DETERMINING THE ENERGETICS AND CHARGE DISTRIBUTION IN
THE MESOPOROUS SEMICONDUCTOR PHOTOANODES USED IN
DYE-SENSITIZED SOLAR CELLS
By
Dhritabrata Mandal

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Chemistry – Doctor of Philosophy
2017

ABSTRACT
DETERMINING THE ENERGETICS AND CHARGE DISTRIBUTION IN THE
MESOPOROUS SEMICONDUCTOR PHOTOANODES USED IN DYE-SENSITIZED
SOLAR CELLS
By
Dhritabrata Mandal

Mesoporous wide bandgap semiconductor electrodes have been widely studied for solar
energy conversion, especially in the context of dye-sensitized solar cells (DSSCs) and related
systems. The knowledge of their band edge energies, trap state distribution and electron density
in various electronic states are essential in order to optimize the photoanode performance and to
obtain a detailed understanding of the associated electron-transfer processes.
This dissertation focuses on spectroelectrochemical and electrochemical analysis of the
mesoporous phoanodes to determine the band edge position, energy distribution of the electronic
states and also their spatial locations.
Also presented here is a preparation method of mesoporous strontium titanate (SrTiO3)
photoanode and a detailed study of its energetics and the charge distribution. The goal of this
work is to explore the pros and cons of SrTiO3 material as a photoanode material in DSSC.

Copyright by
DHRITABRATA MANDAL
2017

To Maa, Baba, Chiku, Yindrila and my dear friends
For their unconditional love and support

iv

ACKNOWLEDGEMENTS

I would like to thank my PhD advisor Prof. Thomas Hamann. Without his adept advice,
continued support and mentoring throughout my PhD career, this would not have been possible.
His dedication for good science and his academic rigor in research have always motivated me to
overcome the struggling period of my graduate research. I would also like to thank my
committee members, Dr. Rémi Beaulac, Dr. Aaron Odom, and Dr. Benjamin G. Levine for their
guidance and support throughout my PhD. Jesse, Yuling and Ben, thank you for your excellent
mentoring and help during my graduate life. I would like to thank all the current members and
former members of the Hamann group, Kelley, Rena, Suraj, Omid, Arianna, Josh, Dan, Yuan,
Hamed, Yujue, Faezeh, Qiong, Austin and Parisa, for their support and for making my time here
memorable. The graduation would be much difficult without your brilliant ideas that have
enriched me and also without the fun that I had in my PhD life. So, thank you all. I had a great
and enjoyable PhD life for all of you. I would also like to acknowledge U.S. Department of
Energy for providing the funding to continue my research.
Friends from my college days, I cannot thank you enough. I feel exceptionally lucky to have
you during the “early” age of my life which shaped not only my career but also my way of life.
Also, the friends I have made during my Spartan life have always been helpful in numerous ways
and most importantly have offered me a great time in East Lansing. The unconditional love and
support that I received from my Maa, Baba and Chiku are priceless. And finally, Yindrila. I have
been blessed by your presence in my life. I cannot count the innumerable ways you have
contributed to my personal and professional development and I eagerly look forward to what is
to come.

v

TABLE OF CONTENTS

LIST OF TABLES………………………………………………………………………...……viii
LIST OF FIGURES………………………………………………………………………………ix
KEY TO ABBREVIATIONS………………………………………………………………...…xiv
Chapter 1 Introduction .................................................................................................................... 1
1.1 Motivation for research on Dye-sensitized Solar Cell (DSSC) ............................................ 1
1.2 DSSC operation and charge transfer processes .................................................................... 3
1.3 Historical development of DSSC .......................................................................................... 5
1.4 Literature review on photoanode materials used in DSSCs.................................................. 7
1.5 Motivation for studying photoanode properties in DSSC................................................... 10
1.6 Overview of the thesis ........................................................................................................ 11
REFERENCES ......................................................................................................................... 13
Chapter 2 Spectroelectrochemical Determination of the Conduction Band Edge Potential ........ 16
2.1 Introduction ......................................................................................................................... 16
2.2 Experimental ....................................................................................................................... 19
2.2.1 TiO2 photoanode preparation ....................................................................................... 19
2.2.2 Electrolyte preparation ................................................................................................. 20
2.2.3 Spectroelectrochemical measurement .......................................................................... 20
2.3 Results and discussion ........................................................................................................ 22
2.3.1 Absorption spectra of the TiO2 electrode..................................................................... 22
2.3.2 Determining band gap energy ...................................................................................... 23
2.3.3 Sources of uncertainty in determining band gap energy .............................................. 25
2.3.4 Burstein-Moss shift under potentiostatic bias .............................................................. 27
2.4 Conclusion: ......................................................................................................................... 33
REFERENCES ......................................................................................................................... 34
Chapter 3 Charge Distribution in Nanostructured TiO2 Photoanode Determined by Quantitative
Analysis of the Band Edge Unpinning ......................................................................................... 38
3.1 Introduction ......................................................................................................................... 38
3.2 Electrochemical techniques for determining charge distribution ....................................... 41
3.2.1 Cyclic voltammetry...................................................................................................... 42
3.2.2 Electrochemical impedance spectroscopy ................................................................... 44
3.2.3 Charge insertion/extraction method ............................................................................. 46
3.3 Experimental ....................................................................................................................... 47
3.3.1 TiO2 photoanode preparation ....................................................................................... 47
3.3.2 Electrolyte preparation ................................................................................................. 48
3.3.3 Measurements .............................................................................................................. 48
3.4 Results and discussions ....................................................................................................... 50
3.4.1 Accurate energy distribution of trap states in mesoporous TiO2 photoanode ............. 50

vi

3.4.2 Spatial location of the trap states ................................................................................. 55
3.5 Conclusion .......................................................................................................................... 59
REFERENCES ......................................................................................................................... 61
Chapter 4 Absorbance Features of Mesoporous TiO2 Electrode under Electron Accumulation .. 65
4.1 Introduction ......................................................................................................................... 65
4.2 Experimental ....................................................................................................................... 67
4.2.1 TiO2 photoanode preparation ....................................................................................... 67
4.2.2 Electrolyte preparation ................................................................................................. 68
4.2.3 Spectroelectrochemical measurement .......................................................................... 68
4.3 Results and discussion ........................................................................................................ 70
4.4 Conclusion .......................................................................................................................... 80
REFERENCES ......................................................................................................................... 81
Chapter 5 Conduction Band Energy and Charge Distribution in Strontium Titanate Nanoparticle
Electrode ....................................................................................................................................... 84
5.1 Introduction ......................................................................................................................... 84
5.2 Experimental ....................................................................................................................... 88
5.2.1 Preparation of SrTiO3 electrode ................................................................................... 88
5.2.2 Characterization of SrTiO3 film ................................................................................... 90
5.2.3 Preparation of electrolyte solutions ............................................................................. 90
5.2.4 Spectroelectrochemical measurement .......................................................................... 90
5.2.5 Electrochemical measurements .................................................................................... 92
5.3 Results and Discussion ....................................................................................................... 92
5.3.1 Material characterization ............................................................................................. 92
5.3.2 Determination of the conduction band and electron distribution................................. 94
5.4 Conclusion ........................................................................................................................ 114
REFERENCES ....................................................................................................................... 116
Chapter 6 Predicting Maximum Attainable Efficiency of DSSC ............................................... 121
6.1 Introduction ....................................................................................................................... 121
6.2 Calculating the power conversion efficiency of DSSC .................................................... 122
6.3 Energy losses in a DSSC................................................................................................... 122
6.3.1 Energy loss during photoexcited electron injection, Vloss, injection ............................... 125
6.3.2 Energy loss during regeneration of the oxidized dye, Vloss, regeneration ......................... 129
6.3.3 Recombinations losses, Vloss, recombination ..................................................................... 131
6.4 Predicting the maximum power conversion efficiency in DSSCs: ................................... 134
6.5 Conclusion ........................................................................................................................ 140
REFERENCES ....................................................................................................................... 142
Chapter 7 Conclusions and future directions .............................................................................. 147
REFERENCES ....................................................................................................................... 150

vii

LIST OF TABLES

Table 2-1 Conduction band positions were calculated at various applied potentials from the
magnitudes of the band gap shift. EG was calculated from the Tauc plots at the applied potentials
mentioned below and EG = EG (negative bias) – EG (+0.445 V vs. SCE). The electrolyte
solution is 0.2 M KCl at pH 12.8. ................................................................................................. 32
Table 4-1 Values of P in presence of different electrolyte solutions. The absorption spectra of
TiO2 electrode in contact with different electrolyte solution were measured and fitted to Drude
equation, A = CP. Global fit of several spectra measured in an electrolyte condition provided
the value of P. ............................................................................................................................... 78
Table 5-1 Calculation of conduction band position from the Burstein-Moss shift. ................... 101
Table 6-1 Table of the photoconversion efficiencies at different absorbance onsets and the
associated loss in potentials. ....................................................................................................... 137

viii

LIST OF FIGURES

Figure 1-1 Schematic of a dye-sensitized solar cell, DSSC (top) and energy diagram of a DSSC
showing major processes (bottom). Negative potential represents higher energy. The mesoporous
TiO2 photoanode is deposited on transparent conductive substrate (TCO). The conduction band
(CB) edge potential of TiO2 photoanode is shown below the excited state potential of dye. EF is
the Fermi level potential of electrons in the photoanode. R+/R represents the redox shuttles in the
solution which regenerate the oxidized dye. VOC is the open circuit potential which is the
potential difference between the solution potential and the Fermi level at the open circuit, EF,Voc.
The charge transfer processes shown in the diagram are described below. .................................... 4
Figure 2-1 SEM image of mesoporous TiO2 photoanodes used in DSSC. The image on the right
shows the cross section of a TiO2 film.......................................................................................... 17
Figure 2-2 Instrumental set-up of spectroelectrochemical measurement. ................................... 20
Figure 2-3 Change in absorbance of a TiO2 electrode in contact with a pH 12.8 aqueous
electrolyte when potential is stepped from + 0.455 V to  1.245 V (red),  1.295 V (green), 
1.345 V (yellow),  1.395 V (blue) and  1.445 V (pink) vs. SCE (from bottom to top). ........... 23
Figure 2-4 Top: Plot of absorption coefficient () vs. wavelength () of TiO2 film. Bottom: Tauc
plot of a TiO2 film. It was measured under an external positive bias + 0.445 V vs. SCE to
discharge any stored electrons from the nanoparticles. The electrolyte solution is 0.2 M KCl at
pH 12.8.......................................................................................................................................... 24
Figure 2-5 Energy vs. crystal momentum diagram (E-k) of a semiconductor with an indirect
band gap showing the Burstein-Moss shift due to the filling of the lowest energy states in the CB
under negative (reductive) potential. Electron transition from the highest-energy state in the
valence band to the lowest-energy state in the conduction band is not possible without a change
in momentum. The transition occurs via the absorption or emission of a phonon (red horizontal
arrow), which provides the required momentum change during the transition. The energy
required for this transition mainly comes from the photon absorbed (violet vertical arrow). ...... 28
Figure 2-6 Plot of absorption coefficient () vs. wavelength () of TiO2 film showing blue shift
of the band gap absorption energy under negative (reductive) potential. The electrolyte solution
is 0.2 M KCl at pH 12.8. ............................................................................................................... 29
Figure 2-7 Band gap widening occurs while moving from +0.445 V (red) towards more negative
potentials -1.245 V (green), -1.345 V (yellow), -1.445 V (blue) vs. SCE. The electrolyte solution
is 0.2 M KCl at pH 12.8. ............................................................................................................... 29
Figure 2-8 Plot of Burstein-Moss shifts (EG) at various applied potentials. ............................. 30
Figure 3-1 (Left) Energy vs. crystal momentum diagram of a semiconductor with an indirect
band gap. Electron transition from the highest-energy state in the valence band to the lowest-

ix

energy state in the conduction band is not possible without a change in momentum. The
transition occurs via the absorption or emission of a phonon, which provides the required
momentum change during the transition. Inter-band localized electronic states bellow the
conduction band, which trap electrons, are shown. (Right) Depiction of the upward shift of the
energetics in TiO2 nanoparticle film. ECB represents the magnitude of the upward shift of the
conduction band energy. ............................................................................................................... 40
Figure 3-2. Cyclic voltammogram plot (left) and chemical capacitance plot (right) of TiO2 film
in aq. 0.2 M KCl solution at pH 12.8. Scan rate was 50 mV / s. The chemical capacitance (C)
was calculated using the relation J = l(1-p)sC, where J is the current density, l (= 6.95 m) is
the electrode thickness, p (= 0.71) is the porosity of the TiO2 film and s is the scan rate. The peak
at approximately  0.75 V vs. SCE is referred to as monoenergetic trap state distribution and the
wave at increasing negative potentials corresponds to the exponential distribution of trap states.
....................................................................................................................................................... 43
Figure 3-3 Equivalent circuit based on transmission line model for fitting Electrochemical
Impedance data of porous photoanode. The fit parameters are described in the text. .................. 45
Figure 3-4 Plot of capacitance (C) of TiO2 film measured by electrochemical impedance
spectroscopy. Electrolyte was 0.2 M aq. KCl solution at pH 12.8. .............................................. 45
Figure 3-5 Typical current vs. time plot measured during charge insertion/extraction process
under potentiostatic. The measurement was performed with mesoporous TiO2 film in contact
with aq. 0.2 M KCl solution at pH 12.8. The reductive bias was  1.045 V and the oxidative bias
was + 0.455 V vs. SCE. ................................................................................................................ 47
Figure 3-6. The position of the conduction band edge potential determined at pH 12.8 and 2.0. 51
Figure 3-7. Plot of the chemical capacitance (C) as a function of applied potential, E, (bottom
axis, red circles) and applied potential which is corrected to include the effect of band edge
unpinning (ECB/q) as shown in equation 7 (top axis, blue triangles). ........................................ 52
Figure 3-8. Plot of absorbance of TiO2 at 780 nm as a function of applied potential (bottom axis,
red circles) and applied potential which is corrected to include the effect of band edge unpinning
(top axis, blue triangles). ............................................................................................................... 54
Figure 3-9. Plot of the concentration of trapped electrons in the bulk (nB) and on the surface (nS)
of TiO2 film in aq. 0.2 M KCl solution at pH 12.8. Extrapolation of the fitted plots to the
conduction band edge gives the density of bulk trap states, NB, and surface traps, NS. ............... 56
Figure 3-10. Plot of electron density in the nanostructured TiO2 photoanode as a function of
applied potential. The total trapped electron density (nTrap) is the sum of the electrons trapped on
the surface (nS) and in the bulk (nB).............................................................................................. 56
Figure 4-1 Transmittance (%T) spectra of TiO2 photoanode in contact with aqueous 0.2 M KCl
solution at pH 12.8. Potentials are given against SCE. ................................................................. 70

x

Figure 4-2 Change in absorbance of a TiO2 electrode under reductive bias. (a) TiO2 film is in
contact with a pH 12.8 aqueous electrolyte when potential is stepped from + 0.455 V to  1.245
V (red),  1.295 V (green),  1.345 V (yellow),  1.395 V (blue) and  1.445 V (pink) vs.SCE
(from bottom to top). (b) TiO2 film is in contact with a pH 2.0 aqueous electrolyte, potential is
stepped from + 0.955 V to  0.495 V (red),  0.545 V (green),  0.595 V (yellow),  0.645 V
(blue) and  0.695 V (pink) ,  0.745 (sky blue) vs.SCE (from bottom to top). .......................... 71
Figure 4-3 Global fit results (black lines) of the absorbance spectra from Fig. 4-2a,b according
to Drude equation. (a) TiO2 film is in contact with a pH 12.8 aqueous electrolyte when potential
is stepped from + 0.455 V to  1.245 V (red),  1.295 V (green),  1.345 V (yellow),  1.395 V
(blue) and  1.445 V (pink) vs.SCE (from bottom to top). (b) TiO2 film is in contact with a pH
2.0 aqueous electrolyte, potential is stepped from + 0.955 V to  0.495 V (red),  0.545 V
(green),  0.595 V (yellow),  0.645 V (blue) and  0.695 V (pink) ,  0.745 (sky blue) vs.SCE
(from bottom to top)...................................................................................................................... 72
Figure 4-4 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolyte is 0.2 M KCl at pH 6.2 adjusted by Citrate buffer (top) and
Phosphate buffer (bottom). Potential shown in the plot is given vs. SCE. ................................... 73
Figure 4-5 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolyte is 0.2 M KCl at pH 7.8 adjusted by Phosphate buffer (top) and
Imidazole buffer (bottom). Potential shown in the plot is given vs. SCE. ................................... 74
Figure 4-6 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolytes are 0.2 M LiClO4 at pH 7.8 (top) and ~ aqueous 0.05 M NaPF6
solution (bottom). The pH of the LiClO4 solution was adjusted at 7.8 by Imidazole buffer. No
buffer was added into aq. NaPF6 solution. Potential shown in the plot is given vs. SCE. ........... 75
Figure 4-7 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolytes are 0.2 M LiClO4 (top) and TBAPF6 (bottom) in acetonitrile.
Potential shown in the plot is given vs. SCE. ............................................................................... 76
Figure 4-8 Density of electrons in conduction band (nCB) is calculated from Burstein-Moss shift,
described in Chapter 2, and absorbance (A780 nm) of TiO2 film is measured at 780 nm under
different applied potentials mentioned in the plot. Electrolyte was 0.2 M KCl at pH 12.8 and the
potentials are given vs. SCE. ........................................................................................................ 80
Figure 5-1 Crystal structures of Perovskite SrTiO3 and anatase TiO2.. ....................................... 85
Figure 5-2 Apparatus setup used for the synthesis of SrTiO3 nanocrystals via vapor diffusion
sol-gel method. .............................................................................................................................. 88
Figure 5-3 Powder X-ray diffraction patterns of the SrTiO3 nanocrystals (top) and scanning
electron micrographs SrTiO3 film deposited on conductive substrate (bottom)........................... 93
Figure 5-4 Plot of absorbance of SrTiO3 electrode in UV region under various applied potentials,
0.0 V (black), -1.3 V (blue), -1.4 V (red), -1.5 V (green) vs. Ag/AgNO3. The electrolyte solution

xi

is 0.1 M LiClO4 in acetonitrile. Increasing negative potential moves the band gap absorption
edge to higher energy. ................................................................................................................... 95
Figure 5-5 Plot of visible-near IR absorbance spectra of SrTiO3 electrode under various applied
potentials, 0.0 V (black), -1.3 V (blue), -1.4 V (red), -1.5 V (green) vs. Ag/AgNO3. .................. 96
Figure 5-6 Plot of absorbance difference spectra of SrTiO3 electrode under various applied
potentials, -1.3 V (blue), -1.4 V (red), -1.5 V (green). This difference absorbance was calculated
by subtracting the absorbance of SrTiO3 electrode at 0.0V vs. Ag/AgNO3 from the absorbance
measured at negative potentials shown in the plot........................................................................ 96
Figure 5-7 Tauc plot of a SrTiO3 film in contact with 0.1 M LiClO4 in acetonitrile. Any
contribution from the electrolyte, substrate and cuvette were subtracted and only the absorbance
of the SrTiO3 electrode contributed to this plot. ........................................................................... 99
Figure 5-8 Plot of band gap widening while moving from 0.0 V (black) towards more negative
potentials -1.3 V (blue), -1.4 V (red), -1.5 V (green) vs. Ag/AgNO3. .......................................... 99
Figure 5-9 Current vs. time plot measured during charge insertion-extraction process under
various potentiostatic biases. A reductive bias (as mentioned in the plot) was applied for 3 min
and then an oxidative bias (0.0 V vs. AgNO3) was applied to extract all the charges stored in
SrTiO3 electrode.......................................................................................................................... 103
Figure 5-10 Plot of electron density in the nanostructured SrTiO3 electrode as a function of
applied potential measured by charge insertion-extraction measurement. ................................. 103
Figure 5-11 Plot of electron density in SrTiO3 and TiO2 electrode under various applied biases
calculated by charge extraction method. .................................................................................... 107
Figure 5-12 Plot of measured capacitance, C (red) and resistance, R (blue) of SrTiO3 electrode
measured by electrochemical impedance spectroscopy. ............................................................. 107
Figure 5-13 Comparison of capacitance of SrTiO3 electrode measured by the electrochemical
impedance spectroscopy and charge insertion-extraction method.............................................. 108
Figure 5-14 Plot of electron density in the nanostructured SrTiO3 electrode as a function of
applied potential. nCB is density of free electrons in the conduction band, nS, and nBulk are density
of electrons trapped on the surface and in the bulk respectively. ............................................... 108
Figure 5-15 (a,b) Current transient data of when applied bias was changed from 0.0 V to the
negative potentials mentioned in the plot. The SrTiO3 electrode is in contact with 0.1 M
LiClO4/Acetonitrile solution. ...................................................................................................... 111
Figure 5-16 Triexponential fit of the current transient data when applied bias was changed from
0.0 V to -1.5 V vs. AgNO3. The experimentally observed decay has the contribution from three
decays (1, 2 and 3 in the plot) shown here. ................................................................................. 112

xii

Figure 5-17 Plot of time constants derived from the triexponential fit of the experimentally
observed current decay data. ....................................................................................................... 113
Figure 5-18 Comparison of the CB and electron distribution between TiO2 and SrTiO3. ........ 115
Figure 6-1 J–V curve and IPCE plot of the DSSC photosensitized collaboratively by ADEKA-1
and LEG4. [Co(phen)3]2+/3+ redox shuttle was used. JV was measured AM-1.5, 100 mW cm2. 123
Figure 6-2 Plot of major energy losses in a typical DSSC. Negative potential represents higher
energy. The mesoporous TiO2 photoanode is deposited on transparent conductive substrate
(TCO). The conduction band (CB) edge potential of TiO2 photoanode is shown below the excited
state potential of dye. EF is the Fermi level potential of electrons in the photoanode. R+/R
represents the redox shuttles in the solution which regenerate the oxidized dye. VOC is the open
circuit potential which is the potential difference between the solution potential and the Fermi
level at the open circuit, EF,Voc. The loss-in-potentials, Vloss, are described in this chapter in details.
..................................................................................................................................................... 124
Figure 6-3 Schematic of back-electron transfer (i.e. recombination) processes from the
semiconductor nanoparticles and the transparent conductive substrate (TCO) into the redox
shuttle (R+/R) in the electrolyte .................................................................................................. 131
Figure 6-4 Energy diagram displaying the distribution of electrons in the TiO2 photoanode and
the recombination processes from the conduction band (green) and from the trap states (red). 132
Figure 6-5 Photon flux of the AM 1.5 G spectrum at 100 mW cm-2 (ASTM G173-03). .......... 134
Figure 6-6 Short-circuit photocurrent density as a function of absorption onset calculated by
integrating the AM 1.5 solar spectrum. ...................................................................................... 135
Figure 6-7 Photoconversion efficiency of DSSC as a function of loss-in-potential at different
absorption onsets of the sensitized photoanode .......................................................................... 138

xiii

KEY TO ABBREVIATIONS

DSSC: Dye-sensitized Solar Cell
J: Joule
TW: Terawatt
CO2: Carbon dioxide
ppm: parts-per-million
CH4: Methane
N2O: Nitrous oxide
PV: Photovoltaic

: Photoconversion efficiency
e: Electron
Dye*: Excited state of the dye molecule
Red: Reduced form
Ox: Oxidized form
TCO: Transparent conductive oxide
EF: Fermi level energy
EF: Fermi level potential
ECB: Energy of the conduction band edge
ECB: Conduction band edge potential
VOC: Open circuit voltage
CB: Conduction band
VB: Valence band
Ti: Titanium
O: Oxygen

xiv

Sr: Strontium
Zn: Zinc
Sn: Tin
Zr: Zirconium
Nb: Niobium
Si: Silicon
LUMO: Lowest unoccupied molecular orbital
eV: Electronvolt
OH: Hydroxyl group
TiO2: Titanium oxide
ZnO: Zinc oxide
SrTiO3: Strontium titanate
SrSnO3: Strontium stannate
Zn2SnO4: Zinc stannate
CdSnO3: Cadmium stannate
BaSnO3: Barium stannate

CB: Extinction co-efficient of the conduction band electrons
ND: Dopant density
NP: Nanoparticle
IR: Infrared
nm: nanometer
m: Micrometer
VTSEC: Variable temperature spectroelectrochemistry
Vis: Visible
NIR: Near infrared

xv

FTO: Fluorine doped tin oxide
p: porosity
mm: Millimeter
g: Gram
cm: Centimeter
M: Megaohms
HCl: Hydrogen chloride
KOH: Potassium hydroxide
%T: Transmittance
UV: Ultraviolet
Ag: Silver
AgCl: Silver chloride
A: Absorbance
A: Difference absorbance

: Absorption coefficient
l: Thickness of the semiconductor film
q: charge of an electron
nCB: Density of electrons in the conduction band
NCB: Density of states in the conduction band
kb: Boltzmann constant
T: Absolute temperature
V: Volt

: Wavelength of light
a.u. : Arbitrary unit
h: Plank’s constant

xvi

: Frequency of light
k: Crystal momentum
EG: Band gap energy
EP: Phonon energy
B-M shift: Burstein-Moss shift
m*: Reduced mass of charge carrier
mh*: Effective mass of electron
me*: Effective mass of hole
me: Mass of an electron
meV: Millielectronvolt
SCE: Saturated calomel electrode
d: Diameter of a nanoparticle
DFT: Density functional theory
CV: Cyclic voltammetry
EIS: Electrochemical impedance spectroscopy
C: Capacitance
C: Chemical capacitance
Q: Charge
s: Scan rate of a cyclic voltammetric scan
DOS: Density of states
KCl: Potassium chloride
Rs: Series resistance
Rt: Transport resistance
Rr: Interfacial resistance
RPt: Resistance at platinum counter electrode

xvii

Aq.: Aqueous
i: current
t: time
H2: Hydrogen
Hz: Hertz
N2: Nitrogen
K: Kelvin
MCB: Molar concentration of conduction band electron
MT: Molar concentration of trapped electron
CH: Helmholtz layer capacitance
CBE: Conduction band electron
p: porosity
min: Minute
ALD: Atomic layer deposition
s: second
AgNO3: Silver nitrate
Pt: Platinum
XRD: X-ray Diffraction
Pmax: Maximum output power
Pin: Power of the incident light
JSC: Short circuit current
ff: Fill factor
J: Current density
V: Voltage
IPCE: Incident photon to current conversion efficiency

xviii

AM: Air mass
mW: Milliwatt

xix

Chapter 1 Introduction
1.1 Motivation for research on Dye-sensitized Solar Cell (DSSC)
The ever increasing demand for energy is a major driving force behind the extensive research
on carbon-neutral energy sources. In 2012, the worldwide energy demand was 5531018 J/year
which is equivalent to an average power consumption of 17.5 TW and in 2100, the average
power consumption is projected to be 43 TW.1,2 Fossil sources like natural gas, oil, coal have
been estimated to provide more than 80% of the global total primary energy supply.3,4
However, the anthropogenic carbon dioxide (CO2) released during the combustion of fossil fuel
is strongly correlated to global warming. CO2 concentration in the atmosphere has drastically
increased in the last century due to the industrialization as well as the other human activities
relying on continuous source of energies. In mid 1800s, the average growth of CO2 concentration
was 280 ppm which has become 399 ppm in 2015 (~ 40% increase in less than 200 years).
During this time the other human activities e.g. agriculture, domestic livestock, biomass burning,
waste etc., which produce greenhouse gases like CO2, CH4, N2O, fluorinated gases, have also
increased. However, the CO2 gas released to meet the huge energy demand shares about 60% of
the global anthropogenic greenhouse gases.5 Moreover, the uneven geographical distribution of
these fossil fuel resources has resulted in several political and economical issues. The solution
lies in moving towards renewable energy resources like solar and wind which are abundant in
nature and potentially cost-effective. Solar energy arguably has the highest potential to meet the
growing energy demand. The sun irradiates our earth with around 1.2×105 TW of power.
Covering less than 0.4% of our planet's surface with 15% efficient solar panels would meet this
demand.6 However, photovoltaic (PV) devices have remained very far from attaining a

1

significant share of the energy production market, primarily, because of their production cost
which is mainly associated with the extreme purity requirement for the active materials, e.g
crystalline silicon PV device requires ~99.9999% purity.7 Additionally, Silicon PV does not
perform well under cloudy or shaded regions and their opacity hinders them from being an
attractive choice as Building-integrated photovoltaics. Dye-sensitized Solar Cells (DSSCs) have
many advantages compared to conventional PV.8,9 They can be manufactured from earth
abundant and cheap materials through cost effective and high throughput manufacturing methods
such as reel-to-reel printing.10 They offer flexibility in shape,11 transparency and even with the
color which makes them a potential candidate for solar windows.12 Because of the rough
materials surface, DSSCs perform much better than the conventional PV devices under diffused
light and low light intensity (cloudy day) which has expanded their versatile use in indoor
applications. The major drawbacks holding DSSCs back from a competitive entry into the PV
market are their stability issues and comparatively low efficiency in large modules.13 A
promising laboratory record efficiency of 14.3% has been achieved so far.14 However, efficiency
of the large modules is much lower and a photoconversion efficiency of 5-8% is considered to be
good.15,16 The photoconversion efficiencies of Si-based photovoltaic modules generally range
from 14 to 18%, much higher than DSSC modules. Making the photoconversion efficiency
higher will further reduce the overall electricity production cost which would make DSSC
technology more competitive in the energy supply market. DSSC has several components and
interfaces and the photoconversion efficiency is hugely challenged by various energy loss
mechanisms. Even after more than 20 years of research, the system has not been well understood
and predicting a roadmap towards the best DSSC, in terms of photoconversion efficiency (), is
still not feasible. Altering a single component from the optimized combination affect the other

2

electron transfer processes which in turn necessitates change in other components.17 This
challenge will only be met through extending our understanding of the interfacial charge transfer
processes and mastering our ability of systematic molecular engineering of each of the
components in the dye-sensitized solar cell.
1.2 DSSC operation and charge transfer processes
The main components of DSSCs are nanostructured semiconductor anode, monolayer of dye
attached to on the surface of this anode, redox shuttle and counter electrode (cathode). The
charge separation takes place at the dye-semiconductor interface. Separation between the
solution potential, E(R+/R) and the Fermi level of electrons in the semiconductor, EF, is the
maximum voltage output from a cell. At the open circuit, this separation is the highest and the
corresponding voltage is called open circuit voltage, VOC. Due to the presence of various
components and interfaces, there are many electron transfer processes that occur in a DSSC as
briefly described below. The numbers denotes the processes as shown in the DSSC energy
diagram, Figure 1-1.
1) Under illumination, the dye absorbs light and an electron is excited.
1) Relaxation of the excited dye directly into its ground state may occur before the injection
process takes place.
2) The photoexcited electron is injected into the conduction band of the adjacent semiconductor
nanoparticle.

3

Figure 1-1 Schematic of a dye-sensitized solar cell, DSSC (top) and energy diagram of a DSSC
showing major processes (bottom). Negative potential represents higher energy. The mesoporous
TiO2 photoanode is deposited on transparent conductive substrate (TCO). The conduction band
(CB) edge potential of TiO2 photoanode is shown below the excited state potential of dye. EF is
the Fermi level potential of electrons in the photoanode. R+/R represents the redox shuttles in the
solution which regenerate the oxidized dye. VOC is the open circuit potential which is the
potential difference between the solution potential and the Fermi level at the open circuit, EF,Voc.
The charge transfer processes shown in the diagram are described below.

4

3) The electrons injected into the semiconductor nanostructure are transported through the
mesoporous network to the conductive substrate where it is collected by the external circuit.
Generally transparent conductive oxides (TCO) are used as the substrate in DSSCs.
4,5) The hole produced in the dye is transported to the cathode by the redox shuttle or hole
collector and thus the dye is regenerated to participate into the next photoexcitation cycle.
6,7) Recombination of the electrons from the conduction band of semiconductor photoanode into
the oxidized form of the redox shuttle and dye.
8,9) Mesoporous semiconductor photoanodes are known to contain a large density of trap states
and trap state mediated recombination processes also take place.
In addition to the above mentioned components and charge transfer processes, a variety of
additives and blocking layers are often used to make the performance better. This also adds some
additional processes in the DSSC.
1.3 Historical development of DSSC
Sensitization of semiconductor to modulate its absorbance is over a century old technology
used in photography.18 In 1938, Gurney and Mott proposed the electron transfer from a dye
excited state into the semiconductor conduction band which is the central idea of the dyesensitization.19 Then, electron generation by sensitizing a wide band gap semiconductor was
reported by Putseiko and Trenin in 1949 who were studying photoconductivity of dyes adsorbed
ZnO under illumination.20 The seminal work by Gerischer and Tributsch in 1968 made a
breakthrough in the understanding of producing current by sensitized semiconductor under
illumination.21,22 Using an electrochemical cell constructed with single wide band gap ZnO and a
solution of fluorescein, rose bengale, or pseudoisocyanine chloride, they observed “Sensitized

5

photo-currents” when irradiated with the light of a wavelength which can only be absorbed by
the dyes. This is the fundamental idea of a dye sensitized solar cell. A later breakthrough came in
1976 when Osa et al. reported a system where the dye is attached to the semiconductor, hence
greatly improving the quantum yield of the electron injection when compared to the previous
system where the dye is dissolved in the solution and a majority of the photoexcited dye decays
before it can inject an electron into the semiconductor.23 However, the attempts to make dyesensitized photoelectrochemical cells were severely hindered by the fact that only a single
molecular layer of dye on a flat semiconductor can inject an electron into the semiconductor. The
light harvesting efficiency of one layer of dye adsorbed on a flat semiconductor crystal was
extremely small and far from producing effective photoconversion. Attempts were made to
increase the internal surface area of semiconductor electrode to enhance the dye adsorption and
hence improve the light harvesting efficiency.24,25 The breakthrough in modern DSSC
technology was made by O’Regan and Grӓtzel in 1991 where a mesoporous semiconductor
electrode was used to increase the internal surface area two orders of magnitude higher than the
geometric area.8 It greatly enhanced the amount of dyes loaded in the path of the incident light.
After a few optimizations with the HOMO-LUMO gap of the dye and electrolyte (redox shuttles
and additives) an excellent photoconversion efficiency of 10% was achieved in 1993.26 This
breakthrough demonstrated the potential of DSSC renewable electricity production and attracted
enormous attention worldwide. Within a few years, engineering the absorption onset of the
sensitizers lead to the photocurrent production beyond 20 mAcm-2 under 1 sun illumination.27,28
However, the overall photoconversion efficiency remained stagnant at around 10-11 % for
almost 18 years.29 A new breakthrough came in 2011 when Yella and Gratzel pushed the
efficiency to 12.3%. This report is very crucial not only because its record efficiency but also in

6

the context of systematic engineering of dye and redox shuttle. Iodide/triiodide redox shuttle was
used in all of the champion DSSCs starting from the beginning in 1991 which was replaced by
cobalt trispyridyl redox shuttles in their 2011 report. Additionally, ruthenium-based sensitizer
had been an essential part of the champion DSSCs throughout the history which was replaced in
their report by a successful co-sensitization of donor-π-bridge-acceptor zinc porphyrin and
organic D-π-A dye (Y123). The efficiency of similar DSSC configuration has been further
pushed to 13% in 2013 which has remained the record till today.14 Apart from the quest for
improving photoconversion efficiency, DSSC research has also advanced our understanding of
fundamental science of complex systems. The knowledge of structure/function relationships that
we acquire from DSSC research can be extrapolated to other solar cell technologies leading to
the establishment of the guidelines for the preparation of new material components.
1.4 Literature review on photoanode materials used in DSSCs
Breakthrough in dye-sensitized photovoltaic technology came through the introduction of
mesoporous photoanode structure making the internal surface area 2 orders of magnitude higher
than the geometric area. A transparent mesoporous film made of wide band gap semiconductor is
deposited on a conductive substrate. Incident light passes though this semiconductor film and
gets absorbed by the monolayer of the dye on the nanostructure. The purpose of the
semiconductor film is to make the internal area higher so that the monolayer of dye can
effectively deliver good light harvesting ability. Furthermore, the nanostructure collects the
photoinjected electron and transports it to the conductive substrate. However, the advantages of
the nanostructures come with their drawbacks. It makes the transport difficult due to
polycrystalline nature and numerous grain boundaries. Additionally, higher surface area unlocks
the chances of interfacial recombination processes.

7

The research on DSSC photoanode mainly focuses on enhancing the electron transport
through nanostructured photoanode and diminution of the interfacial recombination processes.
At the same time, the charge injection from the excited dye to the semiconductor needs to be
energetically and entropically favored. The conduction band of the semiconductor is desired to
be at lower energy than the LUMO of the dye. Additionally, large excess of density of states in
the conduction band than the photoexcited dye entropically favors the electron flow from dye
molecular orbital to semiconductor conduction band.
TiO2 has been the most studied material as DSSC photoanode. Among many crystalline
forms of TiO2, rutile and anatase are widely studied. Anatase has been the preferred choice in
DSSC because of its larger bandgap (3.2 vs. 3.0 eV for rutile) and higher (more negative)
conduction band edge leading to larger photovoltage.
Apart from TiO2, Zinc Oxide (ZnO) has received significant attention as DSSC photoanode.
Higher electron mobility and ease in making desired transparent nanostructures like
nanoparticles, nanowires, nanorods, nanotubes, tetrapods, nanoflowers, nanosheets and branched
nanostructures are some of the great advantages of ZnO photoanodes. ZnO based DSSC has
achieved a promising photoconversion efficiency of 8% so far.30 However, due to the poor
chemical stability in both acidic and basic solution, ZnO has never been the best alternative to
TiO2. Most of the dyes used in DSSCs have acidic carboxylic anchoring group which reacts with
ZnO, form insoluble Zn2+-dye aggregates and precipitate in the pores of the photoanode film.
These inactive dye complexes absorb light but do not inject electrons into the semiconductor.
Modification of dye anchoring group and applying a “protective” layer on the ZnO material have
been reported to improve the stability. Nguyen et al. reduced the precipitation of the Zn2+-dye
aggregates by using a Ru complex with single carboxylated bipyridyl ligand and a promising 4%

8

efficiency was reported. Park and coworkers have reported a SiO2 coated ZnO system with
improved chemical stability and a photoconversion efficiency of 5.2%. Very interestingly, study
of the material property and transport characteristics of nanostructured ZnO photoanode system
along with TiO2 has provided some valuable insights of structure/function correlation. ZnO has
been reported to have lower density of trap states than TiO2 and the electron transport through
nanostructured ZnO film is faster than TiO2 which is attributed to the fact that electron transport
occurs through trapping-detrapping mechanism. The electron life time of ZnO is also longer than
that of TiO2. Thus, a semiconductor photoanode having lower density of trap states is expected
to offer superior performance in the context of diminishing recombination and attaining higher
photovoltage.
SnO2 is another wide band gap semiconductor studied as DSSC photoanode material. Its ECB
is about 0.5 V lower than TiO2 and potentially can be utilized with a dye with low lying LUMO.
New redox shuttles with lower redox potential needs to be explored in order to optimize the
photovoltage with SnO2 and dyes with lower energetics. The record efficiency of a DSSC
constructed with SnO2 photoanode is little over 3% so far.31
Niobium Oxide (Nb2O5) has also received some attention and generally offer higher
photovoltage than TiO2 which is attributed to the higher conduction band position of Nb2O5.
However, making high surface area transparent Nb2O5 photoanode is challenging along with the
poor dye loading. In 2011, Zhang et al. have addressed these issues and made crystalline
Nb3O7(OH) nanorod film through solvothermal process. No annealing was done to preserve the
hydroxyl group on the surface which greatly enhanced the dye loading and thus improvement of
the current. Their reported photoconversion efficiency of 6% has been the best with this material
so far.

9

Ternary oxides have also attracted researchers’ attention as they offer a wider possibility of
tuning the physical–chemical properties by altering the relative ratios of the cationic components.
SrTiO3, SrSnO3, Zn2SnO4, CdSnO3 and BaSnO3 are among the ternary metal oxides utilized as
photoanode.32 However, performance have been much lower than the DSSC constructed with
TiO2 photoanode and further studies need to be performed to assess their potential as DSSC
photoanode material.
1.5 Motivation for studying photoanode properties in DSSC
The journey of DSSC progress has largely kept the initial champion components, like TiO2
photoanode, Ruthenium dye, Iodide redox shuttle and Pt counter electrode, unchanged. In spite
of the huge boom in DSSC research and a large effort to maximize the overall efficiency, it
remained stagnant for almost 18 years. The recent breakthrough in the efficiency came through
the systematic understanding and improvement of the outer sphere redox shuttles which showed
pitiful performance initially.33 Engineering the absorption characteristics, energetics and stability
of sensitizers have attracted broad attention. Ruthenium bipyridine dyes have remained the best
performing sensitizer for two decades starting from the first introduction in nanostructured DSSC.
Through extensive research with various dyes, new types of champion dyes have been
introduced and a donor-π-bridge-acceptor porphyrin dye has been found to be the new champion.
In counter electrode part, the former champion platinum has been challenged by graphene. Thus
among the main components, all the initially champion components have been recently changed
except the photoanode material, titanium dioxide. The photoanode plays an essential role in the
electron injection process from the dye, transportation of these electrons and recombination
processes. Significant energy loss occurs during these processes which needs to be largely
minimized in order to push the efficiency towards 20%. The ideal photoanode should

10

demonstrate quantitative charge injection with minimal energy difference between the dye
excited states and the conduction band edge. Additionally, surface state mediated recombination
processes are among the issues with TiO2 photoanode while using outer sphere redox shuttle
with highly positive redox potential and fast self exchange kinetics.17 New photoanode needs to
be explored to get rid of this recombination issue. Moreover, relying on a single photoanode
material has restricted the use of many sensitizers because of the mismatch in energetics. There
are several studies with alternative photoanodes like ZnO, SnO2, Nb2O5, SrTiO3, SrZnO3 etc. in
literature.34 However, their performances are not comparable to TiO2. Moreover, the reason
behind their poor performance has remained unexplored and needs further studies to understand
the parameters which are detrimental to the photoconversion efficiency of DSSCs.
1.6 Overview of the thesis
Lack of reliable methods to study the important material properties like energetics and charge
distribution has been a major issue behind it. In order to obtain a detailed understanding of
relevant electron-transfer processes the position of CB edge is essential. In the Chapter 2, a
spectroelectrochemical method is described to determine the CB edge of mesoporous TiO2
photoanode. These mesoporous photoanodes are known to have large density of trap states and
the accurate energy distribution as well as spatial location of the trap states are very important
features controlling the key electron transfers processes associated with this photoanode material.
A reliable method to study this trap state distribution is described in the Chapter 3. Another
crucial parameter required in the spectroelectrochemical study of electron transfer kinetics in
DSSC is the extinction coefficient of conduction band electrons (CB). However, due to the
presence of large excess of trapped electrons, the nature of the absorbing species has been a long
standing debate for more than 2 decades which prevented any accurate determination of CB. In

11

the Chapter 4, a detailed spectroeletrochemical study of the absorbance behavior of electrons in
TiO2 film is presented. TiO2 is mostly used as photoanode material in DSSCs. Though TiO2 has
remained the best performing DSSC photoanode so far, it has some disadvantages like sluggish
charge transport; trap states mediated recombination processes; limited energy match with
sensitizers etc. However, alternative materials are still far from being utilized to resolve these
issues. A systemic investigation of the photoanode materials to establish a correlation between
material properties and photoanode functions has been missing in literature. Chapter 5 describes
the study of mesoporous SrTiO3 photoanode. In Chapter 6, the maximum attainable efficiency of
DSSC technology is assessed and the necessity of systematic improvement of photoanode part is
pointed out. Chapter 7 looks into the viability of DSSC technology for reliable renewable energy
production along with the outlook for the future directions in this field. Overall, we have
developed methods to determine crucial properties of photoanode like energetics and electron
distributions. Our effort also is to explore alternative photoanode materials and assess their
viability as DSSC photoanode.

12

REFERENCES

13

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15

Chapter 2 Spectroelectrochemical Determination of the Conduction Band
Edge Potential
Adapted from:
Band energies of nanoparticle semiconductor electrodes determined by spectroelectrochemical
measurements of free electrons, Dhritabrata Mandal and Thomas W. Hamann, Phys. Chem.
Chem. Phys. 2015, 17, 11156–11160
2.1 Introduction
Nanostructured semiconductor electrodes have garnered intense recent interest for their use
in various solar energy conversion systems since they offer the possibilities of circumventing
low efficiencies associated with short diffusion length bulk materials as well as optimizing light
absorption in dye-sensitized solar cells.1–7 In such context, knowledge of the conduction (ECB)
and valence band (EVB) edge positions are the most important electronic properties in order to
optimize the performance and obtain a detailed understanding of relevant electron-transfer
processes.8 However, there is no reliable direct method to measure the band edges in
nanostructured semiconductor electrodes.
Efforts to determine the conduction band edges in these nanostructured photoelectrodes by
electrochemical methods have failed. Mott–Schottky analysis is widely used to determine the
band edge positions in a compact semiconductor electrode. The central idea of Mott-Schottky
equation is modeling the depletion region capacitance as a parallel plate capacitor. However, the
mesoporous photoanodes used in DSSCs are generally made of small nanoparticles as shown in
Figure 2-1. The Mott-Schottky analysis cannot be used here as the dimensions of the
nanoparticles are usually smaller than the depletion region.9,10 The nanoparticles surrounded by

16

the electrolyte solution are unable to support traditional band bending required for the MottSchottky analysis to be valid. On the other hand, this depletion region capacitance is associated
with the dopant density (ND) of the semiconductor. The typical value of ND in anatase TiO2
material is generally in the range of 1016  1017 cm-3.11–13 Assuming this value is valid in
nanoparticles having diameter of 10 nm, one dopant can be present in every 20 nanoparticles or
even in 200 nanoparticles. Thus, a homogenous distribution of depletion region capacitance
throughout the nanoparticle network is not possible and Mott-Schottky equation cannot be
applied. Band edge position can also be determined from the photocurrent onset potential.14
However, determining the exact potential where the photocurrent can be detected in the presence
of the dark current is uncertain.

Figure 2-1 SEM image of mesoporous TiO2 photoanodes used in DSSC. The image on the right
shows the cross section of a TiO2 film.

Fitzmaurice et al. developed a spectroeletrochemical method to determine the flat band
positions in mesoporous semiconductor films.15–21 The absorption of a transparent film was
measured while the film was charged by applying large negative bias (reductive) during the
cyclic voltammetric scan. This absorption in the visible-near IR region was considered to be

17

associated with the intra-band absorption of the free electrons in the conduction band. Their
model is based on the assumption of an accumulation layer, created within each nanocrystalline
particle, under reductive potential more negative than the flat-band potential. However, their
model and the associated assumptions have been debated and the validity of their approach has
been questioned.9,22–27 Many of their key assumptions e.g. flat interface, Schottky junction,
formation of accumulation layer are very unlikely to occur in these small nanoparticles (diameter
10- 20 nm). Additionally, the large negative bias can cause unwanted change in the electrode
especially in the presence of small cations. Scan rate dependence of the measured absorption is
the other drawback of this method, which implies that the system is not under equilibrium and all
the electronic states are not filled during the absorption measurement.28 Their model also
assumes that the conduction band edge does not change while raising the Fermi energy. However
such nanostructured TiO2 films with high roughness factor should have significant electroactive
states on the surface which can cause band edge shift.29 Moreover, it has been argued that the
absorption spectrum arises due to the absorption of the trapped electrons instead of free electrons
in the CB.30–34
A new variable temperature spectroelectrochemistry (VTSEC) method was introduced as a
way to overcome these issues.28 The VTSEC method is not ideal, however, since it relies on two
assumptions: the dominant absorbing species of the visible and near IR (Vis/NIR) wavelengths
measured are free conduction band electrons and the only effect of the variable temperature is
the free electron concentration. The first assumption of the absorbing species has not been firmly
established and is the subject of continued disagreement, with alternative assignments of a
trapped electron absorption or a combination of free and trapped electrons (i.e. total electron
concentration).22,31,34,35 Regarding the second assumption, it is likely that there is a temperature

18

dependence of the band gap, dielectric constant, phonons (thus extinction coefficient) of TiO2
employed that was not accounted for and may lead to a significant error. Further, VTSEC is
fairly tedious to control and not amenable to being a routine measurement. The motive of this
work is primarily to accurately determine the conduction band edge position of nanostructured
semiconductor electrodes. A TiO2 nanoparticle electrode was biased under negative (reductive)
potential which increases the electron population in the TiO2 electrode and the optical absorption
was measured. The change in the band gap absorption was correlated to the electron density in
the conduction band and the position of the CB edge potential was determined.
2.2 Experimental
2.2.1 TiO2 photoanode preparation
The transparent mesoporous anatase TiO2 electrode was prepared by spreading HT/SP TiO2
paste (Solaronix) on fluorine-doped tin oxide (FTO) conducting glass (Hartford Glass) by the
doctor-blade method, followed by sintering at 500°C for 15 min in air. The thickness of the TiO2
film was measured by a Dektak3 Surface Profiler and found to be 6.950.05 μm. The porosity, p,
of the mesoporous TiO2 film was also determined. 15 TiO2 films (geometric area 64 mm2 and
thickness 6.95 m) were collected from the FTO by scraping out with a sharp blade. The total
mass of the collected TiO2 material was measured. Total volume of the 15 films was then
calculated which is 64 mm2  6.95 m 15 and the mass of the solid TiO2 material without any
pores was calculated from the density of anatase material, 3.93 g / cm-3. Porosity is calculated
using the equation, p = 1 – (measured mass of porous film / calculated mass of solid material).

19

2.2.2 Electrolyte preparation
Aqueous electrolyte solutions were made by dissolving recrystallized potassium chloride
(KCl) salts into Millipore water (18.2 M-cm). A Fischer Scientific Accumet pH meter was
used to measure the pH of the solutions. Drops of hydrochloric acid (HCl) and potassium
hydroxide (KOH) were added to adjust the pH to the desired values, pH 12.8 and 2.0 used here.
2.2.3 Spectroelectrochemical measurement

Figure 2-2 Instrumental set-up of spectroelectrochemical measurement.

In spectroelectrochemical measurements, the transmittance (%T) of the film was measured
by a Perkin Elmer Lamda 35 UV-Vis spectrophotometer under an external bias provided by a
potentiostat (-Autolab, Metrohm). A three electrode electrochemical cell, made by customizing
a commercial spectroscopic cuvette (Quartz Spectrophotometer Cell, Starna Cells, Inc), was
placed into the UV-Vis spectrophotometer such that the TiO2 film remained perpendicular to the

20

optical path as shown in Figure 2-2. A platinum wire (diameter 1.5 mm) was used as counter
electrode and a commercial “Leakless Miniature” Ag/AgCl reference electrode (EDAQ ET072)
was used. The TiO2 films were aged overnight in contact with the electrolyte solutions prior to
any experiment. The temperature of the electrochemical cells was 220.5 ⁰C during the
measurements. During spectroelectrochemical measurements, each film was stabilized at an
applied bias for 5 minutes and %T of the electrode was measured. A control experiment was
done with bare FTO electrode to confirm that the FTO has no significant contribution into the
change in %T with varying potential. Stability of the film as well as reproducibility of the results
were checked both spectroscopically as well as electrochemically to make sure that there is no
irreversible change in the film during the measurements.
The difference absorbance spectrum, A, is the absorbance change under external bias. At
first, the transmittance was measured under a significantly positive potential to discharge all the
stored electrons from the film. Then a negative potential was applied to increase the electron
population and the transmittance was measured. Absorbance, A, was calculated from the %T by
using the relation, A = 2  log10%T. Absorbance at positive potential was subtracted from the
absorbance at negative bias to calculate A.
While determining the band gap using a Tauc plot, the absorption spectra measured while
using bare FTO electrode was subtracted from the spectra measured with TiO2 film on FTO.
Thus the absorption of TiO2 film was calculated by eliminating the contribution of everything
else in the optical path (FTO, cuvette and electrolyte). The contribution of the free electron
absorption was calculated in the wavelength range of 350 – 400 nm by extrapolating the
absorption spectra measured in the visible range (discussed in Chapter 4). This calculated
absorption was then excluded from the total absorption measured in this region to determine the

21

absorption of the band gap transition only. Absorption co-efficient () was calculated from
absorbance by using the relation  = (2.303  A) / l, where A is the absorbance and l is the
thickness of the film.36,37
2.3 Results and discussion
2.3.1 Absorption spectra of the TiO2 electrode
Due to the good electronic connectivity among nanoparticles and equipotential environment
surrounding the nanoparticles, the Fermi level (EF) within the TiO2 nanoparticle electrode can be
controlled by applying an external bias to the conductive substrate.38–41 The measured absorption
at a certain applied potential (E) can be correlated to the electron population in the
semiconductor film at the Fermi level EF which is equal to qE (q is the energy of an electron).
Here, E represents energy and E (=E/q) represents the electrochemical potential. This
potentiostatically controlled Fermi level is directly related to the density of electron in the
conduction band. When the Fermi level moves closer to the conduction band (CB) the density of
the electrons (nCB) increases exponentially according to the following relation:
nCB  N CB exp

(EF  ECB )
k bT

(1)

where ECB is the conduction band minima and NCB is the density of states (DOS) in the
conduction band.
Figure 2-3 shows typical difference absorption, A, spectra of a TiO2 film immersed in a pH
12.8 aqueous electrolyte. The absorbance increases in the visible and the near-IR regions with
increasing (negative) applied potential (E) with a concomitant decrease at wavelengths shorter
than ~380 nm. The characteristics of this absorption in visible  near IR region are discussed in
Chapter 4 in details.

22

The band gap transition in anatase material occurs below 380 nm and the decrease in A can
be explained by the blue shift of the band gap absorption.22 This shift is attributed to the filling of
the low energy states of conduction band which block the lowest energy band gap transition.42
Blue shift in the band gap absorption has been observed in the highly doped semiconductor and
is known as Burstein-Moss shift.42–47 This shift has been quantitatively analyzed in our study to
determine the density of the CB electrons and the position of CB edge.

Figure 2-3 Change in absorbance of a TiO2 electrode in contact with a pH 12.8 aqueous
electrolyte when potential is stepped from + 0.455 V to  1.245 V (red),  1.295 V (green), 
1.345 V (yellow),  1.395 V (blue) and  1.445 V (pink) vs. SCE (from bottom to top).

2.3.2 Determining band gap energy
The absorption edge due to the bandgap transition can be determined from a Tauc plot using
the relation,37
( hv)  A' (EG  hv)

23

(2)

where  is the absorption co-efficient, h is energy of incident light, EG is the band-gap energy,
A’ is a constant and the value of  depends on the characteristics of the transition process.

Figure 2-4 Top: Plot of absorption coefficient () vs. wavelength () of TiO2 film. Bottom: Tauc
plot of a TiO2 film. It was measured under an external positive bias + 0.445 V vs. SCE to
discharge any stored electrons from the nanoparticles. The electrolyte solution is 0.2 M KCl at
pH 12.8.

24

For the indirect allowed transition,  is 1/2 and it is 2 for the direct allowed transition. The
band gap transition in anatase is generally accepted to be indirect allowed transition and  = 1/2 is
used to determine the band-gap energy.48–51 Figure 2-4 shows a typical Tauc plot used to
determine the band gap energy of the anatase nanoparticles. The steep fraction of the (h)1/2 vs.
h curve fitted between 3.444 eV to 3.547 eV (360 - 350 nm) was extrapolated to determine the
band gap and it was found to be 3.209 eV which excellently matches to the literature values for
EG of anatase TiO2.48–51 The range of photon energies utilized to fit the Tauc plot was chosen
where a good straight line fit was observed. The energy region should not be too close to the
band gap as various factors (e.g. Urbach tail) can dominate the overall absorption spectra where
the absorption of band gap transition is still relatively low.37 On the other hand, in a scenario
when the photon energy is very much higher the band gap energy, the parabolic approximation
of E-k plot is no longer valid. Also, the direct band gap transition (which occurs at higher energy
than the indirect transition in anatase material) can contribute to the absorption. The maximum
energy applied here is 3.547 eV ( = 350 nm) which is in the energy range where the Tauc plot is
generally fitted in literature for the indirect transition in anatase and at this energy the direct band
gap transition is very unlikely to occur.52 Additionally, we found a value ~ 3.2 eV for band gap
which excellently matched with the literatures values. Participation of the absorption due to
direct band gap transition at higher energy is expected to abruptly increase the absorption rise
which was not observed here.
2.3.3 Sources of uncertainty in determining band gap energy
In the indirect transition, both the energy and the momentum are changed. As a result,
phonon interaction (resulting in thermal vibrations in the crystal lattice) is required.37 Therefore
the band gap transition becomes a two-step process assisted by either phonon absorption or

25

phonon emission which provides the required momentum change during the transition. The
energy required for this transition mainly comes from the photon absorbed. So the energy
required to excite an electron from the valence band to the conduction band can be written as,37
h  EG  Ep

(3)

where EP is the energy of the phonon required to compensate the difference in momentum
between the minima and maxima of the conduction and valence bands, respectively. The
absorption co-efficient for a phonon assisted indirect transition can be given by the following
equations,

 a (hv) 

 e (hv) 

A" (hv  EG  E p ) 2
E
exp p  1
k bT

A" (hv  EG  E p ) 2
 E 
1  exp   p 
 k bT 

(4a)

(4b)

where a(h) and e(h) are the absorption co-efficients corresponding to phonon absorbed and
phonon emitted process, respectively, A” is a constant, kb is Boltzmann constant and T is
absolute temperature. Now, both phonon absorption and emission are possible as the range of
applied photon energy considered to calculate the band edge is much higher than EG. So, the
total absorption co-efficient is given by,

 (hv)   a (hv)   e (hv)

(5)

These equations imply that phonon assisted absorption co-efficient is temperature dependent.
The phonon energy is expected to be constant while changing the potential at constant
temperature. It should also be mentioned that it is not straightforward to determine the absolute
band gap in case of phonon assisted indirect transition. Additionally, in presence of a high

26

dopant density and/or impurity, charge-charge and/or charge-ionic impurity scattering can also
provide the momentum conservation required for the indirect transition.37 The dopant density as
well as impurity concentration in nanostructured TiO2 films has not been precisely determined so
far. Broadening of the absorption curves also contributes to the uncertainty in determining the
band gap energy precisely. Band tail, which is expected to be present in our sample due to
disorder effects and/or defects below the conduction band, can also contribute to this uncertainty.
Significant broadening of absorption curve has been observed in our study (Figure 2-4). It is very
difficult to get rid of this broadening which might cause some error in our band gap
determination. At a constant temperature and electrolyte composition, however, the magnitude of
the broadening remains constant and does not contribute to the shift in the band gap absorption,
which is of primary interest here. In summary, at constant temperature and electrolyte
environment the error in determining the band gap transition remains constant which has allowed
us to accurately determine the magnitude of the shift in band gap energy under external potential
bias.
2.3.4 Burstein-Moss shift under potentiostatic bias
Band gap transition is defined as the lowest energy required to excite an electron from the top
of the VB to the lowest energy states of the CB. Increasing electron population in the CB fills the
lowest energy states and band gap transition requires some extra energy causing a blue shift in
the band gap absorption. This blue shift has been reported to occur due to increasing CB electron
population by doping semiconductor material and is generally described as Burstein-Moss
shift.42–47 In our experiment, reductive bias has been applied to increase the electron population
in the CB and the similar phenomenon has been observed.

27

Figure 2-5 Energy vs. crystal momentum diagram (E-k) of a semiconductor with an indirect
band gap showing the Burstein-Moss shift due to the filling of the lowest energy states in the CB
under negative (reductive) potential. Electron transition from the highest-energy state in the
valence band to the lowest-energy state in the conduction band is not possible without a change
in momentum. The transition occurs via the absorption or emission of a phonon (red horizontal
arrow), which provides the required momentum change during the transition. The energy
required for this transition mainly comes from the photon absorbed (violet vertical arrow).

When the lowest energy states of the conduction band become occupied by the
potentiostatically injected electrons, the energy to excite electrons from valence band to the
unoccupied states of the conduction band increases. As a result, a blue shift in the band gap
absorption is observed as shown in Figure 2-6. The magnitude of this band gap widening (EG)
is correlated to the density of electron in the CB according to the following equation:
EG 

h 2  3nCB 
8m*   

2/3

(6)

where m* is the reduced effective mass of the charge carriers and nCB is the concentration of
electrons in the conduction band.

28

Figure 2-6 Plot of absorption coefficient () vs. wavelength () of TiO2 film showing blue shift
of the band gap absorption energy under negative (reductive) potential. The electrolyte solution
is 0.2 M KCl at pH 12.8.

Figure 2-7 Band gap widening occurs while moving from +0.445 V (red) towards more negative
potentials -1.245 V (green), -1.345 V (yellow), -1.445 V (blue) vs. SCE. The electrolyte solution
is 0.2 M KCl at pH 12.8.

29

Figure 2-8 Plot of Burstein-Moss shifts (EG) at various applied potentials.
Correlating the observed blue shift in the band gap absorption with the density of the
electrons in the CB is based on a few assumptions. The parabolic approximation of energy bands
were made here, which basically describes that the charge carriers (electrons, holes) behave as
free carriers with a parabolic momentum (k) dependence. This parabolic approximation provides
values for the effective mass of the electron (me*) from the bottom energy level of the conduction
band and hole effective mass (mh*) from the top of the valence band. However, at energies far
from the band edges this approximation loses its validity and the effective masses become energy
dependent. In our experiment, the increase in the band gap transition energy is  17.8 meV when
the bottom of the CB is filled which is less than the 1kbT value at room temperature. It is
reasonable to assume that the parabolic approximation is valid in this energy range which
provides energy independent values for me* and mh*. Also, a constant value for the DOS at CB,
NCB, was calculated from the effective mass of electron according to the following equation,

30

 me*k bT 
NCB  2 
2 
 2 

3/2

(7)

Burstein-Moss shift was determined at a range of applied potentials and the corresponding
nCB was calculated from equation 6. A range of values (1me to 10me) are found in literature for
me*.51,53,54 Liu and Wang et al. studied the electron-transport in mesoporous TiO2 photoanode in
a working DSSC which depends on the DOS in the CB.55 They estimated an effective electron
mass of 2.3me from the measured electron density in the CB. In our study, me* = 2.3me was used.
Thulin et al. calculated a value of ~ 1.8me for mh* and Fitzmaurice reported a value of
0.80.2me.52,56 These values were determined based on several assumptions and the accurate
value for the mh* in anatase nanoparticle is uncertain. In our study, we used 1.0me for mh*. The
uncertainty in mh* should not have significant effect in the values of ECB/q (<10 mV in a range of
1me to 5me).
Now, once nCB is known at a given potential, E (= EF/q), the conduction band edge energy
can be calculated directly from equation 1. Table 2-1 shows the values of ECB/q calculated under
a range of applied potentials. These results indicate an upward shift of the conduction band edge
when the applied potential is increased i.e. more negative. This phenomenon can be explained by
the potential drop across the Helmholtz layer. Accumulation of electrons in the electrically active
states on the surface or within close vicinity of surface of the mesoporous TiO2 films can cause a
change in the electric field of the Helmholtz layer resulting in this potential drop.22,57,58 This high
surface area mesoporous TiO2 electrode is made of small TiO2 nanoparticles (10 nm diameter)
connected to each other. Various types of the electroactive states exist on the surface which are
energetically located below the CB. Truncation of the crystal lattice on the particle surface as
well as the point defects are the possible reasons behind the origin of these surface states.

31

Detailed discussions about these electroactive states and the potential drop are provided in
Chapter 3.
Table 2-1 Conduction band positions were calculated at various applied potentials from the
magnitudes of the band gap shift. EG was calculated from the Tauc plots at the applied potentials
mentioned below and EG = EG (negative bias) – EG (+0.445 V vs. SCE). The electrolyte
solution is 0.2 M KCl at pH 12.8.

E vs. SCE / V

EG / meV

nCB / cm–3

ECB/q / V

-1.045

0.22  0.42

2.97  8.47 × 1016

-1.249  0.073

-1.095

0.47  0.42

0.93  1.23 × 1017

-1.270  0.034

-1.145

1.05  0.42

3.09  1.84 × 1017

-1.289  0.015

-1.195

2.25  0.42

9.70  2.70 × 1017

-1.310  0.007

-1.245

4.52  0.42

2.76  0.38 × 1018

-1.334  0.004

-1.295

7.03  0.41

5.36  0.47 × 1018

-1.367  0.002

-1.345

10.07  0.41

9.18  0.56 × 1018

-1.403  0.002

-1.395

13.74  0.41

1.46  0.07 × 1019

-1.441  0.001

-1.445

17.78  0.41

2.16  0.07 × 1019

-1.481  0.001

Another interesting point here is that when the Fermi level of electrons moves very close to
the CB edge, EF  ECB becomes as small as 36 meV. Now, equation 1 is considered to be valid
when EF  ECB  3kbT where kbT is about 26 meV because of the breakdown of the Boltzmann
statistics. Liu and Wang et al. observed that EF eventually reaches to the transport energy in
mesoporous TiO2 suggesting that EF is too close to ECB.55 Thus, in Table 2-1, the values for
ECB/q, calculated when EF/q is more negative than -1.295 vs. SCE, are questionable. The validity
of the parabolic approximation of E-k diagram when the energy is close to the band edges and

32

the applicability of equation 1 (Boltzmann statistics) are two primary conditions for our method
to be valid.
2.4 Conclusion:
Spectroelectrochemical measurement has been performed on transparent polycrystalline TiO2
films. Under negative potential, a blue shift of the band gap transition has been observed. The
observed blue shift can be explained by the filling of the lowest energy states of the CB under
negative bias. This type of blue shift i.e. an apparent band gap widening is known as BursteinMoss shift. Quantitative analysis of this blue shift has provided the density of electrons in the CB
under a range of applied potentials. Position of CB edge has been calculated at different Fermi
level and an upward shift of the CB has been observed. This shift is explained by the potential
drop across the Helmholtz layer causing unpinning of the band positions. The electroactive
surface states on these high surface area electrodes accumulate electrons on the surface of the
nanoparticles under negative bias.33,57–59 To maintain the charge neutrality, positive charges, i.e.
the cations in the electrolyte, are adsorbed at the semiconductor/electrolyte interface which
causes potential drop in the Helmholtz layer. This potential drop is discussed in Chapter 3. The
band edge unpinning has been pointed out while studying the electron transfer processes in
DSSCs.55 However, due to the absence of any reliable methods for quantitative analysis of the
band edge shift, it has been either ignored or only estimated indirectly. Thus, this work solves a
long standing problem of being able to determine the band edge positions in nanoparticle
semiconductor electrodes.

33

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37

Chapter 3 Charge Distribution in Nanostructured TiO2 Photoanode
Determined by Quantitative Analysis of the Band Edge Unpinning
Adapted with permission from:
Charge Distribution in Nanostructured TiO2 Photoanode Determined by Quantitative Analysis of
the Band Edge Unpinning, Dhritabrata Mandal and Thomas W. Hamann, ACS Appl. Mater.
Interfaces 2016, 8, 419−424. Copyright 2016 American Chemical Society.
3.1 Introduction
Mesoporous wide bandgap semiconductor electrodes have been widely studied for solar
energy conversion, especially in the context of dye-sensitized solar cells (DSSC) and related
systems.1,2 The conduction band (CB) edge position, trap state distribution and electron
concentration are arguably the most important properties for detailed understanding of the
various charge transfer processes associated with them.3
The mesoporous anatase titanium oxide (TiO2) electrodes are generally used as the
photoanode in DSSCs. Anatase TiO2 crystal is constructed with chains of distorted TiO6
octahedra. It has a tetragonal lattice with four TiO2 units per unit cell. The CB is formed
predominantly by Ti-3d orbital, with dxy states at the lower edge and the valence band is formed
mainly by O-2p states.4–9 These TiO2 photoanodes are known to have large density of
electroactive states energetically located below the CB (Figure 3-1) and may participate into the
interfacial charge transfer processes.3 The spatial location and nature of these trap states have
been debated. They are believed to be present predominantly on the surface of the nanoparticle
(NP) although trapping of electrons in the bulk nanoparticle is also reported.10–13 The nature of
these trap states is also not clear yet. Localization of excess electron at the Ti4+ centers in the

38

bulk or on the surface are generally considered as trapped electrons and the trapped states are
frequently described as Ti3+ centers. Valentin et al. reported electronic structure calculations
based on density functional theory (DFT) and suggested the presence of undercoordinated Ti 5c3+
which can potentially create a localized electronic center.14,15 Distribution of inter-band trap
states below the CB have been reported in many n-type semiconductors like TiO2, SrTiO3 even
in the single crystals.16,17 The inherent n-type conductivity in these metal oxides is the result of
oxygen vacancies in their crystal structures.18 Missing of one lattice oxygen generate three
undercoordinated (five-fold) Ti centers. Oxygen deficiency in the TiO2 crystal may result in the
localization of an excess electron at a Ti site resulting in the formation of Ti3+ centers.13 On the
surface, Ti3+ surface cations were reported to interact with OH ions and water molecules
forming Ti3+OH bonds which create some electronic states below the CB. Hydroxyl groups
were suggested to favor the localization of the Ti-3d states.14 When a proton is bound to a
neighboring O center (Ti−OH species), a localized extra electron in 3d orbital of Ti center was
calculated to be ~ 180 mV more stable than the scenario when this extra was electron fully
delocalized on a 3dxy CB state.14 It is still a topic of discussion whether the “trapped electron”
resides on a single Ti center or on few Ti centers.
Concentration of the electrons in each of these states, i.e. CB, surface trap and bulk trap,
changes differently with the displacement of the Fermi level. Determining their electron
distributions is thus challenging but needed because they influence carrier transport and
recombination differently.3,19,20 These distributions are known to depend on the film
morphology,21 crystallinity,22 surface area23,24 and contacting solvent25,26. However, absence of
any reliable method to determine the band energetics in nanostructured semiconductor
photoanodes has also hindered an accurate determination of the distribution as well as the nature

39

of the various trap states. Using both spectroelectrochemical and electrochemical techniques, we
have successfully determined the electron densities in each of these states along with the spatial
location of the trap states.27,28 A spectroeletrochemical method is described in Chapter 2 which
helped us to determine the conduction band edge from the apparent shift in the band gap
transition, known as Burstein-Moss shift (B-M shift), in response to an applied bias.27 A very
interesting phenomenon observed in this work was the upward shift or unpinning of the CB
under negative bias which is generally ignored while studying the nanostructured photoanode
and the charge transfer processes related to it.

Figure 3-1 (Left) Energy vs. crystal momentum diagram of a semiconductor with an indirect
band gap. Electron transition from the highest-energy state in the valence band to the lowestenergy state in the conduction band is not possible without a change in momentum. The
transition occurs via the absorption or emission of a phonon, which provides the required
momentum change during the transition. Inter-band localized electronic states bellow the
conduction band, which trap electrons, are shown. (Right) Depiction of the upward shift of the
energetics in TiO2 nanoparticle film. ECB represents the magnitude of the upward shift of the
conduction band energy.

In this chapter, we utilized spectroelectrochemical measurements to determine the magnitude
of the band edge unpinning in the nanostructured TiO2 photoanode and its effect on the overall

40

charge distribution. From these results, we were also able to accurately calculate the total trap
state density and estimate the spatial location of the localized trap states in TiO2.
3.2 Electrochemical techniques for determining charge distribution
Standard electrochemical techniques like cyclic voltammetry (CV),29 electrochemical
impedance spectroscopy (EIS),30

potential step-chronoamperometry (charge

insertion-

extraction)31,32 have been established as effective methods for the determination of the DOS in
nanostructured metal oxide photoanodes. They are based on the measurement of the variation of
the electron density (dn) with displacement of the Fermi Level (dEF) caused by changing the
applied potential (dE). In this chapter, E represents energy and E (= E/q) represents the
electrochemical potential. Any variation of the Fermi level has homogeneous effect on the
electron concentration throughout the film as these photoanodes are made of a network of small
sized nanoparticles, generally 10-20 nm in diameter, and is surrounded homogeneously by
electrolyte.29,33,34 In the absence of significant IR drop along the nanoparticle network, dE = dEF
is well accepted.
The distribution of electrons is depicted by its chemical capacitance which describes the
capability of the system to store or release additional electrons during a variation of chemical
potential.33 Change in the Fermi level, causes a change in the electron density and hence in the
chemical potential of the electrons. Thus, the chemical capacitance can be written as the
variation of the electron density as a function of Fermi level,33

Cμ  q

41

dn
dEF

(1)

3.2.1 Cyclic voltammetry
Cyclic voltammetry has been established as an effective method to determine the chemical
capacitance (i.e. the distribution of the stored electrons) at different Fermi levels. Under cyclic
voltammetric scan, the voltage-injected electrons distribute through the nanoparticle network
until their chemical potential equalizes and the Fermi level becomes homogeneously distributed
throughout the porous film. This capacitance is written as C = dQ/dE which gives us J = l(1p)sC, where J is the current density, l is the film thickness, p is the porosity of the mesoporous
photoanode and s is the scan rate.29 Figure 3-2 shows the cyclic voltammogram and the
calculated C of a mesoporous TiO2 photoanode. A prominent peak appears (region A in Figure
3-2) at around -0.8 V vs. SCE, which is identified as monoenergetic trap states.3,35 At more
negative potentials (region B in Figure 3-2) an exponential distribution of density of states (DOS)
approaching the conduction band was observed which is given by the expression,33,36

g Trap (E) 

N Trap
k bTC

exp

(qE  ECB )
k bTC

(2)

where NTrap is the total density of exponentially distributed trap states, TC is a parameter having
the unit of temperature which implies the depth of the exponentially distributed trap states.
Another interesting feature is the deviation from exponential distribution that appears at higher
negative potential (region C) which will be discussed in details later. The CV plot and the onset
of this capacitance increase (point x in Figure 3-2) is sometimes used to estimate the conduction
band position.37–39 However, we would like to point out that, along with the electron distribution,
this onset also depends on the conductivity of film i.e. the electron diffusion through the
nanoparticle network.29,40 TiO2, along with other wide band gap semiconductors used in DSSCs,
behaves as an insulator in the absence of sufficient reductive bias. When the conductive substrate

42

(which holds the porous film) is biased, initially a gradient of the Fermi level will exist. Then,
the electrons spread by trapping-detrapping process from localized states into CB or/and hopping
between trap sites until a homogeneous occupancy is attained though the film. Now, trappingdetrapping method requires certain electron density in the CB and the hopping process needs
large enough density of electrons in the trap states for fast quantum-mechanical tunneling
transition.23

Figure 3-2. Cyclic voltammogram plot (left) and chemical capacitance plot (right) of TiO2 film
in aq. 0.2 M KCl solution at pH 12.8. Scan rate was 50 mV / s. The chemical capacitance (C)
was calculated using the relation J = l(1-p)sC, where J is the current density, l (= 6.95 m) is
the electrode thickness, p (= 0.71) is the porosity of the TiO2 film and s is the scan rate. The peak
at approximately  0.75 V vs. SCE is referred to as monoenergetic trap state distribution and the
wave at increasing negative potentials corresponds to the exponential distribution of trap states.

Accurate and homogeneous distribution of chemical capacitance will only be determined
when the charge equilibration is fast enough. A very common observation of this CV analysis is
that, under very fast scan, the onset moves to more negative potential suggesting that this
equilibration has not been reached. However, a slower scan is not always better. The

43

characteristic capacitance filling disappears when the scan rate is slow enough where the current
loss through Faradaic processes dominates.29 Proper range of scan rates need to be chosen where
the Fermi level equilibration occurs through the nanoparticle network and current loss through
the Faradaic processes are negligible.
3.2.2 Electrochemical impedance spectroscopy
Electrochemical impedance spectroscopy (EIS) is another widely used technique to study the
capacitive processes in the semiconductor.30,41 A transmission line model needs to be used in
case of porous photoanodes instead of simple Randal circuit. The equivalent circuit suitable for
this mesoporous photoanode film is shown in Figure 3-3. This circuit illustrates the internal
distribution of chemical capacitance in response to the modulated small perturbation of the
steady state bias. Distribution of C with energy, determined by EIS using transmission line
model, is shown in Figure 3-4. Rs is series resistance accounting for the transport resistance of
the conductive substrate, Rt is the electron transport resistance through photoanode nanostructure,
Rr is the resistance at the nanoparticle/electrolyte interface. Simple Randal circuit is still being
used by some researchers to fit the impedance data. However, it should be taken into account that
Randal circuit can only be applicable when this nanoparticle network is sufficiently conductive
i.e. Rt is negligible. To study this porous semiconductor photoanode in a wide range of bias,
transmission line model needs to be used. Also, at low cathodic potentials, measured capacitance
is attributed to the substrate/electrolyte interface and should not be confused with NP/electrolyte
interface.42,43 Moreover, the apparent onset in the capacitance plot is not the flat band potential; it
is the point where the chemical capacitance begins to dominate the measured capacitance.

44

Figure 3-3 Equivalent circuit based on transmission line model for fitting Electrochemical
Impedance data of porous photoanode. The fit parameters are described in the text.

Figure 3-4 Plot of capacitance (C) of TiO2 film measured by electrochemical impedance
spectroscopy. Electrolyte was 0.2 M aq. KCl solution at pH 12.8.

45

3.2.3 Charge insertion/extraction method
Charge insertion/extraction measurement provides a direct method to determine the total
electrons stored in the photoanode at a certain Fermi level.31,32 In this method, the electrons are
inserted into the photoanode under a bias, e.g. illumination or potentiostatic bias. Then, after the
Fermi level stabilizes and all the states below that energy level are filled, the electrons are
extracted by removing the previous bias or by applying discharging (oxidative) bias. Using
Chronoamperometric setup, the current (i) is measured with time (t) and the total charge, Q, is
calculated by integrating the area under current-time curve (Q = i.t). Figure 3-5 shows a typical
current-time plot of charge insertion and extraction under potentiostatic bias. The charge
accumulated under that negative (reductive) bias can be calculated from the current decay curve
in both charging region and discharging region. Ideally, they should provide the same value.
However, in presence of any Faradaic process (e.g. H2 evolution) or any irreversible ion insertion
process, the extracted charge is lower than inserted charge.44 Charge calculated during the
extraction process is more reliable to give information about the amount of electrons stored at
any energy level. We can write,
EF

Q  q  N ( E )dE

(3)

E0

where N(E) is the electron density as a function of the Fermi level (EF = E), E0 is the discharging
(oxidative) bias or the solution potential. Thus, we can directly get the distribution of the density
of states from this relation,

N (E) 

46

1 dQ
q dE

(4)

The above methods are effective to calculate the overall electron density in the mesoporous
photoanodes. However, they cannot separate the density of delocalized CB electrons from the
trapped electrons and, also, are unable to differentiate the surface trapped electrons from the
electrons trapped in the bulk. Each of these states responds to the electron transfer mechanisms
very differently and, therefore, needs to be determined separately.3

Figure 3-5 Typical current vs. time plot measured during charge insertion/extraction process
under potentiostatic. The measurement was performed with mesoporous TiO2 film in contact
with aq. 0.2 M KCl solution at pH 12.8. The reductive bias was  1.045 V and the oxidative bias
was + 0.455 V vs. SCE.

3.3 Experimental
3.3.1 TiO2 photoanode preparation
The transparent mesoporous anatase TiO2 electrode was prepared by spreading HT/SP TiO2
paste (Solaronix) on fluorine-doped tin oxide (FTO) conducting glass (Hartford Glass) by the
doctor-blade method, followed by sintering at 500°C for 15 min in air. The thickness of the TiO2
film was measured by a Dektak3 Surface Profiler and found to be 6.950.05 μm. The porosity, p,

47

of the mesoporous TiO2 film was also determined. 15 TiO2 films (geometric area 64 mm2 and
thickness 6.95 m) were collected from the FTO by scraping out with a sharp blade. The total
mass of the collected TiO2 material was measured. Total volume of the 15 films was then
calculated which is 64 mm2  6.95 m 15 and the mass of the solid TiO2 material without any
pores was calculated from the density of anatase material, 3.93 g / cm-3. Porosity is calculated
using the equation, p = 1 – (measured mass of porous film / calculated mass of solid material).
3.3.2 Electrolyte preparation
Aqueous electrolyte solutions were prepared by dissolving recrystallized potassium chloride
into Millipore water (18.2 M-cm). pH of the electrolytes were adjusted to 12.8 and 2.0 by
adding KOH and HCl, respectively.
3.3.3 Measurements
In spectroelectrochemical measurements, the transmittance (%T) of the film was measured
by a Perkin Elmer Lamda 35 UV-Vis spectrophotometer under an external bias provided by a
potentiostat (-Autolab, Metrohm). A three electrode electrochemical cell, made by customizing
a commercial spectroscopic cuvette (Quartz Spectrophotometer Cell, Starna Cells, Inc), was
placed into the UV-Vis spectrophotometer such that the TiO2 film remained perpendicular to the
optical path as shown in Figure 2-2. A platinum wire (diameter 1.5 mm) was used as counter
electrode and a commercial “Leakless Miniature” Ag/AgCl reference electrode (EDAQ ET072)
was used. All electrochemical measurements done here were three-electrode measurements. The
TiO2 electrode was sealed to an opening of an electrochemical cell with a Viton O-ring. TiO2
films were aged overnight in contact with the electrolyte solutions and N2 gas was purged into
the aqueous electrolytes for 30 minutes, prior to any measurement. During charge extraction

48

method, the electrode was charged for 5 minutes followed by applying a positive bias (+0.455 V
vs. SCE) to extract all the charges stored during charging. The current was measured against time
and the total charge was calculated by integrating the area under the current vs. time curve. Prior
to the cyclic voltammetry scan, a significant positive potential (+0.455 V vs. SCE) was applied to
the film to discharge all the electrons from the film. Electrochemical Impedance (EIS)
measurements were done in the dark. At each potential, the frequencies were equally spaced in
logarithmic steps between 2×10-2 to 1×105 Hz. The counter electrode used in the
spectroelectrochemical measurements was a platinum wire and a high surface area platinum
mesh was used in electrochemical experiments. A homemade Ag/AgCl reference electrode was
used during all the measurements. Its potential was measured against a commercial saturated
calomel electrode (SCE); all the applied potentials are reported vs. SCE. The TiO2 films were
aged overnight in contact with the electrolyte solutions prior to any experiments. The
temperature of the electrochemical cells was 220.5 ⁰C during the measurements. During
spectroelectrochemical measurements, each film was stabilized at an applied bias for 5 minutes
and %T of the electrode was measured. A control experiment was done with bare FTO electrode
to confirm that the FTO has no contribution into the change in %T with varying potential.
Stability of the film as well as reproducibility of the results was checked both spectroscopically
as well as electrochemically to make sure that there is no irreversible change of the film during
the measurements. The difference absorbance spectrum, A, is the absorbance change under
external bias. At first, the absorbance was measured under a significantly positive potential to
discharge all the stored electrons from the film. Then a negative potential was applied to increase
the electron population and the absorbance was measured. Absorbance measured at positive
potential was subtracted from the absorbance at negative bias and thus A was calculated.

49

3.4 Results and discussions
3.4.1 Accurate energy distribution of trap states in mesoporous TiO2 photoanode
The upward shift of ECB when the applied potential is increased to more negative values was
shown in Chapter 2. This shift was attributed to the potential drop across the Helmholtz layer.45–
47

Change in the electric field of the Helmholtz layer occurs due to the accumulation of electrons

in electrically active states on the surface or in close vicinity of the surface of mesoporous TiO2
films.
In order to calculate the magnitude of the upward shift of conduction band, ECB, an initial
position of the conduction band, E*CB, needs to be determined. Figure 3-6 shows a plot of EG
determined as a function of E. A linear extrapolation of this plot to the intercept, corresponding
to no bandgap shift, produced values of –1.17 V vs. SCE at pH 12.8 and –0.55 V at pH 2.0 for
E*CB. Though no theoretical background of this linear behavior can be found, it gives an estimate
of the initial value for CB edge potential. The expected Nernstian shift of the conduction band
with pH was observed, which can be expressed by:
E*CB / q  0.435V(vs.SCE)  0.058  pH

(5)

This Nernstian behavior is well known for metal oxide semiconductors in aqueous electrolytes.48

50

Figure 3-6. The position of the conduction band edge potential determined at pH 12.8 and 2.0.

Knowledge of the band edge shift, ECB/q (= E*CB/q  ECB/q), is required for accurate
determination of the charge distribution by electrochemical methods.
Now, equation 2 is expected to provide the actual distribution of localized states only if ECB
is fixed, which is not the case. At more negative applied potentials, the parameter ECB/q, i.e. the
potential drop across the Helmholtz layer, needs to be included. Thus, equation 2 should be
rewritten as:

g ETS ( E ) 

N ETS
(qE  ECB  ECB )
exp
k bTC
k bTC

(6)

Therefore, C is expected to increase exponentially with (E  ECB/q) instead of E, as
depicted in Figure 3-7. Inclusion of ECB/q causes two major modifications to the plot of the
chemical capacitance. 1) The deviation of C from the exponential behavior at high negative
potentials disappears and 2) the exponential slope as well as the value of TC changes significantly.

51

At lower potentials, the magnitude of the potential drop is small and there is an overlap between
the tail of the Gaussian distribution and the exponential distribution of trap states which may be
the reason behind the exponential like increase of C. However, at those potentials the lnC vs. E
plot does not necessarily represent the actual distribution of the localized states as the corrected
TC (682 K) is significantly different than the values of TC (975 – 1667 K) calculated from the
lnC vs. E plot without considering band edge unpinning. Therefore, the common practice of
interpreting electrochemical data assuming a fixed band edge position without the necessary
consideration of the band edge shift gives rise to a significant error in the determination of the
electron distribution in nanostructured semiconductor photoanodes. The monoenergetic trap
states shows a peak at ~0.8 V vs. SCE in CV scan and is not observed in the potential range
where the chemical capacitance (Figure 3-7) is measured by EIS measurements.

Figure 3-7. Plot of the chemical capacitance (C) as a function of applied potential, E, (bottom
axis, red circles) and applied potential which is corrected to include the effect of band edge
unpinning (ECB/q) as shown in equation 7 (top axis, blue triangles).

52

Another example where the band edge shift needs to be considered is in the interpretation of
the visible absorbance (A) of the TiO2 photoanodes for the spectroelectrochemical analysis of the
charge transfer processes in DSSCs.49,50 The calculated nCB showed an excellent linear
relationship with the measured A in accordance with the Beer-Lambert law:

A   CBl (1  p)M CB

(7)

where CB is the extinction coefficient of delocalized CB electrons and MCB is the molar
concentration (mole L-1) of CB electrons.27 However, participation of the trapped electrons in the
absorbance spectra has been invoked by many researchers, primarily because of the close
resemblance of the slope of absorbance (A) vs. E with the slope of nTrap vs. E as well as the slope
of nTotal, total concentration of the electrons in the film, vs. E.13 Density of both free and trapped
electrons increase with negative potential, in addition to conduction band edge movement.
Explaining the correlation between the intra-bandgap trapped electrons and the measured
absorbance based on the resemblance of their slopes is not straightforward and might be
misleading.
Assuming a fixed conduction band, the absorbance of the CB electrons should increase
exponentially with E (= EF/q) according to the following equation,
nCB  N CB exp

(EF  ECB )
k bT

(8)

Thus, a semi-logarithmic plot of A vs. E, should be linear with a slope of 1/kbT = 39.2 V-1.
However, the experimental slope of ln(A780nm) vs. E was found to be ~11 V-1, as shown in Figure
3-8. Because of the upward movement of ECB, the magnitude of change in (ECB/q – E) is actually
smaller than the change in the applied bias, E. Thus the slope of ln(A780nm) vs. E is much lower

53

than the ideal slope 39.2 V-1. Considering the band edge movement, however, equation 9 can be
rewritten as:

nCB  N CB exp

(EF  ECB  ECB )
k bT

(9)

Combining equations 7 and 9, the following expression is produced to describe the expected
dependence of absorbance with applied potential:

ln( A)  ln( CBEl (1  p) N CB ) 

ECB (qE  ECB )

k bT
k bT

(10)

Figure 3-8 shows excellent agreement between the slope of ln(A780nm) vs. (E  ECB/q) and the
ideal slope of 39.2 V-1 (1/kT).

Figure 3-8. Plot of absorbance of TiO2 at 780 nm as a function of applied potential (bottom axis,
red circles) and applied potential which is corrected to include the effect of band edge unpinning
(top axis, blue triangles).

54

3.4.2 Spatial location of the trap states
The band edge shift can also provide information about the spatial location of the trap states.
Trap states are reported to be present predominantly on the surface of the nanoparticle (NP)11
although trapping of electrons in the bulk nanoparticle is also reported.10 The band edge
unpinning suggests that the nanostructured TiO2 film has a high density of surface states which
can accumulate electrons under negative bias. To maintain the charge neutrality, this electron
accumulation is accompanied by positive charges, i.e. the cations in the electrolyte, at the
semiconductor/electrolyte interface which causes potential difference in the Helmholtz layer.
The potential drop across the Helmholtz layer i.e. the upward shift of the conduction band,
ECB/q, and the surface charge concentration (nS) can be related by the following equation:

ECB / q 

qnS
CH

(11)

Here CH is the Helmholtz layer capacity which was determined by measuring the capacitance of
a flat TiO2 film by electrochemical impedance spectroscopy and found to be ~6 Fcm-2. The
total concentration of electrons in the film can be expressed as nTotal = nCB + nTrap. Charge
extraction was performed to determine nTotal as a function of potential, and nCB was determined
from the B-M shift, thus allowing calculation of nTrap. The total concentration of trapped
electrons can be expressed as the sum of surface trapped electrons and the bulk trapped electrons,
nB.

55

Figure 3-9. Plot of the concentration of trapped electrons in the bulk (nB) and on the surface (nS)
of TiO2 film in aq. 0.2 M KCl solution at pH 12.8. Extrapolation of the fitted plots to the
conduction band edge gives the density of bulk trap states, NB, and surface traps, NS.

Figure 3-10. Plot of electron density in the nanostructured TiO2 photoanode as a function of
applied potential. The total trapped electron density (nTrap) is the sum of the electrons trapped on
the surface (nS) and in the bulk (nB).

56

Figure 3-10 shows a plot of the concentration of electrons in surface traps calculated from
equation 12 and bulk traps determined by subtracting the surface traps from the total traps. Both
nS and nB increase with negative bias, but their slopes are different. NS, density of surface states,
and NB, density of bulk traps, are found to be 2.4  1019 cm-3 and 1.4 1021 cm-3, respectively
(Figure 3-9). The trap states are localized Ti3+(3d) states which can accept (trap) electrons and
releasing (detrapping) this electrons needs some driving force. They are energetically located
below CB edge. Above this edge, electrons are delocalized “free” electrons. The surface states
are the localized sites on the surface or in close vicinity to surface those can trap electrons.
Presence of under coordinated TiIV/TiIII centers or any terminal oxo/hydroxo sites have been
observed on the surface of the nanoparticles.51,52 Additionally, electrons are also trapped in the
bulk.48,53 When a negative (reductive) bias is applied to the photoanode the electron is first
injected into the CB and transported through the delocalized CB states distributed uniformly in
the bulk photoanode material. Thus, the availability of electrons to be captured by the trap
centers in the bulk and on the surface is the same. The excess negative charge of these injected
electrons in the photoanode must be neutralized by the equivalent charge of the cations. At low
applied potentials, the trapped electron density is dominated by the electrons in surface traps.
The negative charge on the surface can be compensated by electrolyte cations such as K + or H+
present in the aqueous solutions. Since the electrolyte contains ~1012 times more K+ than H+ in a
pH 12.8 solution with 0.2 M KCl, we suggest K+ is the more likely surface charge compensating
cation. Considering NS = 2.4 1019 cm-3, the area available for each compensating cation
adsorbed on the NP surface is ~7 nm2. K+ ions has an effective ion radius of 1.38 Å54 which
implies that sufficient space is present to accommodate the solvated K+ ions compensating the
surface charge. As shown in Figure 3-10, at low reductive region, the trapped electron density is

57

dominated by the electrons in the surface traps because they are easily charge compensated by
K+ and/or H+. More negative bias forces the H+ to insert into the nanoparticle to compensate the
charge which involves bond length adjustment or/and breaking of Ti-O bonds. Another very
interesting observation is, while the density of surface states does not change much with the
increasing negative potential, the bulk trap states increases rapidly with an exponential
dependence on the applied potential. We have explained it by the fact that the available sites to
adsorb K+(solvated) is limited by their steric hindrance as well as columbic repulsion. Although
K+ is unlikely to penetrate into the bulk and compensate the electron charge arising from
trapping electrons in bulk states,55 H+ insertion into the TiO2 material under negative bias has
been found to be reversible in the potential range used here.48,56 Under increasing negative
potential, the bulk trapped electrons are therefore compensated by H+ insertion. This H+ can
reside in the interstitial space in an O6 octahedral site or can form a covalent bond with a
neighboring oxygen.57 Additionally, under reductive bias, proton insertion is known to create
TiIII centers which trap electrons.48 With increasing negative potential, the bulk trap starts
dominating the total trap density and at the negative end it has become an order of magnitude
higher than the surface trap as shown in Figure 3-9. It can be explained by the ease of H+
insertion into anatase NPs and availability of more space as well as Ti-centers in the bulk than
the surface (~ 6 times more Ti atoms in the bulk than on the surface). The total density of states
of bulk traps below the CB edge is two orders of magnitude higher than the density of surface
traps (NS = 2.4  1019 cm-3 and NB = and 1.4 1021 cm-3). A very interesting point needs to be
discussed here is the “surprisingly” high densities of the trap states. The value of NS and NB
translates to ~ 4e/nanoparticle and ~ 224e/nanoparticle, respectively. Berger et al. reported ~
650e/nanoparticle based on the charge extraction method.13 The diameter (d) of the nanoparticle

58

(NP) used in their study was 20 nm and the diameter of the nanoparticles used in our study is 10
nm.13 Their findings are quite similar to the values we found for total trapped electron density.
This huge number of electrons is unlikely to be captured by the defect states. Storage of electrons
inside a nanoparticle may have different mechanisms. Though it is not the scope of this study, we
can discuss some of the possibilities based on the findings and hypotheses in the literature.
Hupp et al. showed intercalation of charge-compensating cations in the TiO2 NPs under
electrochemically reduced bias.48,53,58 Interestingly, they observed reversible proton insertion into
the NPs even under conditions where surface adsorption of protons is not plausible. It suggests
two interesting points, 1) charge neutralization processes on the surface and in the bulk are very
different and 2) insertion of electron in the NPs can occur even without the availability of
protons in the aqueous solution like highly basic solution (pH 12.8 was used in our study). The
high density of electrons stored and discharged during the charge insertion-extraction process
can be explained by the processes observed in intercalation-based battery materials. A possible
explanation behind the observed exponential increase in bulk trapped electron density with
applied reductive bias is the higher driving force for electron insertion accompanied by proton
intercalation. This process can electrochemically generate Ti(III) centers even in the absence of
any prior “defect” centers. The proton bounds to a lattice oxygen and the inserted electron is
localized on the adjacent Ti center. Point to be noted that extent of localization of this electron is
a still a topic of debate.48
3.5 Conclusion
A spectroelectrochemical method has been described that allows for the quantitative analysis
of the band edge unpinning in nanostructured semiconductor photoanodes. The position of the
conduction band edge in porous TiO2 photoanode was determined from the Burstein-Moss shift

59

observed under negative potential. The upward shift of the conduction band edge has been
explained by the presence of large density of the electrons accumulated on the surface of
nanoparticles causing potential drop across the Helmholtz layer. The magnitude of the band edge
unpinning should be included while studying the nanostructured photoanode and the charge
transfer processes related to it. Moreover, the trap states are found distributed across the surface
as well as in the bulk and with increasing negative bias bulk traps dominate the overall chemical
capacitance. Knowledge of the spatial as well as the accurate energy distribution of the trap
states are required to study their participation into the electron-transfer processes. The trap states
present on the surface or in close vicinity of the surface are more likely to participate in the
surface mediated charge transfer processes than the bulk traps. Such detailed understanding is
especially important in describing recombination reactions which generally limit the
performance of DSSCs.

60

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64

Chapter 4 Absorbance Features of Mesoporous TiO2 Electrode under
Electron Accumulation
4.1 Introduction
Mesoporous TiO2 films are widely studied for their potential in photovoltaic, photocatalytic
and electrochromic applications. The behavior of the charge carriers in these films under external
bias has been an important field of study. Electrochemical techniques are used to study the
populated states as well as the associated charge transfer processes which rely on the measured
relationships between potential, current, and charge. Furthermore, spectroscopic techniques are
often combined with the electrochemical measurements to get further insight into the
electrochemical processes that cannot be obtained from the electrochemical experiments alone.
In spectroelectrochemical methods, the charge carriers in the bulk electrode or at the electrodeelectrolyte interface are spectroscopically monitored as a function of applied potential. The
measured absorbance or reflectance is then translated into the carrier density provided the
corresponding extinction coefficient is known. However, two major challenges in this process
are 1) assigning a certain absorbing species that contribute to the measured spectra and 2)
determining the extinction coefficient of the species of interest.
Fitzmaurice et al. studied the absorbance of the mesoporous TiO2 film under accumulation
conditions.1,2 In this method, TiO2 films, made of nanoparticles (NPs) with an average diameter
of 15 nm, were deposited on a transparent conductive substrate. Due to the good electronic
connectivity among nanoparticles and equipotential environment surrounding the nanoparticles,
the Fermi level (EF) within the TiO2 nanoparticle electrode can be controlled by applying an
external bias to the conductive substrate.3–6 The absorbance of the film was measured while

65

applying large negative bias during the cyclic voltammetric scan. The measured absorption at a
certain applied potential (E) was correlated to the electron population in the semiconductor film
at the Fermi level EF which is equal to qE (q = charge of an electron). Here, E represents energy
and E (=E/q) represents the electrochemical potential. They observed that the absorbance in the
visible region was increased while raising the Fermi level which was attributed to the absorption
by the increasing population of the electrons. The characteristic of the absorbance spectra shows
resemblance with the free carrier absorption generally described as Drude absorption.7 The
density of free electrons, flat band position and the extinction co-efficient were determined from
this absorbance data assuming a Schottky junction model. The key idea of this model was the
formation of an accumulation layer within each nanoparticle as the applied potential was shifted
negative of the flat-band potential. Assumption of a flat interface and Schottky junction is
unlikely in these small nanoparticles and the validity of the model has been debated.8–10
Moreover, the nature of the absorbing species has also been a long debated issue. Large density
of trapped electron is known to be present in the mesoporous TiO2 electrodes. Many researchers
have assigned this absorption to the trapped electrons primarily because of the close resemblance
between the slope of absorbance vs. E and the slope of trapped electron density vs. E or the slope
of total electron density vs. E as well.11–15 However, it is not that straightforward and might be
misleading as both free and trapped electrons increase with negative potential. Additionally,
conduction band edge shift, as described in Chapter 2, makes it difficult to determine the
accurate slope. Thus analyzing localized electronic states, such as Ti(III) created under reduced
conditions, from the measured absorption might lead us to erroneous interpretation.
Moreover, extinction coefficient of the CB electrons (CB) needs to be known in various
spectroscopic studies of the electron transfer processes in DSSCs. While performing

66

spectroscopic studies on various DSSC components other than the photoanode, the absorption
contribution of the photoanode needs to be subtracted from the measured absorption to monitor
the spectroscopic behavior of the desired component. The literature values of CB are typically
determined by correlating the absorbance with the concentration of electrons in the TiO2
electrode measured either by chronoamperometry or titration. These techniques, however,
measure the total concentration of electron in the TiO2 film, both trapped and free electrons.
Considering that trapped electron concentration is orders of magnitude higher than the free CB
electrons, as shown in Chapter 3, the measured extinction coefficients of free CB electrons are
underestimated by one or two orders of magnitude.
In this work, the absorbance characteristics of mesoporous TiO2 film under reductive bias
have been revisited. Detailed spectroeletrochemical study was performed with nanostructured
TiO2 photoanode films in contact with various electrolyte solutions. The extinction coefficient of
the electrons has been determined by spectroelectrochemical method.
4.2 Experimental
4.2.1 TiO2 photoanode preparation
The transparent mesoporous anatase TiO2 electrode was prepared by spreading HT/SP TiO2
paste (Solaronix) on fluorine-doped tin oxide (FTO) conducting glass (Hartford Glass) by the
doctor-blade method, followed by sintering at 500°C for 15 min in air. The thickness of the TiO2
film was measured by a Dektak3 Surface Profiler and found to be 6.950.05 μm. The porosity, p,
of the mesoporous TiO2 film was also determined. 15 TiO2 films (geometric area 64 mm2 and
thickness 6.95 m) were collected from the FTO by scraping out with a sharp blade. The total
mass of the collected TiO2 material was measured. Total volume of the 15 films was then

67

calculated which is 64 mm2  6.95 m 15 and the mass of the solid TiO2 material without any
pores was calculated from the density of anatase material, 3.93 g / cm-3. Porosity is calculated
using the equation, p = 1 – (measured mass of porous film / calculated mass of solid material).
4.2.2 Electrolyte preparation
Aqueous electrolyte solutions were made by dissolving recrystallized salts into Millipore
water (18.2 M-cm). Anhydrous acetonitrile (Sigma Aldrich) was used as received.
Tetrabutylammonium hexafluorophosphate (TBAPF6), lithium hexafluorophosphate (LiPF6),
lithium perchlorate (LiClO4) and sodium hexafluorophosphate (NaPF6) were recrystallized and
dried under vacuum at 80 C for 48 hours prior to any use. All the aqueous and acetonitrile
electrolytes contain 0.2 M inert salts i.e. KCl, TBAPF6, LiPF6, LiClO4, NaPF6. A Fischer
Scientific Accumet pH meter was used to measure the pH of the aqueous electrolytes. pH were
maintained by different types of buffer systems like citrate buffer (pH 6.2), imidazole buffer (pH
6.2 and pH 7.8) and phosphate buffer (pH 7.8). Drops of hydrochloric acid (HCl) and potassium
hydroxide (KOH) were added to adjust the pH to the desired value. pH 12.8 was made with
KOH only and pH 2.0 was made with HCl only.
4.2.3 Spectroelectrochemical measurement
In spectroelectrochemical measurements, the transmittance (%T) of the film was measured
by a Perkin Elmer Lamda 35 UV-Vis spectrophotometer under an external bias provided by a
potentiostat (-Autolab, Metrohm). A three electrode electrochemical cell, made by customizing
a commercial spectroscopic cuvette (Quartz Spectrophotometer Cell, Starna Cells, Inc), was
placed into the UV-Vis spectrophotometer such that the TiO2 film remained perpendicular to the
optical path as shown in Figure 2-2. A platinum wire (diameter 1.5 mm) was used as counter

68

electrode and a commercial “Leakless Miniature” Ag/AgCl reference electrode (EDAQ ET072)
was used. The TiO2 films were aged overnight in contact with the electrolyte solutions prior to
any experiment. The temperature of the electrochemical cells was 22  0.5 ⁰C during the
measurements. During spectroelectrochemical measurements, each film was stabilized at an
applied bias for 5 minutes and %T of the electrode was measured. A control experiment was
done with bare FTO electrode to confirm that the FTO has no significant contribution into the
change in %T with varying potential. Stability of the film as well as reproducibility of the results
were checked both spectroscopically as well as electrochemically to make sure that there is no
irreversible change in the film during the measurements.
The difference absorption spectrum, A, is the absorbance change under external bias. At
first, the absorbance was measured under a significantly positive potential to discharge all the
stored electrons from the film. Then a negative potential was applied to increase the electron
population and the absorbance was measured. When the Fermi level moves closer to the
conduction band (CB) the density of the electrons (nCB) increases exponentially according to the
following relation:
nCB  N CB exp

(EF  ECB )
k bT

(1)

where ECB is the conduction band minima and NCB is the density of states (DOS) in the
conduction band. Absorbance measured at positive potential was subtracted from the absorbance
at negative bias and thus A was calculated. The wavelength range was selected from 450 nm to
800 nm considering the appearance of a broad peak at ~400 nm and a strong solvent absorbance
in the near IR region starting at ~ 900 nm. The peak ~400 nm was correlated to the surface trap
states in literature.16

69

4.3 Results and discussion
Figure 4-1 shows the change of transmittance (%T) when reductive potential was
applied. %T shown here is the transmittance of the electrochemical cell which includes
mesoporous TiO2 film, FTO glass substrate, cuvette and electrolyte in the optical path. In the
absence of a TiO2 film, %T of the other components in the optical path did not change in
response to the applied potential range of interest herein. Therefore, we attribute this change
in %T exclusively to the TiO2 film.

Figure 4-1 Transmittance (%T) spectra of TiO2 photoanode in contact with aqueous 0.2 M KCl
solution at pH 12.8. Potentials are given against SCE.

The absorbance difference (A), in 4-2a,b, shows the change in the absorbance of the TiO2
film when electron population is changed under applied potential. The absorbance increases in
the visible and the near-IR regions with increasing (negative) applied potential with a
concomitant decrease at wavelengths shorter than ~380 nm. The absorption bleaching below

70

~380 nm is attributed to the filling of conduction band states which gives rise to the Burstein–
Moss shift.17–22
(a)

(b)

Figure 4-2 Change in absorbance of a TiO2 electrode under reductive bias. (a) TiO2 film is in
contact with a pH 12.8 aqueous electrolyte when potential is stepped from + 0.455 V to  1.245
V (red),  1.295 V (green),  1.345 V (yellow),  1.395 V (blue) and  1.445 V (pink) vs.SCE
(from bottom to top). (b) TiO2 film is in contact with a pH 2.0 aqueous electrolyte, potential is
stepped from + 0.955 V to  0.495 V (red),  0.545 V (green),  0.595 V (yellow),  0.645 V
(blue) and  0.695 V (pink) ,  0.745 (sky blue) vs.SCE (from bottom to top).

71

(a)

(b)

Figure 4-3 Global fit results (black lines) of the absorbance spectra from Fig. 4-2a,b according
to Drude equation. (a) TiO2 film is in contact with a pH 12.8 aqueous electrolyte when potential
is stepped from + 0.455 V to  1.245 V (red),  1.295 V (green),  1.345 V (yellow),  1.395 V
(blue) and  1.445 V (pink) vs.SCE (from bottom to top). (b) TiO2 film is in contact with a pH
2.0 aqueous electrolyte, potential is stepped from + 0.955 V to  0.495 V (red),  0.545 V
(green),  0.595 V (yellow),  0.645 V (blue) and  0.695 V (pink) ,  0.745 (sky blue) vs.SCE
(from bottom to top).

72

(a)

(b)

Figure 4-4 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolyte is 0.2 M KCl at pH 6.2 adjusted by Citrate buffer (top) and
Phosphate buffer (bottom). Potential shown in the plot is given vs. SCE.

73

(a)

(b)

Figure 4-5 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolyte is 0.2 M KCl at pH 7.8 adjusted by Phosphate buffer (top) and
Imidazole buffer (bottom). Potential shown in the plot is given vs. SCE.

74

(a)

(b)

Figure 4-6 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolytes are 0.2 M LiClO4 at pH 7.8 (top) and ~ aqueous 0.05 M NaPF6
solution (bottom). The pH of the LiClO4 solution was adjusted at 7.8 by Imidazole buffer. No
buffer was added into aq. NaPF6 solution. Potential shown in the plot is given vs. SCE.

75

(a)

(b)

Figure 4-7 Global fit results (black lines) of the absorption spectra of TiO2 film according to
Drude equation. Electrolytes are 0.2 M LiClO4 (top) and TBAPF6 (bottom) in acetonitrile.
Potential shown in the plot is given vs. SCE.

The increasing visible and near-IR absorption with bias is due to the increasing electron
population in the TiO2. We attribute this broad absorption to free (delocalized) electrons in the
TiO2 conduction band, CB. The conduction band electrons (CBEs) are delocalized and they have

76

a continuum of possible electronic excited states resulting in a broad absorption in visible and
near IR region. It showed a monotonic increase of absorptivity of TiO2 film with the wavelength
According to the Drude-Zener theory, the absorption of delocalized (free) electrons gives rise to
a wavelength dependent absorption spectrum according to,

A  C P

(2)

where C is a scaling parameter,  is the wavelength of light and the exponent, P, is a value from
1.5 – 3.5, depending on the scattering mechanism. Scattering by acoustic phonons gives rise to P
= 1.5, scattering by optical phonons produces P = 2.5 a scattering by ionic impurities gives P = 3
– 3.5.7
Figure 4-2a,b shows the difference absorption spectra in the wave length range of 450 nm to
800 nm and the results of a global fit of P to all spectra in equation 1. The fit produces a value of
P = 1.66 and 1.85 when the TiO2 electrode is in contact with 2.0 and 12.8, respectively, which
are well matched to the theoretical value of P for the absorption by free electrons coupled with
acoustic phonon scattering. Analogous measurements were performed in a variety of pHs and
non-aqueous electrolytes. The results of fitting the absorption spectra under these different
conditions to equation 1 are shown in Table 4-1. In all cases, the P value is close to 1.5. This is
consistent with the assignment of the absorption in this wavelength range being dominated by
free conduction band electrons since this absorbance is a property of the nanoparticle and
independent of contacting electrolyte. Panayotov et al. have done detailed study of the free
electron absorption in TiO2.23–28 The free CB electrons were increased by UV- photoexcitation,
n-doping (by atomic hydrogen) and thermal reduction, and the characteristic absorption spectra
showed excellent agreement with the Drude equation (equation 2). Values of P were found to be
1.5 – 1.7 in their study which matches closely to the values we observed when we increased the

77

CB electrons by applying reductive potential. In a recent report, Trizio et al. observed similar
free electron absorption in visible and IR region when the CB electron population in TiO2
nanoparticles was increased by niobium doping.29 It implies that the free CB electrons have
major contribution to the visible absorbance of mesoporous TiO2 film under reduced bias.
Table 4-1 Values of P in presence of different electrolyte solutions. The absorption spectra of
TiO2 electrode in contact with different electrolyte solution were measured and fitted to Drude
equation, A = CP. Global fit of several spectra measured in an electrolyte condition provided
the value of P.

Electrolyte solution

P

Aq. 0.2 M KCl, pH 2.0, pH adjusted by HCl

1.66

Aq. 0.2 M KCl, pH 6.2, Citrate Buffer

1.66

Aq. 0.2 M KCl, pH 6.2, Imidazole Buffer

1.57

Aq. 0.2 M KCl, pH 7.8, Imidazole Buffer

1.47

Aq. 0.2 M KCl, pH 7.8, Phosphate Buffer

1.63

Aq. 0.2 M LiClO4, pH 7.8, Imidazole Buffer

1.41

Aq. 0.2 M KCl, pH 12.8, pH adjusted by KOH

1.85

Aq. 0.2 M NaPF6

1.58

0.2 M TBAPF6 / Acetonitrile

1.56

0.2 M LiClO4 / Acetonitrile

1.99

Now, as discussed in Chapter 2, filling the lowest energy states of the CB blocks the band
gap transition i.e. the minimum energy required to excite an electron from the top of the valence
band to the bottom of the CB. The extra energy required to find the available energy states in the
CB results in a blue shift in the band gap absorption which is generally known as Burstein-Moss
shift. The magnitude of this shift translates into the density of electrons in the CB. These CB

78

electrons can absorp light in the visible – near IR region. Figure 4-8 shows the plot of absorbance
measured at 780 nm vs. the density of electron calculated from the Burstein-Moss shift observed
in UV region. The linear correlation of nCB and A further supports our assignment of absorbing
species to the free CB electrons and also allows for the calculation of the extinction coefficient
(CB) of these electrons from the slope according to Beer’s law:

A   CBl (1  p) M CB

(3)

where l is the electrode thickness, p is the porosity and MCB is the molar concentration (mol L-1).
Using values of l = 6.95 m and p = 0.71, CB was calculated to be 1.7  104 M-1cm-1 at 780 nm
when TiO2 is in contact with pH 12.8. Our calculated value of CB is approximately an order of
magnitude higher than the values found in literature measured using different methods.30–34 Prior
methods did not discriminate free conduction band electrons from the large total concentration,
ntotal, of trapped electrons. Thus, a large fraction of electrons in TiO2 are not participating in the
absorption pattern in the visible range, which supports the higher value of CB determined here.
When we use charge extraction method (described in Chapter 3) to quantify ntotal in TiO2, a
valued of CB = 7  102 M-1 cm-1 is determined, consistent with literature underestimates.

79

Figure 4-8 Density of electrons in conduction band (nCB) is calculated from Burstein-Moss shift,
described in Chapter 2, and absorbance (A780 nm) of TiO2 film is measured at 780 nm under
different applied potentials mentioned in the plot. Electrolyte was 0.2 M KCl at pH 12.8 and the
potentials are given vs. SCE.

4.4 Conclusion
Detailed study of the absorbance pattern of the TiO2 was performed in contact with various
electrolytes. Free electrons in the conduction band have the major contribution to the monotonic
absorbance pattern of TiO2 semiconductor film in the visible – near IR region. The visible
absorbance showed excellent linear co-relation with the density of the electrons in the CB. From
this correlation the extinction co-efficient of the free CB (CB) electrons was calculated using
Beer’s law. Determination of CB can provide a valuable insight into the electron transfer
processes in various photoelectrochemical cells.

80

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Chapter 5 Conduction Band Energy and Charge Distribution in Strontium
Titanate Nanoparticle Electrode
5.1 Introduction
Nanostructured wide bandgap semiconductor photoanodes are being widely used in solar
energy conversion systems like Dye-sensitized Solar Cell (DSSC) as their high surface area (2-3
orders of magnitude higher than geometric area) can be utilized to optimize the light harvesting
efficiency.1–7 Additionally, they offer the possibilities of overcoming the challenges associated
with short diffusion length of various materials in bulk structure. In the context of DSSC and
related solar energy conversion systems, TiO2 is extensively used as a photoanode material.
Relying on a single photoanode material has restricted the use or optimization of many
sensitizers because of the mismatch in energetics. In DSSCs, the photoanode directly participates
in the charge injection processes from the photoexcited dye, transporting these electrons and also
in the recombination processes. In order to properly understand these processes, photoanode
materials having different energetics and charge distributions need to be studied. Though other
metal oxides like ZnO, SnO2, Nb2O5, SrTiO3 have been used, their performances have been
much lower than the DSSCs constructed with TiO2 photoanodes.8 Those reports are primarily
based on the optimization of photoconversion efficiencies. Proper correlation between the
material properties (e.g. energetics and charge distribution) and electron transfer processes (e.g.
recombination processes) are inadequate in literature. Thus further study needs to be performed
to assess their potential and to understand the photoanode related charge transfer processes.
Strontium titanate (SrTiO3) has the potential to be a good photoanode material in DSSCs.9–11
It has Perovskite structure and has structural similarities with anatase TiO2 as shown in Figure 5-

84

1.12 Perovskite structure is described by the chemical formula ABO3 where the B atoms (Ti here)
have a 6-fold coordination and O atoms form octahedra surrounding the B atoms. Each A atom
(Sr here) is surrounded by four TiO6 octahedra. SrTiO3 Perovskite structure contains titanium
atoms in 6-fold octahedral coordination, similar to the titanium atoms in anatase TiO2. They both
are wide band gap semiconductor and do not absorb light in the Visible spectra which is essential
requirements for a semiconductor to be used in Dye-sensitized photoconversion technologies.13,14
Additionally, similar to TiO2, the conduction band in SrTiO3 is mainly made of the Ti 3d states
with a small component from the O 2p states.15,16 It has been reported that d-orbitals provide
more effective overlap with the sensitizer and facilitate more efficient electron transfer from the
Ruthenium based sensitizers. Unlike TiO2, the CB of SnO2 and ZnO are sp-type.17,18
Additionally, CB band composed of empty d-orbitals has high density of states (DOS). The
injection efficiency in sensitized photoanodes has been found in the following order:
TiO2>SnO2~ZnO. The DOS in the CB of TiO2 and SrTiO3 are similar (~ 1020 cm-3).19

Figure 5-1 Crystal structures of Perovskite SrTiO3 and anatase TiO2. This figure is reprinted
with permission from reference 12 (Bera, A.; Wu, K.; Sheikh, A.; Alarousu, E.; Mohammed, O.
F.; Wu, T. J. Phys. Chem. C 2014, 118, 28494–28501). Copyright 2014 American Chemical
Society.

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Sensitized SrTiO3 anode has been reported to provide higher photovoltage than TiO2 which
implies higher conduction band (CB) energy or/and lower photoanode related recombination
processes in SrTiO3 than TiO2.10,20,21 Under illumination, the photoexcited dye injects electron
into the semiconductor. It increases the electron population in the semiconductor and the Fermi
level of electrons (EF) moves closer to the CB according to the following equation:
nCB  N CB exp

(EF  ECB )
k bT

(1)

where nCB is the density of electrons in the CB, ECB is the CB energy minimum, kb is the
Boltzmann constant, T is the absolute temperature and NCB is the density of states (DOS) in the
CB which is calculated by,

 m*k T 
NCB  2  e b2 
 2 

3/2

(2)

where me* is the effective mass of CB electrons.
The charge separation in DSSC takes place at the dye-semiconductor interface.13 Separation
between the solution potential and the Fermi level of the electrons in the semiconductor is the
voltage output from a cell. At open circuit, this separation is the highest and the corresponding
voltage is called open circuit voltage, VOC. Thus, if the CB of a material is higher than TiO2,
higher photovoltage can be generated by pushing the Fermi level potential, EF, at higher potential.
SrTiO3 could potentially offer higher VOC if the recombination losses are minimized. There are
reports on DSSCs constructed with SrTiO3 photoanode.9–11,22 The quality of those photoanodes,
however, are not ideal for systematic physical studies of the material properties. In 1999,
Burnside et al. showed the potential of SrTiO3 as a DSSC photoanode and observed about 100
mV higher VOC comparing to TiO2 based DSSC.10 However, the size and shape of the SrTiO3

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particles have large distribution and even have bimodal particle distribution. Additionally, trace
amounts of SrCO3 was present in their sample.10 The following reports also suffered from the
presence of SrCO3.11 In 2014, Jayabal et al. reported a method to eliminate the impurities by
heating the SrTiO3 sample at a very high (900 C) temperature. However, well defined
nanoparticles were not observed possibly because the particle morphology was changed during
the heating at such a high temperature.9 Nanostructured SrTiO3 has also been used in Hybrid
Perovskite (CH3NH3PbI3−xClx) Solar Cells and the open circuit voltage, VOC, was found to be ~
120 mV higher that solar cell constructed with TiO2.12
One of the major issues, in the context of exploring new nanostructured photoanode materials,
is the lack of reliable methods to determine important material properties of the photoanodes
such as the conduction band edge position, distribution of electrons with the energetics and, also,
the spatial locations of the trap states. Recently, we have developed a spectroelectrochemical
method to determine the conduction band edge and charge distribution in nanostructured
photoanodes.19,23 In this work, we report a reliable method to make mesoporous transparent
SrTiO3 photoanode and, in order to characterize its potential for photoanode applications, a
detailed spectroelectrochemical and electrochemical studies of its energetics and the charge
distribution have been performed. The spectroelectrochemical method is described in Chapter 2
and 3 where the CB edge of TiO2 has been determined in presence of aqueous electrolyte (0.2 M
KCl, pH 12.8). The CB edge of SrTiO3 electrode was determined in contact with dry acetonitrile
solution (0.1 M LiClO4). Aqueous solution could not be used with SrTiO3 because the light
absorption measured in the UV range (band gap transition) under negative bias goes through
irreversible change. SrTiO3 has been reported to be capable of photoassisted electrolysis of water

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and the generated gaseous bubbles, trapped in the mesoporous structure, might be the reason
behind the irreversibility of measured light absoption.20
5.2 Experimental
5.2.1 Preparation of SrTiO3 electrode
Synthesis of SrTiO3 nanoparticles: SrTiO3 nanoparticles were made through a vapor diffusion
sol−gel (VDSG) method developed by Brutchey el al.24,25 Strontium titanium alkoxide (SrTi[OCH2CH(CH3)OCH3]6; 0.7 M in n-butanol/3-methoxypropanol) was used as precursor and
were used as received from Gelest, Inc. It was stored in a N2 glove box. ACS grade hydrochloric
acid was used.

B
A

C

Figure 5-2 Apparatus setup used for the synthesis of SrTiO3 nanocrystals via vapor diffusion
sol-gel method.

All procedures were done under N2 atmosphere using a standard Schlenk-line system. A 100 mL
three-neck flask was connected to vacuum adapter-glass stopcocks. Two of the adapters were

88

used as N2 purging line and vent, respectively and the third one was used to flow acidic vapor
into the reaction flask. A glass bubbler was filled with 150 mL of 0.75 M HCl solution. A
flowmeter was used to control the N2 flow though the bubbler.
The flask was initially purged with N2 for 30 minutes. In this configuration, adapters B and C
(one for N2 in and one for vent) are connected to the 3-neck flask and one of the necks, A is
closed by a septum. N2 gas was then bubbled into the HCl/H2O to remove the dissolved air (CO2
specifically) and to saturate the N2 gas flow with H2O vapor. After 30 min N2 purging, the
strontium titanium alkoxide precursor has been injected into the 3-neck flask. Then the bubbler
was connected to the 3-neck flask (A) and the adapter which connects the flask with the N2 flow
(B) was closed. Thus, in this setup, two adaptors were open, one for flowing HCl/H2O/N2 into
the flask (A) and other for venting (C). The flow rate was 0.02 L min-1. A venting adapter was
also connected to a bubbler to prevent any air exposure into the reaction flask. After ~7 hours a
gel appeared which eventually cracked. After 5 days, the flask was opened and the gel was
collected and washed with ethanol. During the washing process, the gel was sonicated with 5 mL
ethanol for 15 min and centrifuged at 6000 rpm for 1 hour. This washing was repeated 3 times.
The resulting powder was dried under vacuum for overnight at 60 C and was grounded in a
mortar pestle to make SrTiO3 powder.
Preparation of SrTiO3 paste: SrTiO3 powder was mixed with ethanol and dispersed using an
ultrasonic horn. The dispersion was then centrifuged at 2000 rpm to remove the larger particles
and aggregates. The decant was then mixed with ethyl cellulose and -terpineol and was
ultrasonicated again. The excess solvent was then evaporated using a rotavap at 60 C until a
viscous paste was formed. This paste was kept overnight before further use.

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Preparation of SrTiO3 electrode: The transparent mesoporous SrTiO3 film was prepared by
spreading SrTiO3 paste on transparent conductive substrate. This substrate was made by
depositing ~10 nm thick layer of TiO2 on fluorine-doped tin oxide glass (FTO) (Hartford Glass)
by atomic layer deposition (ALD). This film was first annealed at 360°C for 30 min in the air
and then it was annealed at 560 C under hydrogen/nitrogen mixture (5% H2).
5.2.2 Characterization of SrTiO3 film
Powder X-ray diffraction (XRD) of SrTiO3 was measured by Bruker Davinci Diffractometer
(Cu K radiation ( = 1.5406 Å). The 2 range was 20-70, step size was 0.02 and the
collection time was 3 s per step. The size, shape of SrTiO3 nanoparticles and the morphology of
the SrTiO3 film were characterized by using a scanning electron microscope (Hitachi S-4700 II
FESEM).
5.2.3 Preparation of electrolyte solutions
Lithium perchlorate (Sigma-Aldrich, battery grade, dry, 99.99% trace metals basis) was
dissolved in anhydrous acetonitrile to make a 0.1M solution.
5.2.4 Spectroelectrochemical measurement
In spectroelectrochemical measurements, the transmittance (%T) of the film was measured
by a Perkin Elmer Lambda 35 UV-Vis spectrophotometer under an external bias provided by a
potentiostat (-Autolab, Metrohm). A three electrode electrochemical cell setup was made by
making a rectangular hole in a cuvette which can be sealed by a cap. A platinum mesh was used
as counter electrode and a homemade Ag/AgNO3 was used as reference electrode. This cuvette
was placed into the UV-Vis spectrophotometer such that the SrTiO3 electrode remained
perpendicular to the optical path. The SrTiO3 electrodes were aged overnight in the glove box in

90

contact with the electrolyte solutions prior to any experiment. The temperature of the
electrochemical cells was 220.5 ⁰C during the measurements. During spectroelectrochemical
measurements, each film was stabilized at an applied bias for 3 minutes and %T of the electrode
was measured. Stability of the film as well as reproducibility of the results were checked both
spectroscopically as well as electrochemically to make sure that there is no irreversible change in
the film during the measurements. The cuvette was sealed in the glove box and all the
measurements were done under sealed condition i.e. in dry N2 atmosphere.
The absorbance of SrTiO3 electrode was determined by subtracting the absorbance of the cell
having a bare conductive substrate without a SrTiO3 film from the absorbance measured with
SrTiO3 film to eliminate the contribution of everything else in the optical path (FTO, cuvette and
electrolyte) and provides only the changes in the SrTiO3 film. Absorbance, A, was calculated
from the measured %T by using the relation, A = 2  log10%T.
The difference absorbance spectrum, A, is the absorbance change under external bias. At
first, the absorbance was measured under a sufficiently positive potential (0.0 V vs. Ag/AgNO3)
to discharge all the stored electrons from the film. Then a negative potential was applied to
increase the electron population and the absorbance was measured. The absorbance measured at
positive potential was subtracted from the absorbance at negative bias to calculate A.
During the study of the band gap transitions in the UV region (330 – 400 nm) under potential
bias, the absorption in the visible-near IR (400 - 1100 nm) was fitted to a Gaussian fit using
OriginPro 9.0 and was extrapolated in the UV region. It was then subtracted from the absorbance
measured in the UV region to determine the absorbance of the band gap transition only.
Absorption co-efficient () was calculated from absorbance by using the relation  = (2.303  A)
/ l, where A is the absorbance and l is the thickness of the film.26,27 The thickness of the films

91

varied from 1.9 to 2.1 m. The thicknesses of the films were measured after each
spectroelectrochemical measurement for accurate calculation of the absorption properties of the
SrTiO3 electrode.
5.2.5 Electrochemical measurements
Cyclic voltammetry (CV), Electrochemical Impedance Spectroscopy (EIS) and Charge
Extraction methods were performed to study the electron distribution in SrTiO3 electrodes. A
three electrode set up was used. A Pt mesh was used as counter electrode and a homemade
Ag/AgNO3 (in anhydrous Acetonitrile) reference electrode was used. All the measurements were
done under dry N2 atmosphere.
5.3 Results and Discussion
5.3.1 Material characterization
SrTiO3 nanoparticles were synthesized through a vapor-diffusion sol–gel route at room
temperatures, in the absence of any structure-directing template.28–30 Nanoparticles were formed
through a kinetically controlled coalescence processes by slowly reacting acidic water vapor with
the metal alkoxides. The chemical reaction can be expressed as,
HClcat .
SrTi[OCH 2CH3OCH3 ]6  3H 2O 
 SrTiO3  6HOCH 2CH (CH3 )OCH3

These nanoparticles were used to make films which were annealed at 560 C under a reducing
atmosphere (5% H2 / N2). Powder XRD analysis showed that the nanoparticle film is comprised
of pure SrTiO3 with a cubic Perovskite phase.25 No other peaks associated to other phases or
impurities were observed. Scanning electron microscope analysis revealed the nanocrystal
diameter of about 152 nm.

92

Figure 5-3 Powder X-ray diffraction patterns of the SrTiO3 nanocrystals (top) and scanning
electron micrographs SrTiO3 film deposited on conductive substrate (bottom).

93

5.3.2 Determination of the conduction band and electron distribution
Spectroelectrochemical analysis of SrTiO3 electrode: The Fermi level of electron within this
semiconductor nanoparticle film can be controlled by the potential applied to the conductive
substrate.31–33 Figure 5-4 and 5-5 show how the absorbance of the SrTiO3 electrode changed
when the electron population was increased by applying a negative (i.e. reductive) potential. In
the visible-near IR region an absorbance peak appeared at ~894 nm under negative bias which
increased gradually with the increasing bias. A visible-near IR absorbance was also observed for
TiO2 electrodes under negative bias, however no peak was observed and the absorbance spectra
was dominated by free electron absorbance.23
The difference absorbance spectra of SrTiO3 (Figure 5-6), shows the change in absorbance
when the electron population was changed. Under, negative potential, the densities of both
trapped electrons and delocalized (also called “free”) CB electrons were increased. According to
the Beer’s law, the total absorbance, A, can be defined as, A / l   CB M CB   T M T where l is the
electrode thickness, MCB and MT are the molar concentrations (mole L-1) of CB electrons and the
trapped electrons, respectively. CB and T are the extinction coefficients of the free CB electrons
and trapped electrons, respectively. According to the Drude-Zener theory, the absorption of
delocalized (free) electrons gives rise to a wavelength dependent absorption spectrum according
to A  C P , where C is a scaling parameter,  is the wavelength of light and the exponent, P, is
a value from 1.5 – 3.5, depending on the scattering mechanism. Scattering by acoustic phonons
gives rise to P = 1.5, scattering by optical phonons produces P = 2.5 and a scattering by ionic
impurities gives P = 3 – 3.5. In addition to the absorbance peak at ~894 nm (Figure 5-6) a
featureless absorbance was also observed in the wavelength range of 1500-2200 nm. Both the
peak and the featureless absorbance increased with increasing electron population. A possible

94

assignment of the absorbance peak is the inter-band localized electronic states though it is not
possible to explain the nature and distribution of these localized states, based on this
observation.34 The featureless absorbance can be explained by the intra-band absorption of the
free electrons in the CB.

Figure 5-4 Plot of absorbance of SrTiO3 electrode in UV region under various applied potentials,
0.0 V (black), -1.3 V (blue), -1.4 V (red), -1.5 V (green) vs. Ag/AgNO3. The electrolyte solution
is 0.1 M LiClO4 in acetonitrile. Increasing negative potential moves the band gap absorption
edge to higher energy.

95

Figure 5-5 Plot of visible-near IR absorbance spectra of SrTiO3 electrode under various applied
potentials, 0.0 V (black), -1.3 V (blue), -1.4 V (red), -1.5 V (green) vs. Ag/AgNO3.

Figure 5-6 Plot of absorbance difference spectra of SrTiO3 electrode under various applied
potentials, -1.3 V (blue), -1.4 V (red), -1.5 V (green). This difference absorbance was calculated
by subtracting the absorbance of SrTiO3 electrode at 0.0V vs. Ag/AgNO3 from the absorbance
measured at negative potentials shown in the plot.

96

In the UV region, the band gap transition of SrTiO3 occurs below 380 nm. Interestingly, a
gradual blue shift of the absorption onset was observed with increasing negative potential i.e.
with the increasing electron population in the SrTiO3 film. Band gap energy is the lowest energy
required to excite an electron from the valance band top to the CB bottom. This blue shift of the
band gap transition can be explained by the filling of the bottom of the CB which blocks the
lowest energy band gap transitions. If the lowest energy states in CB are filled, band gap
transition needs higher energy to find the lowest empty states. Similar blue shift in the band gap
absorption onset has been observed in the highly doped semiconductors where the introduced
dopant increases the population of the CB electrons. This phenomenon is generally described as
the Burstein-Moss shift.35–40
Determination of the conduction band edge: This apparent band gap widening (EG) is
correlated to the density of electrons in the CB (nCB) according to the following equation:
EG 

h 2  3nCB 
8m*   

2/3

(3)

where m* is the reduced effective mass of the charge carriers and h is the Plank’s constant.
Knowledge of nCB leads to the position of ECB according to the equation 1.
The band gap energy (EG) of a semiconductor material can be determined from a Tauc plot
using the relation,27
( hv)  A' (EG  hv)

(4)

where  is the absorption coefficient, h is the energy of the incident light, A’ is a constant and
the value of  describes the characteristics of the transition process. The band gap transition in
SrTiO3 material is known to be indirect in nature i.e. electron transition from the highest-energy
state in the valence band to the lowest-energy state in the conduction band is not possible without

97

a change in momentum.16,41,42 The transition occurs via the absorption or emission of a phonon
which provides the required momentum change during the transition. The energy required for
this transition mainly comes from the photon absorbed.  in equation 4 is 1/2 in case of indirect
semiconductor. Figure 5-7 shows the Tauc plot of SrTiO3 film. The range of photon energies
utilized to fit the Tauc plot was chosen where a good straight line fit was observed beyond the
band gap transition energy. The energy region should not be too close to the band gap as various
factors (e.g. Urbach tail) can dominate the overall absorption spectra where the absorption of
band gap transition is still relatively low. On the other hand, in a scenario when the photon
energy is very much higher the band gap energy, the parabolic approximation of E-k plot is no
longer valid. Also, the direct band gap transition (which occurs at higher energy than the indirect
transition in anatase material) can contribute to the absorption. The maximum energy applied
here is 3.55 eV ( = 350 nm) and the direct interband direct transition (i.e. trasition from VB to
CB without change in momentum) has been reported to occur above this energy range. 43,44 We
observed a sudden rise of the absorption spectra at energies higher than ~ 3.6 eV presumably due
to the contribution of direct inter band transition. Direct allowed transition shows sharp rise of
the absorption co-efficient with beyond the energy required to excite an electron from VB to CB
without changing the momentum.27 The (h)1/2 vs. h curve fitted between 3.543 eV to 3.647
eV (350 - 340 nm) was extrapolated to determine the band gap and it was found to be 3.066 eV.
Though 3.2 eV is frequently reported as the band gap energy of SrTiO3 material, Li et al.
reported a band gap energy of 3.01 eV for SrTiO3 micro-structures.11,16,20,41,43–46 The value of EG
we observed is in the lower end of the literature values for the band gap of SrTiO3.

98

Figure 5-7 Tauc plot of a SrTiO3 film in contact with 0.1 M LiClO4 in acetonitrile. Any
contribution from the electrolyte, substrate and cuvette were subtracted and only the absorbance
of the SrTiO3 electrode contributed to this plot.

Figure 5-8 Plot of band gap widening while moving from 0.0 V (black) towards more negative
potentials -1.3 V (blue), -1.4 V (red), -1.5 V (green) vs. Ag/AgNO3.

99

There are some possible sources of uncertainty in determining the band gap energy in our
experiment. In the indirect transition, both the energy and the momentum are changed. As a
result, phonon interaction, a quantum mechanical demonstration of thermal vibrations in the
crystal lattice, is required to conserve the momentum. Therefore the band gap absorbance
becomes a two-step process assisted by either phonon absorption or phonon emission. So the
energy required to excite an electron from the valence band to the conduction band can be
written as,27
h  EG  Ep

(5)

where EP is the energy of the phonon required to compensate the difference in momentum
between the minima and maxima of the conduction and valence bands, respectively. Now, both
phonon absorption and emission are possible as the range of applied photon energy considered to
calculate the band edge is much higher than EG. The phonon energy is expected to be constant
while changing the potential at constant temperature. It should also be mentioned that it is not
straightforward to determine the absolute band gap in case of phonon assisted indirect transition.
Additionally, in presence of a high dopant density and/or impurity, charge-charge and/or chargeionic impurity scattering can also provide the momentum conservation required for the indirect
transition.27 The dopant density as well as impurity concentration in nanostructured SrTiO3 films
has not been accurately determined so far. Broadening of the absorption curves also contributes
to the uncertainty in determining the band gap energy accurately. Band tail, which is expected to
be present in our sample due to the disorder effects and/or defects below the conduction band,
can also contribute to this uncertainty. Significant broadening of the absorption is observed in
our measurements (Figure 5-7). It is very difficult to get rid of this broadening which might
cause some error in our band gap determination though the magnitude of this broadening should

100

remain constant for a specific measurement setup, which we observe. Thus, at constant
temperature and electrolyte environment, the error in determining the band gap transition
remains constant and does not contribute to the magnitude of the shift in the band gap absorbance
which is of primary interest here.
Figure 5-8 shows a continuous apparent increase of the measured band gap. The magnitudes
of Burstein-Moss shift were calculated at a range of negative potentials and nCB was calculated
from equation 3. me* = 5me and mh* = 1.2me have been used in this study.41,47–52 The position of
the conduction band edge ECB/q was then calculated according to equation 1 as shown in table 1.
Table 5-1 Calculation of conduction band position from the Burstein-Moss shift.

E vs. AgNO3/V

EG/meV

nCB/cm-3

ECB/q/V

-1.5

72.07  1.91

6.66  0.265  1019

-1.537  0.001

-1.45

60.08  1.93

5.07  0.244  1019

-1.494  0.001

-1.4

49.48  1.95

3.79  0.224  1019

-1.451  0.002

-1.3

33.44  1.98

2.10  0.187  1019

-1.366  0.002

-1.2

20.05  2.0

9.78  1.46  1018

-1.286  0.004

-1.1

11.32  2.02

4.15  1.11  1018

-1.207  0.007

A very interesting feature is observed in this table. The position of the conduction band is
shifting upwards (i.e. more negative) while raising the Fermi level, EF/q (which is equal to the
applied potential, E). This result is consistent with our prior report (described in Chapter 2)
where similar upward shift of CB was observed in nanostructured TiO2 photoanodes.23 This
upward shift of band energies occurs due to the potential drop across the double layer
(nanoparticle-electrolyte interface). The electron accumulation is accompanied by positive

101

charges, i.e. the cations in the electrolyte. Accumulation of electrons in the electrically active
states on the surface or within close vicinity of the surface of SrTiO3 nanoparticle changes ionic
distribution and hence the electric field in this interfacial double layer. Though the physical
nature of these electrically active states is uncertain, they are most likely to be localized states
arising from the under coordinated TiIV or TiIII centers, hydroxyl group or any other crystal
‘defects’ on the surface or within very close vicinity of the surface that can trap electrons. 53 We
refer to these states as “surface states” in the following sections.
Determination of the total electron density, nTotal: nTotal was calculated over a range of Fermi
levels by a charge insertion-extraction method. The applied bias was switched from 0.0 V vs.
AgNO3 to a negative bias, E, to initiate a charge insertion process and the reverse process (E 
0.0 V) was performed to extract the charge. The charge accumulated under a negative bias was
calculated by integrating the current-time curves as shown in Figure 5-9. A reasonable match
between the inserted charge and the extracted charge was observed which suggests that the
charge insertion is reversible and no significant redox reaction occurred under negative bias.

102

Figure 5-9 Current vs. time plot measured during charge insertion-extraction process under
various potentiostatic biases. A reductive bias (as mentioned in the plot) was applied for 3 min
and then an oxidative bias (0.0 V vs. AgNO3) was applied to extract all the charges stored in
SrTiO3 electrode.

Figure 5-10 Plot of electron density in the nanostructured SrTiO3 electrode as a function of
applied potential measured by charge insertion-extraction measurement.

103

Determination of the density of trap states on the surface (nS) and in the bulk (nB): The
upward shift of the CB provided a method to calculate the density of surface states, nS, since it
should be correlated to ΔECB by following relationship:
ECB / q 

qnS
CH

(6)

Here CH is the capacitance of the Helmholtz layer formed on the surface of the nanoparticles.
This capacitance depends on the width of the Helmholtz layer and its corresponding dielectric
constant. To the best of our knowledge, CH has not been measured for SrTiO3 electrode in
contact with dry acetonitrile solvent. CH was reported to be 52 F cm-2 for TiO2 electrode in
presence of dry acetonitrile.54,55 Considering the structural similarity between SrTiO3 and TiO2,
CH of SrTiO3 electrode in dry acetonitrile solvent was assumed to be 52 F cm-2 in our
calculation.53 Additionally, the density of the bulk trap states, nB, can also be calculated from the
following equation,

nTotal  nCB  nS  nB

(7)

In order to calculate nS, the magnitude of the CB shift, ΔECB, needed to be determined which
required the information of the minimum CB position, E*CB, without the effect of the potential
drop. However, it is not straightforward to determine where the surface state distribution starts to
cause significant potential drop in the Helmholtz layer. Thus, we need to rely on a rational
estimation based on the electrochemical data. The charge insertion and extraction data (Figure 510) suggested that the electron density in the SrTiO3 starts increasing when the Fermi level is
pushed beyond -1.0250.025 V vs. AgNO3. The measured capacitance by electrochemical
impedance measurement also supported it as shown in Figure 5-12. Thus the position of CB at

104

this Fermi level provides a good estimation of E*CB and was calculated to be  1.123 V vs.
AgNO3. ECB (= E*CB  ECB) was calculated over a range of Fermi levels, EF/q (= E) to
determine the energy distribution of surface trap states.
nB was calculated by subtracting nCB + nS from nTotal. Figure 5-13 shows the distribution of
nCB, nS and nB as a function of applied potential (= EF/q). Interestingly, nS does not increase with
applied bias as much as nB does. The Li+ cations are the primary charge compensating ion here.
The electrons trapped on the surface can easily be charge compensated by Li+ ions in the
electrolyte solution. However, to compensate bulk electrons, Li+ ions are likely to be inserted
into the nanoparticle which involves reorientation of the bond lengths in the nanocrystals. Thus,
initially, when the negative bias is not high enough, more electrons are trapped on the surface
because they can be easily charge–compensated by the available Li+ cations. However,
increasing Coulombic repulsions among the surface adsorbed Li+ cations limits the capacity to
trap a large density of electrons on the surface. In the bulk of the nanoparticle, more electrons
can be stored if charge-compensating Li+ can reside in the interstitial space in an O6 octahedral
site similar to the anatase crystal. Thus, when the potential was negative enough to overcome the
energy requirement for Li+ insertion, a large amount of electrons were trapped in the bulk.19
Determination of the density of states from electrochemical methods: The DOS can be
calculated from the measured charge density while changing the Fermi level by the following
relations,

N (E) 

105

dn
dE

(8)

n

EF

 N ( E )dE

(9)

E0F

The electron distribution is also described by its chemical capacitance (C) which describes the
capacity of the nanostructured film to store/release electrons during a change in the chemical
potential, n.32 When Fermi level, EFn (=E) changes, it causes a change in the electron density
which changes the chemical potential of the electrons. This can be written as dEFn = dn and the
chemical capacitance can then be written as the variation of the electron density as a function of
Fermi level,32
Cμ  q

dn
dEFn

(10)

Note that, equation 8 and 10 are essentially describing the same thing. Figure 5-13 shows the C
calculated from the charge insertion-extraction data and from EIS measurements.56,57 A
transmission line model was used to fit the EIS data in case of porous photoanodes, as shown in
Figure 3-3. This circuit illustrates the internal distribution of chemical capacitance in response to
the modulated small perturbation of the steady state bias.58,59

106

Figure 5-11 Plot of electron density in SrTiO3 and TiO2 electrode under various applied biases
calculated by charge extraction method.

Figure 5-12 Plot of measured capacitance, C (red) and resistance, R (blue) of SrTiO3 electrode
measured by electrochemical impedance spectroscopy.

107

Figure 5-13 Comparison of capacitance of SrTiO3 electrode measured by the electrochemical
impedance spectroscopy and charge insertion-extraction method.

Figure 5-14 Plot of electron density in the nanostructured SrTiO3 electrode as a function of
applied potential. nCB is density of free electrons in the conduction band, nS, and nBulk are density
of electrons trapped on the surface and in the bulk respectively.

108

Analysis of current decay (charge insertion and extraction): Wang et al. investigated the trap
states in nanoparticle TiO2 electrode based on current decay measurements.60 Lindstrom et al.
studied the current decay characteristics of nanoparticle TiO2 films in the presence of Li+
cations.61 They found that the shape of the current decay is controlled by the filling of trap states.
The current decay was studied on nanoparticle ZnO films as well.62 Current decay characteristics
of TiO2 film was also reported under photoexcitation.63,64 Here, a detailed analysis of the current
decay characteristics of nanoparticle SrTiO3 film is presented.
When a reductive bias is applied to the photoanode, the conductive substrate (FTO here)
injects electrons into the nanoparticles directly attached to FTO. These electrons then diffuse
through the nanoparticle network. At the same time, the cations from the electrolyte (Li + here)
are either adsorbed on the surface of the nanoparticle or diffuse into the nanoparticles to maintain
charge neutrality. Weppner et al. studied the movement of these electrons and suggested a cation
coupled electron transport.65
Figure 5-9 shows that as soon as the potential was shifted from 0.0V vs. AgNO3 to more
negative potentials, a sharp cathodic current peak was observed which then decayed with time.
The characteristics of the decay remained almost same from -0.8 to -1.05 V vs. AgNO3 and the
current decays were notably faster than the decays observed when the applied bias is more
negative than -1.05 V (Figure 5-15). Moreover, the charge, Q, calculated from the decay plot (i-t)
remained almost similar from -0.8 to -1.05 V. Beyond, ~ -1.05 V, the decay became noticeably
slower and Q increased exponentially towards more negative potential. Now, the SrTiO3 is a
wide band gap semiconductor and generally behave as an insulator.20,66 Moderate electron
conductivity can be achieved under reduced condition. When the negative (reductive) potential
was applied, the electron density in the material and hence the electron conductivity was

109

increased. At the potentials more positive than -1.05 V vs. AgNO3, the electron transport through
the SrTiO3 nanoparticles were very low and the observed current decays were possibly due to the
reorganization of electrolyte at the conductive substrate (FTO). Figure 5-11 shows that the
electron distribution in the nanostructured SrTiO3 effectively starts from -1.05 V vs. AgNO3
which was also supported by the electrochemical impedance data (Figure 5-12).
The current decay characteristics, observed when the applied bias is more negative than -1.05
V, were analyzed to extract information about the density of states (DOS) of the trap states. In
nanoparticle TiO2 and ZnO, the characteristics of the current decay were observed to be
controlled by the filling of the trap states and similar explanation can be provided in case of
SrTiO3.61–64 When a negative (reductive) potential was applied the electrons were injected from
the conductive substrate into the SrTiO3 nanoparticles. The injected electrons were trapped by
the localized trap states followed by detrapping (i.e. releasing the electrons). Interestingly, we
observed that the current decay is significantly influenced by the applied potentials which
implies that some type of driving force was associated to the filling of the empty states. Also,
more than one characteristic were observed in the current decay plot (Figure 5-15) which
suggested that multiples processes were going on when a reductive potential was applied. We
tried to deconvolute the decay plot in order to extract information about distributions of the
density of states in this mesoporous SrTiO3 photoanode. Our previous measurements suggested
that the mesoporous SrTiO3 film has mainly three types of electronic states, CB states, bulk trap
states and surface trap states. Based on this idea and the observation of three decay
characteristics, we fitted the current transient (i vs. t) plot as a tri-exponential decay. After
deconvoluting the parameters associated to decay from each of the electronic states, the total
charge inserted into those states were calculated. We would also like to mention the uncertainty

110

(a)

(b)

Figure 5-15 (a,b) Current transient data of when applied bias was changed from 0.0 V to the
negative potentials mentioned in the plot. The SrTiO3 electrode is in contact with 0.1 M
LiClO4/Acetonitrile solution.

in extracting the parameters from a triexponential fit. Relying only on this fitting to determine
the DOS of different states could lead to erroneous results. It requires a careful analysis of the

111

time constants and the DOS calculated at each electronic state throughout a range of potentials.
The results were also compared with the spectroelectrochemical results.

Figure 5-16 Triexponential fit of the current transient data when applied bias was changed from
0.0 V to -1.5 V vs. AgNO3. The experimentally observed decay has the contribution from three
decays (1, 2 and 3 in the plot) shown here.

112

Figure 5-17 Plot of time constants derived from the triexponential fit of the experimentally
observed current decay data.

Figure 5-17 shows three distinctive trends of time constants. Assigning these time constants
to certain electronic states and establishing a quantitative co-relation between the time constant
and the driving force of electron trapping are complicated and beyond the scope of our current
study. Multiple parameters like the charge mobilities, ease of charge neutrality by Li+ adsorption
or insertion, distribution of the DOS etc. can have contributions into the characteristics of the
current decay. However, we can make some reasonable hypotheses about the time constant.
Presence of trap filling was reported to slow down the current decay during the current transient
measurements.60 The electrons trapped on the surface can easily be charge compensated by Li+
present in the electrolyte whereas to compensate the charge in the bulk the Li+ is most likely
need to be inserted into the crystal which involves bond reformation or/and bond elongation.
Thus, an assumption can be made that the fastest current decay (curve 3 in Figure 5-16) was
associated with the trapping of electrons on the surface. The corresponding electron density
(4.61019 cm-3) was calculated and found to match well with the surface state density (nS)

113

calculated from spectroelectrochemical method (nS = 5.21019 cm-3). For the curve 1 in figure 516, this method provided a value of 7.61019 cm-3 whereas under the curve 2 the electron density
was found to be 8.91019 cm-3. The spectroelectrochemical method gave us nCB = 6.71019 cm-3
and nB = 9.31019 cm-3 which are close to the values calculated under the curve 1 and 2. In all
cases, the decay time shortens while moving towards more negative potential which can be
explained by the larger driving force for the trap filling.
5.4 Conclusion
SrTiO3 nanocrystals were synthesized by a vapor diffusion sol-gel method and mesoporous
electrode was made. It was studied to compare its photoanode properties with anatase TiO2. The
energetics and the electron distribution in mesoporous SrTiO3 electrode were measured by
combining spectroelectrochemical method with electrochemical techniques like charge insertionextraction method and electrochemical impedance method. The band gap was found to be ~3.1
eV (~ band gap of anatase TiO2 is 3.2 eV) and the conduction band was found to be ~ 200 mV
higher (more negative) than anatase. In SrTiO3 the free electron density in CB is comparable to
the trapped electron density whereas in TiO2 the trapped electron density is orders of magnitude
higher than CB electrons. -18 shows an energy level diagram of DSSC constructed with TiO2
and SrTiO3. The higher CB edge position in SrTiO3 provide an opportunity to push the electron
Fermi level in semiconductor to a higher position than in the TiO2 photoanode. Also, the lower
trap states in SrTiO3 can potentially offer lower possibility of trap state mediated recombination
processes. Moreover, exploring a photoanode material having different energetics and electron
distribution than TiO2 will help to understand the photoanode related electron transfer processes.

114

Figure 5-18 Comparison of the CB and electron distribution between TiO2 and SrTiO3.

115

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116

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Chapter 6 Predicting Maximum Attainable Efficiency of DSSC
6.1 Introduction
The maximum theoretical power-conversion efficiency of single-junction solar cells is
generally described by the Shockley–Queisser limit of ~33%.1 In addition to this, several
multijunction technologies have been developed and as a result, power conversion efficiencies as
large as 46% have recently been reported. The single junction photovoltaic cells constructed with
Silicon and GaAs have both exceeded efficiencies beyond 25%.2 The small differences between
the record photoconversion efficiencies and the Shockley–Queisser limit are attributed to a few
practical concerns. In spite of the textured surface and use of an anti-reflective coating on the
surface of solar cell, a small fraction of the sunlight is always reflected back. Some current loss
occurs at the junctions and electrical contacts.
The maximum power conversion efficiency of a Dye-sensitized Solar Cell (DSSC) reported
so far (under 1 Sun illumination in laboratory) is 14.3%.3 The highest certified power conversion
efficiency of a DSSC is 11.9% (Sharp, 2012), which is much lower than for Si-photovoltaics or
thin film solar cells.4 The working principle and energy loss pathways of DSSCs are very
different from the Si-solar cells and thin film solar cells. The mechanisms of the energy losses in
DSSCs are yet to be optimized.
The main advantage of dye-sensitized technology is that the photogenerated electrons and
holes reside in different phases which hinders the electron-hole recombination mechanisms in the
semiconductor. It dramatically increases the charge lifetime and the DSSC performs strikingly
well in spite of the fact that the charge-carrier mobility across the nanostructured semiconductor
photoanode is about one million times slower than in crystalline silicon.5,6 However, the DSSC
system is complex and even after more than 25 years of research, predicting a roadmap towards

121

the best DSSC, in terms of photoconversion efficiency (), is still not feasible. A DSSC has
many components and interfaces. Altering a single component from the optimized combination
affects the other electron transfer processes which in turn necessitates the change of other
components.7 In this chapter, our primary focus is to predict a reasonable target for the maximum
photoconversion efficiency in the light of the recent advancement in our understanding of
minimizing the energy-losses.
6.2 Calculating the power conversion efficiency of DSSC
The photoconversion efficiency () of a solar cell is the ratio of the maximum electrical
power obtained, Pmax, to the power of the incident light, Pin.
% 

Pmax J scVoc ff

Pin
Pin

(1)

where JSC is the short-circuit current, VOC is the open circuit voltage and ff is the fill factor. Thus,
instead of maximizing the current and voltage individually, an optimization should be made to
get maximum value of current  voltage.
6.3 Energy losses in a DSSC
The maximum power conversion efficiency of DSSC (Figure 6-1) achieved so far is 14.3%
where JSC is 18.36 mA cm-2, VOC is 1.013 V and ff is 0.770.3 The fill factor, mainly attributed to
the recombination losses and resistive losses, has nearly reached the optimal value.5 Incident
photon-to-current conversion efficiency (IPCE) was reported to be ~91%. Remaining ~9% is due
to reflection loss of incident light which can potentially be decreased by utilizing the textured
surface and use of anti reflection coating. However, reflection loss always exists even in the
record performing photovoltaics and large improvement in the IPCE beyond 91% is quite
unlikely to be achieved.

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Figure 6-1 J–V curve and IPCE plot of the DSSC photosensitized collaboratively by ADEKA-1
and LEG4. [Co(phen)3]2+/3+ redox shuttle was used. JV was measured AM-1.5, 100 mW cm2.
This figure is reprinted from reference 3 (Kakiage, K.; Aoyama, Y.; Yano, T.; Oya, K.; Fujisawa,
J.; Hanaya, M. Chem. Commun. 2015, 51, 15894–15897) with permission from Royal Society of
Chemistry.

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Figure 6-2 Plot of major energy losses in a typical DSSC. Negative potential represents higher
energy. The mesoporous TiO2 photoanode is deposited on transparent conductive substrate
(TCO). The conduction band (CB) edge potential of TiO2 photoanode is shown below the excited
state potential of dye. EF is the Fermi level potential of electrons in the photoanode. R+/R
represents the redox shuttles in the solution which regenerate the oxidized dye. VOC is the open
circuit potential which is the potential difference between the solution potential and the Fermi
level at the open circuit, EF,Voc. The loss-in-potentials, Vloss, are described in this chapter in details.
Thus, this is very close to the maximum photocurrent possibly achieved with this absorption
onset of the sensitized photoanode. The photoanode was co-sensitized with an alkoxysilyl anchor
dye ADEKA-1 and a carboxy-anchor organic dye LEG4. Interestingly, the optical band gap of
the dyes (LEG: 1.91 eV and ADEKA: 1.85 eV) used here is about 0.8 V higher than the VOC.
Now, looking at the equation 1, all the parameters (JSC, ff) except VOC were optimized. Thus, the
major losses in “efficient” DSSCs are reflected in V. We would like to use the parameter “lossin-potential, Vloss” here which describes the difference in energy between the optical bandgap of
the sensitized photoanode and the open-circuit voltage produced by the solar cell.
Vloss 

Eopt
q

 VOC

(2)

where Eopt is the optical band gap of the dye, q is the charge of an electron. Vloss in the DSSC
showed in the Figure 6-1 is ~0.8 V. Vloss for the previously champion DSSC was 0.88 V ( =

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13%, 2014) which used a porphyrin dye and [Co(bpy)3]2+/3+ redox couple.4 The optical band gap
of the dye was 1.79 eV, VOC = 0.91 V, JSC = 18.1 mA cm–2, ff = 0.78. The iodide/iodine based
highly efficient DSSCs also suffer from >0.8 V voltage losses. Nazeeruddin et al. reported a
11.18% efficient DSSC (JACS, 2005) based on N719 dye (Di-tetrabutylammonium cisbis(isothiocyanato)bis(2,2’-bipyridyl-4,4’-dicarboxylato)ruthenium(II)) and iodine/iodide based
redox shuttle where JSC = 17.730.5 mAcm-2, VOC = 0.8460.020 V, ff = 0.75 and Vloss was >0.9
V.8 These are probably the maximum efficiencies that can be achieved with this much of loss-inpotential.9 The loss-in-potential for state-of-the-art Si and GaAs solar cell have been reduced to
~0.3 V. In order to push the photoconversion efficiency of DSSC closer to Si or GaAs solar cells,
the potential losses must be reduced significantly. The sources behind the overall potential losses
are shown in Figure 6-2 and are described below.
6.3.1 Energy loss during photoexcited electron injection, Vloss, injection
The ultrafast electron injection from the excited dye into the conduction band of the
semiconductor photoanode is far from a straightforward electron transfer process between two
energy states.10–18 Efficient electron injection depends on several factors including the position
of the conduction band edge in the semiconductor (ECB), excited state energy of the dye, overlap
between the occupied states of the dye and the empty density of states (DOS) of the
semiconductor.19–22 Several injection processes take place from a range of excited states during
the thermal relaxation pathway, e.g. injection from singlet states, intersystem crossing to the
triplet states followed by injection into the semiconductor, etc. The injection rate can be
optimized in several ways. Ardo and co-workers observed an increase in the electron injection
from the excited state of Ru(bpy)2(dcb) (where dcb = 2,2′-bipyridyl-4,4′-dicarboxylate) to TiO2
in the presence of Li+ ions.22 Presence of small cations like Li+ lowers the ECB of TiO2 and as a

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result, more acceptor states (TiO2 DOS) are thermodynamically accessible.23 The injection rate
has been found to be increased in the presence of cations, Ca2+ > Ba2+ ≈ Sr2+ > Li+ > Na+ > K+ >
Rb+ ≈ Cs+ ≈ TBA+ and also with a range of solution auto-ionization constant, MeOH > EtOH >
aqueous pH 8 > DMF which is explained by the downward (more positive) shift of ECB in the
same order.15,24–28 McCusker and co-workers studied the injection kinetics with cisRu(dcb)2(CN)2/TiO2 along with their osmium analogues and they observed that the injection is
directly related to the dye excited-state reduction potential.29 Degree of photoanode crystallinity
was also found to have an effect on this injection process. ‘Hot’ injection from upper vibrational
excited states of the dye has been observed when the semiconductor conduction band edge is
above the excited-state energy of the dye.30–32 Although this type of system is far from the ideal
solar cell, it may compensate for the injection yield losses while minimizing the difference
between the conduction band and the excited state energy of the dye. These observations imply
that knowledge of the energetics in the semiconductor/dye interface is essential to optimize the
“loss-in-potential”. A significant difficulty in studying the energetics at the semiconductor/dye
interface has been the absence of effective method to determine the ECB accurately. A new
spectroelectrochemical method to accurately measure ECB is presented in Chapter 2.33 Though
predicting the minimum “loss-in-potential” in the injection process is difficult and complicated,
we can, however, estimate the minimum difference between the CB band position in TiO2 and
the excited state of the dye in an optimized DSSC.
Figure 6-2 shows the energy alignment of a DSSC. The difference between the Fermi level of
electron in the semiconductor under illumination and the solution potential defines the voltage
output. At open circuit, the difference is the maximum and the corresponding voltage is called
open circuit voltage, VOC. Using, iodine/iodide redox shuttle and ruthenium bipyridine sensitizer

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(N719), more than 800 mV of open circuit voltage can be generated without compromising with
the current output. Nazeeruddin et al. reported a DSSC where JSC = 17.73 mA cm-2, VOC =
84620 mV, ff = 0.75 and  = 11.18%.8 The IPCE was reported to be ~ 90%. Considering the
reflection-loss of the incident light (~10%) this is the maximum possible current output based on
this sensitizer. Thus, it can be assumed that the injection rate of the photoexcited electron from
the dye excited state into the empty density of states (DOS) of TiO2 is “fast enough”. Now,
solution potential, EF,0, of the iodine/iodide (1:10 concentration ratio) based redox shuttle is ~ 
0.11 V vs. SCE and the lowest excited state potential of the N719 dye is  0.9 V vs. SCE.18,34–36
In the scenario of VOC = 846 mV, EF,Voc can be estimated to be  0.736 vs. SCE. We measured the
CB of TiO2 using a spectroelectrochemical method as described in Chapter 2. It is important to
point out that our measurement was done with a mesoporous TiO2 film in contact with 0.1 M Li+
and dry acetonitrile was used as solvent. The energetics of the TiO2 film changes significantly
with the type and concentration of the cations in the surrounding. Now, the electrolyte of an
optimized solar cell generally contains 0.1 M Li+ in addition to tert-butylpyridine (generally 0.5
M is used). Other additives e.g. guanidinium thiocyanate are also added to improve the
performance. The CB of TiO2 becomes ~200-300 mV higher in presence of tert-butylpyridine. 37–
39

Additionally, some protons are adsorbed during the dye loading process which can come from

the protons of the carboxylic group of the dye and also from the solvent where the dye solution is
made. The dye solutions are made both in protic (e.g. ethanol) and aprotic (e.g. acetonitrile)
solvents and the dye adsorption is generally done on bench top where the photoanodes are
exposed to the moisture as well as the trace amount of water impurities in the solvents.
Adsorption of proton is known to make the TiO2 CB lower.38,40 Thus, predicting the CB position
in the working DSSC is complicated. Our spectroelectrochemical measurements showed upward

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movement of the CB while raising the Fermi level. In presence of 0.1M Li+/acetonitrile
electrolyte and in the similar range of Fermi level, we found that the CB was 60 - 140 mV above
the Fermi level. Thus, at the Fermi level calculated above ( 0.736 vs. SCE), the estimated range
of the CB is  0.80 to  0.88 V vs. SCE. Now, considering the excited state position of the N719
dye ( 0.9 V vs. SCE) it can be stated that “fast enough” injection from dye to semiconductor is
possible even when TiO2 CB edge is closely aligned to the dye excited state energy. We would
like to point out that this value is only valid for TiO2 and N719 (or N3) dye. Bauer, Hagfeldt et al.
reported electron injection from the Ru(tcterpy)(NCS)3 dye (tcterpy = 4,4′,4′′-tricarboxy2,2′:6′,2′′-terpyridine), known as black dye, to TiO2 where the excited state potential (triplet state)
lies at the same potential than the TiO2 CB.41 This electron transfer rate depends on the extent of
electronic coupling between the π* orbitals of the dye excited state and the empty 3d orbital of
TiO2. Ruthenium based sensitizers have the advantage of efficient electron injection without
significant Vloss,injection. However, recently, versatile organic dyes are being used in DSSCs having
much higher excited state potentials. Their excited state potentials need to reside >300 mV above
the TiO2 CB in order to achieve efficient electron injection. Kakiage and Hanaya et al. reported a
DSSC where VOC is >1 V and the IPCE is >90% using [Co(phen)3]3+/2+ redox shuttles and a
combination of alkoxysilylanchor dye ADEKA-1 and a carboxy-anchor organic dye LEG4.3,42
The excited states of these dyes are ~ 1.1 V vs. SCE and the solution potential, EF,0, is 0.34 vs.
SCE. EF can be estimated to be 0.67 vs. SCE which implies a range of CB edge from 0.81 to
0.73 V vs. SCE. The difference between the dye excited state and the CB edge is 290-370 mV.
Now, this difference is not necessarily universal and several factors can be tuned to reduce this as
discussed in the early part of this section. For our discussion we can make a range of 0 to 300
mV for Vloss, injection.

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6.3.2 Energy loss during regeneration of the oxidized dye, Vloss, regeneration
The largest loss-in-potential in DSSC generally occurs during the regeneration of the
oxidized dye, after the photoinduced electron injection into the semiconductor, by a redox shuttle.
The regeneration efficiency is defined as the probability of an oxidized dye reduced by the redox
shuttle before the recombination occurs with an electron in the semiconductor.
Iodide/triiodide was used as the champion redox shuttle until recent advancements with
cobalt complexes were achieved. Till date, iodide/triiodide had the major share of DSSCs
research because of its slow recombination, high efficiency to regenerate the commonly used
dyes e.g. N3, Z907 (reg ≈ 1) and excellent diffusion coefficient due to its small size and good
solubility in commonly used electrolyte solvents.35,43–45 However, a driving force ∆G0 (= q.Vloss,
regeneration, q

= charge of an electron) is required for this process. Iodide/triiodide needs ~0.75 V to

efficiently regenerate Ru(dcbpy)2(NCS)2 dye (N719) and ~0.6 V to efficiently regenerate
Ru(tcterpy)(NCS)3, popularly known as Black dye. Vloss,

regeneration

for iodide/triiodide based

DSSCs is thus huge and limits the overall photoconversion efficiency of a DSSC.8,46 The redox
shuttle in the champion DSSC (shown in Figure 6-1), at present, is [Co(phen)3]3+/2+ and it needs
0.37 eV driving force to regenerate ADEKA-1 dye.3 Using the same TiO2-dye system, the
regeneration driving forces for [Co(bpy)3]3+/2+ and [Co(Cl-phen)3]3+/2+ were found to be 0.43 eV
and 0.27 eV, respectively.47

This large regeneration driving force is attributed to large

reorganization energy and slow self-exchange kinetics.48 One possible way to minimize this
driving force is to use a redox shuttle with much faster self exchange rate constant which can be
achieved by minimizing the reorganization energy. However, the advantage of this large
reorganization energy (1.73 eV associated with the electron transfer at TiO2/[Co(bpy)3]3+/2+
interface) is the slow recombination of electrons from the semiconductor to redox shuttles. 48

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Ferrocene shows excellent dye-regeneration capability with much lower driving force, however,
recombination is detrimental to the cell performance.49,50 An organic dye (carbz-PAHTDTT) has
been shown to have regenerated efficiently by ferrocene and its derivatives with a driving force
of 0.19 eV.49,51,52 The four orders of magnitude higher self-exchange rate constant compared to
[Co(bpy)3]3+/2+ translates into approximately 100-fold faster regeneration kinetics which would
allow a significant decrease in the driving force without affecting the efficient regeneration
kinetics.53 Using a low spin cobalt based redox shuttle which has smaller barrier from low spin
Co(II) (t2g6eg1) to low spin Co(III) (t2g6eg0) electron transfer, Xie et al. showed the potential of
applying low-spin redox shuttles in DSSCs.54 They observed that a driving force of ~200 mV
would be enough for excellent regeneration of MK-2 dye (2-Cyano-3-[5′′′-(9-ethyl-9H-carbazol3-yl)-3′,3′′,3′′′,4-tetra-n-hexyl-[2,2′,5′,2′′,5′′,2′′′]-quarter thiophen-5-yl] acrylic acid) by low spin
cobalt bis-trithiacyclononane, [Co(ttcn)2]3+/2+.54,55 On the other hand, Ru(III)/Ru(II) based redox
shuttles have also been demonstrated to have achieved good regeneration efficiency with
minimal or nearly zero driving force, though, the performance is still affected by their low
solubility, slow diffusion in commonly used electrolyte solvent and large light absorption
behavior in the visible sprectrum.56 Yum et al. has reported a 10% efficient DSSC with an
overpotential (= Vloss, regeneration) of 230 mV using an organic dye Y123.57 Based on these findings
it seems plausible to push the regeneration overpotential (Vloss,

regeneration)

below 200 mV by

utilizing dyes and redox couples with facile electron transfer kinetics. However, it also demands
the blocking of recombination processes through careful surface treatments of photoanodes (e.g.
deposition of Al2O3 or siloxane layer) or/and utilizing alternative photoanode materials.58–62

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6.3.3 Recombinations losses, Vloss, recombination
A very important feature of DSSC devices is the efficient transport of photoinjected electrons
through the nanoparticle network in the photoanode to the conductive substrate, with minimal
losses. Electrons can be lost from the nanoparticles as well as from the conductive substrate.7,63
As noted above, in order to improve the voltage by minimizing the dye-regeneration
overpotential, outer-sphere redox shuttle with large self exchange rate constant needs to be
utilized. Moving from I3-/I- to outer sphere redox shuttles offer a huge range of choices for dyeredox shuttle pairs. However, to realize their full potential, the origin of each of the
recombination processes need to be studied and minimized.

Figure 6-3 Schematic of back-electron transfer (i.e. recombination) processes from the
semiconductor nanoparticles and the transparent conductive substrate (TCO) into the redox
shuttle (R+/R) in the electrolyte.

The photoanodes in DSSCs are generally made of TiO2 nanoparticles. The open-circuit
voltage is generated by the potential difference between the redox potential of the electrolyte and
the quasi-Fermi level of electrons, EF, in the semiconductor photoanode. Thus, moving the EF

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closer to the conduction band edge (ECB) by populating the electron density will produce more
voltage. These electrons come from the photoexcited dye and may be lost through the
recombination processes. The processes are generally described in terms of electron lifetime, the
average time an electron “survives” in the semiconductor electrode before recombining with
acceptors in the electrolyte. Lowering (more positive) the redox potential of the redox shuttles
also increases the driving force for recombination and facilitates trap states mediated
recombination processes as depicted in Figure 6-4. Using the redox shuttle Ruthenium(II)
bis(2,2’-bipyridyl)-bis(N-methylimidozole), [Ru(bpy)2(MeIm)2]3+/2+, with a very positive redox
potential (> 0.8 V more positive than Co(bpy)33+2+ and I3-/I-) and small self-exchange (0.41 eV,
about 25% of Co(bpy)33+/2+), Ondersma et al. observed that the back electron transfer from the
trap states dominated the overall recombination processes.7

Figure 6-4 Energy diagram displaying the distribution of electrons in the TiO2 photoanode and
the recombination processes from the conduction band (green) and from the trap states (red).

The density of electrons in trap states in a TiO2 photoanode is about 2 orders of magnitude
higher than for free electrons in the conduction band.64 Thus providing enough driving force for

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the trap state mediated electron transfer processes by using highly positive redox shuttle would
be detrimental to the cell performance. Interestingly, Ondersma et al. have observed a behavior
consistent with Marcus inverted region of the recombination kinetics from conduction band to
this redox shuttle.65 This demonstrates a pathway to achieve higher photovoltage by utilizing
highly positive redox shuttle without making the recombination of CB electrons worse provided
the trap state mediated recombination is controlled.
One or two layers of Al2O3 are often used to block back-electron transfers and has been
shown to improve electron diffusion length and hence charge collection efficiency in case of
cobalt(II/III) complexes like [Co(bpy)3]3+/2+ and [Co(ttcn)2]3+/2+.48,54,60 However, it is not enough
to circumvent the recombination processes while using redox shuttles having fast self exchange
kinetics like [Co(ttcn)2]3+/2+ where the cell performance were found to be limited by the electron
diffusion length. Making this insulating layer thicker is detrimental to the photoelectron injection
from the dye. A better roadmap may be to find a new photoanode material which has higher
interfacial charge transfer resistance and better charge transport properties. 1D structures (like
nanorods) or arrays of nanowires which direct the electron transport to transparent conductive
substrate (TCO) and thus improve overall charge collection efficiency may be utilized.66,67
Photoanode materials having lower trap states also need to be investigated. Additionally,
Benkstein et al. showed the effect of the nanoparticle network geometry on the electron transport
through mesoporous photoanode.68 They observed that transport slowed down with increasing
porosity which was attributed to the decrease in the average coordination number of the particles
leading to more dead ends. Thus, porosity adds one more parameter to the improvement of
electron transport which leads to increasing charge collection. Using bulky dye is another way to
reduce the recombination loss.69 There are several parameters controlling the recombination

133

processes and predicting the minimum “loss-in-potential” due to recombination loss is thus not
feasible at present.
Additionally, Ondersma et al. showed that while using a redox shuttle with very positive
potential, blocking the recombination losses from the transparent conductive substrate (TCO)
becomes more challenging.63 A thin compact layer of metal oxide, e.g. TiO2, is generally
deposited on TCO to block recombination from the TCO to the redox shuttle which is sufficient
when using traditional outer sphere redox shuttles like [Co(bpy)3]3+/2+ and similar Co3+/2+
complexes. However, when the driving force for the recombination electron transfer is larger, in
case of highly positive redox shuttle, TiO2 layer is unable to stop this process. Ondersma et al.
showed that in this scenario an insulating film such as poly-phenol oxide (PPO) is a good choice
as the blocking layer on FTO.63

6.4 Predicting the maximum power conversion efficiency in DSSCs:

Figure 6-5 Photon flux of the AM 1.5 G spectrum at 100 mW cm-2 (ASTM G173-03).

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Solar energy is harvested by the dye adsorbed on the mesoporous semiconductor; harvesting
more of the solar spectrum, shown in Figure 6-5, will result in higher photogenerated current
densities. However, harvesting longer wavelengths of light, i.e. the lower energy region of the
spectrum, also results in lower voltages. The solar spectrum shows strong atmospheric
absorption features around 930, 1110 and 1320 nm which corresponds to 1.33, 1.12 and 0.94 eV,
respectively. The photoconversion efficiency is a product of current and voltage (i x V). Thus, it
is reasonable to propose that, in order to get optimum current without losing voltage considering
these atmospheric absorption regions, the absorption onset (Eopt) of the sensitized semiconductor
should begin around 930 or 1110 or 1320 nm as shown in Figure 6-6.

Figure 6-6 Short-circuit photocurrent density as a function of absorption onset calculated by
integrating the AM 1.5 solar spectrum.

The maximum current attainable from the solar spectra by absorbing light up to 930, 1110
and 1320 nm are 33.9, 42.4 and 50.1 mA cm-2, respectively. The maximum incident photon to
current conversion efficiency (IPCE) values in the champion DSSCs have reached as high as
91%.3 Considering ~10% loss of the incident light due to the reflection loss, this is the highest

135

limit of IPCE. Utilization of textured surface and anti-reflective coating can potentially lower
down the reflection loss resulting higher IPCE. To the best of our knowledge, however, higher
IPCE has not been achieved yet. Considering a IPCE = 90%, the short circuit current associated
with the absorption onsets of 930, 1110 and 1320 nm are 30.5, 38.2 and 45.1 mA cm-2,
respectively. The following sections will discuss how the other parameters of a working cell
would be adjusted to maximize the photovoltage associated with each of these three photocurrent
scenarios. A reasonable fill factor (ff) of 75% is assumed for all of the calculations.32,70–75 We
point out that larger values of Voc also allow for larger ff. ff is defined by the ratio of the area
under a J-V corresponding to the maximum power output to the area defined by Jsc and Voc.
Increasing the VOC would increase the contribution of the smaller rectangle (J-V), provided the
diode quality factor is not compromised. Thus, the ratio, i.e. the ff will increase. The ff shown in
Figure 6-1 is 77% and the VOC is >1 V. However, as discussed in the following sections, the
journey towards 20% photoconversion efficiency of a DSSC would likely come through the
utilization of the near-infrared spectra of the sunlight which requires sensitizers of low optical
band gap resulting low VOC (~ 0.7 V). Thus, it is reasonable to assume ff = 75% in our calculation.
Note that, in case of Si PV, ff = 80% has been achieved with the same range of VOC. The
maximum open circuit voltage, VOC can be written as VOC = Eopt/q – Vloss. The short circuit
current, voltage and “loss-in-potential” corresponding to those 3 absorption onsets are shown in
Table 6-1.
In case of 930, 1110 and 1320 nm absorption onset scenarios, photoconversion efficiency, 
= 20% is achievable with loss-in-potential as large as 450, 420 and 350 mV, respectively. As
discussed in Section 2.3.1, the ruthenium based dyes like N719, N3, black dye can inject electron
into TiO2 even when Vloss, injection = 0 V. Assuming Vloss, injection = 0 V and ECBEF = ~100 mV,

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making 20% efficient DSSC looks plausible if Vloss, regeneration can be made <350, 320 and 250 mV,
respectively, for the three absorption onset scenarios. It is a reasonable target as discussed in
section 2.3.2. However, Vloss, injectron > 300 mV for the organic dyes used in the recent champion
DSSCs. In a scenario of Vloss, injectron = 300 mV, Vloss, regeneration = 200 mV and ECBEF = ~100 mV
it is not possible to go beyond 17% (see Figure 6-7).

Table 6-1 Table of the photoconversion efficiencies at different absorbance onsets and the
associated loss in potentials.

Absorption onset / nm

%

JSC / mAcm-2

VOC / V

Vloss / V

1.55

0.22

1.17

0.6

13

1.01

0.76

20

0.88

0.45

0.66

0.67

13

0.57

0.76

20

0.7

0.42

0.52

0.6

13

0.45

0.67

20

0.59

0.35

0.44

0.5

0.38

0.56

20
700

930

1110

1320

15

15

15

15

17.2

30.5

38.2

45.1

13

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Figure 6-7 and Table 6-1 show that 15% efficient DSSCs can be made in all of the absorption
onset scenarios mentioned here. The record efficiencies have already reached to 14.3%. However,
harvesting the solar spectrum upto 930 nm would be the best choice to reach 15% efficiency
because it would be achieved without much effort to decrease the loss in potential.

Figure 6-7 Photoconversion efficiency of DSSC as a function of loss-in-potential at different
absorption onsets of the sensitized photoanode.

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Making a 20% efficient DSSC is, however, challenging. Using sensitizers with the absorption
onset of 700 nm, it is very unlikely to make a DSSC having  = 20%. The total loss-in potential
needs to be minimized to 220 mV and considering EF  ECB = ~100 mV, combination of Vloss,
injection

+ Vloss, regeneration needs to be reduced to 120 mV which is very unlikely to happen. The

near-infrared photons of the solar spectrum need to be harvested to achieve 20%
photoconversion efficiency. We would also like to point out that Table 5-1 does not imply that
targeting a higher energy absorption onset would offer an easier target for low loss-in-potential.
The optimum photovoltage corresponding to higher energy onset is also higher which would
provide some extra driving force for recombination processes. Suppressing these recombination
processes to realize the maximum photovoltage output could be challenging. DSSC with an
absorption onset 930 nm (i.e. 1.33 eV) needs a photovoltage of 0.88 V with a Vloss not larger than
0.45 V. However, for 1110 nm (i.e. 1.12 eV) the VOC is 0.7 V and Vloss is 0.42 V as shown in
Figure 6-7. Thus, using a sensitizer having an absorbance onset of 1110 nm instead of 930 nm
will face ~180 mV less driving force for recombination processes. However, Vloss, associated with
both of them is almost same, ~450 mV. Thus, we believe, to achieve 20% efficiency, the scenario
of 1110 nm absorption onset is likely to be a better choice than 930 nm scenario. Also, it is very
unlikely that a single dye will absorb light throughout this whole wavelength region. A mixture
of dyes need to be used to obtain maximum current from a working cell.4 The potential of 1320
nm onset scenario would only be realized by choosing a proper combination of dyes which is
also not very straightforward.
The current record efficiency is 14.3 % where Vloss, injectron = ~370 mV, Vloss, regeneration = 370
mV, ECBEF = ~60 mV which gives ~0.8 V overall potential loss. The optical band gap of the
ADEKA-1 dye used there is 1.85 eV corresponding to ~670 nm. ~100 nm broadening of the

139

absorption width (IPCE, Figure 6-1) is present here which is generally observed when the
sensitizer molecule is strongly coupled to the TiO2. It improves the overall light harvesting
efficiency and Jsc was found to be as large as 18.36 mA cm-2. VOC was found to be 1.013 V which
is the maximum attainable VOC considering ~0.8 V potential loss. Thus, with this combination of
semiconductor photoanode, dye and redox shuttle, the maximum possible photoconversion
efficiency has already been achieved, as shown in Figure 6-7. Vloss, injectron and Vloss, regeneration are
required to be reduced in order to push the photoconversion efficiency beyond this.54,76
6.5 Conclusion
In this chapter, the maximum attainable power conversion efficiency of DSSCs has been
estimated. A plausible roadmap towards 20% photoconversion efficiency has been predicted. The
main energy loss mechanisms have been pointed out and an outlook to minimize them has been
presented. The challenges will only be met through extending our understanding of the
interfacial charge transfer processes and mastering our ability to systematically engineer each of
the components of the dye-sensitized solar cell. The journey of DSSC progressed keeping the
initial champion components, like TiO2 photoanode, ruthenium dye, Iodide redox shuttle and
platinum counter electrode, unchanged. In spite of the huge boom of DSSC research and a large
effort to maximize the overall efficiency, it remained almost stagnant for two decades. The recent
breakthrough in the efficiency has come through the systematic understanding and improvement
of the outer sphere redox shuttles which showed pitiful performance initially.50 The absorption
onset needs to be extended to near-infrared region by using proper combination of sensitizers.
Additionally, great effort needs to be applied to develop a redox shuttle having very fast electron
transfer kinetics which can efficiently regenerate oxidized dye with minimum driving force.
However, it will also worsen the recombination mechanisms from the photoanode. Thus,

140

alternative photoanode materials need to be investigated which offer faster charge transport
through nanostructured network and higher interfacial charge transfer resistance. An extended
literature of various potential photoanode materials needs be developed.

141

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Chapter 7 Conclusions and future directions
We have developed a spectroelectrochemical method to determine the conduction band edge
(ECB) in nanostructured photoanodes. ECB has been determined at different Fermi levels and an
upward shift of the ECB position has been observed. This upward shift occurs due to the potential
drop across the double layer (nanoparticle-electrolyte interface). The electron accumulation is
accompanied by positive charges, i.e. the cations in the electrolyte. Accumulation of electrons in
the electrically active states on the surface or within close vicinity of the surface of metal oxide
nanoparticle changes the ionic distribution and hence the electric field in this interfacial double
layer. The band edge unpinning has been mentioned in the nanostructured photoanode systems
and has also been pointed out in other studies while studying the electron transfer processes in
DSSCs.1,2 However, determination of the magnitude of this ECB shift has been missing in the
literature. Hence, this phenomenon, in most of the studies related to DSSCs, has been ignored
and in few cases, estimated indirectly. Thus, our work has solved a long standing problem in the
context of studying the material properties of nanostructured semiconductor electrodes.
Additionally, this method is versatile and can be applied to determine the band edge position in a
variety of porous semiconductor materials provided a transparent film can be made.
In addition to the conduction band position, trap state distribution is another important
parameter required to study the various electron transfer processes related to the photoanodes. By
combining spectroelectrochemical method with the electrochemical method we have determined
the accurate electron distribution of nanoparticle photoanodes (TiO2 and SrTiO3). The magnitude
of the band edge unpinning has been included to get a real picture of the electron distribution.
The position of the trapped electrons is also important because the electrons trapped on the
surface behave very differently from the electrons trapped in the bulk. However, their position

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has been debated. Our studies have shown that the trap states are distributed on the surface as
well as in the bulk and, with increasing negative bias, bulk traps dominate the overall trap state
distribution. Such detailed understanding is important in studying the recombination reactions
associated to the photoanode which generally limit the performance of DSSCs.
A detailed study has been performed to determine the energetics and the charge distribution
of mesoporous SrTiO3 electrode. Ternary oxides offer wider possibility for tuning the physical–
chemical properties by altering the relative ratios of the cationic components. SrTiO3, SrSnO3,
Zn2SnO4, CdSnO3 and BaSnO3 are among the ternary metal oxides utilized as photoanode in
DSSCs.3–5 However, their performances have been much lower than the DSSCs constructed with
TiO2 photoanode and further study needs to be performed to assess their potential as a DSSC
photoanode material. TiO2 is being extensively used as photoanode material in DSSCs. Having
another photoanode material, with different energetics and electron distributions from TiO2, will
provide more choices for dyes and electrolytes. In comparison to TiO2, 200 mV higher
conduction band edge position and a very different distribution of trapped states have been
observed in SrTiO3. Overall density of trap states have been found to be lower than TiO2 which
indicates a possibility of lower trap state mediated recombination processes. The charge
separation in DSSC takes place at the dye-semiconductor interface. Separation between the
solution potential, E(R+/R) and the Fermi level of the electron in the semiconductor, EF, is the
voltage output from a cell. At the open circuit this separation is the highest and the
corresponding voltage is called open circuit voltage, VOC. Thus, SrTiO3 could offer higher VOC if
the recombination losses are minimized.
The photoanode plays an essential role in the charge injection process from the dye,
transporting these electrons and in recombination processes. The ideal photoanode should

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demonstrate quantitative charge injection with minimal energy difference between the dye
excited states and the conduction band edge. Additionally, the interfacial recombination
processes also need to be minimized. To push the photoconversion efficiency of DSSC beyond
15%, a significant breakthrough is desired in the photoanode part of the device. One-electron,
outer-sphere redox shuttles having ‘fast’ electron transfer kinetics can reduce the overpotential
associated to the regeneration of the excited dye, which generally causes the largest voltage loss
in a DSSC. Utilization of ‘fast’ redox shuttles also increases the electron recombination kinetics
from nanoparticle to redox shuttle and results in a poor electron collection. In this context,
photoanodes having faster electron transport and/or higher interfacial charge transfer resistance
are highly desired. Exploring alternative photoanode material can lead us to the device
configuration where the regeneration loss can be minimized by utilizing fast outer-sphere redox
shuttles.

149

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