Towards a Net-zero Carbon Energy System:

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Towards a Net-zero Carbon Energy System: High Efficiency Photovoltaics and Electrocatalysts
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Omelchenko, Stefan Thomas
(2019)
Towards a Net-zero Carbon Energy System: High Efficiency Photovoltaics and Electrocatalysts.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/B6AS-EA22.
Abstract
Modern society is dependent on energy. Despite increases in energy efficiency, human development and economic goals are expected to increase the global demand for energy by almost 30% in the next 20 years. At the same time, anthropogenic carbon dioxide emissions must approach zero to stabilize global temperatures below the 2°C target set out by international climate agreements. Realizing a net-zero carbon energy system will depend on the development of a highly reliable, sustainable electricity grid to power society and the ability to produce chemicals and fuels in a carbon-free manner. Developing cheap, efficient solar photovoltaics and highly active and selective electrocatalysts is thus pivotal to achieving this goal.
In this work, we address issues limiting photovoltaics and electrocatalysts. Our work on photovoltaics analyzes two effects often neglected in the evaluation of efficiency limits for photovoltaic materials. We show that the shape of the band tail and, in particular, the extent of sub-gap absorption, controls the open-circuit voltage, emission, and ultimately the achievable efficiency of a solar cell. These findings are generalizable to any luminescent material and our analysis suggests that efficiency limits for a material can be determined through simple experimental characterization. In addition, we develop a device physics model which accounts for the presence of excitons, which are the fundamental excitation in a host of emerging photovoltaic materials. A case study in cuprous oxide shows that excitonic effects can play a large role in the device physics of materials with large exciton binding energies and that standard models can drastically underestimate the efficiency limits in these systems. Our work on photovoltaics, culminates in the realization of a novel device architecture for tandem silicon/perovskite solar cells that opens the possibility of achieving efficiencies >30%. Finally, we develop a method to tune the catalytic activity of electrocatalysts for the oxygen-evolution and chlorine-evolution reactions. Our method is based on group electronegativity and is likely generalizable to other reactions and catalysts. The analyses and technologies developed herein are promising steps towards a zero-carbon energy system.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Photovoltaics, electrocatalysis, excitons, detailed balance, tandem solar cells, perovskites
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Lewis, Nathan Saul (co-advisor)
Atwater, Harry Albert (co-advisor)
Thesis Committee:
Schwab, Keith C. (chair)
Johnson, William Lewis
Lewis, Nathan Saul
Atwater, Harry Albert
Defense Date:
28 September 2018
Record Number:
CaltechTHESIS:06022019-111830413
Persistent URL:
DOI:
10.7907/B6AS-EA22
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DOI
Article adapted for Chapter 3.
DOI
Article adapted for Chapter 4.
DOI
Article adapted for Chapter 5.
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ORCID
Omelchenko, Stefan Thomas
0000-0003-1104-9291
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No commercial reproduction, distribution, display or performance rights in this work are provided.
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11605
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CaltechTHESIS
Deposited By:
Stefan Omelchenko
Deposited On:
05 Jun 2019 18:51
Last Modified:
08 Nov 2023 00:12
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Towards a Net-zero Carbon Energy System:
High Efficiency Photovoltaics and Electrocatalysts

Thesis by

Stefan Omelchenko

In Partial Fulfillment of the Requirements for
the degree of
Doctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2019
Defended September 27, 2018

ã 2018
Stefan Thomas Omelchenko
ORCID: 0000-0003-1104-9291

iii

“Adventure is when everything goes wrong. That’s when the adventure starts.”
- Yvon Chouinoard

To those who don’t know how they got here or where they’re going. Welcome to an
adventure.

Acknowledgements
I am indebted to many people, without whom I would not be here writing this thesis.
First, I would like to thank my advisors Harry Atwater and Nathan Lewis. Sir Isaac Newton once said
“If I have seen further it is by standing on the shoulders of giants,” and that is certainly applicable for
my relationship with Harry and Nate, whose breadth of knowledge seem limitless and whose support
and inspiration is also so. I am incredibly grateful to have been in your groups and been given the
freedom to make (many) mistakes and find my own way.
I would also like to thank the rest of my committee, Professors Bill Johnson and Keith Schwab for
their helpful discussion and time in reviewing this thesis. Professor Johnson is an incredible lecturer
and the deep insights into thermodynamics in his courses proved to be an invaluable foundation in
many of my research projects. I am honored to have Professor Schwab as the chair of my committee
and as a friend whom I can always turn to for academic and professional advice and the latest in
garbage culture.
My road to Caltech started in high school where I was fortunate enough to have stellar calculus and
physics teachers. I would like to thank Mr. Poska and especially, Mr. Walz for showing me the
intimate connections math and physics have in our world and for inspiring me – one person can have
a huge difference in your life.
My research at Caltech would not have been possible without the guidance of my mentor, Yulia
Tolstova, The Fearless Leader. As a scientist, she taught me to be skeptical of everything and be
meticulously detail oriented. As a friend, I am grateful for all the cups of tea and for the lessons you
taught me about our motherland and Ukranian vodka.
The works in this thesis would not have been possible alone and I am thankful for my colleagues and
co-authors: Samantha Wilson, Raymond Blackwell, Amanda Shing, Carlos Read, Michael
Lictherman, Heping Shen, Daniel Jacobs, Joeson Wong, and all the others who contributed to my
studies.
I would like to thank everyone in the Atwater Group and the Lewis Group for making our groups the
two best on campus and for providing friendship and scientific guidance throughout my time at
Caltech. I am particularly thankful for those who put up with me on a daily basis in G131. Xinghao

Zhou, Jingjing Jiang, Weilai Yu, Katie Hamann, Madeline Meier, Katie Chen and Kathleen
Kennedy, thank you for making our office so clearly superior to G135. I would like to thank Erik
Verlage for daring himself to wax his legs and then actually doing it when he missed his deadline. Ke
Sun was an invaluable office resource who, no matter how busy, would help me solve any problem I
might have. I would also like to thank Paul Nuñez for bearing the brunt of my presence and sitting
next to me for 5 years and enlightening me to alternative lifestyles where checking email is taboo.
Although the faces in the office changed a lot over my tenure, Kimberly Papadontanakis was there
with me for the long haul. I will be hard pressed to find an office mate again who is as cynical and as
giving and kind as you. If you were to ever leave, the Lewis Group would miss you dearly. I would
also like to thank Katherine “Chatty Kathy” Rinaldi for the cups of tea we shared.
Caltech and (the Lewis and Atwater Groups in particular) would not run without the work of many
people behind the scenes. This is no more evident than in Harry’s administrators who function as
schedulers, therapists, advisors, and genuinely make life easier for all of the A-Team – thank you to
Jennfier Blakenship, Liz Jennings, and Lyann Lau. I would also like to thank Barbara Miralles who
plays a similar role in the Lewis Group and without whom the group would be lost. I would especially
like to thank Jonathan Gross, Tiffany Kimoto, and Christy Jenstad for being friends foremost. People
like you are the reason that Caltech is a special place.
I am most indebted to my family and friends. Thank you to my friends at Caltech who helped me
escape life as a graduate student and helped keep me grounded. The soccer crew of Chris Kucharczyk,
Saneyuki Ohno, Réda Boumasmoud, Ottman Tertuliano, Marius Lemm, Leon “The Knee” Harding,
and Philipp Moesta were always down for a game (or a beer) and will always be a source of
international companionship while watching a match. During the work day, my friends at lunch were
always a source of a midday escape and interesting conversation – thank you to Mikhail HanewichHollatz, Vatsal “My Wife” Jahlani, and Nathan Schoepp for always being there and to everyone else
that I have shared lunch with over the years. Thanks to Sisir Yalamanchili who was helped distract
me from the doldrums of RCA cleaning silicon with silly YouTube videos, music, and philosophical
discussions and for also being my travel partners to conferences and for making me part of your
family in India. Thanks to Azhar Carim for being the Czar of Liibations and always being down to
watch college football and to Fadl Saadi for always making me laugh and for being my pseudomentor in the Lewis Group. I must also thank my roommates Thom Bohdanowicz, Fish Mattman,
and Christian Fagan who have managed to survive living with me and tell the tale. Nafeesa Andrabi,
Cody Finke, Justin Jasper, Marisa Palucis, Cooper Jasper, and Matt Shaner were always down to help

vi
me get rad and teach me a thing or two during the long car rides to and from climbing, skiing, trail
running, or mountain biking. Nafeesa and Cody are owed special thanks for always accepting me as
their constant third wheel. Thank you to Thuy Jacobson for always being down to work out, get rad,
and eat way too much food afterwards and of course, thank you for all your future healing once you
are a certified PT. I owe the love of my life, Teddy Albertson, and the love of his life, Lorinda Dajose,
for always being there for me and coming with me on climbing trips even when we had to walk really
far (“We’re almost there Lori”). I cannot forget Greeeeeg Smetana even if he is lurking quietly in the
shadows – you were my first friend at Caltech and continue to be one of my best. Out of all my
friends, I owe Will and Sarah Whitney the most; thank you for simultaneously being my best friends,
life coaches, adventure partners, and for sheltering me on your couch for almost half a year– I will
forever owe you. But I am certainly most indebted to my parents without whom none of this would
have been possible. Thank you so much for your love and support over the years. If anything, life has
taught me that I am incredibly lucky to have such good role models and to be your son. Thank you to
Michael and Monica for being the best siblings (and friends) that I could ever ask for and for being
the test subjects on which I honed my skills for annoyance. I love you all.

Stefan Omelchenko
September 2018
Pasadena, CA

vii

Abstract
Modern society is dependent on energy. Despite increases in energy efficiency, human
development and economic goals are expected to increase the global demand for energy by
almost 30% in the next 20 years. At the same time, anthropogenic carbon dioxide emissions
must approach zero to stabilize global temperatures below the 2°C target set out by
international climate agreements. Realizing a net-zero carbon energy system will depend on
the development of a highly reliable, sustainable electricity grid to power society and the
ability to produce chemicals and fuels in a carbon-free manner. Developing cheap, efficient
solar photovoltaics and highly active and selective electrocatalysts is thus pivotal to
achieving this goal.
In this work, we address issues limiting photovoltaics and electrocatalysts. Our work on
photovoltaics analyzes two effects often neglected in the evaluation of efficiency limits for
photovoltaic materials. We show that the shape of the band tail and, in particular, the extent
of sub-gap absorption, controls the open-circuit voltage, emission, and ultimately the
achievable efficiency of a solar cell. These findings are generalizable to any luminescent
material and our analysis suggests that efficiency limits for a material can be determined
through simple experimental characterization. In addition, we develop a device physics
model which accounts for the presence of excitons, which are the fundamental excitation in
a host of emerging photovoltaic materials. A case study in cuprous oxide shows that excitonic
effects can play a large role in the device physics of materials with large exciton binding
energies and that standard models can drastically underestimate the efficiency limits in these
systems. Our work on photovoltaics, culminates in the realization of a novel device
architecture for tandem silicon/perovskite solar cells that opens the possibility of achieving
efficiencies >30%. Finally, we develop a method to tune the catalytic activity of
electrocatalysts for the oxygen-evolution and chlorine-evolution reactions. Our method is
based on group electronegativity and is likely generalizable to other reactions and catalysts.
The analyses and technologies developed herein are promising steps towards a zero-carbon
energy system.

viii

Published Content and Contribution
Portions of this thesis have been drawn from the following publications
S. T. Omelchenko*, J. Wong*, N. S. Lewis, H. A. Atwater, “Effects of imperfect
bandgaps and disorder on photovoltaic efficiency,” in preparation.
S.T.O and J.W. conceived the theory, designed the model, and performed the simulations
for this work along with co-authors. The manuscript was prepared by S.T.O and J.W. with
input from co-authors.
H. Shen*, S. T. Omelchenko*, D. Jacobs*, S. Yalamanchili*, Y. Wan, Y. Wu, P. Phang,
T. Duong, J. Peng, Y. Yin, D. Yan, C. Samundsett, N. Wu, T. P. White, G. G. Andersson,
N. S. Lewis, K. R. Catchpole, “Ohmic p-Si/titania contact enables high efficiency,
interconnect-free monolithic perovskite/silicon tandem solar cells”, Science Advances, 4,
12, 2019
doi: 10.1126/sciadv.aau9711
S.T.O, S.Y., and N.S.L. conceived of the device structure for this work. S.T.O, S.Y., H.S.,
and D.J. designed and fabricated the structure, conceived of the experiments, and
conducted the measurements, along with co-authors. The manuscript was prepared by H.S.,
S.T.O., S.Y., and D.J. with input from co-authors.
C. E. Finke, S. T. Omelchenko, J. Jasper, M. F. Lichterman, C. G. Read, N. S. Lewis, M.
R. Hoffmann, “Enhancing the activity of oxygen-evolution and chlorine-evolution
electrocatalysts by atomic layer deposition of TiO2,” Energy Environ. Sci, 12, 358, 2019
doi: 10.1039/c8ee02351d
S.T.O contributed to the concept of this work along with co-authors. S.T.O. assisted with
the design of experiments, collection of measurements, and analysis of data. The
manuscript was prepared by C.F. and S.T.O. with input from co-authors.
S. T. Omelchenko, Y. Tolstova, H. A. Atwater, Jr., N. S. Lewis, “Excitonic Effects in
Emerging Semiconductors: A Case Study in Cu2O”, ACS Energy Lett., 2, 431, 2017
doi: 10.1021/acsenergylett.6b00704
S.T.O was responsible for the conception of this work along with co-authors. S.T.O.
designed the experiments, collected the measurements, and analyzed the data. The
manuscript was prepared by S.T.O. and Y.T. with input from co-authors.

ix
Y. Tolstova, S. T. Omelchenko, R. E. Blackwell, A. M. Shing, H. A. Atwater, Jr.,
“Polycrystalline Cu2O Photovoltaic Devices Incorporating Zn(O,S) Window Layers”,
Sol. Energy Mater. and Sol. Cells, 160, 340, 2017
doi: 10.1016/j.solmat.2016.10.049
S.T.O contributed to the concept of this work along with co-authors. STO assisted with
device fabrication, design of experiments, collection of measurements, and analysis of data.
The manuscript was prepared by Y.T. and S.T.O. with input from co-authors.
S. T. Omelchenko, Y. Tolstova, H. A. Atwater, N. S. Lewis, “Excitonic Effects in
Materials with Large Excitonic Binding Energies,” 43nd IEEE PVSC (2016)
doi: 10.1109/PVSC.2016.7750347
S.T.O was responsible for the conception of this work along with co-authors. S.T.O.
designed the experiments, collected the measurements, and analyzed the data. The
manuscript was prepared by S.T.O. and Y.T. with input from co-authors.
S. T. Omelchenko, Y. Tolstova, S. S. Wilson, H. A. Atwater, N. S. Lewis, “Single
crystal Cu2O Photovoltaics by the floating zone method,” 42nd IEEE PVSC (2015)
doi: 10.1109/PVSC.2015.7355920
S.T.O was responsible for the conception of this work along with co-authors. S.T.O. grew
the samples, designed the experiments, collected the measurements, and analyzed the data.
The manuscript was prepared by S.T.O. and Y.T. with input from co-authors.

Table of Contents
Acknowledgements................................................................................................................... iii
Abstract................................................................................................................................... vii
List of Publications.......................................................................... Error! Bookmark not defined.
Table of Contents ...................................................................................................................... x
List of Figures ........................................................................................................................ xiii
List of Tables ......................................................................................................................... xxii
Chapter 1 Introduction ............................................................................................................. 1
1.1 A Net-Zero Carbon Emission Energy System ..................................................................... 1
1.2 Challenges to Realizing Net-Zero Carbon........................................................................... 3
1.3 Solar Photovoltaics............................................................................................................ 4
1.3.1 The Solar Cell Market ................................................................................................ 4
1.3.2 Basics Operating Principles of Photovoltaics ............................................................... 6
1.4 Electrocatalysis for Production of Fuels and Chemicals......................................................10
1.5 Scope of This Thesis ........................................................................................................12
Chapter 2 Efficiency Limits of Light Absorbers ......................................................................14
2.1 Detailed Balance Limit .....................................................................................................14
2.2 Imperfect Absorption and Modified Detailed Balance ........................................................16
2.2.1 Absorption in real materials .......................................................................................16
2.2.2 Modified Detailed Balance ........................................................................................19
2.3 Sub-gap Absorption and Solar Cell Performance ...............................................................21
Chapter 3 The Effect of Excitons on Photovoltaic Performance: A Case Study in Cu2O ........32
3.1 Introduction .....................................................................................................................32
3.2 Equilibrium Concentration of Excitons..............................................................................34
3.3 Experimental Observations of Excitons in Cu2O Photovoltaics...........................................38
3.3.1 Growth of Cu2O substrates.........................................................................................39
3.3.2 Photoluminescence of the Exciton Peak in Cu2O.........................................................40
3.3.3 Excitons in the Spectral Response of Cu2O-based Photovoltaics ..................................42
3.4 The Role of Excitons in Photovoltaic Device Physics.........................................................44
3.4.1 Device Model Including Excitons ..............................................................................45
3.4.2 Model Parameters for Cu2O .......................................................................................48
3.4.3 Effects of Excitons on Carrier Diffusion Length in Cu2O ............................................51
3.4.4 Equilibrium Concentration of Excitons and Free Carriers ............................................53
3.4.5 Absorption, Generation, and Jsc ..................................................................................54
3.4.6 Voc, FF, and Efficiency ..............................................................................................55
3.4.7 Model Results ...........................................................................................................56
3.5 Conclusion .......................................................................................................................62
Chapter 4 Interconnect-free Perovskite/Silicon Tandems .......................................................63

xi
4.1 Increasing Silicon Efficiency: Tandem Si Solar Cells...................................................... 63
4.2 The Rise of Perovskites and Silicon/Perovskite Tandems ...................................................63
4.3 Interconnect-free Perovskite Silicon Tandem .....................................................................67
4.3.1 Interconnect-free Cell Architecture and Fabrication ....................................................68
4.3.2 Current-Voltage and TiO2/Si Contact Characteristics ..................................................71
4.3.3 TiO2/Si Band Alignment and Charge Transport Mechanism ........................................79
4.3.4 Cell Stability .............................................................................................................90
4.4 Conclusion .......................................................................................................................94
Chapter 5 Tuning the Catalytic Activity of Oxygen- and Chlorine-Evolution Electrocatalysts
with Atomic Layer Deposition .................................................................................................96
5.1 Introduction .....................................................................................................................96
5.2 Material Selection, Sample Preparation, and Characterization ............................................97
5.2.1 Material Selection and Group Electronegativity ..........................................................97
5.2.2 Sample Preparation....................................................................................................98
5.2.3 Catalyst Microstructure............................................................................................ 100
5.3 Catalyst Performance...................................................................................................... 105
5.3.1 Catalyst Overpotential ............................................................................................. 106
5.3.2 Specific Activity...................................................................................................... 109
5.3.3 Stability of Enhanced Catalyst Performance ............................................................. 111
5.4 Catalyst Surface Electronics............................................................................................ 115
5.4.1 Potential of Zero Charge Measurements ................................................................... 116
5.4.2 XPS Characterization of TiO2 Coated Catalysts ........................................................ 118
5.5 Conclusion ..................................................................................................................... 126
Chapter 6 Conclusion and Outlook........................................................................................ 127
Appendix A Band Tailing Code ............................................................................................. 130
Appendix B Floating Zone Crystal Growth ........................................................................... 190
B.1 Zone Melting Background.............................................................................................. 190
B.2 The Floating Zone Method ............................................................................................. 194
B.2.1 General Growth Process Overview .......................................................................... 195
B.3 The Caltech System ....................................................................................................... 196
B.3.1 The Floating Zone Furnace ..................................................................................... 196
B.3.2 Growth of Feed Rods .............................................................................................. 197
B.3.3 Tips for Floating Zone Growth ................................................................................ 199
Appendix C Electrochemical Methods for Catalysis.............................................................. 201
C.1 Experimental Setup and Catalyst Testing ........................................................................ 201
C.2 Calculating Overpotentials ............................................................................................. 202
C.2.1 Electronegativity and Overpotential Calculations ..................................................... 202
C.3 Calculating Faradaic Efficiency...................................................................................... 203
C.4 Determination of Solution and System Resistance ........................................................... 204
C.5 Determination of the Double Layer Capacitance and Electrochemically Active Surface Area
........................................................................................................................................... 206
C.6 Calculating Specific Activities using ECSA and Surface Area Measured by AFM............ 209
C.7 Determination of EZC by Electrochemical Impedance Spectroscopy ................................. 210
Appendix D Details of XPS Analysis ...................................................................................... 217

xii
D.1 XPS Data Collection and Peak Fitting ........................................................................ 217

xiii

List of Figures
Figure 1.1 A sustainable energy system with near zero carbon emissions, reproduced
from(6). Renewable electricity is used directly as a source of energy for
transportation or to produce fuels, chemicals and materials electrochemically. ........2
Figure 1.2 Power output from a 4.6 MW solar photovoltaic power plant in Arizona on a
cloudy day. From (20)...........................................................................................6
Figure 1.3 A simplified semiconductor energy band diagram depicting absorption,
thermalization, and radiative recombination. The semiconductor has a band gap
𝐸𝑔 = ℎ𝜈𝑔𝑟𝑒𝑒𝑛 and thus absorbs green photons and photons with higher energy
(shorter wavelength) while photons with less energy are transmitted (red photon).
Upon absorption electrons (filled gray circle) in the valence band (VB) are excited to
the conduction band (CB) leaving behind an effectively positively charged hole
(white circle) in the valence band. Absorption of a photon with excess energy (blue
photon) promotes an electron to an excited state in the conduction band above the
band gap. The excited electron rapidly decays back to the valence band edge in a
process known as thermalization (dark red steps), transferring its energy to the
semiconductor lattice in the process. In radiative recombination, electrons recombine
across the band gap emitting a photon in the process. .............................................7
Figure 1.4 Current density-voltage characteristics of an ideal solar cell. In the dark, the solar
cell operates as an ideal diode (red dashed curve) with an exponential dependence on
the applied voltage. The light curve (blue) is a superposition of the dark curve and
the absorbed photon flux. The short circuit current is equal to the total absorbed
photon flux and corresponds to the point V = 0, where there is no radiative
recombination. By contrast, the Voc is at the point when the incident photon flux is
completely balanced by the radiative emission of the cell and occurs when the light
curve intersects the abscissa. The power producing region of the light curve is thus
in the fourth quadrant. The maximum power point is represented by the dark gray
box. The ratio of the area of the dark gray box to the light gray box is the fill-factor,
which is a measure of resistance and non-idealities in the cell. ...............................9
Figure 1.5 Reaction energetics for a reaction X to Y with (red) and without (blue) a catalyst.
The catalyst lowers the activation energy (EA) for the reaction resulting in greater
kinetics and reaction efficiency. .......................................................................... 11
Figure 2.1 a) The AM1.5G photon flux. b) The Shockley-Queisser Limit for the AM 1.5G
spectrum: photovoltaic cell efficiency as a function of band gap. .......................... 15
Figure 2.2 The band edge absorption of GaAs adapted from (34). GaAs exhibits an
exponential band tail below the band gap and band to band absorption above gap. 17
Figure 2.3 The deficit in the experimentally achieved open-circuit voltage from that of the
S-Q Limit as a function of Urbach parameter for common photovoltaic materials. 19
Figure 2.4 a) The spectral response of a solar cell with a 1.5 eV band gap for different Urbach
energies in units of kBT. using the absorption model outlined in Section 2.2.2. The
sub-gap absorption increases deeper into the gap with increasing Urbach parameter
b) The modified detailed balance efficiency as a function of cell band gap for

xiv
different Urbach energies. Increasing the Urbach parameter has a deleterious
effect on cell performance. .................................................................................. 22
Figure 2.5 Line cuts at 1.5 eV (left) and contour plots (right) of the photovoltaic figures of
merit as a function of Urbach parameter. The red dashed line in the left figures
indicates the thermal energy kBT (25.8 meV at 300 K).......................................... 24
Figure 2.6 Effect of sub-gap absorption on a 1.5 eV band gap solar cell. a) Current densityvoltage characteristics with different Urbach parameters. b) The FF as a function of
Urbach parameter. The red dashed line indicates kBT. .......................................... 25
Figure 2.7 a) Spectral response (solid lines) and photoemission (dashed lines) for an absorber
with a 1.5 eV band gap for different Urbach parameters. The dot-dashed lines indicate
the effective band gap distribution. b) The ratio of sub-gap photoemission to the total
photoluminescence.The red dashed line indicates kBT. ......................................... 27
Figure 2.8 The photoluminescence peak shift for a 1.5 eV band gap absorber as a function
of Urbach parameter. .......................................................................................... 28
Figure 2.9 Spectral response for a 1.5 eV band gap solar cell with different absorber
thicknesses and an Urbach parameter of 0.1 kBT................................................... 29
Figure 2.10 Photovoltaic performance metrics for a 1.5 eV solar cell as a function of Urbach
energy for different levels of incomplete above-gap absorption. The red lines indicate
the thermal energy kBT. ....................................................................................... 30
Figure 2.11 Photovoltaic figures of merit as a function of Urbach parameter for a 1.5 eV
band gap solar cell with varying sub-gap carrier collection efficiencies. The red
dashed lines indicate the thermal energy kBT. ....................................................... 31
Figure 3.1 The fraction of free electrons and holes relative to the total excitation density 𝑥 =
𝑛𝑒ℎ𝑁 in Cu2O. The upper limit of the branching ratio between excitons and free
electrons and holes during photovoltaic operation is 27.7%, suggesting that
substantial exciton densities should be present during typical device operating
conditions. .......................................................................................................... 38
Figure 3.2 Photoluminescence spectra of the free exciton peak in Cu2O at room temperature
under different visible light excitation. The free exciton peak is observed for all
excitations above the Cu2O band gap. .................................................................. 41
Figure 3.3 Photoluminescence spectrum of the free exciton peak in thermally oxidized,
polycrystalline Cu2O wafers at room temperature using a 2.4 mW, 514 nm excitation.
........................................................................................................................... 42
Figure 3.4 Spectral response of a polycrystalline Cu2O /Zn(O,S) solar cell. The red dashed
line indicates the Cu2O electronic band gap beyond which, in the shaded region, are
wavelengths for which only excitons can exist. .................................................... 44
Figure 3.5 The simulated electron, exciton and effective diffusion lengths for Cu2O for
doping densities a) 1012, b) 1014, and c) 1016. ....................................................... 52
Figure 3.6 The equilibrium ratio of excitons to free carriers as a function of doping density
for temperatures ranging from 200 to 500 K. ....................................................... 54
Figure 3.7 Comparison between the simulated device performance of a p-n+ Cu2O-based
solar cell using a model incorporating excitonic effects relative to the FC model,
denoted by the superscript x and fc, respectively. (a) The simulated dark saturation
current density. (b) The ratio of the dark current density, when excitons are included,

xv
to the dark current density using the FC model. The dark current density increases
substantially when excitonic effects are included. (c) The calculated short-circuit
current density. Experimental Jsc values (the circles) agree well with the Jsc values
obtained using the excitonic model (103, 104). (d) The absolute difference in shortcircuit current density between the excitonic and FC models. At room temperature
and a doping density of 1016, excitonic effects account for an additional 2.84 mA×cm2
. (e) The open-circuit voltage obtained from the excitonic and FC models. In the
low temperature limit, the Voc approaches the exciton band edge and electronic band
gap for the excitonic model and the FC model, respectively. The turquoise circle
represents the record experimental Voc for Cu2O solar cells (105). (f) The difference
between the open-circuit voltage as calculated from the excitonic model and the FC
model. The change in voltage is small over the calculated temperature range. (g) The
simulated photovoltaic efficiency under the AM 1.5 spectrum. (h) The absolute
difference in the practical efficiency in Cu2O-based solar cells between the excitonic
model and the FC model. At room temperature, the FC model underestimates the
efficiency by 1.9 absolute percent. ....................................................................... 59
Figure 3.8 The simulated fill-factor for the excitonic and FC models. The fill factors were in
close agreement except at the highest doping densities, where large enhancement in
the Jsc dominates and leads to an increase in the solar-cell efficiency relative to the
FC case............................................................................................................... 61
Figure 4.1 Perovskite record cell efficiency, adapted from (30, 122). The record at the time
of writing is 23.3%.............................................................................................. 65
Figure 4.2 Simplified diagram of the 2-terminal (left) and 4-terminal (right) tandem solar
cell device architectures. In each design, the top contact is a transparent electrode
(TE), which allows the light to pass through to the two cells, while the bottom contact
need not be transparent. In the 2-terminal design the high and low band gap sub-cells
are in ohmic contact by means of either a transparent conductive oxide (TCO) or
tunnel junction (TJ). In a 4-terminal design two additional transparent electrode
contacts are needed on the rear side of the high band gap sub-cell and on the top of
the low band gap sub-cell. ................................................................................... 67
Figure 4.3(A) Schematic of the interconnect-free monolithic perovskite/c-Si tandem solar
cell (not to scale). Initial tests were carried out on homojunction Si cells with SpiroOMeTAD as the top perovskite contact; however, our best performance was obtained
with polysilicon bottom-cells and PTAA as the top hole-selective layer. (B) Crosssectional scanning-electron microscope (SEM) image of the tandem device based on
Si homojunction subcell from the top surface to the p+-Si layer (Spiro-OMeTAD is
used as HTM). The anti-reflection layer was not included due to the large thickness
of ~ 1 mm, (C) Scanning transmission-electron microscopy (STEM) bright field (BF)
image and (D) high-resolution STEM BF image of the TiO2/p+-Si interface. ........ 70
Figure 4.4 AFM image of TDMAT-ALD TiO2 on a p+-Si substrate. ............................... 71
Figure 4.5 (A) J-V behavior of the proof-of-concept tandem device with both reverse and
forward scanning at 0.05 V/s based on heterojunction poly-Si subcell. (B)
Absorbance (1-R, where R is the reflectance) of the tandem device (grey shading),

xvi
external quantum efficiency (EQE) of the perovskite top cell (blue), and EQE of
the c-Si bottom sub-cell (red). ............................................................................. 72
Figure 4.6 (A) J-V behavior of the proof-of-concept tandem device with both reverse and
forward scanning at 0.05 V/s based on Si homojunction subcell. (B) Absorbance (1R, where R is the reflectance) of the tandem device (grey shading), external quantum
efficiency (EQE) of the perovskite top cell (blue), and EQE of the c-Si bottom subcell (red). (C) schematic of single-junction Si homojunction solar cell including
ALD-TiO2 on a flat p+-Si emitter (not to scale), (D) photovoltaic performance of a
single-junction homojunction Si solar cell. .......................................................... 73
Figure 4.7(A) Schematic of the structure used for measuring contact resistivity. (B)
Comparison of the J-V behavior of ITO/p+-Si and various TiO2/p+-Si structures
before and after annealing at 400 °C in air. TiCl4-ALD TiO2 listed here is deposited
with the reactor chamber temperature of 75 °C. (C) Simulated band diagram of the
TiO2/p+-Si at equilibrium assuming n-type doping of 5x1018 cm-3 on the TiO2 and
1019 cm-3 for p+-Si (appropriate for our test structure with TDMAT TiO2, see table
S3. The unknown interfacial energy gap Δ is shown here for illustrative purposes as
600 meV, which falls within the range of reported measurements (152)). Both
mechanisms of direct- and tunneling assisted capture by interfacial defects are shown.
........................................................................................................................... 75
Figure 4.8 J-V curves of the TiCl4-ALD TiO2 deposited at low temperatures on different p+Si wafers. The samples receive no further heat-treatment. TiO2 deposited at 150 °C
on top of p+-Si with a doping density of (A) ~9.3´1019 cm-3, the extracted contact
resistivity is ~850 mΩcm2 and (C) ~1.7´1020 cm-3, the extracted contact resistivity is
~445 mΩcm2. TiO2 deposited at 200 °C on top of p+-Si with a doping density of (B)
~9.3´1019 cm-3, the extracted contact resistivity is ~210 mΩcm2 and (D) ~1.7´1020
cm-3, the extracted contact resistivity is ~99.6 mΩcm2.......................................... 76
Figure 4.9 J-V data of a 2-T perovskite/Si tandem device with ITO as the recombination
layer. .................................................................................................................. 77
Figure 4.10 J-V data of monolithic perovskite/Si tandem solar cells with (top) TTIP-ALD
TiO2, (bottom) TiCl4–ALD TiO2 (deposited at 75°C). .......................................... 78
Figure 4.11 (A) Combined UPS valence band spectrum and IPES, and (B) the secondary
electron cut-off region, and (C) calculated energy diagram from the above
measurement, of an annealed TDMAT-ALD TiO2 layer. The error for the work
function was ±0.2 eV, and the extraction of valence band and conduction band had
an error of ±0.1 eV.............................................................................................. 80
Figure 4.12 (A) Combined UPS valence band spectrum and IPES, and (B) the secondary
electron cut-off region representative, and (C) calculated energy diagram from the
above measurement of an annealed TTIP-ALDTiO2 layer. ................................... 80
Figure 4.13 (A) Combined UPS valence band spectrum and IPES, and (B) the secondary
electron cut-off region representative, and (C) calculated energy diagram from the
above measurement of an annealed TiCl4-ALD TiO2 layer (deposited at 75°C). .. 81
Figure 4.14 (A) Simulated J-V curves for varying interfacial gaps Δ. A single neutral midgap SRH defect was included with 𝑆𝑛 = 𝑆𝑝 = 105 cm/s. The dashed curves are
computed with tunneling to defects included. (B) Simulated small voltage resistivity

xvii
𝜌 = 𝑑𝑉𝑑𝐼|𝑉 = 0 with the TiO2 donor density fixed at 10 cm and variable pSi acceptor doping. Measurements are included as data points in red. Calculations for
neutral (solid lines), acceptor-type (dotted lines) and donor-type (dot-dashed lines)
are shown to demonstrate the important effect of defect charge on the interfacial
carrier balance. (C) Simulated band diagram of the full tandem device based on
homojunction Si subcell with high work-function cp-TiO2 at illuminated opencircuit. The inset depicts the two important energetic offsets Δ and δ, respectively,
defined as the valence-to-conduction band offset at the TiO2-Si interface and the
difference in work functions between our solution-processed mesoporous TiO2 layer
and that of the ALD compact layer. ..................................................................... 82
Figure 4.15 Calculated small-voltage resistivity as in Fig. 4B of the main text, this time
showing the effect of tunneling. Tunneling has a minor effect for neutral and
acceptor-type defects, but significantly affects the donor-defect models when the
acceptor doping is large because tunneling effects are most significant when the
depletion region is small which occurs for large acceptor doping concentrations. .. 84
Figure 4.16 Voc yield of transparent single-junction perovskite solar cells (with p+-Si as the
substrate) with and without mesoporous-TiO2. Results for TDMAT-ALD TiO2 are
shown on the left while results for TTIP-ALD TiO2 are shown on the right. Both
titania compact layers have high work functions with the deposition conditions used
in this work......................................................................................................... 87
Figure 4.17 Simulated band diagram at 0 V (left) and J-V behavior (right) of a singlejunction perovskite solar cell with and without an additional “mesoporous” titania
layer inserted between the perovskite and high work-function compact titania. This
represents a 1D simplification of the complex 3-dimensional mesoporous structure
present in our tandem cell design, but captures the qualitative effect of including
titania layers with contrasting work functions. The mesoporous layer functions
primarily to maintain the built-in voltage in the perovskite cell, as seen in the band
diagram (left) and consequently discrepant open-circuit voltages (right). Here
electron affinities of 4.1 eV and 4.5 eV were used for the compact and mesoporous
titania layers respectively. ................................................................................... 87
Figure 4.18 J-V curve of a monolithic perovskite/Si tandem solar cells with as-deposited
TiCl4-ALD TiO2 (200 °C). The top perovskite subcell has a planar structure without
the inclusion of the mesoporous TiO2 film, and is fabricated with low-temperature
processes. ........................................................................................................... 88
Figure 4.19 J-V curves of the TiCl4-ALD TiO2 deposited at low temperatures on different
p+-Si wafers. The samples receive no further heat-treatment. TiO2 deposited at 150
°C on top of p+-Si with a doping density of (A) ~9.3´1019 cm-3, the extracted contact
resistivity is ~850 mΩcm2 and (C) ~1.7´1020 cm-3, the extracted contact resistivity is
~445 mΩcm2. TiO2 deposited at 200 °C on top of p+-Si with a doping density of (B)
~9.3´1019 cm-3, the extracted contact resistivity is ~210 mΩcm2 and (D) ~1.7´1020
cm-3, the extracted contact resistivity is ~99.6 mΩcm2.......................................... 89
Figure 4.20 (A) Excess carrier lifetime of a Si substrate with and without TiO2 passivation
(TiCl4-ALD TiO2 deposited at 150 °C without further annealing) as a function of the
measured injection level. The implied Voc (iVoc) is increased by ~50 mV with the
18

-3

xviii
TiCl4 TiO2 coating. (B) J-V curve of a TiCl4-ALD (150 °C) TiO2/p -Si sample
(p+-Si has a doping density of ~1.5*1019 cm-3). .................................................... 90
Figure 4.21 Damp heat test (85 °C in a relative humidity level of 85%) of a semitransparent
perovskite solar cell. Evolution of the photovoltaic characteristics including (a) Voc,
(b) Jsc, (c) FF and (d) PCE during damp heat stability of an encapsulated singlejunction perovskite device for 1414 h. ................................................................. 91
Figure 4.22 PCE evolution of the proof-of-concept perovskite/Si homojunction tandem
device undergoing four different aging stages. (A) Stage 1: 1 Sun continuous
illumination in air for ~2.1 h, biased near maximum power point); (B) Stage 2: device
stored in dark in a N2 cabinet for ~1224 h; (C) Stage 3: device under 1 Sun continuous
illumination in air for ~19 h, biased at ~1.3 V, and Stage 4: device underwent
light/dark cycles for seven cycles, with total illumination of over 800 h. The
measurement under light was taken at 25 °C. Corresponding Voc evolution (D-F) of
the same device under the same conditions. ......................................................... 94
Figure 5.1 X-ray diffraction patterns for typical IrO2 and RuO2. All observed peaks were
indexed to standard diffraction patterns for IrO2 and RuO2, respectively. ............ 100
Figure 5.2 Material characterization of typical electrocatalyst samples. (A) SEM image of
an IrO2 catalyst with 1000 ALD TiO2 cycles. (B) AFM map of IrO2 with 10 ALD
cycles of TiO2. (C) HAADF-STEM image of an IrO2-based electrocatalyst with 10
ALD cycles of TiO2. The underlying crystalline material is IrO2 while the hair-like
material at the surface is TiO2. (D,E) Energy dispersive X-ray spectroscopy (EDS)
maps of IrO2-based electrocatalysts with 10 and 40 ALD cycles of TiO2, respectively.
The red color indicates Ir and green indicates Ti. Note that green and red intermix
throughout this cross section due to the inherent roughness of the sample. .......... 101
Figure 5.3 Representative topographic atomic force microscopy images of IrO2, RuO2, and
FTO each with 0, 3, 10, and 1000 ALD cycles of TiO2....................................... 102
Figure 5.4 Representative conductive atomic force microscopy tunneling current images of
IrO2, RuO2, and FTO each with 0, 3, 10, and 1000 ALD cycles of TiO2. ............ 103
Figure 5.5 High-Angle Annular Dark-Field Scanning Transmission Electron Microscopy
(HAADF-STEM) images of different IrO2 + 10 ALD cycles of TiO2 samples. The
crystalline sublayer is IrO2 and the “hairy” top layer is amorphous TiO2. ............ 105
Figure 5.6 Specific activities (js) and overpotentials (η) for the OER and CER on IrO2, RuO2,
and FTO coated at various ALD cycles of TiO2. Overpotentials were measured at 10
mA/cm2geo for the OER and at 1 mA/cm2geo for the CER (normalized to geometric
surface area). Specific activities for the OER were measured at 350 mV (IrO2 and
RuO2) or 900 mV (FTO). Specific activities for the CER were measured at 150 mV
(IrO2 and RuO2) or 700 mV (FTO). The red squares indicate available literature
values. .............................................................................................................. 107
Figure 5.7 Group electronegativity vs overpotential at 1 mA/cm2AFMSA. Overpotential data
was taken from Seh et al. (blue and orange circles) and from this work (red circles).
For LaCrO3, LaMnO3, LaFeO3, LaCoO3, LaNiO3, RuO2, IrO2, and PtO2 group
electronegativites were estimated by taking the geometric mean of the Allen Scale
electronegativities of the constituent atoms. For IrOx/SrIrO3, Ir2SrO7 was assumed
for group electronegativity calculations (208). For IrO2/TiO2, IrTiO4 was assumed
for group electronegativity calculations For NiFeOx, NiFe2O4 was was assumed for

xix
group electronegativity calculations (200). For NiCoOx NiCo2O4 was assumed for
group electronegativity calculations (200). For NiCoOx, NiCo2O4 was assumed for
group electronegativity calculations (200). For CoFeOx, FeCo2O4 was assumed for
group electronegativity calculations (200). For CoOx, CoO1.5 was assumed for group
electronegativity calculations (200). For NiOx, Ni2O3 was assumed for group
electronegativity calculations (200). .................................................................. 108
Figure 5.8 Tafel plots from IrO2 coated with 0 (dark blue), 3 (orange), 6 (yellow), 10
(purple), and 20 (green) ALD cycles of TiO2 all from this work are shown next to
those of IrOx/SrIrO3 at 0 (red) and 30 (light blue) hrs of activation as taken from
literature (208). To calculate the current density, the surface area was measured by
AFM (Table 4.1). .............................................................................................. 110
Figure 5.9 Example stability testing data of IrO2 + 0 (blue), 10 (orange), and 40 (yellow)
ALD cycles in 1 M H2SO4 at 10 mA/cm2geo. ...................................................... 112
Figure 5.10 X-ray photoelectron spectroscopy of the Ti 2p region for IrO2, RuO2, and FTO
electrocatalysts with 10 cycles, 10 cycles, and 30 cycles of TiO2, respectively, before
and after stability testing for the OER. Note the peak still visible in the “after” RuO2
spectra is associated with the Ru 3p core levels. ................................................. 114
Figure 5.11 X-ray photoelectron spectroscopy of the Ti 2p region for an RuO2 electrocatalyst
with 60 cycles of before and after 24-hour stability testing for the CER. The TiO2 is
still present after testing. ................................................................................... 115
Figure 5.12 EZC of IrO2 (blue), RuO2 (red), and FTO (green) anodes coated with various
ALD cycles of TiO2. Black dots and circles with black borders indicate the catalysts
with the highest specific activity for each catalyst for the OER and CER, respectively.
......................................................................................................................... 118
Figure 5.13 X-ray photoelectron spectroscopy of the Ti 2p3/2 region for IrO2, RuO2, and FTO
catalysts with varying TiO2 thicknesses. Bulk TiO2 is shown as the blue peak in each
spectrum. The slightly and highly reduced Ti peaks are shown in green and red,
respectively, and the most highly oxidized Ti peak is shown in orange. .............. 120
Figure 5.14 X-ray photoelectron spectroscopy of the Ti 2p region for IrO2, RuO2, and FTO
catalysts. Bulk TiO2 is shown as the blue peak in each spectrum. The slightly and
highly reduced Ti peaks are shown in green and red, respectively, and the most highly
oxidized Ti peak is shown in orange. ................................................................. 121
Figure 5.15 Ti 2p3/2 overall peak shift relative to bulk TiO2 as a function of TiO2 cycle
thickness for IrO2, RuO2, and FTO. ................................................................... 122
Figure 5.16 X-ray photoelectron spectroscopy of the Ir 4f, Ru 3d, and Sn 3d5/2 region for
IrO2- RuO2- and FTO-based electrocatalysts as a function of TiO2 thickness. ..... 124
Figure 5.17 Overall peak shift of the main peak of the Ir 4f, Ru 3d, and Sn 3d5/2 spectra
relative to the bare metallic (0 cycle) metal-oxide substrate as a function of TiO2 cycle
thickness for IrO2, RuO2, and FTO, respectively. ............................................... 125
Figure B.1 (Top) Diagram of the typical solidification process, known as normal freezing.
The distribution of solute (impurities) in the solid is controlled by the distribution
coefficient k, the rate of the advance of the solid-liquid interface, and the mixing in
the liquid. (Bottom) The solute concentration for a normal freezing process as a
function of the fraction of solidification for different distribution coefficients k. . 192

xx
Figure B.2 (Top) Diagram of the zone melting process, in which a molten zone is passed
along the length of a solid. (Bottom) The solute concentration for the zone melting
process as a function of the fraction of solidification for different distribution
coefficients k. Zone melting results in regions of purification and uniform solute
distribution. ...................................................................................................... 193
Figure B.3 Image of a floating zone during growth of single crystalline Cu2O. The bright
regions in the background are the halogen lamps which serve as the heat source. 194
Figure B.4 Typical floating zone setup before (left) and after (right) the feed and seed rods
are brought into contact..................................................................................... 195
Figure B.5 The optical floating zone furnace from Crystal Systems Inc. Adapted from (211).
......................................................................................................................... 197
Figure B.6 The Bridgeman vertical tube furnace and crane assembly (211). .................. 198
Figure B.7 Top view of a seed rod sample holder (gray) with an improperly sized seed rod
(red) during different stages of rotation. The sample holder is sized for a sample of
the size traced out by the black dashed circle. The center of a seed rod this size is
collinear with the rotational axis (black dot) of the sample holder and feed rod. The
improperly sized seed rod, however, has a rotational axis (red dot) different than that
of the sample holder. Thus, rotation of the sample holder leads to the center of the
seed rod tracing a circle around the axis of rotation of the float zone assembly (black
dot). This leads to a “wobbly”, unstable molten zone. ........................................ 200
Figure C.1 System resistance as measured by electrochemical impedance spectroscopy in
5.0 M NaCl at pH 2.0 (CER) and 1.0 M H2SO4 (OER). The resistivity of the system
did not apprecaibly change between 0 and 60 ALD cycles of TiO2. For IrO2 based
electrodes, the average system resistance was 9.1 ± 0.6 Ω for CER condtions and 5.4
± 0.6 Ω for OER conditions. For RuO2 based electrodes, the average system
resistance was 8.0 ± 1.0 Ω for CER condtions and as 5.3 ± 0.7 Ω for OER conditions.
For FTO-based electrodes, the average system resistance was 30 ± 7 Ω for CER
condtions and 23 ± 6 Ω for OER conditions. ...................................................... 205
Figure C.2 Example double-layer capicitance measurements for determining ECSA for IrO2
with 10 cycles of ALD TiO2 in 1.0 M H2SO4. (Left) Cyclic voltamogramms in the
non-Faradaic region at 0.005, 0.01, 0.025, 0.05, 0.1, 0.2, 04, and 0.8 V/s. (Right)
Cathodic (yellow disks) and anodic (blue disks) charging currents measured at 0.95
V vs SCE plotted as a function of scan rate. ....................................................... 207
Figure C.3 Example impedence spectroscopy for IrO2 with 0 cycles of ALD TiO2 in 5.0 M
NaCl pH 2.0 at Eoc. These data were fit to a resistor in series with a parallel
combination of a capacitor and a shunt resistor. The resulting capacitance was taken
as the Cd which in this case was was 3.24×10-6 F. .............................................. 208
Figure C.4 ECSA for IrO2, RuO2, and FTO based catalysts in 1.0 M H2SO4 and 5.0 M NaCl,
pH 2.0. All catalysts presented here had a geometric surface area of 0.13 cm2,
yielding electrochemical roughness factors between 0.1 and 6.0. ........................ 209
Figure C.5 Sample Bode (above) and Nyquist (below) plots of electrochemical impedence
spectroscopy data of IrO2 coated with 10 ALD cycles of TiO2. The Bode plot shows
the frequency of the alternating current signal (Hz) versus the phase shift of the
impedance response (degrees). The Nyquist plot shows the real (Z’) and imaginary
(Z”) components of the impedance response to the alternating current signal. Data

xxi
presented in the figure were collected at 105 mV vs SCE in 5.0 M NaNO3 at pH
2.0. The resulting equivelent circuit [Rs-(Rp-C)] fit of these data yielded a capacitance
of 5.8× 10-6 F. ................................................................................................... 213
Figure C.6 Electrochemical impedance spectroscopy of (A) IrO2, (B) RuO2, (C) and FTO
coated with various ALD cycles of TiO2 at 25 mV intervals in 5.0 M NaNO3 at pH
2.0. The resulting Nyquist plots were modeled as Rs-(C-Rp) circuits. The calculated
capacitance values (dots) for each sample (set of dots) are shown here. The minimum
value of each curve represents the EZC. The magnitude of the capacitance represents
the surface area of the sample. ........................................................................... 214
Figure C.7 Sample Mott-Schottky (E vs 1/C2) plots of RuO2 with 0 (red), 1000 (blue) ALD
TiO2 cycles. The fit, using a geometric surface area of 7.1 X 10-6 m2, yielded Nd = of
5.4 X 1019 cm-3. ................................................................................................ 215
Figure C.8 Potential of zero charge as a function of TiO2 cycle number for IrO2, RuO2, and
FTO electrocatalysts. Black dots and disks with black borders indicate the catalysts
with the highest specific activity for each substrate for the OER and CER,
respectively. ..................................................................................................... 216
Figure D.1 X-ray photoelectron spectroscopy of the Ti 2p region for a bulk TiO2 film. The
peak associated with Ti4+ is shown in blue. The slightly and highly reduced Ti peaks
are shown in green and red, respectively, and the most highly oxidized Ti peak is
shown in orange. ............................................................................................... 218
Figure D.2 X-ray photoelectron spectroscopy of the Ti 2p region for a bare RuO2 film. The
3 orange, red, and purple peaks define the Ru 3p core level photoemission associated
with RuO2......................................................................................................... 219

xxii

List of Tables
Table 2.1 Experimentally observed Urbach parameters of common photovoltaic materials.
........................................................................................................................... 18
Table 3.1 Exciton binding energies (Ex) and dielectric constants for established and emerging
photovoltaic materials. The exciton binding energy scales with the inverse square of
the dielectric constant.......................................................................................... 33
Table 4.1 Hall-effect measurements for annealed TDMAT-ALD TiO2 ............................ 85
Table 5.1 Surface area (measured by AFM) as a percent of geometric surface area. Dividing
these values by 100 yields topographic roughness factors. .................................. 104
Table 5.2 A summary of the Tafel slopes and exchange current densities from this work
(IrO2 + TiO2 catalyts) and previous work (SrIrO3 catalysts) (208). All current density
data reported here is based on surface area that is measured by AFM (Table S1). 110
Table 5.3 Summary of overpotential data as measured from CVs to reach 10 mA/cm2geo in
1 M H2SO4 for the OER and 1 mA/cm2geo in 5 M NaCl pH 2.0 for CER at 0 min, 10
min, 2 h, and 24 h of testing in constant current mode. The right-most column
displays the overpotential that was reported in the main text. N/A indicates that a
rapid loss in activity was noticed before the time of measurement. ..................... 113
Table 5.4 The areal peak ratios of the main peak to the satellite peak for the Ir 4f, Ru 3d, and
Sn 3d core-level photoemission. ........................................................................ 125
Table B.1 Faradaic efficiencies for the OER and CER .................................................. 204

Chapter 1
Introduction
1.1 A Net-Zero Carbon Emission Energy System
The rapid increase in human development over the last several centuries has come with an
increased dependence on energy to provide the services that society relies on. Despite
increases in energy efficiency, the global energy demand is expected to increase by almost
30% in the next 20 years as emerging economies continue to develop (1, 2). At the same
time, net emissions of carbon dioxide (CO2) from anthropogenic sources must approach zero
(or negative values) if global temperatures are to stabilize at or below the 2ºC target of
international climate agreements (3-5).
Electricity production, transportation, and industrial chemical production together account
for the vast majority of global annual CO2 emissions; 22.3 Gt of the 33.9 Gt of CO2 emitted
each year (6). Of this total, electricity generation is responsible for 38% of annual carbon
dioxide emissions as ~80% of the global electricity generation was still derived from fossil
fuel sources in 2017 (6, 7). Transportation accounts for an additional 22% of annual CO2
emissions. While roughly 70% of these emissions are from short distance transport where
electrification is already playing a role in decarbonization, the remaining 30% is due to
aviation, long distance rail and road transport, and long-route shipping where electrification
is much more difficult (6, 8, 9). Chemicals and chemistry are used to make almost everything
that society produces. The chemical industry is energy intensive, often requiring high
temperatures and pressures to run reactions efficiently and in the process producing ~6% of
the world’s annual CO2 emissions – a number that is expected to grow as developing
economies grow and the demand for industrial chemicals increases (10). Thus, a transition
to a near zero net emissions future will likely require a robust, emissions-free grid system
capable of producing vast amounts of inexpensive electricity; electrification of most fuel

consuming devices and carbon-neutral fuels for the parts of the transportation system that
are not easily electrified; and new electrochemical methods and catalysts for electrification
of commodity chemical production.

Figure 1.1 A sustainable energy system with near zero carbon emissions, reproduced
from(6). Renewable electricity is used directly as a source of energy for transportation or
to produce fuels, chemicals and materials electrochemically.
An example of a near net zero carbon energy system is depicted in Fig. 1.1. In such a system,
a cheap, reliable electricity grid primarily powered by renewable energy (solar, wind or

hydro) is used as the major energy source to power the rest of the energy services. Lightduty and short-distance medium- and heavy-duty vehicles have been electrified or consume
clean burning fuels (e.g. hydrogen). Major industrial chemicals and transportation fuels are
produced (photo)electrochemically and are thus powered by the vast amounts of inexpensive,
renewable electricity. Other industries that are more difficult to decarbonize (e.g. cement and
steel manufacturing) can use carbon capture and storage technology to offset their emissions.
Despite an increased societal awareness of anthropogenic climate change and an increased
adoption of renewable energy technologies, the world is far from realizing a net-zero carbon
emissions energy system.

1.2 Challenges to Realizing Net-Zero Carbon
Creating a global net-zero carbon energy system is not an easy task. The largest and most
immediate barrier preventing the implementation of a carbon-neutral energy system is the
substantial cost associated with known technological alternatives to the current carbon
emitting system. These costs are exacerbated by current economic and development goals
and trends in international trade and travel that are expected to fully double the global energy
demand by 2100, such that difficult-to-eliminate emissions could be in the future comparable
to current total emissions (6). Beyond cost reductions, rapid innovation is needed to increase
efficiency and develop new processes and technologies to replace difficult to those energy
services which are difficult to decarbonize. Nowhere is this truer than in the electricity
generation, energy storage, and chemical production sectors which largely rely on
technologies developed over 100 years ago. This thesis focuses on cost reductions and
technological innovations in solar photovoltaics, a promising renewable electricity
generation technology, and catalysis for the electrochemical production of fuels and
industrial chemicals.

1.3 Solar Photovoltaics
The majority of CO2 emissions related to electricity generation can be mitigated by switching
to renewable energy sources (e.g. solar, wind, and hydro). Solar photovoltaics, which convert
solar energy directly into electricity and are commonly referred to as solar cells, are a
particularly attractive carbon-free technology. More energy from sunlight is incident on the
Earth’s surface in an hour and a half than was consumed globally in 2014 (11, 12) and yet,
photovoltaics make up only a miniscule fraction of the total global electricity generation, less
than 2% in 2017 (13).

1.3.1 The Solar Cell Market
The global solar cell market began as a fledgling industry in the early years of the second
half of the 20th century, scraping by in niche applications. Since then the solar cell market
has grown at a near exponential rate to a robust market with over 400 GW of installed global
capacity (14). The market is dominated by crystalline silicon (Si) photovoltaics, which at
present account for 95% of global solar energy production. The growth of the solar cell
market has been largely driven by a drastic reduction in Si module cost and increase in cell
efficiency, such that photovoltaic electricity generation is now cost competitive with
traditional electricity generation technologies (15). Indeed, at the time of writing, the balance
of system costs (installation, permitting, support structure, electrical wiring, etc.) account for
over 70% of the cost of a fully installed Si module (16).
Despite the recent decrease in the cost of Si solar modules, further cost reductions are needed
to account for the high cost of solar energy storage if solar is to replace baseload power at
large penetrations (16, 17). Reductions in the recombination losses at the Si surface and metal
contacts through better passivation and minimization of shadow losses at the top contacts
have resulted in incremental improvements in the Si cell efficiency. The current laboratory
record power-conversion efficiency (h) for single-junction Si solar cells is 26.6% (18),
closely approaching the theoretical limit of 29.4% (record module efficiencies are closer to

23%) (19). Further reductions in the cost of Si photovoltaics can be most readily met by
increasing the module efficiency, and thereby reducing the area-related balance of systems
costs. For example, replacing a 15% efficient solar module with a 20% efficient module, all
else being equal, leads to a 25% reduction in land acquisition, installation, cleaning, and
permitting costs on a per watt basis. Thus, other approaches beyond the incremental
improvement of Si cells are needed to increase cell efficiencies past the Si single junction
theoretical limit.
Beyond improvements in efficiency, the electricity produced from photovoltaics is inherently
time-varying (the sun is not always shining) as is illustrated in Fig. 1.2. The diurnal day-night
cycle and weather limit the capacity factor of photovoltaics to only ~25%, even in the most
favorable locations. This intermittency necessitates so-called “load following” electricity
generation, which is typically supplied by natural gas-fired generators that can ramp up and
down quickly to meet the time varying gap between the supply and demand (6). One
renewable alternative is to store the solar energy in a chemical fuel which can be used later
(when demand peaks and sunlight wanes) using a photovoltaic-powered electrolyzer.
However, improvements in the electrocatalysis and system efficiencies are needed (see
Section 1.4).

Photovoltaic Integration
Larger megawatt-scale photovoltaic installations will need energy storage due to the occurrence
of large voltage sags and rapid demand shifts due to cloud effects. These effects can be even
more severe than wind ramps because they are much faster. Rapid voltage excursions (Figure 3-6
below) present a significant challenge to utilities trying to integrate and manage these resources
on their systems.

Figure 3-6

Output
of Large
Photovoltaic
Plantsolar
over One
Day, with Rapid
Variability
Figure 1.2
Power
output
from a Power
4.6 MW
photovoltaic
power
plantDue
intoArizona on a
Clouds
cloudy day. From (20).

In recent years, the increase of photovoltaic penetration on the distribution grid has presented
operational problems for utilities. Energy storage systems can potentially alleviate voltage
in the distribution grid. Large photovoltaic applications may also require high-power,
1.3.2 swings
Basics
Operating Principles of Photovoltaics
low-energy storage systems that can perform many cycles and are capable of fast response. Such
systems would generally be in the size range of 500 kW to 1 MW or larger with 15 minutes to 1
hr of storage, and could include advanced lead acid batteries, lithium-ion batteries, and superIn order
to understand how to improve the efficiency of solar cells we must first understand
capacitors.

how they work. The operating principle behind solar cells is the photovoltaic effect – the
spontaneous generation of a voltage by a material under illumination. Though first observed
in photosensitive electrodes immersed in an electrolyte by Becquerel in 1839, modern
photovoltaics are solid-state devices that consist of one or more semiconductor materials. A
3-8

brief description is provided below for the lay reader but there are many thorough treatments
of the device physics of photovoltaics and the interested reader is directed to references (2123).
By far, the most common type of solar cell is the single-junction consisting of a single
absorbing semiconductor material with a p-n homojunction device architecture. A
semiconductor. A semiconductor is characterized by a distribution of electronic states in
bands separated by forbidden gaps in which no electronic states exist. At thermal
equilibrium, the electrons in a semiconductor are governed by Fermi-Dirac statistics and will
occupy states up to the Fermi-energy. The highest occupied band is referred to as the valence

band (VB) and the lowest lying band above the Fermi level is known as the conduction
band (CB). The difference in energy between the VB and the CB is known as the band gap
(Eg), which typically ranges from 50 meV to 3.5 eV (though the distinction between a very
wide band gap semiconductor and an insulator is somewhat arbitrary).
The energy band gap gives rise to the characteristic optical response of a semiconductor (Fig.
1.3). When light is absorbed by a semiconductor, an electron in the valence band is excited
to a conducting state in the conduction band, leaving behind an effective positive charge,
which can be treated as a quasiparticle. Hence, in order for a semiconductor to absorb a
photon, the photon must have an energy at least equal to the band gap 𝐸345657 ≥ 𝐸9 ; photons
with a lower energy are not absorbed and are transmitted through the semiconductor. Photons
with an energy greater than the band gap are absorbed and electrons are promoted to higher
states in the conduction band. However, this excess energy is lost rapidly as the electron
couples to the semiconductor’s crystal lattice vibrations (phonons) in a process known as
thermalization and the electron decays back to the conduction band edge.

Energy

Figure 1.3 A simplified semiconductor energy band diagram depicting absorption,
thermalization, and radiative recombination. The semiconductor has a band gap 𝐸9 =
ℎ𝜈9:;;7 and thus absorbs green photons and photons with higher energy (shorter
wavelength) while photons with less energy are transmitted (red photon). Upon absorption

electrons (filled gray circle) in the valence band (VB) are excited to the conduction band
(CB) leaving behind an effectively positively charged hole (white circle) in the valence
band. Absorption of a photon with excess energy (blue photon) promotes an electron to an
excited state in the conduction band above the band gap. The excited electron rapidly
decays back to the valence band edge in a process known as thermalization (dark red steps),
transferring its energy to the semiconductor lattice in the process. In radiative
recombination, electrons recombine across the band gap emitting a photon in the process.
Electrons excited to the conduction band have a finite lifetime, eventually they will
recombine with the hole in the valence band. In an ideal material, this process is always
radiative – a photon is emitted when the electron and hole recombine, which is emitted to
free space or reabsorbed by the semiconductor. However, non-radiative recombination is
always present in real materials and represents a major loss mechanism in most solar cells.
This non-radiative recombination is often mediated through defect states either at
semiconductor surfaces or in the bulk (or both!).
Under continuous illumination, a steady-state population of electrons and holes are
generated. In response, the electron and hole systems develops electrochemical potential and
the cell builds up a voltage equal to the electrochemical potential difference between the two
carrier populations. Thus, the voltage is limited to the band gap of the solar cell, though for
realistic solar cells the voltage is always lower due to imperfections and entropic losses.

Current Density

Voc

Voltage

Jsc
Figure 1.4 Current density-voltage characteristics of an ideal solar cell. In the dark, the
solar cell operates as an ideal diode (red dashed curve) with an exponential dependence on
the applied voltage. The light curve (blue) is a superposition of the dark curve and the
absorbed photon flux. The short circuit current is equal to the total absorbed photon flux
and corresponds to the point V = 0, where there is no radiative recombination. By contrast,
the Voc is at the point when the incident photon flux is completely balanced by the radiative
emission of the cell and occurs when the light curve intersects the abscissa. The power
producing region of the light curve is thus in the fourth quadrant. The maximum power
point is represented by the dark gray box. The ratio of the area of the dark gray box to the
light gray box is the fill-factor, which is a measure of resistance and non-idealities in the
cell.

The recombination in the solar cell is (intuitively) voltage dependent. The current-voltage
characteristics of an ideal solar cell are illustrated in Fig. 1.4. In the dark, the solar cell is
simply a p-n junction diode with an exponential dependence on voltage. Under illumination,
the solar cell absorbs photons and a photocurrent is generated. Hence, the light curve is a
superposition of the dark curve. At short-circuit, the conduction band and the valence band
in the semiconductor are connected via an external conductor such that the radiative

10
recombination is zero and thus the short-circuit current density Jsc is simply the total
photogenerated current. Because each absorbed photon corresponds to a single electron hole
pair, the magnitude of the Jsc indicates the efficiency of absorption. At open-circuit there is
no current pathway and the absorbed photon flux exactly balances the radiative emission
from the cell. Therefore, the open circuit voltage Voc is indicative of the material and junction
quality, being higher for cells with lower non-radiative recombination. The cell produces
power equal to the product of the current and voltage in the region of the curve between the
Jsc and Voc. The voltage and current density at the maximum power point of the cell (Vmpp

and Jmpp, respectively) are determined by minimizing the power density (𝑀33 = => 𝑃 =
=>

𝐽(𝑉 ) ∗ 𝑉 = 0). The efficiency of the cell 𝜂 is then determined by dividing the maximum

power by the power incident on the cell from the solar spectrum (~1000W/m2 at the Earth’s
surface). The fill factor FF is the ratio of the maximum power produced by the cell and the
product of the Jsc and Voc and is a measure of the resistive losses, non-radiative
recombination, and general non-ideality of the cell. Thus, the Jsc, Voc, FF, and 𝜂 are the key
performance metrics for photovoltaics.

1.4 Electrocatalysis for Production of Fuels and Chemicals
Society relies on chemistry and chemical products for almost everything we produce.
Catalysts lower the thermodynamic barrier necessary to run a reaction and improve reaction
kinetics (Fig. 1.5) and are used in the vast majority (> 90%) of chemical processes. The
chemical industry in its vastness is (unsurprisingly) a large consumer of energy (10% of
global energy consumption was consumed by chemical processes in 2013). Thus, improving
catalysis is a large lever to reducing the CO2 emissions of the entire chemical industry.

Energy

Without catalyst
With catalyst

Reaction Path
Figure 1.5 Reaction energetics for a reaction X to Y with (red) and without (blue) a
catalyst. The catalyst lowers the activation energy (EA) for the reaction resulting in greater
kinetics and reaction efficiency.
Indeed, catalysts play an integral in the production of widely consumed chemicals, such as,
hydrogen (50 Mt/yr), ethylene (115 Mt/yr), and ammonia (175 Mt/yr), which are possible to
produce sustainably by coupling electrochemical production with a renewable electricity
grid, but which remain much more expensive and less efficient than conventional production
methods (6, 9). In fact, chlorine is one of the only major commodity chemicals produced
electrochemically. Thus, development of improved electrocatalysts with higher efficiencies
and selectivities is imperative not only to realizing a variety of electrochemical
transformations at scale but also to improving the energy efficiency of existing reactions.

12
In this thesis, we focus on improving catalysts for the oxygen-evolution and chlorineevolution reactions (OER and CER, respectively), because of their major role in the global
economy and zero-carbon future.
The OER is the limiting half reaction in water splitting, which produces hydrogen through
water electrolysis. Stored electrolytic hydrogen can be used in a variety of energy scenarios.
In a power-to-gas-to power system, stored hydrogen is converted back to electricity through
combustion in hydrogen burning turbines or in fuel cells. Hence, P2G2P systems can be used
to complement the time variability of renewable sources such as wind and solar. The high
energy efficiency of hydrogen fuel cells also makes hydrogen an attractive choice for a clean
transportation fuel. Indeed, Toyota has recently introduced a line of fuel cell cars and a
heavy-duty fuell cell/battery hybrid truck with impressive ranges and there are large
investments planned in hydrogen for transportation Germany and in California (24-26).
Thus, development of new, efficient OER electrocatalysts is need to usher in an era of clean
hydrogen.
The CER is the largest electrochemical process in the world, accounting for 2% of global
energy usage alone. Chlorine is used in 50% of industrial chemical processes, 85% of all
pharmaceuticals and 95% of all crop protection chemicals as well as in almost all water
treatment facilities (27). The operating expenses of a chlor-alkali plant make are dominated
by electricity costs and make up 50% of the total cost of chlorine (28). Improving the
efficiency of existing OER catalysts, thus represents a large potential reduction in CO2
emissions.

1.5 Scope of This Thesis
This thesis works towards a net-zero carbon emission future by focusing on improvements
in photovoltaic efficiency and electrocatalysis through fundamental understanding and
development of new technologies. In Chapter 2, we extend the classical Shockley-Quiesser
detailed balance model to include non-ideal band edge shapes. We find that even with perfect

13
above gap absorption significant below gap band tailing severely limits the solar cell
efficiency and external radiative efficiency. In Chapter 3, we investigate the effects of bound
electron-hole pairs (excitons) on photovoltaic performance using an emerging
semiconductor, cuprous oxide, as a case study. Chapter 4, develops a novel, interconnectfree tandem perovskite/silicon solar cell architecture. We demonstrate that our cell contacting
scheme is highly efficient, transparent, and has the promise to push cell efficiencies beyond
30%. In Chapter 5, we demonstrate a new tool to tune the catalytic activity of heterogeneous
electrocatalysts for the chlorine-evolution and oxygen-evolution reactions, which are
important componenets of industrial chlorine production and the fuel-forming water splitting
reaction, respectively. Finally, we conclude in Chapter 6 by summarizing our findings and
providing outlook for future work in these directions.

Chapter 2
Efficiency Limits of Light Absorbers
2.1 Detailed Balance Limit
Understanding the fundamental energy conversion limits of how efficiently a photovoltaic
device can operate is important; it yields insight into effective strategies for device design,
and materials selection. A solar energy converter operating as a heat engine with the hot
reservoir at the temperature of the sun (~5800 K) and the cold reservoir at the temperature of
the earth (~300 K), could operate at a maximum Carnot efficiency of 94.8%. However, the
Carnot efficiency is much larger than that achieved by photovoltaic devices and ignores
fundamental entropic and thermalization losses that are associated with absorption and
emission in traditional photovoltaic devices.
The reciprocity between absorption and emission in photovoltaic devices was first outlined
by Shockley and Queisser (S-Q) in their seminal paper on the fundamental efficiency limits
of photovoltaics in 1961 (29). The theory laid out by S-Q is known as detailed balance
because it balances the absorbed solar flux with the luminescent emission and current
extraction from the solar cell. The S-Q theory is subject to three key assumptions: 1) the
solar cell operates in the radiative limit (the external radiative efficiency is unity) and there
is no non-radiative recombination, 2) perfect carrier collection (the internal quantum
efficiency, IQE, is unity) so that every absorbed photon creates an electron-hole pair that is
collected as current, and 3) that the semiconductor absorber has a perfect forbidden energy
gap with perfect absorption above gap and zero sub-gap absorption. Under these
assumptions, the current-voltage characteristics of an ideal solar cell are given by the balance
of the light generated current from the absorbed solar flux and the radiative current:

𝐽(𝑉 ) = −𝑞 ∫M 𝛷IJ7 (𝐸 )𝑎(𝐸 )𝑑𝐸 + ∫M 𝑏(𝐸, 𝑉, 𝑇S;TT )𝑎(𝐸 )𝑑𝐸

15
(1)

− ∫M 𝑏(𝐸, 0, 𝑇;U:64 )𝑎(𝐸 )𝑑𝐸

where, J is the current-density, V is the voltage, q is the fundamental electron charge, Eg is
the band gap, 𝛷IJ7 is the incident solar flux, a is the absorptivity, and we have employed
Kirchoff’s law to substitute 𝑎(𝐸 ) = 𝜖(𝐸) in the second term and
MZ

𝑏(𝐸, 𝑉, 𝑇) = 4YS Z [\]^

(2)

; _` a bc

is the Planck blackbody formula accounting for the chemical potential of the cell (i.e. the
quasi-Fermi level splitting taken here as the cell voltage, 𝛥𝜇 = 𝑞𝑉) where, E is the photon
energy, V is the voltage and T is absolute temperature in Kelvin. The first term is the absorbed
solar flux, the second is the radiative current and the third term is the absorbed solar flux
from the blackbody radiation of the Earth. The performance metrics of a single junction solar
cell with band gap Eg are thus readily calculated from Eq. 1 as follows: Jsc occurs at V=0, the
Voc is determined by solving for the roots of Eq. 1., and the efficiency 𝜂 is found by finding

the maximum power produced from the cell with respect to voltage (=> 𝑃 = => 𝑉 ∗ 𝐽(𝑉 ) =

4 × 10

3 × 1021
2 × 10

η (%)

Photon flux (photons/m2/eV)

0) and dividing by the incident power.

20
15
10

1 × 1021

0.0

1.0
2.0
3.0
Photon Energy (eV)

4.0

0.5

1.0

1.5
Eg (eV)

2.0

2.5

Figure 2.1 a) The AM1.5G photon flux. b) The Shockley-Queisser Limit for the AM 1.5G
spectrum: photovoltaic cell efficiency as a function of band gap.

Unsurprisingly, the band gap of the absorber material plays a central role in determining the
ultimate device efficiency as it controls the absorption characteristics of the cell. Increasing
a cell’s bandgap increases the Voc at the expense of the Jsc. These opposing driving forces, in
concert with the spectral make-up of the incident solar flux, lead to an optimal band gap for
a photovoltaic converter. Figure 2.1a shows the Air Mass 1.5 Global (AM 1.5G) photon
flux, so called because it refers to the incident solar photon flux at 37º latitude such that
sunlight passes through the equivalent of 1.5 atmospheres before reaching the Earth’s
surface. Global includes both direct and diffuse sunlight and is relevant for cells without
concentration. The detailed balance efficiency for the AM 1.5G spectrum is plotted as a
function of band gap energy in Fig. 2.1b. The optimum efficiency of 33.6% occurs at a band
gap 𝐸9 = 1.34 eV, though there are multiple peaks owing to the spectral profile. As a
comparison, at the time of writing the record single junction efficiency is 28.8% for a GaAs
(𝐸9 = 1.42 eV) solar cell (30).

2.2 Imperfect Absorption and Modified Detailed Balance
The Shockley-Queisser Limit is a useful tool to understand the ultimate limits of perfect
photovoltaic energy conversion. However, in practice, semiconductors are far from ideal
owing to a variety of defect states that present themselves in the fundamental optoelectronic
processes governing solar cell performance. Herein, we develop a modified detailed balance
model that accounts for these no idealities, namely the non-zero sub-gap absorption
exemplified by typical photovoltaic materials.

2.2.1 Absorption in real materials
A key assumption of the S-Q model is that the solar cell is a perfect absorber - all photons of
energy higher than the band gap are absorbed and the absorption below gap is zero. However,

17
real materials exhibit sub-gap absorption due to impurities and disorder as illustrated in
Fig. 2.2. (31-33). This sub-gap absorption is typically characterized by a linear exponential
band tail below the gap and has been observed in a wide range of absorber materials including
amorphous, organic, perovskite and II-VI, III-V and group IV semiconductors (31, 34-42).
This phenomenon was first observed by Urbach in 1953 for AgBr and other ionic materials
MbM

and band tails with the form 𝛼(𝐸 ) = 𝛼h exp l n m o are known as Urbach tails, with the
steepness of the decay determined by the Urbach parameter 𝛾 (43). Though the exact physical
origin of the band tailing is material dependent, any band tail with a linear exponential can

ba
ch

Ta
il

be characterized with an Urbach parameter.

Figure 2.2 The band edge absorption of GaAs adapted from (34). GaAs exhibits an
exponential band tail below the band gap and band to band absorption above gap.
The Urbach parameters for photovoltaic The Urbach parameters for photovoltaic absorber
materials varies widely based on material quality and inherent disorder (31). The

18
experimentally derived Urbach parameters for common photovoltaic parameters are
tabulated in Table 2.1. High quality materials (e.g. GaAs, InP) have Urbach parameters in
the range of a few meV, whereas more disordered materials (e.g. a-Si, CZTS) typically
exhibit Urbach parameters on the order of several k T (~25.8 meV at 300 K).

Material
E0 (meV)
GaAs
6.7 (34)
InP
7.1 (35)
CdTe
9.0 (36)
c-Si
11 (37)
Cu2O
14 (38)
CH3NH3PbI3
15 (39)
CIGS
24 (40)
a-Si
48 (41)
CZTS
65 (42)
Table 2.1 Experimentally observed Urbach parameters of common photovoltaic materials.
Although the sub-gap absorption in an Urbach tail is exponentially small (see Fig. 2.2) there
is a relationship between the experimental photovoltaic performance and Urbach parameter
for a given photovoltaic materials. Figure 2.3 plots the difference between the open-circuit
voltage predicted by the detailed balance from S-Q and the experimentally achieved opencircuit voltage for different materials as a function of their Urbach parameters. Small values
of 𝑉5S,Ibq − 𝑉5S,Mr3 indicate larger experimental open-circuit voltages and more ideal cell
performance. There is a striking correlation between a material’s Urbach parameter and the
ideality of the cell: high quality materials (GaAs, Si, InP, perovskites) have open-circuit
voltages approaching that of the S-Q Limit, whereas more disordered materials exhibit opencircuit voltages that are far from ideal.

qVoc,S-Q - qVoc,Exp (eV)

1.0
0.8
a-Si (1.7-1.85 eV)

0.6

CZTS
(1.54 eV)

CIGS (1.52 eV)

0.4

InP
(1.34 eV)

0.2

Cu2 O (1.9 eV)
CH3 NH3 PbI3 (1.57 eV)
c-Si (1.12 eV)

GaAs (1.42 eV)

0.0

γ (meV)
Figure 2.3 The deficit in the experimentally achieved open-circuit voltage from that of the
S-Q Limit as a function of Urbach parameter for common photovoltaic materials.

2.2.2 Modified Detailed Balance
To better understand the correlation between photovoltaic performance and sub-gap
absorption we develop a modified detailed balance model for single junction solar cells that
includes the effects of band tailing:

𝐽(𝑉 ) = −𝑞 ∫h s𝛷tuc.wx (𝐸 ) + 𝛷yy (𝐸, 0, 𝑇MU:64 )z𝑎(𝐸, 𝑉 )𝑑𝐸
+|

}~•

∫ 𝛷yy (𝐸, 𝑉, 𝑇S;TT )𝑎(𝐸, 𝑉 )𝑑𝐸
(>) h

(3)

where, 𝜂;r6 is the external radiative efficiency of the solar cell and we have again used
Kirchoff’s law to replace the emissivity with the absorptivity in the second term on the
right. As in S-Q’s original detailed balance model, the current collected J(V) is a balance of
the photogenerated current and the carrier loss from radiative and non-radiative

20
recombination. For simplicity, we assume that our cell operates in the radiative limit with
perfect carrier collection efficiency where 𝜂;r6 = 1 and 𝐼𝑄𝐸 = 1, such that 𝐸𝑄𝐸 (𝐸, 𝑉 ) =
𝐼𝑄𝐸 (𝐸, 𝑉 )𝑎(𝐸, 𝑉 ) = 𝑎(𝐸, 𝑉 ) (see Section 2.3.1 for analysis of the non-radiative limit and
imperfect carrier collection. We consider a flat plate solar cell with zero-front surface
reflection and perfect back reflector so that the absorptivity is described by Beer-Lambert
absorption:
𝑎(𝐸, 𝑉 ) = 1 − exp (−2𝛼𝐿)

(4)

where, L is the cell thickness. To parameterize the band-edge we use an absorption model
that convolutes a sub-gap exponential density of states with a parabolic density of states
above gap that describes band-to-band absorption (44), which yields:
𝛼h„ (𝐸 ) = 𝛼h …𝛾𝐺 ‡

𝐸 − 𝐸9

with

• exps−|𝑥 Ž |• z √𝑥 − 𝑥 Ž 𝑑𝑥 Ž ‘
𝐺 (𝑥 ) = 𝑅𝑒 Š
1 bL
2Γ l1 + 𝜃 o
where, 𝛼h„ (𝐸) is the absorption coefficient at absolute zero and 𝜃 = 1 represents the case
of an Urbach tail. It is important to note that this absorption accounts only for the density of
states but not for the occupation of these states and leads to a divergence in the generalize
Planck law (44, 45) and an overestimation of the effects described below (46, 47). The
resolution is to include an occupation factor 𝑓“ − 𝑓S where fv is the occupation of holes in
the valence band and fc is the occupation of electrons in the conduction band. Then, the
total absorption coefficient is:
𝛼 (𝐸, 𝑉 ) = 𝛼h„ (𝐸 ) ∗ (𝑓“ − 𝑓S )

21
We consider the case of perfectly parabolic density of states with equal electron and hole
effective masses. Under such conditions, the occupation factor has the following form:
(𝑓“ − 𝑓S ) = tanh ‡

𝐸−𝑉
4𝑘š 𝑇

and thus, the solar cell’s absorption is not only dependent on the incident photon energy but
also on the cell’s operating voltage. While the occupation factor of real material systems is
more complicated, we note that 𝑓“ − 𝑓S is generally a function with limiting values from -1
to 1 with a sign flip at 𝐸 = Δ𝜇, which is captured by the simple expression above.
In the following sections, we use this modified detailed balance model to analyze the
performance metrics of the solar cell when the effects of sub-gap absorption are included.
Although, the absorption model presented here is general it can easily be fit to capture the
optical response of any semiconductor absorber in general so that more specific results can
be obtained (44).

2.3 Sub-gap Absorption and Solar Cell Performance
Using the modified detailed balance model developed in Section 2.2.2 we analyze the effects
of sub-gap absorption on solar cell performance. The calculations below assume 𝛼h 𝐿 =10,
which leads to full absorption above gap (the effects of incomplete absorption are treated
later) and that the cell and Earth are at room temperature 𝑇S;TT = 𝑇MU:64 = 300 K. Urbach
parameters ranging from 1 meV to 1 eV are considered. The Mathematica code used to
calculate the findings below can be found in Appendix A.
The spectral response of a solar cell with a 1.5 eV band gap is shown in Figure 2.4a for
different Urbach parameters in units of kBT. Naively from Fig. 2.4a, sub-gap absorption
would seem to have a muted effect on the solar cell performance, as the cell exhibits unity
photoconversion above gap for all Urbach parameters and shows exhibits only some band
tailing below the gap with absorption extending deeper into the gap with increasing Urbach

22
parameter. Though, one should note that even for the lowest Urbach parameters the cell
spectral response is not perfect as in the S-Q case. However, we find that the increasing the
Urbach parameter to even ~3 kBT has detrimental effects on the maximum theoretical
efficiency, especially for band gaps less than the optimum 1.34 eV band gap from the S-Q
Limit (Fig. 2.4b). For the lowest Urbach parameters the efficiency approaches that of the SQ Limit with a maximum efficiency near 33.6%, but for Urbach parameters > kBT there is a
significant penalty and at 3kBT the maximum efficiency is only half of the S-Q limit with an
efficiency of only 16.7%.

1.0

a γ (k T )

B cell

EQE

0.6
0.4

S-Q
0.1

0.5

η (%)

0.8

20
15

10
0.2

0.0
0.0

0.5

1.0

1.5

Photon Energy (eV)

2.0

2.5

0.5

1.0

1.5
Eg (eV)

2.0

2.5

Figure 2.4 a) The spectral response of a solar cell with a 1.5 eV band gap for different
Urbach energies in units of kBT. using the absorption model outlined in Section 2.2.2. The
sub-gap absorption increases deeper into the gap with increasing Urbach parameter b) The
modified detailed balance efficiency as a function of cell band gap for different Urbach
energies. Increasing the Urbach parameter has a deleterious effect on cell performance.
The drastic decrease in solar cell efficiency can be understood by examining the figures of
merit of solar cell performance as a function of increasing Urbach parameter as illustrated in
Fig. 2.5. For small increases in the Urbach parameter 𝛾 < 𝑘š 𝑇, increasing sub-gap
absorption leads to a monotonic decrease in the open-circuit voltage and monotonic increase
in short-circuit current density that effectively cancel out and result in only a slight decrease

23
in the limiting efficiency as compared to that of the S-Q analysis. For 𝛾 > 𝑘š 𝑇, there is a
drastic decrease in the achievable efficiency which can only be attributed to a dramatic
decrease in the Voc, which trends to zero for exceedingly large values of 𝛾, and subsequent
decrease in fill factor (see Fig. 2.6b below). Meanwhile, the the tailing of absorption below
the gap has a lesser effect on the Jsc because the marginal increase in absorption below gap
is small in comparison to the total absorption, which is dominated by band-to-band
transitions above gap. Indeed, the short-circuit currenty density does not significantly until
𝛾 > 100 meV and asymptotes at the total incident solar flux for the largest Urbach
parameters. The significant reduction in Voc with increasing 𝛾 dominates the effects on the
solar cell efficiency, which shows a similar trend with Urbach parameter, approaching the SQ efficiency at low 𝛾 and decreasing significantly for 𝛾 > 𝑘š 𝑇. These qualitative effects are
true irrespective of band gap (see the contour plots in Fig. 2.5)

24
1.4
1.2

Voc (V)

1.0
0.8
0.6
0.4
0.2
0.0
10-3

10-2

10-1

100

10-1

100

10-1

100

γ (eV)

120

Jsc (mA/cm2 )

100
80
60
40
20
10-3

10-2
γ (eV)

35
30

η (%)

25
20
15
10
10-3

10-2
γ (eV)

Figure 2.5 Line cuts at 1.5 eV (left) and contour plots (right) of the photovoltaic figures of
merit as a function of Urbach parameter. The red dashed line in the left figures indicates
the thermal energy kBT (25.8 meV at 300 K).
Unsurprisingly, the effects of increasing Urbach parameter on the Voc and Jsc manifest in the
solar cell’s current-voltage characteristics, as depicted in Fig. 2.6. As is expected, small
values of the Urbach parameter lead to current voltage characteristics similar to the S-Q limit,
while larger values of 𝛾 lead to non-ideal diode behavior (Fig. 2.6a). For 𝛾 > 𝑘š 𝑇 there is a
drastic decrease in the J-V curve’s fill-factor before it levels off to 25.8%.

25
1.0

0.8

0.6

20
10
0.0

Eg =1.5 eV

J (mAcm-2 )

γ (kB Tcell )
S-Q
0.1
0.5

0.4
0.2
0.0

0.5

1.0
V (V)

1.5

10-3

10-2

10-1
γ (eV)

100

101

Figure 2.6 Effect of sub-gap absorption on a 1.5 eV band gap solar cell. a) Current densityvoltage characteristics with different Urbach parameters. b) The FF as a function of Urbach
parameter. The red dashed line indicates kBT.
It is interesting to note that the open-circuit voltage decreases dramatically at 𝛾~𝑘š 𝑇. To
further understand this phenomenon, we can examine the photoluminescence (PL) of the
solar cell as a function of Urbach parameter. Assuming all carriers are thermalized and hence,
can be described by a single Fermi distribution, the reciprocity between absorption and
emission dictates that the solar cell emit radiation according to the generalized Kirchoff
(Lasher-Stern-Würfel) law (45). The photoluminescence (dashed lines) along with the
spectral response (solid lines) of a 1.5 eV band gap semiconductor with different Urbach
parameters is plotted in Fig. 2.7a. There is qualitatively different behavior for 𝛾 < 𝑘š 𝑇 and
𝛾 > 𝑘š 𝑇. Increasing Urbach energies for 𝛾 < 𝑘š 𝑇 leads to a broadening of the PL, though
the peak remains essentially at the band-edge. In contrast, increasing 𝛾 beyond 𝑘š 𝑇 leads to
a broadened PL peak that is Stoke’s shifted (Fig. 2.8) to lower energy relative to the EQE
band edge. Indeed, the total photoluminescence in this case is dominated by sub-gap PL (Fig.
2.7b), which is indicative of a shift in the dominant radiative recombination pathways from
band-to-band to tail-to-tail, tail-to-band, or band-to-tail. At 𝛾~𝑘š 𝑇 the luminescence is
almost entirely from sub-gap states.

Upon further analysis of the Stokes shift, we find that the peak position of the luminescence
actually occurs roughly at the quasi-Fermi level splitting. In other words, 𝐸Ÿ¡Ur ≈ 𝑞𝑉5S . This
peculiar fact can be reconciled with the physical picture shown in Fig. 2.9. In an ideal
semiconductor with a perfect band-edge, the quasi-Fermi levels are below the band-edge
(assuming 1-Sun illumination). Thus, as carriers are excited into the conduction band, they
relax to the band-edge and eventually luminescence with a photon energy given by the
bandgap. With the introduction of sub-gap absorption, the notion of a perfect forbidden
energy gap is destroyed and rather the semiconductor effectively has a distribution of
bandgaps, which can be calculated from the effective distribution of bandgaps by taking a
derivative of the spectral response with respect to energy (48). For 𝛾 < 𝑘𝑇, the situation is
similar to the ideal case because the band gap is still well defined (Fig. 2.7a and Fig. 2.9b).
However,s when the width of the band gap distribution is larger than 𝑘𝑇 (which occurs
roughly when 𝛾 ~ 𝑘𝑇), the Stokes shift occurs, suggesting that luminescence at the bandedge only occurs for a sufficiently well-defined bandgap.
For 𝛾 > 𝑘𝑇, the physics of luminescence drastically changes, as shown in the right-most
schematic of Figure 2.9. In this case, as carriers are excited into the conduction band, they
rapidly thermalize as they did in the perfect semiconductor. On the other hand, since the
band-edge is no longer well-defined, it is possible in principle for carriers to completely
thermalize to the valence band without emitting a photon. For sufficiently slow
thermalization between the valence and conduction band, an out-of-equilibrium population
can form in the semiconductor in steady-state operation, characterized by two quasi-Fermi
levels. While the quasi-Fermi level splitting is lower for increasing 𝛾, the role of the quasiFermi levels in this scenario is two-fold: it Pauli-blocks incoming photons with energies
beneath this splitting and also prevents excited carriers from rapidly relaxing to the valence
band, forming an electron bottle neck. The carriers, therefore, eventually luminescence as
the quasi-Fermi splitting position, and the quasi-Fermi level splitting becomes an effective
bandgap for the semiconductor. Thus, the Stokes shift can be qualitatively described by a

27
two-bandgap picture, where the peak position of the distribution of bandgaps defines the
higher energy bandgap, while the quasi-Fermi level splitting defines the lower energy
bandgap.
The qualitative picture described above illustrates the importance of including band-filling
when applying Würfel’s generalized Planck’s law to examine sub-gap absorption. Indeed,
without including band-filling, we get quantitative and qualitatively different results that are
physically inconsistent with experiment

1.0

Emission Intensity (a.u.)

γ=2.60 kB T

0.8

γ=1.40 kB T
γ=1.00 kB T
γ=0.60 kB T

PLE

γ=2.20 kB T
γ=1.80 kB T

0.6
0.4
0.2

γ=0.20 kB T

0.5

1.0

1.5
E0 (eV)

2.0

2.5

0.0 -3
10

10-2

10-1

100

γ (eV)

Figure 2.7 a) Spectral response (solid lines) and photoemission (dashed lines) for an
absorber with a 1.5 eV band gap for different Urbach parameters. The dot-dashed lines
indicate the effective band gap distribution. b) The ratio of sub-gap photoemission to the
total photoluminescence. The red dashed line indicates kBT.

Emission Peak Shift (eV)

1.0
0.8
0.6
0.4
0.2
0.0
0.0

0.5

1.0 1.5 2.0
γ (kB Tcell )

2.5

3.0

Figure 2.8 The photoluminescence peak shift for a 1.5 eV band gap absorber as a function
of Urbach parameter.

Figure 2.9 Schematic depiction of the density of states profile along and photogeneration,
relaxation and radiative recombination of carriers for a semiconductor with different
Urbach parameters.

2.3.1 Effect in Weakly Absorbing Limit and Limit of Imperfect Subgap Carrier Collection
The effects outlined above assumed that 𝛼h 𝐿 =10 so that the cell was thick enough to absorb
all incident photons and the EQE above gap was unity. In addition, we assumed that the subgap carrier collection was perfect. Below, we detail the effect of sub-gap absorption in the
weakly absorbing limit and in the limit of imperfect sub-gap carrier collection.

1.0

γ=0.1 kBTcell

0.8

EQE

0.6

α0 L
0.01
0.1
0.3

0.4

0.2
0.0
0.0

0.5
1.0
1.5
2.0
Incident Photon Energy (eV)

2.5

Figure 2.10 Spectral response for a 1.5 eV band gap solar cell with different absorber
thicknesses and an Urbach parameter of 0.1 kBT.
Figure 2.10 shows the spectral response of a 1.5 eV band gap solar cell with an Urbach
energy equal to 0.1 kBT for varying ranges of incomplete absorption. In the weakly absorbing
limit the effect of the Urbach parameter on the photovoltaic figures of merit is much the same
as in the case of complete absorption (Fig. 2.11). The Voc decreases significantly for 𝛾 > 𝑘š 𝑇
but the Voc is slightly less than that predicted by S-Q theory for weaker absorption. This stems

30
from the significant decrease in the photogenerated current and thus Jsc, owing to
incomplete absorption of the incident solar spectrum. Again, this drastic decrease in opencircuit voltage leads to a significant decrease in the ultimate device efficiency for large
Urbach parameters, though the obtainable efficiency is lower than the S-Q limit even at low
values of 𝛾 due to the deficit in Jsc.

1.2
α0 L
0.01

0.8

Jsc (mA/cm2 )

Voc (V)

1.0

0.1
0.3

0.6

0.4

100

30
25

80
60
40
20

10-1
γ (eV)

100

101

10-3

10-2

0.2
0.0
10-3

120

η (%)

1.4

10-2

10-1
γ (eV)

100

101

10-3

10-2

10-1
γ (eV)

100

101

Figure 2.11 Photovoltaic performance metrics for a 1.5 eV solar cell as a function of
Urbach energy for different levels of incomplete above-gap absorption. The red lines
indicate the thermal energy kBT.
In contrast, to the weakly absorbing limit, imperfect carrier collection has the effect to
tolerate larger amounts of sub-gap absorption. In reality, the sub-gap carrier collection
efficiency is a complicated function of the physical origin of the defects and of the sub-gap
band structure. For simplicity, here we consider constant below-gap carrier collection
efficiencies ranging from 10-8 to 1 (Fig. 2.12) and assume we are still in the radiative limit,
though we note that further analysis of the exact relationship between carrier collection and
external radiative efficiency is needed. Decreasing the sub-gap carrier collection efficiency
effectively makes the sub-gap states dark, preventing carrier collection from those states.
Thus, for low carrier collection efficiencies, increased sub-gap absorption from an increase
in the Urbach parameter has a muted effect and the figures of merit for solar cell performance
are only effected at subsequently larger Urbach parameters.

1.2
IQE

0.8

10-2

0.6

10-4

0.4

Jsc (mA/cm2 )

Voc (V)

1.0

10-6
10-8

100

60
40

10-1
γ (eV)

100

101

10-3

20
15
10

10-2

0.2
0.0
10-3

120

η (%)

1.4

10-2

10-1
γ (eV)

100

101

10-3

10-2

10-1
γ (eV)

100

101

Figure 2.12 Photovoltaic figures of merit as a function of Urbach parameter for a 1.5 eV
band gap solar cell with varying sub-gap carrier collection efficiencies. The red dashed
lines indicate the thermal energy kBT.

2.4 Conclusion and Outlook
Detailed balance is a useful tool to analyze absorbing (and by reciprocity, emitting) materials.
In the case of solar cells, our modified detailed balance model can be used to calculate the
realistic efficiency limits of photovoltaic materials with sub-gap absorption that arises from
defects and disorder. Using this model, we find that the S-Q model drastically overestimates
the efficiency limits of materials with large sub-gap absorption (i.e. large Urbach parameters)
and that even weak sub-gap absorption can have significant effects on the cell’s achievable
open-circuit voltage and efficiency. The effects on Voc manifest in the cell’s
photoluminescence leading to a broadening and red-shift of the luminescence peak. Our work
therefore suggests that it is prudent to carefully measure the absorption edge (or
photoluminescence) when evaluating photovoltaic materials. Furthermore, the general nature
of this model and the fundamentality of the sub-gap density of states in semiconductors
implies that our findings are likely relevant for other luminescent devices (e.g. lasers and
light emitting diodes).

Chapter 3
The Effect of Excitons on Photovoltaic
Performance: A Case Study in Cu2O
3.1 Introduction
Materials that can act as the top cell in a dual-junction architecture with traditional solar cells
like silicon (Si), cadmium telluride (CdTe), and copper indium gallium diselenide (CIGS)
could potentially reduce the levelized cost of electricity by producing increased photovoltaic
efficiencies (16). Novel materials could also provide optionality for ultrathin, flexible
photovoltaic technologies (16, 49-51). The performance of photovoltaics is generally
evaluated using the “free carrier” (FC) device model, in which the negatively charged
electron and positively charged hole are treated as independent, non-interacting particles.
However, substantial interactions between charge carriers can lead to the formation of
excitons, comprising a coulombically bound state between a photo-excited electron in the
conduction band and a hole in the valence band. For Si, CdTe, and GaAs, the interaction
between the electron and hole is weak, with exciton binding energies of 15, 10 and 4 meV,
respectively (52-54). Excitonic binding energies less than the thermal energy at room
temperature (25.6 meV) allow for facile dissociation of photogenerated excitons into free
electrons and holes at room temperature. Even in these devices, the role of excitons may be
important in certain device configurations (55-57).
Many emerging photovoltaic materials, however, exhibit large exciton binding energies (>
> 𝑘š 𝑇, see Table 3.1), so appreciable exciton densities are present at room temperature. For
example, cuprous oxide (Cu2O), a promising candidate material for the top cell in a tandem
solar cell with Si, has an exciton binding energy (Ex) of 151 meV (58). Cu2O has been the
subject of intense investigation of the Bose-Einstein condensation phenomenon, which

33
requires extremely large exciton densities (~10 cm ) (59-62). Additionally, these large
18

-3

exciton densities lead to excitonic charge transport in Cu/Cu2O Schottky junctions even at
room temperature (63-65).

Material

Ex
[meV]

GaAs

4.2 (54)

12.9 (54)

15.0 (52)

11.9 (21)

CdTe

10.0 (53)

11.0 (36)

ZnO

60 (66)

8.6 (67)

Cu2O

150 (68)

7.0 (69)

m-WS2

710 (70)

20 (71)

m-MoS2
910 – 1100 (72, 73) 25 (71)
Table 3.1 Exciton binding energies (Ex) and dielectric constants for established and
emerging photovoltaic materials. The exciton binding energy scales with the inverse
square of the dielectric constant.
In the following, we examine how photovoltaic device performance is effected by the
incorporation. In particular, we demonstrate that in materials with large exciton binding
energies, such as Cu2O, excitons play a fundamental role in photovoltaic operation and that
the FC model consequently underestimates the potential photovoltaic device efficiency.
Specifically, the Saha-Langmuir equation, which governs ionization events, has been used
to calculate the branching ratio at quasi-equilibrium between free electrons and holes and
excitons as a function of temperature and total-excitation density. The exciton densities have
been investigated experimentally under visible illumination by examination of a free exciton
peak in the photoluminescence spectrum of Cu2O at room temperature. The photovoltaic
device performance has also been evaluated by comparing traditional FC device physics
models to models that include levels of excitonic transport that are consistent with both
theoretical and experimental results.

3.2 Equilibrium Concentration of Excitons
When an exciton is created by absorption of a photon, the exciton diffuses to the device
junction, where a strong electric field ionizes the exciton into a free electron and hole that
are subsequently collected as current. The extent of excitonic effects in a photovoltaic device
is therefore governed during solar cell operating conditions by the branching ratio between
free carriers and excitons.
The exciton Bohr radius of technologically relevant semiconductors is typically 1-50 nm,
which implies that exciton-exciton interactions occur only for exceedingly large exciton
densities (> 1019-1020 cm-3). This process can, therefore be neglected during normal
photovoltaic operation, under 1-100 Sun illumination intensities for most photovoltaic
semiconductors (74). Under such conditions, the interchange between the charge-neutral
exciton and its ionized state, a free electron and hole, can be modeled in accord with the
ionization of an ideal gas.
Consider the entropy of a “gas” containing the concentration nx of excitons in coexistence
with their ionized states electrons and holes with concentrations ne and nh, respectively,
u !

u !

𝑆 = 𝑘š ln l(u b7} )!7 !o + 𝑘š ln l(u b7¦ )!7 !o + 𝑘š ln l(u b7~ )!7 !o

(1)

where Mi is the concentration of available states for the ith particle and kB is Boltzmann’s
constant. Then using Sterling’s approximation ln(𝑛!) ≈ 𝑛 ln(𝑛) − 𝑛 for large n gives:
𝑘š ln l(u

u§!

§ b7§ )!7§ !

o ≈ 𝑘š [𝑀© ln(𝑀© ) − 𝑛© ln(𝑛© ) − (𝑀© − 𝑛© )ln (𝑀© − 𝑛© ) − 𝑀© − (𝑀© − 𝑛© )]

= 𝑘š «𝑀© ln(𝑀© ) − 𝑛© ln l𝑀© u§ o − (𝑀© − 𝑛© ) ln ¬𝑀© l1 − u§ o- + 𝑛© ®

35
7§

7§

u§

= 𝑘š ¯𝑀© ln(𝑀© ) − 𝑛© lln(𝑀© ) + ln l oo − (𝑀© − 𝑛© ) ln 𝑀© + ln(1 −

) + 𝑛© °

Then cancelling terms and using 𝑀© ≫ 𝑛© yields

≈ 𝑘š ¯−𝑛© ln lu§ o + 𝑛© °

(2)

So that the entropy of the exciton-free carrier system is

𝑆 = 𝑘š ¯−𝑛; ln lu} o − 𝑛4 ln lu¦ o − 𝑛r ln lu~ o + 𝑛; + 𝑛4 + 𝑛r °

Then the total free energy is given by
𝐺 = 𝑛; 𝐸9 + 𝑛r s𝐸9 − 𝐸r z
+ 𝑘š 𝑇 ²−𝑛; ln ‡

𝑛;
𝑛4
𝑛r
ˆ − 𝑛4 ln ‡ ˆ − 𝑛r ln ‡ ˆ + 𝑛; + 𝑛4 + 𝑛r ³
𝑀;
𝑀4
𝑀r

where we have set the potential energy scale to zero at the valence band such that 𝑈; = 𝐸S =
𝐸9 , and 𝑈r = 𝐸S − 𝐸y = 𝐸9 − 𝐸r and Ex is the exciton binding energy. The total density of
states is simply given by the inverse of the volume occupied by each quasiparticle (taken as
the cube of the particles thermal wavelength) 𝑀©bc = 𝑣© = 𝜆·© , 𝜆© =

…WX¡§ ¸` ¹

, where mi is

the mass of the ith particle and h is the Planck constant. Substituting into the free energy yields
𝐺 = 𝑛; 𝐸9 + 𝑛r s𝐸9 − 𝐸r z
+ 𝑘š 𝑇[−𝑛; ln(𝑛; 𝑣; ) − 𝑛4 ln(𝑛4 𝑣4 ) − 𝑛r ln(𝑛r 𝑣r ) + 𝑛; + 𝑛4 + 𝑛r ]
(3)
Under illumination, the total photo-generated carrier density N, is equal to the sum of the
density of photo-generated excitons and electrons, i.e., 𝑁 = 𝑛; + 𝑛r , then 𝑛; = 𝑁 − 𝑛r .
Substituting into Eq. 3.3 and using the fact that the electron and hole concentrations are equal
(𝑛4 = 𝑛; = 𝑁 − 𝑛r ≡ 𝑛;4 , where neh is the free carrier concentration) gives

36
𝐺 = (𝑁 − 𝑛r )𝐸9 + 𝑛r s𝐸9 − 𝐸r z
+ 𝑘š 𝑇»−2(𝑁 − 𝑛𝑥 ) lns(𝑁 − 𝑛𝑥 )𝑣𝑒 z − 𝑛𝑥 ln(𝑛𝑥 𝑣𝑥 ) + 2𝑁 − 𝑛𝑥 ]¼
=x

Thermal equilibrium occurs at the minimum of the free energy (namely, =7 = 0) resulting

in the following equation
𝐸r + 𝑘š 𝑇 ²ln ‡

s(½b7~ )“} z
7~ “~

ˆ³ = 0

Rearranging and defining the fraction of free carriers 𝑥 = ½}¦ gives the Saha-Langmuir
equation (75):
rZ

WX¾¸ ¹ Z b
= ½ ∗ l 4 Z ` o 𝑒 _` a
cbr

(4)

where µ is the reduced exciton mass. Thus, the concentration of free electrons and holes and
the concentration of excitons depends on the exciton binding energy Ex, which determines
the time before excitons dissociate into free carriers, as well as the total excitation density N,
which governs the probability of a free electron and free hole interacting to form an exciton.
In particular, Equation 3.4 shows that the fraction of free carriers (x) increases with
temperature, as the thermal energy approaches Ex and a larger number of excitons thus
dissociate into free carriers. The fraction of excitons also increases with increasing excitation
density, because the probability of free electron and holes binding into excitons also
increases.
The Saha-Langmuir equation is a powerful tool to estimate the quasi-equilibrium exciton
density in material systems and requires only knowledge of the reduced exciton mass and
exciton binding energy (76, 77). For materials with large binding energies (>> kBT), Equation
3.4 implies large exciton densities may occur even at room temperature. Figure 3.1 shows
the calculated free electron and hole fractions in Cu2O as a function of the total excitation
density, as T is varied form room temperature down to 40 K. The shaded region labeled “PV

37
Regime” refers to the total, steady-state generated excitation density in Cu2O (where an
excitation can be either an exciton or free carriers) under standard photovoltaic operating
conditions. The absorbed solar flux was estimated by integrating the absorption in Cu2O over
the standard Air Mass (AM) 1.5 solar spectrum, that is,
𝑁9;7 = 𝜏r ∫ 𝐴𝑀 1.5(𝐸 ) 𝛼(𝐸 ) 𝑑𝐸
In Cu2O, the ground-state exciton is split by the spin exchange into a spin singlet
“paraexciton” state and a spin triplet “orthoexciton” state, with the orthoexciton lying 12
meV higher than the paraexciton (78, 79). The inversion symmetry of the Cu2O crystal makes
the paraexciton transition dipole- and quadrupole-forbidden, and the orthoexciton dipoleforbidden. This characteristic leads to long exciton lifetimes for both the paraexciton and
orthoexciton. The small energetic splitting between the ortho- and paraexcitons causes fast
exchange (on the picosecond timescale) between the two states. Consequently, for
temperatures relevant to photovoltaic operation, the ortho- and paraexciton lifetimes are
mutually similar, and the “excitonic” lifetime is given by the fastest radiative decay. The
paraexciton lifetime has been measured to be as large as 14 µs – 10 ms (59, 80, 81). However,
at room temperature, the orthoexciton lifetime has been measured to be 350 ns (82, 83). We
have thus conservatively estimated the lifetime as 100 ns to 10 µs, which yields a steadystate excitation density between 1015 and 1017 cm-3. Hence, at the excitation densities
expected during photovoltaic cell operation, excitons represent a substantial fraction, greater
than 20%, of the total excitation density in Cu2O. In the high exciton lifetime limit, the
branching ratio is as high as 28% at T = 300 K, and at lower temperatures, excitons become
the dominant charge-carrier population.

100

x (neh / N) / %

300K
240K

60
40

200K

PV Regime

160K
120K
80K
40K

0 13
10

1015

1017
N / cm-3

1019

1021

Figure 3.1 The fraction of free electrons and holes relative to the total excitation density
l𝑥 = ½}¦ o in Cu2O. The upper limit of the branching ratio between excitons and free
electrons and holes during photovoltaic operation is 27.7%, suggesting that substantial
exciton densities should be present during typical device operating conditions.

3.3 Experimental Observations of Excitons in Cu2O
Photovoltaics
The large exciton concentrations predicted by the Saha-Langmuir equation (as much as 28%
of the total photo-generated carrier population at room temperature under photovoltaic
operating conditions) suggest that excitonic signatures should be experimentally observable
in Cu2O and Cu2O-based devices. In this section, we detail the experimental methods and
results for the growth of Cu2O substrates, exciton photoluminescence measurements, and
photovoltaic device fabrication and characterization.

3.3.1 Growth of Cu2O substrates
Cu2O substrates were prepared by two different techniques: 1) thermal oxidation of Cu foil,
which tended to lead to polycrystalline samples, and 2) the floating zone method, which
produced single crystalline substrates.
High purity (99.9999%, 0.5 mm thick, Alfa Aesar) Cu foil was used to produce the
polycrystalline Cu2O wafers. The growth process used in this study was based off of other
growth procedures from our labs and elsewhere that resulted in high efficiency Cu2O based
devices (84-86). Our preparation is as follows. The foils were cut into squares with ~ 1 cm
sides, cleaned, and suspended from a quartz hanger. The hanger assembly was heated in a
quartz tube under N2(g) to 1025 °C at 1000 °C/h. The foils were then oxidized in air for 24
h and cooled under N2(g) to room temperature. The resulting substrates were ~ 0.8 mm thick
and the grain size of these wafers was typically of the order of several millimeters and in
some cases almost the size of the entire wafer (~1 cm2). Hall measurements indicated that
the polycrystalline wafers had carrier concentrations of ~1013 cm-3 and hole mobilities ~65
cm2/V·s. The polycrystalline substrates were used to fabricate Cu2O/Zn(O,S) heterojunction
photovoltaics (whose fabrication is discussed in detail later).
The other Cu2O growth technique, the floating zone method, was used to produce highquality, single crystalline substrates. Feed and seed rods were grown by the thermal oxidation
of high-purity Cu rods (Alfa Aesar, 99.999%) in a vertical tube furnace (Crystal Systems
Inc.) in air for 100 h at 1050 °C. The rods were then cooled in N2 at 120 °C/h. Prior to
growth, the rods were cleaned in acetone and etched using dilute nitric acid (0.1 M) for 60
seconds. The rods were suspended by either Cu or Pt wire. Single crystals were grown in
an optical floating zone furnace (CSI FZ-T-4000-H-VII-VPO-PC). Crystals were grown in
air with the seed and feed rods counter-rotating at 7 rpm. Single crystallinity was confirmed
using x-ray diffractometry and pole figure analysis. The resulting single crystalline boules
were diced into wafers along the growth axis and mechanically polished to a specular finish
using diamond grit. For further information regarding the floating zone process and single
crystal preparation and characterization see Appendix B.

3.3.2 Photoluminescence of the Exciton Peak in Cu2O
At low temperature (4 K), cuprous oxide exhibits a peak in its photoluminescence (PL)
spectrum due to the recombination of the free orthoexciton at 610 nm as well as several
phonon-assisted exciton luminescence peaks at slightly lower energies (59, 87-90). At higher
temperature the peak redshifts and thermally broadens, becoming convoluted with the 𝛤 12
phonon-assisted peak, which is only separated by 13.6 meV from the exciton peak (82, 90).
A Ti:sapphire laser (Libra, Coherent Inc.) with a fundamental 800 nm laser pulse, 120 fs
pulse width, and 10 kHz repetition rate was used to pump an optical parametric amplifier
(Opera Solo, Coherent Inc.) and generate visible light. Single crystalline Cu2O wafers grown
by the float-zone method were illuminated with wavelengths ranging from 400 to 550 nm.
The time-averaged photoluminescence spectra were collected using a time-correlated singlephoton-counting method using a streak camera (Hamamatsu Inc.) with 20 ps time resolution.
Figure 3.2 shows the photoluminescence spectra of the orthoexciton peak in our single
crystalline Cu2O samples grown by the floating zone method for a selection of optical
excitation wavelengths at T = 300 K. The orthoexciton peak was observed for all excitation
energies below the Cu2O electronic band edge (2.1 eV, 590 nm). Observation of the
orthoexciton peak at 300 K under visible light excitation is direct evidence of the photogeneration of excitons at room temperature under conditions relevant to photovoltaic
operating conditions.

485nm

Normalized Intensity

505nm
525nm
550nm

��

λ / nm

Figure 3.2 Photoluminescence spectra of the free exciton peak in Cu2O at room
temperature under different visible light excitation. The free exciton peak is observed for
all excitations above the Cu2O band gap.
Room temperature photoluminescence spectra were also collected for the polycrystalline
Cu2O wafers grown by thermal oxidation, which were used in device fabrication. The spectra
were collected using a 514 nm excitation for powers ranging from 85 µW to 5.4 mW. The
photoluminescence spectrum near the orthoexciton luminescence peak is shown in Figure
3.3. The unusual peak shape is due to the convolution of the orthoexciton peak and the
phonon-assisted exciton peak, which broadens and grows at higher temperatures where the
absorption probability of phonons by excitons is large (88-90). The peak was evident even
at the lowest of excitation powers (0.85 µW). Thus, excitons are generated under visible
excitation even in polycrystalline Cu2O substrates used in photovoltaic fabrication.

Normalized Intensity

575

600

625

650

λ / nm

Figure 3.3 Photoluminescence spectrum of the free exciton peak in thermally oxidized,
polycrystalline Cu2O wafers at room temperature using a 2.4 mW, 514 nm excitation.

3.3.3 Excitons in the Spectral Response of Cu2O-based Photovoltaics
Given the large exciton densities observed in Cu2O through photoluminescence
measurements, Cu2O-based photovoltaics were fabricated in order to investigate excitonic
signatures in solar cell performance. Photovoltaic devices in this work were fabricated on the
polycrystalline Cu2O wafers grown by thermal oxidation of copper foil with a sputtered
Zn(O,S) window layer, and an indium tin oxide (ITO) top contact and a Au back contact
(84).

The photovoltaic cells in this study were fabricated using a circular shadow mask

resulting in an ultimate cell size ~0.02 cm2 so that individual solar cells were generally
isolated to only 1 or 2 grains.
Prior to fabrication, the polycrystalline Cu2O substrates were cleaned with isopropanol and
loaded into a magnetron sputtering system with a base pressure of 1.7x10-7 Torr. The Cu2O

43
wafers were heated in vacuum for 90 min at 100 °C. A 45 nm layer of Zn(O,S) was cosputtered from ZnO and ZnS targets at a working pressure of 5 mTorr Ar. The power on the
ZnO target was 100W and the power on the ZnS target was 85W. After deposition, the
samples were cooled to room temperature in vacuum and removed from the chamber. A
shadow mask was placed over the samples and a 60 nm ITO layer was sputtered at 50 W in
an Ar atmosphere with a working pressure of 3 mTorr at room temperature. A 100 nm Au
back-contact was then sputter deposited on the back of the sample.
Figure 3.4 shows the spectral response of a typical Cu2O /Zn(O,S) cell. The spectral response
measurements were performed using a Xe arc lamp and slit monochromator (Newport Inc.),
and a calibrated reference Si photodiode (Thor Labs Inc.) with a known spectral responsivity.
The external quantum yield approached zero at 650 nm, which is consistent with the 1.91 eV
optical band edge in Cu2O. However, the quantum yield was substantial in the region
between the Cu2O electronic band gap (2.1 eV, 591 nm) and the Cu2O optical band gap (1.91
eV, 650 nm). In this region, absorption of a photon generates an exciton, so the current
collection below 2.1 eV must be attributed solely to excitonic transport (60, 88). A similar
spectral response characteristic has been observed in high-quality Cu/Cu2O Schottky diodes
with the current collection in the exciton region explained by exciton diffusion to the
Schottky junction followed by ionization of the exciton into an electron and hole by the
strong electric field in the depletion region (65, 91). The current in the excitonic region
accounts for 9.3% of the short-circuit current density of the Cu2O/Zn(O,S) cells. Although
this value is less than the ~27% predicted by the branching ratio, the 9.3% value does not
account for excitonic transport in the region having excitation energies greater than 2.1 eV,
where the PL data indicate that excitons are also generated. Aside from direct generation
through bandgap absorption of a photon, excitons may also form via free carrier relaxation
processes, such as when “hot” carriers that arise from above-band-gap photon absorption
thermally relax to the band edge. These free carrier cooling mechanisms may further
contribute to excitonic transport in the region in which excitation energies are > 2.1 eV. The
presence of substantial external quantum yield in our Cu2O/Zn(O,S) solar cells even at the
low light intensities (<< 1 Sun) of spectral response measurements is clear evidence that

exciton diffusion provides a fundamental charge transport mechanism in

44
Cu2O

photovoltaics.

100

EQE / %

350

400

450

500
550
λ / nm

600

650

Figure 3.4 Spectral response of a polycrystalline Cu2O /Zn(O,S) solar cell. The red
dashed line indicates the Cu2O electronic band gap beyond which, in the shaded region,
are wavelengths for which only excitons can exist.

3.4 The Role of Excitons in Photovoltaic Device Physics
The current-voltage characteristics of a solar cell can be expressed by the diode equation:
𝐽 = 𝐽h «𝑒

](^\ÃÄÅ )
_` a

− 1® +

>ÆÇÈÅ
ÈÅ¦

−𝐽ÉS

(5)

where J is the total current density, J0 is the dark saturation current density, q is the unsigned
fundamental electronic charge, V is the voltage, Rs is the area-normalized series resistance,
Rsh is the area-normalized shunt resistance, and Jsc is the short-circuit current density. Thus,

45
J0 and Jsc are fundamental parameters that ultimately govern the solar-cell efficiency.
Traditionally, J0 and Jsc are solved for using the free-carrier model in which electrons and
holes are treated as independent, non-interacting particles and any exciton effects are
neglected. However, several studies have shown that even materials with relatively small
steady-state exciton densities (e.g., Si, CdTe), excitons can have a large effect on
photovoltaic performance in certain device configurations (55-57). Hence, it is expected that
in materials with room temperature exciton densities, such as Cu2O, excitons could play a
significant role in the device physics. We therefore use a device model that accounts for
excitonic effects.

3.4.1 Device Model Including Excitons
Cu2O is intrinsically p-type due to the thermodynamic favorability of copper vacancy
formation and the absence of an n-type doping scheme. Our cell has thus been modeled as
a simplified, “one-sided” p-n+ junction with an infinite p-type base and a negligibly thin ntype emitter subject to the following assumptions: (1) the depletion approximation; (2) the
drift and diffusion currents are opposite and equal in magnitude within the depletion region;
(3) recombination is neglected in the depletion region; (4) the solar cell is operating in lowlevel injection; (5) in the bulk, minority carriers flow by diffusion (92). The inclusion of
excitons requires the modification of the “free carrier” model to include an additional term
that accounts for the exchange between the excitons and free-carrier populations. In this
case, the excess minority- carrier (Dne) and excess exciton (Dnx) concentrations are governed
by the following coupled differential equations:
=Z ∆7

∆7

𝐷; =Ì Z } = Í } − 𝐺; 𝑒 bÎÌ + 𝑏(∆𝑛; 𝑁t − ∆𝑛r 𝑛∗ )

=Z ∆7

∆7

𝐷r =Ì Z ~ = Í ~ − 𝐺r 𝑒 bÎÌ − 𝑏(∆𝑛; 𝑁t − ∆𝑛r 𝑛∗ )

(6)

(7)

46
where D is the diffusion coefficient, t is the lifetime, and G is the wavelength-dependent
generation rate (55). The subscripts e and x refer to electrons and excitons, respectively. The
third term in Eq. 3.6 and 3.7 is the net rate at which electrons and holes bind to form excitons,
and is derived from the law of mass action, where b is the coefficient for binding free carriers
into excitons, NA is the p-type doping density and n* is the equilibrium constant for the
exchange between excitons and free carriers (in equilibrium 𝑛∗ 𝑛r = 𝑛; 𝑛4 ). Further, free
carriers and excitons were assumed to be in quasi-equilibrium at the edge of the depletion
region. The coupled differential equations yield analytical solutions for the dark saturation
current density, J0, and the short-circuit current density, Jsc,:

cbn

𝐽h = 𝑒𝐷; 𝑛h l +

cbÐ

o + 𝑒𝐷r 𝑛rh l +

cbn

(8)

cbÐ

𝐽ÉS = 𝑒𝐺; lÎÆ \Ï + ÎÆ \Z o + 𝑒𝐺r lÎÆ \Ï + ÎÆ \Z o

(9)

where e is the fundamental unsigned charge on an electron; n0 and the nx0 are the equilibrium
concentrations of electrons and excitons, respectively; and a is the wavelength-dependent
absorption coefficient (56). Additionally:

𝛾 =W−

𝜁 =W+

ZÒZÏ Ó~
Ó}

uÑ Æ

W√Ô
ZÒÏZ Ó}
Ó~

uÑ b

𝐿c =
𝐿W =

W√Ô
√Ö Ï
√ ÖZ

𝜀c = W (𝑀cc + 𝑀WW − √𝛿)

𝜀W = W (𝑀cc + 𝑀WW + √𝛿)

(10)

(11)
(12)
(13)
(14)
(15)

𝑀Ù = 𝑀cc − 𝑀WW

47
(16)

𝛿 = 𝑀ÙW + 4𝑀cW 𝑀Wc

(17)

𝑀cc = lÍ + 𝑏𝑁t o Ú
𝑀WW = lÍ + 𝑏𝑛∗ o Ú
y7 ∗

𝑀cW = − Ú

y½

𝑀Wc = − Ú Û

(18)

(19)

(20)
(21)

The “free carrier” solutions for the dark saturation and short-circuit current densities,
respectively, for an p-n+ solar cell are given by:
𝐽h,ÜÝ = −

;Ú} ∆7m

𝐽ÉS,ÜÝ = ÎÆ }\Ï

(22)
(23)

Equation 3.22 and 3.23 were used to compare the performance of the excitonic model to that
of the traditional “free carrier” model. The major effect of excitons, effecting a coupling
between the electron and hole population and exciton population, alters the diffusion
characteristics of both free carriers and excitons, as can be seen from Eqs. 3.8-3.9 and 3.223.23. Thus, a fraction g of photogenerated electrons move with a diffusion length L1 and the
remaining photogenerated electrons (1-g) diffuse with a diffusion length L2, where L1 and L2
are effective diffusion lengths that account for the interactions between the exciton and free
carrier populations. Similarly, a portion of photogenerated excitons z and the remaining
exciton fraction (1-z) have diffusion lengths L1 and L2, respectively.

3.4.2 Model Parameters for Cu2O
Equation 3.8 and 3.9 are fundamentally dependent on the experimentally measured
parameters D and t, which are affected by temperature and doping density. The performance
of the p-n+ Cu2O solar cell can then be evaluated a function of temperature and NA. The
dependence of the exciton binding energy on doping density can be estimated assuming that
the exciton binding energy falls off to zero as the doping density approaches the Mott density:

𝐸r = 𝐸rL ²1 − Þ7

½Û
Òß••

(24)

where Ex¥ is the unscreened exciton binding energy, 150 meV in Cu2O (91, 93). The Mott
density was estimated using the value for Si as a function of temperature:
U á§

Ö á§

𝑛u566 = 10cà âã`Z ä ÖâãZ ä 𝑇

(25)

where aB is the exciton Bohr radius and e is the dielectric constant. The superscripts Si and
Cu2O refer to silicon and Cu2O, respectively. The unscreened exciton binding energy is
assumed to be independent of temperature.
The electronic band gap Eg of Cu2O was measured down to 4 K using the threshold energy
of the free exciton peak in the photoluminescence spectrum. The temperature dependence of
Eg was fit using an oscillator model that accounts for exciton-phonon coupling:
ℏé

𝐸9 (𝑇) = 𝐸9 (0) + 𝑆ℏ𝜔 − 𝑆ℏ𝜔 coth lW¸ ¹ o

(26)

where Eg(0) = 2.173 eV is the electronic band gap at T = 0 K, S =1.89 is a material specific
constant, and ℏ𝜔 = 13.6 meV is the phonon energy of the phonon (𝛤cW
) emitted during

exciton luminescence (90).

49
The electron mobility was estimated from majority-carrier data in literature. The effect of
temperature and doping density on the majority carrier mobility was estimated as:
¾¦

=¾ +¾

(27)

where
𝜇 ¹ = 8511 × 10bh.hhàí·¹

(28)

is the mobility caused by lattice vibrations, with the value determined from as-grown Cu2O
crystals (94, 95). Empirical data for the mobility as a function of hole concentration due to
Na doping was used as an interpolating function in the model for µI (96).
The minority-carrier lifetime is an important materials property that plays a significant role
in determining the performance of solar cells in the free carrier model. Generally, the electron
lifetime is estimated from the electron diffusion length fit from the external quantum
efficiency, and varies from ~100 ns for undoped samples to on the order of ~ 1 ns for doped
samples (85, 97). As such, we have estimated the electron lifetime as:
chh

𝜏; = cÆch\Ïî ½

(29)

The lowest lying exciton states in Cu2O are the spin singlet “paraexciton” and spin triplet
“orthoexciton”, which are split by a spin exchange, with the paraexciton lying 12 meV lower
than the orthoexciton. The paraexciton transition is dipole- and quadrupole-forbidden, and
the transition is dipole-forbidden for the orthoexciton due to inversion symmetry of the Cu2O
crystal. This behavior leads to long-lived exciton states; the paraexciton lifetime, for
example, has been measured to be > 14 µs at low temperatures (59). The small energetic
splitting between the two states causes the orthoexciton to decay into the paraexciton state
on the picosecond time scale, while paraexcitons up-convert to orthoexcitons at the same rate
(82, 98). Consequently, for temperatures relevant to photovoltaic operation, the ortho- and
paraexciton lifetimes are the same, given by the most rapid recombination pathway. Thus,

the temperature-dependent orthoexciton lifetime data from Ref. [14] was used for tx

(implemented as an interpolating function in our code), assuming that the exciton lifetime is
< 1µs (83).

The mean time for excitons to form is given by 𝜏y = y7∗ , where n* is found by treating the
exciton and electron-hole system as an ideal gas mixture and neglecting exciton-exciton
interactions:
𝑛∗ =

7m} 7m¦
7m~

𝑇 ·/W 𝑒 bM~ /¸` ¹

(30)

with the density of states,
𝑛h© =

9§ (WX¡§ ¸` )Y/Z
4Y

(31)

where 𝑔© is the degeneracy term, mi is the translational mass and h is Planck’s constant. For
Cu2O 𝑔; = 2, 𝑔4 = 2 and 𝑔r = 𝑔; 𝑔4 = 4 and 𝑚; = 0.99𝑚h , 𝑚4 = 0.58𝑚h , and 𝑚r =
3.0𝑚h , where m0 is the fundamental electron mass. The exciton binding coefficient b has not
been measured in Cu2O, so we have used the variation of b with temperature for Si:
𝑏 = 10b· 𝑇 bW + 2.5 × 10bà 𝑇 bc/W + 1.5 × 10bó

(32)

in units of cm3×s-1 (99). This is likely an underestimation of b in Cu2O, because the exciton
binding energy in Cu2O is approximately an order of magnitude larger than that in Si.
The diffusion lengths of electrons and excitons were calculated by use of:
𝐿; = …𝐷; 𝜏;

(33)

𝐿r = …𝐷r 𝜏r

(34)

The diffusion coefficient of electrons in Cu2O has yet to be measured, so De was estimated
using the Einstein relation:

c ¡¦

𝐷; = ; ¡ 𝜇4 𝑘š 𝑇

51
(35)

where the electron mobility was estimated by weighting the hole mobility by the ratio of the
electron and hole translational masses. This approach yields values of ~2 µm for Le, which
agrees well with measured values from the literature (65, 85, 97, 100). Similarly, the exciton
diffusion length was calculated using:
𝐷r = 𝜇r 𝑘š 𝑇

(36)

The exciton mobility µx has been measured accurately down to low temperatures. Above 10
K, the following expression was found to be in good accord with the experimentally
measured exciton mobility:
𝜇r =

W√WXℏô õ“öZ
ø/Z

·𝒟 Z ¡~

(𝑘š 𝑇)b·/W

(37)

where, 𝜌 = 6.11 g×cm-3 is the mass density of the Cu2O crystal, 𝑣T = 4.5 × 10w m×s-1 is the
thermal velocity, and 𝒟 = 1.2 is the deformation potential (101).

3.4.3 Effects of Excitons on Carrier Diffusion Length in Cu2O
The principal effect of excitons on solar cell performance is to modify the diffusion
characteristics of photogenerated species by effectively coupling the motion of free carriers
and excitons (55, 56). Figure 3.5 shows the effect of temperature and doping density on the
diffusion lengths Le, Lx, L1, and L2. The exciton diffusion length is approximately constant
with temperature, and is almost an order of magnitude greater than Le, which varies
significantly with temperature. For low-to intermediate doping densities, this behavior causes
L1 to approach Le, especially at high temperatures. At low temperatures, where excitons
dominate, L1 tends towards Lx. L2 is substantially lower than L1 for all temperatures.

52
a 10-1
Diffusion Length / cm

NA=1012

-2

L2
Le

10-3

10-4
10-5
10-6
200

250

300

350 400
T/K

450

500

10-1

Diffusion Length / cm

NA=1014

-2

-3

-4

L2
Le
Lx

10-5
10-6
200

250

300

350 400
T/K

450

500

10-1

Diffusion Length / cm

NA=1016

10-2

L1
L2
Le

10-3

10-4
10-5
10-6
200

250

300

350 400
T/K

450

500

Figure 3.5 The simulated electron, exciton and effective diffusion lengths for Cu2O for
doping densities a) 1012, b) 1014, and c) 1016.

3.4.4 Equilibrium Concentration of Excitons and Free Carriers
A fundamental assumption in our model is that excitons and free carriers are in equilibrium
in the Cu2O bulk up to the edge of the depletion region, such that:
𝑛©W = 𝑛h 𝑝h = 𝑛rh 𝑛∗

(38)

where, n0, p0, and n0x are the electron, hole concentrations, respectively. Here, we assume
that the hole concentration is given by the ionized dopant density NA and thus, in equilibrium,
the ratio of excitons to free electrons is given by:
7~m
7m

= 7Û∗

(39)

The equilibrium exciton ratio is shown in Figure 3.6. As expected, the excitonic fraction of
the photogenerated population increases with decreasing temperature and increasing doping
density. The exciton density is greater than the free carrier population at room temperature
for large doping densities. From, Eq. 3.37 and 3.38 the equilibrium exciton concentration is
given by:
7Z

𝑛rh = 7§∗

(40)

and the equilibrium electron concentration is given by the typical expression:
7Z

𝑛h = ½ §

(41)

The intrinsic carrier concentration can be calculated from the effective density of states in
the valence and conduction bands, respectively:

WX¡ ¸ ¹ Z
𝑁Ý (𝑇) = 2 l 4}Z ` o = 4.75 × 10cw 𝑇 ·/W

(42)

𝑁> (𝑇) = 2 l

WX¡¦ ¸` ¹
4Z

o = 2.14 × 10cw 𝑇 ·/W

[N (a)

𝑛©W (𝑇) = 𝑁Ý 𝑁> 𝑒 _`a

(43)

= 1.014 × 10·c 𝑇 ·/W

(44)

in cm-3 (21). Using these values and the parameters outlined above, the dark saturation
current density J0 can be calculated.

103
200 K

101

300 K
400 K

nx0 n0

500 K

10-1

10-3

10-5 12
10

1013
1014
1015
Doping Density / cm-3

1016

Figure 3.6 The equilibrium ratio of excitons to free carriers as a function of doping
density for temperatures ranging from 200 to 500 K.

3.4.5 Absorption, Generation, and Jsc
The calculation of Jsc requires knowledge of the generation rate of excitons and free carriers,
as well as the absorption coefficient in the visible spectrum. We have calculated Jsc using the
full wavelength dependence of Ge and a. The experimentally determined absorption
coefficient was used, and the absorption coefficient of Cu2O was assumed to not vary

55
substantially over the temperature range evaluated in this study (200 – 500 K) (102). The
wavelength-dependent electron and exciton generation rate were estimated by:
𝐺(𝜆) = 𝛼 (𝜆)𝛷(𝜆)

(45)

where 𝛷 is the photon flux from the global AM 1.5 solar spectrum. To differentiate between
exciton and free carrier generation, the free carriers were assumed to be generated for
absorption of a photon with energy above the electronic band gap, and excitons were
assumed to be generated only in the case for photon excitation with an energy between the
electronic band gap and the excitonic band edge (Eg-Ex). Thus, the short-circuit current
density is the summation of two parts, one free-carrier and one excitonic:

𝐽ÉS = 𝑒 • 𝛼 (𝜆)𝛷(𝜆) ¬
MN

1−𝜂
- 𝑑𝜆
bc
𝛼(𝜆) + 𝐿c
𝛼 (𝜆) + 𝐿bW

+𝑒•

𝛼 (𝜆 )𝛷 (𝜆 ) ¬

MN bM~

1−𝜁
- 𝑑𝜆
𝛼(𝜆) + 𝐿bc
𝛼(𝜆) + 𝐿bW

(46)
This approach is an oversimplification, as we have demonstrated experimentally in the
previous section. Even above-band-gap illumination leads to excitonic generation that is
observable as a free-exciton peak in the photoluminescence spectrum.

3.4.6 Voc, FF, and Efficiency
The open-circuit voltage (Voc) can be calculated by solving Equation (3.5) for the case when
J = 0. To calculate the fill-factor (FF), a J-V characteristic was generated by numerically
solving Eq. 3.1 for J, with Rs = 20 W×cm2 and Rsh = 875 W×cm2, as a function of V (103). The
J-V behavior was then used to determine the power density so that the current and voltage at
the maximum power point (Jmpp and Vmpp, respectively) could be extracted by maximization

56
of the power density. These parameters were then used to calculate the fill factor FF and
ultimately the photovoltaic efficiency 𝜂, according to

üýý
𝐹𝐹 = üýý
Ç >
Åþ ßþ

(47)

where, Jmpp and Vmpp are the current-density and voltage at the maximum power point and

𝜂 = ßþŸÅþ

ÜÜ

§ÿ

(48)

where Pin is the power incident on the Cu2O cell, in this case, the standard AM 1.5 solar
spectrum.

3.4.7 Model Results
The magnitude of the excitonic effects is dependent on the temperature and total excitation
density (see Figure 3.1), so the photovoltaic behavior was evaluated as a function of doping
density over temperatures relevant to solar cell operation (200 – 500 K) using empirical data
from the literature (see Section 3.4.2, above). Intrinsic hole concentrations in high-quality
Cu2O are typically ~ 1012 cm-3, however, recently Cu2O doped with Na has shown carrier
concentrations as high as 1016 cm-3 while maintaining the high mobility necessary for
efficient carrier collection. We have therefore considered doping densities (NA) ranging from
1012 to 1016 cm-3 (96, 103). Higher-order excitonic effects, such as the binding of excitons
to impurities, have been neglected, to provide an upper bound of solar cell performance when
excitons are considered.
Figure 3.7 compares the predictions obtained from the excitonic model and the FC model.
At intrinsic doping levels, J0 is similar for both models across all temperatures.

However,

at large doping densities, J0x increased substantially compared to the value of J0 produced by
the FC model, due to the extra recombination created by excitons that is not considered in
the FC model. At lower temperatures and large doping densities, the concentration of

excitons increases and J0 increases substantially compared to J0 . The simulated dark
current densities when excitonic effects were either included or neglected were substantially
smaller than experimental results for J0. This discrepancy is likely due to recombination
sources that were not included in the model, such as interfacial defects and surface states.

10-5

NA=1014

10-15

J0 x J0 fc

J0 / mA·cm-2

NA=1012

NA=1012 X
NA=1012 FC
NA=1014 X
NA=1014 FC
NA=1016 X
NA=1016 FC

10-25
10-35

200 250 300 350 400 450 500
T/K

10-45
200 250 300 350 400 450 500
T/K

NA=1016

5.0
Jsc x - Jsc fc / mA·cm-2

Jsc / mA·cm-2

NA=1012 X
NA=1012 FC
NA=1014 X
NA=1014 FC
NA=1016 X
NA=1016 FC

200 250 300 350 400 450 500
T/K

4.0

NA=1012
NA=1014
NA=1016

3.0
2.0
1.0
0.0
200 250 300 350 400 450 500
T/K

Eg
Eg-Ex

Voc x - Voc fc / mV

2.0

Voc / V

1.5
1.0
0.5
0.0

NA=1012 X
NA=1012 FC
NA=1014 X
NA=1014 FC
NA=1016 X
NA=1016 FC

100

200 300
T/K

400

-40
-60
-80
200 250 300 350 400 450 500
T/K

500

10
12

NA=10 X
NA=1012 FC
NA=1014 X
NA=1014 FC
NA=1016 X
NA=1016 FC

200 250 300 350 400 450 500
T/K

η x - η fc / %

η /%

-20

NA=1012
NA=1014
NA=1016

200 250 300 350 400 450 500
T/K

59
Figure 3.7 Comparison between the simulated device performance of a p-n Cu2O-based
solar cell using a model incorporating excitonic effects relative to the FC model, denoted by
the superscript x and fc, respectively. (a) The simulated dark saturation current density. (b)
The ratio of the dark current density, when excitons are included, to the dark current density
using the FC model. The dark current density increases substantially when excitonic effects
are included. (c) The calculated short-circuit current density. Experimental Jsc values (the
circles) agree well with the Jsc values obtained using the excitonic model (103, 104). (d)
The absolute difference in short-circuit current density between the excitonic and FC models.
At room temperature and a doping density of 1016, excitonic effects account for an additional
2.84 mA×cm-2. (e) The open-circuit voltage obtained from the excitonic and FC models. In
the low temperature limit, the Voc approaches the exciton band edge and electronic band gap
for the excitonic model and the FC model, respectively. The turquoise circle represents the
record experimental Voc for Cu2O solar cells (105). (f) The difference between the opencircuit voltage as calculated from the excitonic model and the FC model. The change in
voltage is small over the calculated temperature range. (g) The simulated photovoltaic
efficiency under the AM 1.5 spectrum. (h) The absolute difference in the practical efficiency
in Cu2O-based solar cells between the excitonic model and the FC model. At room
temperature, the FC model underestimates the efficiency by 1.9 absolute percent.

Figure 3.7c shows the calculated short-circuit density. The experimental values for Jsc are
larger than the current densities predicted by the FC model at T = 300 K but agree well with
values for Jsc predicted using the excitonic model (103, 104). At low temperature, the
inclusion of excitons leads to an enhancement of Jsc (Figure 3.7d). This enhancement of Jsc
decreases with increasing temperature, and converges to the value of Jsc calculated from the
FC model at higher temperatures, when the excitation density is primarily due to free
electrons and holes. The increase of Jsc is driven predominantly by the effective band gap
narrowing of Cu2O from the electronic band gap (2.1 eV) to the exciton band edge (1.91 eV),
which increases by Ex = 150 meV the range over which Cu2O absorbs light. The large
increase in Jsc at the highest doping level is caused by a decrease in the electron lifetime and
the subsequent decrease in the electron diffusion length, due to increased scattering off of
impurity centers (Figure 3.5). The decrease in the electron diffusion length has a more
substantial effect on the FC model because only a small fraction of the photogenerated
minority carriers in the excitonic model move with the electron diffusion length, whereas the
remaining electrons diffuse with an effective diffusion length between that of excitons and
electrons (56).

60
The enhancements in the excitonic model of J0 and Jsc counteract one another, so that Voc
is essentially unchanged compared to that produced by FC model, except for the largest
doping density where the enhancement in J0 exceeds that of Jsc. Excitons therefore produce
a decrease in Voc for the largest doping density compared to what is expected from the FC
model (Figure 3.7e/f). At T = 300 K, the difference between the models is at most ~40 mV
(for the highest doping density considered), and this difference decreases as free carriers
begin to dominate as the temperature is further increased. For a photovoltaic cell in the
radiative recombination limit, Voc should approach the band edge of the absorber material as
the temperature goes to T = 0 K (106). In the low-temperature limit of our simulations, Voc
tends to the excitonic band edge when excitonic effects are included. In contrast, Voc tends
to the electronic band edge for the FC model, which suggests that the models correctly
capture the physics of solar cell operation in both cases. Intrinsically doped Cu2O-based
photovoltaics have exhibited open-circuit voltages as high as 1.20 V at room temperature
(the turquoise dot in Figure 3.7e), within 100 mV of the results of our simulations (105).
Such high-quality Cu2O junctions have exhibited Voc that extrapolates to the exciton band
edge (1.91) at 0 K, again demonstrating that the device physics of Cu2O photovoltaics under
such conditions are governed primarily by excitonic effects.

100
80

FF / %

60
40
20
200

NA=1012 including excitons
NA=1012 FC
NA=1014 including excitons
NA=1014 FC
NA=1014 including excitons
NA=1014 FC

250

300

350
T /K

400

450

500

Figure 3.8 The simulated fill-factor for the excitonic and FC models. The fill factors were
in close agreement except at the highest doping densities, where large enhancement in the
Jsc dominates and leads to an increase in the solar-cell efficiency relative to the FC case.
The calculated fill factor (~75-80% at room temperature) is comparable for both models (see
Figure 3.8). The difference in efficiency between the models is thus dominated by the
substantial changes in Jsc when excitons are included, which can intuitively be seen from Eq.
3.9. The photovoltaic efficiency calculated from each model (Figure 3.7g) is less than the
detailed-balance efficiency limit for Cu2O, which is 20.5% at 300 K. The source of this
difference is the non-ideality of Cu2O charge transport that has been represented in our model
by using empirical data from the literature. As in the case of Jsc, the simulated efficiency
using the excitonic model is enhanced relative to the efficiency obtained from the FC model
at low temperatures, where excitons dominate, and converges to the efficiency obtained from
the FC model at high temperatures, where the photogenerated population consists entirely of
free electrons and holes. Hence, at temperatures relevant to photovoltaic operation, the free-

62
carrier model substantially underestimates the performance of Cu2O solar cells, with the
difference as much as 1.9 absolute percent for the case when NA = 1016 cm-3 at T = 300 K.

3.5 Conclusion
In conclusion, neglecting excitonic effects by adopting the traditional “free carrier” model
fails to capture a fundamental photoconversion and charge-transport mechanism in Cu2O.
Using a thermodynamic model that governs ionization events, the quasi-equilibrium
branching ratio between excitons and free carriers in Cu2O indicates that during photovoltaic
operation up to 28% of photogenerated carriers are excitons. These large exciton densities
were directly observed as a free-exciton peak in the photoluminescence spectrum of Cu2O at
room temperature under visible-light excitation. Spectral response measurements of a
Cu2O/Zn(O,S) solar cell indicated substantial excitonic current collection at energies below
the Cu2O electronic band gap, under conditions for which only excitons are generated. In
the case of Cu2O, the “free carrier” model was shown to underestimate the efficiency of a
Cu2O solar cell by as much as 2 absolute percent at room temperature.

Chapter 4
Interconnect-free Perovskite/Silicon
Tandems
4.1 Increasing Silicon Efficiency: Tandem Si Solar Cells
Combining multiple junctions in a single device is one of the most practical and welldemonstrated approaches to exceed the single absorber Shockley-Queisser limit (29). In such
a design, each sub-cell is optimized to absorb a different part of the solar spectrum, producing
two separate quasi-Fermi level splittings, thereby reducing thermalization losses. The
utilization of tandem device architectures with Si bottom cells would increase the theoretical
cell efficiency beyond 40% and ultimately allow the production of photovoltaic modules in
excess of 30%, all while leveraging Si’s already dominant market share (107).
To that end there has been considerable effort to develop efficient Si-based tandem solar
cells. For over two decades, research has primarily focused on Si-based tandems which
utilize III-V semiconductors as the top cell material owing to III-V’s maturity, reliability and
high efficiency (108-115). Indeed, Si/III-V tandems have obtained efficiencies above the
single-junction Shockley-Queisser limit of 32% (116) under one-sun illumination, however,
a number of obstacles impede the commercial viability of this pairing, including the high
materials and fabrication costs of III-V semiconductors.

4.2 The Rise of Perovskites and Silicon/Perovskite Tandems
Recently, the inorganic-organic metal-halide perovskites (henceforth, simply perovskite)
have emerged as an alternative to III-Vs as a top cell material in a tandem structure with Si.

64
Since their introduction as purely organic, dye-sensitized solar cells in 2009 (117, 118),
the efficiency of single junction, solid-state perovskite solar cells has risen from 10.9% (119)
at a near meteoric rate to 23.3% (Fig. 4.1). Along with the drastic increase in efficiency of
perovskite solar cells has come a significant increase in device stability. Initially, perovskite
devices were unstable in air, their performance rapidly decayed in the presence of oxygen
and moisture in a matter of seconds. The introduction of multication perovskites
incorporating cesium (Cs) and/or formamidinium (FA), in addition to methylammonium
(MA), has led to stable solar cell performance that are now capable of passing the standard
1,000 hour damp heat test (120). Additionally, the band gap of perovskites, like that of the
III-Vs, can be tuned over a large range (121) making the perovskites attractive candidates for
multijunction solar cells on top of Si (and other narrower band gap materials on the market,
such as, cadmium telluride and copper indium gallium selenide). However, unlike the IIIVs, the perovskites have simple processing requirements and low materials cost, thus
presenting a pathway to improving efficiency to over 30% while preserving low module cost.
Perovskite tandems with Si have now attained monolithic perovskite/Si tandem device with
world-record efficiencies of 27.3%, though no details of this record-efficiency cell structure
have yet been provided (122).

65
Solid-State

Electrolyte

Efficiency (%)

2008

2012

2016

2020

Year
Figure 4.1 Perovskite record cell efficiency, adapted from (30, 123). The record at the time
of writing is 23.3%.
Design approaches for creating tandem cells have either two or four electrical terminals per
tandem pair (Fig. 4.2). While four-terminal Si/perovskite tandems have been the focus of
many works (124-127) and have demonstrated efficiencies close to the single junction Si
record (26.7%) (128), the added wiring complexity and need for multiple transparent contacts
has prevented their widespread use commercially. The two-terminal (2-T) configuration
allows for monolithic fabrication, in which the cells are constructed as a single unit, allowing
simple electrical integration at the system level and relaxing the need for additional front and
rear transparent electrodes. In place of transparent electrodes, however, the monolithic

66
approach requires an interconnection layer that effectively facilitates the flow of
photogenerated carriers from one sub-cell to the other. Ideally this should be achieved with
low electrical and optical losses and at minimal processing cost. Tunnel junctions consisting
of two heavily doped p+ and n+ regions are a common choice for such an interconnection
layer (129). Indeed, the first demonstration of a 2-T perovskite/Si tandem device used a
partially crystallized, heavily doped n-type Si layer to form a tunnel junction on top of a
crystalline p+-Si emitter in its Si homojunction bottom cell, resulting in h =13.7% (130).
Improved light management, combined with advances in perovskite photovoltaics, yielded
h = 22.7% by use of heavily-doped hydrogenated nanocrystalline Si (nc-Si:H) tunneling
layers on a Si heterojunction with intrinsic thin-layer (HIT) bottom cell (131). This approach
has been further developed recently by texturing the HIT bottom cell whilst conformally
depositing the perovskite and contact layers using thermal evaporation. Reduced reflection
and an improved infrared response in this design has yielded an efficiency of 25.2% for a
monolithic perovskite/Si tandem solar cell (132). An alternative to utilizing tunnel junctions
for interconnection is to employ a recombination layer, typically in the form of a transparent
conductive oxide (TCO), common choices being indium-doped tin oxide (ITO) (120, 133,
134) and indium-doped zinc oxide (IZO) (135). The previous record efficiency of 23.6% for
monolithic perovskite/Si tandems was obtained accordingly by incorporating an ITO
intermediate layer to connect a HIT bottom cell and perovskite top cell (120). Impediments
to further improvements in such TCO-containing interconnection systems include substantial
parasitic absorption due to free-carrier absorption at long wavelengths, and the prevalence of
shunt paths through the top cell, caused by surface roughness (131).

2-Terminal
TE

High Eg

TCO
or
TJ

4-Terminal

Low Eg

Figure 4.2 Simplified diagram of the 2-terminal (left) and 4-terminal (right) tandem solar
cell device architectures. In each design, the top contact is a transparent electrode (TE), which
allows the light to pass through to the two cells, while the bottom contact need not be
transparent. In the 2-terminal design the high and low band gap sub-cells are in ohmic contact
by means of either a transparent conductive oxide (TCO) or tunnel junction (TJ). In a 4terminal design two additional transparent electrode contacts are needed on the rear side of
the high band gap sub-cell and on the top of the low band gap sub-cell.

4.3 Interconnect-free Perovskite Silicon Tandem
We demonstrate herein a third and distinct strategy for fabrication of efficient monolithic,
two-terminal perovskite/Si tandem solar cells. The approach forgoes the use of a
conventional interconnection layer and instead places the perovskite top cell in direct contact
with the Si bottom cell (Fig. 4.3A). Development of this concept was stimulated by the
observation of highly Ohmic contact between TiO2 deposited by atomic-layer deposition
(ALD) and p-type Si in photoanodes that efficiently and stably evolve O2(g) from water
(136). Preliminary testing revealed that despite the absence of an intentional recombination
layer between the two materials, a sufficiently conductive contact can be produced to enable

68
the operation of an efficient tandem cell. The contact resistance was subsequently found
to be strongly dependent on the band alignment at the TiO2/p+-Si interface and on the relative
doping densities of the TiO2 and p-Si, both of which are sensitive to the TiO2 preparation
method. Although in our work the TiO2 was prepared by atomic-layer deposition, other
studies have shown that under certain deposition and annealing conditions TiO2 films with
similar behavior can be obtained using sputtering (137). Hence analogous behavior may be
obtainable with other deposition techniques, including spin-coating or spray-coating. For our
first proof-of-concept tandem devices we employed n-type homojunction Si cells, making
their p+ emitter the substrate for a conventional (semi-transparent) solution-processed
perovskite top cell based on TiO2 and 2,2’,7,7’-Tetraakis-(N,N-di-4-methoxyphenylamino)9,9’-spirobifluorene (Spiro-OMeTAD). Subsequently we found that Ohmic contact can also
be achieved between TiO2 and the boron-doped, recrystallized a-Si layer of a heterojunction
cell (138), yielding even higher tandem voltages relative to the homojunction. We discuss
both cell types herein to demonstrate the general applicability of the interconnect-free
concept, but primarily make use of the homojunction cells with their physically simpler
structure to perform our mechanistic analyses.

4.3.1 Interconnect-free Cell Architecture and Fabrication
The perovskite top cell in our demonstration devices consisted of a conventional n-i-p
structure with a stack of cp-TiO2 (compact TiO2) /ms-TiO2 (mesoporous-TiO2) /perovskite
/Spiro-OMeTAD or PTAA (poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine)/MoOx / IZO
/Au grid, as illustrated in the cross-sectional SEM image in Fig. 4.3B. The ALD-deposited
TiO2 was uniform and conformal with a low surface roughness of ~0.77 nm (Fig. 4.4). A ~54
nm thickness of TiO2 was found to be optimal, covered by a ~70-80 nm ms-TiO2 layer and
an ultra-thin PCBM (Phenyl-C61-butyric acid methyl ester) /PMMA (Poly(methyl
methacrylate)) passivation layer to improve the cell voltage and reduce hysteresis in the
current-voltage (J-V) characteristics (139). Multi-cation perovskites, which have consistently
outperformed their single-cation originators (140), were used in the cells and fabricated using
an

anti-solvent

one-step

method

(141).

composition

69
Cs0.05Rb0.05FA0.765MA0.135PbI2.55Br0.45 yielded stable films with an appropriate bandgap
(Eg= 1.63 eV) (142). Current matching between the two sub-cells was obtained by deposition
of a relatively thin (~310 nm) perovskite layer. For both four-terminal and two-terminal Si
tandems, a bandgap of ~1.7 -1.8 eV is expected to yield higher cell voltages (143), all other
things being equal, than the 1.63 eV bandgap material used herein. At present, the high
bandgap perovskites show a greater difference between the bandgap and cell Voc than the
more optimized lower bandgap compositions (127, 128, 140, 144), mitigating the potential
gains in voltage. Layer thicknesses of ~120 nm and ~50 nm (128) were used for the organic
hole selective layers (Spiro-OMeTAD and PTAA respectively). Before sputtering ~40 nm
of IZO for the front contact, a 10 nm MoOx buffer layer was deposited to protect the
underlying organic layer from sputter damage.
For the Si bottom cells, we have used both n-type homojunction cells and passivating-contact
heterojunction cells with pyramidally textured and passivated rear surfaces. Si homojunction
cells constitute > 80% of the current PV market share for the moment, primarily on p-type
wafers, although a trend towards using n-type substrates as employed here is widely
anticipated (145). Passivating-contact cells are an emerging technology well suited for
tandems, due to their higher cell voltages, simple processing requirements (146) and strong
performance in the infrared (147). The heterojunction cell we employed incorporated a thin
(<1.4 nm) oxide layer buried beneath ~50 nm of heavily boron-doped, recrystallized a-Si
(138). For brevity, these devices will be referred to as “polysilicon” (poly-Si) cells, although
the top layer is likely a mix of amorphous and partially crystallized silicon.

Figure 4.3(A) Schematic of the interconnect-free monolithic perovskite/c-Si tandem solar
cell (not to scale). Initial tests were carried out on homojunction Si cells with SpiroOMeTAD as the top perovskite contact; however, our best performance was obtained with
polysilicon bottom-cells and PTAA as the top hole-selective layer. (B) Cross-sectional
scanning-electron microscope (SEM) image of the tandem device based on Si homojunction
subcell from the top surface to the p+-Si layer (Spiro-OMeTAD is used as HTM). The antireflection layer was not included due to the large thickness of ~ 1 mm, (C) Scanning
transmission-electron microscopy (STEM) bright field (BF) image and (D) high-resolution
STEM BF image of the TiO2/p+-Si interface.

Figure 4.4 AFM image of TDMAT-ALD TiO2 on a p+-Si substrate.

4.3.2 Current-Voltage and TiO2/Si Contact Characteristics
As a direct demonstration of the interconnect-free concept, Fig. 4.5A shows the photovoltaic
J-V performance exhibited by our highest-performing polysilicon tandem cell and the
corresponding photovoltaic metrics. The performance of the homojunction tandem is
likewise shown in Fig. 4.6. A steady-state efficiency of 24.1% was obtained for the
polysilicon interconnect-free tandem under 100 mW cm-2 of simulated Air Mass 1.5G
illumination, with a Voc of ~1.76 V, a short-circuit current (Jsc) of 17.8 mA cm-2, and a fill
factor (FF) of ~0.78. Compared to the polysilicon tandems, the best homojunction tandems
had a steady-state efficiency of 22.9% (Fig. 4.9A) with slightly lower voltages of ~1.70 V
and currents densities of 17.2 mA cm-2. Although both efficiency values are uncertified, the
spectral response data predicts short-circuit current densities under standard illumination test

72
conditions that are in close agreement with those observed experimentally herein. We thus
expect that certified efficiencies would be very similar to the values reported herein. Any
spectral mismatch would have its greatest effect on the short-circuit current density, whereas
the voltage and fill factor would be mostly unaffected. These latter metrics are our main
concerns for evaluating the interconnect-free concept, as they pertain to the passivation and
electrical connection at the sub-cell interface, respectively.

Figure 4.5 (A) J-V behavior of the proof-of-concept tandem device with both reverse and
forward scanning at 0.05 V/s based on heterojunction poly-Si subcell. (B) Absorbance (1R, where R is the reflectance) of the tandem device (grey shading), external quantum
efficiency (EQE) of the perovskite top cell (blue), and EQE of the c-Si bottom sub-cell
(red).
Efficient operation of the interconnect-free tandem device requires facile charge transfer
between the Si cell’s front-surface and the TiO2 layer. Specifically, photogenerated electrons
collected in the TiO2 layer must be able to recombine, while incurring minimal voltage loss,
with corresponding holes from the Si emitter region. The n-type character of TiO2 would be
expected to produce a rectifying p-n heterojunction with p-type Si, whether monocrystalline,
polycrystalline or amorphous. (148, 149) Despite this, the J-V characteristics of our tandem
devices did not exhibit S-shaped curves, nor the fill-factor losses that would be expected if a
rectifying contact were present (150, 151).

Figure 4.6 (A) J-V behavior of the proof-of-concept tandem device with both reverse and
forward scanning at 0.05 V/s based on Si homojunction subcell. (B) Absorbance (1-R,
where R is the reflectance) of the tandem device (grey shading), external quantum
efficiency (EQE) of the perovskite top cell (blue), and EQE of the c-Si bottom sub-cell
(red). (C) schematic of single-junction Si homojunction solar cell including ALD-TiO2 on
a flat p+-Si emitter (not to scale), (D) photovoltaic performance of a single-junction
homojunction Si solar cell.
To explicitly demonstrate the existence of facile electrical contact between TiO2 and p-type
Si, the structure depicted in Fig. 4.7A was used to investigate the electrical properties of the
TiO2/p+-Si interface in our homojunction tandem devices – the operating principles for our
polysilicon tandems presumably being similar. Analogous test structures were also fabricated
using an ITO film instead of TiO2 to emulate the recombination layer used in previous
tandem designs (120, 133, 134). The contact resistivity (ρc) of a given film with respect to

74
p -Si was determined via the method devised by Cox and Strack (152). We note values so

derived include not only the desired metal oxide/p+-Si contact resistivity, also the bulk metal
oxide as well as the oxide/Al contact resistance, so these measurements are to be interpreted
as an upper bound on the former quantity. In our initial tests of the TiO2/p+-Si interface all
samples exhibited a relatively high contact resistance as seen in Fig. 4.7B, which was only
improved upon annealing at 400 °C in dry air. After annealing, the highest performing TiO2
samples achieved a contact resistance better than 30 mΩcm2, surpassing that of the ITO
samples at ~230 mΩcm2 by a wide margin. By contrast, annealing had a detrimental effect
on the ITO/p+-Si contact, correlating with a previous observation of reduced bulk
conductivity when annealing ITO on quartz (133). Subsequent testing has revealed that
whilst helpful, the annealing step is not strictly necessary for the TiO2/p+-Si contact because
acceptable resistivity (~100 mΩcm2) can be achieved without annealing, by instead
increasing the ALD chamber temperature from 75 °C to 200 °C (Fig. 4.8).

Figure 4.7(A) Schematic of the structure used for measuring contact resistivity. (B) Comparison

of the J-V behavior of ITO/p+-Si and various TiO2/p+-Si structures before and after annealing at
400 °C in air. TiCl4-ALD TiO2 listed here is deposited with the reactor chamber temperature of 75
°C. (C) Simulated band diagram of the TiO2/p+-Si at equilibrium assuming n-type doping of 5x1018
cm-3 on the TiO2 and 1019 cm-3 for p+-Si (appropriate for our test structure with TDMAT TiO2, see
table S3. The unknown interfacial energy gap Δ is shown here for illustrative purposes as 600 meV,
which falls within the range of reported measurements (153)). Both mechanisms of direct- and
tunneling assisted capture by interfacial defects are shown.

Figure 4.8 J-V curves of the TiCl4-ALD TiO2 deposited at low temperatures on different
p+-Si wafers. The samples receive no further heat-treatment. TiO2 deposited at 150 °C on
top of p+-Si with a doping density of (A) ~9.3´1019 cm-3, the extracted contact resistivity
is ~850 mΩcm2 and (C) ~1.7´1020 cm-3, the extracted contact resistivity is ~445 mΩcm2.
TiO2 deposited at 200 °C on top of p+-Si with a doping density of (B) ~9.3´1019 cm-3, the
extracted contact resistivity is ~210 mΩcm2 and (D) ~1.7´1020 cm-3, the extracted contact
resistivity is ~99.6 mΩcm2.
Regarding the comparison with ITO, tandem devices fabricated with ITO as a recombination
layer exhibited overall inferior photovoltaic performance as determined by all device metrics,
with Voc = 1.510 V, Jsc = 15.8 mA/cm2 and FF = 0.637 (Fig. 4.9). The current loss in this test
device is likely a result of parasitic absorption in the ITO layer and reflection loss on the
ITO/Si interface, and the reduced Voc and FF are ascribable to inferior contact between the
sub-cells (as supported by the J-V measurements of Fig. 4.7B), as well as shunting due to
pinholes in sputtered ITO layers. This indicates that our interconnect-free tandem cells can
not only be fabricated in fewer steps, but enjoy performance benefits relative to the standard
design incorporating an ITO-based recombination layer.

Figure 4.9 J-V data of a 2-T perovskite/Si tandem device with ITO as the recombination
layer.
It is notable that TiO2 layers prepared using different ALD precursors yielded quite
drastically different J-V characteristics in our TiO2/p+-Si test structures, as highlighted in Fig.
4.7B. Ohmic, highly conductive behavior between TiO2 and p+-Si was observed in samples
with TiO2 prepared using tetrakisdimethylamidotitanium (TDMAT) as the ALD precursor
(Fig. 3B, green solid line), whereas by contrast very low conductivity (ρ>10 Ωcm2) in the
low-bias region was obtained when using titanium tetrachloride (TiCl4) instead (Fig. 4.7B,
blue solid line), despite otherwise identical processing conditions. The use of titanium
tetraisopropoxide (TTIP) resulted in intermediate performance, displaying conductive but
distinctly non-linear J-V behavior (Fig. 4.7B, yellow solid line). The conductivity of these
TiO2/p+-Si test structures was found to correlate well with the behavior of tandem devices
constructed using the same material, with h =21% obtaining for homojunction tandems using
TTIP as the precursor and h =3.6% for TiCl4 as the precursor (75 °C deposition) (Fig. 4.10).
These drastic variations motivated the need for a fundamental understanding of the contact

78
between TiO2 and p-Si. Below we present arguments which indicate that the contact is
mediated by interfacial defects, a distinct mechanism to the one that predominates in
conventional p-n tunnel junctions.

Figure 4.10 J-V data of monolithic perovskite/Si tandem solar cells with (top) TTIPALD TiO2, (bottom) TiCl4–ALD TiO2 (deposited at 75°C).

4.3.3 TiO2/Si Band Alignment and Charge Transport Mechanism
One aspect of clear relevance to the transport of carriers between TiO2 and Si is the interfacial
band alignment, whatever the underlying mechanism. Based on X-ray photoelectron
spectroscopic (XPS) measurements of the electron affinity (𝜒 ¹©"Z ) for our TiO2 samples
(4.35-4.7 eV, Figures 4.11, 4.12, 4.13) and the Si ionization energy (I.E.Si), taken here as 5.15
eV, the band alignment at an idealized TiO2/p+-Si junction should result in an energy gap of
¹©"Z

𝛥 = 𝐸S

− 𝐸“I© = 𝜒 ¹©"Z − 𝐼. 𝐸.I© ≈ 0.45-0.8 eV, between the top of the Si valence band

and the bottom of the TiO2 conduction band (Fig. 4.7C). Less idealized, experimental
determinations of Δ that include the surface dipole contribution require combining data from
several techniques, and have only been reported rarely for TiO2/p-Si interfaces (153, 154).
In those studies values of Δ between 0.45 eV and 0.8 eV were obtained depending strongly
on the 1-2 nm interlayer composition, which could partly account for our observation of a
pronounced sensitivity to processing. A non-vanishing gap at the TiO2/p+-Si interface
prohibits band-to-band tunneling between the TiO2 conduction band and the Si valence band
at 0 V as would occur in a standard tunnel junction, due to a lack of overlap in the bulk
density of states at equilibrium (see Fig. 4.7C). Under sufficient reverse bias the necessary
overlap will occur, but carriers would then need to tunnel through the sum of the depletion
and interlayer widths, estimated to be 10’s of nanometers for TiO2 doping in the range of
1017-1019 cm-3. This distance is at the upper limit of what is physically reasonable, and
indicates that band-to-band tunneling at reverse bias is only likely to occur when both
depletion regions are very small, corresponding to high doping (155). At forward bias, the
band overlap is decreased and band-to-band tunneling becomes prohibited, requiring a
separate mechanism to explain the presence of a high forward current. In place of tunneling,
at forward bias a current could be carried via the thermionic emission of conduction-band
electrons from TiO2 over the barrier due to the conduction-band offset 𝐸9I© − ∆, but this
would predict a strong tradeoff between the forward and reverse current, contrary to the
observed Ohmic behavior (i.e., large gaps ∆ would provide a small barrier for the forward
thermionic emission current while enlarging the threshold voltage for reverse tunneling
current, and vice versa). We conclude that our observation of high conductivity in both the

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forward and reverse direction are indicative of an operating mechanism distinct from that
of a familiar p-n tunnel junction.

Figure 4.11 (A) Combined UPS valence band spectrum and IPES, and (B) the secondary
electron cut-off region, and (C) calculated energy diagram from the above measurement,
of an annealed TDMAT-ALD TiO2 layer. The error for the work function was ±0.2 eV,
and the extraction of valence band and conduction band had an error of ±0.1 eV.

Figure 4.12 (A) Combined UPS valence band spectrum and IPES, and (B) the secondary
electron cut-off region representative, and (C) calculated energy diagram from the above
measurement of an annealed TTIP-ALDTiO2 layer.

Figure 4.13 (A) Combined UPS valence band spectrum and IPES, and (B) the secondary
electron cut-off region representative, and (C) calculated energy diagram from the above
measurement of an annealed TiCl4-ALD TiO2 layer (deposited at 75°C).
The considerations above indicate that the presence of a pristine interfacial energy gap Δ is
not readily compatible with the observed highly conductive contact between TiO2 and p+-Si.
A more likely alternative is the presence of a substantial density of localized mid-gap states
at the interface between Si and TiO2. Such interfacial states can facilitate band-to-band
tunneling at reverse bias and act as generation-recombination centers at all bias voltages
(150, 156-158). In such a scenario, electrons move into and out of the defects states via local
capture/emission as well as tunneling (Fig. 4.7C). As generation-recombination centers, the
interface states would have a substantial influence on charge transport by facilitating the
recombination of majority carriers in Si at forward bias without requiring emission over the
interfacial barrier. At reverse-bias, every recombination center becomes a source of
generation, and high conductivity can be obtained by thermally generated carriers.
Conceptually this situation is similar to having a recombination-layer of atomic dimensions
between the TiO2 and p-Si, created in situ and intrinsically via the native material contact,
without the introduction of substantial optical losses. For the contact resistance, the relevant
recombination induced by the interfacial defects occurs between majority holes in the p-Si
and electrons in TiO2, just as in a conventional (e.g. ITO) recombination layer. Such defects
may also induce unwanted recombination between majority holes and the minority electrons
in p-Si, thereby degrading the open-circuit voltage of the bottom cell. In homojunction cells,
minority carriers are capable of reaching the TiO2 interface, making this a relevant concern.

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In contrast, in passivating-contact cells these defects will not affect the degree of
passivation due to the selective barrier (buried oxide in the polysilicon design) between
minority carriers and the TiO2 interface. Hence, in homojunction cells the interfacial defects
must be carefully controlled so as not to overly compromise the silicon cells’ voltage,
whereas in selective-contact designs this tradeoff should be largely alleviated, depending on
the degree of selectivity.

Figure 4.14 (A) Simulated J-V curves for varying interfacial gaps Δ. A single neutral midgap SRH defect was included with 𝑆7 = 𝑆3 = 105 cm/s. The dashed curves are computed
=>

with tunneling to defects included. (B) Simulated small voltage resistivity l𝜌 = =# |>$h o
with the TiO2 donor density fixed at 1018 cm-3 and variable p-Si acceptor doping.
Measurements are included as data points in red. Calculations for neutral (solid lines),
acceptor-type (dotted lines) and donor-type (dot-dashed lines) are shown to demonstrate

83
the important effect of defect charge on the interfacial carrier balance. (C) Simulated
band diagram of the full tandem device based on homojunction Si subcell with high workfunction cp-TiO2 at illuminated open-circuit. The inset depicts the two important energetic
offsets Δ and δ, respectively, defined as the valence-to-conduction band offset at the TiO2Si interface and the difference in work functions between our solution-processed
mesoporous TiO2 layer and that of the ALD compact layer.
Numerical drift-diffusion models based on SCAPS (159) were used to investigate the impact
of interfacial generation-recombination centers on the interfacial contact resistance. These
models were designed to compute the current across a TiO2/p+-Si heterojunction assuming
Ohmic metal contacts on both sides, and therefore mainly addressed the junction current,
with only minor contributions from bulk conduction through the small layers thicknesses (50
nm and 100 nm for TiO2 and Si, respectively). Shockley-Read-Hall (SRH) recombination
centers were added at the TiO2/p+-Si interface to physically correspond to localized states
that are expected to form in the interfacial energy gap. Such defects are likely to occur at a
high density, given the relatively low degree of lattice matching between TiO2 and Si, the
possibility of precursor remnants, Si dangling bonds, and the presence of a 1-2 nm
amorphous alloy interlayer observed in our samples between the two bulk crystals (Figures
4.3C, D). Interlayers are known to have a profound effect on the interface dipole or bandalignment of semiconductor-semiconductor contacts (160), as well as on the mechanisms of
charge transfer (161), and may therefore play a key role in our experimental system. For
simplicity in our modeling, the contribution of the interlayer capacitance was neglected,
while the defect density of the interlayer was captured in the interfacial SRH parameters.
Tunneling due to defects was not accurately modeled due to a lack of detailed knowledge of
the interface parameters, but calculations with tunneling processes included are presented in
Fig. 4.14A and Fig. 4.15 to illustrate qualitatively the behavior that results from this effect.

Figure 4.15 Calculated small-voltage resistivity as in Fig. 4B of the main text, this time
showing the effect of tunneling. Tunneling has a minor effect for neutral and acceptor-type
defects, but significantly affects the donor-defect models when the acceptor doping is large
because tunneling effects are most significant when the depletion region is small which
occurs for large acceptor doping concentrations.
Fig. 4.14A shows the computed J-V characteristics of a TiO2/p+-Si heterojunction with
varying gaps Δ in the range of 0.4-0.9 eV, and with a high density of neutral mid-gap defects
(recombination velocities 𝑆7 = 𝑆3 = 105 cm/s), all other parameters being equal (see Table
4.1). These J-V characteristics bear a striking resemblance to the experimental behavior of
Fig. 4.7B in that they both exhibit the full range of qualitative characteristics seen
experimentally, namely highly conductive Ohmic behavior (e.g. Δ = 0.4), asymmetric
exponential-type curves (Δ = 0.5, 0.6 eV) and strong rectification (Δ = 0.7-0.9 eV). The
detrimental effect of a large band offset can only be compensated by higher recombination
velocities up to the physical limit of 𝑆7,3 = 𝑣64 ≈ 107 cm/s, likely ruling out high defectmediated conductivity for band offsets greater than ~0.7 eV. A somewhat less trivial
prediction of the SRH model concerns the balance of carrier densities at the interface.
According to equation S1 (supplementary information), the interfacial carrier densities must
be balanced to achieve maximal conductivity (in particular 𝑣7 𝑛h ≈ 𝑣3 𝑝h where 𝑛h , 𝑝h are

85
the equilibrium carrier densities at the interface and 𝑣7,3 their quasi-recombination
velocities). Experimentally the interfacial conductivity was found to benefit from a high
substrate doping (Fig. 4.14B, red markers), which is consistent with donor type defects at the
interface that require excess acceptors to achieve the relevant balance. Donor defects are
frequently present at both TiO2 and un-passivated Si surfaces in the form of oxygen vacancies
(162) and dangling bonds (Pb centers) (163), respectively. The SRH theory thus consistently
accounts for the Ohmic conductivity between TiO2/p+-Si, in accord with the behavior
observed previously for TiO2-protected Si photoanodes (136, 164).
Field [G]

Resistivity
[ohm cm]

1.0000x103
3.0000x103
5.0001x103

8.4670x10-1
8.4615x10-1
8.4497x10-1

Hall
Coefficient
[cm³/C]
-8.2446x10-1
-7.8738x10-1
-7.8614x10-1

Type

Carrier Density
[1/cm³]

7.5713x1018
7.9278x1018
7.9403x1018

Hall
Mobility
[cm²/(VS)]
9.8962x10-1
9.4511x10-1
9.5362x10-1

Table 4.1 Hall-effect measurements for annealed TDMAT-ALD TiO2
According to the SRH theory outlined above, the diverse behavior seen in Fig. 4.7B with
respect to preparation conditions likely results from variations in the band offset between the
TiO2 conduction-band edge and the Si valence band (∆), as well as in the TiO2 doping density
and interfacial defect properties. In accordance with this picture our highest-performing
material in the homojunction designs was TDMAT-ALD TiO2, which exhibited relatively
large electron affinities for anatase (Fig. 4.11). Although vacuum levels are only an
approximate indicator of the actual band alignment, the data suggest a small ∆, in addition to
sufficiently conductive TiO2 layer (Table 4.1), is helpful for obtaining a high-conductivity
contact between to p+-Si. This raises a related issue regarding the TiO2 work function’s
influence on the perovskite cell’s built-in or flat-band voltage. A larger n-type selective
contact work function predicts a reduced built-in voltage, all other things being equal, and
therefore a reduced perovskite Voc. This is contrary to our experimental observation that the
perovskite cells on TDMAT-ALD TiO2 function without substantial losses to their opencircuit voltage. The observed cell performance is thus indicative that the mesoporous TiO2
layer inserted between the compact TiO2 layer and the perovskite in the standard cell

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architecture functions to maintain the top-cell voltage, likely due to its smaller work
function (139). Indeed, single-junction perovskite cells fabricated without a mesoporous
TiO2 layer (i.e. directly on the TDMAT-ALD TiO2 compact layer) exhibited drastically
reduced open-circuit voltages as predicted by the preceding argument (Fig. 4.16: note that
this does not indicate an intrinsic limit of planar cells, as solution-processed compact layers
yielded uncompromised, high open-circuit voltages (165)). This reasoning is also supported
by our drift-diffusion simulations of single-junction perovskite solar cells with and without
a mesoporous layer (Fig. 4.17). The mechanism of work function adjustment imputed to the
mesoporous titania is illustrated in the simulated band diagram of Fig. 4.14C. Devices whose
compact titania layers have a large work function (e.g. our TMDAT-ALD TiO2) therefore
seem to benefit substantially from inclusion of the mesoporous layer. Mesoporous layers are
typically annealed at high (~400 °C) temperatures to drive off the organic suspension agents,
but options exist for low temperature preparation (166, 167), and for the deposition of layers
with analogous functionality that do not require heat treatment (168). As a preliminary
demonstration of a low-temperature interconnection-free process, we fabricated tandems
with open-circuit voltages as high as ~1.75 V (Fig. 4.18) without exceeding 200 °C in the
processing sequence, by optimizing the TiCl4-ALD TiO2 (Fig. 4.19). With its lower workfunction, TiCl4-ALD TiO2 allows uncompromised top-cell voltages in a planar architecture
without mesoporous TiO2, although wetting issues in the perovskite deposition seem to have
compromised the fill factors of these cells. This behavior is a common issue for solutionprocessed planar cells that can be adequately addressed by low-temperature interface
engineering (169, 170).

Figure 4.16 Voc yield of transparent single-junction perovskite solar cells (with p+-Si as the
substrate) with and without mesoporous-TiO2. Results for TDMAT-ALD TiO2 are shown
on the left while results for TTIP-ALD TiO2 are shown on the right. Both titania compact
layers have high work functions with the deposition conditions used in this work.

Figure 4.17 Simulated band diagram at 0 V (left) and J-V behavior (right) of a singlejunction perovskite solar cell with and without an additional “mesoporous” titania layer
inserted between the perovskite and high work-function compact titania. This represents a
1D simplification of the complex 3-dimensional mesoporous structure present in our tandem
cell design, but captures the qualitative effect of including titania layers with contrasting

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work functions. The mesoporous layer functions primarily to maintain the built-in voltage
in the perovskite cell, as seen in the band diagram (left) and consequently discrepant opencircuit voltages (right). Here electron affinities of 4.1 eV and 4.5 eV were used for the
compact and mesoporous titania layers respectively.

Figure 4.18 J-V curve of a monolithic perovskite/Si tandem solar cells with as-deposited
TiCl4-ALD TiO2 (200 °C). The top perovskite subcell has a planar structure without the
inclusion of the mesoporous TiO2 film, and is fabricated with low-temperature processes.

Figure 4.19 J-V curves of the TiCl4-ALD TiO2 deposited at low temperatures on different
p+-Si wafers. The samples receive no further heat-treatment. TiO2 deposited at 150 °C on
top of p+-Si with a doping density of (A) ~9.3´1019 cm-3, the extracted contact resistivity
is ~850 mΩcm2 and (C) ~1.7´1020 cm-3, the extracted contact resistivity is ~445 mΩcm2.
TiO2 deposited at 200 °C on top of p+-Si with a doping density of (B) ~9.3´1019 cm-3, the
extracted contact resistivity is ~210 mΩcm2 and (D) ~1.7´1020 cm-3, the extracted contact
resistivity is ~99.6 mΩcm2.
According to our analysis, an enabling feature of interconnect-free tandems is the presence
of intra-gap states that bridge the energetic offset between the Si sub-cell and the adjoining
contact layer (TiO2 in our demonstration). For homojunction Si cells, minority carriers may
recombine at the same defects, compromising the Si cell’s voltage. Nonetheless, for the
homojunction cells with TiO2, open-circuit voltages of 654 mV were obtained in just a few
attempts whilst retaining an adequate contact resistance of 0.96 Ωcm2 (Fig. 4.20) suggesting
that considerable room for improvement utilizing homojunctions may remain in achieving
the optimal balance between passivation and contact resistance. For perovskite/Si tandems,
the issue of series resistance is much less severe (by a factor of ~5 (171)), due to the higher

90
voltage and lower cell current. For the polysilicon cell, this trade-off is entirely avoided
due to the carrier-selective buried oxide layer, which blocks the passage of minority carriers
to the TiO2 interface (138). Carrier-selectivity, a common feature among passivating-contact
designs, allows the TiO2 interfacial defect density to be freely tuned for optimal contact
resistance without detrimentally affecting the open-circuit voltage of the Si cell. Considering
the already superior performance of passivating-contact type cells for use in tandems, the
interconnect-free concept seems most promising for such cells as compared to homojunction
designs.

Figure 4.20 (A) Excess carrier lifetime of a Si substrate with and without TiO2 passivation
(TiCl4-ALD TiO2 deposited at 150 °C without further annealing) as a function of the
measured injection level. The implied Voc (iVoc) is increased by ~50 mV with the TiCl4
TiO2 coating. (B) J-V curve of a TiCl4-ALD (150 °C) TiO2/p+-Si sample (p+-Si has a doping
density of ~1.5*1019 cm-3).

4.3.4 Cell Stability
4.3.4.1 Perovskite Damp Heat Test
Stability is a serious issue for all perovskite devices reported in the literature to date. The
stability of our devices with respect to heat and moisture was investigated by performing the
damp heat test according to the testing protocol 61215 defined by the International

91
Electrochemical Commission (IEC) (85 °C in 85% relative humidity). These tests were
performed on encapsulated semi-transparent perovskite solar cells, the perovskite cell being
the primary source of instability in our tandems. Data showing the evolution of photovoltaic
metrics under aging is provided in Fig. 4.21. These devices maintained ~89% of their original
output after testing for > 1000 h, putting them very close to passing protocol 61215, which
requires 90% retained efficiency, and shows that our cells are well within the stability range
established by McGehee et al. (120) and the more recent work by Ballif et al. (132). Multiple
causes could contribute to the observed performance decreases, including sub-optimal
encapsulation, degradation of the organic HTM, migration of extrinsic ions introduced into
the HTM, and metal electrode diffusion into the perovskite (172, 173).

Figure 4.21 Damp heat test (85 °C in a relative humidity level of 85%) of a semitransparent
perovskite solar cell. Evolution of the photovoltaic characteristics including (a) Voc, (b) Jsc,
(c) FF and (d) PCE during damp heat stability of an encapsulated single-junction perovskite
device for 1414 h.

92
4.3.4.2 Si/perovskite Tandem Stability
We also tested the long-term stability of our tandem perovskite/Si homojunction cells.
Though there has been a range of studies dealing with the stability of the single-junction
perovskite solar cell, the stability of the tandem device, especially the light stability has only
been reported in the recent work on tandem device by Ballif et al (132). Our perovskite/Si
tandem device maintained an efficiency of ~18.4% after an aging period of ~2500 h in total,
including overall illumination for ~800 h, corresponding to over 80% of its original output.
Notably the cell spent more than 20 h during this aging period under 1-sun illumination in
air. In detail, the aging test included four stages (Fig. 4.22). Stage 1 and Stage 3 were stress
tests, entailing exposure to air, continuous illumination at full spectrum 1-sun intensity, and
biasing near the maximum power point. Stage 2 consisted of storing the devices in the dark
in an N2 cabinet, after which the cells were taken out for J-V characterization (1200 h). Stage
4 consisted of light/dark cycles under a constant N2 flow (with illumination for over 800 h).
Unsurprisingly the fastest degradation occurred in the stress tests of Stage 1 and Stage 3 (Fig.
4.22A and Fig. 4.22C, highlighted in yellow), where moisture, oxygen and the interaction of
light with these species are all potential culprits. The performance degradation under these
conditions was almost linear, which is consistent with the recently published result shown
for the tandem device with record efficiency (132). However, we found that such degradation
can be mostly reversed after resting the cells in the dark, as seen by the efficiency returning
to ~20.4 % as compared to ~20.7% before stress testing in Fig. 4.22C. This indicates that
irreversible chemical degradation by moisture and oxygen is a minor factor under short-term
exposure to air and illumination. The interaction of light with oxygen and light-enhanced ion
migration could then be the major contributors for the reduction during the stress tests. This
“dark recovery” has been previously reported for single junction perovskite solar cells (174,
175), whilst this is the first time that has been investigated on the perovskite/Si tandem. In
Stage 2 (Fig. 4.22B), with storage of the device in dark for ~1200 h, no performance recovery
was observed, but the performance degradation was also relatively small (with the efficiency

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dropping from 21.9% to 21.4% after ~700 h aging in the dark). A further reduction to
~20.7% efficiency was observed after another ~500 h aging.
The degradation of the tandem device under illumination in N2 atmosphere was slow over
the ~800 h light/dark cycles. A 10% reduction measured from the start of each cycle (20.4%
for the starting point of the first cycle and 18.4% for the seventh cycle) was observed over
the full light/dark cycling test (7 cycles of approx. 120 h). This is somewhat comparable to
the current record tandem cell (132), wherein an efficiency drop of ~10% during the course
of ~250 h illumination was reported, although a different testing protocol and the
phenomenon of dark recovery makes direct comparison difficult. Similarly, we observe clear
dark recovery after comparable storage time in all the light/dark cycles. Overall, our
perovskite/Si tandem exhibited respectable stability, with over 80% efficiency remaining
after aging under various conditions for >2500 h.
Whilst protocols of assessing the perovskite solar cell still vary largely (175), our perovskitebased device shows promising stability after industry standard stress tests (including the
damp heat test and light soaking at 60°C) and the long-term tracking of our perovskite/Si
tandem device performance including over 800 h illumination and dark recovery.
The titania is on the rear side of the top-cell and is therefore almost completely shielded by
the perovskite and other front-side layers that strongly absorb UV. This configuration may
therefore have benefits in terms of stability, as the photocatalytic effect of TiO2 (176, 177)
has been discussed as one of the main causes of as-prepared perovskite degradation.

Figure 4.22 PCE evolution of the proof-of-concept perovskite/Si homojunction tandem
device undergoing four different aging stages. (A) Stage 1: 1 Sun continuous illumination in
air for ~2.1 h, biased near maximum power point); (B) Stage 2: device stored in dark in a N2
cabinet for ~1224 h; (C) Stage 3: device under 1 Sun continuous illumination in air for ~19
h, biased at ~1.3 V, and Stage 4: device underwent light/dark cycles for seven cycles, with
total illumination of over 800 h. The measurement under light was taken at 25 °C.
Corresponding Voc evolution (D-F) of the same device under the same conditions.

4.4 Conclusion
In conclusion, we have demonstrated two proof-of-concept 2-terminal perovskite/Si tandem
devices that function without a conventional interconnection layer between their sub-cells.
In principle this concept may be generalized to other cell designs including those based on
the use of HIT silicon, as well as newer passivating-contact Si cells (146). Whereas
fabrication of an nc-Si tunnel-junction interconnect is relatively straightforward for HIT
cells, these layers introduce a small but potentially significant amount of parasitic loss in the
region of ~550-700 nm [16] where the nc-Si is absorbing and the perovskite top cell’s

95
absorption is simultaneously incomplete. Optical calculations indicate that this loss can be
as large as ~1.0-1.5 mA cm-2 under the AM1.5G spectrum for standard tunnel-junction
thicknesses. Larger losses can be expected for ITO recombination layers deposited without
annealing [16]. The interconnect-free concept thus offers dual advantages of simpler
processing and reduced optical losses compared to TCO and tunnel-junction interconnection
layers. Sub-optimal optics on our tandem device’s front side was identified as the main
performance limitation in our demonstration devices, which could be markedly improved by
using a silicon cell with front-surface texturing for anti-reflection and thinner, less absorbing
hole-transport materials. The contact between TiO2 and Si should not be substantially
affected by micron-scale texturing, making the interconnect-free design described here fully
compatible with evaporating a perovskite top-cell cell onto a textured Si wafer, which leads
to very low optical losses (132). In principle, the desired device properties can also be
obtained from a variety of TiO2 deposition and processing conditions, and from other
materials. The publication of a similar scheme using SnO2 (178) instead of TiO2 whilst this
paper was under review demonstrates the wide applicability of the interconnect-free concept.
Jointly, our work highlights the potential of emerging perovskite photovoltaics to enable lowcost, high-efficiency tandem devices through straightforward integration with commercially
relevant and emerging Si solar cells.

Chapter 5
Tuning the Catalytic Activity of Oxygenand Chlorine-Evolution Electrocatalysts with
Atomic Layer Deposition
5.1 Introduction
Highly active electrocatalysts are required for the cost-effective generation of fuels and
commodity chemicals from renewable sources of electricity (179, 180). Despite potential
advantages (e.g., facile product separation), the industrial use of many heterogeneous
electrocatalysts is currently limited in part by suboptimal catalytic activity and/or selectivity.
In addition, there are limited methods to tune the selectivity and activity of heterogeneous
electrocatalysts (179). Methods and design tools such as doping, inducing strain, and mixing
metal oxides have been used to improve the catalytic activity of heterogeneous
electrocatalysts (181-184). The activity of heterogeneous electrocatalysts can also be tuned
by applying thin layers of another material, leading to an altered surface charge density on
the resulting composite material relative to the bulk charge density of either individual
material (185-190). This approach has been widely used to alter the catalytic and electronic
properties of core/shell nanoparticles, although additional tuning of the particle support
structure is necessary to create an efficient heterogeneous electrocatalyst (191, 192). Density
functional theory calculations have shown that a single atomic layer of TiO2 on RuO2 should
lead to enhanced selectivity for the chlorine-evolution reaction (CER) relative to the oxygenevolution reaction (OER) (186). Enhanced catalytic activity for the OER has been reported
for WO3 photocatalysts coated with 5 nm of alumina, with the activity increase ascribed to
an alteration in the electronic surface-state density (193). Enhanced catalytic activity has also

97
been observed at the interface between TiO2 and RuO2, with charge transfer between RuO2
and TiO2 resulting in a mixed phase with an intermediate charge density (182).
Herein, atomic layer deposition (ALD; a stepwise deposition technique) has been used to
tune the surface charge density, and consequently tune the catalytic activity, of
electrocatalytic systems in a fashion consistent with estimates based on group
electronegativity concepts (see Figs. S1-S5 in the Supplementary Materials for further
discussion of ALD, surface homogeneity, and group electronegativity estimates). To test
these predictions, the activities of the known electrocatalysts, IrO2, RuO2, and F-doped SnO2
(FTO) were tuned and evaluated for the chlorine-evolution reaction (CER) and the oxygenevolution reaction (OER). The CER provides a promising approach to infrastructure-free
wastewater treatment as well as for the production of chlorine, an important industrial
chemical whose global annual demand exceeds seventy million metric tons (194, 195). The
OER is the limiting half-reaction for water splitting that could provide hydrogen for
transportation and could also provide a precursor to energy storage via thermochemical
reaction with CO2 to produce an energy-dense, carbon-neutral fuel (196).

5.2 Material Selection, Sample Preparation, and
Characterization
5.2.1 Material Selection and Group Electronegativity
Each material tested was selected based on its theoretical group electronegativity (𝝌).
Electronegativities were estimated for heterogeneous electrocatalysts by taking the
geometric mean of the electronegativities of the constituent atoms (187, 197). Allen scale
electronegativities were used because it is superior to other electronegativity scales (e.g.
Pauling, Mulliken, Allred-Rochow) at differentiating between the electronegativities of the
transition metals (198-200). As an example, for TiO2: Ti (χ = 1.38) and O (χ = 3.61), therefore
TiO2 (χ ≈ (1.38×3.612)1/3 = 2.62).

RuO2 (𝝌 ≈ 2.72), was firstly selected because it is the most active catalyst for the OER in the
benchmarking literature (Fig. S5) as well as the most active catalyst for the CER (201). IrO2
(𝝌 ≈ 2.78) and FTO (𝝌 ≈ 2.88) were also investigated because they have higher
electronegativities than RuO2, and therefore using ALD to overcoat these catalysts with TiO2
(𝝌 ≈ 2.62) is expected to shift their surface electronic properties (i.e., the potential of zero
charge, EZC) and catalytic activities towards that of RuO2, the optimal single metal oxide
catalyst. In the case of FTO, the electronegativity of SnO2 was estimated because it is not
known how small quantities of F would change the electronegativity of SnO2.
Electronegativity is a useful theoretical concept for estimating the directions in which surface
charge availability and the corresponding catalyst-reacting-species bond strength may move,
but not to estimate the magnitude of change or any complex details of any physical
parameter. These materials were also chosen because TiO2, IrO2, RuO2, and other materials
are commonly used to form mixed metal oxide electrodes, most notably the dimensionally
stable anode (DSA), in which TiO2 increases the anode’s stability, but does not confer
enhanced activity to the aggregated material (202).

5.2.2 Sample Preparation
The three catalysts were prepared on substrates that had very low roughness to minimize
effects in geometric overpotential measurements due to surface area differences.
Specifically, IrO2 and RuO2 samples consisted of a ~300 nm metal-oxide film sputter
deposited on a (100)-oriented Si substrate. The samples were heated to 300 oC and Ir or Ru
were sputtered using an RF source under an Ar/O2 plasma with a constant flow of 20 sccm
Ar and 3 sccm O2 for 22.42 min for Ir, and 13.5 sccm Ar and 1.5 sccm O2 for 22 min for Ru.
The chamber pressure was maintained at 5 mTorr during deposition, and the base pressure
of the chamber was held at < 10-7 Torr between depositions. The phase purity of the samples
was confirmed by X-ray diffraction measurements, as detailed below (Fig. 5.1). TEC 15 FTO

99
glass substrates were used in the case of FTO-based electrocatalysts. TiO2 overlayers were
then deposited on top of the electrocatalysts.
TiO2 films were deposited on IrO2, RuO2 and FTO at 150 °C using an Ultratech Fiji 200
Plasma ALD System (Veeco, Waltham, MA). The IrO2, RuO2, and FTO were prepared as
described above. Prior to ALD, one 0.060 sec pulse of H2O was applied to the sample. Each
ALD cycle consisted of a 0.250 sec pulse of tetrakis(dimethylamido)titanium (TDMAT,
Sigma-Aldrich, St. Louis, MO, 99.999%, used as received), followed by a 0.060 sec pulse of
H2O (18 MΩ cm, Millipore). A 15 sec purge under a constant 0.13 L/min flow of researchgrade N2 was performed between each precursor pulse. While idle, the ALD system was
maintained under a continuous N2 purge with a background pressure of 0.50 Torr.
Following ALD of TiO2, a tungsten-carbide-tipped scribe was used to contact a galliumindium eutectic (Alfa Aesar, Ward Hill, MA, 99.99%, used as received) onto the back side
of the IrO2 and RuO2 samples. A coiled zinc-plated copper wire (Consolidated Electrical
Wire and Cable, Franklin Park, IL) was placed onto the gallium-indium and the wire was
covered with one-sided copper foil tape (3M, Maplewood, MN, used as received).
For the FTO electrodes, a coiled zinc-plated copper wire was placed onto the conductive side
of the FTO electrode and secured with one-sided copper foil tape.
To protect the contact and define the geometric surface area, circular holes were punched in
a strip of 1-inch width 3M vinyl electroplating tape using a 2 or 3 mm diameter circular
punch. The entire electrode was then covered with this tape, only exposing the 3 mm
diameter circle of the electrode. The wire covered the tape for at least 4 cm, such that neither
the wire housing nor the metallic wire was exposed to the electrolyte.

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Figure 5.1 X-ray diffraction patterns for typical IrO2 and RuO2. All observed peaks were
indexed to standard diffraction patterns for IrO2 and RuO2, respectively.

5.2.3 Catalyst Microstructure
The microstructure of a heterogeneous electrocatalyst is important to characterize. Increasing
a catalyst’s surface area, which generally increase the active-site density, can lead to
enhanced catalytic activity without changing the intrinsic catalytic activity of the catalyst (9).
Therefore, understanding a catalyst’s surface morphology is vital to discerning the
mechanism(s) behind enhanced catalytic performance. The microstructure of a typical IrO2based electrocatalyst with a thick (1000 cycle) TiO2 overlayer is shown in the cross-sectional
scanning electron microscopy (SEM) image in Figure 5.2A. The catalyst consists of a
crystalline IrO2 layer with a conformal amorphous TiO2 overlayer.
5.2.3.1 Atomic Force Microscopy
Atomic Force Microscopy (AFM) measurements were conducted to further characterize the
catalysts’ microstructure. A Bruker Dimension Icon was used in Peak Force Tunneling AFM
Mode (PF-TUNA) for all topography and conductive AFM measurements. Even at low cycle
numbers (< 20 cycles) the resulting electrocatalysts were very smooth with low surface

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roughness (Fig. 5.2B) such that the surface area as measured by atomic-force microscopy
(AFM) was roughly equivalent to the measured geometric surface areas (Table 5.1).

Figure 5.2 Material characterization of typical electrocatalyst samples. (A) SEM image of
an IrO2 catalyst with 1000 ALD TiO2 cycles. (B) AFM map of IrO2 with 10 ALD cycles
of TiO2. (C) HAADF-STEM image of an IrO2-based electrocatalyst with 10 ALD cycles
of TiO2. The underlying crystalline material is IrO2 while the hair-like material at the
surface is TiO2. (D,E) Energy dispersive X-ray spectroscopy (EDS) maps of IrO2-based
electrocatalysts with 10 and 40 ALD cycles of TiO2, respectively. The red color indicates
Ir and green indicates Ti. Note that green and red intermix throughout this cross section
due to the inherent roughness of the sample.
Representative surface topology (Fig. 5.3) and conductive AFM (TUNA current) (Fig. 5.4)
for 0, 3, 10, and 1000 ALD TiO2 cycles are shown for IrO2, RuO2, and FTO substrates. AFM
images of RuO2, IrO2, FTO, and substrates coated with 1000 cycles of TiO2 were consistent
with previously reported images of materials grown under similar conditions (203-206).

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Figure 5.3 Representative topographic atomic force microscopy images of IrO2, RuO2, and
FTO each with 0, 3, 10, and 1000 ALD cycles of TiO2.

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Figure 5.4 Representative conductive atomic force microscopy tunneling current images
of IrO2, RuO2, and FTO each with 0, 3, 10, and 1000 ALD cycles of TiO2.

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AFM Measured Surface Area as a
Percentage of Geometric Surface Area
TiO2 Cycle
Number

IrO2

RuO2

FTO

104.52%

107.75%

108.35%

103.87%

102.45%

107.98%

103.12%

103.93%

110.24%

102.94%

104.08%

108.05%

103.32%

104.61%

110.60%

30
40

108.92%
102.70%

102.61%

108.27%
108.18%

103.60%

500

102.00%

1000

102.01%

101.65%

108.10%

111.02%

104.15%

Table 5.1 Surface area (measured by AFM) as a percent of geometric surface area.
Dividing these values by 100 yields topographic roughness factors.
The surface area as measured by AFM was at most 112% of the geometric surface area (Table
5.1). For IrO2 and FTO, the surface topography was similar for all cycle numbers of TiO2.
The only observable change as the number of ALD cycles increased was that the conductivtiy
and surface area decreased uniformly as TiO2 was deposited, suggesting that TiO2 coated the
catalysts’ surface reasonably evenly. Based on AFM data, no holes were visible in the TiO2
coating at any cycle number for FTO and IrO2. The surface topography of bare RuO2 was
rippled (0 cycles), and gradually morphed into a flake-like structure (3-6 cycles), a columnar
structure similar to IrO2 (10-30 cycles), and then back into flakes similar to FTO (>30 cycles).
Furthermore, for RuO2 at 3 ALD cycles some holes in the TiO2 were clearly visible in both
the topological and the conductive AFM images. No such holes were visible at > 3 cycles
TiO2. Conductive AFM showed uniformly drecreasing conductivity with cycle number once
no holes were visible (>3 cycles TiO2).

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5.2.3.2 Transmission Electron Microscopy
The growth rate of ALD TiO2 (0.50-0.65Å/cycle) suggests that for low cycle numbers (< 20
cycles, ~2 nm) the AFM resolution is insufficient to accurately discern the catalysts’ surface
morphology. Therefore, high-resolution transmission electron microscopy images and
energy dispersive x-ray spectroscopy mapswere aquired of 10 and 40 ALD cycles of TiO2
on IrO2 (Fig. 5.2C-E and Fig. 5.5). ALD of 10 cycles of TiO2 on IrO2 exhibited a
semicontinuous film where the majority of imaged areas were covered with TiO2 with
relatively small gaps of what appeared to be uncoated area. However, 40 ALD cycles resulted
in a fully continuous film for all areas imaged.

Figure 5.5 High-Angle Annular Dark-Field Scanning Transmission Electron Microscopy
(HAADF-STEM) images of different IrO2 + 10 ALD cycles of TiO2 samples. The
crystalline sublayer is IrO2 and the “hairy” top layer is amorphous TiO2.

5.3 Catalyst Performance
After TiO2 deposition the samples were tested for their catalytic performance for the OER
and CER. The three major electrocatalyst figures of merit for catalyst performance are the
overpotential, specific activity, and stability. In the following sections, we report the

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performance of our electrocatalysts as a function of TiO2 deposition thickness. Details
regarding the electrochemical testing procedure and analysis can be found in Appendix C.

5.3.1 Catalyst Overpotential
Overpotentials (η; the excess potential beyond the equilibrium potential required to reach a
given current density) were determined for IrO2, RuO2, and FTO as a function of the
successive number of TiO2 ALD cycles for the OER at 10 mA/cm2geo in 1.0 M H2SO4 and
for the CER at 1 mA/cm2geo in 5.0 M NaCl adjusted to pH 2.0 with HCl. Current densities
were chosen to produce > 95% measured Faradaic efficiency for each catalyst (Table S2),
and current-potential data were corrected for the solution resistance (< 2.0 mV correction) as
measured by electrochemical impedance spectroscopy (see Appendix B. 2 for details).
The measured OER overpotentials at 10 mA/cm2geo for bare RuO2 and IrO2 agreed well with
values reported for catalysts prepared on similarly flat surfaces, however we are unaware of
comparable OER data for FTO or for CER catalysts (207). The overpotentials for IrO2 and
FTO, for both the OER and CER, initially showed an improvement (i.e., reduction) with
increasing ALD cycle number, before exhibiting an inflection point due to an increase in
overpotential at higher ALD cycle numbers (Fig. 5.6). The triangular shape observed
between the overpotential and the TiO2 ALD cycle number is typical of a volcano-type
relationship that exemplifies the Sabatier principle (208). The overpotential reductions
between bare IrO2 and FTO catalysts and those at the peak of the volcano curve for the OER
were ∆ηOER ≈ -200 mV at 10 cycles and -100 mV at 30 cycles, respectively. For the CER,
the observed overpotential reductions were ∆ηCER ≈ -30 mV at 3 cycles and -100 mV at 10
cycles, for IrO2 and FTO respectively (Fig. 5.6). A volcano-type relationship between cycle
number and overpotential was also observed for RuO2 facilitating the OER, with ∆ηOER
≈ -350 mV between 0 and 10 cycles. However, for the CER, the overpotential of the RuO2based catalyst increased with TiO2 ALD cycle number.

107

Figure 5.6 Specific activities (js) and overpotentials (η) for the OER and CER on IrO2,
RuO2, and FTO coated at various ALD cycles of TiO2. Overpotentials were measured at
10 mA/cm2geo for the OER and at 1 mA/cm2geo for the CER (normalized to geometric
surface area). Specific activities for the OER were measured at 350 mV (IrO2 and RuO2)
or 900 mV (FTO). Specific activities for the CER were measured at 150 mV (IrO2 and
RuO2) or 700 mV (FTO). The red squares indicate available literature values.

108
5.3.1.1 Electronegativity and Catalytic Activity
To better understand how group electronegativities may be correlated with catalytic activity
for heterogeneous electrocatalysts, group electronegativities were calculated for oxygen
evolution catalysts from this work and for the catalysts compared in Seh et al. and plotted
against overpotentials at 1 mA/cm2AFMSA for each catalyst (Fig. 5.7, Appendix B. 2.1 for
details). The overpotential and electronegativity show a similar volcano-like relationship as
to that of the overpotential and ALD cycles of TiO2, suggesting that the changes in the
thickness of the TiO2 overlayer may be correlated with changes in the group
electronegativity. This is explored further in Section 5.4.

Figure 5.7 Group electronegativity vs overpotential at 1 mA/cm2AFMSA. Overpotential data
was taken from Seh et al. (blue and orange circles) and from this work (red circles). For
LaCrO3, LaMnO3, LaFeO3, LaCoO3, LaNiO3, RuO2, IrO2, and PtO2 group
electronegativites were estimated by taking the geometric mean of the Allen Scale
electronegativities of the constituent atoms. For IrOx/SrIrO3, Ir2SrO7 was assumed for
group electronegativity calculations (209). For IrO2/TiO2, IrTiO4 was assumed for group
electronegativity calculations For NiFeOx, NiFe2O4 was was assumed for group
electronegativity calculations (201). For NiCoOx NiCo2O4 was assumed for group
electronegativity calculations (201). For NiCoOx, NiCo2O4 was assumed for group
electronegativity calculations (201). For CoFeOx, FeCo2O4 was assumed for group

109
electronegativity calculations (201). For CoOx, CoO1.5 was assumed for group
electronegativity calculations (201). For NiOx, Ni2O3 was assumed for group
electronegativity calculations (201).

5.3.2 Specific Activity
The specific activity (i.e., the current density normalized to the electrochemically active
surface area (ECSA)) is a standard quantity for comparing the OER activity of heterogeneous
electrocatalysts. For IrO2 and RuO2 catalysts, the OER specific activities of the uncoated
catalysts were in good agreement with previously reported values (201). We are unaware of
reported specific activities for FTO for the OER or for any catalyst for the CER. The specific
activities for the OER and CER were characterized by volcano-type relationships as a
function of the TiO2 ALD cycle number (Fig. 5.6). In fact, IrO2 coated with 10 ALD cycles
of TiO2 showed an 8.7-fold increase in OER specific activity at η = 350 mV relative to
uncoated IrO2, resulting in the highest ECSA-based specific activity reported to date for Irbased OER catalysts at η = 350 mV in 1.0 M H2SO4. Recently, IrOx/SrIrO3 has been reported
as an especially active catalyst using current normalized to atomic force microscopy
measured surface area (AFMSA) in 0.5 M H2SO4. To compare these catalysts, we measured
the roughness of our catalysts using AFM (Table 5.1). For our catalysts, bare IrO2 exhibited
a Tafel slope of ~60 mV/dec in good agreement with previously reported OER catalysts
(210). As the activity of our IrO2 based catalyst increased from bare IrO2 to 10 TiO2 ALD
cycles, the Tafel slope remained constant at ~60 mV/dec while the exchange current density
(i0) increased from ~1×10-7 to ~2×10-5 mA/cm2AFMSA. Initially the IrOx/SrIrO3 catalyst also
had an OER Tafel slope of ~60 mV/dec and an i0 of ~7×10-6 mA/cm2AFMSA. For the
IrOx/SrIrO3, however, after a period of activation the Tafel slope improved dramatically to
~40 mV/dec, which indicates a previously unknown OER mechanism, while the i0
deteriorated to ~3×10-7 mAAFMSA (Fig. 5.8, Table 5.2). In our case, IrO2 coated with 10 ALD
cycles of TiO2 exhibited lower overpotentials than the freshly prepared IrOx/SrIrO3 catalyst
at current densities < 1 mA/cm2AFMSA and lower overpotentials than the activated IrOx/SrIrO3
catalyst at < 0.02 mA/cm2AFMSA, but substantially higher overpotentials at the more
industrially relevant current densities of > 10 mA/cm2AFMSA (179, 209).

110

Figure 5.8 Tafel plots from IrO2 coated with 0 (dark blue), 3 (orange), 6 (yellow), 10
(purple), and 20 (green) ALD cycles of TiO2 all from this work are shown next to those of
IrOx/SrIrO3 at 0 (red) and 30 (light blue) hrs of activation as taken from literature (209).
To calculate the current density, the surface area was measured by AFM (Table 4.1).

Catalyst
IrO2 + 0 ALD cycles of TiO2
IrO2 + 3 ALD cycles of TiO2
IrO2 + 6 ALD cycles of TiO2
IrO2 + 10 ALD cycles of TiO2
IrO2 + 20 ALD cycles of TiO2
IrOx/SrIrO3 0 h
IrOx/SrIrO3 30 h

i0
(mA/cm2AFMSA)
1.0×10-7
8.0×10-6
2.0×10-5
2.0×10-5
8.0×10-6
7.0×10-6
3.0×10-7

slope
(mV/mA/cm2AFMSA
decade)
59
65
64
61
61
57
38

Table 5.2 A summary of the Tafel slopes and exchange current densities from this work
(IrO2 + TiO2 catalyts) and previous work (SrIrO3 catalysts) (209). All current density data
reported here is based on surface area that is measured by AFM (Table S1).

111

5.3.3 Stability of Enhanced Catalyst Performance
To test the longevity of the enhanced catalytic performance with TiO2 deposition, we
performed 24 h stability testing at 10 mA/cm2 for both the CER and the OER for the uncoated
catalyst and the most active catalyst for each material system. The stability testing procedures
and results are detailed below.
5.3.3.1 24-Hour Stability Test Procedure
For each catalyst, the uncoated and the most active, coated catalysts were tested for 24 h
stability. For the OER, IrO2 with 40 ALD cycles of TiO2 was also tested. 10 mA/cm2 in 1 M
H2SO4 Electrodes were as prepared as described above except, instead of vinyl tape,
electrode surface area was defined by Hysol 9460 epoxy (Henkel, Dusseldorf, Germany)
(209). Geometric surface areas were measured as previously described by scanning the
electrode surface using a Ricoh MP 301 scanner (Tokyo, Japan) and estimating the surface
area using ImageJ software (209). The catalyst stability was assessed by maintaining the
electrodes galvanostatically at either 10 mA/cm2 or 1 mA/cm2 for the OER and CER,
respectively, for 24 hrs. At 0 min, 10 min, 2 h, and 24 h, the electrolyte was replaced with
fresh electrolyte, and either O2(g) or Cl2(g) was bubbled through the solution as described
above. After > 1 min of gas bubbling, electrochemical impedance spectroscopy was
preformed to determine the system resistance followed by 5 CVs which were run from the
OCV to a potential that yielded 10 mA/cm2 or 1 mA/cm2 for the OER and CER, respectively.
The voltage required to reach 10 mA/cm2 for the OER and 1 mA/cm2 for the CER,
respectively, is tabulated in Table 5.3 below. Initial overpotential measurements agree well
with overpotential measurements using vinyl tape on electrodes reported in Fig. 5.9 (Table
S3). A sample 24 h stability test of 0, 10, and 40 ALD cycles of TiO2 on IrO2 under OER
conditions is presented in Fig. 5.9 below.

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Figure 5.9 Example stability testing data of IrO2 + 0 (blue), 10 (orange), and 40 (yellow)
ALD cycles in 1 M H2SO4 at 10 mA/cm2geo.

OER overpotential to reach 10 mA/cm2geo
MOx + X ALD initial 10 min
2h
24 h
Cycles of TiO2
IrO2 + 0 cyc
720
670
N/A
N/A
IrO2 + 10 cyc
540
510
N/A
N/A
IrO2 + 40 cyc
800
610
560
N/A

Reported initial
value (Fig. 1.)
710 ± 30
520 ± 20
810 ± 50

RuO2 + 0 cyc
RuO2 + 10 cyc

770
430

880
470

N/A
440

N/A
N/A

740 ± 70
430 ± 10

FTO + 0 cyc
FTO + 30 cyc

1870
1740

1820
1620

N/A
N/A

1870 ± 50
1720 ± 70

CER overpotential to reach 1 mA/cm2geo
IrO2 + 0 cyc

160

220

230

N/A

148 ± 6

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IrO2 + 3 cyc

120

200

190

122 ± 5

RuO2 + 0 cyc
RuO2 + 60 cyc

140
160

220
160

140
100

210
100

116 ± 6
160 ± 10

FTO + 0 cyc
FTO + 10 cyc

870
760

980
1150

990
1000

970
740

890 ± 30
760 ± 40

Table 5.3 Summary of overpotential data as measured from CVs to reach 10 mA/cm2geo
in 1 M H2SO4 for the OER and 1 mA/cm2geo in 5 M NaCl pH 2.0 for CER at 0 min, 10
min, 2 h, and 24 h of testing in constant current mode. The right-most column displays
the overpotential that was reported in the main text. N/A indicates that a rapid loss in
activity was noticed before the time of measurement.
5.3.3.2 Stability Results
The catalysts investigated herein were not optimized for stability and, as was previously
reported for thin IrO2 and RuO2 catalyst depositions (201, 211), the overpotential on
uncoated catalysts for the OER in 1 M H2SO4 degraded rapidly after < 1 h of operation at 10
mA/cm2geo. For thinly coated catalysts (3-10 cycles) the OER stability improved from about
1 h to about 4 h, while for thicker TiO2 coatings (> 30 cycles) the OER stability increased to
> 9 h (Fig. 5.9). For the CER, all catalysts were relatively stable over the 24 h testing period
except for the FTO-based catalysts which followed the same trend as the OER, with thicker
TiO2 coatings stabilizing the electrodes.
X-ray photoelectron spectra were taken before and after 24-hour stability testing to
understand the longevity of the catalytic enhancement. Figure 5.10 shows XPS spectra of the
Ti 2p core-level before and after testing for the catalysts with the lowest overpotential for the
OER for each materials system, 10 cycles, 10 cycles, and 30 cycles of TiO2 for IrO2, RuO2,
and FTO, respectively. After testing, no Ti species was detectable for any of the
electrocatalysts tested in this study, which correlates well with the loss in catalytic
performance over the duration of the stability test. The peak in the Ti 2p region for RuO2
after testing is due to the Ru 3p core-level peaks and not to species associated with TiO2.
XPS spectra were also collected after 24-hour stability tests of the electrodes for the CER.

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Unlike for the OER, all electrocatalysts (except for the FTO based catalysts, which
performed similarly as for the OER) showed stable performance over the duration of the
stability test. XPS spectra after testing indicate that TiO2 films are still present. A
representative XPS spectra of the Ti 2p region for a RuO2-based electrocatalyst before and
after stability testing for the CER is shown in Fig. 5.11.
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After

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FTO

467 465 463 461 459 457 455 467 465 463 461 459 457 455
Binding Energy (eV)
Binding Energy (eV)

Figure 5.10 X-ray photoelectron spectroscopy of the Ti 2p region for IrO2, RuO2, and FTO
electrocatalysts with 10 cycles, 10 cycles, and 30 cycles of TiO2, respectively, before and
after stability testing for the OER. Note the peak still visible in the “after” RuO2 spectra is
associated with the Ru 3p core levels.

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Normalized Counts (arb. units)

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Figure 5.11 X-ray photoelectron spectroscopy of the Ti 2p region for an RuO2
electrocatalyst with 60 cycles of before and after 24-hour stability testing for the CER. The
TiO2 is still present after testing.

5.4 Catalyst Surface Electronics
The enhancement in catalytic performance observed with deposition of TiO2 is not readily
explained by surface morphological changes of the electrocatalyst. Deposition of TiO2 does
not substantially affect the electrochemically active surface area, a metric believed to be
related to active site density, and changes in the surface area alone do not account for the
magnitude of the enhancement in the specific activity (Fig. 5.6). Furthermore, while highangle annular dark-field scanning transmission electron microscopy (HAADF-STEM)
images and STEM electron dispersive X-ray spectroscopy (EDS) maps of IrO2 samples with
10 cycles of TiO2 (Figs. 5.2C, D) indicate that the TiO2 film is semi-continuous with small
areas of the underlying IrO2 exposed, deposition of 40 cycles of TiO2 results in a uniform,
continuous film (Fig. 5.2E) and catalysis commensurate with the bare IrO2 samples. These
facts suggest the phenomenon does not arise from surface morphological effects alone,

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instead suggesting that TiO2 is playing a partial role in enhancing the activity of the active
sites. To that end we investigated the catalysts’ surface electronic properties using the
potential of zero charge and x-ray photoelectron spectroscopy.

5.4.1 Potential of Zero Charge Measurements
To investigate the electrocatalysts’ surface electronic properties the potential of zero charge
(EZC) of the electrocatalysts was measured as a function of TiO2 thickness (Fig. 5.12). EZC is
the potential that must be applied to produce a neutral surface and is an indicator of a
material’s willingness to lose electrons, with more positive EZC values indicating surfaces
that are less willing to lose their electrons (see Appendix B. 7). EZC thus yields insight into
the strength of the bonds on the catalyst surface (212, 213). Measured EZC values for bare
RuO2 and IrO2 (50 and 30 mV vs. SCE, respectively) were consistent with previously
reported values for Ru and Ir (214). We are unaware of reported EZC values for FTO. As the
RuO2 and IrO2 samples were coated with increasing ALD cycles of TiO2 the EZC shifted from
lower to higher potentials in both cases and eventually reached the value for bulk TiO2. This
behavior is consistent with the expected trends for equilibrated group electronegativities.
The EZC for bare FTO (450 mV vs SCE) was less than that for bulk TiO2 and greater than
bare IrO2 or RuO2. The FTO EZC decreased with increasing TiO2 cycles up to 10 cycles and
as the TiO2 cycles increased beyond 10 the EZC increased until it reached the bulk value of
TiO2 at large cycle numbers. The overall trend of the FTO EZC increasing to higher values
with increasing TiO2 cycle number is consistent with group electronegativity arguments.
However, the intermediate behavior where the EZC decreases and then increases is not well
explained by group electronegativity and could, in part, arise from the complicated behavior
of the F dopant atoms (further discussion on the limits of group electronegativity are found
in the Supplementary Materials). For all catalysts, the EZC continued to shift even beyond the
point where TEM data indicated that the film is continuous (40 ALD cycles). This suggests
that the exposed metal oxide is not fully responsible for the shift in EZC and that the surface
TiO2 is likely responsible in part for the Ezc shift. Shifts in EZC with incremental TiO2
deposition suggest that ALD can be used to tune the catalytic performance. These data reveal

117
that the catalysts with the highest activity for the CER have EZC values between 50 and
75 mV vs SCE (Fig. 5.12), consistent with the observation that addition of TiO2 layers to
RuO2 decreased the activity of RuO2 electrocatalysts (EZC = 50 mV vs SCE) for the CER.
Additionally, active OER and CER catalysts for all systems investigated have EZC values
between 25 and 200 mV vs SCE with the best OER catalysts having a somewhat higher EZC
(~110 mV vs SCE) than the best CER catalysts (~60 mV vs SCE).

118

Figure 5.12 EZC of IrO2 (blue), RuO2 (red), and FTO (green) anodes coated with various
ALD cycles of TiO2. Black dots and circles with black borders indicate the catalysts with
the highest specific activity for each catalyst for the OER and CER, respectively.

5.4.2 XPS Characterization of TiO2 Coated Catalysts
To further understand the surface states of the catalysts, X-ray photoelectron spectroscopy
was used to measure the Ti oxidation state. Details of the data collection and peak fitting can
be found in Appendix D. Analysis of the catalyst XPS is found below.

119
5.4.2.1 Ti 2p Core-level Photoemission Spectra
Figures 5.13 and 5.14 show the Ti 2p3/2 and full Ti 2p core-level photoemission, stacked from
bottom to top, for increasing ALD TiO2 thickness, with 0 cycles indicating the bare catalyst
substrate. Deposition of low cycle numbers of ALD TiO2 on IrO2 and RuO2 produced Ti
core-level peaks that were at ~456.6 eV and ~457.6 eV, which is consistent with previously
reported binding energies for Ti3+ states (215, 216). As the ALD cycle number increased, the
Ti oxidation state for these samples gradually increased to its bulk oxidation state (~+4), and
signals indicative of bulk TiO2 were eventually observed (Figs. 5.13 and 5.14). In the case
of ALD TiO2 on FTO, the lower cycle number thicknesses instead produced binding energies
primarily at the bulk position, in addition to a peak at a higher binding energy. This additional
peak can be ascribed to a mixed phase between the substrate (FTO) and the thin TiO2 film,
in which the chemical nature of the phase produces a more oxidized metal, with the mixed
phase most likely dominated by Ti4+ sites.

120

Figure 5.13 X-ray photoelectron spectroscopy of the Ti 2p3/2 region for IrO2, RuO2, and FTO
catalysts with varying TiO2 thicknesses. Bulk TiO2 is shown as the blue peak in each
spectrum. The slightly and highly reduced Ti peaks are shown in green and red, respectively,
and the most highly oxidized Ti peak is shown in orange.

121

Figure 5.14 X-ray photoelectron spectroscopy of the Ti 2p region for IrO2, RuO2, and FTO
catalysts. Bulk TiO2 is shown as the blue peak in each spectrum. The slightly and highly
reduced Ti peaks are shown in green and red, respectively, and the most highly oxidized
Ti peak is shown in orange.
The variation in the Ti oxidation state with ALD TiO2 cycles is accompanied by a peak shift
of the Ti2p3/2 peak relative to the bulk TiO2 peak position (Fig. 5.15). The Ti2p3/2 peak of the
IrO2- and RuO2-based catalysts shifts from reduced, lower binding energies to the more

122
oxidized, higher binding energies typical of bulk TiO2. The FTO-based Ti2p3/2 peak shifts
from more oxidized, high binding energies at low TiO2 cycles to lower binding energies for
intermediate TiO2 cycles (10-40 cycles) before increasing again to higher binding energies
at large TiO2 thicknesses (>60 cycles). The Ti2p3/2 peak shift is qualitatively consistent with
the variation in Ezc with TiO2 cycle number suggesting that the change in the surface charge
density is correlated with a change in the Ti oxidation state.
0.2
0.

Peak shift (eV)

-0.2
-0.4
-0.6
IrO2

-0.8

RuO2
FTO

-1.
-1.2

100

Cycles of TiO2

Figure 5.15 Ti 2p3/2 overall peak shift relative to bulk TiO2 as a function of TiO2 cycle
thickness for IrO2, RuO2, and FTO.
5.4.2.2 Metal-oxide Core-level Emission Spectra
The shift in the Ti 2p3/2 peak position and variation in the Ti oxidation state with TiO2
thickness can be explained by charge transfer from the underlying metal oxide substrate. In
this scenario, a more reduced Ti species present at low deposited cycles of TiO2 on IrO2 and
RuO2 would be accompanied by a more oxidized metal oxide substrate. In order to confirm
this hypothesis, we measured the Ir 4f, Ru 3d, and Sn 3d core-level photoemission (Fig.

123
5.16). Unlike in the case of the Ti 2p spectra, the Ir 4f, Ru 3d, and Sn 3d core-level
photoemission exhibited very small changes between the bare metal oxide substrate and
those with varying thicknesses of TiO2. This was reflected in the peak shifts of the main peak
for the Ir 4f, Ru 3d, and Sn 3d spectra with TiO2 thickness relative to that of the bare substrate
(Fig. 5.16), which were an order of magnitude lower than those for the Ti 2p core-level
photoemission and mostly within the error of the measurement (± 0.1 eV). While peak fitting
(see Appendix C) of these spectra indicates that initial deposition of TiO2 leads to a slightly
more oxidized Ir and Ru state, and a slightly more reduced Sn state for FTO, no trend with
thickness was observed for any of the substrates, and changes in the oxidation state of the
underlying catalyst are likely below the detection limit for the techniques used in this study
(Fig 5.16, 5.17, and Table 5.4).

124
r 4f

Ru 3d

Sn 3d5 2

288 285 282 279
B nd ng Energy eV

490 488 486 484
B nd ng Energy eV

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70 68 66 64 62 60
B nd ng Energy eV

Figure 5.16 X-ray photoelectron spectroscopy of the Ir 4f, Ru 3d, and Sn 3d5/2 region for
IrO2- RuO2- and FTO-based electrocatalysts as a function of TiO2 thickness.

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Metal oxide peak shift (eV)

0.2

-0.2

IrO2

-0.4

RuO2
FTO

-0.6

100

Cycles of TiO2

Figure 5.17 Overall peak shift of the main peak of the Ir 4f, Ru 3d, and Sn 3d5/2 spectra
relative to the bare metallic (0 cycle) metal-oxide substrate as a function of TiO2 cycle
thickness for IrO2, RuO2, and FTO, respectively.
TiO2 Cycles
10
20
30
40
50
60
100

Ir 4f
4.76
4.73
4.7
4.95
8.78
4.65
6.86

Ru 3d
1.42
1.34
1.33
1.51
1.58
1.59
1.62
1.52

Sn 3d
0.42
1.30
0.81
0.69
0.41
0.50
1.01
0.435

Table 5.4 The areal peak ratios of the main peak to the satellite peak for the Ir 4f, Ru 3d,
and Sn 3d core-level photoemission.

126

5.5 Conclusion
In summation, surface characterization suggests that atomic layer deposition of low cycle
numbers of TiO2 can tune surface electron densities of the catalyst in a direction consistent
with predictions from group electronegativity concepts (Fig. 5.6). Given that concomitant
changes in electrochemical activity were observed with deposition of TiO2, this approach is
a promising method to tune the performance of other electrocatalysts (beyond metal oxides)
for diverse reactions, including those critical for renewable energy storage and wastewater
treatment.

127

Chapter 6
Conclusion and Outlook
Throughout this thesis we have presented analyses and developed technologies for highefficiency photovoltaics and electrocatalysis with the goal of enabling a pathway to a netzero carbon emission energy system. Such an energy system relies on a renewable electricity
grid and thus our research in photovoltaics centered around increased efficiency, which is a
primary driver in reducing the levelized cost of electricity, the metric by which all electricity
generating technologies are ultimately evaluated. We developed two new models for
evaluating the photovoltaic efficiency limits in new (and existing) materials and
demonstrated the first interconnect-free tandem silicon/perovskite solar cell with a 24.1%
efficiency. Our work also focused on new methods to improve electrocatalysis which is key
to enabling the clean production of fuels and commodity chemicals. Our technique allows
for the tuning of the catalytic activity of multiple electrocatalysts for a variety of reactions.
In Chapter 2, we presented a modified detailed balance model in which we took into account
the non-ideal absorption profile of photovoltaic materials. We showed that there is an
intimate relationship between the sub-gap absorption tail and a photovoltaic’s efficiency and
luminescence. In particular, we found that significant sub-gap absorption (Urbach parameter,
𝛾 > 𝑘š 𝑇) nullifies the notion of a single forbiddgen gap and leads to a distribution of band
gaps that limits the quasi-Fermi level splitting and thus the open-circuit voltage. The
generalized absorption parameterization used in this model can be directly fit to the
experimentally measured absorption of real materials. Thus in tandem with our model,
careful measurement of the sub-gap absorption (and/or emission) profile can yield insights
into the efficiency limits of a candidate photovoltaic material.
We further analyzed material efficiency limits in Chapter 3, where we examined the effects
of excitons on photovoltaic performance using cuprous oxide (Cu2O) as a case study.
Excitons are the fundamental optical excitation in a slew of emerging materials with large

128
exciton binding energies (>>100 meV, e.g. the transition metal dichalcogenides)). In
Cu2O, for example, we found that the quasi-equilibrium excitation density is comprised of
greater than 20% excitions under photovoltaic operating conditions. Excitonic signatures
were found in the photoluminescence of Cu2O and in the spectral response of Cu2O/Zn(O,S)
photovoltaics. Using a device physics model that accounted for excitonic effects, we found
that the ultimate photovoltaic efficiency of Cu2O solar cells is underestimated by 2 absolute
percent when excitons are neglected.
In Chapter 4, we demonstrated a novel tandem device architecture in which the top and
bottom cells are interconnected without the use of a tunnel junction or recombination layer.
We realized this device using a perovskite top cell fabricated directly on top the silicon
bottom cell. The electron selective contact, a TiO2 layer deposited by atomic layer deposition,
spontaneously formed a recombination layer in the form of an atomic-scale defect layer at
the Si/TiO2 interface. Tandem photovoltaics incorporating this interconnect-free design
reached photovoltaic efficiencies in excess of 24% with thousands of hours of stability. The
interconnect-free design is compatible with other solar cell types (e.g. HIT cells) as well as
textured cells and has superior optical and processing properties compared to the traditional
ITO contact used in other silicon/perovskite tandems. Importantly, our simulations show that
the interconnect free tandem design enables a pathway to low cost, high efficiency (>30%)
silicon/perovskite tandems.
Finally, in Chapter 5 we develop a method to tune the catalytic activity of heterogeneous
electrocatalysts for the chlorine-evolution and oxygen-evolution reactions. Specifically, we
showed that atomic layer deposition of TiO2 (~3-30 cycles) on RuO2, IrO2, and FTO
electrocatalysts resulted in significant enhancement of the catalytic activity (an 8.7-fold
increase in the case of IrO2 for the OER) and a reduction in hundreds of mVs in overpotential
compared to the uncoated catalysts. The enhancement in catalytic performance was
associated with an alteration of the surface electronics of the catalyst in a manner consistent
with simple arguments in group electronegativity. Our results suggest that atomic layer

129
deposition may be a promising tool to tune the catalytic performance of other catalysts
(beyond metal oxides) for a variety of important chemical reactions.
This work took important steps towards a net-zero carbon energy system but the road to
realizing such a system is an arduous one. Although adoption of solar photovoltaics is on the
rise, the majority of global electricity generation is still derived from dirty fossil fuel sources
and while our results on electrocatalyst enhancement are promising, many new
electrocatalysts must be developed if traditional CO2-intensive reactions are to be replaced.
Beyond electricity generation and fuel/chemical production, many CO2 emissions are
difficult to eliminate (e.g. those associated with steel and cement production) (6). It is my
sincere hope that this work inspires smart people, like the ones I have worked aside at
Caltech, to continue to be driven to reduce societies reliance on a centuries-old, dirty energy
system.

130

Appendix A
Band Tailing Code
The Mathematica code used for calculating the modified detailed balance model of Chapter
2 is provided in the following pages.

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Appendix B
Floating Zone Crystal Growth
B.1 Zone Melting Background
Zone melting or zone refining, is a crystal growth technique developed by William Pfann at
Bell Labs for the purification of germanium for use in transistors (217). Unlike in a normal
freezing process (Fig. B1, top) where solidification occurs as the solid-liquid interface
advances, in zone melting (Fig. B2, top) a molten zone is passed along the length of a solid.
As the zone advances, new, previously unmelted solid is melted at the leading solid-liquid
interface joining the molten zone and leaving behind a purer, recrystallized solid at the
trailing solid-liquid interface.
The distribution of solute (impurities) in a solid is largely governed by its distribution
coefficient k, the ratio of solute in a material’s solid phase to that in its liquid phase. k < 1,
indicates that an impurity will result in the lowering of the freezing temperature of the liquid
phase of a material. This is typical for most materials. In a normal freezing process, where
we have assumed that there is no diffusion in the solid and the solute concentration is uniform
in the liquid, the concentration C of solute in the solid after a fraction g depends on the
distribution coefficient as follows (217):
Ým

= 𝑘(1 − 𝑔)¸bc

(1)

where, C0 is the original solute concentration in the liquid. This results in a non-uniform
distribution of solutes for a solid that has undergone normal freezing (Fig. B.1, bottom). The
concentration of solute across the length of the solid is much different in a zone melting
process. A single pass of the zone melting process results in (217):

Ým

= 1 − (1 − 𝑘 )𝑒

b¸r/T

191
(2)

where, 𝑙 is the length of the molten zone. As can be seen from Fig. B.2, for k < 1, this results
in a region of purification and a region of uniform impurity distribution in the solid. As the
molten zone proceeds along the rod, it freezes out (at x = 0) a concentration kC0 but melts
unpure material at the leading edge of the molten zone, thus increasing the concentration of
impurities in the zone and subsequently solidifies out higher concentrations. This process of
purification continues (at an ever-decreasing rate) until the concentration of impurities in the
molten zone becomes C0/k and the solid freezing out has the same impurity concentration as
that being melted. After this point is reached the impurity concentration remains constant in
the solid until the end of the road (x = L-l) is reached and normal freezing occurs. Using
multiple passes of the molten zone the degree of purification and size of the purification
region can be greatly extended.

192

Normal Freezing
Fraction
Solidified

Solid

Liquid

k=5

Solute Concentration, C

k=3
k=2

0.50

k=0.9
k=0.5

k=0.1

0.10
0.05

k=0.01

0.01
0.

0.2
0.4
0.6
0.8
Fraction solidified, g

Figure B.1 (Top) Diagram of the typical solidification process, known as normal freezing.
The distribution of solute (impurities) in the solid is controlled by the distribution
coefficient k, the rate of the advance of the solid-liquid interface, and the mixing in the
liquid. (Bottom) The solute concentration for a normal freezing process as a function of
the fraction of solidification for different distribution coefficients k.

193

Zone Melting
Heater

Crystallized
Solid

Length
Solidified

Molten
Zone

Unmelted Solid

Figure B.2 (Top) Diagram of the zone melting process, in which a molten zone is passed
along the length of a solid. (Bottom) The solute concentration for the zone melting process
as a function of the fraction of solidification for different distribution coefficients k. Zone
melting results in regions of purification and uniform solute distribution.

194

B.2 The Floating Zone Method
The floating zone method is a technique that developed out of traditional zone melting for
materials that are reactive or effective solvents when molten. The floating zone technique
was originally developed for the growth and purification of single crystalline silicon and is
still widely used for the growth of high-quality silicon in industry today. As the name
implies, the floating-zone technique, as depicted in Fig. B.3, employs a molten zone
suspended between two vertical rods that is held in place by only its own surface tension.

Figure B.3 Image of a floating zone during growth of single crystalline Cu2O. The bright
regions in the background are the halogen lamps which serve as the heat source.
A typical floating zone apparatus is depicted in Fig. B.4. As in regular zone melting, the solid
sample to be refined is generally suspended in a quartz tube which allows for control of the
growth atmosphere and viewing the crystal during growth. The heating sources for the

195
floating zone technique vary but induction, electron beam, and optical heaters are the
most common. Research-grade floating zone growth furnaces are now available
commercially from Crystal Systems Inc.
Before Contact

After Contact

Feed rod
Quartz
Tube

“Floating”
Molten Zone

Molten tips

Heater
Seed rod

Figure B.4 Typical floating zone setup before (left) and after (right) the feed and seed rods
are brought into contact

B.2.1 General Growth Process Overview
The floating zone growth process begins with two solid cylindrical rods: a so-called seed rod
and a feed rod. Ideally, the seed rod is single crystalline in nature, providing a “seed” for the
crystal orientation of the new growth. If a single crystalline seed is not available, a
polycrystalline rod may be used as the seed. A polycrystalline rod can effectively function
as a single crystalline seed if a single grain is isolated (e.g. by sharpening the rod to a point)
or if the grain size is large enough that the seed rod only “sees” one grain. The feed rod plays
the role of the unmelted solid in Fig. B.2, providing the material feedstock for the refined

196
crystal. In most cases the feed rod is considerably longer than the seed rod, which need
only provide the growth template, so that a sufficiently large crystal can be grown.
At the beginning of growth, the feed rod and seed rod are separated. The rods are then brought
into close proximity and heat is applied so that the tips of the rods become molten (Fig. B.4,
left) and typically made to rotate to improve heating uniformity. Once molten, the rods are
slowly moved together until the molten tips touch and a molten zone is formed (Fig. B.4,
right). The molten zone is then moved up the length of the feed rod at the selected growth
rate generally slowly (~1-20 mm/hr) to allow sufficient time for recrystallization. When the
end of the feed rod is reached the feed rod is separated from the newly grown crystal, unless
multiple passes are to be made.

B.3 The Caltech System
B.3.1 The Floating Zone Furnace
The floating zone furnace that was used in this work is a Crystal Systems Inc. Model FZ-T4000-H-VII-VPO-PC housed in the Molecular Materials Research Center at the Beckman
Institute at Caltech. The furnace (Fig. B.5) is an optical floating zone furnace which employs
four 1 kW halogen lamps as the heating source. The lamps are focused by 4 ellipsoidal
mirrors (Fig. 4B) to produce a heating zone on the order of ~1-3 mm. The optical heating
system is capable of reaching temperatures up to 2000 ºC, although measurement of the
actual temperature of the molten zone is very difficult as the lamps operate on a percentage
of full power rating system.
In this setup, the seed rod is affixed to a sample post and the feed rod is hung from a malleable
hook, which allows for adjustment in the alignment of the rods. Growth is accomplished by
moving the lamp assembly up along the length of the feed rod and be monitored by a CCD
camera that is part of the lamp assembly. The growth atmosphere is controlled by gas housing
and can be configured to be air, O2, Ar, or vacuum at a variety of pressures.

197
The manual provided by Crystal Systems Inc. is thorough and provides step by step
instructions for operating the furnace and is available on the MMRC website. Tips for
successful growth are provided later in this appendix.

Figure B.5 The optical floating zone furnace from Crystal Systems Inc. Adapted from
(218).

B.3.2 Growth of Feed Rods
In order to ensure a stable molten zone, an appropriate sized and shape feed rod must be
fabricated. The stability and shapes of the molten zone have been treated theoretically (219,
220) and verified experimentally. While there is no theoretical upper limit to the diameter of
the feed rod, large diameters generally are more difficult to stabilize because of the large heat
requirement necessary to melt the entire cross section. A general rule of thumb is to use feed
and seed rods with the same diameter. The Crystal Systems Inc. system supports 0.5 cm and
1 cm seed rods, and thus those sized feed rods were also targeted.

198
Feed rods were grown in the Bridgeman vertical tube furnace (Fig. B.6). The vertical tube
furnace includes a crane assembly that can be programmed to ensure the length of the rod is
evenly heated in the furnace’s primary heating zone. Operation instructions for the vertical
tube furnace and crane assembly are available on the MMRC website.

Figure B.6 The Bridgeman vertical tube furnace and crane assembly (218).
Rods were suspended from the crane via a hook. To attach the sample rod to the furnace
hook, a hole was (carefully) drilled into the rod and a metallic wire was fed through the hole
and tied to make a support ring. It is important to note that the wire must be mechanically

199
stable enough to support the sample rod during the feed rod growth and floating zone
processes. Metals that oxidize and become brittle may not be suitable for this purpose and
therefore, platinum is generally because of its high temperature stability and resistance to
oxidation.

B.3.3 Tips for Floating Zone Growth
Floating zone growth, and crystal growth in general, is somewhat of a black magic. Although
the theory of the floating zone growth technique is well established, there is no way to predict
a priori the growth parameters necessary to create a stable molten zone for a given material.
As such, the floating zone process is often time consuming and requires lots of trial and error
(read frustrating). I have provided tips below that should ease some of the pain.
0. Be patient – Read the above. Crystal growth is hard and floating zone growth is slow
even when it works. But if things go work
1. Read the literature – The crystal growth community is large and it has been around
a long time. Someone has probably tried to grow what you are trying to grow before
or at least something similar and although their system was likely different their
growth parameters can be used as a guide.
2. Be clean – Impurities are bad and can have a major effect on the outcome of your
growth. Clean the quartz tube when growing a new material and have dedicated tools
(tweezers, beakers, etc.) for each material system.
3. Alignment of Feed and Seed Rods – In alignment of the feed and seed rod during
the growth is one of, if not the most, important factors that dictates the stability of the
molten zone. If the feed and seed rods are misaligned along the rotational (vertical)
axis then it is very hard to stabilize the zone and uneven heating may occur. Spend
the time to carefully align the feed and seed rods before growth begins and adjust the
feed rod accordingly during growth if it becomes off-axis.

200
4. Correctly Size the Seed (and Feed) Rod – As mentioned above, misalignment
along the vertical axis can lead to an unstable molten zone. Because the Crystal
Systems Inc. float zone furnace uses seed rod sample holders of a fixed diameter (0.5
cm and 1 cm), attempting to use a seed rod of a larger or smaller size will result in
the seed rods rotation axis differing from that of the sample holder and consequently
the feed rod (see Fig B.7). Maintaining a stable zone during growth under such
conditions is extremely difficult.
5. Ensure the Seed and Feed Rods are Cylindrical – This helps with alignment. See
tips 3 and 4, above.

Figure B.7 Top view of a seed rod sample holder (gray) with an improperly sized seed rod
(red) during different stages of rotation. The sample holder is sized for a sample of the size
traced out by the black dashed circle. The center of a seed rod this size is collinear with the
rotational axis (black dot) of the sample holder and feed rod. The improperly sized seed
rod, however, has a rotational axis (red dot) different than that of the sample holder. Thus,
rotation of the sample holder leads to the center of the seed rod tracing a circle around the
axis of rotation of the float zone assembly (black dot). This leads to a “wobbly”, unstable
molten zone.

201

Appendix C
Electrochemical Methods for Catalysis
C.1 Experimental Setup and Catalyst Testing
With assistance from a large-gauge needle guide, the lead of each electrode was inserted
through a rubber septum, and the electrode was placed in a 25 mL, 14/20, 4-necked, round
bottom flask (Chemglass, Vineland, NJ). The flask was filled with 15 mL of 1.0 M H2SO4
or 5.0 M NaCl at pH 2.0 (adjusted using HCl and measured using a calibrated Thermo
Scientific Orion 3 Star pH probe). A saturated calomel electrode (SCE; CH Instruments,
Austin, TX) reference electrode was washed and placed in the solution.
For OER and CER experiments, O2(g) or Cl2(g) was flowed through a bubbler that contained
either 1.0 M H2SO4 or 5.0 M NaCl at pH 2.0, respectively, and then into the reactor using a
Teflon tube that extended ~1 cm below the surface of the electrolyte. To ensure that the
reactor was pressurized to 1 atm, gas could freely escape through an identical Teflon tube
that went from the reactor flask to the back of the fume hood. Prior to data collection, the gas
was bubbled through the solution for > 1 min. The counter electrode was a 0.5 mm diameter
coiled platinum wire (Sigma Aldrich, 99.9%). All purging and experiments were performed
under continuous stirring. The distance between the working electrode and reference
electrode was 1.0 cm.
To measure overpotential, the following experiments were run on a Bio-Logic (SeyssinetPariset, France) potentiostat/galvanostat model VSP-300 with EIS capability:
1) Open circuit voltage for 30 sec.
2) Two cyclic voltammograms (CVs) to clean the electrode, scanning from 1.0 to 1.45 vs
SCE for RuO2 and IrO2 in 1.0 M H2SO4 (prior to OER); from 1.2 to 1.8 vs SCE for FTO in

202
1.0 M H2SO4 (prior to OER); from 1.1 to 1.2 V vs SCE for RuO2 and IrO2 in 5.0 M NaCl
at pH 2.0 (prior to CER); and from 1.1 to 2.0 V for FTO in 5.0 M NaCl at pH 2.0 (prior to
CER).
3) Hold the potential at open circuit for 30 sec.
4) Two CVs to measure the overpotential, scanning from 1.0 to 2.5 vs SCE for RuO2 and
IrO2 in 1.0 M H2SO4 (OER), 1.5 to 3.5 for FTO in 1.0 M H2SO4 (OER), 1.1 to 1.35 V vs
SCE for RuO2 and IrO2 in 5.0M NaCl at pH 2.0 (CER), and for 1.1 to 3.0 V FTO in 5.0 M
NaCl at pH 2.0 (CER).
All CVs were conducted at a 5 mV/sec scan rate and were corrected for solution resistance
as described below, unless otherwise stated. The system resistance was also measured for
each sample prior to each experiment. For each electrode, at least 4 replicates were tested.

C.2 Calculating Overpotentials
For the OER, standard conditions were assumed, and the thermodynamic potential of 1230
mV vs RHE was used to determine the OER overpotential at 10 mA/cm2.
For the CER, the activity for Cl- was estimated to be 4.36 using the Pitzer model (221) and
the fugacity of 1 atm Cl2 was taken to be 0.07267 (222). Using these values, a thermodynamic
potential of 1288 mV vs NHE was calculated from the Nernst equation.

C.2.1 Electronegativity and Overpotential Calculations
Group electronegativities were calculated for oxygen evolution catalysts from this work and
for the catalysts compared in Seh et al. and plotted against overpotentials at 1 mA/cm2AFMSA
for each catalystLike in Seh et al., for catalysts with no AFM data, if they were prepared on
flat substrates (e.g. (100) silicon), a roughness factor of 1 was assumed(179). In the case of
catalysts with undefined elemental ratios, XPS data on the oxidation state was used to

203
estimate elemental composition, and then fractional compositions were rounded to the
nearest half. If there was no XPS data, Pourbaix diagrams were consulted and the
predominant species at the relevant potentials were used for group electronegativity
calculations. In most cases, assumptions were the same as the assumptions made for active
site composition in Seh et al. For layered catalysts (e.g. IrOx/SrIrO3) the geometric mean of
all the atoms in the overlayer and underlayer was used as the group electronegativity of the
material. Overpotentials at 1 mA/cm2AFMSA was either taken from Seh et al. or from this
work. Most overpotential data presented in Fig. 5.6 was collected in a basic electrolyte (blue
circles), for catalysts tested in acidic electrolytes, red circles indicate values from this work
measured in 1 M H2SO4 and the orange circle indicates the catalyst tested in 0.5 M H2SO4
from Seitz et al. (209). Electronegativity, like other theoretical constructs that are related to
bond strength, demonstrates a nice volcano type correlation with activity for the oxygen
evolution reaction (209).

C.3 Calculating Faradaic Efficiency
For the OER, the faradaic efficiency of the electrodes was measured as previously described
using a pneumatic trough (223). A graduated cylinder was filled with electrolyte and placed
upside down in a bath of electrolyte. The working electrode was inserted to a height > 1 cm
into the cylinder. The reference electrode was placed near the cylinder and the counter
electrode was placed > 5 cm away from the cylinder. The cylinder was closed to the bulk
solution except for the pour spout of the cylinder, hence ions were allowed to pass freely.
The electrode was biased to pass 10 mA of current at 10 mA/cm2geo, and the resulting oxygen
bubbles were collected in the cylinder for 1 h. The resulting head-space volume was
measured and compared using the ideal gas law to the expected total charge passed. Similar
to other studies, 105-115% faradaic efficiencies were measured (Table S2). The excess is
attributed to electrolyte sticking to the cylinder walls, narrowing the diameter of the cylinder.

204
For the CER, electrodes were operated at a constant current of 1mA/cm geo for 10 min in

15 mL of 5.0 M NaCl at pH 2.0, which, given 100% faradaic efficiency, should yield 22.08
ppm Cl2(g) in our experimental configuration. Immediately after the reaction, one milliliter
of electrolyte was transferred to a 25 mL beaker and chlorine was measured by titrating
excess potassium iodide with a starch indicator using 0.50 mN Na2S2O3 (224). Greater than
90% faradaic efficiency was measured for samples with 40-60 ALD cycles of TiO2 and
greater than 95% faradaic efficiency was measured for samples with fewer than 40 ALD
cycles of TiO2 (Table B.1).
OER
TiO2 Cycle
Number

CER

IrO2

RuO2

FTO

IrO2

RuO2

FTO

108%

122%

114%

101%

95%

97%

86%

96%

99%

102%

120%

122%

97%

99%

96%

120%

107%

103%

101%

96%

98%

114%

122%

114%

96%

99%

96%

114%

104%

95%

98%

15
20

114%
117%

122%

114%

120%

114%

108%

114%

95%

91%

103%

114%

120%

114%

103%

91%

95%

113%

100

114%

107%

114%

92%

91%

15%

Table C.1 Faradaic efficiencies for the OER and CER

C.4 Determination of Solution and System Resistance
The solution resistance was estimated using electrochemical impedance spectroscopy on a
coiled Pt wire working electrode and Pt wire counter electrode system. The wire coil was 3

205
mm in diameter to simulate the working electrode and was placed 1 cm from the SCE
reference electrode to simulate the distance between working and reference electrode.
Measurements were taken in 5.0 M NaCl at pH 2.0 under 1 atm Cl2 (CER) or in 1.0 M H2SO4
under 1 atm O2 (OER). No correction was performed for the resistance of the Pt electrodes,
due to the low resistivity (< 0.0001 Ω/cm) of Pt. For 5.0 M NaCl at pH 2.0, a solution
resistance of 3.45 ± 0.02 Ω was measured. For 1.0 M H2SO4, a solution resistance of 1.91 ±
0.02 Ω was measured. These values were used to correct the electrodes for the IR drop. No
correction was made for the electrode resistivity, as it is an intrinsic electrode property.
Typical corrections from solution resistance were ~1.4 mV and ~0.3 mV for the OER at 10
mA/cm2geo and the CER at 1 mA/cm2geo respectively.
The system resistance was also measured as described above, but instead of Pt wire TiO2
coated IrO2, RuO2, and FTO electrodes were used as the working electrodes. The measured
solution resistance was a lower bound for the system resistances (Fig. B.1). Data was not
corrected for system resistance because this is an intrinsic property of the electrode. Neither
the magnitude nor the shape of the change in overpotential or specific activity shown in Fig.
1 were explained by the magnitude or the pattern of the system resistivity which would have
resulted in corrections of < 10 mV for the OER and < 3 mV for the CER.

Figure C.1 System resistance as measured by electrochemical impedance spectroscopy in
5.0 M NaCl at pH 2.0 (CER) and 1.0 M H2SO4 (OER). The resistivity of the system did

206
not apprecaibly change between 0 and 60 ALD cycles of TiO2. For IrO2 based
electrodes, the average system resistance was 9.1 ± 0.6 Ω for CER condtions and 5.4 ± 0.6
Ω for OER conditions. For RuO2 based electrodes, the average system resistance was 8.0
± 1.0 Ω for CER condtions and as 5.3 ± 0.7 Ω for OER conditions. For FTO-based
electrodes, the average system resistance was 30 ± 7 Ω for CER condtions and 23 ± 6 Ω
for OER conditions.

C.5 Determination of the Double Layer Capacitance and
Electrochemically Active Surface Area
In order to make a fair comparison between values herein and in the benchmarking study,
the double-layer capacitance (Cd) was measured and linearly related to the electrochemically
active surface area (ECSA) by Eq. B1 in the same manner as described in the benchmarking
literature (201). For the OER, briefly, Cd was measured by plotting the non-Faradaic current
vs scan rate and extracting the slope of the linear best-fit line. An initial CV was conducted
to identify the non-faradaic region, which in general was a 50 mV window around the opencircuit potential (Eoc). Scans were then conducted at scan rates of 0.005, 0.01, 0.025, 0.05,
0.1, 0.2, 0.4, and 0.8 V/s and 100% of the current was collected for each step (Fig. B.2).
Between potential sweeps, the working electrode was held at Eoc for 30 sec. The non-faradaic
current at Eoc for each scan rate was plotted versus scan rate (Fig. B.3). The average of the
absolute value of the positive and negative slopes of the linear fits of the data was taken to
be Cd. Because of the narrow potential window between oxidation of Cl- and reduction of
Cl2, Cd was determined from electrochemical impedience spectroscpy at Eoc. Nyquist plots
were fit to a resistor in series with a parallel combination of a capacitor and a shunt resistor
(Fig. B.3). The resulting capacitance was taken as the Cd. In both cases Cd values were used
as described previously to calculate the ECSA (201). Briefly, Cd was divided by the specific
capacitance (Cs) of an average metal substrate in an acidic electrolyte (Fig. B.4, Eq. B.1).
Few literature values exist for Cs in concentrated acidic brine, and Cs does not change
apprecaibly with ionic strength for H2SO4. Both the CER and OER electrolytes were acidic,
so the same value of Cs was used to calculate the ECSA for both the CER and OER:

𝐸𝐶𝑆𝐴 = 𝐶= /𝐶É

207
(1)

where CS is specific capacitance (i.e., 0.035 mF/cm2 for 1.0 M H2SO4 and 5.0 M NaCl, pH
2.0). To ensure mutual comparability, we chose the same Cs value that was used in the
benchmarking literature for the OER (201).

Figure C.2 Example double-layer capicitance measurements for determining ECSA for
IrO2 with 10 cycles of ALD TiO2 in 1.0 M H2SO4. (Left) Cyclic voltamogramms in the
non-Faradaic region at 0.005, 0.01, 0.025, 0.05, 0.1, 0.2, 04, and 0.8 V/s. (Right)
Cathodic (yellow disks) and anodic (blue disks) charging currents measured at 0.95 V vs
SCE plotted as a function of scan rate.

208

Figure C.3 Example impedence spectroscopy for IrO2 with 0 cycles of ALD TiO2 in 5.0
M NaCl pH 2.0 at Eoc. These data were fit to a resistor in series with a parallel combination
of a capacitor and a shunt resistor. The resulting capacitance was taken as the Cd which in
this case was was 3.24×10-6 F.

209

Figure C.4 ECSA for IrO2, RuO2, and FTO based catalysts in 1.0 M H2SO4 and 5.0 M
NaCl, pH 2.0. All catalysts presented here had a geometric surface area of 0.13 cm2,
yielding electrochemical roughness factors between 0.1 and 6.0.

C.6 Calculating Specific Activities using ECSA and Surface
Area Measured by AFM
As discussed in detail in prevous reports, reporting overpotential data relative to geometric
current density can be misleading because geometric overpotentials can be influenced both
by the roughness and the intrinsic activty of the catalyst (179, 209). Specific activities (Fig.
5.5) were calculated as previously described, by normalizing the current from cyclic
voltamagrams to the electrochemically active surface area (201). For RuO2 and IrO2 based
catalysts, specific activities were calculated at 350 mV overpotential for the OER, and at 150
mV overpotential for the CER. For FTO, specific activities were calculated at 900 mV
overpotential for the OER, and at 700 mV vs NHE for the CER.
Alteratively, specific activities were calculated by normalizing the measured current density
to the topographic surface area measured by atomic force microscopy (AFM; see Section

210
5.2.3.1) for direct comparison with catalysts reported by Seitz et al (209). Roughness
factors for these calculations are reported in Table 5.1.

C.7 Determination of EZC by Electrochemical Impedance
Spectroscopy
To ensure high capacitance values, 5.0 M NaNO3 at pH 2.0 was prepared by dissolving
NaNO3 (J.T. Baker, Center Valley, PA, 99.6%, used as received) in 900 mL of water (18
MΩ cm, Millipore, Billerica, MA), adjusting the pH using HNO3 (Sigma Aldrich, ≥ 60%,
used as received), and diluting with water to 1 L. Working electrodes were prepared as
described above. A working electrode, an SCE reference electrode (CH instruments), a coiled
platinum wire counter electrode (Sigma Aldrich), and 20 mL of NaNO3 solution were added
to a 25 mL 4 neck 14/20 round bottom flask reactor. The reactor was gently bubbled with N2
for at least 15 min before experiments, as well as during experiments. The impedance was
measured using a Bio-Logic potentiostat/galvanostat model VSP-300 with EIS capability.
All studies were performed at 25 ± 2 °C. Impedance spectra were recorded in the frequency
range of 1 MHz to 10 mHz, with a modulation amplitude of 5 mV. An initial potential range
of 1.1 to 0 V vs SCE, with a step size of 25 mV, was performed to identify the EZC region. A
narrower potential range (typically ± 200 mV around the apparent EZC) was then used to
measure the EZC value.
EIS data were fit as described previously, using ZView software, to an Rs-(Rp-C) circuit,
where Rs is solution resistance at high frequencies, C is capacitor that represents double-layer
capacitance in mid-range frequencies, and Rp is charge transfer resistance at low frequencies
(Figs. S5 and S6) (225).
As previously reported, for FTO, IrO2, and RuO2 the capacitance values extracted from
impedance spectroscopy are expected to approximate a traditional double layer capacitance
(CDL) to first order (226, 227). For samples with partial, semi-continuous and continuous
TiO2 coatings (Fig. 5.3-5.5), the TiO2 layers are so thin for reasonably active catalysts (<

211
1.95 nm or 30 ALD cycles of TiO2), the TiO2 is assumed to be fully carrier-depleted
within the potentials in question, so the changes in CDL measured by impedance may be used
to approximate a traditional EZC.
To confirm this assumption, Mott-Schottky analysis of the capacitance data was performed
for the various samples. For an equivalent circuit comprising a series resistor combined with
a parallel combination of a capacitor (C) and a shunt resistance, the inverse of the square of
the capacitance (Farads) taken from the fit of the full frequency range on the nyquist plots
was plotted against the potential with respect to NHE, ENHE. For the low-cycle numbers of
ALD TiO2 on the substrates, a local maximum was observed, corresponding to the local
minimum of Q vs ENHE, and thus the EZC. However, for samples in which 100 or 1000 cycles
of ALD TiO2 were deposited, corresponding to ~6.5 and ~65 nm respectively, a linear plot
from Q-2 vs ENHE was obtained. These plots were analyzed through application of the MottSchottky equation (Eq. B2), where ε0 is the permittivity of free space, ε is the specific
permittivity of TiO2, A is the area of the electrode, q is the (unsigned) charge on an electron,
Nd is the dopant density, Vfb is the flat band potential, kb is the Boltzmann constant, T is
temperature, and V is the applied potential, and C is the capacitance.
ÝZ

= ÖÖ tZ {½ (𝑉 − 𝑉*y −

¸+ ¹

(2)

From the 500 and 1000 TiO2 ALD cycle samples, a value of Nd = (8.1 ± 4.2) X 1019 cm-3
was found, and the flat-band potential for the TiO2, Vfb, was calculated to be 282 ± 15 mV
positive of NHE. From these parameters, in conjunction with Eq. B3 and at an applied
potential of 0.25 V vs NHE (the lowest EZC value), the TiO2 in question would have a
depletion width of 7.3 ± 1.4 nm, which is substantially higher than the actual thickness of
TiO2 present in any of the catalytically relevant samples analyzed here (< 60 TiO2 ALD
cycles, or less than 3.9 nm).
W-- >

𝑊 = Þ {½m +§

(3)

212
Within the framework of this analysis, the TiO2 film deposited on the substrates is under
full depletion throughout the course of these experiments, and the capacitive effects from
this film may therefore be ignored when the potential of zero charge is calculated by
impedance spectroscopy.
Because EZC is believed to be a fundamental property of a material, changing the electrolyte
may change the absolute value of the EZC, but should not change the trend in the values of
materials measured in the same electrolyte (212).

213

Figure C.5 Sample Bode (above) and Nyquist (below) plots of electrochemical impedence
spectroscopy data of IrO2 coated with 10 ALD cycles of TiO2. The Bode plot shows the
frequency of the alternating current signal (Hz) versus the phase shift of the impedance
response (degrees). The Nyquist plot shows the real (Z’) and imaginary (Z”) components
of the impedance response to the alternating current signal. Data presented in the figure
were collected at 105 mV vs SCE in 5.0 M NaNO3 at pH 2.0. The resulting equivelent
circuit [Rs-(Rp-C)] fit of these data yielded a capacitance of 5.8× 10-6 F.

214

Figure C.6 Electrochemical impedance spectroscopy of (A) IrO2, (B) RuO2, (C) and FTO
coated with various ALD cycles of TiO2 at 25 mV intervals in 5.0 M NaNO3 at pH 2.0.
The resulting Nyquist plots were modeled as Rs-(C-Rp) circuits. The calculated capacitance
values (dots) for each sample (set of dots) are shown here. The minimum value of each
curve represents the EZC. The magnitude of the capacitance represents the surface area of
the sample.

215

Figure C.7 Sample Mott-Schottky (E vs 1/C2) plots of RuO2 with 0 (red), 1000 (blue)
ALD TiO2 cycles. The fit, using a geometric surface area of 7.1 X 10-6 m2, yielded Nd =
of 5.4 X 1019 cm-3.

216

Figure C.8 Potential of zero charge as a function of TiO2 cycle number for IrO2, RuO2,
and FTO electrocatalysts. Black dots and disks with black borders indicate the catalysts
with the highest specific activity for each substrate for the OER and CER, respectively.

For thick (>100 cycles) ALD TiO2 films, the EZC values converged, indicating that all
surfaces were electronically similar, bulk TiO2. For The CER, the most active catalysts had
EZC values of ~55, ~50, and ~75 mV vs SCE (IrO2 + 3 ALD TiO2 cycles, RuO2 + 0 ALD
TiO2 cycles, and FTO + 10 ALD TiO2 cycles respectively) and for the OER the optimal EZC
was ~80, ~175, and ~75 mV vs SCE (IrO2 + 10 ALD TiO2 cycles, RuO2 + 10 ALD TiO2
cycles, and FTO + 10 ALD TiO2 cycles respectively) (Figs. B.7 and B.8).

217

Appendix D Details of XPS Analysis
D.1 XPS Data Collection and Peak Fitting
X-ray photoelectron spectroscopy (XPS) data were collected using a Kratos AXIS Ultra
spectrometer (Kratos Analytical, Manchester, UK) equipped with a hybrid magnetic and
electrostatic electron lens system, a delay-line detector (DLD), and a monochromatic Al K
± X-ray source (1486.7 eV). Data were collected at pressures of ~2 x 10-9 Torr with
photoelectrons collected along the sample surface normal. The analyzer pass energy was 80
eV for survey spectra and 10 eV for high-resolution spectra, which were collected at a
resolution of 50 meV. The instrument energy scale and work function were calibrated using
clean Au, Ag, and Cu standards. The instrument was operated by Vision Manager software
v. 2.2.10 revision 5.

218
Bulk TiO2
○○
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●●● ●
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● ●

Normalized Counts (arb. units)

●●

● ●

468

466

464

462
460
458
Binding Energy (eV)

456

454

Figure D.1 X-ray photoelectron spectroscopy of the Ti 2p region for a bulk TiO2 film. The
peak associated with Ti4+ is shown in blue. The slightly and highly reduced Ti peaks are
shown in green and red, respectively, and the most highly oxidized Ti peak is shown in
orange.
XPS data were analyzed using CasaXPS software (CASA Software Ltd). The Ti 2p corelevel photoemission spectra were fit constraining the peak separation and the peak area
ratio between Ti 2p3/2 and Ti 2p1/2 peaks to 5.75 eV and 2:1, respectively. The peak area
ratios were allowed to deviate 5% from the 2:1 ratio to account for inaccuracies in the
background. All peaks were fit using a Gaussian-Lorentzian with 30% Lorentzian
character. A bulk TiO2 sample (1000 cycles) was used as a standard to determine the peak
positions for the Ti 2p3/2 core-level photoemission (Fig. C.1). The bulk TiO2 sample fit
exhibited a main peak at 458.24 eV, which is consistent with reports of the peak position
for TiO2 and therefore was ascribed to the Ti4+ oxidation state, and two additional peaks at
lower binding energies, 457.6 eV and 456.6 eV, respectively, associated with a more
reduced Ti state, likely Ti3+(215, 216, 228, 229). These peaks were propagated through for
IrO2 for all thicknesses of TiO2. In addition to these peaks, a fourth peak at slightly higher
binding energy (458.5 eV) was needed to fit the FTO spectra.

219

Normalized Counts (arb. units)

Bare RuO2

475

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460

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Figure D.2 X-ray photoelectron spectroscopy of the Ti 2p region for a bare RuO2 film. The
3 orange, red, and purple peaks define the Ru 3p core level photoemission associated with
RuO2.
In the case of RuO2, the Ru 3p core level exhibited a broad peak in the Ti 2p region (Fig.
C.2), which was well-fit by 3 Gaussian-Lorentzian peaks at 461.5 eV, 462.3 eV, and 464.5
eV, respectively. These Ru 3p core level photoemission peaks were propagated through for
the fits of the spectra with ALD TiO2. In addition to the 3 peaks associated with the Ru 3p
core level, the spectra were also fit with the 3 peaks associated with bulk TiO2, as described
above. To deconvolute the effect of Ru 3p core level photoemission from the TiO2 signal,
the Ru 3p core level peaks were subtracted from the spectra resulting in spectra
corresponding purely to the Ti 2p core level photoemission.

220
The photoemission from the underlying metal oxide substrates was also measured. Peak
fitting was performed on the bare metal oxide substrate and then propagated through to the
spectra with ALD TiO2. The Ir 4f and Ru 3d photoemission core-level spectra were fit
according to previous reports in the literature (230, 231).

221

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