First-year physics seminars for faculty overviews of research, fall 2017
(aimed at first-year graduate students and advanced undergraduates, open to all)
Wednesdays 9:30-10:20 in COB1 322 (Willow Room)
Aug 30: David Strubbe. "Finding order in disorder: theoretical studies of amorphousmaterials and excited-state forces for photovoltaics"
Sept 6: Venkattraman Ayyaswamy. ”The exciting future of microplasmas: Role ofcomputations”
Sept 13: Ajay Gopinathan
Sept 20: Dustin Kleckner
Sept 27: Bin Liu
Sept 29 colloquium is Roland Winston.
Oct 4: Jay SharpingOct 11: Chih-Chun Chien
Oct 18: Linda Hirst
Oct 20 colloquium is Jing Xu.
Oct 25:
Nov 1: Sayantani GhoshNov 8: Lin Tian
Nov 15: Michael Scheibner
Nov 22 is a non-instructional day.
Nov 29: Kevin Mitchell
Dec 6:

Finding order in disorder:
theoretical studies of amorphous materials
and excited-state forces for photovoltaics
David A. Strubbe

Physics, University of California, Merced

First-Year Student Seminar, UC Merced Physics
30 August 2017

My research
1. Amorphous materials

2. Excited-state dynamics

3. Methods and code development

3What is it like to do computational condensed-matter theory?
Developing calculation approaches
Implementation in computer code
Running codes
Analyzing results
Comparing to experimental data
Making simple models
What do you need to know?
- Condensed matter physics- Quantum mechanics- Sometimes electrodynamics and statistical mechanics- Numerical methods, e.g. linear algebra and differential equations- Programming4

Current students
Enrique Guerrero – amorphous silicon. Structure generation,interfaces, defects, voids

Kuntal Talit – hybrid perovskites. Electronic structure, vibrations,
optical spectrum.

(CH3NH3)PbI35

Collaborators
Amorphous silicon:
Gergely Zimányi, UC Davis (theory)
Frances Hellman, UC Berkeley (experiment)
Hybrid perovskites:
Sayantani Ghosh, physics (experiment)
Boaz Ilan, applied mathematics (theory)
Vincent Tung, materials science and engineering (experiment)

Methods and codes:
Steven Louie, UC Berkeley (theory)
Angel Rubio, Max Planck Institute for Structural Dynamics (theory)

6Computation
Laptop, 8 cores

MERCED cluster, SE2 basement, ~2000 cores

Edison (100k) and Cori (600k) supercomputers,
National Energy Research Supercomputing Center,Lawrence Berkeley National Laboratory,Berkeley, CA

7Versatility of theory•
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Scanning tunneling microscopy simulation
Light-driven change of molecular structure
Non-linear optics (second-harmonic generation) in liquids
Conductivity of single-molecule devices
Thermoelectricity in single-molecule devices
Excitons in organic semiconductors
Thermoelectricity in nanoporous silicon
Raman spectroscopy and strain in amorphous silicon
Photovoltaic effects in patterned functionalized graphene
Solar energy storage by change in molecular structure
Thermodynamic limits on solar energy capture and storage

8

Condensed-matter physics
Solid-state physics

Hard condensed matter

AtomisticQuantum
mechanics

First principles(ab initio)

Liquids (e.g. superfluid helium)

Soft condensed matter

Continuum

Classical
force fields

Semi-empirical,
models, tight-binding

9Basic theoretical technique: density-functional theory (DFT)
Quantum mechanics for electrons (“electronic structure”):
time-independent Schrödinger equation

Many-electron Hamiltonian:One-electron Kohn-Sham Hamiltonian:reformulated interms of density nReducing to effective one-electron problem. Only for ground state.

10Time-dependent density-functional theory (TDDFT)
Time-dependent Schrödinger equation

Start at non-equilibrium condition, propagate in timeOr, solve for excited states by response to oscillating electric field
Good for optical properties of molecules (including non-linear)

Density-functional perturbation theory
Response to perturbation (e.g. moving atoms).

S. Baroni, et al., Rev. Mod. Phys. 73, 515 (2001)
D. A. Strubbe et al., in Fundamentals of TDDFT (Springer, 2012)11

GW approximation/Bethe-Salpeter approachStart with DFT, treat exchange and correlation as a perturbation
GW self-energy: single-electron energy levels from Green’s function, screened
Coulomb interaction (band structure, ionization potential, electron affinity)

Bethe-Salpeter equation: electron-hole interaction (optical spectrum, excitons)
More computationally expensive than TDDFT but more generally applicable (solids)

eMark S. Hybertsen and Steven G. Louie, Phys. Rev. B 34, 5390 (1986)
Michael Rohlfing and Steven G. Louie, Phys. Rev. B 62, 4927 (2000)

h+12Electronic structure methods
Density-functional
theory (DFT)Cheap, good for structuralproperties, ground state

Time-dependent
density-functional
theory (TDDFT)

Mid-price. Good for opticalproperties in molecules, not sogood for solids

GW / Bethe-Salpeter
Equation (BSE)

Expensive, quasiparticle band
structure, optical excitations.
Generally accurate for all systems.

Quantum Monte
Carlo (QMC)

Extremely expensive, but accurateand general, for ground and excitedstates

Amorphous materials
amorphous:
only shortrange order

crystalline:
short- and long-rangeorder (periodic)

No single structure: continuum of variation
Non-equilibrium growth, sensitive dependence
on conditions
inhomogeneity, voids, coordination defects
Theory and experimental challenges:
extended but non-periodic, long length scales
14

R. A. Street, Hydrogenated Amorphous Silicon (1991)

Amorphous Si

Photovoltaics, transistors, MEMS, batteries.
Hydrogenated to passivate dangling bonds (a-Si:H)
Long-studied model amorphous system(other amorphous semiconductors and insulators)
Raman spectroscopy is key characterization tool:
crystallization, order, temperature, interfaces, strain, …
Theory helps in interpretation.
20% efficient dopant-free asymmetric heterojunction (DASH) cell
J. Bullock et al., Nature Energy 1, 15031 (2016)15

Stress: properties and characterization
Stress from deposition,processing, nanostructuring
Affects properties, e.g.
electron mobilities in a-Si:H
H. Gleskova et al., Appl. Phys. Lett.
79, 3347 (2001)

Raman microscopy characterization:
stress alters vibrational frequencies(e.g. c-Si optical phonon)I. de Wolf, Semicond. Sci. Technol. 11,139 (1996)
E. Anastassakis et al., Solid State
Commun. 8, 133 (1970)

Inconclusive theory and experiment for a-Si16

Raman spectroscopy
Light creates (or destroys) vibrations
through excited states
Raman tensor from polarizability derivativewith respect to atomic positions

phonon creation

17

Amorphous structure generation
Not a single structure – big structures, statistical sampling and averaging required“WWW method” : classical Monte Carlo method

F. Wooten, K. Winer, and D. Weaire, Phys. Rev. Lett. 54, 1392 (1985)

Add H2 to initial lattice to produce a-Si:H with ~10% H

E. J. Johlin, L. K. Wagner, and J. C. Grossman, Phys. Rev. Lett. 110, 146805 (2013)
D. A. Strubbe, L. K. Wagner, E. J. Johlin, and J. C. Grossman, CHASSM code
(Computational Hydrogenated Amorphous Semiconductor Structure Maker)

c-Si

34 structures of Si64H618

Raman spectrum: theory vs. experiment������ ���������� ���������� ������ ���� ������� ��������� ����� ������TO

4-point bending rods

c-Si

c-Si wafer

LALO

TATA
2LA/Si-H
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19

D. A. Strubbe, E. C. Johlin, et al., Phys. Rev. B 92, 241202(R) (2015)����� ��������� ����� ������Shifts with applied strain������ ����������������� ������������� �������0.5% uniaxial strain

c-SiTO0.3% uniaxial stress����� ������������ �����������������������������

����������� ����� ������tensile

compressive

D. A. Strubbe, E. C. Johlin, et al., Phys. Rev. B 92, 241202(R) (2015)20

Comparing strain coefficients
Strain in exp’t inferred from c-Si shift

Theory:s = -460 ± 10 cm-1

Experiment: s = -500 ± 100 cm-1
E. Anastassakis et al., Solid State
Commun. 8, 133-138 (1970)�����������
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calibration curve
to infer strain������������������������������ �� ������ ��������

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21

D. A. Strubbe, E. C. Johlin, et al., Phys. Rev. B 92, 241202(R) (2015)

Conclusions (I)First ab initio calculation of Raman spectrum ofa-Si:H, in agreement with experiment

Methods work well for this property�����

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Strain calibration for micro-Raman strain mapping,confirmed by agreement of new theory/exp’t��������������������

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D. A. Strubbe, E. C. Johlin, T. K. Kirkpatrick, T. Buonassisi,
and J. C. Grossman, Phys. Rev. B 92, 241202(R) (2015)22

Pentacene: an organic semiconductor
Applications: thin-film transistors,
photovoltaics, and optoelectronics.
Model organic crystal semiconductor
Self-trapped exciton forms

2 molecules,
72 atoms / cell

Important for excitonic transport,
perhaps singlet fission: S → T + T(get two electrons for one photon)e-h+Stokes shift = 0.19 eV

T. Aoki-Matsumoto et al., Int. J.
Mod. Phys. B 15, 3753 (2001)

23

Optical absorption spectrum of pentacene

Lowest singlet exciton 1.7 eVLong-ranged charge transfer to neighboring molecules.
Need GW/BSE to describe correctly.

ML Tiago, JE Northrup, and SG Louie, Phys. Rev. B 67, 115212 (2003)
S Sharifzadeh, A Biller, L Kronik, and JB Neaton, Phys. Rev. B 85, 125307 (2012)

e-h+24

Self-trapped excitonsa-quartz (SiO2)

x-x0
E1

E2

Stokes shift = E1 - E2

Finite differences would require 3N
calculations. Total scaling O(N6)!

Si-O bond breaks(red = Si, blue = O)
Stokes shift = 6 eV
Sohrab Ismail-Beigi and Steven G. Louie,Phys. Rev. Lett. 95, 156401 (2005)

25

Excited-state forces in Bethe-Salpeter equation

derivatives with respect to atomic displacements

DFT ground-state forces= excited statev = valence, occupied, holec = conduction, unoccupied, electron26

Excited-state forces in BSE: new approach
Previous approach (schematically):

Sohrab Ismail-Beigi and Steven G. Louie, Phys. Rev. Lett. 90, 076401 (2003)

Derivatives from density-functional perturbation theory (as for a-Si:H phonons) withsome approximations for computational feasibility
New approach (Hellman-Feynman Theorem):David A. Strubbe, Ph.D. thesis, University of California, Berkeley (2012)

No need for extra summations on unoccupied states
Improved accuracy, efficiency, scalingAlso: more accurate and consistent approximation of GW derivatives

27

Forces on pentacene singlet exciton~0.1 eV/Å

Similar distortion needed forsinglet fission in pair calculations

28

P. M. Zimmermann et al., J. Am. Chem. Soc. 133, 19944 (2011)

Conclusions (II)Reformulation of excited-state forces from the Bethe-Salpeter equation forimproved efficiency and convergence. Only mean-field derivatives required.
Access to self-trapped excitons, Stokes shifts, etc.
Implemented in freely available BerkeleyGW code.
Distortion from singlet exciton of pentacene crystal: molecular rotation.

J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie,
Comput. Phys. Comm. 183, 1269 (2012); www.berkeleygw.org

29

Photovoltaics

a-Si/c-Si tandem HIT 28%
perovskites (not stabilized) 22%
a-Si:H (stabilized) 14%
Organic cells (various types) 11.5%

https://www.nrel.gov/pv/assets/images/efficiency-chart.png
30

Light-induced degradation of hybrid perovskites

Wanyi Nie et al., Nat. Commun. 7, 11574 (2016)(CH3NH3)PbI3
What kind of defect states are being created?
How can we design a more stable material or device?

31