescence spectrum of solid rubrene.8,21 One
obvious explanation of this phenomenon would be that rubrene is undergoing two photon
absorption (TPA, resonant or non-resonant), emitting from its singlet excited state, in which casethe upconversion yield would vary with the square of the incident light intensity. However, using
both cw and fs-pulsed radiation ca. 800 nm, a quartic dependence on the laser intensity at thelowest laser intensities is observed, implying a four-photon process rather than the quadratic

89

signature of TPA.8,25 This suggests the existence of a resonant intermediate state in the rubrene
crystal which absorbs NIR light. This intermediate state then transfers energy to rubrene triplet
excitons, which can then undergo TTA.
We used upconversion photoluminescence excitation (UCPLE) spectroscopy to measure
the wavelength-dependent absorption characteristics of the species giving rise to the intermediate
absorption in the NIR, using rubrene powders (Sigma-Aldrich, sublimed grade 99.99%) as well as
single crystals grown using physical vapor transport.27,29 For collecting UCPLE spectra, wescanned the frequency of an optical parametric oscillator pumped by a Nd:YAG laser (pulse
duration 5-7 ns, see sections 2.4.1 - 2.4.4 for experimental details), and measured the intensity of
the upconversion photoluminescence as a function of laser frequency (Figure 5.5).

90Figure 5.5: Bottom panel: solution absorption spectra of the rubrene radical cation (orange line)
and radical anion (blue line); data in the lower panel were adapted from Tagawa and co-workers.42
Top panel: UCPLE spectrum of crystalline rubrene, corrected for a four-photon process bydividing the raw UCPL intensity by the fluence to the fourth power. The open circles are individual
data points, the black trace is a 20-point-smoothed curve to guide the eye. The red line is thearithmetic product of the absorption spectra of the radical ions shown in the lower panel.

91

We observed three distinct features in the NIR with enhanced upconverted
photoluminescence, at ca. 11,100 cm-1 (900 nm), 12,200 cm-1 (820 nm), and 13,000 cm-1 (769 nm),respectively. The mechanism for electrochemiluminescence of rubrene in solution sheds light on
the mechanism for UCPL in the crystals. It involves the recombination of a rubrene radical cation
and a rubrene radical anion, producing an excited triplet and a ground state, both neutral
molecules.43–45 If the presence of both excited anions and cations is necessary to observe UCPL,
then the UCPLE spectrum of rubrene should be proportional to the product of cation and anion
absorption spectra:
𝑌&#'( (𝜔) ∝ 𝛼) (𝜔) · 𝛼" (𝜔)5.2

where 𝑌&#'( (𝜔) is the upconversion yield, and 𝛼) (𝜔) and 𝛼" (𝜔) are the absorption coefficientsof the rubrene radical cation and radical anion, respectively. Figure 5.5 shows a comparison of theexperimental data and the product of the absorption spectra of the radical ions, taken from the workof Tagawa and coworkers.42 The overall shape of the UCPLE spectrum agrees quite well with the
product of the ion spectra, strongly suggesting that the excitation of both cations and anions isnecessary for the observation of UCPL in rubrene. Deviations between our experimental results
and the product of the ion absorption spectra are likely due to the fact that the ion absorption
spectra were measured in solution whereas our measurements were performed on solid crystals.42
These deviations are in all cases less than ca. 200 cm-1, which is a reasonable expectations for
shifts due to solvatochromic and crystal effects.
While the analogy to solution phase chemiluminescence is compelling, we must also ruleout other possible mechanisms such as non-resonant TPA. Neutral rubrene does not absorb
resonantly in this region, and there is disagreement in the literature over the non-resonant TPA
spectrum of rubrene.46,47 To test if TPA was responsible for the UCPL, we measured the UCPL

92

intensity as a function of laser intensity with the laser frequency resonant with the observed peaks.
If TPA were the origin of UCPL, the UCPL intensity would scale quadratically with the intensity.
However, we found a quartic dependence on intensity, in agreement with previous work by
Bardeen and coworkers (Figure 5.6).8

Figure 5.6: Dependence of the UCPL signal intensity on the excitation laser intensity at three
excitation wavelengths. Signals were scaled to compare results from multiple samples. Opencircles are raw data, the blue line is a fit of the laser intensity dependence to the experimental data.
Laser excitation wavelength was set to 769 nm (A), 821 nm (B), and 890 nm (C) to be resonantwith the observed transitions in the UCPLE spectrum. The exponents from the fit of the data are
4.16 ± 0.20 for 769 nm, 4.16 ± 0.22 for 821 nm, and 3.73 ± 0.30 for 890 nm excitation.

93

Rubrene powders used as purchased without further purification (at 99.99% nominal
purity) qualitatively show the same UCPLE spectrum as twice sublimed rubrene crystal samples(Figure 5.7) with similar overall UCPL signal intensities, so the presence of a chemical impurity
causing UCPL is very unlikely.

Figure 5.7: UCPLE spectrum of rubrene powder as received from Sigma Aldrich. Raw data points
are plotted as open circles. The black trace is a 50-point-smoothed curve to guide the eye.

Rubrene can undergo reactive changes when exposed to light in the presence of oxygen,although the most recent literature shows that typical amounts of photooxidation products at thesurface of rubrene crystals handled at normal conditions are rather small.48 In addition, theconjugation in rubrene is broken in all common degradation products. As a result, one would
expect that the degradation products have larger HOMO-LUMO gaps and S0 ® S1 transitionenergies that are higher than for rubrene itself, ruling out the possibility of a degradation productsensitizing TTA in the NIR.

94

Since recombination of radical anions and cations in solution results in the formation of
two neutral molecules, one in the ground state and the other in the T1 triplet state,44,45 a mechanistic
picture emerges that explains the shape of the UCPLE spectrum (Figure 5.5 and Figure 5.7) insolid rubrene, as well as the quartic intensity dependence of the process (Figure 5.6). NIR radiation
is not energetic enough to produce charged radical ion species in rubrene, so the charged species
must already exist in the crystal prior to excitation.22 However, this begs the question as to why
the observed UCPL process in solid rubrene requires excitation, since electrogenerated
chemiluminescence in rubrene solutions through the formation of a triplet is observed without
prior photoexcitation.44,45
In solution, cationic and anionic species can freely migrate to find one another,recombining and forming triplet excited molecules. If this were the case in solid rubrene, thecharged species would rapidly recombine, leaving little to none left for UCPL. However, if thecharged species are immobilized within the crystal lattice at surface sites or defects, excitation may
be necessary to overcome the trap barrier, allowing diffusion through the crystal. Therefore, thestarting species for the observed UCPL process may be localized, immobile rubrene anions andcations. The charged nature of the rubrene anions and cations likely distort the local crystal lattice,which can be thought of as charged defect sites. After excitation, these charged sites become
mobile, leading to the formation of charge transfer (CT) polarons,49–51 enabling the charges tomove through the crystal after excitation. Although the lifetimes of such CT polarons in crystalline
rubrene have not been measured to our knowledge, these relaxation processes occur by losing
energy to phonon excitations as the mobile charge distorts the lattice as it moves. If a similar timescale as relaxation of the S1 → S0 in neutral rubrene, relaxation of the charged species may happen
on the 100 ps – 100 ns time scale.7 The cation and the anion are both doublets so when they95

combine in a spin allowed process, they can produce a triplet exciton (assuming the same spin on
the cation and the anion) or a singlet exciton (assuming opposite spin on the cation and anion) as
well as a neutral ground state molecule (Figure 5.8).43,45 Once there is a sufficient population of
triplet excitons, they can recombine via TTA, producing a rubrene molecule in the S1 state andanother in the neutral ground state.
This proposed process has many opportunities for loss along the way, which is apparent in
the low yield of UCPL. For example, the CT polaron could non-radiatively relax before it finds a
partner of opposite charge, immobilizing the charge once again. The triplet excitons may relax
through a process other than TTA, which will not provide an excited singlet. Or, since SF has afaster rate than fluorescence in rubrene, the produced excited singlet may share its excitation witha neighboring molecule, remaking two triplets.8,9,52 There are of course even more potential loss
mechanisms than what was mentioned here.

Figure 5.8: (A) Qualitative reaction diagram showing the recombination of electrons and holes in
the proposed mechanism of UCPL from the excitation of trapped electrons (left) and holes (right)

96

through relaxation processes in the crystal to the generation of a triplet exciton (center). (B)Schematic electron configurations in the reaction mechanism. Ground and excited state electron
configurations of rubrene ions have been determined using TDDFT (see Supporting Information).

A simple kinetic model which takes into account as much of the known information about
each step of the proposed mechanism as possible should corroborate the quartic dependence of theexcitation intensity if this mechanism is indeed correct. The excited mobile negative and positive
charge carriers, Ne and Nh, are governed by𝑑𝑁*= Φ(t)𝑁*! 𝜎#+* − 𝑘, 𝑁* 𝑁- − 𝑘( 𝑁*𝑑𝑡

5.3

and 𝑑𝑁= Φ(𝑡)𝑁-! 𝜎#+- − 𝑘, 𝑁* 𝑁- − 𝑘( 𝑁𝑑𝑡

5.4

where 𝑁*! and 𝑁-! are the initial densities of the trapped electrons and holes, Φ(t) is the photon
fluence (in photons per cm2 and s, the time dependence encodes the laser pulse duration), and 𝜎#+*and 𝜎#+- are the mobile charge carrier formation cross sections. The parameter 𝑘, is the charge
recombination rate constant, and 𝑘( is the rate constant for loss processes, depleting the mobile
charge carriers (set to be the same for negative and positive carriers for simplicity). The density of
triplets, NT, is described by𝑑𝑁+= 𝑘, 𝑁* 𝑁- − 𝑘. 𝑁+/ + 2𝑘01 𝑁0 − 𝑘2 𝑁+
𝑑𝑡

5.5

where 𝑁0 is the density of singlet excitons formed by TTA, 𝑘. is the TTA rate constant, 𝑘01 thesinglet fission rate constant, and 𝑘2 a triplet quenching rate constant. Finally, the singlet populationis governed by

97

𝑑𝑁0
= 𝑘. 𝑁+/ − 𝑘'( 𝑁0 − 𝑘01 𝑁0
𝑑𝑡

5.6

where 𝑘'( is the PL rate constant. Several of the individual steps in the proposed mechanism havebeen studied, and therefore we can find several parameters of the proposed model from theliterature and are summarized in Table 5.1.8 There are of course unknown parameters in the
proposed model and others that could be added to our model to account for more loss mechanisms
such as triplet-triplet quenching. The unknown parameters in that were included in the current
model are 𝜎#+* , 𝜎#+- , 𝑘, , and 𝑘( . A wide range of these unknown parameters exists for which themodel reproduces the experimentally observed quartic intensity dependence of UCPL and aretabulated in Table 5.1. Although the model is relatively simple, the match with our experimental
data supports the proposed mechanism.

Table 5.1: Parameters used in the kinetic model𝝈𝑪𝑻𝒆 , 𝝈𝑪𝑻𝒉 (cm2)(a)𝒌𝑹 (cm3 s-1)(a)𝒌𝑳 (s-1)(a)𝒌𝑨 (cm3 s-1)(b)𝒌𝑺𝑭 (s-1)(b)𝒌𝑸 (s-1)(b)𝒌𝑷𝑳 (s-1)(b)

10-21 – 10-15

10-15 – 10-9

105 – 10610-12

5·10101.67·104

6.25·107(a)Range of parameters tested in the present work that produce quartic intensity dependence.

(b)

Values taken from Table 2 in ref. 8.

The initial source of the localized charges is not entirely clear, but they could originate
from charges that tunnel into the rubrene from surrounding surfaces, such as the borosilicate tube
the crystals were made in, or from the surface of the cuvette that they were mounted to formeasurements. What is clear is that the proposed mechanism will result in a depletion of the98initially localized charge carriers over time as they are lost due to recombination. This is consistent
with the observation of significant photobleaching (Figure 5.9) of the UCPL. This was also
observed by Nienhaus and coworkers in other processes that involve intrinsic charge carriers inrubrene and tied to surface effects.22 Irradiation of rubrene in paraffin oil with a pulsed excitation
source operating at 20 Hz and a time-averaged intensity of 50 mW/cm2 results in the UCPL signal
decaying, reaching 45% of its initial value after ca. 450 s (7.5 minutes) and only slightly decreasingfrom this value over the course of hours (Figure 5.9). In paraffin oil, the UCPL signal does notrecover when left in the dark, allowing to study the effect of pressure on the UCPL intensity underhigh pressure when using paraffin oil as a pressure transmitting medium. This is an importantdetail because our pressure experiments require a twenty-minute equilibration time (see section
2.2 for details) between measurements, so there cannot be significant changes to the UCPL
intensity before and after the equilibration period.

Figure 5.9: Bleaching of UCPL under constant irradiation of 765 nm pulsed radiation operating
at 20 Hz and an average power of 50 mW/cm2. The red dashed line guides the eye to the slow
decay of intensity over the course of hours. The vertical blue dashed lines indicate when the laser
was blocked from irradiating the sample.

99

5.4

Pressure-Response of the Intermediate StateWe measured the UCPLE spectrum from 12,200 cm-1 (820 nm) to 13,600 cm-1 (735 nm) at

ambient pressure in the diamond anvil cell (DAC) as well as at an elevated pressure of 1.65 GPa(Figure 5.10). The signal to noise is much lower for these measurements than the previous UCPLE
spectra shown due to the significant decrease in rubrene material that can be used in the DAC (seesection 2.2 and 2.4.3 - 2.4.4 for experimental details). Under pressure the UCPLE feature ca. 765
nm blue shifts and broadens. Once we knew roughly how the absorption spectra of the cation andanions in the rubrene sample evolve under pressure, we then measured how the intensity of the PL
and UCPL spectra change as a function of pressure, as a means to indirectly measure the efficiency
of SF and TTA as a function of pressure.

Figure 5.10: UCPLE spectra of rubrene crystals in the DAC. Spectra were recorded at ambient(red data points) and 1.65 GPa (blue data points). The red and blue traces are 300-point-smoothedcurves to guide the eye.

100

5.5

Pressure Quenching of Photoluminescence and Upconversion Photoluminescence
We measured the UCPL and PL intensity as a function of pressure as a way to qualitatively

probe changes to the intermolecular coupling due to decreased intermolecular distances ofneighboring rubrene molecules in the crystal. The rubrene samples were excited with 406 nm CW
laser light and the resulting PL spectra were recorded on a fiber optic spectrometer (see section
2.4.4 for experimental details). For the UCPL spectra, the rubrene was excited with 765 nm lightfrom output of the OPO and the resulting UCPL spectra were recorded on a fiber optic
spectrometer (see section 2.4.4 for experimental details). The NIR excitation wavelength waschosen because it remains resonant with the UCPLE feature in Figure 5.10 throughout a large
portion of the pressure range tested here.

Figure 5.11: UCPL (purple) and PL (red) quenching under pressure. The relatively large error bars
on the UCPL data come fluctuations in the intensity of the output of the OPO, which has a large
effect on the UCPL, due to the quartic dependence.

101

Figure 5.11 shows the integrated intensities of the UCPL and PL spectra as a function ofpressure. Not only do both UCPL and PL experience quenching, but when scaled to have the same
initial integrated intensity, the two behaviors are nearly identical. This may seem curious, as the
UCPL goes through excitation of radical ions, energy transfer to triplet excitons, and then TTA to
finally fluoresce from the S1 state in rubrene, while intrinsic PL only requires an excitation fromthe ground state to S1. However, in rubrene crystals, only a fraction of 10-3 of an initially excited
singlet exciton will undergo fluorescence, due to very efficient SF.9 The triplets generated fromSF may recombine, reforming an S1 and S0 state on neighboring molecules, which can thenundergo fluorescence. This process of fission and fusion can repeat multiple times and accounts
for nearly all the PL observed from crystalline rubrene.9 Given this fact, it is not surprising that
the UCPL and PL have nearly the identical response to changes in the crystal structure induced bypressure.
The increase in the packing density and intermolecular interactions is to blame for thequenching of the UCPL and PL. Due to the C2h symmetry of each rubrene molecule, if they werestacked perfectly so that the tetracene backbones were face-to-face, the intermolecular electronic
coupling constant between the LUMO of one molecule and the HOMO of a neighboring molecule,which is responsible for SF, would be exactly zero.5 In the orthorhombic crystal structure, themolecules are not perfectly face to face, but the overlap of out of phase p-orbitals still exist (Figure5.12). The HOMO and the LUMO interactions are not the only orbitals responsible for the couplingthat produces SF, but understanding how they interact gives a picture of how pressure will enhance
SF.

102

LUMO

HOMO

Figure 5.12: Schematic drawing of two rubrene molecules in an orthorhombic crystal. The
molecule on the left shows the p-orbitals of the LUMO, while the molecule on the right shows thep-orbitals of the HOMO. Decreasing the distance between neighboring molecules enhances theorbital overlap, increasing the intermolecular electronic coupling.

The only reason SF is possible in rubrene crystals is because the orthorhombic crystal
structure has rubrene molecules in a position such that the tetracene backbones are slipped relative
to one another and kept far apart by the phenyl groups. When pressure is applied, the molecules
are forced closer together increasing the orbital interactions, which may increase the overall
intermolecular electronic coupling. As the intermolecular electronic coupling increases, the rates
for both SF and TTA would increase as well. Since SF is in competition with fluorescence, anincrease in the rate of SF would manifest itself as a decrease in PL intensity as a function ofpressure, which is what we have observed here (Figure 5.11).3 UCPL relies on TTA in order toproceed, so on may ask why do we see a decrease in the UCPL signal as a function of pressure as103

well? Ultimately, UCPL must reach the S1 state before emitting light. If the SF rate has increased,
the S1 state prepared through TTA will be more likely to internally convert back to the 1(TT) state,quenching the UCPL signal.
In order to understand exactly what the applied pressure is doing to the crystal lattice, andtherefore what is causing the enhancement of SF, we would need to do in situ XRD of rubrene
under pressure to determine exactly how the crystal (and possibly the individual rubrenemolecules) deform. The quenching of the PL and UCPL signals decrease linearly until a criticalpressure where the intensity does not drop further with increasing pressure. At this pressure, itappears that further pressure does not increase the SF rate any further. It is not clear from our dataon its own whether or not the SF rate remains constant or begins to fall. At these high pressures,
there are likely more contributions to PL and UCPL quenching besides the SF rate.
5.6

Conclusion
In conclusion, we propose that the UCPL observed in rubrene crystals and powders is dueto the excitation of interband states that correspond to excited states of radical cations and radical
anions in the crystal. We measured the rubrene UCPLE spectrum in crystalline samples as well as
powders and found that the measured UCPLE features in the NIR are in good agreement with aproduct of the experimental absorption spectra of the two radical ion species. Excitation of
localized, molecular charge carriers results in mobile charge carriers, which can recombine to
produce triplet excitons. These triplet excitons can then undergo TTA, resulting inphotoluminescence. This model accounts for the features in the UCPLE spectrum, the quartic
intensity dependence of the UCPL signal, and the photobleaching of UCPL. Under pressure, theincrease in the orbital interactions between neighboring molecules quenches the UCPL and PL
signal. This is likely due to an increase in the SF rate, which competes with fluorescence. This is104

a potentially important finding, as increasing the rate of SF has the potential to improve
photovoltaic devices.
5.7

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Appendix
Kinetic Model MATLAB Code:%% RubreneKinetics% This script simulates the model for rubrene upconversion using radical% ions as sensitizers. Values for constants are below, change them in the% code under "Declaration of constants" section if need be.
% Author: JCB% Date: 2020-07-20%% Declaration of constants%Time step (s)dt = 1E-13; %0.1 ns time step
ttot = 2E-4; % total time for simulation in seconds
n = round(ttot/dt); % number of steps
t = zeros(n,1); % time array% Populations
Neo = zeros(n,1); % trapped electons
Neo(1) = 1E19; % initial value of trapped electrons
Nho = zeros(n,1); % trapped holes
Nho(1) = 1E19;
Ne = zeros(n,1); % mobile electrons
Nh = zeros(n,1); % mobile holes
Nt = zeros(n,1); %triplet excitons
Ns = zeros(n,1); %singlet excitons
Npl = zeros(n,1); % total number of photons that have been emitted%Excitation
Istart = input("Enter starting fluence: "); %photon fluence in photons/(cm^2*s)
num_iter = input("Enter number of data points: ");P = zeros(num_iter,2); % Array for storing fluence and PL
xcte = 1E-16; % electron CT exciton formation cross section
xcth = 1E-16; % hole CT exciton formation cross sections

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%Rate constants
kR = 1E-12; % CT exciton recombinatino rate constantkL = 300000; % mobile hole or electron loss rate constantkA = 1E-12; % TTA rate constantksf = 5E10; % singlet fission rate constantkq = 1.67E4; % triplet quenching rate constantkttq = 1E-14; %triplet-triplet quenching rate constant
kpl = 6.25E7; %PL rate constant%% Kinetics
for j = 1:num_iter
I = Istart*10^(j-1);
P(j,1) = I;i = 2; % start at i=2 so that i-1 gives first row of vectors
while i < n+1t(i) = t(i-1) + dt; % calculate the time at this step.
% to simulate a 5ns pulse, use laser fluence above until the time is% greater than 5 ns and then set I = 0.
if t(i) > 5E-9
I = 0;end% Excitation (CT exciton formation)
Neo(i) = Neo(i-1)+(-I*Neo(i-1)*xcte + kL*Neo(n-1))*dt;
Nho(i) = Nho(i-1)+(-I*Nho(i-1)*xcte + kL*Nho(n-1))*dt;
Ne(i) = Ne(i-1)+(I*Neo(i-1)*xcte - kR*Ne(i-1)*Nh(i-1) - kL*Ne(i-1))*dt;
Nh(i) = Nh(i-1)+(I*Nho(i-1)*xcth - kR*Ne(i-1)*Nh(i-1) - kL*Nh(i-1))*dt;%Triplet population
Nt(i) = Nt(i-1)+(kR*Ne(i-1)*Nh(i-1) - kA*Nt(i-1)^2 + 2*ksf*Ns(i-1) kq*Nt(i-1))*dt;%Singlet population
Ns(i) = Ns(i-1)+(kA*Nt(i-1)^2-kpl*Ns(i-1) - ksf*Ns(i-1))*dt;%Photoluminescence
Npl(i) = Npl(i-1)+(kpl*Ns(i-1))*dt;
i = i+1;
end
P(j,2) = Npl(n);endscatter(P(:,1),P(:,2));127