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Modeling water oxidation at photoanodes

Citation for published version (APA):George, K. (2020). Modeling water oxidation at photoanodes: a multiscale approach. Technische UniversiteitEindhoven.

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https://research.tue.nl/en/publications/5a948e4e-f534-4e39-8f66-24c9008808ce

Modeling water oxidation at

photoanodes: A multiscale approach

Kiran George

The work presented in this thesis was funded by Netherlands Organization for Scientific

Research (NWO)-Shell industrial partnership program number i32 “Computational Sciences

for Energy Research (CSER - PhD)”. The research was conducted at the Dutch Institute for

Fundamental Energy Research (DIFFER), Eindhoven, the Netherlands. DIFFER is part of the

Netherlands Organization for Scientific Research (NWO).

A catalogue record is available from the Eindhoven University of Technology Library.

ISBN: 9789464190311

NUR: 925

Cover illustration by Kiran George

Printed by: Gildeprint – The Netherlands

© Copyright 2020 Kiran George

Modeling water oxidation at photoanodes: A multiscale approach

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus prof.dr.ir. F.P.T. Baaijens,

voor een commissie aangewezen door het College voor Promoties, in het openbaar te verdedigen op vrijdag 16 oktober 2020 om 13:30 uur

door

Kiran George

geboren te Thrissur, India

Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de promotiecommissie is als volgt: voorzitter: prof. dr. ir. G.M.W. Kroesen promotor: prof. dr. ir. M.C.M. van de Sanden copromotor(en): dr. sc. techn. A. Bieberle-Hütter (DIFFER) dr. ir. M. van Berkel (DIFFER) leden: prof. dr. R. van de Krol (Helmholtz-Zentrum Berlin) dr. S. Haussener (École Polytechnique Fédérale de Lausanne) prof. dr. S. Weiland prof. dr. M.T.M. Koper (Universiteit Leiden)

Het onderzoek of ontwerp dat in dit proefschrift wordt beschreven is uitgevoerd in overeenstemming met de TU/e Gedragscode Wetenschapsbeoefening.

Table of Contents

PART A: Framework and overview of the research ............................................................................. 11

1 Introduction ............................................................................................................................... 13

1.1 Global energy scenario .................................................................................................. 13

1.2 Solar energy to chemical bonds .................................................................................... 14

1.3 Photoelectrochemical cells ........................................................................................... 15

2 Photoanode-electrolyte interface ............................................................................................. 17

2.1 Oxygen evolution reaction (OER) at the photoanode-electrolyte interface ................. 17

2.1.1 Mechanism of OER .................................................................................................... 17

2.1.2 Charge carrier dynamics within the semiconductor ................................................. 18

2.1.3 Surface states ............................................................................................................ 20

2.2 Measurement of OER characteristics ............................................................................ 21

2.2.1 Photocurrent measurement ...................................................................................... 21

2.2.2 Electrochemical impedance spectroscopy ................................................................ 24

2.3 Modeling of OER ............................................................................................................ 27

2.3.1 Density functional theory .......................................................................................... 28

2.3.2 Microkinetic modeling ............................................................................................... 31

2.3.3 Modeling of charge carrier dynamics ........................................................................ 33

2.3.4 Multiscale modeling of semiconductor-electrolyte interface ................................... 35

3 Research approach and goal of the thesis ................................................................................ 36

3.1 Research approach ........................................................................................................ 37

3.2 Outline of chapters in part B ......................................................................................... 38

4 General conclusions .................................................................................................................. 49

5 Outlook ...................................................................................................................................... 53

References ......................................................................................................................................... 57

PART B: Publications ............................................................................................................................. 67

Chapter 1: Why does NiOOH cocatalyst increase the oxygen evolution activity of α-Fe2O3? ........... 69

Abstract ............................................................................................................................................. 69

1 Introduction ............................................................................................................................... 70

2 Methodology and computational details .................................................................................. 71

3 Results and discussion ............................................................................................................... 73

3.1 Cluster geometry ........................................................................................................... 73

3.2 Strip geometry ............................................................................................................... 74

3.3 Wider strip geometry .................................................................................................... 76

4 Conclusions ................................................................................................................................ 79

References ......................................................................................................................................... 81

Supporting information ..................................................................................................................... 85

Chapter 2: Impedance spectra and surface coverages simulated directly from the electrochemical

reaction mechanism: A nonlinear state-space approach .................................................................... 89

Abstract ............................................................................................................................................. 89

1 Introduction ............................................................................................................................... 90

2 Model and Method ................................................................................................................... 92

2.1 Mechanism of water oxidation ..................................................................................... 93

2.2 Calculation of reaction rates ......................................................................................... 94

2.3 Rate equations and charge balance relations ............................................................... 95

2.4 State-space model ......................................................................................................... 96

2.5 Linearization of state-space model and impedance calculation ................................... 96

3 Case study: Hematite – water interface .................................................................................... 98

3.1 Input parameters ........................................................................................................... 99

3.2 Assumptions ................................................................................................................ 100

3.3 Simulated data from the electrochemical model ........................................................ 101

3.3.1 Current-voltage characteristic ..................................................................................... 101

3.3.2 Species coverage plot ................................................................................................... 101

3.3.3 Electrochemical Impedance Spectrum (EIS) ............................................................... 102

3.4 Model order reduction ................................................................................................ 103

3.5 Simulation of extended EIS and comparison to experiment ....................................... 105

4 Summary and Outlook ............................................................................................................. 107

References ....................................................................................................................................... 109

Chapter 3: Understanding the impact of different types of surface states on photoelectrochemical

water oxidation: A microkinetic modeling approach ........................................................................ 115

Abstract ........................................................................................................................................... 115

1 Introduction ............................................................................................................................. 116

2 Theory and method ................................................................................................................. 118

2.1 Microkinetic Model ..................................................................................................... 119

2.2 Charge carrier dynamics .............................................................................................. 120

2.3 Potential across the space charge region .................................................................... 122

2.4 Current density ............................................................................................................ 123

2.5 Capacitances ................................................................................................................ 124

3 Results and discussion ............................................................................................................. 124

3.1 Validation of input-output relationship ...................................................................... 126

3.2 The impact of r-SS ....................................................................................................... 127

3.3 The impact of i-SS ........................................................................................................ 129

4 Summary ................................................................................................................................. 134

References ....................................................................................................................................... 137

Supporting Information ................................................................................................................... 143

Chapter 4: The critical role of the series resistance in impedance measurements of photoelectrodes

............................................................................................................................................................. 155

Abstract ........................................................................................................................................... 155

1 Introduction ............................................................................................................................. 156

2 Theory and method ................................................................................................................. 158

2.1 Calculation of capacitance ........................................................................................... 158

2.2 Calculation of current density ..................................................................................... 159

3 Results and discussion ............................................................................................................. 162

3.1 Impact of 𝑅s on current-voltage curves ...................................................................... 162

3.2 Impact of 𝑅s on EIS data ............................................................................................. 165

3.2.1 Surface state capacitance ........................................................................................ 167

3.2.2 Capacitance of the space charge layer .................................................................... 168

3.2.3 Charge transfer resistance ...................................................................................... 169

3.2.4 Simulation of EIS ...................................................................................................... 170

4 Summary and conclusions ....................................................................................................... 173

References ....................................................................................................................................... 177

Supporting information ................................................................................................................... 181

Summary ............................................................................................................................................. 189

Publications and presentations .......................................................................................................... 193

Acknowledgments .............................................................................................................................. 195

Curriculum Vitae ................................................................................................................................. 199

PART A: Framework and overview of the research

Introduction 13

1 Introduction

1.1 Global energy scenario

Global energy demand is increasing with the increase in population and economic growth. The

global energy demand as of 2015 was around 570 Exajoules and is expected to increase to

1000 Exajoules by the year 2070.1 The increase in energy demand in itself is not a major

problem, but the carbon dioxide emission associated with it is the prime concern.2 Over the

past century, there has been a steady increase in the average global temperature due to

excessive CO2 emission mainly from the burning of fossil fuels. For this reason, the Paris

climate agreement of 2015 has laid down a goal of holding the global average temperature

rise to be less than 2˚C above the pre-industrial level and to pursue efforts to limit the increase

to 1.5°C.3 The infographics in Figure 1a shows the global population and energy demand along

with emission data from 2015 and a prediction for 2070.1

Figure 1 a) Infographics showing the population, energy consumption, and CO2 emission data for the year 2015

along with a predicted scenario for 2070. Net-zero emission is necessary for the predicated scenario to stay

within the Paris climate agreement. (adapted from ref.1) b) Infographics showing the share of different

technologies/fuels in the energy landscape as of 2017. (adapted from ref.1)

The prediction states that with such an increase in energy demand, it is necessary to achieve

net zero-emissions to stay within the Paris climate agreement.4 However, the current trend in

CO2 emission is not promising. In the year 2018 alone, the global energy-related CO2 emission

increased by 1.7% to around 33 Gigatons.5 Based on the data shown in Figure 1b, about 80%

of the global energy demand is met by different forms of fossil fuels.1 Since the energy demand

is going to increase further, carbon neutral and carbon negative energy solutions should be

developed and employed at the earliest to stay within the Paris climate agreement.4 Hence,

a b

14 Solar energy to chemical bonds

the focus has to be shifted from a fossil fuel-based energy economy to a renewable energy-

based one.

1.2 Solar energy to chemical bonds

In the predicted scenarios about sustainable energy landscape, the harvesting of solar energy

has a huge weightage.2,4 With the support of cutting edge research and mass production,

efficient and cost-effective photovoltaic (PV) cells are now available in the market. However,

due to the intermittent nature of sunlight, cost-effective ways of storing solar energy is

necessary.6 Compared to batteries, chemical fuels are advantageous due to high energy

density and ease of transportation.7 Direct conversion of solar energy into chemical fuels is a

promising concept and the generation of hydrogen by water splitting using solar energy is

considered a possible solution in this regard.8,9 Hydrogen is considered as a green-fuel

alternative to fossil fuels.7

For producing hydrogen by solar water splitting, there are mainly three different strategies;

by using photochemical (PC) system, photoelectrochemical (PEC) system, and photovoltaic-

electrolyzer (PV-E) system. The schematic representations of these three systems are shown

in Figure 2.8

Figure 2 Schematic of photochemical (PC), photoelectrochemical (PEC), and photovoltaic-electrolyzer (PV-E)

system (alternative: principle). PC system and PV-E have the respective limitations of low efficiency and high cost,

while PEC cell lies intermediate for achieving high efficiency at an affordable cost. Adapted from ref.8

In the PC system, a photocatalytic material is dispersed in an aqueous solution, which upon

illumination catalyzes the water-splitting reaction. In such particle-based systems, the solar to

hydrogen (STH) conversion efficiency is reported to be less than 1% and the hydrogen and

oxygen produced are not well separated.8,10 In the PV-E system (right part of the image), a PV

cell is coupled with a water electrolyzer. Such a set-up is estimated to give an STH efficiency

of more than 10%. One drawback of such a design is its cost due to the integration of two

separate systems.8,11

A PEC system integrates solar energy conversion and water electrolysis into a single device.12

The light absorption and electrolysis are integrated by using semiconductor electrodes. The

Introduction 15

configuration of a PEC system can be with a single photo-absorber or dual photo-absorber. In

a single photo-absorber system, only one of the electrode is made of a semiconductor and the

counter electrode is metallic.11 In a dual photo absorbing system, two photo-absorbing

semiconductors, one with a wide bandgap and another one with a small bandgap are

connected in tandem to enhance the light absorption.8,13 The connection is such that the

incident light is directed from the large bandgap material to the short bandgap material.8

Additionally, in the design of PEC system, two compartments or an ion exchange membrane

may be present similar to PV-E system, to avoid the crossover of the products formed at the

electrodes.8 Recently, a configuration of the PEC cell which uses a polymeric electrolyte

membrane (PEM) has been reported with promising scalability and robustness.14

A recent techno-economic analysis comparing different solar hydrogen generation

technologies showed that the PEC system has an advantage over the PV-E system.15 This is

due to the higher costs associated with transport and conditioning of electricity from PV

panels to electrolyzers in the case of the PV-E system.15 PC systems and PV-E have the

respective limitations of low efficiency and high cost, while the PEC system has the potential

for achieving high efficiency at an affordable cost.8,11 Therefore, the PEC water splitting is a

promising option towards sustainable production of carbon-free fuel. However, based on the

calculations, the hydrogen generation using PEC water splitting can compete with hydrogen

generation using fossil fuels only if the overall efficiency of the PEC cell can be improved to >

10% and if a stability of > 5 years can be achieved.8 At present, no PEC system design has

achieved these requirements in efficiency and stability. Hence, more research is needed to

develop economically feasible PEC cells that meet the efficiency and stability requirements.

1.3 Photoelectrochemical cells

A simplified representation of a photoelectrochemical cell with a semiconductor anode

(photoanode) and a metallic cathode is shown in Figure 3. Such a PEC configuration is used

throughout this thesis. Under illumination, electron-hole pairs are generated inside the

photoanode. The generated holes, under the influence of applied potential, move towards the

photoanode-electrolyte interface, and oxidize water. The electrons, on the other hand, move

towards the counter electrode through the external circuit as shown in Figure 3, and reduce

water to form hydrogen. Thus, there are mainly two half-reactions in PEC water-splitting; the

hydrogen evolution reaction (HER) which occurs at the cathode, and oxygen evolution

reaction (OER) which occurs at the photoanode. The chemical reactions for HER and OER

occurring at the electrodes in an alkaline electrolyte can be written as7

4𝐻2𝑂 + 4𝑒− ⇌ 2𝐻2 + 4𝑂𝐻

− (1)

4𝑂𝐻− + 4ℎ+ ⇌ 𝑂2 + 2𝐻2𝑂 (2)

16 Photoelectrochemical cells

The reaction under acidic condition can be written as7

4𝐻+ + 4𝑒− ⇌ 2𝐻2 (3)

2𝐻2𝑂 + 4ℎ+ ⇌ 4𝐻+ + 𝑂2 (4)

The theoretical thermodynamic potential required for electrochemical water-splitting is 1.23

V. However, in experiments, applied potentials more than 1.23 V are usually required for

water splitting to occur.16 The amount by which the actual potential required for water

splitting exceeds 1.23 V is called overpotential (𝜂).17 Among the two half-reactions, OER

contributes more to the overpotential of water splitting reaction, as it involves the transfer of

four charge carriers for the generation of one O2 molecule.18 Additionally, the sluggish kinetics

of OER occurring at the photoanode is identified as one of the performance-limiting processes

in solar water splitting.11,19 Hence, for increasing the efficiency of PEC cells, it is necessary to

improve the efficiency of OER occurring at the photoanode. Therefore, this thesis focuses on

OER occurring at the photoanode-electrolyte interface.

Figure 3 Overview of a photoelectrochemical (PEC) cell with an alkaline electrolyte: the photoanode (left) absorbs

light, driving the oxygen evolution reaction at the photoanode and the hydrogen evolution reaction at the

cathode (right). Adapted from ref.16

The photoanode in a PEC cell is made of an n-type semiconductor. For a semiconductor

material to be used as a photoanode, it should meet certain stringent criteria. The bandgap of

the semiconductor should be approximately 1.8 eV - 2.4 eV which is suitable for absorbing

energy from the visible spectrum of sunlight.7 The conduction band edge (𝐸c) and valence

band edge (𝐸v) positions must straddle the water reduction (𝐸red,water) and oxidation

potential (𝐸ox,water); 𝐸c > 𝐸red,water and 𝐸v < 𝐸ox,water.7,9 The mobility and life-time of the

minority carriers should be high enough to enable efficient charge transfer across the

semiconductor-electrolyte interface.7 Additionally, the material should be low cost, abundant,

Photoanode-electrolyte interface 17

non-toxic, and should be stable in the electrolyte under operating conditions.20 Certain metal

oxide semiconductors, like Fe2O3, WO3, and BiVO4, are identified in the literature as potential

electrode materials for visible-light-driven water splitting.21–23 In this thesis, Fe2O3 is used as

the model photoanode material.

Fe2O3 (hematite) is a widely investigated photoanode material in the field of PEC water

splitting due to its suitable bandgap, abundance, low cost, non-toxicity, and stability under

operating conditions.24–27 The bandgap of hematite is ~ 2.1 eV which is in the range suitable

for harvesting energy from the visible spectrum of sunlight.7 Theoretically, hematite can

achieve an STH efficiency as high as 15% which is higher than the benchmark STH efficiency of

10% required for practical implementation.28 However, the experimental efficiencies reported

for hematite have not met this benchmark efficiency yet.29,30 Further research is required for

the identification of the rate-limiting processes and performance improvement of hematite

photoanodes.

The photoanode performance depends on the availability of holes at the photoanode surface

and the rate of hole transfer across the semiconductor-electrolyte interface. The availability

of holes at the photoanode surface depends on light absorption, generation, recombination,

trapping of charge carriers, and charge transport within the bulk of the semiconductor.16,19

Similarly, the efficient transfer of these holes across the photoanode-electrolyte interface

depends on the catalytic efficiency of the elementary steps in OER on the semiconductor

surface. Thus, several processes influence the efficiency of OER occurring at the photoanode

surface. However, it is not clear which of these processes lead to the lower overall efficiency

of OER at the photoanode surface. A thorough understanding of the limiting processes at the

photoanode-electrolyte interface is therefore necessary for improving the efficiency of OER

at photoanodes and ultimately the efficiency of PEC water splitting.

2 Photoanode-electrolyte interface

In this section, the theoretical aspects of OER at the photoanode-electrolyte interface are

discussed first. Subsequently, the experimental techniques and modeling methods employed

in the literature for studying OER, particularly relevant to this thesis, are discussed.

2.1 Oxygen evolution reaction (OER) at the photoanode-electrolyte interface

2.1.1 Mechanism of OER

The generation of an O2 molecule during electrochemical water splitting involves a transfer of

four charge carriers (holes) as shown in Eq. (2) and Eq. (4). These equations represent the

overall OER under different pH of the electrolyte and are written as single-step reactions.

However, it is generally accepted that OER proceeds via intermediate steps each involving

18 Oxygen evolution reaction (OER) at the photoanode-electrolyte interface

transfer of a single electron/hole.31–33 Different mechanisms for OER have been proposed in

the literature defining the nature of the intermediates involved.34–38 The proposed

mechanisms have some similarities as most of them involve OH and O intermediates. The

difference mainly arises from the mechanism of O-O bond formation which leads to the

formation of oxygen.39 Some mechanisms propose oxygen formation by direct combination

of two O intermediates from two different sites and some mechanisms propose the formation

of OOH intermediate at the same site, which subsequently forms oxygen. A recent

experimental study of OER intermediates on hematite surface by Zandi and Hamann40

proposed that the mechanism of OER involves OH, O, and OOH as the adsorbed intermediates.

This is in agreement with the widely accepted mechanism proposed by Rossmeisl et al.38

Under alkaline conditions, the multistep mechanism of OER on metal oxide semiconductors

can be written as41

∗ + 𝑂𝐻− + ℎ+𝐾b1⇌𝐾f1

𝑂𝐻ad (5)

𝑂𝐻ad + 𝑂𝐻− + ℎ+

𝐾b2⇌𝐾f2

𝑂ad + 𝐻2𝑂 (6)

𝑂ad + 𝑂𝐻− + ℎ+

𝐾b3⇌𝐾f3

𝑂𝑂𝐻ad (7)

𝑂𝑂𝐻ad + 𝑂𝐻− + ℎ+

𝐾b4⇌𝐾f4

𝑂2,ad +𝐻2𝑂 (8)

𝑂2,ad𝐾f5→ 𝑂2,des + ∗ (9)

where * represents an adsorption site at the electrode-electrolyte interface, the subscript ad

represents that a species is adsorbed on the surface, 𝐾fi and 𝐾bi represent the rate constants

for the forward and backward reaction in each step. All the four electrochemical steps from

Eq. (5) - Eq. (8) involve the transfer of a single hole. The last step is the desorption of oxygen

leaving an adsorption site available for the next cycle of reaction.42 The energetics and kinetics

of these elementary steps in OER influence the efficiency of OER at the electrode-electrolyte

interface.

2.1.2 Charge carrier dynamics within the semiconductor

According to Eq. (5) - Eq. (8), the availability of holes (ℎ+) at the photoanode-electrolyte

interface is necessary for the reactions to proceed.36 The availability of holes at the

photoanode-electrolyte interface depends on the processes occurring within the photoanode

and at the photoanode surface. A schematic representation of a photoanode under

illumination in the presence of an applied bias is shown in Figure 4.


Upon illumination, electrons (red circles) from the valence band (VB) are excited to the

conduction band (CB) leaving holes (blue circles) in the valence band. Since electrons are the

majority carriers in an n-type semiconductor, the relative increase in the number of electrons

is only marginal.43 The number of holes in the VB increases under illumination. These holes

move towards the semiconductor-electrolyte interface (SEI) under an applied potential. The

number of holes reaching the SEI per unit area of the electrode, defined as the hole flux (𝐽G),

can be calculated using the Gartner equation as44

𝐽G = 𝐼0 (1 −

exp(−𝛼𝑊sc)

1 + 𝛼𝐿p)

(10)

where 𝐼0 is the illumination intensity, 𝛼 represents the absorption coefficient for a given

wavelength of the incident light, 𝐿prepresents the minority carrier diffusion length, and 𝑊sc

represents the width of the space charge region. The space charge region is a region formed

inside the photoanode side of the SEI, which is devoid of majority carriers.45 𝑊sc is given by7

𝑊sc = √2𝜖r𝜖0𝑒𝑁D

(𝑈sc −𝑘B𝑇

𝑒)

(11)

where 𝜖r is the permittivity of the semiconductor material, 𝜖0 is the permittivity of free space,

𝑁D is the doping density, 𝑈sc is the potential across the space charge region, 𝑒 is the charge

of an electron, 𝑘B is the Boltzmann constant, and 𝑇 is the temperature. The potential across

the space charge region (𝑈sc) depends on the applied bias potential. Hence, the availability of

holes at the SEI depends on two input parameters; the applied potential and the illumination

intensity.

In reality, not all of the generated holes reach the SEI, depending on the mobility of holes in

the semiconductor material, direct recombination with the electrons in the bulk and

recombination within the space charge region.46 Additionally, at the surface of the

semiconductor, the periodic crystal symmetry might not hold due to different reasons and this

leads to the formation of electronic states within the bandgap of the semiconductor.47 These

energy states within the bandgap are often called surface states (see further discussion in

section 2.1.3). Some of the holes get trapped at theses surface states as well. The excitation,

recombination, and trapping of charge carriers are representatively shown in Figure 4. Out of

the generated holes, the ones left after recombination with electrons and after trapping are

available for the water oxidation reaction.8,46 Hence, the charge carrier dynamics within the

semiconductor which involves the generation, recombination, and surface trapping of charge

carriers is an important factor defining the performance of OER on the semiconductor surface.

20 Oxygen evolution reaction (OER) at the photoanode-electrolyte interface

Figure 4 A simplified band diagram of a photoanode under illumination (𝐼0) in the presence of an applied bias

potential (𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑). The processes occurring in the semiconductor are (1) charge excitation by light, (2) electron

extraction through the back contact, (3) hole transfer to surface states, (4) hole transfer to the electrolyte, (5)

bulk recombination, (6) recombination in the space charge region and (7) electron recombination in surface

states. The recombination processes are shown using red arrows. Modified from ref.8

2.1.3 Surface states

As mentioned before, crystal symmetry can be disrupted at the semiconductor surface which

leads to the formation of electronic energy states at the surface, these are called surface

states. The disruption in crystal symmetry can be due to the existence of dangling bonds,

vacancies, impurities, etc. at the surface or due to the adsorption of species at the surface

from the electrolyte.7,48,49 For instance, in the case of hematite photoanodes, there are surface

states reported with an energy level right below the conduction band.50,51 These sub-

conduction band surface states act as recombination centers for electrons and holes, and are

referred to as r-SS (recombining surface state).49 Additionally, there are surface states

observed in experiments that are found to be existing only in the presence of water.52,53 These

surface states are proposed to be due to the adsorbed OER intermediates and are referred to

as i-SS (intermediate surface state).49

The presence of r-SS with energy level right below the conduction band makes the Fermi level

of the semiconductor to be pinned at the surface state energy level as shown in Figure 5a.50

For this reason, the band bending will not occur on the application of a bias potential until the

Fermi level crosses the surface state energy level.50 The phenomenon is called Fermi level

pinning. Due to Fermi level pinning, the potential available across the space charge region

(𝑈sc) will not increase upon application of bias potential. The band diagram after selective

removal of r-SS is shown in Figure 5b. The selective removal of r-SS results in an increased

band bending which in turn enhances the electron-hole separation. The OER performance of

the photoanode is found to increase after the removal or passivation of r-SS.50 The i-SS is

present in Figure 5a and Figure 5b due to the formation of OER intermediates during water

oxidation.


Figure 5 Simplified band diagram of hematite electrodes under conditions with (a) and without (b) Fermi level

pinning by the sub-conduction band surface states (r-SS); the surface states due to OER intermediates are

denoted as i-SS. Modified from ref.50

The role of i-SS on OER performance is a topic of debate in the literature: In some of the

studies, it is proposed that the presence of i-SS results in a lower OER performance.52 On the

other hand, some studies suggested that such surface states mediate the OER. 54,55 In another

study, Shavorskiy et al.56 states that OER is not mediated through the surface states. Thus, the

role of surface states on OER performance is still debated in the PEC literature. Clear

knowledge about the role of surface states in OER is necessary for the performance

improvement of photoanodes.57 The impact of surface states on the photoanode performance

is investigated in this thesis.

2.2 Measurement of OER characteristics

Different types of measurements are used in the experimental characterization of PEC. Some

of the key measurements used in PEC characterization that are relevant to this thesis are

described in this section.

2.2.1 Photocurrent measurement

The magnitude of current density through the cell gives information about the solar to

hydrogen conversion efficiency, based on the assumption that 100% of the photocurrent is

used for water splitting.7 Therefore, the current density as a function of applied potential is

an important measurement for determining the performance characteristics of photoanodes.

Measurements are done either in the dark or under illumination. The main information

obtained from the current density measurement are a) the onset potential and b) the

magnitude of current density at a given potential. The lower the overpotential is, the better is

22 Measurement of OER characteristics

the performance of the photoanode as an OER catalyst. The magnitude of current density is

used to calculate the solar to hydrogen conversion efficiency.7 For example, the ‘applied bias

photon to current efficiency’ (ABPE) is one of the standard metrics used in the quantification

of photoanode performance. The photocurrent measured at 1.23 V vs the reversible hydrogen

electrode (RHE) is used in the calculation of ABPE.58 Depending on the type of measurement

technique the current density measurements can be classified into several techniques.

2.2.1.1 Linear sweep voltammetry

In linear sweep voltammetry (LSV), the current density is measured as a function of an applied

potential at a constant scan rate. The scan rate usually ranges between 1 mV/s to 50 mV/s but

sometimes even higher scan rates are used.7 The LSV can be measured in the dark or under

illumination. Figure 6a shows experimental LSV curves measured in the dark and under

different illumination intensities.59 The current densities under illumination start increasing at

potentials higher than 0.9 V which defines the onset potential.59 On further increase in applied

potential, the photocurrent exhibits a sharp increase and saturates around 1.5 V. The sharp

increase in current density after 1.6 V is related to the electrochemical water oxidation at high

potentials similar to the dark current.

2.2.1.2 Cyclic voltammetry

Cyclic voltammetry (CV) measurements are obtained by measuring the current density for

both forward scan and reverse scan of the applied potential. CV measurements give

information about oxidation processes occurring at the photoanode-electrolyte interface

during the forward scan, and reduction processes during the reverse scan.60 The reduction

peaks observed in the CV during the reverse scan are used in the analysis of surface states.50,61

Figure 6b shows an experimental CV from the literature measured in the dark for different

scan rates.52 The plot shows the variation in the reduction peaks for different scan rates. The

reduction peaks visible in the CV are interpreted as the reduction of surface trapped holes in

the reverse cycle in the literature.52,62

2.2.1.3 Chopped light measurements

In chopped light measurements (CLM), the current density is measured with the illumination

turned on and off at a fixed pulse rate, while the potential is swept at a constant scan rate.

Figure 6c shows an example of a CLM (grey line) from the literature.52 transients are observed

in the measured current when the light is turned on and off. The sudden spike in the current

upon illumination is due to the instantaneous formation of holes. The spike in the

photocurrent gradually settles to an equilibrium value due to the recombination of generated

holes with electrons.63 When the light is turned off, the hole current abruptly becomes zero

and the current in the circuit becomes negative as the electrons move towards the surface to

recombine with the remaining holes.63 The negative current also settles back to the

equilibrium value once all the surface holes recombine. The analysis of transients in CLM is


used to get information about the accumulation of holes at the surface, the trapping of

electrons and holes at the surface state, and the accumulation of electrons in the bulk.7

Figure 6 Typical experimental measurements and results for hematite photoelectrodes measured in 1M NaOH

electrolyte: a) Linear sweep voltammetry curves under different illumination intensities and in the dark (adapted

from ref.59 ); b) Cyclic voltammetry measured in the dark for different scan rates (50, 100, 250, and 500 mV s−1).

The black dots represent the maxima of the reduction peaks and the arrows represent the scan direction(adapted

from ref.62); c) Chopped light measurement (grey line), LSV measurement under 1 sun (red line) and current

density measured with a hole scavenger ([Fe(CN)6]3-/4-) added to the electrolyte (orange line). (adapted from

ref.52).

2.2.1.4 Hole scavenger measurements

Hole scavenger measurements (HSM) are carried out similar to photocurrent measurements

for water oxidation, the only difference is that a fast hole scavenger is added to the electrolyte.

Some of the widely used hole scavengers are H2O2 and [Fe(CN)6]3-/4-.50,52 The above-

mentioned measurements, such as LSV, CV, and CLM, can all be measured in the presence of

a hole scavenger. By adding a hole scavenger to the electrolyte the surface recombination

effect is suppressed and the hole current to the surface can be measured.52 Figure 6c shows

an example of an HSM (orange line) measured with the electrolyte containing [Fe(CN)6]3-/4-

redox couple.52 The current density due to water oxidation is shown using a red line for

b a

c


comparison.52 The hole collection efficiency of [Fe(CN)6]3-/4- redox couple is almost 100%.52

Hence, the difference between the current density measured with [Fe(CN)6]3-/4- redox couple

and the water oxidation current shows the lower hole collection efficiency during water

oxidation conditions.52

2.2.2 Electrochemical impedance spectroscopy

Electrochemical impedance spectroscopy (EIS) is used to measures the complex impedance of

the photoanode.64,65 For the measurement, an alternating voltage denoted by a complex

quantity 𝑉(𝑖𝜔) is applied to the photoanode, where 𝜔 is the frequency of perturbation and 𝑖

is the unit imaginary number. The complex current response of the system 𝑗(𝑖𝜔) for the input

𝑉(𝑖𝜔) is then measured. The ratio between the voltage response and current response gives

the complex impedance 𝑍(𝑖𝜔) as a function of frequency.65,66

𝑍(𝑖𝜔) =

𝑉(𝑖𝜔)

𝑗(𝑖𝜔)

(12)

The complex impedance 𝑍(𝑖𝜔) has generally real and imaginary parts.65 The measured

impedance can be plotted as a Nyquist plot or a Bode diagram.67 In the Nyquist plot, the

imaginary part of the impedance is plotted against the real part of the impedance as shown in

Figure 7a. The plot in Figure 7a represents the impedance measured for a given applied

potential over a chosen frequency range. The frequency increases towards the origin of the

plot. The Bode diagram of the same data is shown in Figure 7b. The blue curve represents the

magnitude of the impedance vs the log of the frequency and the red curve represents the

phase angle between the real and imaginary part vs. the same frequency axis. Information

about different processes occurring in the system can be obtained from the analysis of EIS.64

Figure 7 Electrochemical impedance measurement data: a) Nyquist representation and b) Bode diagram of

measured impedance data.

a b


2.2.2.1 Equivalent circuit analysis

EIS measurements are typically characterized by fitting the data to an equivalent circuit

model.55,68,69 Equivalent circuits are an approximate electrical representation of the

physicochemical processes occurring at the electrode.64 An example of an equivalent circuit

model used for representing the metal oxide semiconductors under illumination is shown in

Figure 8a. In an equivalent circuit model, the resistive components account for the bulk

resistance of the material or even chemical reactions at the electrode.65 The series resistance

(𝑅s) usually represents the back contact resistance and the solution resistance.70 The

capacitive components in the circuit are associated with the capacitance due to the space

charge polarization region, species adsorption at the surface etc.65 Fitting equivalent circuit

models to the EIS data over different applied potentials deliver values for the resistive and

capacitive components for corresponding applied potentials. An example of the data obtained

after the equivalent circuit fitting is shown in Figure 8b. The magnitude of the resistance and

capacitance and their variation as a function of applied potential is used for studying the

processes occurring during OER.55 For instance, Klahr et al.55 used the strong correlation

between the 𝐶trap peak and 𝑅ct,trap valley in Figure 8b around the OER onset to substantiate

that OER occur via surface trapped holes.

Figure 8 a) An example of an equivalent circuit model used in the analysis of EIS (adapted from ref.55); b) 𝐶𝑡𝑟𝑎𝑝

(orange triangles) and 𝑅𝑐𝑡,𝑡𝑟𝑎𝑝 (red circles) obtained from equivalent circuit fitting, a 𝐽 − 𝑉 curve (green solid

line) is overlayed over these values for correlating with onset potential (adapted from ref.55).

Even though equivalent circuit models are used widely in the analysis of EIS, there are some

limitations associated with it. One limitation is that the equivalent circuits used for EIS data

fitting are not unique; different equivalent circuits can be used for characterizing the same EIS

data delivering different values for the equivalent circuit elements.59 Additionally, there is no

direct relation between the electrical quantities and physical and chemical processes at the

semiconductor-electrolyte interface; especially the connection to elementary reaction steps,

and intermediate species is missing.

In this thesis, an alternative model to the equivalent circuit model is developed, which is called

(non-linear) state-space modeling.71 The state-space model uses the chemical equations

a b


combined with electrical equations to describe the system at hand. The state-space

representation is widely used in control theory as it provides a compact and convenient

method of describing and analyzing the system of interest.71 State-space modeling defines the

input-output relationship of the system in terms of the state variables of the system, by using

first-order differential equations. The state variables describe the system at any given

operating point. Since the state-space representation defines the input-output relation in

terms of the internal variables (state variables), it is advantageous for gaining a fundamental

understanding of the internal behavior of the system and the processes within the system.71

This is a major advantage of state-space modeling compared to equivalent circuit modeling

which defines the system in terms of resistive and capacitive elements.

It is important to note that an equivalent circuit with resistances and capacitances which vary

with input voltage is not necessarily the same as the non-linear description of the system such

as formulated in a non-linear state-space representation. This is explained and analyzed in

much more detail in systems and control theory.72 In this field, an equivalent circuit with

voltage-dependent resistances and capacitances is a form of a model known as a linear

parameter varying model. The equivalent circuit is linear but its parameters vary with voltage,

for which only under special conditions, it is an exact description of the non-linear (state-

space) system.72 Therefore, the equivalent circuit model is generally an approximate

representation of the (non-linear) system. The non-linear state-space model of the system is

a more accurate description of the system compared to equivalent circuit models. In this

thesis, a non-linear state-space model of the semiconductor electrolyte interface is developed

which defines the impedance in terms of the rate constants for the intermediate reactions.

2.2.2.2 Mott-Schottky analysis

In the case of n-type semiconductors, the space charge layer consists of the positively charged

dopant ions from which the free electrons originated.7 Additionally, the negatively charged

ions from the electrolyte get accumulated at the semiconductor-electrolyte interface.73 This

charge separation results in a capacitance associated with the space charge layer. The

differential capacitance of the space charge region can be extracted from the total impedance

of the system.7 In equivalent circuit models, the capacitance due to the space charge region is

denoted as 𝐶sc or 𝐶bulk. The Mott-Schottky equation relates the capacitance of the space

charge layer with the doping density of the semiconductor and the potential across the space

charge region (𝑈sc) given by7

(1

𝐶sc)2

= (2

𝜖r𝜖0𝑒𝑁D𝐴2) (𝑈sc −

𝑘B𝑇

𝑒)

(13)

where, 𝑁D is the doping density and the other parameters are as discussed earlier. The plot of

1 𝐶sc2⁄ vs applied potential is called a Mott-Schottky plot. From Eq. (13), the slope of the Mott-

Schottky plot is proportional to 1 𝑁D⁄ and the intercept of the plot at the potential axis will


give the flat band potential.55,74 The flat band potential is the potential that needs to be

applied to the semiconductor for the band bending at the interface to be canceled out.7 Thus

doping density and flat band potential of the photoanode can be calculated using Mott-

Schottky analysis. Additionally, Mott-Schottky analysis gives information about Fermi level

pinning and surface states.52,55 In the presence of surface states, the applied potential will not

completely fall across the space charge region as some of this potential is accommodated in

the filling of surface states (surface state charging).43,55 For the range of potential in which the

surface states are getting filled, the Fermi level remains pinned at the energy level of the

surface state. Hence, the band bending and 𝐶sc remain constant in this potential range. In

Figure 9, experimental Mott-Schottky plots for two cases are shown: 1) with surface states

(blue curve) and 2) without surface states (green curve).75 These Mott-Schottky plots

corresponds to the cases discussed in Figure 5a and Figure 5b, respectively. In Figure 9, the

plateau region (shaded region) in the blue curve is associated with Fermi level pinning due to

the surface states.52 This plateau region disappears after the surface states are selectively

removed as shown in the green curve.

Figure 9 Mott-Schottky plot of a sample with the surface state (blue) showing Fermi-level pinning (denoted by

the shaded region). The plot for the same sample after the passivation of surface states is shown in green. The

plateau region is absent in the latter case. Adapted from ref.75

2.3 Modeling of OER

Photoelectrochemical water splitting involves processes occurring over time scales ranging

from femtosecond to hours and length scales from angstrom to centimeters.18 These

processes take place within the semiconductor bulk and at the semiconductor-electrolyte

interface. Based on the process of interest, different methods are employed in the

computational study of OER spanning a range of length and time scales. A selection of the

computational modeling techniques employed in the study of photoanode interfaces, that are

relevant to this thesis, are discussed in this section.

28 Modeling of OER

2.3.1 Density functional theory

Density functional theory (DFT) is a first principle-based method used to perform ground state

electronic structure calculations of atoms, molecules, and solid-state materials.76 DFT is widely

used in the analysis of OER on semiconductor photoanodes.18,33,34,77–79 The analysis involves

the examination of OER mechanism, key intermediates, their bonding to the surface, the

energetics of the elementary steps etc.37 Using DFT, the binding energy of different OER

intermediates on the photoanode surface can be calculated. This is calculated based on the

difference between the ground state energies of the free surface and the surface with the

adsorbed species. The theoretical OER overpotential for any material of interest can be

calculated based on these DFT calculated energies of the elementary steps in OER.

Rossmeisl et al.38 have described a method for calculating the free energies of OER

intermediate steps on metal oxide surfaces using DFT simulations. In this method, the

reference potential is set to that of the standard hydrogen electrode. The free energy changes

are calculated at standard conditions defined by the electrode potential (𝑈)(), the electrolyte

pH, the pressure (p) , and the temperature (𝑇) with values U = 0 V, pH = 0, p = 1 bar, and T =

298 K.38 The method is based on the four-step mechanism of OER mentioned in 2.1.1. The

binding energy of each intermediate (𝑖) on the surface is calculated using DFT; 𝑖 stands for

OH, O, OOH, and O2.38 Figure 10 shows the example of geometries used for calculating the

binding energies of OER intermediates on hematite (100) surface.

Figure 10 Examples of the (100) hematite surface geometries used for DFT analysis of OER. The dashed green

circle shows the position of the site that is investigated using DFT. The geometries show vacant site (a) and

different intermediate species OH (b), O (c), and OOH (d) adsorbed at the selected site. Adapted from Ref.17

The free energies for the intermediate steps in OER are calculated for pH = 0 as

Δ𝐺1 = 𝐸(𝑂𝐻) − 𝐸(∗) − 𝐸H2O +

1

2𝐸H2 + (𝛥𝑍𝑃𝐸 − 𝑇𝛥𝑆)1

(14)

Δ𝐺2 = 𝐸(𝑂) − 𝐸(𝑂𝐻) +

1

2𝐸H2 + (𝛥𝑍𝑃𝐸 − 𝑇𝛥𝑆)2

(15)


Δ𝐺3 = 𝐸(𝑂𝑂𝐻) − 𝐸(𝑂) − 𝐸H2O +1

2𝐸H2 + (𝛥𝑍𝑃𝐸 − 𝑇𝛥𝑆)3 (16)

Δ𝐺4 = 𝐸(∗) − 𝐸(𝑂𝑂𝐻) + 𝐸O2 +1

2𝐸H2 + (𝛥𝑍𝑃𝐸 − 𝑇𝛥𝑆)4 (17)

where 𝐸(𝑖) represents the binding energy of each OER intermediate, 𝐸(∗) represents the

ground state energy of the vacant site, 𝐸x represent the binding energy of the gaseous species

with x = H2O, H2, O2, 𝛥𝑍𝑃𝐸 is the zero-point energy due to the reaction, and 𝛥𝑆 is the change

in entropy.32 For accommodating any change in pH, a correction term given by – 𝑘B 𝑇 ⋅

log10 pH has to be added to the free energies calculated at standard conditions (Eq. (14) - (17)),

where 𝑘B is the Boltzmann constant and 𝑇 is the temperature.38 Similarly for any applied bias

potential 𝑈 relative to the standard hydrogen electrode, a correction term – 𝑒𝑈 is added to

the free energies calculated using Eq. (14)-(17).38 The theoretical overpotential is calculated as

𝜂 (𝑉) =

max(Δ𝐺1, Δ𝐺2, Δ𝐺3, Δ𝐺4) 𝑒𝑉

𝑒− 1.23 𝑉

(18)

A plot of the calculated free energy steps gives a clear picture of the rate-determining step.

An example of the plot of free energies on the hematite (100) surface is shown in Figure 11a.17

Under zero applied voltage (U = 0 V, black curve), all free energy steps are uphill and, hence,

OER will not take place. For the OER to proceed under an applied potential, the free energies

of all the steps should be downhill. For an applied potential of 1.23 V, which is the theoretical

potential required for water oxidation, OER will not take place as two steps are still uphill (red

curve). At an applied potential of 2.02 V (𝜂OER = 0.79 V, blue curve), all steps are downhill and

thus all the intermediate reactions in OER will occur on the application of this potential. The

rate-determining step, in this case, is the O-OOH step as marked with the purple shading in

Figure 11a.

Ideally, the overpotential will be zero when Δ𝐺1 = Δ𝐺2 = Δ𝐺3 = Δ𝐺4= 1.23 eV. However,

based on several DFT studies on different materials, it is reported in the literature that there

exists usually a constant energy difference of approximately 3.2 eV between the free energies

of OH and OOH intermediate, i.e. Δ𝐺2 + Δ𝐺3 = 3.2 eV.31,80,81 Ideally, the sum of Δ𝐺2 and Δ𝐺3

should be 2 ⋅ 1.23 eV = 2.46 eV. Due to the non-ideal energetics, the approximate minimum

of overpotential attainable will be (3.2 eV-2.46 eV)/2e = 0.37 V.82 This is known as the so-

called scaling relation between OH and OOH and results in a constraint for the minimum

possible OER overpotential.31 For this minimum possible overpotential, the optimum scenario

will be when Δ𝐺2 = Δ𝐺3 = 3.2 eV/2. Therefore, one of these two energy steps are usually

used as a descriptor for the OER activity. A graphical representation of the variation in

overpotential for different metal oxides as a function of Δ𝐺2 (Δ𝐺2 = Δ𝐺O − Δ𝐺OH) result in a

volcano plot as shown in Figure 11b. The best OER catalysts are those at the top of the volcano.

30 Modeling of OER

The minimum achievable overpotential is also marked in the plot. Thus, based on DFT results,

circumventing the limitation put-forth by the scaling-relations is one way to decrease the OER

overpotential.37 Strategies, like selective stabilization of intermediates using some external

mechanism and three-dimensional catalytic sites, have been proposed in the literature to

circumvent the scaling relations.81

Figure 11 a) Free energies of the intermediates on hematite (100) surface at three different potentials (U = 0,

1.23, and 2.02 V). The region marked purple shows the intermediate step that determines the overpotential, i.e.

from O to OOH (adapted from ref.17); b) Volcano plot showing the activity trends for oxygen evolution reaction

(OER) on different metal oxide catalyst surfaces (black line). The negative value of theoretical overpotential is

plotted against 𝛥𝐺𝑂 − 𝛥𝐺𝑂𝐻. The overpotential corresponding to the peak of the volcano plot shows the

minimum achievable overpotential for OER (adapted from ref.82).

In general, DFT calculations give information about the thermodynamic activity and limitations

of OER on the surface of the catalyst of interest. There are some techniques proposed in the

literature for improving the catalytic activity of photoanodes. One of the strategies is to use a

suitable co-catalyst layer over the photoanode surface.18 Doping and alloying is another

proposed strategy for improving catalysis.81 DFT studies have been employed to find out

suitable co-catalysts, dopants, and alloying materials for improving the catalytic activity of

photoanodes.32,80,83 By identifying the best materials and from the knowledge of the most

active sites, DFT simulations can lead to the design of high-performance photoanodes. Other

than catalysis, DFT calculations are used for investigating the structural and optoelectronic

properties of semiconductors. In this thesis, the DFT simulations are used for calculating the

reaction free energies of OER intermediates on photoanode surfaces.

There are some limitations associated with DFT simulations which limit the comparison of

simulated data with experiments. DFT calculations are performed on perfect systems. Under

operational conditions, the experimental photoanodes will have vacancies, defects, etc. which

cannot be modeled exactly in DFT simulations. To some extend doping and vacancies can be

introduced in the model by selective removal or addition of atoms.84 However, the exact

b a


modeling of the experimental systems is challenging due to limitations in the development of

such geometries and computational cost. Additionally, DFT calculations assume vacuum at the

surface, as explicit modeling of solvent at the surface is computationally expensive. Implicit

solvation models are used in some cases to approximate the effect of solvents.85 Thus even

though DFT analysis provides critical information regarding the catalytic activity of

photoanode materials, a direct comparison with experiments is challenging due to the above

reasons. Additionally, DFT calculations deliver the energetics of the elementary steps in OER

which is inaccessible to measurements. The differences in the data obtained from DFT and

experimental measurements make direct comparison challenging. The comparability to

experimental measurements can be enabled by linking the energetic obtained from DFT

calculations with a microkinetic model.

2.3.2 Microkinetic modeling

Microkinetic modeling is a technique used for studying complex chemical reactions in terms

of the elementary steps and their interaction with each other.86 The term ‘microkinetic’ refers

to detailed elementary steps in the reaction.87 In the literature, microkinetic modeling is

widely used in the study of catalytic reactions.42,88,89 Microkinetic modeling starts with a

proposed mechanism of the reaction of interest. A representation of an elementary step in a

reaction is given as

∗ + 𝐴

𝐾b1⇌𝐾f1 𝐴∗

(19)

where A is a species, * represents an adsorption site, 𝐾f1 and 𝐾b1 represent the forward and

backward rate constants, respectively. The mechanism is used to write down the rate of

formation of the intermediate species at an active site. The rate equation for the adsorbed

species 𝐴∗ is written as

𝑑𝐴∗

𝑑𝑡= 𝐾f1[𝐴][∗] − 𝐾b1[𝐴

∗] (20)

The above representation shows the case for a single-step reaction. In complex reactions at

the catalyst surface, there can be several of such elementary reaction steps and, hence,

several rate equations. These rate equations form a set of differential equations. The set of

differential equations is then solved simultaneously with the given boundary conditions and

model parameters, for calculating the steady-state concentrations of each intermediate. The

rate constants (𝐾f and 𝐾b) for the intermediate reactions are critical parameters for simulating

quantitative data from the microkinetic model. The theoretical rate constants can be

estimated based on the atomistic data obtained from first-principle calculations, like DFT.42

The catalytic reactions considered for microkinetic modeling can be thermochemical or

electrochemical.90 In Eq. (20) the representative reaction does not involve any direct charge

32 Modeling of OER

transfer. Such a reaction is called a thermochemical reaction. In the microkinetic modeling of

thermochemical reaction, the rate constants depend on temperature, and, hence,

temperature is the only mandatory model parameter.90 Electrochemical reactions involve

charged species and the rate of reaction depends on the applied potential as well.90 Thus, in

microkinetic modeling of electrochemical reactions applied potential is included as a model

parameter. For this reason, microkinetic modeling of electrochemical reaction is more

complex compared to that of thermochemical reactions. This thesis deals with the

microkinetic modeling of OER at the photoanode surface which is an electrochemical reaction.

Microkinetic modeling is considered as an important tool for enabling direct theory-

experiment comparison in the case of electrochemical reactions.91 For extending the

observables at a catalytic site to that of the interface, a mean-field approximation is used in

which a uniform distribution of adsorbates and catalytic sites is assumed.87 Bieberle and

Gauckler92 employed a microkinetic modeling approach for identifying the limiting reactions

in solid oxide fuel cells. The microkinetic model was formulated in a state-space form and the

EIS of the system was simulated.92 The rate constants for different elementary steps were

estimated from the comparison of simulated EIS with experimental EIS.92 Nørskov et al.42

employed a microkinetic model to investigate the selectivity of metallic electrodes towards

different mechanisms in electrochemical oxygen reduction reaction (ORR). The theoretical

rate constants for the elementary steps were obtained based on the DFT calculations. The

current density due to the reaction was simulated based on the charge transferred during the

elementary steps. This simulated current density from the model was comparable to that of

experiments. The authors also identified the existence of a kinetic volcano using the model

similar to the thermodynamic volcano for ORR on Pt. The above mentioned microkinetic

models were developed for metallic electrodes.

In the case of OER, microkinetic modeling studies in the literature were so far also carried out

for metallic electrodes. Garćia-Osorio et al.93 have modeled the EIS for OER on metallic

electrodes based on the four-step OER mechanism. By comparing the simulated EIS with the

experimental EIS, the rate constants for the elementary steps in OER were estimated.

Shinagawa et al.94 used microkinetic studies on OER to point out the rate-limiting elementary

step by comparing the Tafel plot from simulation and experiments. A Tafel plot is obtained by

plotting the applied potential against the log of current density. The study also underlined the

importance of employing a microkinetic model which takes into account the coverage of

intermediate species for studying the electrocatalytic reactions. From these studies, in some

cases, the models were used to simulate data similar to experiments for understanding the

effect of certain parameters on the measurements. In other cases, a reverse approach was

used such that using optimization techniques, the theoretical models were tuned to match


with experiments.93 The resulting optimized parameters gave information about the rate

constants for the processes occurring in OER.

All these models were developed solely for metallic electrodes. In metallic electrodes, all the

applied voltage falls across the Helmholtz layer, changing the free energy of the reactions at

the surface and, hence, the rate constants of these reactions.42 For modeling the

electrochemical reactions at metallic electrodes, the rate constants for the electrochemical

steps can be calculated based on the transition state theory assuming that applied potential

reduces the free energy of the electrochemical steps involved.42

For semiconductor electrodes, the modeling has to be treated differently from that of the

metallic electrodes. In the case of semiconductors, most of the applied voltage falls across the

space charge region and the rest falls across the Helmholtz layer. Hence, the rate constants of

the reactions at the surface almost remain the same. However, the concentration of the

charge carriers taking part in the reaction changes due to the potential drop across the space

charge layer. For this reason, the rate constants for the charge transfer reactions cannot be

calculated similar to metals. Additionally, in semiconductors, charge transfer can occur via

conduction band and valence band. Thus, the existence of valence band and conduction band

and the potential drop over space charge region in the case of semiconductors makes the

modeling more complex compared to metallic electrodes. Thus, a new approach is needed for

microkinetic modeling of OER on semiconductor electrodes. In this thesis, a microkinetic

model of OER specifically for the semiconductor-electrolyte interface is developed.

2.3.3 Modeling of charge carrier dynamics

The charge carrier dynamics within the semiconductor has already been discussed in section

2.1.2. Modeling of charge carrier dynamics involves the calculation of the concentration of

charge carriers at the semiconductor surface based on the different processes within the

semiconductor and at the SEI. The schematic of charge carrier dynamics within an n-type

semiconductor is shown in Figure 12 again to explain the calculation. The figure shows the

generation, recombination, surface state trapping of the charge carriers, and charge transfer

towards OER along with the characteristic parameters. By modeling these processes, the hole

density (𝑝vb), electron density (𝑛s), and the fill factor of electrons (𝑓T) trapped in the surface

states can be calculated.

Based on Figure 12, the hole density and the fill factor of trap states can be calculated as68,95,96

𝑑𝑝vb𝑑𝑡

= 𝐽G𝑑− 𝑘rec𝑛s𝑝vb − 𝑘p𝑝vb𝑁T𝑓T − 𝑘V𝑝vb𝐶red

(21)

𝑁T𝑑𝑓T𝑑𝑡 = 𝑘n𝑛s𝑁T(1 − 𝑓T) − 𝑘p𝑝vb𝑁T𝑓T + 𝑘T𝑁T𝑓T𝐶ox

(22)

34 Modeling of OER

where 𝐽G represents the hole flux under illumination (Eq. (10)). The term 𝑑 is used to convert

surface density of holes (per cm2) to volume density (per cm3).63 𝑘rec represents the rate of

direct recombination between holes and electrons in the space charge region,97 𝑛s represents

the concentration of electrons in the conduction band, and 𝑘p represents the rate at which

holes get trapped in the trap states. 𝑁T is the trap state density and 𝑓T represents the fill factor

of the trap states. 𝑘V represents the rate of OER occuring via the valence band, 𝑘T represents

the rate of OER occuring via the surface state, 𝐶red and 𝐶ox represent the concentration of

reduced and oxidized species at the surface, respectively.

Figure 12 Schematic of charge carrier dynamics under illumination showing generation of electrons (red circles)

and holes (blue circles), direct recombination of electrons and holes within the space charge region, trapping of

charge carriers at trap states, and oxygen evolution reaction via valence band and trap states.

For n-type materials, electrons are the majority carriers and the electron concentration in the

conduction band under illumination can be approximated as an exponential function of

potential across the space charge region according to 44,98

𝑛s = 𝑛s0𝑒𝑥𝑝 (−

𝑒𝑈sc𝑘B𝑇

) (23)

where 𝑛s0 represents the concentration of surface electrons in the dark under zero bias. By

solving the Eq. (21)-(23), the charge carrier concentrations 𝑛s, 𝑝vb, and 𝑓T are calculated.

Information regarding how the charge carrier concentration gets affected by operating

conditions and semiconductor properties can be obtained using such models.

In the literature, charge carrier dynamics were part of several simulations where theory and

experiments were compared.99–103 For example, Iqbal et al.100 have simulated the effect of

different rate constants of processes within the semiconductor on PEC data, like trap state

capacitance, space charge layer capacitance, and Helmholtz capacitance. These simulations

were done with TiO2 as the photoanode material.100 Bertoluzzi et al.99 investigated the impact

of the recombination rates and trapping rates on the cyclic voltammetry curves. The relation

between the peaks found in the CV and trap states was elucidated using a computational

model. These modeling studies, though implemented the charge carrier dynamics, usually


simplified the water oxidation reaction as a single step reaction and did not account for the

intermediate steps in OER. However, to study the rate-limiting processes at the

semiconductor-electrolyte interface, the interplay between all intermediate steps in OER and

the charge carrier dynamics within the semiconductor is important to be modeled and

investigated, which is part of this thesis.

2.3.4 Multiscale modeling of semiconductor-electrolyte interface

The processes occurring at the semiconductor-electrolyte interface range over several time

and length scales as mentioned ealier. Typically, a computational technique focuses on the

system behavior at one particular time scale or length scale.18 For example, DFT calculations

focus on atomic-scale calculations. A classification of the scales based on the length and time

scale is shown in Figure 13. Examples of methods used at the molecular scale (Molecular

Dynamics), the coarse-grained scale (kinetic Monte Carlo), and the continuum scale

(microkinetic modeling) are shown in the figure.18

Figure 13 A schematic showing different scales of modeling based on the length and time scales with an

example of the methods used in each scale. (Modified from ref.18)

Continuum scale model approximates the system to be continuous rather than having discrete

components. For instance, in the case of semiconductor-electrolyte interface, DFT calculation

use surface with discrete atoms whereas the microkinetic model defines the interface as a

continuous system using a set of differential equations. Continuum scale models enable

comparison of simulations with experimental data. In the literature, continuum scale

modeling at the device level has been used for developing strategies to optimize the design of

PEC cells.104,105 Haussener et al.104 have employed a device level continuum model that

couples charge transfer, species transfer, fluid flow, and electrochemical reactions to

formulate design guidelines for PEC water splitting systems. Device-level continuum models

36 Modeling of OER

are developed by accurate coupling of several component level continuum models defining

different aspects of the PEC cell.106 This thesis focuses on the continuum scale modeling

(microkinetic model) of the semiconductor-electrolyte interface.

The overall behavior of the semiconductor-electrolyte interface is influenced by processes

occurring over several length/time scales. Therefore, two or more computational techniques

spanning different time/length scales are coupled together to study the overall behavior of

the interface.85 Such a modeling approach that combines two or more computational tools of

different time/length scales is called multiscale modeling.18

The length and time scale of the multiscale model depends on the constituent single scale

methods. Multiscale models can even go up to predicting macroscopic behavior of the system

from microscopic scale calculations.87 Zhang and Bieberle18 have suggested a multiscale

modeling approach that combines all the four scales for understanding the limiting processes

at PEC interfaces.18 In the suggested approach, the output data from the smaller time/length

scales are inputs to the next scale and goes on to the continuum level.18 The comparability of

the results with the experiments is then used to identify the limiting processes and validate

the model.18

Multiscale modeling approach which combines two scales has been widely used in the study

of electrochemical interfaces. De Morais et al.107 developed a multiscale theoretical

methodology for calculating electrochemical observables by combining DFT and elementary

kinetic model in the case of ORR on Pt electrodes. Simulated current density due to the

reactions was used to investigate different proposed mechanisms of ORR. Nørskov et al.42

have studied the selectivity of oxygen reduction pathways on Pt electrodes by combining DFT

and microkinetic modeling.42 In this thesis, a multiscale approach combining DFT (atomistic

scale) and microkinetic modeling (continuum scale) of OER specifically for the semiconductor-

electrolyte interface is discussed. The model is used to simulate electrochemical data similar

to experiments.

3 Research approach and goal of the thesis

A thorough understanding of all the factors influencing the OER is necessary to increase its

efficiency and ultimately the efficiency of solar water splitting. Experimental studies on

photoanodes have investigated the correlation between performance metrics and tunable

parameters, like film thickness, doping density, surface structure, annealing temperature, etc.

These experimental studies have delivered valuable information towards the improvement of

photoanode performance. However, further efforts are needed to elucidate the performance

limiting factors/processes at the photoanode-electrolyte interface for achieving the

efficiencies required for commercialization. Theory-experiment comparison is proposed to be

Research approach and goal of the thesis 37

pivotal in this regard.91 Therefore, the aim of this dissertation is to develop an approach that

simulates the semiconductor-electrolyte interface under realistic conditions to compare

simulated data with experiments. This will allow for understanding the factors that influence

the efficiency of OER at semiconductor-electrolyte and eventually the performance limiting

factors at the interface.

Theory-experiment comparison in the case of OER requires a model of the photoanode-

electrolyte interface that captures the physicochemical processes involved in OER. As

mentioned earlier, the efficiency of OER on the photoanode surface depends on the

energetics and kinetics of the elementary steps in OER. The combined effect of energetics and

kinetics of OER have been modeled in the case of metallic electrodes, using microkinetic

models.93,94 However, these models use transition state theory for the calculation of rate

constants for the elementary steps which cannot be used in the case of semiconductor

electrodes.63 Additionally, the charge carrier dynamics within the semiconductor will also

affect the elementary steps in OER and vice versa. Therefore, to enable theory-experiment

comparison in the case of semiconductor photoanodes, a new approach is necessary which

couples the energetics and kinetics of the elementary steps in OER with the charge carrier

dynamics within the semiconductor.

For this, a new computational approach is developed that brings together density functional

theory (DFT), microkinetic modeling, and modeling of charge carrier dynamics within the

photoanode. The approach enables the bridging of the processes within the semiconductor

and elementary steps in OER to experimental data. Such a model along with experimental

data will facilitate the deconvolution of processes occurring at the SEI during OER. The

knowledge obtained from such comparisons will be crucial in the identification of

performance limiting factors at the SEI and its mitigation for performance improvement. The

approach is generic and can be applied to different photoanode materials. In this thesis,

hematite is used as the model material. A step by step approach is adopted in the

development of such a model.

3.1 Research approach

This thesis aims to develop an approach that simulates the semiconductor-electrolyte

interface (SEI) under realistic conditions and to compare simulated data with experiments.

Therefore, the following research steps are taken in this thesis.

1. Calculate the energetics of OER intermediates on the model photoanode

material using DFT. Investigate the relation between the energetics of the

multiple steps in OER calculated using DFT and the experimental OER

overpotential.

38 Outline of chapters in part B

2. Develop a microkinetic model of OER on semiconductor electrodes based on

the mechanism of OER and energetics calculated with DFT, to simulate

electrochemical data similar to experiments. Compare the simulated data with

experimental data.

3. Add the effect of illumination on the approach developed in step 2, by

combining charge carrier dynamics within the semiconductor along with the

microkinetic model of OER. Simulate electrochemical data from the model

using different input conditions to investigate the impact of parameters, such

as surface state density, rate constants of the elementary steps in OER, and

series resistance, on the photoanode performance.

The above approach resulted in four manuscripts; one each from step 1, and step 2, and two

from step 3. These manuscripts are discussed as four chapters in Part B of the thesis. The

contents of these chapters are summarized in the following section.

3.2 Outline of chapters in part B

Chapter 1. Why does NiOOH co-catalyst increase the oxygen evolution activity of α- Fe2O3?

Modified from the publication: Kiran George, Xueqing Zhang, and Anja Bieberle-Hütter J.

Chem. Phys. 150, 041729 (2019).

In Chapter 1, the energetics of the intermediate steps in OER on hematite coated with NiOOH

co-catalyst are calculated using DFT. Experimental studies in the literature have shown that

NiOOH co-catalyst improves the OER performance of hematite (Fe2O3). The reason behind this

increase in performance is investigated based on the energetics of OER on the NiOOH/ Fe2O3

heterostructure calculated using DFT.

Different geometries of NiOOH/Fe2O3 heterostructure with NiOOH as a cluster and as a

continuous strip on the hematite surface are investigated. The cluster geometry is found to

undergo several reconstructions during the calculation and cannot explain the reason for the

OER activity of the heterostructure. The geometry with NiOOH as a continuous strip on the

hematite surface is found to be stable and suitable for investigating the OER activity of the

heterostructure. The unit cell of the geometry of NiOOH as a continuous strip on Fe2O3 is

shown in Figure 14a. The possible adsorption sites on the heterostructure are marked in Figure

14b. The Gibbs free energies of formation of different OER intermediates are investigated at

these sites using DFT calculations as described in section 2.3.1. The most active sites on the

geometry are identified based on the overpotentials (𝜂) calculated using these Gibbs free

energies.


Figure 14 a) Unit cell of Fe2O3 (110)surface with NiOOH as a continuous strip; b) Top view of the unit cell showing

the Ni edge sites A, B, C, the OH edge sites D, E, F, and the bridge sites (1-9) on the wider strip geometry; c) Free

energies of OER intermediates at sites A, B and, C for the wider strip geometry. The potential determining step

for each site is highlighted; d) Volcano plot of the overpotentials of all sites on the wider strip geometry. The

black marker in the plot indicates the overpotential of bare hematite (110). All the three edge sites (blue markers)

show lower overpotential and the bridge sites 1-9 (red markers) show higher overpotential compared to the

hematite (110) surface.

The free energies of formation of OER intermediates at sites A, B and, C are plotted in Figure

14c. The OER overpotentials of these sites on NiOOH/Fe2O3 heterostructure range between 𝜂

= 0.39 V and 0.58 V compared to the theoretical overpotential of 𝜂 = 0.78 V for bare hematite.

This correspond to a cathodic shift in overpotential by 0.39 V and 0.2 V, respectively.84 The

results are in agreement with experimental findings in the literature which show a reduction

in overpotential by 0.15 V - 0.2 V for hematite photoanode with NiOOH/NiOx co-catalyst.108,109

The OER activities of all 9 OH-sites (marked 1 - 9 in Figure 14b) are calculated and the

overpotentials at all these 9 sites are found to be higher than that of bare hematite. The

overpotentials for these sites together with the overpotentials for the edge sites are plotted

in Figure 14d as a volcano plot. The volcano plot is generated by plotting the negative value of

overpotential vs ΔGOH - ΔGO as discussed in section 2.3.1. The higher the point is in the volcano

plot, the higher is the activity. From the volcano plot, the improved activity of the

a b

c d


NiOOH/Fe2O3 heterostructure arises from the Ni edge sites (A, B, and C) on the NiOOH co-

catalyst rather than from the sites on the co-catalyst basal plane.

The DFT calculations with the continuous strip geometries successfully identify the reason

behind the activity of the NiOOH/Fe2O3 heterostructure. The improved activity of the NiOOH‐

Fe2O3 system arises from the Ni edge sites on the NiOOH co-catalyst layer. It is observed that

the bridge sites which are located on the NiOOH basal plane, show high overpotential, i.e. low

electrochemical activity. This indicates that there is no direct correlation between the OER

performance and the area of the NiOOH layer. This is in agreement with the experimental

study by Malara et al.108 in which a lower performance was observed when surface coverage

of the NiOx layer on Fe2O3 is higher. However, the correlation between the activity and Ni

edges sites were not identified from the experiments.

Based on the DFT results, a regime is proposed for the deposition of NiOOH co-catalyst on

hematite; the co-catalyst should be deposited such that it forms nano-islands over the

hematite surface rather than forming a continuous coating on the surface. The geometry of

these nano-islands should be such that they have a high ratio of edge length (Ni-Fe edge sites)

to its area (basal plane sites). The identification of the most active sites based on energetics

enables the design of high-performance catalysts.

Chapter 2. Impedance spectra and surface coverages simulated directly from the

electrochemical reaction mechanism: a nonlinear state-space approach

Modified from the publication: Kiran George, Matthijs van Berkel, Xueqing Zhang, Rochan

Sinha & Anja Bieberle-Hütter, J. Phys. Chem. C 123, 9981–9992 (2019).

In this chapter, a microkinetic model of OER on the semiconductor-electrolyte interface is

developed which can simulate current density as a function of applied potential, similar to the

experiments. The theoretical rate constants for the microkinetic model are calculated using

energetics of the elementary steps calculated using DFT and the Gerischer theory for

semiconductors. Thus, microkinetic modeling brings together kinetics and energetics of the

elementary steps in OER specific to semiconductors. The charge carrier density at the

semiconductor surface is defined as an exponential function of applied potential. The rate

equations for the formation of OER intermediates are formulated and the resulting set of

differential equations is formulated as a non-linear state-space model. A schematic

representation of the implementation of the model is shown in Figure 15a. The formulation

of the model as a nonlinear state-space model significantly simplifies the simulation and

analysis due to the availability of standard toolboxes.


Figure 15 (a) Representation of the state-space model of an electrochemical system. The input variable is the

applied voltage, the output variable is the current density, and the state variables are the concentration of

intermediate species from mass balance equation; (b) Nyquist plots of impedance spectra from the simulation

at potentials 1.5 V, 1.6 V and 1.7 V compared against experimental EIS at same potentials; (c) Bode diagrams of

the same data as in b) showing the variation of the magnitude of impedance and phase angle against the

frequency of perturbation between 0.1 Hz and 30 kHz.

Hematite is used as the photoanode material for the simulations. The model can simulate

electrochemical data, such as 𝑗 − 𝑉 plots and EIS. Additionally, the surface coverage of OER

intermediates can be calculated as a function of applied potential. The formulation of the

model in a state-space form makes it convenient to simulate EIS directly from the

electrochemical equations. The EIS simulated for hematite under dark condition is compared

with in-house experimental EIS for hematite. Figure 15b shows the side-by-side comparison

of the Nyquist plots of the simulated EIS and experimental EIS. The model calculates the

impedance arcs and features similar to the experiments. To get a clear comparison of the

Experiment Simulation

Experiment Simulation

a

b

c


frequency response, the Bode diagram of the same data is shown in Figure 15c. From the Bode

diagram, the magnitudes of impedance (blue curves) and its variation over different potentials

and frequency are captured well by the model. Likewise, the frequencies corresponding to the

position of the phase peaks (red curves) from the simulated plots are in good agreement with

the corresponding experimental curves. The minor differences observed between the

experimental and simulated data are believed to be related to the electrochemical

heterogeneity of the experimental hematite surface as compared to the ideal surface assumed

in the model.

Thus, for the first time, an approach is developed specifically for semiconductor electrodes,

that can calculate electrochemical data similar to experiments directly from the mechanism

of OER. One of the advantages of this approach is that the electrochemical data can be

simulated without using equivalent circuits. This aids in relating features and trends in the

electrochemical data directly to underlying electrochemistry. The model can also simulate the

coverage of OER intermediates at the surface sites at different operating potentials which is

extremely challenging to obtain experimentally. Recently there have been experimental

efforts in the identification of OER intermediates.40,110 The simulated surface coverage plot

can be used as a reference in future experimental studies in this direction. The model is

generic and it can be applied to different materials by using corresponding DFT data and model

parameters.

Chapter 3. Understanding the impact of different types of surface states on

photoelectrochemical water oxidation: A microkinetic modeling approach

Kiran George, Tigran Khachatrjan, Matthijs van Berkel, Vivek Sinha, and Anja Bieberle-Hutter.

Submitted

In this chapter, illumination is added to the model developed in Chapter 2. This is done by

coupling charge carrier dynamics under illumination along with the microkinetic model of

OER. A schematic representation of the model implementation is shown in Figure 16a. Along

with the generation and recombination, the trapping of charge carriers in recombining surface

states (r-SS) is included in the model. r-SS is defined in the model as monoenergetic states

with surface state density 𝑁T and energy level 𝐸T. The surface states due to OER intermediates

(i-SS) are part of the model, as it takes the elementary step in OER into account. The impact

of these surface states on the performance of photoanodes is a debated topic in the field of

PEC. Therefore, in this chapter, the impact of different types of surface states on PEC data is

systematically investigated with the model. The model can directly simulate PEC data like 𝑗 −

𝑉 plots, hole flux, current density under chopped light, and electrochemical impedance data,

based on the electrochemical reactions and the processes within the semiconductor. The

impact of r-SS and i-SS on the PEC data is investigated using the simulated plots.


From the simulation, r-SS leads to a capacitance (𝐶r−SS) before the onset potential and i-SS

leads to a capacitance (𝐶i−SS) around the onset potential. A schematic plot of surface state

capacitances indicating the location and magnitude of both the capacitances with respect to

the 𝑗 − 𝑉 plot is shown in Figure 16b. The magnitude of the peak of 𝐶r−SS is an order of

magnitude lower than that of 𝐶i−SS. The features in the PEC data arising from r-SS and i-SS are

analyzed by varying the model parameters related to r-SS and i-SS.

Figure 16 a) Extended microkinetic modeling approach with charge carrier dynamics; illumination intensity (𝐼0)

and applied potential (𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑) are the input and current density (𝑗) is the output; b) a schematic plot of surface

state capacitances (𝐶𝑟−𝑆𝑆 and 𝐶𝑖−𝑆𝑆 ) and current density as a function of applied potential showing the relative

magnitude and position of the capacitance peaks; c) 𝐶𝑟−𝑆𝑆 and 𝑗 − 𝑉 plots for two different surface state

densities; the dotted line represents the case with higher surface state density; d) 𝐶𝑖−𝑆𝑆 and 𝑗 − 𝑉 plots for two

different backward rates for the OER intermediate reactions; the dotted line represents the case with higher rate

constants for the backward reactions.

a

b

c d


The impact of r-SS on PEC data is analyzed by varying the surface state density of r-SS (𝑁T).

Figure 16c shows 𝐶r−SS and current density as function of applied potential for two different

𝑁T. The bold line represents the initial case and the dotted line represents the case after an

increase in 𝑁T. A bell-shaped curve is found for 𝐶r−SS. The bell-shape becomes wider, the

maximum of 𝐶r−SS increases, and the potential corresponding to the peak increases with an

increase in 𝑁T. Increase in 𝑁T leads to higher onset potential and lower saturation current

density in the 𝑗 − 𝑉 plots. From the simulated Mott-Schottky plots, r-SS leads to a Fermi level

pinning (FLP) before the onset potential, and FLP increases with 𝑁T. Therefore, r-SS reduces

the potential available across the space charge region.

As i-SS is related to the intermediate steps in OER, the impact of i-SS on PEC data is

investigated by varying the rate constant of the intermediate reactions. Figure 16d shows a

combined plot of the surface state capacitance and the current densities for the two different

backward rate constants for the intermediate reactions. The bold line represents the initial

case and the dotted line represents the case with an increased backward rate constant. The

magnitude of the peak of 𝐶i−SS decreases and the peak position shifts to a higher potential

with an increase in the backward rate constant (dotted line). The comparison of the

photocurrent densities shows that the onset potential increases with an increase in the

backward rate constant. A higher backward reaction rate is unfavorable for OER and leads to

a lower catalytic performance of OER on the photoanode surface. Thus, based on these

results, a decrease in 𝐶i−SS can be an indication of a decrease in the catalytic performance of

the photoanode surface. Only the onset potential is affected in this regard and the saturation

current density is unaffected by the change in 𝐶i−SS. In contrast to r-SS, the presence of i-SS

does not result in FLP and, hence, does not affect the potential across the space charge region.

In summary, a model of the SEI is developed which takes into account the energetics and the

kinetics of OER as well as the semiconductor properties. The model can simulate typical

experimental PEC data, such as 𝑗 − 𝑉 plots, current density under chopped light, hole flux,

and different contributions in the EIS. The comparability of simulated data with experiments

aids in relating features and trends in PEC measurements to the underlying theory and the

electrochemical quantities. By systematically varying the model parameters, the impact of

each parameter on the PEC data can be analyzed. This is a significant advantage of the

modeling compared to experiments, where it is challenging to vary a parameter without

affecting other parameters. Additionally, the parameters that are challenging to vary in

experiments can be varied easily in the simulations to understand their impact on OER. The

results discussed here are from the simulation using hematite as the model material.

However, the model is generic and can be used for simulating different photoanode materials.


Chapter 4. The critical role of the series resistance in impedance measurements of

photoelectrodes

Manuscript in preparation.

When analyzing PEC measurements with equivalent circuit models, one of the elements is a

resistance that is in series to all other equivalent circuit elements. The series resistance is

present in an electrode due to the back-contact resistance and the resistance of the

electrolyte. The series resistance of the photoanode is reported to increase with certain

electrode treatments, like annealing aimed at performance improvement.111,112 When

analyzing experimental impedance data, this series resistance is usually subtracted from the

total impedance data and is assumed to have no significant impact on the PEC data. However,

in reality, the potential drop over the series resistance increases with an increase in current

density due to OER occurring at the photoanode. This can be visualized in a schematic sketch

as a feedback loop as shown in Figure 17a. The figure shows the relation between potential

across the semiconductor layer and current density in terms of the series resistance.

As discussed in Chapter 3, the model can simulate impedance components like surface state

capacitance and capacitance due to the space charge layer, directly based on the processes

involved. Additionally, the model can calculate the charge transfer resistance. By

systematically varying 𝑅s in the simulation, the impact of 𝑅s on the 𝑗 − 𝑉 curves, and the

impedance components namely surface state capacitance, the capacitance of the space

charge layer, and the charge transfer resistance is investigated. The impact of 𝑅s on the EIS is

calculated based on the impact of 𝑅s on the individual impedance components calculated

using the model.

Figure 17b shows 𝑗 − 𝑉 plots simulated for different values of series resistance keeping all

other parameters the same. The onset potential of photocurrent is found to be independent

of the series resistance as the potential drop over 𝑅s depends on the product of current

density and 𝑅s and there is no significant current in the circuit before the onset potential.

After the onset, the current density ramps up rapidly and reaches a saturation current density.

Therefore, the slope of the 𝑗 − 𝑉 ramp decreases with an increase in series resistance. The

saturation current density is also lower with higher 𝑅s.

The impact of 𝑅s on the capacitance of the space charge layer is shown with simulated Mott-

Schottky plots in Figure 17c. A flattening is observed in the Mott-Schottky plot between 0.6 V

and 0.8 V. This flattening is due to the Fermi level pinning over r-SS as discussed in Chapter 3.

There is a second flattening observed after the onset potential. This flattening can be

explained as follows. Since the current density in the cell increases directly after the onset

potential, the potential drop across the series resistance drastically increases after the onset

potential and concomitantly 𝑈sc decreases. For this reason, a plateau region similar to Fermi


level pinning is visible in the Mott-Schottky plot after the onset potential. The potential range

of the flattening coincides with the potential range of the ramp in the 𝑗 − 𝑉 plot. This pinning

like behavior is much pronounced when 𝑅s is higher as the potential drop increases with an

increase in 𝑅s.

Figure 17 a) Schematic representation of the implementation of series resistance in the model; b) 𝑗 − 𝑉 curves

and c) Mott-Schottky plots for multiple resistance values; d) Electrochemical impedance spectra calculated for

an applied potential of V = 1.1 V using the simulated values of capacitance and resistance. The plot shows that

the polarization resistance increases with an increase in 𝑅𝑠. The frequency corresponding to the peak of the low-

frequency arc (marked in the figure) decreases with an increase in 𝑅𝑠; e) Simulated 1/(𝐶𝑠𝑐)2 plotted against 𝑉 (

solid line) and 𝑉 − 𝑗 ⋅ 𝑅𝑠 (dotted line) for 𝑅𝑠 = 100 Ωcm2. The dotted line shows only one flattening which is the

Fermi level pinning due to trap states.

b

a

c

d

𝑉onset

e


In the case of EIS, the increase in series resistance is generally identified as a linear shift of the

Nyquist plot along the positive x-axis. Simulated EIS for different series resistances are shown

in Figure 17d. It is found that the total impedance of the functional layer, i.e. the polarization

resistance, increases with an increase in series resistance. The frequencies corresponding to

the maxima in the low-frequency semicircles (local minima of imag[Z]) are marked in Figure

17d. The peak frequency for the low-frequency arc is observed to decreases with an increase

in 𝑅s. Thus, the impact of series resistance on EIS is more than a linear shift of the Nyquist

plot.

The study shows that 𝑅s has a significant impact on the EIS and 𝑗 − 𝑉 curves. Therefore, it is

necessary to correct current density and impedance data for the potential drop over 𝑅s in

order to avoid underestimation of the OER performance of the semiconductor material. The

𝑗 − 𝑉 data and data obtained from the analysis of EIS can be corrected for 𝑅s by plotting

against 𝑉applied − 𝑗. 𝑅s instead of 𝑉applied. An example of this correction applied to the Mott-

Schottky plot is shown in Figure 17e. The figure shows the Mott-Schottky plot for 𝑅s = 100 Ω

cm2 without correction (bold line) and with correction (dotted-line). The flattening of the

Mott-Schottky plot is visible at two locations in the case of the uncorrected Mott-Schottky

plot. As discussed earlier, the first flattening is related to the Fermi level pinning due to r-SS,

and the second flattening which is observed after the onset potential is due to the potential

drop over 𝑅s . This second flattening is not visible when the 𝑗. 𝑅s correction is applied to the

voltage axis (dotted line). The corrected plot shows only the Fermi level pinning due to the

surface states, omitting the potential drop across 𝑅s. Hence, the correction enables accurate

identification of surface state phenomena from the Mott-Schottky plot.

The impact of 𝑅s on 𝑗 − 𝑉 data is corrected in very few experimental studies in the literature.

However, the data obtained from the analysis of EIS, like the Mott-Schottky plot, surface state

capacitance, etc. are usually not corrected for in the literature. Therefore, we emphasize in

our work that it is necessary to perform correction on both 𝑗 − 𝑉 data and EIS data to draw

accurate conclusions about the functional layer. The results from the study show that to

correct for 𝑅s in the measurements, subtracting 𝑅s from the total impedance is not sufficient

as the potential drop over 𝑅s increases with an increase in current density. We show that the

current density and the data obtained from the analysis of EIS can be corrected for 𝑅s by

plotted against 𝑉applied − 𝑗. 𝑅s instead of 𝑉applied. The importance of this correction is higher

in the case of measurements with a high-performing electrode as the current density in the

cell will be higher in the case of high-performing electrodes. Additionally, the 𝑅s of the

photoanode is not always reported in the literature. The results show that it is important to

quantify and report 𝑅s along with the PEC measurements.

General conclusions 49

4 General conclusions

This thesis aims to develop an approach that simulates the semiconductor-electrolyte

interface (SEI) under realistic conditions and to compare simulated data with experiments.

Based on theory, the OER occurring at the SEI involves multiple intermediate steps which are

challenging to investigate experimentally. Hence, for enabling theory-experiment comparison

of the SEI, an approach is developed that can simulate measurable quantities directly from

the intermediate steps in OER. For this, a systematic multiscale approach is used in this thesis

that combines density functional theory (DFT) calculations and microkinetic modeling of OER

on semiconductor electrodes. Additionally, the processes within the semiconductor also

influence the reactions at the semiconductor surface and vice versa. Hence, the charge carrier

dynamics within the semiconductor is modeled together with the microkinetic model of OER.

Thus, for the first time, an approach is developed which combines DFT, microkinetic model of

OER on the semiconductor surface, and charge carrier dynamics within the semiconductor.

The sensitivity of the electrochemical data to semiconductor properties and rate constants

are probed by selective variation of the model parameters. The theory-experiment

comparability of the adopted computational approach is made use of in each chapter. A

summary of the main conclusions associated with the research approach in 3.1 is given below.

Relating the energetics of the OER intermediates on a photoanode surface using DFT and

the experimental photoanode performance:

- A stable geometry of the co-catalyst layer on the catalyst surface is necessary to

identify the active sites on the heterostructure using DFT calculations. The co-catalyst

layer modeled as a continuous strip on the photoanode surface delivers a stable

geometry.

- The overpotential calculated using DFT does not compare well with experimental

overpotential as DFT deals with perfect geometries and experimental systems are

imperfect due to defects, vacancies, dopants, etc. However, the relative improvement

in the overpotential of the catalyst material upon the addition of the co-catalyst layer

can be quantified using DFT and can be compared to the relative improvement

observed in experimental overpotential.

- The structure of the co-catalyst layer on the photoanode surface can be optimized for

high performance based on the energetics of the intermediate reactions in OER

calculated using DFT.

- In Chapter 1, it is identified that the Ni-Fe edge sites formed due to the addition of

NiOOH on Fe2O3 lead to the improved performance of the heterostructure.

Additionally, the sites on the NiOOH layer are found to be inactive towards OER. Based


on these results it is concluded that NiOOH coated as nano-islands will result in higher

performance compared to a uniform layer of NiOOH on hematite.

Developing a microkinetic model of OER specific to semiconductor electrodes:

- To develop a microkinetic model of OER specific to semiconductor electrodes, the rate

constants have to be defined based on the Gerischer theory of semiconductors.

- The numerical values of the theoretical rate constants specific to the semiconductor

material are based on the energetics of the intermediate steps obtained from DFT

calculations.

- Formulating the rate equations in a state-space form aids in simulating the EIS directly

from the elementary reactions at the SEI. For the first time, EIS is calculated directly

based on the rate constants of intermediates steps in OER.

- This method paves the way for identifying the rate-limiting processes in OER by

comparison of simulated data with experiments.

- Another important data available from the microkinetic model is the surface coverage

of OER intermediates as a function of applied potential. Such surface coverage data is

challenging to obtain in experiments. Simulated surface coverage data can be used as

a reference for experimental investigation of OER intermediates.

- Thus, the developed microkinetic model is an important tool in studying the catalysis

of OER on the photoanode surface.

Combining charge carrier dynamics within the semiconductor and microkinetic model of

OER:

- The effect of elementary steps in OER on the charge carrier density at the surface and

vice versa is captured by the model, which enables simulation of PEC data under

illumination.

- The charge carrier dynamics together with intermediate steps in OER enables to

investigate the impact of recombining surface states (r-SS) and surface states due to

OER intermediates (i-SS) on the photocurrent and potential distribution within the

semiconductor.

- Monoenergetic surface states which act as recombination centers, result in a

capacitance before the onset potential and result in Fermi level pinning before the

onset potential.

- The OER intermediates result in a capacitance around OER onset. However, the surface

states due to OER intermediates do not result in Fermi level pinning.

- As the i-SS is comprised of OER intermediates, the characteristics of 𝐶i−SS is an

indication of the catalytic performance of OER on the photoanode surface.

General conclusions 51

- An increase in backward rate constants for elementary steps in OER resulted in lower

capacitance and higher onset potential. Thus, a lower peak magnitude of 𝐶i−SS can be

an indication of lower catalytic performance of the photoanode surface.

- Potential drop over the series resistance increases with the current in the cell and

affects the potential distribution within the semiconductor. Hence, it is important to

include the potential drop over the series resistance in the microkinetic model to

enable theory-experiment comparison

- The impact of back contact resistance on the impedance of the functional layer is

discussed by selective variation of series resistance by keeping all other model

parameters constant.

- The series resistance has a significant impact both on the polarization resistance as

well as on the time-constants of processes as observed in the EIS.

- The current density and the data obtained from the analysis of EIS should be plotted

against 𝑉applied − 𝑗. 𝑅s instead of 𝑉applied for correcting the data for 𝑅s and drawing

accurate conclusions about the functional layer.

The step by step research approach adopted in this dissertation resulted in the development

of a method that can simulate electrochemical data similar to experiments; a novel approach

that brings together DFT, semiconductor physics, and microkinetic modeling. For the first

time, the impedance spectra related to OER on semiconductor electrodes are simulated

directly based on the processes occurring at the interface. This feature of the approach is

advantageous in identifying the limiting processes in OER by comparison with experimental

data, without using equivalent circuit models. Furthermore, the model can explain features in

PEC measurements that are difficult to explain experimentally. For instance, surface states

and their impact on OER performance are topics of debate in the field of PEC. In this thesis,

the features in the PEC data related to surface states are studied with the systematic variation

of the model parameters related to surface states.

The impact of OER intermediates on the PEC data is simulated for the first time. Against the

general assumption, the surface states due to OER intermediates were found not to result in

Fermi level pinning around OER onset. Additionally, in a computational model, it is easier to

single out the effect of a certain parameter. For instance, in Chapter 4, the impact of back

contact resistance on the impedance of the functional layer is discussed by selective variation

of the series resistance by keeping all other model parameters constant. It is observed that

the series resistance has a significant impact on the polarization resistance and the time-

constants of processes as observed in the EIS. Hematite is used as a model material in this

thesis, however, the approach is generic and can be applied to other photoanode materials.

The microkinetic model can be used to predict the PEC characteristics of other photoanode

materials based on corresponding energetics from DFT calculations and material properties.


The models developed in this dissertation bridge experimental observations directly to the

physicochemical processes in water oxidation, especially the four-step OER mechanism.

Additionally, the state-space modeling approach brings together semiconductor

electrochemistry and control theory. This opens up opportunities for bringing in the expertise

from the field of control theory in regards to the identification of rate constants from the

theory-experiment comparison. The individual and combined effects of thermodynamics,

reaction kinetics, and semiconductor properties on the OER performance are elucidated by

the simulations. The use of multiscale models together with experimental data will aid in

identifying how different material processing influences the processes at the SEI. Such

knowledge will aid in the design of high-performing photoanodes.

Outlook 53

5 Outlook

This section discusses some of the possible prospects of the approach developed in this thesis

and opportunities for future research.

• Identification of rate constants in OER using the state-space model

The OER occurring at the semiconductor-electrolyte interface proceeds via multiple

intermediates. The rate constants of these intermediate steps affect the photocurrent density

and onset potential. It is possible that one of the intermediate steps in OER can be the rate-

limiting step. In Chapter 2, a state-space model of OER is developed which can simulate EIS

similar to experiments, in terms of the rate constant of the intermediate steps. The theoretical

rate constants used in the model are calculated based on the energetics calculated using DFT

such as shown in Chapter 1. The rate-limiting steps can be identified more accurately if the

rates can be extracted from experimental data. The proposed strategy is that the state-space

model can be optimized against experimental data for extracting the rate constants based on

measurements.

A schematic representation of the proposed method of theory-experiment comparison for

extracting the rate constants is shown in Figure 18. However, the state-space model of OER is

a fourth-order model due to the four intermediate reactions, and, hence, the optimization of

the full non-linear model is a challenging problem. However, the analysis in Chapter 2 shows

that depending on the potential the complexity (model order) of the model changes. At lower

applied potentials, only OH is the intermediate that is formed. Hence, the system can be

represented by a first-order model with one rate constant. For this first-order model, which

considers only the first step in the OER mechanism, the rate constant can be estimated.113 The

result from the first-order model is promising and this same method can be extended to the

fourth-order model of OER by sequentially increasing the order of the model. The theoretical

rate constants for the elementary steps calculated using DFT can act as a starting point for the

optimization. In the case of the theoretical rate constant, the calculation has an exponential

term and a pre-exponential term. The rate constants obtained after the optimizing of the

model gives the experimental rate constants. The relative magnitudes of these rate constants

will give information about the rate-limiting processes in OER. However, the rate constant

obtained after the optimization will not distinguish the pre-exponential term and the

exponential term as in the case of theoretical rate constants. Assuming the exponential term

to be the same as in the case of theoretical rate constants, the pre-exponential term can be

calculated from the optimized rate constant.

The optimization of the model can be done against various experimental data. The rate

constants obtained by optimizing the model against different sets of experimental

measurements can vary depending on the operating point, the photoanode properties, and

54 Outlook

fabrication techniques used in each experiment. The correlation between the experimental

rate constants and fabrication techniques will be highly useful in tuning photoanodes for high

performance.

Figure 18 A schematic representation of the approach for identifying rate constants and rate-limiting processes

using theory-experiment comparison.

• Investigating the interaction between recombining surface states and OER

intermediates

The model discussed in Chapter 3 simulates recombining surface states (r-SS) and surface

states due to OER intermediates. As mentioned earlier r-SS is present due to discontinuities

at the SEI, like dangling bonds, dopants, and vacancies. OER may occur at sites corresponding

to r-SS or these sites can influence the OER occurring at active sites in their vicinity. In the

model developed in Chapter 3, the active sites on the photoanode and the sites corresponding

to r-SS are treated separately and are assumed to not interact with each other. However,

lateral interaction between adsorbates at different sites is believed to influence the catalysis

at the surface.114 Hence, lateral interaction between OER intermediates at sites corresponding

to r-SS and those at the active sites on the semiconductor surface should be included in a

future model. This would require the calculation of a probability function to include the

probability of different possible configurations of adsorbates.114 These probability functions

can be obtained using kinetic Monte Carlo (kMC) methods as proposed in the literature.114

From the multiscale perspective, the inclusion of kMC adds one more dimension to the model.

The interaction between r-SS sites and the active sites in the vicinity can be investigated with

such a model. Data regarding, the nature of the interaction, the impact of such an interaction

on the photoanode performance, how the distribution of r-SS sites at the surface affect the

photoanode performance, and how the surface state energy influences such an interaction,

Outlook 55

can be obtained from this study. These data will aid in identifying any possible scenarios in

which r-SS can mediate OER or enhance OER at neighboring sites. If there is such a strong

effect of r-SS on the catalytic performance of the active sites, tuning the characteristics of r-

SS will be important in the development of high-performance photoanodes.

• Investigating the impact of adsorbed OER intermediates on the Helmholtz layer

capacitance

Usually, the Helmholtz capacitance is assumed to be constant in simulations. The same

assumption is used in the model developed in Chapter 3. From the literature, it is proposed

that the adsorption of species at the catalytic surface may alter the Helmholtz layer

properties.115 Any variation in Helmholtz capacitance is critical as it affects the potential drop

over the surface states and, hence, the potential distribution across the SEI. In the model

discussed in Chapter3, the effect of surface coverage on the Helmholtz capacitance can be

modeled by defining a suitable function for the variation of Helmholtz capacitance with

surface coverage. The impact of the relation between surface coverage and Helmholtz

capacitance on PEC measurements and whether such an effect is visible in experiments can

be investigated.

• Simulating the photoelectrochemical characteristics of prospective materials

The developed model is generic and can be used to simulate PEC data for other photoanode

materials like WO3, TiO2, and BiVO4. The inputs needed for the simulation are the energetics

of OER at the photoanode surface calculated using DFT and the optoelectronic properties of

the photoanode material. Similarly, PEC data for proposed materials that are not yet studied

experimentally, can be predicted approximately. The simulated data from the microkinetic

modeling will give information about the feasibility of the proposed material as a photoanode.

• Developing a full multi-scale model of the semiconductor electrolyte interface

The multiscale modeling approach developed in Chapter 2 and Chapter 3 uses atomistic data

from DFT calculations together with a microkinetic model of OER to simulate electrochemical

data comparable to experiments. To further improve the theory-experiment comparison of

the processes occurring at the SEI, the other two levels, namely molecular level, and coarse-

grain level can be incorporated in the approach to develop a full multiscale model.18 In such

an approach, the DFT data will be used as an input to molecular dynamics (MD) simulations to

calculate the effect of water adsorption and adsorption induced reconstructions at the

photoanode interface. DFT simulations can be performed again on the reconstructed

geometry to calculate the energetics of OER. The results from these DFT calculations and MD

simulations will be used as input to kMC simulations. The kMC simulations can simulate the

OER by including lateral interactions and diffusion of adsorbed species at the surface. As

56 Outlook

mentioned earlier, the kMC results can be used to define probability functions for including

lateral interactions in the microkinetic model. Thus, a multiscale model of the semiconductor-

electrolyte interface covering all four scales of modeling can be developed. Theory experiment

comparison with such a model can be used to identify the rate-limiting processes at the

interface and verify different proposed OER mechanisms based on comparison with

experiments. Additionally, this model can be used to represent the semiconductor-electrolyte

interface in continuum models of PEC cells that are used for device-level optimizations.

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67

PART B: Publications

Chapter 1 69

Chapter 1: Why does NiOOH cocatalyst increase the oxygen

evolution activity of α-Fe2O3?

Abstract

Nickel oxyhydroxide (NiOOH) is known to increase the oxygen evolution reaction (OER)

performance of hematite (Fe2O3) photoanodes. In recent experimental studies, it has been

reported that the increased OER activity is related to the activation of the hematite (α-Fe2O3)

surface by NiOOH rather than the activity of NiOOH itself. In this study, we investigate the

reason behind the higher activity and the low overpotentials for NiOOH-Fe2O3 photoanodes

using first-principle calculations. To study the activity of possible catalytic sites, different

geometries with NiOOH as cluster and as strip geometry on hematite (110) surfaces are

studied. Density functional theory (DFT) + U calculations are carried out to determine the OER

activity at different sites of these structures. The geometry with a continuous strip of NiOOH

on hematite is stable and can explain the activity. We found that the Ni atoms at the edge

sites of the NiOOH cocatalyst are catalytically more active than Ni atoms on the basal plane of

the cocatalyst; the calculated overpotentials are as low as 0.39 V.

Adapted from: George, K.; Zhang, X.; Bieberle-Hütter, A. Why Does NiOOH Cocatalyst Increase

the Oxygen Evolution Activity of α-Fe2O3? J. Chem. Phys. 2019, 150 (4), 41729.

70 Introduction

1 Introduction

Carbon neutral and sustainable energy is a necessity at present due to concerns over global

warming and climate change.1 Technologies that can harvest solar energy are a promising way

in achieving this.1,2 Among these technologies, the ones which can produce chemical fuels

directly using solar energy are eagerly sought after as the so-called ‘solar fuels’ can be stored

like conventional fuels.3,4 Photo-electrochemical cells (PEC) are devices that can perform this

conversion of solar energy into chemical energy.5,6 In a typical PEC, water is split into hydrogen

and oxygen using solar energy and an additional external bias potential. The two sets of

reactions involved are referred to as hydrogen evolution reaction (HER) and oxygen evolution

reaction (OER), respectively. Among these, OER is more complex and is believed to proceed

through multiple steps that involve four charge transfer reactions.7,8 Additionally, the OER

requires more energy and is non-spontaneous compared to HER.9,10

For OER to occur, the photoanode material needs to absorb sunlight and thereby generate

electron-hole pairs with sufficient excitation. This depends on the bandgap of the

semiconductor material used as the photoanode.2 Hematite (α-Fe2O3; abbreviated in the

following as Fe2O3) is a promising material to be used as a photoanode due to its suitable

bandgap of 2.1 eV, low cost, abundance, and non-toxicity.11–13 However, the overpotential is

rather high (0.78 V) which means that the OER redox potential is higher than the theoretical

value and, hence, an additional bias potential is required for water splitting.9 One way to

decrease the OER overpotential for hematite photoanode is by using a cocatalyst on top of

the hematite.13,14 In literature, it has been experimentally reported that nickel oxyhydroxide

(NiOOH) is a good cocatalyst for hematite as it reduces the OER overpotential of hematite by

0.15 V.15 Additionally, it was reported that the photocurrent measured for the NiOOH-Fe2O3

heterostructure at 1.23 V vs. RHE is 50% higher than that for bare Fe2O3.15

Nickel oxyhydroxide and nickel hydroxide (together represented by NiOx) have been

investigated in several studies in the literature due to its application in batteries and OER

catalysis.16–20 Tkalych et al. studied the structural and electronic properties of β-Ni(OH)2 and

β-NiOOH using first-principles calculations and identified the (001) surface as the

thermodynamically most stable surface for both.21 In a separate DFT+U study, the OER activity

of β-NiOOH was investigated and OER overpotential as low as 0.52 V was found for β-NiOOH.22

These results were for undoped NiOx, however, doping with Fe is known to increases the

performance of NiOx electrodes.23–26 It has been reported that the ‘Fe’ sites in the NiOOH

structure act as active sites for OER.27 Li and Selloni reported that the activity of Ni-Fe oxides

is due to the formation of Fe-doped β-NiOOH and some extend to the formation of NiFe2O4

during the doping process.28 A very low overpotential of 0.26 V for Fe doped β-NiOOH

structure was reported.28 The case is different when NiOOH is used as a cocatalyst layer on

hematite. In an experimental study by Malara et al., NiOx was deposited as a thin cocatalyst

Chapter 1 71

layer on hematite using electrodeposition and photodeposition.29 Such a structure showed

high activity towards OER with a cathodic shift in overpotential of around 0.2 V.29 The low

overpotential was not attributed to the electrocatalytic activity of the cocatalyst layer itself

but to the quenching of electron-hole recombination and passivation of surface defects at the

hematite surface by the NiOx layer. However, no studies have been carried out so far on

identifying the active sites formed on the hematite electrode when coated with NiOOH

cocatalyst.

The aim of this work is to investigate why NiOOH cocatalyst increases the OER activity of

α-Fe2O3. For this, we use density functional theory (DFT) + U calculations for identifying the

most active OER sites on the NiOOH-Fe2O3 heterostructure.30,31 The geometries used for the

DFT calculations are constructed by modeling NiOOH as a layer on top of a hematite (110)

surface. Three different geometries are employed for studying OER activity. Using these

geometries, active sites with overpotentials as low as 0.39 V were identified. Based on the

results, an optimum design regime for the geometry of the cocatalyst is proposed which will

improve the OER performance of NiOOH-Fe2O3 photoanode considerably.

2 Methodology and computational details

Density functional theory (DFT) +U was used to calculate free energies. The calculations were

performed using Vienna ab initio simulation package (VASP).30,31 PBE functional and

pseudopotentials using project augmented wave (PAW) method were used.32,33 The Hubbard

U value of 4.3 eV is used for Fe.34,35 For bare NiOOH a U value of 5.5 eV is generally used.22

The system here is different from bare NiOOH as we have a structure with a monolayer of

NiOOH over a hematite slab, with sites involving both Ni and Fe in close vicinity. Therefore,

we chose the U value of 3.8 eV from Toroker et al., which was used in the study of Ni and Fe

oxide alloys for solar energy conversion applications.36 A converged plane wave kinetic energy

cut off of 500 eV and a k point mesh of (5x5x1) were used for all simulations. For hematite,

experimental observations suggest that (110) and (104) are the most dominant facets.37 For

this study, the (110) surface of hematite is chosen since the (110) facet is reported to be more

OER active compared to (104).9,37 Hematite slabs with four layers were used for all

calculations. The slab sizes are given in the supporting information. The free energy profile for

OER on different sites are calculated similar to previous studies.23,38,39

Mechanism: We assume the four-step OER mechanism proposed by Rossmeisl et al.38

𝐻2𝑂 +∗ → 𝑂𝐻∗ + 𝐻+ + 𝑒− (1)

𝑂𝐻∗ → 𝑂∗ + 𝐻+ + 𝑒− (2)

𝑂∗ + 𝐻2𝑂 → 𝑂𝑂𝐻∗ + 𝐻+ + 𝑒− (3)

72 Methodology and computational details

𝑂𝑂𝐻∗ → ∗ +𝑂2 + 𝐻+ + 𝑒− (4)

The overall reaction is

2𝐻2𝑂 → 𝑂2 + 4𝐻+ + 4𝑒− (5)

where * signifies adsorption site and OH*, O*, and OOH* are the OER intermediates adsorbed

at the adsorption site. The thermodynamic energy required for dissociation of two moles of

water to give one mole of oxygen (eq 5) is equal to 475 kJ which is equivalent to 4.92 eV.40

Given that it involves the transfer of four electrons, ideally a potential equal to 1.23 V (4.92

eV/4e) should be sufficient for OER to occur.7 However, this is not the case in reality since

even the best known OER catalysts require applied potentials higher than 1.23 V.11 The

amount by which the applied potential exceeds 1.23 V is called the overpotential (𝜂).

To calculate the overpotential, the free energy change (Δ𝐺i) in each of the four-step (eq 1-4)

has to be calculated. We use the method defined by Rossmeisl et al. for calculating the free

energies of OER intermediates on metal oxide surfaces.38 In this method the reference

potential is set to that of the standard hydrogen electrode. The free energy changes are

calculated at standard conditions defined by electrode potential (𝑈) =0, pH=0, pressure (𝑝) =

1 bar, and temperature (𝑇)=298K.38 They are calculated for each step in eq 1 - 4 based on

literature. 34,41 The equations are given as

Δ𝐺1 = 𝐸(𝑂𝐻∗) − 𝐸(∗) − 𝐸H2O +

1

2𝐸H2 + (ΔZPE − TΔS)1 (6)

Δ𝐺2 = 𝐸(𝑂∗) − 𝐸(𝑂𝐻∗) +

1

2𝐸H2 + (ΔZPE − TΔS)2 (7)

Δ𝐺3 = 𝐸(𝑂𝑂𝐻∗) − 𝐸(𝑂∗) − 𝐸H2O +

1

2𝐸H2 + (ΔZPE − TΔS)3 (8)

Δ𝐺4 = 𝐸(∗) − 𝐸(𝑂𝑂𝐻∗) + 𝐸O2 +

1

2𝐸H2 + (ΔZPE − TΔS)4 (9)

Where 𝐸 represents the reaction energies, 𝛥𝑍𝑃𝐸 is the zero-point energy due to the reaction,

and 𝛥𝑆 is the change in entropy. Further details about the calculations are given in the

supporting information. For accommodating any change in pH, a correction term given by –

𝑘𝑇 log10 pH has to be added to the free energies calculated at standard conditions (eq 6-9),

where 𝑘 is the Boltzmann constant and 𝑇 is the temperature.38 Similarly for any applied bias

potential 𝑈 relative to the standard hydrogen electrode, the correction term to be added is –

𝑒𝑈.38 The overpotential is calculated as

𝜂 = max (Δ𝐺i 𝑒𝑉/1𝑒 − 1.23) 𝑉 (10)

for i=1 to 4.

Chapter 1 73

For comparing the OER activity of different sites, the calculated OER overpotential for NiOOH-

Fe2O3 heterostructure is benchmarked against the OER overpotential value of bare Fe2O3

which is 0.78 V.9

3 Results and discussion

Three different geometries were investigated in this study: the cluster, the strip, and the wider

strip geometry. All geometries are discussed below and a comparison of the slabs is shown in

Figure S1 in the support information.

3.1 Cluster geometry

The cluster geometry is modeled using a single layer of NiOOH consisting of four molecules on

the hematite slab. The hematite slab size is chosen such that the NiOOH clusters will have a

sufficient distance between themselves under periodic boundary conditions. For optimization

of the geometry, first, the hematite (110) slab is relaxed and then the NiOOH layer with the

four molecules is introduced over the relaxed hematite surface. This combined structure is

relaxed again to get the final structure which is used for the OER study. An example of the

final, relaxed geometry is shown in Figure 19. Two adsorption sites are investigated in this

study and are labeled in Figure 19 as terminal site and bridge site. The names terminal and

bridge site comes from the OH which is bound to these sites in NiOOH. In both cases, the Ni

atom serves as the adsorption site.

Figure 19 Cluster model of NiOOH on hematite (110) after optimization of the geometry. The OER activity is calculated for the terminal site and the bridge site.

Figure 1 shows the cumulative free energies of the OER intermediates at the terminal site of

the cluster model. The largest free energy step is found to be the O2 formation (red shadow

in Figure 1). It requires an energy of 2.52 eV. The overpotential at the terminal OH site is

calculated as 2.52 V – 1.23 V = 1.29 V. This value is higher than 0.78 V which is the

overpotential for bare hematite.9


Figure 1 Cumulative free energies of OER intermediates at the terminal site of the cluster geometry. The OOH to

O2 formation step accounts for the largest energy step (highlighted) and is, hence, the potential determining

step.

At the bridge OH site, a very high free energy of 8.4 eV is found for the deprotonation of OH

to form the O intermediate. This means that the bridge site is not active towards OER. Hence,

both sites on the cluster geometry have high free energy steps and therefore result in high

overpotential. This does not agree with experimental findings that show low overpotentials

for NiOOH-Fe2O3 heterostructure.15,29 Going back to the atomic structures of the cluster after

adsorption of intermediate species, we find that the adsorbed intermediate species induce

reconstruction of the cluster (FigureS1); hence, the cluster geometry is not stable. The

reconstruction lowers the free energy of the system. Therefore, the energies of OH and O

states are lower than expected. This results in the O2 formation as the potential determining

step, since – according to the methods used - the sum of the four steps is fixed to 4.92 eV (=

4 * 1.23 eV).

To study the OER activity of NiOOH-Fe2O3, a geometry of NiOOH which is more stable than the

cluster is required. The idea is to have a stable continuous geometry of NiOOH over hematite.

A strip geometry is continuous when the periodic boundary condition is applied and is a simple

geometry to implement. The choice of strip geometry is motivated by the study of cobalt oxide

nano-islands on gold surface by Fester et al.42 Thus, a geometry with NiOOH as a continuous

strip on Fe2O3 (110) (referred to as strip geometry henceforth) is introduced.

3.2 Strip geometry

In the strip geometry, the NiOOH layer is a two-atom-wide strip on top of Fe2O3. The

dimension of the Fe2O3 layer and the length of NiOOH strip are chosen such that the

periodicity of both NiOOH and Fe2O3 is maintained (see supporting information: Slabs and

geometries). This structure is then optimized and the resulting structure is shown in Figure 2a.

When the periodic boundary condition is applied, the NiOOH layer forms a continuous strip

over hematite (Figure 2b). The strip geometry has well-defined edges and the nomenclature

Chapter 1 75

of these edge sites is given in Figure 2c. At the left side edge (with sites A, B, and C), Ni is

exposed at the edge; we call this the “Ni edge”. On the right edge, the OH group is exposed

(sites D, E, and F); this edge is called the “OH edge”. Different edge sites were also reported

for β-CoOOH nanoislands by Fester et al.42 First, the Ni edge sites (A, B, C) are chosen for

analyzing the OER activity. Figure 2d shows the geometries with different OER intermediates

at the A site. The O atom of the adsorbed species is shown in blue for easier identification that

this O comes from the adsorbed water. The free energies of formation of the OER

intermediates at sites A, B, and C are calculated as described in the chapter “Methodology and

computational details” and the results are plotted in Figure 3.

Figure 2 a) Unit cell of Fe2O3 with NiOOH strip; b) supercell (1x4x1) which shows the continuous strip of NiOOH

on applying continuous periodic boundary condition; c) Top view of the cocatalyst strip showing the different

sites A to F; d) The geometries showing different OER intermediates at the A site; the adsorbed oxygen is shown

in blue color to differentiate it from the oxygen atoms from Fe2O3 and NiOOH.

Large differences in the cumulative free energies at the different sites A, B, and C of the Ni

edge are found (Figure 3). The largest step for the A site is the O2 formation step and for the

C site, it is O formation resulting in overpotentials of 0.40 V and 0.49 V, respectively. These

overpotentials are much lower than the overpotential of bare hematite (0.78 V).9 Hence, the

A and the C site are very active for OER. The B site, in contrast, shows a high overpotential

(1.49 V) with the formation of O as the potential determining step. Even though the sites A, B,

and C look similar they are geometrically different because of the lattice mismatch between

NiOOH and Fe2O3 (Supporting information: Lattice mismatch).

a b c

d


Figure 3 Cumulative free energies of OER intermediates at sites A, B and, C for the two-atom-wide model. The

potential determining step for each site is highlighted. Site A and C have lower overpotential compared to bare

hematite (0.78 V). Site B has higher over due to high ΔGOH - ΔGO.

On the OH edge, the OER activity is analyzed at site E. The OH intermediate is adsorbed at

the Ni atom at site E with sufficient distance from the existing OH groups. This first adsorption

step showed low free energy of formation. While optimizing the geometry for O adsorption,

the adsorbed O atom formed a bond with a neighboring O atom on the Fe2O3 layer which

made further steps in the assumed OER mechanism not feasible. This happens because of the

spatial limitation imposed by the neighboring OH groups on each side of Ni atom at site E. This

geometrical limitation holds for sites D and F and, hence, they are not analyzed for OER.

Therefore, the OH edge of NiOOH (D, E, and F) is not active towards OER.

From the strip geometry, it is seen that only the A site and C site are OER active compared

to bare hematite. The B site shows higher overpotential compared to A site and C site. Even

though the sites have differences due to lattice mismatch as mentioned previously, the

overpotential at B site is dramatically higher than the overpotential at the other two sites. On

further analysis of the optimized geometries, it was found that the two-atom-wide NiOOH

strip shows reconstructions in the geometry upon adsorption of OER intermediates. The

reconstructions were observed on the non-adsorbing edge, which was evident especially in

the case of adsorption at B site (Figure S3). Due to this adsorption induced geometric

instability, the two-atom-wide geometry is found not suitable for studying the activity of

NiOOH cocatalyst layer over hematite. The width of the cocatalyst strip is then increased from

two atoms to three atoms to get a more stable geometry. Additionally, a wider cocatalyst layer

will be better in representing an experimental cocatalyst layer.29

3.3 Wider strip geometry

The wider strip geometry consists of a strip with three atoms in width. Hence, compared to

the two-atom-wide geometry there is an additional column of Ni atoms in between the edge

sites, which represent sites on the basal plane. The geometry is obtained similar to the

Chapter 1 77

previous case: The wider strip of NiOOH and the Fe2O3 slab are optimized together to get the

starting geometry. Figure 4a shows the optimized unit cell and Figure 4b shows the supercell

(1x4x1) with NiOOH as a continuous strip. All Ni edge sites, OH edges sites and the bridge OH

sites on the NiOOH layer are shown in Figure 4c. The Ni edge sites are denoted as A, B, and C,

and the OH edge sites are denoted as D, E, and F. The bridge sites on the NiOOH layer are

denoted using the numbers 1-9.

Figure 4 a) Unit cell of Fe2 O3 with three-atom-wide NiOOH strip; b) supercell(1x4x1) which shows the continuous strip of NiOOH on applying continuous periodic boundary condition. c) Top view showing the Ni edge sites A, B, C, the OH edge sites D, E, F, and the bridge sites (1-9) on the wider strip geometry. The inset shows a bridge site (site 9); d) The geometries showing different OER intermediates at B site on the Ni-edge. The intermediates form coordination between Ni and Fe after geometry optimization

First, the OER activity for the edge sites A, B, and C are calculated. Figure 4d shows the

geometries with the adsorbed intermediates at the B site after optimization. The adsorbed

intermediates are shared between the Ni atom and the adjacent Fe atom. The free energies

of formation of OER intermediates at sites A, B and, C are plotted in Figure 5a. Similar to the

previous case, A and C sites show low OER overpotentials. In contrast to the previous result,

with this geometry, the B site also shows low overpotential. At the A and the B site, the O

formation step is the potential determining step which results in overpotentials of 0.49 V and

0.39 V, respectively. At the C site, the O2 formation step is the potential determining step with

an overpotential of 0.58 V. Among the three sites, the B site shows the lowest overpotential.

Unlike the two-atom-wide geometry, no adsorption induced reconstructions were observed

in the case of the wider strip geometry (Figure S4).

a b c

d


Figure 5 a) Cumulative free energies of OER intermediates at sites A, B and, C for the wider strip geometry. The

potential determining step for each site is highlighted. All the three sites show low OER overpotential; b) Volcano

plot of the overpotentials of all sites on the wider strip geometry. The black marker in the plot indicates the

overpotential of bare hematite (110). All the three edge sites (blue markers) show lower overpotential and the

bridge sites 1-9 (red markers) show higher overpotential compared to hematite (110).

The OER activity at the OH edge site is analyzed at site E. The O intermediate at site E forms a

bond with a neighboring O atom on Fe2O3 slab as observed in the case of two-atom-wide

geometry. This is due to the spatial limitation as explained in the previous section. Itis also

true for sites D and F. Hence, the OH edge is catalytically not active toward OER. The OH groups

on top of Ni in the NiOOH layer can also be possible reaction sites. These are bridge sites

shared between Ni atoms on the basal plane and are denoted using the numbers (1-9) in

Figure 4c. If the existing OH at these sites deprotonates and an OH from the solution can get

adsorbed at the remaining O, it can form the OOH intermediate and further deprotonation of

it will form O2. The above-mentioned steps form the same mechanism of OER as explained in

the section “Methodology and computational details”. The OER activity of all 9 OH-sites is

calculated and the overpotentials at all these 9 sites were higher than that of bare hematite.

b)

a

Chapter 1 79

The results are plotted in Figure 5b together with the edge site overpotentials in the form of

a volcano plot using ΔGOH - ΔGO as the descriptor. This analysis using the volcano plot and the

choice of the descriptor ΔGOH - ΔGO, is followed from the literature.7,43

In the volcano plot the negative value of the overpotential is plotted against ΔGOH - ΔGO, so

the higher the data point in the plot, the better the OER performance. The volcano plot shows

that the three edge sites (blue markers) have lower overpotential than the bare hematite

(black marker), which is the benchmark. All bridge sites (red markers) show inferior OER

performance compared to hematite. Thus, the Ni edge sites (blue markers) are responsible

for the increased activity of NiOOH-Fe2O3 heterostructure. It is also observed that these Ni

edge sites are in proximity of Fe atoms from the hematite surface. This result is in agreement

with the observations reported by Malara et al.15,29 In their experimental analysis the authors

found more activity with photo-deposited NiOx which had more area of hematite surface

exposed, than electrodeposition. Such a surface will have more Ni-Fe edge sites, which are the

active sites according to our study.

4 Conclusions

The low OER overpotential for NiOOH cocatalyst on hematite is studied by DFT+U calculations.

The OER activities for different sites are investigated using three different geometries. While

the cluster geometry was not stable, the results from the strip geometries show that the

NiOOH cocatalyst can reduce the OER overpotential of hematite photoanodes. However, the

two-atom-wide geometry showed adsorption induced reconstructions which makes it not

suitable for the study of catalytic activity. A stable three-atom-wide strip geometry was

therefore used which showed no adsorption induced reconstructions. All final conclusions are

drawn based solely on the results from the wider strip geometry.

From the OER analysis on the wider strip geometry, all the three Ni edge sites are found to

be active and the OER overpotentials of the active sites on NiOOH- Fe2O3 heterostructure

range between 0.39 V and 0.58 V. This corresponds to a cathodic shift in overpotential by

approximately 0.4 V and 0.2 V, respectively, compared to bare hematite (η= 0.78 V ).44 This is

in agreement with experimental findings in the literature which show a reduction in

overpotential by 0.15 V - 0.2 V for hematite photoanode with NiOOH/NiOx cocatalyst.15,29 We

can explain that the improved activity of the NiOOH-Fe2O3 system arises from the Ni edge sites

on the NiOOH cocatalyst rather than from sites on the cocatalyst basal plane. The Ni edge sites

which are highly active for OER, are located in proximity to Fe atoms from the hematite

surface. At these sites, the intermediate species are found to be coordinated between the Ni

and neighboring Fe atom. This finding emphasizes the need for designing the geometry of the

cocatalyst such that the number of Ni-Fe edge sites are maximized. We also observe that the

bridge sites which are located on the NiOOH basal plane, show high overpotential, i.e. low

electrochemical activity. This indicates that there is no direct correlation between the OER

80 Conclusions

performance and the area of the NiOOH layer. Based on these results, we propose a regime

for deposition of NiOOH cocatalyst on hematite: The cocatalyst should be deposited such that

it forms nano-islands over the hematite surface rather than forming a fully continuous coating

of the surface. The geometry of these nano-islands should be such that they have a high ratio

of edge length (Ni-Fe edge sites) to its area (basal plane sites). The DFT+U calculations using

the continuous strip geometries successfully identify the reason behind the activity of the

NiOOH-Fe2O3 cocatalyst system. Such a geometry can also be extended to other systems for

investigating the electrochemical activity.

Acknowledgments

George acknowledges funding from the Shell-NWO/FOM “Computational Sciences for Energy

Research” PhD program (CSER-PhD; nr. i32; project number 15CSER021). Zhang and Bieberle-

Hutter acknowledge the financial support from NWO (FOM program nr. 147 “CO2 neutral

fuels”) and M-ERA.NET (project “MuMo4PEC” with project number M-ERA.NET 4089).

Supercomputing facilities of the Dutch national supercomputers SURFsara/Lisa and Cartesius

are acknowledged. We also thank Rochan Sinha for many fruitful discussions.

Chapter 1 81

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Chapter 1 85

Supporting information Slabs and geometries

Different geometries of NiOOH on Fe2O3 were used in this study: the cluster, the strip, and the

wider strip geometry. Different slab sizes were used depending on the geometry. In each case,

the NiOOH layer and the Fe2O3 slab were first optimized separately. The relaxed structures

were then optimized together. These finally relaxed geometries are shown in Figure S1 in top

view representation. There is a vacuum of 9 Å in the z-direction for all geometries.

Figure S1 Top views of the slabs of NiOOH on Fe2O3 of the three different geometries used in this study i) cluster, ii) strip, and iii) wider strip geometries. All geometries are the final geometries after optimization.

Reconstructions in cluster geometry during OER at the terminal site

The cluster geometry shows reconstructions when it is optimized with adsorbed OER

intermediates. Figure S2 shows the reconstructions observed in the cluster geometry during

the adsorption of OER intermediates at the terminal site.

Figure S2 Side views of geometries showing OER intermediates adsorbed at the terminal site of the cluster (blue

circle). The reconstructions in these geometries after optimization are marked by the black circles.

86 Supporting information

Lattice mismatch

Due to different lattice constants of NiOOH and Fe2O3, it is important to check for lattice

mismatch in the optimized geometries. In the case of geometry ii and iii (Figure S1), the length

of the hematite slab in b direction is 8.87 Å and the length of the NiOOH strip in b direction is

8.44 Å before optimization. Hence, there is a lattice mismatch of 4.84% ((8.87 Å - 8.44 Å)/8.87

Å) between the hematite slab and NiOOH strip before optimization. The full cell was optimized

and after optimization, the NiOOH strip relaxed over the hematite slab to match the b

dimension of 8.87 Å. This results in a final optimized geometry without lattice mismatch.

Calculation of ΔG for OER intermediates

From Kanan et al., the 𝛥𝑍𝑃𝐸 − 𝑇𝛥𝑆 values are found to be similar for OER at different oxide

materials.1 Hence, previously reported values for 𝛥𝑍𝑃𝐸 – 𝑇𝛥𝑆 were used in this chapter for

the calculations of free energy changes.2 The values are 0.4 eV, -0.39 eV, and 0.47 eV for the

formation of OH, O, OOH, respectively, and 4.92 eV for 𝛥𝐺 (2H2O → O2 + 2H2).2 Energies of

non-adsorbed species, i.e. H2, O2, and H2O, were also derived from the literature: the values

are −6.77 eV, −9.87 eV, and −14.22 eV, respectively.2,3

Adsorption induced reconstructions in two-atom-wide geometry

The Ni-Fe bond lengths in different geometries (A, B, C site) with adsorbed OH are compared

against the optimized geometry without any adsorbed species (*) in Figure S3. The bond

length changes in all three geometries: 0.322 nm for A site, 0.305 nm for B site, and 0.317 nm

for C site vs 0.326 nm for plain geometry. This indicates that two-atom-wide geometry is not

stable enough. The B site adsorption results in the highest displacement compared to the A

site and the C site.

Figure S3 Side views of geometries showing the relaxed two-atom-wide geometry and geometries with OH

adsorbed at A, B, and C sites. An Fe-Ni bond length on the non-adsorbing side is chosen as reference (black arrow)

to show the displacement of the cocatalyst layer with respect to the hematite surface.

Chapter 1 87

Adsorption on wider strip geometry

The wider strip geometries are analyzed similar to the two-atom-wide geometry above (Figure

S4). In this case, after adsorption of species at A, B, and C sites, the bond lengths remain

approximately the same, unlike the two-atom-wide geometry. Hence, the three-atom-wide

geometry does not show any adsorption induced reconstructions and is stable.

Figure S4 Side views of geometries showing the relaxed wider strip geometry and geometries with OH adsorbed

at A, B, and C sites. An Fe-Ni bond length on the non-adsorbing side is chosen as reference (black arrow) to show

the displacement of the cocatalyst layer with respect to the hematite surface.

References



(3) Neufeld, O.; Toroker, M. C. Platinum-Doped α-Fe2O3 for Enhanced Water Splitting Efficiency: A DFT+U Study. J. Phys. Chem. C 2015, 119 (11), 5836–5847. https://doi.org/10.1021/jp512002f.

Chapter 2 89

Chapter 2: Impedance spectra and surface coverages

simulated directly from the electrochemical reaction

mechanism: A nonlinear state-space approach

Abstract

Current-voltage curves and electrochemical impedance spectra (EIS) are crucial for

investigating the performance and the electrochemical limitations of electrochemical cells.

Therefore, we developed an approach that allows the direct simulation of such data based on

micro-kinetic modeling. This approach allows us to assess the influence of various input

parameters on the EIS and the current-voltage curves and, hence, the overall performance of

electrochemical cells. We develop our approach for the oxygen evolution reaction (OER)

taking place at the semiconductor-electrolyte interface. At this interface, the micro-kinetic

equations, i.e., electrochemical reactions, for the multiple steps in OER are formulated and

the resulting set of equations are modeled in a state-space form. As input to the state-space

model, we use the theoretical reaction rates calculated using density functional theory and

Gerischer theory for semiconductors. Then, the electrochemical data is simulated as a

function of applied potential. Next to the theory and the model development, a case study on

the hematite-electrolyte interface which is a typical interface in photo-electrochemical cells is

presented. Current-voltage curves and EIS data for the hematite interface are simulated from

the electrochemical model. The data is compared to experimental measurements. Apart from

the current density and the EIS, the model can simulate the coverage of intermediate species

as a function of applied potential which is highly sought after for identifying the limiting

processes at the interface, but not available from experimental studies. The approach is

generic and can be used for other electrochemical interfaces, such as present in fuel cells,

electrolyzers, or batteries.

Adapted from: George, K.; van Berkel, M.; Zhang, X.; Sinha, R.; Bieberle-Hütter, A. Impedance

Spectra and Surface Coverages Simulated Directly from the Electrochemical Reaction

Mechanism: A Nonlinear State-Space Approach. J. Phys. Chem. C 2019, 123 (15), 9981–9992.

90 Introduction

1 Introduction

Solar energy conversion technologies will play a crucial role in satisfying the global demand

for clean and sustainable energy. In particular, the conversion of solar energy into chemical

energy is a promising path.1 Photo-electrochemical cells (PEC) are a possible solution to

perform this conversion.2 Due to the intermittent nature of solar irradiation, cost-effective

storage of energy is very important for solar energy conversion devices. PECs have an

advantage here compared to other solutions as they convert solar energy directly into storable

fuels.3,4 However, the conversion efficiencies of PECs using earth-abundant materials need to

be significantly improved such that they can be commercialized. This calls for specific research

towards identifying the limiting processes at the electrochemical interface and improving their

efficiency.

In a PEC, water is split into hydrogen and oxygen at its electrodes using solar energy. The

anode of a PEC is generally made of a semiconductor material (binary metal oxides, such as

TiO2,5 Fe2O3,6 WO3

7 or complex metal oxides, such as BiVO4 8) which generates electron-hole

pairs under illumination. The holes move towards the semiconductor-electrolyte interface,

where they oxidize the water to form oxygen. This is called the oxygen evolution reaction

(OER). Meanwhile, the electrons move to the back contact and further to the counter

electrode where they reduce water to form hydrogen (hydrogen evolution reaction, HER). Of

these two half-reactions, the OER is a more complex process since it requires the transfer of

four electrons.9 This exchange of electrons takes place in several steps and results in various

intermediate species.

Several experimental and theoretical approaches are proposed in the literature to improve

our understanding of PEC in view of identifying the processes that limit the performance of

PECs.10,11 These processes consist of a combination of thermodynamics, semiconductor

properties, and reaction kinetics.

The thermodynamics of the intermediate species are mostly studied in theory using density

functional theory (DFT) by calculating the free energies of formation of intermediates and the

overpotentials.11–15 Additionally, DFT is used for calculating semiconductor properties, like

bandgaps, band edge positions16,17, as well as the effect of doping, vacancies, or surface

orientation on the OER overpotential.18–20 The reaction kinetics of solid-water interfaces are

studied by molecular dynamics (MD)21–23 simulations. These theoretical approaches have

helped in understanding the behavior of electrode materials at atomistic and molecular scale.

A recent review by Zhang et al.24 summarizes the different approaches and results.

Experimentally, PEC interfaces are in the first instance characterized by current-voltage

curves, which allow for direct assessment of the overpotential. The overpotential is

determined by the thermodynamics, semiconductor properties, and the kinetics at the

interface. The kinetics of processes happening at the electrodes are studied by analyzing

Chapter 2 91

electrochemical impedance spectra (EIS)25,26 at single operating points. The measured EIS data

is usually fitted to electrical circuits consisting of resistances, capacitances, and inductances,

which are called the equivalent circuit models.27 These equivalent circuit elements are

attributed to physical and chemical processes at the electrochemical interface, such as the

electrical double layer, charge transfer reactions, space-charge layer, and external circuit

contacts.28,29 However, there exists no direct relation between the electrical quantities and

physical and chemical processes at the interface; the connection to individual reaction steps

and intermediate species is missing.

An alternative approach in the theoretical study of PEC is based on analytical models 30–32

which use semiconductor properties along with a thermodynamic single-step reaction for the

OER. These studies allow to predict the overall performance of the cells under given operating

conditions and consider the semiconductor properties, such as carrier generation, charge

transport, recombination, charge transfer, band bending, and the Helmholtz layer4,33–36.

However, as only a single step OER mechanism is considered, the full thermodynamics and

kinetics of the intermediate species are not considered.

In reality, however, intermediate species are present and were also proven experimentally

by methods, such as transient absorption spectroscopy (TAS)37, Fourier transform infrared

spectroscopy (FTIR)38,39, and transient (optical) grating spectroscopy (TGS)40. There is still an

ongoing debate in the literature about which reaction paths are of importance24,41, which

intermediate reaction steps are rate-limiting24, and whether intermediate species exist long

enough to be observed in experiments. However, to answer these fundamental questions it is

crucial to arrive at an approach that combines thermodynamics, the reaction kinetics of the

multi-step reactions, and semiconductor properties in a way that the outcome of such a model

can be compared directly to experimental observations. Such an overall approach can only be

achieved by considering the microkinetics, which has been recognized in the literature as

highly necessary.42,43 Exner et al.44 summarized that “microkinetics is of course the missing

link for critical theory/experimental comparison”.

To close this gap, we propose here a new approach to model electrochemical data and to

reproduce experimental data directly from theory. This approach combines DFT and

microkinetics with the Gerischer model45 of electron transfer for semiconductors. Thereby,

we demonstrate for the first time that measurable quantities, such as onset potential and

electrochemical impedance, can be simulated based on a pure electrochemical model.

Additionally, our approach allows for the calculation of the coverage of intermediate species

which is currently experimentally not measurable. Semiconductor properties, such as the

valence band position and hole density are included in our model and it can be studied how

they affect the EIS, overpotential, and coverage of intermediate species. The model itself has

been formulated as a nonlinear state-space model, which significantly simplifies the analysis

and simulations due to the availability of standard tool boxes46,47. The model is built using

92 Model and Method

electrochemical reactions derived from the literature. Different reaction mechanisms can be

easily implemented which is a tremendous advantage of this approach when it comes to

identifying the limitations at electrochemical interfaces using theory/experiment comparison.

The schematic representation of the state-space model of our electrochemical system is

shown in Figure 1.

Figure 1 Representation of the state-space model of an electrochemical system. The input variable is the applied voltage, the output variable is the current density, and the state variables are the concentration of intermediate species from mass balance equation.

It is important to note that this work is in part inspired by previous, preliminary microkinetic

modeling studies that were carried out on metals (not on semiconductors). These include a)

microkinetic simulations of multi-step Oxygen Reduction Reactions (ORR) by Hansen et al.48;

these simulations were combined with DFT and MD simulations; b) microkinetic simulations

of the cathodic and anodic reactions in solid oxide fuel cells (SOFC) by Mitterdorfer et al. 49

and Bieberle et al.50, respectively. Additionally, different methods for identifying the reaction

rates have been discussed in the literature based on microkinetic modeling and Butler-Volmer

theory for metallic electrodes.51–53

In summary, the novel approach that we introduce in this study is a bridge between first-

principle calculations and experimental measurements for semiconductor electrodes. It

combines thermodynamics, semiconductor properties, and reaction kinetics in one model.

The model simulates quantities that are measured in experiments and enable the calculation

of experimentally unavailable data, such as surface coverages of intermediate species. The

chapter is divided into two parts: a) model and method and b) a case study on the hematite

(Fe2O3)-water interface.

2 Model and Method

This section introduces the microkinetic model and the corresponding nonlinear state-space

model. Concrete values of parameters are not given here but will be discussed in section 3

with the case study of the hematite (Fe2O3)-water interface.

Chapter 2 93

2.1 Mechanism of water oxidation

The first step in model construction is to choose the mechanism of OER. In an electrochemical

cell, the electrolyte can be acidic or alkaline. Depending on the pH of the electrolyte, OER can

proceed in two different ways. In an acidic environment, the OER is given by24

2𝐻2𝑂 + 4ℎ+ → 𝑂2 + 4𝐻

+ (1)

and in an alkaline environment it is54

4𝑂𝐻− + 4ℎ+ → 𝑂2 + 2𝐻2𝑂 (2)

These overall reactions can proceed via different multistep mechanisms. Since OER involves

the transfer of four electrons/holes, it has been proposed in the literature that the entire

reaction consists of four single charge-transfer steps. A detailed review of different

mechanisms that have been suggested in the literature can be found elsewhere.24 In this

study, reactions in an alkaline environment are considered and the mechanism proposed by

Hellman et al.55 is chosen. This mechanism is based on the multistep OER proposed earlier by

Rossmeisl et al.13 The four-step electron transfer reactions in the alkaline environment are

∗ + 𝑂𝐻− + ℎ+𝐾b1⇌𝐾f1 𝑂𝐻ad (3)

𝑂𝐻ad + 𝑂𝐻− + ℎ+

𝐾b2⇌𝐾f2 𝑂ad + 𝐻2𝑂 (4)

𝑂ad + 𝑂𝐻− + ℎ+

𝐾b3⇌𝐾f3 𝑂𝑂𝐻ad (5)

𝑂𝑂𝐻ad + 𝑂𝐻− + ℎ+

𝐾b4⇌𝐾f4 𝑂2,ad + 𝐻2𝑂 (6)

Here * represents an adsorption site and the subscript ad means that the species are

adsorbed on the surface. Thus, 𝑂𝐻ad, 𝑂ad, 𝑂𝑂𝐻ad, and 𝑂2,ad are the intermediate species

adsorbed on the surface during the OER. The forward and backward reaction rates of these

charge transfer reactions are represented by 𝐾fi and 𝐾bi, respectively, where 𝑖 = 1 to 4. After

adsorbed oxygen (𝑂2,ad) is formed at the site, it desorbs (𝑂2,des) from the surface at a rate of

𝐾f5 which is given by

𝑂2,ad →𝐾f5 𝑂2,des + *

(7)

This step does not involve charge transfer and, hence, the desorption rate 𝐾f5 is chosen as

a constant.

Once the mechanism is selected, the next step is to model these reactions such that the net

current due to charge transfer can be calculated. In order to do this, corresponding rates of

94 Model and Method

the multi-step reactions have to be known. For electron transfer reactions, rates can be

calculated based on the Butler-Volmer theory, the Marcus theory,56 or the Gerischer theory.57

The Butler-Volmer theory uses first-order reaction rates and is best suited for reactions

involving metallic electrodes.58 This has been used in the modeling of SOFC by Mitterdorfer et

al.,59 Bieberle et al.,50 and Hansen et al.48 However, for modeling semiconductor interfaces,

the Butler-Volmer theory is not suitable.58 Unlike metals, in the case of semiconductors, most

of the applied potential falls across the space charge layer and charge transfer occurs via the

conduction band or valence band.45 The Gerischer theory takes this into account and defines

separate expressions for the charge transfer rate for electron transfer via valence band and

conduction band. We, therefore, use the Gerischer theory in this study.

2.2 Calculation of reaction rates

An n-type semiconductor anode under reverse bias is considered for the model discussed

here. Hole transfer via the valence band is believed to drive the reaction at the semiconductor-

electrolyte interface. Hence, the Gerischer expression for the hole transfer via the valence

band is used. For calculating charge transfer rates for each intermediate step (Eq. 3 – 6), the

Fermi level of the redox system in the original expression is replaced with the redox level of

each intermediate species. Thus, forward and backward charge transfer rates for each

intermediate step, 𝑘fi and 𝑘bi , respectively, are calculated as60

𝑘fi = 𝑘v,max exp [ −(𝐸v − 𝐸F,redox,i

0 − 𝜆)2

4𝑘B𝑇𝜆] (8)

𝑘bi = 𝑘v,max exp [ −(𝐸v − 𝐸F,redox,i

0 + 𝜆)2

4𝑘B𝑇𝜆] (9)

where 𝑘v,max is a pre-exponential factor with the dimension [cm4/s],60 𝐸v is the energy at

the upper edge of the valence band of the semiconductor, 𝑘B is the Boltzmann constant, 𝑇 is

the temperature, 𝜆 represents the solvent reorganization energy,61 and 𝐸F,redox,i0 is the redox

potential of the 𝑖𝑡ℎ reaction.

The redox potential for each intermediate can be determined from Gibbs free energy

change of formation (𝛥𝐺i) of the corresponding intermediate species at the surface. The

relation between Gibbs free energy and redox potential is given as62

∆𝐺i = 𝑛𝐹𝐸F,redox,i0 (10)

where 𝑛 is the number of electrons transferred and 𝐹 is the Faraday constant. The values of

∆𝐺i are material dependent and are derived from DFT calculations, such as shown in Rossmeisl

et al.13 In Eq. 10, 𝐹 can be omitted as these DFT calculations give ∆𝐺i (𝑒𝑉) for single electron

transfer reactions.

The forward and backward current densities [A cm-2] are then calculated as60

Chapter 2 95

𝑗fi = 𝑒𝑘fi 𝑝s𝑐red,i (11)

𝑗bi = 𝑒𝑘bi 𝑁v𝑐ox,i (12)

where 𝑒 is the elementary charge of an electron, 𝑁v [cm-3] is the effective density of states

of the valence band, 𝑝s [cm-3] represents the hole density at the surface of the semiconductor,

𝑐red,i and 𝑐ox,i are the concentrations of reduced and oxidized intermediate species [cm-3],

respectively. The hole density increases exponentially as a function of applied potential u

given by60

𝑝s = 𝑝s0 exp (

𝑢

𝑘B𝑇) (13)

where 𝑝s0 is the equilibrium hole density at the surface in the dark. The concentrations of

intermediate species are calculated by solving the rate equations, which is explained in the

following section.

2.3 Rate equations and charge balance relations

The reaction steps given in Eq. 3-7 are used to formulate rate equations for all the

intermediate species adsorbed on the semiconductor surface assuming Langmuir adsorption

isotherm. These equations form a set of coupled nonlinear ordinary differential equations as

listed in Eq. 14 - 17.

��OH = 𝐾f1𝑥OH 𝜃ad − 𝐾b1𝜃OH − 𝐾f2𝜃OH𝑥OH + 𝐾b2𝜃O𝑥H2O (14)

��O = 𝐾f2𝑥OH 𝜃OH − 𝐾b2𝜃O𝑥H2O − 𝐾f3𝜃O𝑥OH + 𝐾b3𝜃OOH (15)

��OOH = 𝐾f3𝜃O𝑥OH − 𝐾b3𝜃OOH − 𝐾f4𝜃OOH𝑥OH + 𝐾b4𝜃O2𝑥H2O (16)

��O2 = 𝐾f4𝜃OOH𝑥OH − 𝐾b4𝜃O2𝑥H2O − 𝐾f5𝜃O2 (17)

𝜃ad = 1 − 𝜃OH − 𝜃O − 𝜃OOH − 𝜃O2 (18)

where 𝜃ad is a dimensionless quantity representing the fraction of free adsorption sites. The

value of 𝜃ad ranges between 0 and 1. All other 𝜃i are the fractional coverages of intermediate

species i, where i represents OH, O, OOH, and O2. The terms 𝑥OH and 𝑥H2O are the mole

fractions of hydroxyl ions and water in the bulk electrolyte, respectively. In Eq. 14 – 17, 𝐾fi

and 𝐾bi are defined as

𝐾fi = 𝑘fi 𝑝s (19)

𝐾bi = 𝑘bi 𝑁v (20)

The concentration is defined as the number of intermediate species adsorbed per site

which, by Eq. 3 - 6, relates to the number of holes transferred. Thus, the model uses fractional

concentrations of species per unit site. However, the current density is the collective hole

96 Model and Method

transfer rate from the multi-step reactions at each site on the surface. Therefore, the number

of adsorption sites (𝑁0) available at the electrode surface is necessary for the calculation of

the total current density. The current balance equations in Eq. 11 - 12 become

𝑗f = 𝑒𝑁0(𝐾f1𝜃ad + 𝐾f2𝜃OH + 𝐾f3𝜃O + 𝐾f4𝜃OOH)𝑥OH (21)

𝑗b = 𝑒𝑁0(𝐾b1𝜃OH + 𝐾b2𝜃O𝑥H2O + 𝐾b3𝜃OOH + 𝐾b4𝜃O2𝑥H2O ) (22)

𝑗 = 𝑗f − 𝑗b (23)

where 𝑗 [A cm-2] is the total current density and 𝑁0 is the density of adsorption sites at the

semiconductor surface [cm-3]. The rate equations and charge balance relations are then

modeled in a state-space form.

2.4 State-space model

The rate equations and charge balance relations can be formulated in a general nonlinear

state-space model, which results in 63 64

𝜕Θ(𝑡)

𝜕𝑡= 𝑓(Θ(𝑡), 𝑢(𝑡))

(24)

𝑱(𝑡) = 𝑔(Θ(𝑡), 𝑢(𝑡)) (25)

Here, Eq. 24 is called the state equation and Eq. 25 the output equation. In these equations,

Θ represents the set of state variables, u is the input variable and 𝑱(𝑡) is the output vector.

Together, Eq. 24 and Eq. 25 forms the general form of a state-space model. Comparing this

general form to the mass and charge balance equations (Eq. 14 - 18 and Eq. 21 - 23), it can be

seen that this set of equations forms a state-space model.

The fractional concentrations of intermediate species, 𝜃OH, 𝜃O, 𝜃OOH, 𝜃O2and 𝜃O2,des, are

the state variables (Θ) and the current density 𝑗 is the output (𝑱). The concentrations of

adsorbed species and current density vary with applied potential 𝑢, which is the input variable

in this system. The resulting model is a single input (applied voltage) - single output (current

density) model with four state variables (concentrations of four intermediate species). The

state-space model is implemented using MATLAB/Simulink65 and the resulting model is a

nonlinear state-space model. It is nonlinear because the carrier density at the surface varies

exponentially with the applied potential. The set of equations is solved along with the site

conservation constraint given in Eq. 18. From the solution, the coverage of different

intermediate species can be calculated for any applied potential.

2.5 Linearization of state-space model and impedance calculation

The state-space model can be used to simulate impedance spectra at different potentials

similar to experiments. In order to calculate the impedance, the model has to be linearized

Chapter 2 97

around the chosen operating point.63 The reaction rates in the model are written in the

expanded form using Eq. 13, 19, and 20. The input variable, state variables, and output are

defined as

𝑢 = 𝑢eq + �� (26)

Θ = Θeq + Θ (27)

𝑱 = 𝑱𝐞𝐪 + �� (28)

Here, 𝑢eq represents any equilibrium potential, Θeq represents the state variables at this

potential, and 𝑱𝐞𝐪 represents the corresponding output. The added terms, ��, Θ and ��

represent the perturbation of the respective variables around the equilibrium. The

perturbation of the state variable Θ is a vector given by

Θ = [��OH ��O ��OOH ��O2]𝑇

(29)

The linearization is calculated using a Taylor series expansion of Eq. 24 and Eq. 25 which is

truncated after the first-order derivatives. Thus, assuming �� and corresponding responses

Θ and �� to be small, the linearized model around the equilibrium point is obtained as

𝜕Θ

𝜕𝑡= 𝐴Θ + 𝐵�� (30)

�� = 𝐶Θ + 𝐷�� (31)

where,

𝐴 =𝜕𝑓

𝜕Θ|𝑢eq,Θeq

𝐵 =𝜕𝑓

𝜕𝑢|𝑢eq,Θeq

𝐶 = 𝜕𝑔

𝜕Θ|𝑢eq,Θeq

𝐷 = 𝜕𝑔

𝜕𝑢|𝑢eq,Θeq

(32)

The expressions for 𝐴, 𝐵, 𝐶, and 𝐷 are listed in Table. 1. In order to simplify these

expressions, we define the term

𝑈eq = 𝑝s0 𝑒𝑥𝑝 (

𝑢eq

𝑘B𝑇) (33)

Table 1. Expressions for matrix coefficients from linearization in terms of intermediate reaction rates.

𝐴 =

[ −𝑈eq(𝑘f1 + 𝑘f2 )𝑥OH − 𝑁v𝑘b1 𝑁v𝑘b2 𝑥H2O − 𝑈eq𝑘f1

𝑥OH −𝑈eq𝑘f1 𝑥OH −𝑈eq𝑘f1 𝑥OH

𝑈eq𝑘f2 𝑥OH −𝑁v𝑘b2 𝑥H2O − 𝑈eq𝑘f3 𝑥OH 𝑁v𝑘b3 0

0 𝑈eq𝑘f3 𝑥OH −𝑁v𝑘b3 − 𝑈eq𝑘f4 𝑥OH 𝑁v𝑘b4 𝑥H2O

0 0 𝑈eq𝑘f4 𝑥OH −𝐾f5 − 𝑁v𝑘b4 𝑥H2O]

98 Case study: Hematite – water interface

For calculating the impedance spectra, an input-output relation in the frequency domain

has to be derived. This is done by applying Laplace transform (ℒ) on Eq. 30 and Eq. 31 and

solving the resulting equations to get a relation between output and input variable given by47

��(𝑠)

��(𝑠)= 𝐻(𝑠) = 𝐶(𝑠𝐼 − 𝐴)−1𝐵 + 𝐷 (34)

where 𝑠 represents the Laplace variable. 𝐻(𝑠) is measurable only on the imaginary axis.

Hence, we consider 𝑠 = 𝑖𝜔, where 𝑖 = √−1 and 𝜔 is the frequency of perturbation on the

input variable.66 ��(𝑠) and ��(𝑠) represent the Laplace transform of output and input variable,

respectively. 𝐻(𝑠) is called the transfer function matrix and in this case it represents

admittance 𝑌(s) of the system. The impedance 𝑍(𝑠) is defined as the reciprocal of admittance

𝑌(s) given by

𝑍(𝑠) = 𝑌(𝑠)−1 = 𝐻(𝑠)−1 (35)

This expression allows generating impedance spectra directly from electrochemical

equations which is a novelty for PEC interfaces and electrochemical interfaces in general.


In this section, we demonstrate the implementation of the developed model for hematite

(Fe2O3)-water interface. Hematite is a widely studied photoanode material because of its

abundance, low cost, and non-toxicity.6,67,68 Hematite is stable over a wide pH-range and has

a suitable bandgap (2.1 eV) for water oxidation under visible light.69,70 Theoretically, PEC cells

made with hematite photoanodes can reach an efficiency of 15%,67 which along with the

above-mentioned factors make hematite a suitable material for PEC anodes. However, under

experimental conditions, hematite shows lower efficiency compared to the theoretical

predictions, most likely due to sluggish reaction kinetics at the hematite-water interface and

due to the short hole diffusion length (2-4 nm).6 It is therefore of utmost interest to

𝐵 =𝑈eq

𝑘B𝑇

[ (𝑘f1 𝑥OH𝜃s

𝑒𝑞− 𝑘f2 𝑥OH𝜃OH

𝑒𝑞 )

(𝑘f2 𝑥OH𝜃OH𝑒𝑞− 𝑘f3 𝑥OH𝜃O

𝑒𝑞)

( 𝑘f3 𝑥OH𝜃O𝑒𝑞− 𝑘f4 𝑥OH𝜃OOH

𝑒𝑞)

(𝑘f4 𝑥OH𝜃OOH𝑒𝑞) ]

𝑇

𝐶 = 𝑁0 𝑞e

[ −𝑘b1 𝑁v + (−𝑘f1 + 𝑘f2 )𝑈eq

−𝑘b2 𝑥𝐻2𝑂𝑁v + (−𝑘f1 + 𝑘f3 )𝑈eq

−𝑘b3 𝑁v + (−𝑘f1 + 𝑘f4 ) 𝑈eq

−𝑘b4 𝑥𝐻2𝑂𝑁v − 𝑘f1 𝑈eq ] 𝑇

𝐷 = 𝑈eq𝑁0𝑞e

𝑘B𝑇[𝑘f1 𝜃s

𝑒𝑞+ 𝑘f2 𝜃OH

𝑒𝑞+ 𝑘f3 𝜃O

𝑒𝑞+ 𝑘f4 𝜃OOH

𝑒𝑞]

Chapter 2 99

understand the limitations at the (Fe2O3)-water interface. The implementation of the

hematite-water interface in this chapter is done by substituting hematite-specific parameters

into the model that was developed in section 2. The hematite (110) surface is used in this

study since this surface has been observed to be the most active surface according to both

theoretical11 and experimental studies.71

In experimental studies, measurements are done in both dark and illuminated conditions.72,73

The OER mechanism remains the same irrespective of whether the reactions are taking place

under illumination or in the dark. Regarding the kinetics at the interface, mainly the number

of electron-hole pairs increases during illumination. Hence, the model itself does not change

and can be used for simulation of electrochemical data under illumination and in dark

conditions. However, for simulating EIS under illumination the effects of light on the

semiconductor bulk also has to be taken into account. This needs further analysis and is

therefore planned for the future.

3.1 Input parameters

There are different material dependent and system-dependent parameters needed for the

calculation of the reaction rates. The parameters used in the model are listed in Table. 2.

The concentration of 𝑂𝐻− ions in the electrolyte solution is calculated from the pH-value of

13.8 that is used in experiments. In order to investigate the reaction kinetics and to calculate

the redox potential for each intermediate (Eq. 10), we use the Gibbs free energies calculated

Table 2. Description of parameters used in the model with values used for simulating hematite-water

interface.

Parameter Description Value

𝑘v,max Rate constant pre-exponential factor for valence band

hole transfer

10-16 cm4s -1 74

𝑁v Density of energy states at the upper edge of the

valence band

1022 cm-3 75

𝜆 Solvent reorganization energy 1 eV 45,76

𝐸v Energy at the upper edge of valence band 2.4 eV 67

𝐸F,redox0 Redox potential of the species involved from DFT calculation

𝑢 Applied potential 0 - 1.8 V vs RHE

𝑁0 Number of adsorption sites calculated for hematite

(110) surface

2.43x 1015 cm-3

pH pH of the solution 13.8

𝑇 Temperature 298 K

𝐾f5 Rate of desorption 108 s-1 48


by Zhang et al.11 on Fe2O3 (110) surface (Table 3). These DFT calculations were done for the

solid-gas interface and do not consider the solid-liquid interface present in the experiments.

Additionally, the Gibbs free energies from DFT are calculated for the case of zero bias potential

at the surface. For any applied bias at the interface, a correction has to be made by subtracting

the bias potential value from the DFT calculated value.13 At the electrode-electrolyte interface,

there is a bias due to the potential drop across the Helmholtz layer.77 Therefore, to

accommodate this, the value of the Helmholtz potential is subtracted from the free energy

values in Table 3 in the model.

Table 3. DFT calculated Gibbs free energies for reaction intermediates in OER steps on Fe2O3 (110) surface used

for calculating reaction rates.11

OER Step ΔG (eV)

OH adsorption 1.461

O adsorption 2.011

OOH adsorption 1.204

O2 adsorption 0.239

Note that the reaction rates do not change with pH since the band positions and redox

potentials shift to the same extent with a change in pH.2 The number of adsorption sites (𝑁0)

is obtained from the geometry of hematite (110) surface used for DFT analysis. This is done by

calculating the number of atoms present per unit area of the optimized hematite surface. We

consider all the atoms on the Fe2O3 surface to act as adsorption sites for reaction

intermediates. Experimental electrodes usually do not have a flat surface. Due to surface

roughness, the density of adsorption sites per unit geometric area of the electrode is larger

than that of the flat surface. In order to accommodate the surface roughness in the

simulations, the density of active sites on the surface (𝑁0) calculated from flat surface is

multiplied by a constant factor. A multiplication factor of 5 is used for the simulations in this

case study. The hole density at the surface at equilibrium in the dark, 𝑝s0, is calculated using

carrier density equations for doped semiconductors.78

3.2 Assumptions

For this case study, we use the following assumptions:

- All reactions are considered to take place in the dark and the reactions proceed with

the application of an external potential.

- Any change in applied potential falls across the electrode only and the potential drop

across the Helmholtz layer (𝑉H) remains constant.2

- The pH of the solution and the temperature remain constant during the reaction.

- For calculating the reaction rates, pre-exponential factor (𝑘v,max) and solvent

reorganization energy (𝜆) are assumed to be the same for all the steps in OER.

Chapter 2 101

DFT calculations are based on the solid-gas interface and do not consider the solid-liquid

interface which is the real interface in experiments.

3.3 Simulated data from the electrochemical model

In this section, we show the calculation of current-voltage characteristics, coverage plots,

and impedance spectra from the developed electrochemical model.

3.3.1 Current-voltage characteristic

A linearly varying potential u from 0 to 1.8 V is chosen as input to the model. The current

density plot is obtained by plotting the output of the model (𝑗) against the applied potential.

For the simulation results to be similar to the experiments, the series resistance (𝑅s)

associated with the back contact, which leads to a potential drop, needs to be considered. The

potential drop associated with this series resistance is 𝑗. 𝑅s. Hence, for an applied potential of

𝑢, the effective potential available across the semiconductor-electrolyte interface will be 𝑢 −

𝑗. 𝑅s. This potential drop is accommodated in the model and for the simulations in this study,

an 𝑅s value of 30 Ohms is used. The calculated current density is plotted against the applied

input potential 𝑢 in Figure 2a. The plot shows an onset potential of around 1.7 V. The current

density plot from the model qualitatively compares well with the experimental dark current

measurements in the literature.72,79 We need to note that simulation results in Figure 2a

(current density and onset potential) depend on the reaction rates and input parameters in

Table 2 which are derived from DFT calculations and literature. For example, if a higher surface

hole density (𝑝s0) is chosen, the onset will take place at a lower applied potential. This trend

is similar to experimental results under illumination, as surface hole density is higher under

illumination, the onset will be at lower potentials.

3.3.2 Species coverage plot

Unlike the current-voltage characteristic, which is experimentally measurable, the coverage

of intermediate species cannot be obtained from measurements straightforwardly. However,

with our model, we can calculate the coverage of intermediate species at the surface based

on the theoretical reaction rates. Figure 2b shows the fractional coverage of intermediate

species adsorbed on hematite as a function of applied potential. Up to an applied voltage of

about 1.3 V, θ is 1 which means that all adsorption sites are free. At potentials higher than 1.3

V, adsorbed OH increases, and 𝜃 decreases. Between 1.5 V and 1.7 V, OH is the only species

adsorbed at the surface. At potentials higher than 1.7 V all the other intermediates O, OOH,

and O2 are formed. The adsorbed O and O2 are not visible in this plot since the coverages are

relatively small. This coverage plot is based on the theoretical reaction rates and the input

values used in the model. It proves that once the model is established, trends for the surface

coverages can easily be calculated which delivers data which is extremely challenging to obtain


experimentally. In particular, surface coverages can be scanned for different input values for

the electrochemical interface and for different electrochemical models. The trends of surface

coverages as a function of applied potential give novel insight into the kinetics at the interface.

Once the model parameters are optimized with experimental data, quantitative data can be

obtained as well.

Figure 2 (a) Current-voltage characteristic plotted using the nonlinear state-space model. The onset potential is

around 1.7 V which is close to the experimentally observed value. The onset potential depends on the reaction

rates and the input parameters; (b) Surface coverages of intermediate species adsorbed on the hematite surface

as a function of applied potential. 𝜃 is the fractional ratio of free adsorption sites available and 𝜃𝑖 is the fractional

coverage of intermediate species 𝑖. The concentration of species 𝑂 (𝜃𝑂) and 𝑂2 (𝜃𝑂2) are not visible as the

coverage is small compared to the other species; (c) Impedance spectrum calculated at 1.7 V from the linearized

state-space model. This impedance spectrum represents the impedance from interface reactions at 1.7 V,

according to the rates calculated using the Gerischer model, for the frequency range of 0.8 Hz to 30 kHz.

3.3.3 Electrochemical Impedance Spectrum (EIS)

Impedance spectra are calculated at different applied potentials by linearization of the

model at the specific potentials, as explained in section 2.5. Technically, EIS can be calculated

for any applied potential. The calculation requires corresponding equilibrium values of state

variables at that potential, i.e. fractional coverage of intermediate species, as derived in

section 2.5. For this, first, the potential for which the impedance spectrum is calculated is

given as a constant input to the nonlinear model. Then, the steady-state values of all the state

a b

c

Chapter 2 103

variables in equilibrium at this applied potential are calculated. These equilibrium values of

the state variables and the potential are substituted in the linearized model to calculate the

impedance spectrum at that specific potential. A representative EIS at a potential of 1.7 V (just

before the onset potential) is shown in Figure 2c in the frequency range of 0.8 Hz to 30 kHz.

This spectrum represents the impedance only from charge transfer reactions at the electrode-

electrolyte interface based on the assumed mechanism of OER (Eq. 3-6). It does not consider

other contributions, like impedance related to the back contact, semiconductor bulk,

trapping/de- trapping resistance of hole transfer from the valence band, which are part of

experimental spectra. Hence, for the comparison of simulated impedance from the model to

the experiments, other impedance contributions have to be added to the charge transfer

impedance part; this is discussed in section 3.5.

3.4 Model order reduction

Model order reduction is a technique that allows to simplify a model based on the behavior

of a system and the order of the transfer function of the model. We want to show in this

section, how model order reduction can be used to simplify the charge transfer reaction model

to determine reaction rate constants.

The EIS from the linearized model, as previously discussed, can be represented as a transfer

function. This transfer function is of rational form with numerator and denominator which are

polynomials in Laplace variable 𝑠. The highest degree of these polynomials in numerator and

denominator depends on the number of state variables (reaction intermediates). In our

current model, we have four state variables. This results in a rational polynomial in the

denominator and numerator with a degree of four. Hence, we call this a fourth-order transfer

function.

Figure 2b shows that at potentials below 1.7 V, adsorbed OH (𝜃OH) is the only intermediate

species that is present. Hence, at these operating points, technically the fourth-order transfer

function can be approximated using a first-order transfer function. In the following, an applied

potential of 1.65 V is chosen to demonstrate model order reduction.

The model is simplified, i.e., the order is reduced using singular value decomposition

method and using only the information belonging to significant singular values. This model

reduction algorithm is available in the MATLAB control system toolbox.80 From the analysis,

we found that at the potential of 1.65 V, the model order can be reduced to one. For

comparing the fit, Bode plots are generated from both the nonlinear state-space model

(𝑍sim) and the first-order model (𝑍red) (Figure 3). The relative error between the full model

and the reduced-order model is in the order of 10−3 for both magnitude (|Z|) and phase (𝜙).

These low values of relative error indicate that the impedance from the fourth-order model

at this voltage can be well approximated using a first-order transfer function at an applied

potential of 1.65 V.


Figure 3. Bode plot at an applied potential of 1.65 V from first-order approximate transfer function (reduced

model) compared against the fourth-order transfer function (full model). The relative errors are in the order of

10-3 for both magnitude and phase.

The coefficients of this first-order transfer function can be used for identifying the reaction

rates involving the OH intermediates (𝜃OH). However, an analytical expression of the first-

order transfer function involving these rates is necessary for the identification. In order to get

this analytical expression, the model is linearized using 𝜃OH as the only adsorbed species. This

gives

𝐴 = −𝑈eq (𝑘f1 + 𝑘f2 )𝑥OH − (𝑁v𝑘b1 ) (36)

𝐵 =𝑈eq

𝑘B𝑇(−𝑘f2 𝑥OHθOH

𝑒𝑞 + 𝑘f1 𝑥OH(1 − 𝜃OH

𝑒𝑞)) (37)

𝐶 = 𝑁0𝑞e(−𝑘b1 𝑁v + (−𝑘f1 + 𝑘f2 )𝑈eq) (38)

𝐷 =𝑈eq𝑁0𝑞e

𝑘B𝑇(𝑘f1 (1 − θOH

𝑒𝑞) + 𝑘f2 θOH

𝑒𝑞) (39)

The impedance of this system can then be expressed as a transfer function using Eq. 34 - 35

and is obtained as

𝑍red(𝑠) =𝑎𝑠 + 𝑏

𝑐𝑠 + 𝑑

(40)

where

𝑎 =𝑈eq𝑁0𝑞e

𝑘B𝑇 ((1 − 𝜃OH

𝑒𝑞) 𝑥OH 𝑘f1 + 𝜃OH

𝑒𝑞 𝑥OH 𝑘f2 )

(41)

Chapter 2 105

𝑏 =2𝑈eq𝑁0 𝑞e 𝑥OH

𝑘B𝑇 (𝑈eq𝑥OH (( 𝜃OH

𝑒𝑞− 1)(𝑘f1 )

2− 𝜃OH

𝑒𝑞(𝑘f2 )

2) − 𝑁v(1 −

𝜃OH𝑒𝑞)𝑘f1 𝑘b1 )

(42)

𝑐 = 1 (43)

𝑑 = (𝑈eq𝑥OH( 𝑘f1 + 𝑘f2 ) + 𝑁v 𝑘b1 )

(44)

Thus, a first-order transfer function (𝑍red) is obtained for impedance at an applied potential

of 1.65 V, which consists of only three reaction rates 𝑘f1 , 𝑘f2 and 𝑘b1 (Eq. 40 - 44). By fitting

this transfer function to experimental data at the same applied potential, the intrinsic reaction

rates 𝑘f1 , 𝑘f2 and 𝑘b1 can be identified directly from experimental measurements. For doing

so, the fitting can be formulated as an optimization problem in which the reaction rates are

varied until the simulated data matches the experimental data. The theoretically derived

reaction rates from the DFT calculations and the Gerischer model can serve as starting values

for this optimization. This fitting of the transfer function (Eq. 40 - 44) in the complex plane is

beyond the scope of this chapter.

Model order reduction is advantageous when it comes to the identification of rate constants

because a transfer function of lower order has fewer rate constants and is, therefore, easier

to identify. Furthermore, a parallel RC loop in an equivalent circuit also has a first-order

transfer function. Our analysis shows that the first-order model gives a good fit at low

potentials. This result validates the use of an RC parallel loop to represent charge transfer

impedance at low potentials (1.2 - 1.7 V in this case). At higher potentials, the order of transfer

function is higher because of multiple intermediates and a single RC loop is insufficient at such

potentials to represent the charge transfer impedance.

3.5 Simulation of extended EIS and comparison to experiment

As mentioned before, the experimentally measured EIS represents not only the charge

transfer reactions at the interface but additional contributions. Hence, to simulate an EIS

similar to experiments, these other contributions also have to be included. In principle, these

impedance contributions can be added to the nonlinear state-space approach as physical and

chemical models. A stitching algorithm was recently suggested by Weddle et al.81 for the case

of Li-ion batteries. In the current study, we use a simple equivalent circuit model to include

additional contributions (Figure 4).

The literature suggests different equivalent models for hematite.82,83 The common part in

these models is the series resistance 𝑅S, and a bulk capacitance, 𝐶bulk, in parallel with the

impedance from the electrochemical interface. The interface impedance is generally

represented by one or more R-RC loops either in series or parallel, attributed to different

processes taking place at the interface. We replace these equivalent circuit elements with the

impedance calculated from the linearized model (section 3.3.2) and call it 𝑍sim. To compare


simulated EIS to experimental EIS, 𝑅s = 30 Ω and 𝐶bulk = 3 𝜇𝐹 are used, which are in

agreement with values from the literature.3,79 Both 𝑅s and 𝐶bulk are kept constant in the

chosen applied potential range.

Figure 4 Equivalent circuit model of the hematite-water interface with impedance from the state-space model

represented as 𝑍𝑠𝑖𝑚. 𝑅𝑆 represents the series resistance and 𝐶𝑏𝑢𝑙𝑘 represents the bulk capacitance.

The EIS calculated using this model is shown in Figure 5. A potential range of 1.5 – 1.7 V and

a frequency range of 0.1 Hz to 30 kHz are chosen. Experimental EIS for the same potentials

and frequency range are also plotted. Experimental EIS was performed using a 3 electrode set-

up with a Pt wire counter electrode and an Ag/AgCl reference electrode in a 1 M NaOH

electrolyte solution as described in Sinha et al.84 The measurements were carried out in a

frequency range of 0.05 Hz to 300 kHz using a Biologic SP-150 potentiostat. The magnitude of

the modulation signal applied to the potential was 10 mV. The potential at which the EIS scans

were performed was increased step-wise by 23 mV between 1 V and 1.7 V versus RHE.

The Nyquist representation of both simulated and experimental EIS are shown in Figure 5a.

It can be seen that the model calculates the impedance arcs and features similar to the

experiments. To get a clear comparison of the frequency response, the Bode plot of the same

data are shown in Figure 5b. It is seen that the magnitudes of impedance and its variation over

different potentials (blue curves) and frequency are captured well by the model. Likewise, in

the phase plot (red curves), the frequencies corresponding to the position of the peaks from

the simulated plots are in good agreement with the corresponding experimental curves. The

only minor difference observed between the experimental and simulated data is the

depressed semi-circles in the experimental Nyquist plot and the concomitant spread of the

curve in the Bode phase plot due to the electrochemical heterogeneity of the measured

hematite surface85 as compared to the ideal (110) surface assumed in the model. Since the

added RC component values are kept constant, all the variations in the simulated plots at

different potentials are due to the impedance from the electrochemical model (𝑍sim).

Chapter 2 107

Figure 5 (a) Nyquist plots of impedance spectra from the simulation at potentials 1.5 V, 1.6 V, and 1.7 V compared

against experimental EIS at the same potentials. (b) Comparison between Bode representations of the same data

showing the variation of the absolute value of impedance and phase angle against the frequency of perturbation

between 0.1 Hz and 30 kHz.

The fact that the model can calculate impedance spectra similar to the experiment, with the

applied voltage as the only variable input, is remarkable. It implies that the electrochemical

interface data at any operating potential can be simulated with the model. Such a continuous

nonlinear description of an electrochemical system cannot be achieved by using traditional

equivalent circuit analysis, as it defines the system at discrete operating potentials. Thus, the

developed nonlinear state-space approach in this study captures the actual chemistry and

gives a continuous non-linear description of the system which is a milestone in the analysis of

electrochemical data.

4 Summary and Outlook

We have developed a new approach to calculate electrochemical data directly from

multistep reactions. The feasibility of the method is proven with a case study on a typical

interface in a photo-electrochemical cell, the α-Fe2O3 - electrolyte interface. Using the

developed state-space model, the current-voltage characteristics and electrochemical

impedance spectra were simulated. These two are also the main plots that are experimentally

measured in order to investigate such interfaces. The advantage of this approach is that 1) the

electrochemical data is fully simulated from an electrochemical model (no equivalent circuits,

no experimental input); 2) the data can be directly related to the underlying electrochemistry

b Experiment Simulation

Experiment Simulation a

108 Summary and Outlook

as it is simulated from an electrochemical model; 3) the model can simulate the coverage of

OER intermediates at the surface sites at different operating potentials; this data is extremely

challenging to obtain experimentally.; 4) the model is modular, such that other chemical and

physical processes like diffusion and illumination, can be added as well. Due to the generic

nature of our approach, it can be applied to different materials straightforwardly. Also, the

impact of different reaction mechanisms and parameters for different materials can be

studied quickly and easily.

As an outlook, we propose to integrate simulations and experiments for identifying reaction

rates. To do this, our model which currently considers only charge transfer reactions needs to

be extended to represent the entire electrochemical interface. A first step towards this is

already explained in section 3.5 where the developed state-space model is added as a circuit

component in a typical equivalent circuit model of an electrochemical interface in water

splitting. These equivalent circuit elements need to be replaced by physical and chemical

models that are integrated into the state-space model. Possibly, additional contributions to

the electrochemical interface are required as well. In a second step, the entire model can be

optimized for the reaction rates by fitting to experimental data. The theoretical reaction rates,

currently calculated by DFT and Gerischer model, serve as the best starting values for the

optimization. The reaction rates which are obtained after this optimization will be more

realistic than the theoretically derived ones as they are derived from a real system

(optimization with experimental data from the solid-liquid interface). Thus, the reaction rates

for intermediate reactions can be derived by using this method. This will facilitate the

identification of rate-limiting processes at semiconductor-electrolyte interfaces in a new

manner and unprecedentedly close to real systems under operation.

Acknowledgments

George acknowledges funding from the Shell-NWO/FOM “Computational Sciences for

Energy Research” PhD program (CSER-PhD; nr. i32; project number 15CSER021). Zhang and

Bieberle-Hütter acknowledge the financial support from NWO (FOM program nr. 147 “CO2

neutral fuels”) and M‐ERA.NET (project “MuMo4PEC” with project number M‐ERA.NET 4089).

Supercomputing facilities of the Dutch national supercomputers SURFsara/Lisa and Cartesius

are acknowledged. Van Berkel acknowledges that this work has been carried out within the

framework of the EUROfusion Consortium and has received funding from the Euratom

research and training program 2014-2018 under grant agreement No 633053. The views and

opinions expressed herein do not necessarily reflect those of the European Commission. The

fruitful discussions with researchers from the ELEC department of Vrije Universiteit Brussels,

especially with prof. dr. ir. Gerd Vandersteen, are acknowledged. Dr. Aafke Bronneberg is

gratefully acknowledged for reading the manuscript and giving valuable comments.

Chapter 2 109

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(71) Kment, S.; Schmuki, P.; Hubicka, Z.; Machala, L.; Kirchgeorg, R.; Liu, N.; Wang, L.; Lee, K.; Olejnicek, J.; Cada, M.; Gregora, I.; Zboril, R. Photoanodes with Fully Controllable Texture: The Enhanced Water Splitting Efficiency of Thin Hematite Films Exhibiting Solely (110) Crystal Orientation. ACS Nano 2015, 9 (7), 7113–7123. https://doi.org/10.1021/acsnano.5b01740.

(72) Iandolo, B.; Hellman, A. The Role of Surface States in the Oxygen Evolution Reaction on

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(75) Cendula, P.; Tilley, S. D.; Gimenez, S.; Bisquert, J.; Schmid, M.; Grätzel, M.; Schumacher, J. O. Calculation of the Energy Band Diagram of a Photoelectrochemical Water Splitting Cell. J. Phys. Chem. C 2014, 118 (51), 29599–29607. https://doi.org/10.1021/jp509719d.

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(77) Hankin, A.; Alexander, J. C.; Kelsall, G. H. Constraints to the Flat Band Potential of Hematite Photo-Electrodes. Phys. Chem. Chem. Phys. 2014, 16 (30), 16176–16186. https://doi.org/10.1039/C4CP00096J.

(78) Gaudy, Y. K.; Haussener, S. Utilizing Modeling, Experiments, and Statistics for the Analysis of Water-Splitting Photoelectrodes. J. Mater. Chem. A 2016, 4 (8), 3100–3114. https://doi.org/10.1039/C5TA07328F.

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(84) Sinha, R.; Tanyeli, İ.; Lavrijsen, R.; van de Sanden, M. C. M.; Bieberle-Hütter, A. The Electrochemistry of Iron Oxide Thin Films Nanostructured by High Ion Flux Plasma Exposure. Electrochim. Acta 2017, 258, 709–717. https://doi.org/https://doi.org/10.1016/j.electacta.2017.11.117.

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Chapter 3 115

Chapter 3: Understanding the impact of different types of

surface states on photoelectrochemical water oxidation: A

microkinetic modeling approach

Abstract

Oxygen evolution reaction (OER) has been identified as one of the performance-limiting

processes in solar water splitting using photoelectrochemical (PEC) cells. One of the reasons

for the low OER performance is related to the existence of different types of surface states at

the semiconductor-electrolyte interface: recombining surface states (r-SS) and surface states

due to intermediate species (i-SS). Since the impact of surface states on OER is still under

debate, we investigate how different types of surface states affect PEC water oxidation and

how they impact experimental measurements. In a new computational approach, we combine

a microkinetic model of the OER on the semiconductor surface with the charge carrier

dynamics within the semiconductor. The impact of r-SS and i-SS on the current-voltage curves,

hole flux, surface state capacitance, Mott-Schottky plots, and chopped light measurements

are systematically investigated. It is found that a) r-SS results in a capacitance peak below the

OER onset potential, while i-SS results in a capacitance peak around the onset potential; b) r-

SS leads to an increase in OER onset potential and a decrease in saturation current density; c)

r-SS leads to Fermi level pinning before the onset potential, while i-SS does not result in Fermi

level pinning; d) a smaller capacitance peak of i-SS can be an indication of lower catalytic

performance of the semiconductor surface. Our approach in combination with experimental

comparison aids in separating the impact of r-SS and i-SS in PEC experiments. We conclude

that r-SS reduces OER performance and i-SS mediates OER.

Submitted as Kiran George, Tigran Khachatrjan, Matthijs van Berkel, Vivek Sinha, and Anja

Bieberle-Hutter. Understanding the impact of different types of surface states on

photoelectrochemical water oxidation: A microkinetic modeling approach

116 Introduction

1 Introduction

Water splitting using sunlight is a promising path for storing solar energy in chemical bonds

and thereby producing ‘solar fuels’.1 A potential cost-effective method to produce solar fuels

is by using a photoelectrochemical (PEC) cell.2 In a PEC cell, hydrogen is generated at the

cathode, and oxygen is generated at the anode.3 The half-reactions are called hydrogen

evolution reaction (HER) and oxygen evolution reaction (OER), respectively. Among the two

half-reactions, OER accounts for most of the overpotential required for water splitting and is

found to be the performance limiting reaction in PEC water splitting.4,5 Hence, current

research focuses on improving OER and thereby improving the efficiency of PEC water

splitting.6–8 The photoanode of a PEC is typically made of a semiconductor with a suitable

bandgap which provides the thermodynamic potential required for water splitting.9 Fe2O3,

TiO2, WO3, and BiVO4 are some of the metal oxide photoanode materials that are studied in

the literature.10–15 However, the efficiencies of the PEC photoanodes using these materials are

not high enough for commercialization of PEC yet.2

Among the different photoanode materials, Fe2O3 (hematite) is studied extensively in the

literature due to its stability, abundance, low cost, and non-toxicity.9,16 Theoretically, a PEC

cell with a hematite photoanode can achieve a solar to hydrogen conversion efficiency of

around 15.5%; however, practically reported efficiencies are much lower.16,17 One of the

reasons for this lower performance compared to theoretical prediction is attributed to the

existence of mid-band gap energy states, so-called surface states.7,18 In the literature, two

types of surface states are reported in photoanodes. The first type is related to defects at the

surface of the semiconductor, such as vacancies or dangling bonds, which result in the

recombination of charge carriers.3 This type of surface state is referred to as ‘recombining

surface state (r-SS)’.19–21 The second type is due to the presence of adsorbed species on the

surface. Such surface states are observed only during water oxidation and are absent when a

hole scavenger is added to the electrolyte.22 These surface states are assumed to be the

surface intermediates that are formed during OER. They are referred to as ‘surface states due

to OER intermediates (i-SS)’.19–21 These surface states play an important role in the

performance of photoanodes, and hence, a thorough understanding of the function and

impact of surface states is necessary .20

When a potential is applied across an interface having surface states, a fraction of the

applied potential is lost in the charging of the surface states.23 The potential range in which

the surface states are getting charged, band bending of the semiconductor does not occur;

hence, the Fermi level remains pinned.24 Fermi level pinning (FLP) is usually identified from

Mott-Schottky analysis.25,26 FLP and the potential over which the surface state charging occurs,

is seen in Mott-Schottky analysis as a plateau region.

Chapter 3 117

FLP due to both r-SS and i-SS has been reported in the literature. For example, Zandi et al.7,25

have reported FLP at applied potentials lower than the onset potential for Fe2O3. After

selective removal of deleterious surface states (in this context, r-SS) using controlled annealing

of the electrode, the FLP was no longer visible in the Mott-Schottky plot.7,25 Similar studies

have identified such FLP at applied potentials lower than the onset potential.27 In the case of

i-SS, Klahr et al.22 identified FLP occurring around the OER onset potential. From the

electrochemical impedance spectroscopy measurements, a capacitance was observed around

the same potential range. This capacitance was seen only during water oxidation and was

absent during measurements with a hole scavenger.22 Hence, the capacitance and FLP was

attributed to i-SS. In a similar study, positive shifts in the Mott-Schottky plots were observed

with an increase in illumination intensities and were associated with FLP due to the charging

of i-SS.26 Based on these observations, it is believed that i-SS leads to FLP around the OER

onset potential.

Thus, the existence of two distinct types of surface states has been pointed out in the

literature.7 However, the impact of these surface states on the performance of OER is still

debated.28,29 One of the most accepted explanations is that the surface states reduce the

overall performance of OER.22,27 On the contrary, some studies suggest that the surface states

mediate OER.21,26,30 In a recent experimental study, Shavorskiy et al.31 proposed that surface

states do not play a major role in mediating OER. Conclusively, these different views suggest

that the role of surface states is still a topic of debate in the field of PEC.

From experimental observations, it is challenging to pinpoint the individual and combined

impact of surface states on the efficiency of OER. Particularly, the impact of i-SS on the

performance of OER is difficult to analyze. Despite some promising operando studies,

experimental data regarding the impact of OER intermediates are still largely absent due to

experimental challenges associated with the identification of OER intermediates.30,32

However, using modeling and simulations clear insights about each of these surface states can

be obtained by analyzing the sensitivity of measurements to the model parameters associated

with each surface state.

The goal of our study is to pinpoint the impact of r-SS and i-SS on PEC data, such as j-V

curves, surface state capacitance, Mott-Schottky plots, hole flux, and chopped light

measurements. To analyze the impact of i-SS on the PEC data, it is important to include the

elementary steps in OER and the adsorbed OER intermediates in the model. The charge

transferred in the formation of the adsorbed OER intermediates is analogous to charge

carriers getting trapped at the surface. Previously, we developed a microkinetic model of OER

specifically for semiconductor electrodes.33 In the current paper, we add illumination and

charge carrier dynamics to the same framework of the microkinetic model of OER. For

simulating r-SS, a monoenergetic state with energy 𝐸T and density 𝑁T (𝑇 stands for ‘trap’) is

assumed within the bandgap of the semiconductor.34 Thus, we present in this paper an

118 Theory and method

extended model to George et al.33 which brings together the elementary steps in OER and

charge carrier dynamics within the semiconductor. Modeling of charge carrier dynamics has

been done before in the literature.35,36 However, the charge carrier dynamics has so far not

been coupled to the multistep mechanism of OER at the interface.

The impact of the presence of r-SS and i-SS on electrochemical data is pointed out based on

the simulated data. The presence of r-SS results in an increase in the onset potential and

reduces the saturation photocurrent density. We show a direct relationship between the

coverage of OER intermediates and capacitance due to i-SS. From the Mott-Schottky analysis,

we find that the capacitance due to i-SS does not necessarily result in the FLP observed around

the onset potential as reported in the literature. On the contrary, the FLP observed in

experiments around the onset potential is found to be related to the IR drop over series

resistance which drastically increases around the onset potential. The approach presented in

this work shows how a model combining multiple steps in OER and charge carrier dynamics

contributes to a clear understanding of the impact of surface states on typical PEC data.

2 Theory and method

As the OER involves the transfer of four charge carriers, it is proposed that the OER proceeds

through four intermediate steps, each step involving the transfer of a single charge carrier.37,38

In the literature, different mechanisms have been proposed for the electrochemical

mechanism of OER.38–40 Previously, in George et al.33, we have simulated the hematite-

electrolyte interface using a microkinetic model of OER based on the four-step

electrochemical mechanism of OER on the semiconductor surface.33 The model related PEC

data, such as current density and electrochemical impedance spectra to the kinetics of

elementary reactions in OER. The charge carrier density at the surface was simplified as an

exponential function of applied potential. In this work, we extend this microkinetic model of

OER by adding the charge carrier dynamics explicitly. The general approach adopted in the

modeling is summarized in Figure 1. The input-output relationship is similar to that of

experiments: applied potential (𝑉applied) and illumination intensity (𝐼0) are the input to the

model and current density (𝑗) is the output.

Chapter 3 119

Figure 6 General approach for simulating the hematite-electrolyte interface: coupling of a microkinetic model

with the charge carrier dynamics within the semiconductor; applied potential (𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑) and illumination intensity

(𝐼0) are the input to the model and current density (𝑗) is the output.

For ideal semiconductor electrodes, OER can occur by charge transfer via the valence band

(VB) and/or the conduction band (CB).41 For experimental semiconductor electrodes, the

literature has reported about intrinsic mid-band gap states or r-SS at the semiconductor-

electrolyte interface (SEI).42 The r-SS is defined in our model as a monoenergetic state at an

energy level of 𝐸T within the bandgap with a surface state density denoted by 𝑁T.34 All the

charge transfer pathways, namely via VB, CB, and r-SS are considered for OER to occur and

are denoted by the three double-sided arrows in Figure 1. The probability of OER occurring via

VB, CB, and r-SS depends on the kinetics of the multiple steps in OER and the charge carrier

concentrations at each of these bands. In the approach shown in Figure 1, the microkinetic

model considers the kinetics of the multiple steps in OER; the charge carrier concentration is

calculated by modeling the charge carrier dynamics within the semiconductor.

2.1 Microkinetic Model

We have previously developed a microkinetic model of OER specifically for semiconductor

electrodes.33 To give a quick review, the microkinetic model was developed based on the

multi-step mechanism of OER proposed by Rossmeisl et al.38 This mechanism involves OH, O,

OOH, and O2 as the adsorbed intermediates.38,43 Based on the multiple steps in OER, the rate

of formation of the adsorbed OER intermediates is written as a set of ordinary differential

equations. Solving this set of differential equation for a single site on the semiconductor

surface gives the fractional coverage of each OER intermediate, represented as 𝜃OH, 𝜃O, 𝜃OOH,

and 𝜃O2. The charge transfer in this model was assumed to occur via the VB. The rate constant

for charge transfer via VB is calculated using Gerischer theory for semiconductors.41,44 Based

on the charge transferred across the interface during the multistep reactions, the current

density due to the reaction is calculated. More details about the model can be found in George

et al.33


In this paper, we use the same approach for calculating the fractional coverage of OER

intermediates and the current density due to the reactions. The electrochemical mechanism

of OER under alkaline pH is used for developing the microkinetic model (supporting

information S1.1). The rate of formation of OER intermediates is calculated assuming charge

transfer via VB, CB, and r-SS. As mentioned earlier, the presence of r-SS is a deviation from the

ideal surface of the photoanode. For this reason, the sites associated with r-SS (henceforth

denoted as r-SS sites) are different from those of the sites on the ideal photoanode surface

(henceforth denoted as ideal sites). In the model, the OER at r-SS sites and ideal sites are

treated separately and the intermediate species adsorbed at r-SS sites are assumed to not

interact with OER intermediate at the ideal adsorption sites. The OER occurring at the ideal

sites involve charge transfer via VB and CB as in the case of an ideal semiconductor. In the

case of OER at r-SS sites, the charge transfer occurs only via r-SS.

The rate of formation of OER intermediates at the ideal site and the rate constants for

charge transfer via VB and CB are given in the supporting information S1.2. The rate constants

are defined based on the Gerischer model of charge transfer.41 The rate equations for OER at

r-SS sites and the rate constant for charge transfer via r-SS can be calculated similarly to that

of the VB and CB as given in the supporting information S1.3.

By solving the rate equations, the fractional coverage of the four OER intermediates at the

ideal sites can be calculated (𝜃OH, 𝜃O, 𝜃OOH, and 𝜃O2). Similarly, the fractional coverage of OER

intermediates at r-SS sites, denoted by 𝜃𝑇OH, 𝜃𝑇O, 𝜃𝑇OOH, and 𝜃𝑇O2, can be obtained by the

solution of the set of equations in S1.3. For solving the rate equations, it is necessary to input

the charge carrier concentrations at each energy band, which depends on the charge carrier

dynamics within the semiconductor.

2.2 Charge carrier dynamics

The processes that belong to the charge carrier dynamics within the semiconductor are

illustrated in Figure 7. Under illumination (𝐼0), electrons (red circles) in the semiconductor are

excited from the valence band to the conduction band leaving holes (blue circles) in the

valence band. Under an applied potential (𝑉applied), the electrons move towards the back

contact and holes move towards the semiconductor-electrolyte interface (SEI). Some of these

holes recombine directly with the electrons and some of the holes can get trapped at r-SS

where they recombine with electrons from the conduction band. In Figure 7, 𝑘rec represents

the rate of direct recombination of holes and electrons in the space charge region,45 𝑘p

represents the rate at which holes get trapped in r-SS, and 𝑘n represents the rate at which

electrons recombine with holes in r-SS. As mentioned in the previous section, the charge

carriers at the surface take part in OER via VB, CB, and r-SS. The rate constants 𝐾vf,b, 𝐾cf,b and

𝐾tf,b represent the forward and backward rate constants for charge transfer via VB, CB, and r-

SS, respectively. The rate at which charge transfer occurs via VB, CB, and r-SS can affect the

Chapter 3 121

carrier concentrations at respective energy levels. The cumulative effect of all these processes

determines the charge carrier concentrations at the surface. In this section, we calculate the

concentration of holes at the surface (𝑝s), the concentration of electrons at the surface (𝑛s),

and the fill factor of electrons (𝑓T) in r-SS.

Figure 7 Schematic of charge carrier dynamics under illumination within the space charge region showing

recombination, trapping, and oxygen evolution reaction via VB (blue), CB (red), and r-SS (green). The red circles

represent electrons and the blue circles represent holes.

The flux of holes (𝐽G) to the surface for an illumination intensity of 𝐼0 is given by the Gartner

equation as46

𝐽G = 𝐼0(1 −

exp(−𝛼𝑊sc)

1 + 𝛼𝐿p)

(1)

where 𝛼 represents the absorption coefficient at a given wavelength, 𝑊𝑠𝑐 the width of the

space charge region, and 𝐿p the minority carrier diffusion length. The width of the space

charge region is related to the potential across the space charge region (𝑢sc) given by3

𝑊sc = √2𝜖r𝜖0𝑒𝑁D

(𝑢sc − 𝑘𝐵𝑇/𝑒)

(2)


𝑁D is the doping density, 𝑒 is the charge of an electron, 𝑘B is the Boltzmann constant, and 𝑇

is the temperature.

The applied potential (𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑) in the model is defined similar to experiments, in terms of

scan rate (𝑆𝑟), i.e. 𝑉applied = 𝑆𝑟 ⋅ 𝑡𝑖𝑚𝑒.

For n-type materials, electrons are the majority carriers and the electron concentration at

the surface under illumination ( 𝑛s) can be approximated as an exponential function of the

potential across the space charge region given by47

𝑛s = 𝑛s0 𝑒𝑥𝑝 (−𝑢sc

(𝑘B𝑇/𝑒)) (3)

where 𝑛s0 represents the concentration of surface electrons in the dark under zero bias.


The rate of change of hole density at the semiconductor surface (𝑝𝑠) depends on several

factors and can be calculated as follows35,47

𝑑𝑝s

𝑑𝑡 =

𝐽G

𝑑+ (

𝑆𝑟

𝑘B𝑇/𝑒) 𝑝s0 exp (

𝑢sc

𝑘B𝑇/𝑒) − 𝑘rec𝑛s𝑝s − 𝑘p𝑝s𝑁T𝑓T −

𝑁0∑ ((𝐾vf,i𝜃red,i − 𝐾vb,i𝜃ox,i ) + (𝐾𝑐f,i𝜃red,i − 𝐾𝑐b,i𝜃ox,i )) 4

i=1

(4)

The first term represents the hole flux under applied potential and illumination (𝐽G). The term

𝑑 is the thickness of the hole accumulation layer and is used to convert the surface

concentration of holes (per cm2) to volume concentration (per cm3).23 The second term is the

potential-dependent dark current where 𝑝𝑠0 represents the concentration of surface holes in

the dark under zero bias. The third and fourth terms represent the rates at which holes

recombine directly (𝑘rec𝑛s𝑝s) and get trapped at r-SS (𝑘p𝑝s𝑁T𝑓T).47 The last term in Eq. (4)

represents the rate at which holes are consumed in OER via the ideal adsorption sites. 𝑁0

represents the total number of ideal adsorption sites on the semiconductor surface. The

summation Σ over i = 1 to 4 denotes that all four steps in OER (microkinetic equations) are

taken into account for the calculation of the charge carrier concentration. The concentration

of reduced and oxidized OER intermediates at the sites are represented as 𝜃red,i and 𝜃ox,i.

The holes reach the traps at a rate of 𝑘𝑝. These holes can recombine with the electrons from

the conduction band at a rate of 𝑘𝑛 or they can participate in OER with a rate of 𝐾𝑡.35 The

overall effect of these processes at r-SS changes its fill factor of electrons which is denoted

by 𝑓𝑇. The rate of change of electron density in r-SS can be calculated as35,47

𝑁T𝑑𝑓T𝑑𝑡 = 𝑘n𝑛s𝑁𝑇(1 − 𝑓T) − 𝑘p𝑝s𝑁T𝑓T + 𝑁T∑(𝐾tf,i𝜃𝑇red,i − 𝐾tb,i𝜃𝑇ox,i)

4

𝑖=1

(5)

The last summation term in Eq. (5) is similar to that in Eq. (4) and represents the rate at which

holes are consumed for OER via r-SS. This increases the electron density in r-SS and, hence,

the last term has a positive sign. 𝜃𝑇red,i and 𝜃𝑇ox,i represent the fractional concentrations of

OER intermediates at r-SS sites.

The effect of OER intermediates on the charge carrier dynamics is defined in the model

through the last terms in Eq. (4) and Eq. (5). From Eq. (3)-(5), it can be seen that there are two

main input variables similar to experiments, the illumination intensity which enters through

𝐽G and the applied potential which enters through 𝑢sc and 𝑆𝑟. The value 𝐼0 is a constant based

on the illumination intensity. The potential across the space charge region (𝑢sc) is different

from the applied potential and its calculation is discussed in the next section.

2.3 Potential across the space charge region

The potential across the space charge region (𝑢sc) is required for the calculation of the

Gartner hole flux (Eq. (1)-(2)), the electron density (Eq. (3)), and the hole density in the dark

(second term in Eq. (4)). The potential across the space charge region is defined as48,49

Chapter 3 123

𝑢sc = 𝑉applied − 𝑉fb − 𝑉H − 𝑉IR (6)

where 𝑉applied is the applied potential. 𝑉fb is the flat band potential; it depends on the material

of the electrode, the treatment of the electrode, and experimental conditions.50 𝑉fb is

assumed to be constant in the simulations. 𝑉H is the potential across the Helmholtz layer

which can be calculated based on the fill factor and surface state density of r-SS as given by

Memming et al.47

𝑉H =

𝑒𝑁T(1 − 𝑓T)

𝐶H

(7)

where 𝐶H is the Helmholtz capacitance. 𝑉H is assumed to be constant.51 The potential drop

across the Helmholtz layer results in an equivalent shifting of the valence and conduction band

energy levels (𝐸V and 𝐸C) which is considered in the calculation of the rate constants

(supporting information S1.2 and S1.3). 47

The last term in Eq. (6) represents the IR drop over the series resistance (𝑅s). Klotz et al.52

have shown that it is necessary to include series resistance in models aimed at explaining

photoelectrochemical experiments. The series resistance in a PEC is related to the back

contact resistance and the interfacial and bulk resistances of the electrolyte.52–54 The IR drop

over 𝑅s is given by55

𝑉IR = 𝑗 ⋅ 𝑅s (8)

Thus, the IR drop over the series resistance is directly proportional to the current in the system

at that operating point. 𝑅s is usually one or two orders of magnitude lower compared to the

other ohmic contributions in typical equivalent circuit model elements of PEC and is usually

considered negligible. However, from the literature, it is found that certain electrode

treatments like high-temperature annealing also result in a substantial increase in 𝑅s.56,57

Hence, it is important to include the potential drop across 𝑅s. The implementation of the IR

drop in the model is represented as a schematic in Figure S1 of the supporting information.

2.4 Current density

The current density related to OER depends on the intermediate reactions which occur due

to charge transfer via VB, CB, and r-SS. By simultaneously solving the microkinetic rate

equations for OER intermediates (supporting information: Eq. S.15 -S.19 and Eq. S.30-S.34)

along with Eq. (3)-(5), the fractional coverage of OER intermediates and charge carrier

densities can be calculated for any given scan rate and illumination intensity. Using these

calculated quantities, the current due to reactions via VB, CB, and r-SS (𝑗v, 𝑗c, 𝑗t) is calculated

(supporting info Eq. S.22, S.25, S.37). The sum of all these currents gives the current density

related to OER as

𝑗 = 𝑗v + 𝑗c + 𝑗t (9)

The current density associated with the hole flux is called the hole current density (𝑗ℎ) and is

calculated as 58


𝑗h = 𝑒 ⋅ 𝐽G (10)

where 𝐽G is the hole flux from Eq. (1).

2.5 Capacitances

The model considers several capacitances. The Helmholtz capacitance is an input to the

model (Eq. (7)); it is assumed to be a constant. The capacitances related to r-SS, i-SS, and the

capacitance of the space charge region are capacitances which are calculated in post-

processing.

The capacitance due to r-SS (𝐶r−SS) is calculated as34,59

𝐶r−SS = 𝑒2𝑁T𝑓T(1 − 𝑓T)/𝑘B𝑇 (11)

According to the mechanism of OER, as given in the supporting information S1.1, the

formation of intermediate species at the interface means that holes are locked up on the

surface. The fractional coverage of the OER intermediates at the surface of the photoanode

(Eq. S15- Eq. S19) can be calculated using the model for any given input conditions.

The capacitance due to i-SS (𝐶i−SS) is calculated, based on the standard definition of

capacitance (𝐶 = 𝑑𝑞/𝑑𝑉), as the rate of change of charge accumulated in the formation of

OER intermediates with respect to the change in applied potential.20 Hence, for a fractional

coverage of all adsorbed surface species 𝜃ad and for the total number of adsorption sites 𝑁0,

the total charge accumulated at the surface can be calculated as 𝑁0 ⋅ 𝑒 ⋅ 𝜃ad. Here, 𝑒

represents the charge of an electron. The capacitance due to i-SS is thus calculated as

𝐶i−SS =

𝑑𝑞i−SS𝑑𝑉

= 𝑁0 ⋅ 𝑒 ⋅𝑑𝜃ad𝑑𝑉

=𝑁0𝑒(𝑑𝜃OH + 𝑑𝜃O + 𝑑𝜃OOH + 𝑑𝜃O2)

𝑑𝑉

(12)

The capacitance of the space charge region (𝐶sc) is calculated using the Mott-Schottky

relation3

(1/𝐶sc)2 = (2/𝜖r𝜖0𝑒𝑁D𝐴

2)(𝑢sc − 𝑘B𝑇/𝑒) (13)

where 𝑁D is the doping density and 𝐴 is the area of the electrode.

The model is implemented in MATLAB® and the set of differential equations is solved using a stiff

ODE-solver, ‘ode15s’, in MATLAB®.60


The model discussed in section 2 is generic and can be used for simulating PEC

characteristics for any semiconductor photoanode by substituting material-specific constants.

For the simulations in this paper, we chose hematite ( -Fe2O3) as the model system. The Gibbs

free energy changes (Δ𝐺i ) for the OER intermediate reactions on hematite (110) surface are

calculated using DFT (supporting information S2) and are given in Table S2.61 The redox

Chapter 3 125

potential of each intermediate step (𝐸redox,i) can be calculated using the standard relation

between Gibb’s free energy and redox potential.33 These redox potentials are substituted in

the Gerischer equation for calculating the rate constants for the multistep reactions.33 The

calculation of rate constants is described in George et al.33 and the supporting information

S1.2 and S1.3. The parameters used for the simulations in this paper are given in Table 1.

Table 1 Model parameters, their descriptions, and values used in the simulations.

Parameter Description Value Reference

𝐸V Val. band energy level for hematite 2.4 17

𝐸C Cond. band energy level for hematite 0.3 17

𝐸T Trap state energy level 𝐸C + 0.4

𝑛s0 Electron density under zero bias 𝑁D

𝑝s0 Hole density in the dark under zero bias

1 cm-3

𝑅s Series resistance 30 Ω ⋅cm2

𝛼 Absorption coefficient 1.5 x 105 cm-1 23

𝐿p Hole diffusion length 4 x 10-7 cm 62

𝜖r Relative permittivity of hematite 38 63

𝑉fb Flat band potential 0.4 V 63

𝐼0 Illumination intensity 1 x 1016 cm2 23

𝜎p Electron capture cross section of holes 1 x 10-16 cm2 23

𝑣th Thermal velocity of electrons 1 x 105 cm/s 23

𝑘n, 𝑘p Electron and hole trapping rates 𝜎p ⋅ 𝑣th (cm3/s) 23

𝑘rec Direct recombination rate within SCR 1 x 10-6 cm3/s

𝑑 Thickness of hole accumulation layer 1 x 10-7 cm 23,34

𝐶H Helmholtz capacitance 20 x 10-6 F/ cm2 51

𝑁D Doping density 3 x 1018 cm-3 63

𝑁0,ideal No. of ads. sites on ideal hematite surface

2.9 x 1014 cm-2 20

𝑁T Surface state density of r-SS 1 x 1013 cm-2


𝑁0 No. of ads. sites on the surface in the presence of r-SS

𝑁0,ideal − 𝑁T;

Additional constants used in the simulation associated with the microkinetic model are given

in the supporting information in Table S1.

3.1 Validation of input-output relationship

For comparability with experiments, the model is developed such that it holds the same

input-output relationship as experiments with applied voltage and illumination intensity as

the input and current density as the output. To validate the input-output relation of the

model, we simulate current densities as a function of applied potential at different

illumination intensities as shown in Figure 8.

Figure 8 Simulated j-V plots under different illumination intensities. The current density changes as a function of

applied potential and illumination intensity showing qualitative agreement with PEC measurements.26 The onset

potential is around 0.9 V vs. RHE and the saturation current density increases with an increase in illumination

intensity.

The simulated j-V curves have onset potentials around 0.9 V vs. RHE. The sharp increase in

current density around 1.7 V vs. RHE is related to the increase in dark current at high

potentials. It is found that the saturation current density increases with an increase in

illumination intensity. The input-output relationship observed in Figure 8 is in good qualitative

agreement with experimental data from the literature.26 Experimental j-V plots for three

different illumination intensities for hematite electrodes are shown in the supporting

information in Figure S2.26 Thus, the developed model can qualitatively simulate current

density data similar to the experiments for given applied potentials and illumination

intensities.

Chapter 3 127

3.2 The impact of r-SS

In this section, we investigate the impact of r-SS on the electrochemical data, in particular

on the j-V curves, surface state capacitance, Mott-Schottky data, and the hole flux. The

characteristics of r-SS are defined by its energy level (𝐸T), surface state density (𝑁T), and the

trapping rates (𝑘n, 𝑘p). A typical value of 0.4 eV below the conduction band is used for 𝐸𝑇 of

r-SS based on the literature.31 The 𝑁T of these sub-conduction band states in PEC electrodes

usually varies between 1012 to 1014cm−2.64,65 We use three different values for 𝑁T in the

simulations, i.e. 5 ⋅ 1012cm−2, 1 ⋅ 1013cm−2, and 2 ⋅ 1013cm−2. The trapping rates (𝑘n, 𝑘p)

are calculated based on literature using the trapping cross-section and the thermal velocity of

the charge carriers.23 The trapping rates are assumed to be independent of 𝑁T; the values are

given in Table 1. An advantage of the simulations compared to experimental studies is that

the 𝑁T and 𝐸T can be systematically changed and their impact on the PEC characteristics can

be studied. In experiments, it is difficult to perform such investigations systematically and

quantitatively, as often several parameters change at the same time.

The capacitance due to r-SS is calculated according to Eq. (11) and is plotted in Figure 9a as

a function of applied potential. A bell-shaped curve is found for 𝐶r−SS. The bell-shape becomes

wider, the maximum of 𝐶r−SS increases, and the potential corresponding to the maximum

increases with an increase in 𝑁T. 𝐶r−SS reaches maximum values of 10 µF/cm2 to 30 µF/cm2.

These observations can be explained as follows: in the presence of r-SS and under an applied

potential, the generated holes get trapped in the surface states until the surface states are

completely filled. The magnitude of peak capacitance increases with 𝑁T as more charge get

accumulated with an increase in 𝑁T. According to Eq. (11), the maximum capacitance occurs,

when r-SS is half-filled (𝑓T = 0.5). The higher the 𝑁T, the higher the potential required for the

filling of r-SS. Therefore, the potential corresponding to the maximum of 𝐶r−SS increases and

the capacitance peak broadens with higher 𝑁T. For the same energy level of r-SS, i.e. 𝐸T = 0.4

eV below the conduction band, the maxima of 𝐶r−SS are located at different applied potential

due to the change in 𝑁T. This indicates that the applied potential corresponding to the

maximum of 𝐶r−SS cannot be used as a direct indication of the energy level of the surface

state. The peak position depends on a combined effect of 𝐸T, 𝑁T, 𝑘n, and 𝑘p.

The impact of 𝐶r−SS on the potential distribution within the space charge region is

investigated using Mott-Schottky analysis. Figure 9b shows simulated Mott-Schottky plots for

the same model parameters as in Figure 9a. A plateau is observed around an applied potential

of 0.8 V vs. RHE; the plateau widens with an increase in 𝑁T. According to the Mott-Schottky

equation in Eq. (13), (1 𝐶sc⁄ )2 is proportional to 𝑢sc and, hence, the Mott-Schottky plot should

be linear. Usually a plateau in the Mott-Schottky curve is associated with FLP.3 Therefore, the

plateau around 0.8 V vs. RHE indicates FLP due to r-SS as the potential range of the FLP

coincides with the potential range of the maximum of 𝐶r−SS in Figure 9a. This means that the

potential across the space charge region decreases with an increase in 𝑁T.


Figure 9 a) Effect of surface state density of r-SS (𝑁T) on a) the surface state capacitance, 𝐶r−SS, as a function of

applied potential; both the maximum and the full width of half maximum of the 𝐶r−SS increase with an increase

in 𝑁T; b) the Mott-Schottky plots; the pinning coincide with 𝐶r−SS and the FLP is extended when 𝑁T is increased;

c) the j-V plots; higher onset potential and lower saturation current density are found with higher 𝑁𝑇; and d) the

hole current density (𝑗h); a plateau is observed before potentials corresponding to the onset potential from j-V

plots and the plateau increases with an increase in 𝑁T.

The simulated j-V curves are shown as a function of 𝑁T in Figure 9c. The j-V curve shifts

anodically with an increase in 𝑁T which results in higher onset potential and lower saturation

current density. This behavior is in agreement with experimental j-V curves from the literature

showing lower onset potential when surface states are passivated.7,66 The increase in 𝑁T leads

to a decrease in 𝑢sc according to Eq. (6) and (7). Consequently, a higher potential has to be

applied for OER to occur which explains the higher onset potential. The decrease in the

saturation current with the increase in 𝑁T is also related to the decrease in 𝑢sc as it leads to a

decrease in 𝑊sc and the hole flux according to Eq. (1) and Eq. (2).

The impact of r-SS on the hole flux is analyzed in Figure 9d. The hole flux to the surface is

calculated according to the Gartner equation (Eq. (1)) and the hole current density (𝑗h) is

calculated using Eq. (10). 𝑗h is simulated for three different 𝑁T and is shown in Figure 9d. The

simulated 𝑗h shows that the magnitude of hole current at higher potentials decreases with an

increase in 𝑁T. This decrease in hole current at higher potentials explains the decrease in

b a

c d

Chapter 3 129

saturation current density in Figure 9c as the OER photocurrent at higher potentials matches

with the hole current.23,58 Additionally, in Figure 9d, the hole current shows a plateau before

the potential corresponding to OER onset. It is found that the potential range of the plateau

coincides with the potential range of the 𝐶r−SS peaks. The presence of such a plateau is

observed in experimental hole current density reported in the literature.7,22 The relation

between 𝑁T and the plateau observed in hole current density is in agreement with the

experimental data from Zandi and Hamann comparing samples before and after surface state

removal.7 In experiments, the hole current density is measured by adding hole scavengers,

like H2O2 or [Fe(CN)6]3-/4- in the electrolyte. Thus, we show that the existence of r-SS has an

impact on the hole current density/hole flux and a flattening in the hole current density before

the onset potential of photocurrent is an indication of the presence of r-SS.

As discussed in section 2.1, charge transfer via valence band, conduction band, and via r-SS

is included in the model. Charge transfer may occur via these bands and results in OER

depending on the corresponding charge transfer rate constants. In all the cases shown in

Figure 9, OER occurs with charge transfer via valence band and conduction band. No charge

transfer is observed to occur via r-SS as OER intermediates are not formed at the sites

corresponding to r-SS with the assumed energy level, 𝐸T, (0.4 eV below 𝐸𝑐). To check the

sensitivity of the data towards the energy level of r-SS, simulations are run with three different

𝐸T values: 0.3 eV, 0.4 eV, and 0.5 eV below 𝐸C. The simulated data is insensitive to the

variation of the energy level of r-SS in the tested range and with constant trapping rates.

3.3 The impact of i-SS

Experimental studies on photoanodes have reported the existence of a capacitance around

OER onset.19,22 This capacitance is proposed to be due to the presence of OER intermediates

(i-SS). Klahr et al.22,26 have reported FLP associated with the capacitance due to i-SS based on

Mott-Schottky analysis. Accordingly, there is some potential drop over the charging of i-SS

which lowers the potential across the space charge region.22 In this section, we analyze,

whether OER intermediates result in a capacitance as proposed in the experiments and if so,

whether this capacitance can affect the potential across the space charge region. If the

potential drop over i-SS is large, this will hinder the OER performance. The impact of i-SS on

the PEC data is investigated by varying the rate of OER. This is done by individually varying a)

the illumination intensity and b) the backward rate constants for the intermediate steps in

OER.

3.3.1 Impact of the illumination intensity

The capacitance due to the accumulation of charge carriers in OER intermediates (𝐶i−SS) is

calculated according to Eq. (12). The 𝐶i−SS for three different illumination intensities are

calculated (same conditions as in Figure 8) and are plotted as a function of applied potential

in Figure 10a. The 𝐶i−SS curves have a maximum around the onset potential of the j-V curves


in Figure 8. For better illustration, 𝐶i−SS at 1 Sun illumination is plotted together with the

corresponding current density in Figure 10b. The result proves that OER intermediates result

in a surface state capacitance around the OER onset. The maxima of 𝐶i−SS lie between 400

𝜇F/cm2 and 500 𝜇F/cm2 and are comparable to the literature where values between 100

𝜇F/cm2 and 1 mF/cm2 have been reported.19,22,67,68 The simulated capacitance profiles are also

comparable to the literature.19 Furthermore, with an increase in illumination intensity, the

maximum capacitance increases, and the potential corresponding to the maximum

capacitance decreases, which is in qualitative agreement with the literature.22 According to

Eq. (12), 𝐶i−SS depends on the rate of formation of OER intermediates and the number of

adsorption sites at the SEI. Since the number of adsorption sites remains constant for a given

surface, the increase in capacitance with illumination intensity is due to the increase in the

rate of formation of surface intermediates with illumination intensity. The magnitude of 𝐶i−SS

is observed to be an order of magnitude higher than that of 𝐶r−SS.

Figure 10 a) Capacitance due to i-SS simulated at different illumination intensities; b) capacitance due to i-SS and

current density as a function of applied potential for 1 Sun illumination. The plot shows that the capacitance due

to i-SS is observed around the OER onset potential.

The impact of 𝐶i−SS on the potential distribution in the space charge region is investigated

using Mott-Schottky analysis. The Mott-Schottky plots are generated for three different

illumination intensities as shown in Figure 11a (all the model parameters are the same as in

Figure 8 and Figure 10a). Two deviations from a linear behavior are found in the investigated

potential range. The first deviation is a plateau around an applied potential of 0.6 V to 0.8 V

vs. RHE. It is related to r-SS as discussed in the previous section.

The second deviation is comparatively smaller and starts around 1.0 V vs. RHE as shown in

the enlarged plot in Figure 11b. The flattening increases as the illumination increases. The

potential range of this flattening coincides with the potential range of the 𝐶i−SS peaks in Figure

10a. A similar effect is reported in experimental studies in the literature and is interpreted as

FLP due to i-SS.69 However, we find that this flattening vanishes when the series resistance in

the model is set to zero for any illumination intensity (Figure S3). This means that this second

flattening cannot be interpreted as FLP due to i-SS. The reason for the flattening can be

a b

Chapter 3 131

explained as follows. The current density increases directly after the onset potential as shown

in Figure 8. This leads to an increase in the IR drop (𝑉IR) according to Eq. (8) and decrease in

𝑢𝑠𝑐 according to Eq. (6). According to Eq. (13), the decrease in 𝑢sc leads to a decrease in 1/𝐶sc2 .

This is observed as a flattening in the Mott-Schottky plot around the onset potential, as there

is a sudden ramp in current density and 𝑉IR, directly after the onset potential. In Figure 11b,

this flattening looks like FLP, but it is in fact related to the decrease in 𝑢sc due to increase in

𝑉IR. This is in agreement with the experimental study by Shavorskiy et al. 31 in which a

deviation in band bending was attributed to the IR drop of the measurement setup. When the

illumination intensity is increased, the current density in the circuit increases as shown in

Figure 8. For this reason, the IR drop and the second flattening increase with an increase in

illumination intensity as shown in Figure 11b.

Figure 11 a) Mott-Schottky plots showing FLP due to r-SS and flattening around onset potential (shown in the

box); b) Enlarged Mott-Schottky plot of a) around the onset potential to show the increase in pinning with an

increase in illumination intensity; the plot area is same as the portion highlighted with the box in Figure 11a.

It is important to note that our investigations are based on the standard assumption that

the Helmholtz capacitance is constant.3,26 Based on this standard assumption, the presence

of surface adsorbates (i-SS) does not affect the Helmholtz capacitance. In the literature, it has

been reported that surface adsorption can, however, affect the Helmholtz capacitance.70 This

will result in 𝐶H being potential dependent through the potential dependence of surface

coverage. The effect of this coverage dependent 𝐶H is discussed in the supporting information

in section S5 using a simplified model.65

3.3.2 Impact of the backward rate constants of the intermediate steps in OER

The magnitude of 𝐶i−SS depends on the rate of formation of OER intermediates according

to Eq. (12). Therefore, 𝐶i−SS is related to the catalysis of OER on the semiconductor surface.

In this section, the rate constant for backward reactions in OER is increased and it is

b a


investigated how this impacts the current density. The backward rate constants for

elementary reaction steps in OER is equivalent to the recombination rate in the case of i-SS.32

In experiments, the recombination phenomenon is investigated using current density

measured under chopped light.23 The measurement is called a chopped light measurement

(CLM). We simulate CLMs with two different backward rate constants; a potential scan rate of

20 mV/s and light on/off pulses with a pulse time of 1 s is used. Additionally, the photocurrent

and dark current for the same case is calculated.

Figure 12a and Figure 12b show the CLM, the photocurrent, and the dark current simulated

for 𝑁T = 1013cm−2 with two different backward rate constants. The backward rate constants

of all the four steps are changed by changing the pre-multiplier for the backward rate

constants (supporting information S1.2). The pre-multipliers are chosen as 1 ⋅ 𝑘v,max,b and 103

⋅ 𝑘v,max,b. The pre-multiplier for the forward rate constants, 𝑘v,max,f, is kept the same in both

cases. Thus, the ratio 𝑘v,max,b/𝑘v,max,f is three orders of magnitude higher for Figure 12b

compared to Figure 12a. The surface state capacitances associated with both cases are plotted

along with the corresponding photocurrent densities in Figure 12c.

The plot in Figure 12a shows no cathodic or anodic peaks near the OER onset. When

𝑘v,max,b/𝑘v,max,f is increased by three orders of magnitude, the CLM shows both anodic and

cathodic peaks near the OER onset (Figure 12b). Thus, the positive (anodic) and negative

(cathodic) overshoots in the CLM near the onset potential are sensitive to the rate constants

of the intermediate steps in OER steps. The cathodic peak in Figure 12b increases, as a higher

backward reaction increases the reduction of adsorbed intermediates, and subsequently the

cathodic current.

The reason behind the increase in anodic peak is related to the reduction in the

photocurrent density with the increase in the backward reaction rate. The current density

under illumination from Figure 12a is shown as a dotted line in Figure 12b for comparison; the

difference in the current densities (bold yellow line and dotted yellow line) is found only near

the onset potential. Under chopped light conditions, when illumination is turned on, the

current density rapidly increases due to the forward reaction rate. However, due to the higher

backward reaction rate, the current density settled down to the lower equilibrium value. This

explains the anodic peaks in the CLM when the backward reaction rate is increased. Thus, we

show that the rate of OER intermediate reactions, especially the ratio between backward and

forward reaction has an impact on the anodic and cathodic current peaks in CLM found near

the OER onset potential. The presence of overshoots in the current density near the onset

potential is an indication of a higher ratio between backward and forward reaction which in

turn indicates inferior OER catalysis; the higher the ratio is, the higher the overshoots are.

Such an insight about the impact of the rate constants of the intermediate steps on PEC data

is challenging to obtain from experiments. This is due to the challenges associated with the

Chapter 3 133

experimental identification of OER intermediates. However, with our approach, we can

simulate the impact of OER intermediate reactions on PEC data.

Figure 12 Simulations of chopped light measurements (red), current densities under illumination (yellow) and

current densities in the dark (blue) with backward rate constant as a) 1 ⋅ 𝑘v,max,b and b) 103 ⋅ 𝑘v,max,b; the current

density under illumination with 1⋅ 𝑘v,max,b is shown as a dotted line for comparison; c) the plot of the

capacitances and current densities for 1⋅ 𝑘v,max,b (bold line) and 103⋅ 𝑘v,max,b (dotted line) plotted as a function

of applied potential.

Figure 12c shows a combined plot of the surface state capacitance and the current densities

for the two rate constants. The maximum of 𝐶i−SS decreases and the peak position shifts to a

higher potential with an increase in the backward rate constant. The comparison of the

photocurrent densities shows that the onset potential increases with an increase in the

backward rate constant. A higher backward reaction rate is unfavorable for OER and leads to

a lower catalytic performance of OER on the photoanode surface. Only the onset potential is

affected in this regard and the saturation current density is unaffected. According to the

literature, the onset potential is determined by the catalysis of the surface,71 Therefore

according to Figure 12c, a decrease in 𝐶i−SS found for example in experimental data can be an

indication of a decrease in the catalytic performance of the photoanode surface. At higher

potentials the forward reaction dominates as the hole density increases with the applied

b a

c

134 Summary

potential. As 𝐶i−SS does not affect 𝑢𝑠𝑐, the hole density at higher potentials is not affected

which explains the constant saturation current density in both cases.

4 Summary

A microkinetic model based on a multistep OER mechanism which also takes into account

the charge carrier dynamics within the semiconductor is developed. This model allows

simulating and understanding the impact of the recombing surface states (r-SS) and

intermediate surface states (i-SS) on typical PEC measurement data. The impact of r-SS and i-

SS on the PEC data, such as j-V plots, surface state capacitance, Mott-Schottky plots, hole flux,

and chopped light current, are investigated with our model. The features in the PEC data

arising due to r-SS and i-SS are discussed by analyzing the sensitivity of the data to the

parameters related to r-SS and i-SS. The results regarding r-SS and i-SS are summarized in

Figure 13; findings related to r-SS are shown in red color, while findings related to i-SS are

shown in blue color.

We found that both r-SS and i-SS result in capacitive behavior with their maximum

capacitances at characteristic applied voltages (Figure 8a): 𝐶r−SS culminates typically below

the onset potential, while 𝐶i−SS culminates around in the onset potential. Hence, we claim

that the location of the capacitance peaks along the potential axis is a measure to distinguish

r-SS and i-SS. Additionally, the magnitude of the peak of 𝐶r−SS is an order of magnitude lower

than that of 𝐶i−SS. Both these findings are important and help to distinguish between r-SS and

i-SS in experimental studies. As the surface state density (NT) increases, the maximum of 𝐶r−SS

increases and the 𝐶r−SS peak shifts to a higher potential. The maximum of 𝐶i−SS depends on

the illumination intensity (𝐼0) and on the rate constants of the intermediate steps in OER (kOER).

The results are in agreement with experiments.7,21,22

The impact of r-SS and i-SS on the current density is shown in Figure 8b. The presence of r-

SS leads to a delayed onset potential and lower saturation current density. In the case of i-SS,

a lower magnitude of 𝐶i−SS leads to a slightly delayed onset of current density; the saturation

current density is not affected by i-SS. Our study shows that the correlation between the

surface state capacitances and OER performance is different for r-SS and i-SS; an increase in

the magnitude of 𝐶r−SS peak leads to lower photoanode performance, whereas, in the case

of 𝐶i−SS, the increase in the magnitude indicates improved OER catalysis which leads to lower

onset potential.

In Mott-Schottky analysis (Figure 8c), we found deviations from the linear behavior at the

same potentials as that of the maxima of the surface state capacitances. The deviation at low

potential (shown in red) is related to r-SS and is attributed to Fermi level pinning (FLP) which

is in agreement with experimental studies.7 Hence, r-SS reduces the potential available across

the space charge region which explains the higher onset potential and lower saturation

current density as found in Figure 13b. The deviation from the linear behavior in the Mott-

Chapter 3 135

Schottky plot around the onset potential (shown in blue) is less visible as it is located in the

same potential range as 𝐶i−SS. However, we found that this deviation is not related to i-SS but

due to the potential drop over 𝑅s in the circuit. This deviation in the Mott-Schottky plot can

get interpreted in the analysis of PEC data as FLP due to i-SS, since the potential range of the

deviation coincides with that of 𝐶i−SS. We will discuss the impact of 𝑅𝑠 on PEC measurements

in more detail in a forthcoming publication.

Figure 13 a) A representative plot showing the relative magnitudes and positions of surface state capacitances

(𝐶𝑟−𝑆𝑆 and 𝐶𝑖−𝑆𝑆 ) along the potential axis. For an increase in 𝑁𝑇, The maximum of 𝐶r−SS increases and shifts to

higher potential as 𝑁𝑇 is increased. The maximum of 𝐶i−SS depends on the illumination intensity (𝐼0) and the rate

constants of the intermediate steps in OER; b) j-V characteristic showing an increase in onset potential and a

decrease in saturation current density with an increase in 𝐶𝑟−𝑆𝑆; the onset potential increases with a decrease in

𝐶𝑖−𝑆𝑆; c) Mott-Schottky plot shows Fermi level pinning corresponding to r-SS and no Fermi level pinning

corresponding to i-SS; the flattening in the Mott-Schottky plot observed around the onset potential is related to

potential drop over 𝑅𝑠.

The results show that the analysis of PEC experimental data in combination with a

microkinetic model of OER gives additional insights into the catalysis of OER at the

photoanode surface. The model discussed here combines for the first time multistep OER at

the semiconductor surface and charge carrier dynamics within the semiconductor. The

136 Summary

developed model is generic and can be applied to other material systems. Further

development of this model in combination with experiments will aid in a better understanding

of the processes that take place at the semiconductor-electrolyte interface during OER, which

are challenging to deconvolute experimentally.

Acknowledgments

George acknowledges funding from the Shell-NWO/FOM “Computational Sciences for

Energy Research” PhD program (CSER-PhD; nr. i32; project number 15CSER021). Bieberle-

Hütter and Sinha acknowledge the financial support from NWO (FOM program nr. 147 “CO2

neutral fuels”) and M-ERA. NET (project “MuMo4PEC” no. 4089). Supercomputing facilities of

the Dutch national supercomputers SURFsara/Lisa and Cartesius are acknowledged. Erik

Langereis is acknowledged for graphical support. Prof. Michiel Sprik (University of Cambridge,

UK), Prof. dr. Evert Jan Meijer (University of Amsterdam, Netherlands), and Dr. Rochan Sinha

are acknowledged for the fruitful discussions regarding model development.

Chapter 3 137

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Chapter 3 143

Supporting Information

S1. Microkinetic model of OER

The oxygen evolution reaction under alkaline environment is given by

4𝑂𝐻− + 4ℎ+ → 𝑂2 + 2𝐻2𝑂 (S.1)

In this study, reactions in an alkaline environment are considered and the mechanism

proposed by Hellman et al.1 is chosen. This mechanism is based on the multistep OER

mechanism proposed earlier by Rossmeisl et al.2

S1.1 Electrochemical mechanism of OER

The four-step OER in alkaline environment is given as

∗ + 𝑂𝐻− + ℎ+

𝐾b1⇌𝐾f1 𝑂𝐻ad

(S.2)

𝑂𝐻ad + 𝑂𝐻

− + ℎ+𝐾b2⇌𝐾f2 𝑂ad +𝐻2𝑂

(S.3)

𝑂ad + 𝑂𝐻

− + ℎ+𝐾b3⇌𝐾f3 𝑂𝑂𝐻ad

(S.4)

𝑂𝑂𝐻ad + 𝑂𝐻

− + ℎ+𝐾b4⇌𝐾f4 𝑂2,ad + 𝐻2𝑂

(S.5)

Here * represents an adsorption site and the subscript ad means that the species are

adsorbed on the surface. Thus, 𝑂𝐻ad, 𝑂ad, 𝑂𝑂𝐻ad, and 𝑂2,ad are the intermediate species

adsorbed on the surface during the OER. The forward and backward reaction rates of these

charge transfer reactions are represented by 𝐾fi and 𝐾bi, respectively, where 𝑖 = 1 to 4. The

calculation of these rate constants is described in the following sections. After adsorbed

oxygen (𝑂2,ad) is formed at the site, it desorbs (𝑂2,des) from the surface at a rate of 𝐾f5 which

is given by

𝑂2,ad →

𝐾f5 𝑂2,des + ∗

(S.6)

This step does not involve charge transfer and, hence, the desorption rate 𝐾f5 is chosen as

a constant.

S1.2 Charge transfer via valence band and conduction band

Rate constants for charge transfer via valence band and conduction band

For an ideal semiconductor, charge transfer can occur via the valence band (VB) and/or via

the conduction band (CB). The forward and backward rate constants for charge transfer via

VB, 𝐾vfi and 𝐾vbi can be calculated as3

144 Supporting Information

𝐾vfi = 𝑘𝑣fi 𝑝s (S.7)

𝐾vbi = 𝑘𝑣bi 𝑁v (S.8)

𝑘𝑣𝑓𝑖 = 𝑘v,max,f exp [ −

(𝐸v − 𝐸F,redox,i0 −𝑉H − 𝜆)

2

4𝜆𝐾B𝑇]

(S.9)

𝑘𝑣𝑏𝑖 = 𝑘v,max,b exp [ −

(𝐸v − 𝐸F,redox,i0 −𝑉H + 𝜆)

2

4𝜆𝐾𝐵𝑇]

(S.10)

where 𝑝s is the hole density at the surface, 𝑁v is the density of states of the valence band, 𝐸v

is the valence band energy level, 𝐸redox,i is the redox potential of the intermediate steps (𝑖 =

1 to 4), 𝑉H is the potential drop across the Helmholtz layer, 𝜆 is the solvent reorganization

energy, 𝑘B is the Boltzmann constant, and 𝑇 is the temperature. The descriptions of all the

parameters used in the model and their respective values are given in Table S1.

Table S1 Model parameters specific to the microkinetic model, their descriptions, and values

in addition to Table 1 in the main manuscript.

Parameter Description Value Ref.

𝐾B Boltzmann constant 8.61733 x 10-5 eV/K

𝑒 Charge of electron 1.60217662 x 10-19 C

𝜖0 Permittivity of free space 8.8541878128 x 10-14 F cm-2

𝑆𝑟 Scan rate 20 mV/s


pH pH of the electrolyte 13.6

pOH pOH of the electrolyte 14-pH

𝑥OH Mole fraction of hydroxyl ions 10-pOH/(molar conc. of water)

𝑥H2O Mole fraction of water 1-𝑥OH

𝑘v,max,f, 𝑘v,max,b Max. rate constants via val. band 3 x 10-16 cm4/s 4

𝑘c,max,f, 𝑘c,max,b Max. rate constants via cond. band 3 x 10-16 cm4/s 4

𝑘t,max,f, 𝑘t,max,b Max. rate constants via trap state 3 x 10-16 cm4/s 4

𝜆 Solvent reorganization energy 1 eV 5

Chapter 3 145

𝑁C Density of state of cond. band 4 x 1022 cm-3 6

𝑁V Density of state of val. band 1 x 1022 cm-3 6

𝐾f5 Desorption rate of oxygen 8 x 105 cm-1 7

Similarly, the rate constants for charge transfer via CB (subscript c) can be calculated as 3

𝐾cfi = 𝑘𝑐fi 𝑁c (S.11)

𝐾𝑐bi = 𝑘𝑐bi 𝑛s (S.12)

𝑘𝑐fi = 𝑘c,max,f 𝑒𝑥𝑝 [ −

(𝐸c − 𝐸F,redox,i0 −𝑉H − 𝜆)

2

4𝜆𝐾B𝑇]

(S.13)

𝑘𝑐𝑏𝑖 = 𝑘c,max,b 𝑒𝑥𝑝 [ −

(𝐸𝑐 − 𝐸F,redox,i0 −𝑉H + 𝜆)

2

4𝜆𝐾B𝑇]

(S.14)

where 𝑁c is the density of states of the conduction band, 𝑛s is the electron density at the

surface, and 𝐸c is the conduction band energy level.

Rate equations for OER intermediates at semiconductor sites

The rate equations for fractional coverage of intermediates at a semiconductor site due to

charge transfer via both VB and CB can be written as

��OH = 𝐾vf1𝑥OH 𝜃ad −𝐾vb1𝜃OH − 𝐾vf2𝜃OH𝑥OH + 𝐾vb2𝜃O𝑥H2O

+ 𝐾cf1𝑥OH 𝜃ad −𝐾cb1𝜃OH − 𝐾cf2𝜃OH𝑥OH + 𝐾cb2𝜃O𝑥H2O

(S.15)

��O = 𝐾vf2𝑥OH 𝜃OH − 𝐾vb2𝜃O − 𝐾vf3𝜃O𝑥OH +𝐾v𝑏3𝜃OOH + 𝐾cf2𝑥OH 𝜃OH

− 𝐾cb2𝜃O𝑥H2O − 𝐾cf3𝜃O𝑥OH + 𝐾cb3𝜃OOH

(S.16)

��OOH = 𝐾vf3𝜃O𝑥OH − 𝐾v𝑏3𝜃OOH − 𝐾v𝑓4𝜃OOH𝑥OH + 𝐾vb4𝜃O2𝑥H2O

+ 𝐾cf3𝜃O𝑥OH − 𝐾cb3𝜃OOH − 𝐾cf4𝜃OOH𝑥OH + 𝐾cb4𝜃O2𝑥H2O

(S.17)

��O2 = 𝐾vf4𝜃OOH𝑥OH − 𝐾vb4𝜃O2𝑥H2O + 𝐾cf4𝜃OOH𝑥OH − 𝐾cb4𝜃O2𝑥H2O

− 𝐾f5𝜃O2

(S.18)

𝜃𝑎𝑑 = 1 − 𝜃𝑂H − 𝜃𝑂 − 𝜃𝑂𝑂𝐻 − 𝜃𝑂2 (S.19)

where 𝑥OH represents the mole fraction of hydroxyl ions and 𝑥H2O represents the mole

fraction of water.

Current density due to charge transfer via VB and CB

The forward and backward current densities for charge transfer via VB (subscript V) and CB

(subscript C) are calculated as

𝑗vf = 𝑒𝑁0(𝐾vf1𝜃ad + 𝐾vf2𝜃OH + 𝐾vf3𝜃O + 𝐾vf4𝜃OOH)𝑥𝑂𝐻 (S.20)


𝑗vb = 𝑒𝑁0(𝐾vb1𝜃OH + 𝐾vb2𝜃O𝑥H2O +𝐾vb3𝜃OOH + 𝐾vb4𝜃O2𝑥H2O ) (S.21)

𝑗v = 𝑗vf − 𝑗vb (S.22)

𝑗cf = 𝑒𝑁0(𝐾cf1𝜃ad + 𝐾cf2𝜃OH + 𝐾cf3𝜃O + 𝐾cf4𝜃OOH)𝑥OH (S.23)

𝑗c𝑏 = 𝑒𝑁0(𝐾cb1𝜃OH + 𝐾cb2𝜃O𝑥H2O + 𝐾cb3𝜃OOH + 𝐾cb4𝜃O2𝑥H2O ) (S.24)

𝑗c = 𝑗cf − 𝑗cb (S.25)

S1.3 Charge transfer via r-SS

Rate constants for charge transfer via r-SS

The surface states which act as recombination centers are called recombining surface states

(r-SS). The rate constants for charge transfer via r-SS are calculated as 3

𝐾tfi = 𝑘𝑡fi 𝑁T(1 − 𝑓) (S.26)

𝐾𝑡bi = 𝑘𝑡bi 𝑁T𝑓 (S.27)

𝑘𝑡fi = 𝑘t,max,f exp [ −

(𝐸T − 𝐸F,redox,i0 −𝑉H − 𝜆)

2

4𝜆𝐾B𝑇]

(S.28)

𝑘𝑡bi = 𝑘t,max,b exp [ −

(𝐸T − 𝐸F,redox,i0 −𝑉H + 𝜆)

2

4𝜆𝐾B𝑇]

(S.29)

where 𝑁T is the density of states of r-SS and 𝑓 is the fill factor of r-SS.

Rate equations for OER intermediates at sites corresponding to r-SS

The rate equations for fractional coverage of intermediates at an r-SS site due to charge

transfer via r-SS are calculated as

��𝑇OH = 𝐾tf1𝑥OH 𝜃𝑇ad − 𝐾tb1𝜃𝑇OH − 𝐾tf2𝜃𝑇OH𝑥OH + 𝐾tb2𝜃𝑇O𝑥H2O (S.30)

��𝑇O = 𝐾tf2𝑥OH 𝜃𝑇OH − 𝐾tb2𝜃𝑇O𝑥H2O − 𝐾tf3𝜃𝑇O𝑥OH +𝐾tb3𝜃𝑇OOH (S.31)

𝜃��OOH = 𝐾tf3𝜃𝑇O𝑥OH − 𝐾tb3𝜃𝑇OOH − 𝐾tf4𝜃𝑇OOH𝑥OH + 𝐾tb4𝜃𝑇O2𝑥H2O (S.32)

𝜃��O2 = 𝐾tf4𝜃𝑇OOH𝑥OH − 𝐾tb4𝜃𝑇O2𝑥H2O − 𝐾f5𝜃𝑇O2 (S.33)

𝜃𝑇ad = 1 − 𝜃𝑇OH − 𝜃𝑇O − 𝜃𝑇OOH − 𝜃𝑇O2 (S.34)

Current density due to charge transfer via r-SS

The forward and backward current densities for charge transfer via r-SS are calculated as

𝑗tf = 𝑒𝑁ss(𝐾tf1𝜃𝑇ad + 𝐾tf2𝜃𝑇𝑂𝐻 + 𝐾tf3𝜃𝑇O + 𝐾tf4𝜃𝑇OOH)𝑥OH (S.35)

𝑗tb = 𝑒𝑁ss(𝐾tb1𝜃𝑇OH + 𝐾tb2𝜃𝑇O𝑥H2O +𝐾tb3𝜃𝑇OOH +𝐾tb4𝜃𝑇O2𝑥H2O ) (S.36)

𝑗t = 𝑗tf − 𝑗tb (S.37)

S1.4 Calculation of the total current density

The total current density is calculated based on Eq. S.20-S.25 and Eq. S.35-S.37 as

𝑗 = 𝑗v + 𝑗c + 𝑗t (S.38)

Chapter 3 147

𝑗 = 𝑗vf + 𝑗cf + 𝑗tf − 𝑗vb − 𝑗cb − 𝑗tb (S.39)

S1.5 Implementation of IR drop in the model

The potential drop over the series resistance, 𝑅s, depends on the current density in the

circuit. The implementation of the potential drop over 𝑅s in the model is shown as a schematic

in Figure S1.

Figure S14 Schematic representation of the implementation of potential drop over the series

resistance in the model; 𝑢∗ represents the input potential to the model after correcting for a

potential drop over 𝑅𝑠.

S2. Gibbs free energy and redox potential

The Gibbs free energies for the intermediates steps in OER on hematite are calculated using

DFT.8 Previously, in Zhang et al.8, we have calculated Gibbs free energies for OER

intermediates on hematite surfaces using DFT calculations, assuming gas-solid interface. The

gas-solid model does not account for solvent effects in the calculation of the free energies. In

this study, an (implicit) solid-liquid model of the hematite-water interface is used wherein the

solvent effects are accounted for by using a continuum solvation model with the dielectric

constant of water (𝜖 = 78.4) as implemented in VASPsol.9 The redox potentials of the

intermediate steps in OER are calculated using DFT. The spin-polarized DFT+U (U = 4.3 eV)

formalism is chosen in order to treat the correlation effects in 3d electrons in hematite.10 The

Perdew–Burke–Ernzerhof (PBE) XC functional 11 and the projected augmented wave (PAW)12

potentials were used. The molecular geometries were fully optimized with VASPsol when

incorporating solvent effects. A 2x2 supercell of hematite (110) is used which is modeled as

being antiferromagnetic (net zero spin via the MAGMOM keyword in VASP).10,13 Zero-point

energy correction and entropic contributions to the Gibbs free energy were obtained via

Hessian calculation on the optimized geometry.


Table S2 Gibbs free energies calculated for OER intermediate steps on hematite (110) surface.

Parameter Description Value

Δ 𝐺1 Gibbs free energy for the step in Eq. (S.2) 1.87 eV




The redox potential corresponding to each intermediate step can be calculated based on

the relation between Gibbs free energy and redox potential given by14

𝐸redox,i =

Δ𝐺𝑖

𝑛𝐹

(S.40)

where n is the number of electrons transferred in a single step (𝑛 = 1 for all steps here), 𝐹 is

the Faraday’s constant, and 𝐸redox,i is the redox potential of the intermediate step.

S3. Experimental j-V plot for different illumination intensities

Experimental j-V plot for three different illumination intensities replotted from the

literature for comparison with the simulations shown in Figure 3 of the main text.15

Figure S15 Experimental j-V plots for three different illumination intensities for hematite

electrodes replotted from Klahr et al.15

Chapter 3 149

S4. Simulated data for 𝑹𝐬 = 0

The j-V curves, 𝐶𝑖−𝑆𝑆 plots, and Mott-Schottky plots are simulated for three different illumination

intensities by keeping 𝑅s = 0 as shown in Figure S3. For all the three illumination intensities 𝐶𝑖−𝑆𝑆

shows peaks around the OER onset potential. However, no deviation in linearity is observed in the

Mott-Schottky plot around the potential range of 𝐶𝑖−𝑆𝑆. Therefore, the deviation in linearity observed

in the Mott-Schottky plot in Figure 6 of the main text cannot be attributed to 𝐶𝑖−𝑆𝑆.

Figure S16 a) j-v plot, b) surface state capacitance 𝐶i−SS, and c) Mott-Schottky plot simulated

for the case of 𝑅𝑠 = 0. The Mott-Schottky plot shows a deviation from linearity before the

onset potential which is related to FLP due to r-SS. However, the Mott-Schottky plot shows no

deviation in linearity around the potential range of 𝐶i−SS.

a b

c


S5. Coverage dependent Helmholtz capacitance

In the analysis of PEC data, the Helmholtz capacitance is usually assumed to be constant.15,16

However, it has been reported in the literature that surface adsorption can affect the

Helmholtz capacitance.17 This will result in Helmholtz capacitance (𝐶H) to be potential

dependent through the potential dependence of surface coverage. In this section, we look

into a scenario in which the Helmholtz capacitance depends on the coverage of surface

intermediates and how it affects the PEC data. For simulating the coverage dependent

Helmholtz capacitance, we consider the simplest model of Helmholtz capacitance which is

based on a parallel plate capacitor.

The Helmholtz capacitance per unit area (𝐶H0) in this case, is defined as 𝐶H0 = 𝜖 ∗ 𝜖0/𝑙,

where 𝑙 is the thickness of the Helmholtz double-layer, 𝜖0 is the permittivity of free space, and

𝜖 is the relative permittivity of the semiconductor material.18,19 An approximate value of 100

µF cm-2 is obtained for 𝐶H0 using 𝑙 = 3 ⋅ 10-8 cm and 𝜖 = 3820 for hematite.

If we assume that the available area of the capacitor reduces due to surface adsorption, the

capacitance based on potential can be calculated as 𝐶H = 𝐶H0 ∗ 𝜃, where 𝜃 is the fraction of

free sites on the surface per unit area. We note that this is a simplified assumption. The idea

here is to investigate whether a variation in Helmholtz capacitance based on surface coverage

will affect the data. Based on this assumption, the j-V plots, 𝐶i−SS, and Mott-Schottky plots

are simulated for three different illumination intensities as shown in Figure S4. In these

simulations, the contribution due to series resistance is eliminated by keeping 𝑅s = 0. Figure

S4a shows the j-V plots for three different illumination intensities. 𝐶i−SS plots from Figure S4b

show peaks around respective OER onset potential. From Figure S4c, there are two points at

which the Mott-Schottky plots show a deviation from linearity. The first one at lower potential

is due to r-SS as described in the main text. The second deviation from linearity around the

onset potential is enlarged and shown in Figure S4d. The potential range of this second

deviation coincides with that of the peaks in the 𝐶i−SS plot. In the main text, it is shown that

potential drop over 𝑅s can lead to a deviation in the Mott-Schottky plot around the onset

potential. However, in this case 𝑅s = 0 and, hence, the deviation from linearity observed in the

Mott-Schottky plot around the onset potential can be attributed to i-SS. Therefore, if the

Helmholtz capacitance varies as a function of surface coverage, i-SS can result in FLP.

Chapter 3 151

Figure S17 a) j-v plot, b) surface state capacitance 𝐶i−SS, c) Mott-Schottky plot simulated for

the case of 𝐶𝐻 varying as a function of surface coverage. 𝑅𝑠 = 0 in all the simulations; d)

Enlarged Mott-Schottky plot showing deviation in linearity around the onset potential when

the Helmholtz potential is assumed to change with surface coverage, even when 𝑅s = 0.

d c

b a


References









(9) http://vaspsol.mse.ufl.edu/.


(11) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865–3868. https://doi.org/10.1103/PhysRevLett.77.3865.

(12) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50 (24), 17953–17979. https://doi.org/10.1103/PhysRevB.50.17953.

(13) Wang, R. B.; Hellman, A. Hybrid Functional Study of the Electro-Oxidation of Water on Pristine and Defective Hematite (0001). J. Phys. Chem. C 2019, 123 (5), 2820–2827. https://doi.org/10.1021/acs.jpcc.8b06580.

(14) George, K.; van Berkel, M.; Zhang, X.; Sinha, R.; Bieberle-Hütter, A. Impedance Spectra and Surface Coverages Simulated Directly from the Electrochemical Reaction Mechanism: A Nonlinear State-Space Approach. J. Phys. Chem. C 2019, 123 (15), 9981–9992.

Chapter 3 153

https://doi.org/10.1021/acs.jpcc.9b01836.



(17) Bohra, D.; Chaudhry, J. H.; Burdyny, T.; Pidko, E. A.; Smith, W. A. Modeling the Electrical Double Layer to Understand the Reaction Environment in a CO2 Electrocatalytic System. Energy Environ. Sci. 2019, 12 (11), 3380–3389. https://doi.org/10.1039/c9ee02485a.

(18) Bard, A. J.; Bocarsly, A. B.; Fan, F. R. F.; Walton, E. G.; Wrighton, M. S. The Concept of Fermi Level Pinning at Semiconductor/Liquid Junctions. Consequences for Energy Conversion Efficiency and Selection of Useful Solution Redox Couples in Solar Devices. J. Am. Chem. Soc. 1980, 102 (11), 3671–3677. https://doi.org/10.1021/ja00531a001.

(19) Gongadze, E.; Petersen, S.; Beck, U.; Rienen, U. Van. Classical Models of the Interface between an Electrode and an Electrolyte. Proc. COMSOL Conf. Milan 2009, 18–24.


Chapter 4 155

Chapter 4: The critical role of the series resistance in

impedance measurements of photoelectrodes

Abstract

The series resistance (𝑅s) in photoelectrochemical (PEC) cells arises from the back contact

resistance and the resistance of the electrolyte. In the literature, 𝑅s is usually considered to

have a minor impact on the PEC data, since quantification by electrochemical impedance

spectroscopy (EIS) results in rather low values and a serial contribution to the impedance data.

However, due to electrode treatment, like high-temperature annealing, 𝑅s values can be

rather high. Additionally, the potential drop over 𝑅s increases with the increase in current

density (𝑗). Due to these reasons, we systematically investigate in this study the impact of 𝑅s

on electrochemical data, such as j-V plots and EIS. We use a microkinetic model of OER at the

semiconductor-electrolyte interface with hematite (Fe2O3) as the electrode material. We find

that the onset potential in the j-V curves is unaffected by 𝑅s. However, 𝑅s has an significant

impact on (a) the slope of the j-V curve, (b) the saturation current density, (c) the charge

transfer resistance, and (d) the capacitance of the space charge layer. Additionally, in contrast

to the typical assumption that an increase in 𝑅s result mainly in a shift of the Nyquist plot

along the x-axis, we found that an increase in 𝑅s increases the polarization resistance and

decreases the time constants of the processes represented in the EIS. We show that, how

correcting the j-V curves and data obtained from EIS analysis for 𝑅s aids in drawing exclusive

conclusions about the functional layer.

In preparation: The critical role of the series resistance in impedance measurements of

photoelectrodes.

156 Introduction

1 Introduction

Photoelectrochemical (PEC) cells are devices which can perform water splitting using sunlight

to enable sustainable production of hydrogen fuel. 1–4 In a PEC cell, hydrogen is generated at

the cathode, and oxygen is generated at the anode. The half-reactions are called hydrogen

evolution reaction (HER) and the oxygen evolution reaction (OER), respectively.4 Usually, the

anode of a PEC is made of n-type semiconductor material with a suitable bandgap which

provides the thermodynamic potential required for water splitting and is called the

photoanode.4 Upon illumination, electron-hole pairs are generated in the photoanode. Under

an applied bias potential, the generated holes move towards the semiconductor-electrolyte

interface (SEI) to oxidize water. The electrons move towards the cathode through the external

electrode to reduce water. The photoanode should absorb the energy from the solar spectrum

effectively and also catalyze the OER.4,5 The sluggish OER kinetics at the photoanode is

identified as one of the performance-limiting factors in a PEC cell.6 Several potential

photoanode materials have been investigated in the literature and among these, Fe2O3, WO3,

and BiVO4 are some of the single-absorber materials extensively studied in the literature.7–9

However, the efficiencies of photoanodes made of these single absorber materials are not

high enough for the commercialization of PEC. 10–12

The photoanode is constructed by depositing the photoactive semiconductor material

(functional layer) over a transparent conductive oxide (TCO) on a glass substrate.4,13 Usually

fluorine-doped tin oxide (FTO) or indium tin oxide (ITO) is used as the transparent conductive

oxide.1,14 The contact resistance between the functional layer and the TCO contributes to the

series resistance (𝑅s) in the cell.15 Typical values of 𝑅s in the case of hematite – FTO systems

is reported to be around 10 Ωcm2 – 40 Ωcm2.16–19 However, the 𝑅s of photoanodes is reported

to often increase under heat treatment which is aimed at enhancement of the performance.20

For instance, high-temperature annealing is reported to improve the performance of hematite

photoanodes due to the removal of deleterious surface states (passivation of surface states).21

Annamalai et al.22 studied the effect of annealing at 800˚C for different annealing times in the

case of hematite nanorods on FTO and found that the series resistance of the electrode

increases with the annealing time. 𝑅s was reported to increase from 4.4 Ω to 227.7 Ω for an

increase in annealing duration from 2 mins to 20 mins.22 The change in series resistance was

linked to the diffusion of Sn from FTO into the hematite layer during annealing.22 Similar

observation of an increase in 𝑅s with high-temperature annealing was reported by Cho et al.23

in a separate study. In this study, we investigate the impact of increase in 𝑅s on the PEC data.

Experimentally, 𝑅s is quantified using electrochemical impedance spectroscopy (EIS).24 EIS

measurements give the frequency-dependent complex impedance of the electrochemical

system.25 From the EIS, 𝑅s is calculated as the magnitude of impedance at high frequencies,

Chapter 4 157

when the imaginary part of the impedance tends to zero.24,26 A sample Nyquist plot depicting

𝑅s is shown in the supporting information Figure S1. The difference between the high-

frequency intercept and the low-frequency intercept in the Nyquist plot is called the

polarization resistance (𝑅pol). 𝑅pol represents the resistance of the functional layer.

The EIS measurements are usually analyzed by fitting the data to an equivalent circuit model

(ECM) of choice. Different types of ECM are used depending on the nature of the measured

EIS data.17,27,28 Along with the 𝑅s component, the ECM consists of different resistive and

capacitive components, like capacitance of the space charge region, surface state capacitance,

and charge transfer resistance, representing the impedance of the functional layer. By fitting

the EIS measured at different applied potentials to the ECM, a trend in the magnitude of these

components over the applied potential is obtained. The trend in the resistive and capacitive

components over different applied potential is used to draw conclusions regarding the

reactions and processes occurring at the photoanode.29 Hence, it is important to understand

any factors that influence the perceived impedance contribution of these components.

The magnitude of 𝑅s (the resistance due to the TCO contact) is usually one or two orders of

magnitude lower than that of the other ohmic counterparts in the ECM.17 For this reason, 𝑅s

is assumed to have no significant impact on the photoanode performance. Typically, it is

assumed that the entire applied potential falls across the space charge layer of the

semiconductor.30 However, when the current through the cell increases due to the reactions,

a portion of the applied potential drops over 𝑅s and this reduces the potential across the

semiconductor layer.31 The photocurrent depends on the charge carrier density at the

semiconductor surface which depends on the potential across the semiconductor layer.32

Hence increase in 𝑅s results in a reduction in photocurrent density for a given applied

potential which means that the perceived impedance of the semiconductor layer increases.

However, the impact of the potential drop over 𝑅s on the EIS and the impedance data

obtained from the analysis of EIS using ECM is not investigated in the literature.

Experimentally it is challenging to quantify the sole impact of 𝑅s on the impedance of the

semiconductor layer as it is challenging to change 𝑅s alone without changing other

parameters. Computational models can be employed to study the impact of 𝑅s on PEC data.

However, the model should be able to simulate the potential dependent impedance of the

system.

In this study, we employ a microkinetic model of OER, which we have previously developed in

George et al.,33 to investigate the impact of series resistance on current density and different

components in the EIS. The model can calculate the current density as well as typical

components of the equivalent circuit model, like capacitance of the space charge region (𝐶sc),

surface state capacitance (𝐶ss) and total resistance (𝑅total), as a function of applied potential.

It should be noted here that these capacitances and resistances are directly calculated from


the four-step mechanism of OER and processes happening within the semiconductor, and are

not obtained by ECM fitting procedure. The formulation of the model is such that it includes

monoenergetic surface states which act as recombination centers (r-SS) and surface states

due to OER intermediates (i-SS).33 Applied potential and illumination intensity are the input

parameters for the model.

We use this microkinetic model to systematically investigate the impact of 𝑅s on current

density and the impedance components in EIS; 𝐶sc, 𝐶ss and 𝑅total. The results show that 𝑅s

has a significant impact on the j-V data. The simulated scenario of annealing shows the

importance of reporting 𝑅s along with j-V curves for quantifying the performance of the

functional layer. The changes in the 𝐶sc, 𝐶ss and 𝑅total with change in 𝑅s explain how the

increase in series resistance increases the perceived impedance of the functional layer in

photoanodes and the time constants of the processes. The method to correct the effect of 𝑅s

on EIS data is discussed. Additionally, the results show that it is necessary to include 𝑅s in

models aimed at explaining PEC measurement data.26 The advantage of using a microkinetic

model is that the reason for the changes in electrochemical data can be explained based on

the changes in processes occurring at the photoanode.

2 Theory and method

The results shown in this chapter are simulated using the microkinetic model of OER which we

have developed in George et al.33,34 The details about the model can be found in George et

al.33,34 In this section, we discuss the calculation of electrochemical data, like the capacitances

associated with surface states, space charge layer capacitance, and current density in the

presence of 𝑅s, using the model.

2.1 Calculation of capacitance

To give a glance at the microkinetic model from George et al.,33 the model takes into account

the elementary steps in OER and the charge carrier dynamics within the semiconductor. The

model calculates current density as a function of applied potential and illumination intensity.

Additionally the surface coverage of OER intermediates, i.e. OH, O, OOH, and O2 denoted by

𝜃OH, 𝜃O, 𝜃OOH, and 𝜃O2, can be calculated with the model. Thus, the model can simulate

surface states due to OER intermediates denoted as i-SS. The capacitance associated with i-SS

can be calculated in terms of the coverage of OER intermediates as33

𝐶i−SS =

𝑁0𝑒(𝑑𝜃OH + 𝑑𝜃O + 𝑑𝜃OOH + 𝑑𝜃O2)

𝑑𝑉

(41)

where 𝑁0 is the number of adsorption sites at the photoanode surface, 𝑑𝑉 is the change in

applied voltage, and 𝑒 is the unit charge of an electron.

Chapter 4 159

Monoenergetic surface states (r-SS) are also defined in the model with an energy level of 𝐸T

and a surface state density of 𝑁T. The fill factor (𝑓T) of r-SS changes as a function of applied

potential and illumination intensity. The capacitance due to r-SS can be calculated as29

𝐶r−SS =

𝑒2𝑁T𝑓(1 − 𝑓T)

𝑘B𝑇

(42)

where 𝑘B is the Boltzman constant and 𝑇 is the temperature.

The capacitance of the space charge region can be calculated using the Mott-Schottky

equation4

(1

𝐶sc)2

= (2

𝜖r𝜖0𝑒𝑁D𝐴2) (𝑢sc −

𝑘B𝑇

𝑒)

(43)


𝑁D is the doping density, A is the area of the electrode, and 𝑢sc is the potential available across

the space charge region (SCR) of the semiconductor. The SCR is a region devoid of majority

carriers, which is formed at the photoanode side of the SEI.30

2.2 Calculation of current density

The reactions at the semiconductor electrolyte interface and the current density due to the

reactions depend on the hole density at the surface. The hole density at the surface of the

semiconductor under illumination depends on the potential across the space charge layer

(𝑢sc) as shown in supporting information S2. Additionally, the intrinsic charge carrier densities

of electrons and holes at the surface of the semiconductor, in the dark, depend on 𝑢sc.35

Hence, the photocurrent depends on how much of the applied voltage (𝑉applied) falls across

the space charge region. The magnitude of 𝑢sc depends on the potential distribution across

the photoanode and the potential drop over 𝑅s affects this potential distribution.31,36

To analyze the potential distribution across the photoanode, assume that the impedance due

to the functional layer is a single entity represented by 𝑍functional Based on the literature, the

series resistance is found to be independent of the applied potential, unlike 𝑍functional, which

varies with potential.29 For this reason, 𝑍functional is represented as a variable impedance

element as shown in Figure 1.


Figure 1 A simplified representation of the impedance of the photoanode. 𝑅𝑠 represents the series resistance and 𝑍𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙 represents the impedance of the functional layer. The element 𝑍𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙 is represented as a

variable impedance due to its potential dependence.

The total resistance of the circuit in Figure 1 can be calculated as

𝑅total = 𝑅s + 𝑍functional (44)

According to Kirchhoff’s law, the applied potential for this simple circuit of two resistances in

series is shared as

𝑉applied = 𝑉𝑠 + 𝑉functional (45)

and the current in the circuit 𝑗 will be equal to the current flowing through both the resistances

given as

𝑗 = 𝑗s = 𝑗functional (46)

Using Ohms law, the current density can be calculated as

𝑗 =

𝑉applied

𝑅total

(47)

Substituting for 𝑅total from Eq. (44), Eq. (47) can be reformulated as

𝑗 =

𝑉applied

𝑅s + 𝑍functional

(48)

Rearranging Eq. (48), 𝑉applied can be written as

𝑉applied = 𝑗. 𝑅s + 𝑗. 𝑍functional (49)

Comparing Eq.(45) and Eq.(49), the first term in Eq. (49) is the potential drop over 𝑅s and the

second term is the potential drop over 𝑍functional

Thus, the potential drop over 𝑅s is given by

𝑉s = 𝑗. 𝑅s (50)

Chapter 4 161

By using Eq. (45) and Eq.(50), the potential across the functional layer under an applied

potential 𝑉applied can be calculated as

𝑉functional = 𝑉applied – 𝑗. 𝑅s (51)

The magnitude of 𝑢sc can be calculated based on 𝑉functional after subtracting other associated

potential losses, like flat band potential and potential drop over the Helmholtz layer. 36 The

magnitude of 𝑢sc can be calculated as36

𝑢sc = 𝑉functional − 𝑉fb − 𝑉h (52)

where 𝑉fb is the flat band potential and 𝑉h is the potential drop across the Helmholtz layer. In

the model, 𝑉fb is assumed as a constant and 𝑉h is calculated as35

𝑉h =

𝑒𝑁T(1 − 𝑓T)

𝐶H

(53)

where 𝐶H is the Helmholtz capacitance. Substituting Eq. (51) in Eq. (52), 𝑢sc can be written in

terms of 𝑉applied and 𝑅s as

𝑢sc = 𝑉applied − 𝑉fb − 𝑉h– 𝑗 ⋅ 𝑅s (54)

The calculation of the current density in the microkinetic model is based on 𝑢sc.33 Hence,

based on Eq.(54), we can formulate

𝑗 = 𝑓(𝑉applied − 𝑉fb − 𝑉h – 𝑗 ⋅ 𝑅s) (55)

It should be noted that the last term in Eq. (55) is a function of the current density. Thus, there

exists a negative feedback, in the calculation of current density as a function of applied

potential, as shown in Figure 2.

Figure 2 A block diagram showing the negative feedback loop in the calculation of current density.

The microkinetic model is developed using MATLAB and the set of differential equations is

solved using ‘ode15s’ solver in MATLAB.37 We investigate the impact of 𝑅s on the j-V plots,

surface state capacitance, space charge capacitance, and the total resistance. The descriptions

about the formulation of the microkinetic model, surface states, charge carrier dynamics,

calculation of current density, and capacitances are available in George et al.33 Similar to our


previous works, hematite (Fe2O3) is used as the model photoanode material in this work. The

constants corresponding to Fe2O3 used for the simulation are given in the SI Table S1.


Typical electrochemical data are simulated for Fe2O3 (hematite)-electrolyte interface using the

microkinetic model, as discussed above and in George et al.33 The impact of 𝑅s on current

density and the resistive and capacitive components in EIS are discussed in this section.

3.1 Impact of 𝑅s on current-voltage curves

Current density is simulated for the hematite-electrolyte interface using constant illumination

intensity and a constant scan rate of 5 mV/s for the applied potential. The j-V plots are

simulated for different values of series resistance keeping all other parameters constant.

Typically, values of around 10 Ωcm2 – 40 Ωcm2 are reported in the literature for 𝑅s in the case

of hematite – FTO systems.16–19 However, 𝑅s values as high as ~80 Ωcm2, ~230 Ωcm2 and even

higher have also been reported in some experimental studies.20,22,38 Therefore, we simulate

in this study, j-V curves for different 𝑅s values, i.e. 0 Ωcm2 (ideal case), 30 Ωcm2, 100 Ωcm2,

and 200 Ωcm2. Figure 3a shows the simulated j-V plots for different 𝑅s. The onset potential of

the photocurrent is observed to be around 0.9 V vs. RHE which is in agreement with

experimental values for hematite from the literature.39 From the figure, the onset potential is

found to be independent of 𝑅s. This is not surprising, since 𝑅s contributes as 𝑗 ⋅ 𝑅s according

to Eq. 16 and Eq. 17; when 𝑗 is almost zero, the contribution from this term is negligible.

After the onset, the current density ramps up rapidly and reaches a saturation current density.

The saturation current density and the slope of the j-V ramp decrease with an increase in 𝑅s.

At a potential higher than 1.7 V vs. RHE, a rapid increase in current density is seen and is

related to electrochemical water splitting. The current density corresponding to the

electrochemical water splitting also decreases with an increase in 𝑅s.

The observed effects can be explained as follows. Ideally, 𝑢𝑠𝑐 should increase linearly with

increase in 𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑. However, according to Eq. (54), 𝑢𝑠𝑐 does not increase linearly with

𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑; for a given 𝑉applied, 𝑢sc decreases with increase in 𝑗 and 𝑅s. The reason for the

decrease in saturation current density with increase in 𝑅𝑠 is due to the decrease in hole flux

with increase in 𝑅𝑠. According to Eq. (S1)-(S2), the hole flux depends on 𝑢sc and, hence, the

hole flux decreases with an increase in 𝑅s. The rate of reactions at the semiconductor-

electrolyte interface and the saturation current density depends on the hole flux to the

surface. This explains the decrease in saturation current density with increase in 𝑅s. The

decrease in slope of the j-V ramp , in the presence of 𝑅s is also related to the decrease in 𝑢sc.

The 𝑗 for a given applied potential depends on 𝑢sc. Directly after the onset potential, 𝑗

increases rapidly with increase in 𝑉applied resulting in concomitant decrease in 𝑢sc. The slope

Chapter 4 163

decreases as the relative increase in 𝑢sc with increase in 𝑉applied is smaller due to the rapid

increase in 𝑗. The slope of the j-V ramp decrease further with increase in 𝑅s. The decrease in

the current density due to electrochemical water splitting after 1.7 V is also related to the

decrease in 𝑢sc with increase in 𝑅s, as the concentration of intrinsic charge carriers at the

surface depends on 𝑢sc.35

Figure 3 a) j-V curves under different series resistances. The onset potential of photocurrent remains the same

irrespective of the series resistance. The slope of the photocurrent ramp and the saturation current density

decrease with an increase in series resistance. b) j-V curves with both 𝑁𝑇 and 𝑅𝑠 changed systematically to

simulate the scenario of annealing. The blue curve shows the initial case with 𝑁𝑇 = 2 x 1013 cm-2 and 𝑅𝑠 = 30

Ωcm2. The red curve shows the case with lower 𝑁𝑇 (1 x 1013 cm-2) with the same series resistance and the yellow

curves shows the case with lower 𝑁𝑇 (1 x 1013 cm-2) and higher 𝑅𝑠 (200 Ωcm2) compared to the blue curve.

a

b


In Figure3a, only the series resistance is changed keeping all other parameters constant. In

experiments, however, 𝑅s often does not change alone. High-temperature annealing, for

example, increases 𝑅s because of the deterioration of the FTO layer, but also leads to a

reduction in surface state density (𝑁T) of r-SS (often called passivation of r-SS).20,21,23 Hence,

𝑅s and 𝑁T change together during high temperature annealing. A reduction in 𝑁T increases

the performance by lowering the onset potential and increasing the saturation current

density.21 The increase in 𝑅s , on the other hand, will decrease the saturation current density

as seen in Figure 3a. In order to separate these effects, we systematically changed 𝑅s and

𝑁T in the model and simulated different situations of high temperature annealing:

• before annealing: 𝑁T = 2 x 1013 cm-2 , 𝑅s = 30 Ωcm2

• after annealing without increase in 𝑅s: 𝑁T = 1 x 1013 cm-2 , 𝑅s = 30 Ωcm2

• after annealing with increase in 𝑅s: 𝑁T = 1 x 1013 cm-2 , 𝑅s = 200 Ωcm2.

The simulated j-V curves are shown in Figure 3b. The blue curve represents the situation

before annealing. The red curve shows the j-V plot after annealing case without an increase in

series resistance. Comparing the blue line and red line (only 𝑁T is changed), the onset

potential decreases and the saturation current density increases. However, as 𝑅s increases to

200 Ωcm2 (yellow curve), the saturation current density decreases compared to the red curve

and even falls below the initial case (blue curve). The lowering of saturation current density is

exclusively due to the increase in series resistance from 30 Ωcm2 to 200 Ωcm2. The simulated

scenario suggests that the increase in series resistance due to annealing masks the

performance improvement resulting from the passivation of recombining surface states (r-

SS). As, there is a significant reduction in photocurrent around the onset potential exclusively

due to the increase in 𝑅s.

Thus, when it comes to the quantification of OER performance, it is important to report the

magnitude of 𝑅s along with current density measurements. For instance, the current density

at a particular applied potential (usually 1.23 𝑉RHE) is used as a performance metric for

calculating the applied bias photocurrent efficiency (ABPE).3 By comparing the red curve and

the yellow curve in Figure 3b, it can be seen that the current density at 1.23 V is lower when

𝑅s is high. Thus, increase in 𝑅s leads to a lower calculated ABPE for the photoanode. However,

the lowering of ABPE is solely due to the increase in 𝑅s. If 𝑅s is not reported along with the j-

V curve, the functional layer will be perceived as a low-performance material. Such a pitfall

can be mitigated by plotting current density vs. 𝑉applied − 𝑗. 𝑅s instead of 𝑉applied as shown in

Figure 4. The bold line represents the uncorrected j-V plot for 𝑅s = 200 Ωcm2. The dotted line

shows the corrected j-V plot obtained by plotting 𝑗 vs. 𝑉applied − 𝑗. 𝑅s.

Chapter 4 165

Figure 4 Simulated current density for 𝑅𝑠 = 200 Ωcm2 plotted vs. 𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑 (bold line) and vs. 𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑 − 𝑗. 𝑅𝑠 (dotted

line).

In the literature, a few studies have done the correction for 𝑅s as shown in Figure 4.18,40,41

However, such a correction is not widely used in the PEC community. The above results show

that 𝑅s can have a significant impact of the j-V curves and it is necessary to do the correction

for 𝑅s by plotting 𝑗 against 𝑉applied − 𝑗. 𝑅s for getting accurate performance data about the

functional layer.

3.2 Impact of 𝑅s on EIS data

In experiments, 𝑅s is quantified from EIS measurements. From the Nyquist plot of the EIS, the

high-frequency intercept of the Nyquist plot with the x-axis gives the magnitude of 𝑅s as

shown in Figure S1. An increase in 𝑅s is usually seen as a positive shift of the Nyquist plot along

the real axis. For quantifying 𝑅s and the impedance due to the semiconductor layer,

experimental EIS data is usually analyzed by fitting the measurement data with an equivalent

circuit model (ECM). An example of an equivalent circuit used for fitting EIS under illumination

for the hematite-electrolyte interface is shown in Figure 5. There are resistive and capacitive

components in the circuit representing different impedance contributions; 𝑅s represents the

series resistance, 𝑅trap represents the charge trapping resistance and 𝑅ss represents the

charge transfer resistance across the semiconductor-electrolyte interface, 𝐶sc represents the

space charge layer capacitance and 𝐶ss represents the surface state capacitance. The

equivalent circuit models define the system at discrete operating points, represented by a

constant applied potential and illumination intensity. The fitting of the equivalent circuit

model with experimental EIS data measured at each operating point delivers values for the

resistive and capacitive components. The magnitude of the resistance and capacitance


components and their variation as a function of applied potential is used for studying the

processes occurring during OER.29 In this section, the impact of 𝑅s on the EIS is analyzed.

Figure 5 Typical equivalent circuit model (ECM) used for the analysis of electrochemical impedance spectra of

hematite under illumination.42

In our approach, we use a microkinetic model of OER which takes into account the reactions

at the semiconductor-electrolyte interface and the processes occurring within the

semiconductor. It should be noted that the microkinetic model does not use equivalent circuit

elements in the calculation of PEC data. However, the model can calculate the resistive and

capacitive components as a function of applied potential and illumination intensity directly

based on the processes involved. To be comparable with the usual experimental observations

which use ECMs, we calculate the resistive and capacitive components directly from the

microkinetic model. In this chapter, the equivalent circuit shown in Figure 5 is chosen for

comparison with the microkinetic model.

The capacitance 𝐶ss and 𝐶sc are calculated from the microkinetic model as described in Eq.

(41) and Eq. (3). To calculate the resistive components, the total resistance of the system is

calculated from the microkinetic model based on the ratio between the applied potential and

current density as29

𝑅total = 𝑉applied 𝑗⁄ (56)

However, in the case of the ECM in Figure 5, the total resistance is related to other resistive

components given by

𝑅total = 𝑅s + 𝑅trap + 𝑅ss (57)

Thus, for the data from the microkinetic model to be comparable to the usual data obtained

from ECM analysis, these different resistance components have to be calculated discretely.

Other than 𝑅s, which is an input parameter in the microkinetic model, there are two resistance

elements in the ECM; 𝑅trap and 𝑅ss. Since Fe2O3 is used as the model system here, a constant

value of 1000 Ω cm2 is assumed for 𝑅trap based on the literature.29 Thus, only 𝑅ss needs to be

calculated using the microkinetic model.

Chapter 4 167

In the following sections, we use the microkinetic model to individually simulate the impact

of 𝑅s on 𝐶ss, 𝐶sc, and 𝑅ss. Subsequently, in section 3.2.4, the impact of 𝑅s on the EIS is

simulated based on the EIS components calculated from the microkinetic model.

3.2.1 Surface state capacitance

Surface state capacitance (𝐶ss) is calculated from the model using Eq. (41). The 𝐶ss simulated

for different 𝑅s is shown in Figure 6a. The plot shows a peak at an applied voltage between

0.8 V – 1.0 V. From Figure 6a, the maxima of the peak observed between 0.8 V – 1.0 V

decreases slightly with an increase in 𝑅s. In Figure 6a there is a small peak visible after the

onset potential. The smaller peak after the onset potential is shown in an enlarged plot in

Figure 6b. Such multiple peaks have been reported in the case of experimental 𝐶ss by Klahr et

al.43 In Figure 6b, the capacitance corresponding to the maxima of the second peak decreases

and the spread of the peak along the voltage axis increases with an increase in 𝑅s. Based on

these observations, the magnitude of the simulated capacitance after the onset potential is

affected by the increase in 𝑅s as the potential drop is prominent only after the onset potential.

Figure 6 a) Surface state capacitance 𝐶ss simulated for different series resistances: a) at applied voltages of 0.6 V

to 1.8 V; b) at applied voltages higher than the onset potential, i.e. 1.0 V to 1.8 V.

The impact of 𝑅s on 𝐶ss is explained as follows. 𝐶ss is calculated from the microkinetic model

based on the change in charge accumulated at the surface due to the formation of surface

intermediates, with respect to the change in applied voltage. Therefore, 𝐶ss is related to the

surface coverage of OER intermediates (Eq. (41)). The two peaks in 𝐶ss are due to the change

in surface coverage as a function of the applied potential. Surface coverages as a function of

applied potential for different 𝑅𝑠 are shown in SI Figure S2. The surface coverage depends on

the rate of intermediate reactions at the semiconductor-electrolyte interface. As discussed

earlier, the increase in 𝑅s leads to decrease in 𝑢sc after the onset of photocurrent. Since 𝑢sc

decreases after the onset of photocurrent, the rate of the intermediate reactions decreases

a b


and, hence, surface coverages change with an increase in 𝑅s as shown in SI Figure S2. The

change in surface coverage explains the reason for the decrease in the maxima of the second

peak and the broadening of the second peak that is observed after the onset potential.

3.2.2 Capacitance of the space charge layer

The capacitance of the space charge layer (𝐶sc) is calculated using the Mott-Schottky equation

given in Eq. (43). The simulated Mott-Schottky plot for different 𝑅s is shown in Figure 7a. The

plot shows flattening at two locations. The first one around 0.6 V - 0.8 V and the second one

around 1.0 V to 1.3 V. The first flattening is independent of 𝑅s. However the second flattening

becomes more pronounced with increase in 𝑅s. The significance of the flattening of Mott-

Schottky plots is explained as follows. From the Mott-Schottky equation in Eq. (43), (1 𝐶sc⁄ )2 is

proportional to 𝑢sc. The Mott-Schottky plot has 𝑉applied on the x-axis. A flattening means that,

𝑢sc does not increase linearly with 𝑉applied. A deviation from linearity or flattening of the Mott-

Schottky plot is usually associated with Fermi level pinning due to surface states.29,42

The first flattening around 0.6 V - 0.8 V is due to the Fermi level pinning over r-SS as the

capacitance associated with the r-SS (Eq. (42)) is also observed around the same potential

range (SI Figure S3).33 This Fermi level pinning due to r-SS, observed in Figure 7a is in

agreement with the literature.44 The capacitance due to r-SS and the associated Fermi level

pinning is independent of the change in 𝑅s as it is before the onset potential.

The second flattening in Figure 7a increases with an increase in 𝑅s and vanishes when 𝑅s = 0.

By comparing Figure 7a and Figure 3a, the onset of the second flattening coincides with the

onset potential of the j-V curve. Additionally, the potential range of the flattening coincides

with that of the ramp in the j-V curve. Hence, the second flattening found in the Mott-Schottky

is not related to surface states but due to potential drop over 𝑅s and associated decrease in

𝑢sc according to Eq. (54). The reason for the flattening here can be explained as follows: The

potential drop over 𝑅s increases rapidly around the onset potential due to the sudden ramp

in current density after the onset. For this reason, 𝑢sc does not increase linearly with increase

in 𝑉applied. This is observed as the flattening in the Mott-Schottky plot. As 𝑢sc decrease with

increase in 𝑅s, the flattening increases with the increase in 𝑅s. The flattening can be mistaken

for Fermi level pinning due to intermediate surface states as the peak in surface state

capacitance (𝐶ss) is also observed in the same potential range.

The flattening of Mott-Schottky plot due to potential drop over 𝑅s has not been pointed out

in the literature so far. However a similar effect of potential drop over 𝑅s has been reported

in an experimental study on hematite electrodes by Shavorskiy et al.45 The authors reported

a decrease in band bending due to potential drop over series resistance. 45 As band bending is

directly proportional to 𝑢sc,46,47 this experimental observation corroborates our finding.

Chapter 4 169

Figure 7 a) Mott-Schottky plot and b) charge transfer resistance (𝑅𝑠𝑠) simulated using the microkinetic model for

different series resistances.

3.2.3 Charge transfer resistance

The magnitude of charge transfer resistance (𝑅ss) can be calculated based on Eq. (56) and (57)

as

𝑅ss = 𝑉applied 𝑗⁄ − 𝑅trap − 𝑅s (58)

A logarithmic plot of 𝑅ss as a function of applied potential is shown in Figure 7b for different

𝑅s. It is observed that 𝑅ss decreases upon increasing the applied potential, reaches a minimum

around the potential corresponding to the end of the OER ramp, and then starts increasing

slightly with a further increase in applied potential. The variation in 𝑅ss as a function of applied

potential from Figure 7b is in agreement with the experimentally reported trend in 𝑅ss.19,29

The plot enlarged for applied potentials higher than the onset potential is shown in the SI

a

b


Figure S4. 𝑅ss around the onset potential is observed to be higher when 𝑅s is high. The impact

of 𝑅s on charge transfer resistance can be explained as follows: Due to the increase in 𝑅s, 𝑢sc

decreases (Eq. (54)). This decrease in 𝑢sc reduces the Gartner hole flux (Eq. (10)) which

reduces the charge carrier density at the surface and subsequently the rate of OER. The

decrease in the rate of OER leads to an increase in charge transfer resistance.

3.2.4 Simulation of EIS

The impact of 𝑅s on the individual components in the ECM shown in Figure 5, is obtained using

the microkinetic model. The change in these individual components will affect the total

impedance of the photoanode. To understand the effect of 𝑅s on the total impedance, the EIS

of the photoanode is simulated by substituting the potential dependent values of 𝑅ss, 𝐶sc and

𝐶ss in the equivalent circuit shown in Figure 5, along with the constant values of 𝑅s and 𝑅trap.

The impedance is calculated based on the ECM in Figure 5 as

𝑍 = 𝑅s +

1

𝑖𝐶sc𝜔 +1

𝑅trap +1

𝑖𝐶ss𝜔 +1𝑅ss

(59)

Where 𝜔 is the frequency of perturbation and 𝑖 represents the unit imaginary number. From

Figure 6 and Figure 7, the impact of 𝑅s is more pronounced after an applied potential of 1.0

V. Hence an applied potential of 1.1 V which is higher than 1.0 V is chosen for simulating the

EIS.

The Nyquist plot of the simulated EIS at 1.1 V for different 𝑅s is shown in Figure 8a. The

frequency increases in the direction as indicated by the arrow. Two depressed semicircles are

visible in the Nyquist plot for each 𝑅s. This is in agreement with, the two semicircles usually

observed in the experimental EIS. The high-frequency semicircle is usually attributed to the

processes within the bulk of the semiconductor and the low-frequency semicircle is attributed

to the charge transfer at the interface.27 The high-frequency intercept of the plot with the

real[Z] axis is the magnitude of 𝑅s.

From Figure 8a, the 𝑅pol at 1.1 V increases with an increase in 𝑅s. This shows that the

perceived impedance of the functional layer at a given applied potential increases with an

increase in 𝑅s. In terms of the equivalent circuit elements in Figure 5, 𝑅pol = 𝑅trap + 𝑅ss. As

𝑅trap is assumed to be constant, this increase in 𝑅pol is solely due to the increase in 𝑅ss at 1.1

V (Figure 7b). This means that the charge transfer at 1.1 V becomes less efficient with an

increase in series resistance. Thus, the impact of 𝑅s on the Nyquist plot is not just a shift in

the high-frequency intercept of the plot with the real[𝑍] axis; the polarization resistance is

also affected by 𝑅s. From Figure 8a, even the usual resistance of 30 Ωcm2 results in a significant

Chapter 4 171

increase in the polarization resistance compared to the ideal case of 𝑅s = 0. Hence, 𝑅s has an

impact on the entire EIS and not just the high-frequency intercept of the Nyquist plot.

Figure 8 Electrochemical impedance data at different series resistances 𝑅𝑠 and for an applied potential of V = 1.1 V: a) Nyquist representation; the arrow indicates the direction of the increase in frequency. The peak frequencies for the low-frequency semicircles are marked for different; b) the Bode diagram showing the phase plot.

Apart from the magnitude of impedance, the characteristic time constants for the processes

in OER can be obtained from the analysis of EIS. The frequencies corresponding to the peak

points of the low-frequency semicircles (local maxima of -imag[Z]) are marked in Figure 8a.

The peak frequency for the low-frequency arc is observed to decreases with an increase in 𝑅s.

A clear picture about the relation between 𝑅s and the frequencies of different processes can

be obtained using a Bode representation. A Bode phase (𝜙) plot of the same EIS data is shown

in Figure 8b. The two peaks present in the phase plot correspond to the two semicircles in the

Nyquist representation. The maxima of the phase peaks and the frequencies corresponding

to the maxima change with an increase in 𝑅s. The characteristic frequencies for both the high-

frequency peak and low-frequency peak decrease with an increase in 𝑅s. The decrease in

a

b


frequency means that the time constant for the processes at the interface and within the bulk

increases with an increase in 𝑅s. As mentioned earlier the increase in 𝑅s decreases the 𝑢sc

(Eq. (54)) and results in a lower concentration of holes at the interface (Eq.(S1)-(S2)). This

results in a lower rate of OER at the interface. As 𝑅trap is assumed to be a constant, the change

in the time constant for the high-frequency arc in the simulation is due to the change in 𝐶sc

with 𝑅s. Thus, increase in 𝑅s reduces the overall OER performance. A similar trend is observed

in the EIS simulated for different applied potentials as shown in the SI Figure S5.

The results show that if the impact of 𝑅s on 𝑅pol is not taken into account, it will lead to an

underestimation of the catalytic efficiency of the photoanode material. Similarly, the time

constants of the processes at the interface also decrease due to an increase in 𝑅s. Thus, it is

necessary to correct the impedance data for the impact of 𝑅s. The data obtained from EIS

analysis can be corrected by plotting the data vs. 𝑉applied − 𝑗. 𝑅𝑠 instead of 𝑉applied. An

example of this correction is shown using a simulated Mott-Schottky plot in Figure 9. The

Mott-Schottky data is calculated for the case of 𝑅s = 100 Ωcm2 using Eq. (43). The data is

plotted vs. both 𝑉applied (uncorrected) and 𝑉applied − 𝑗. 𝑅s (corrected).

Flattening of the Mott-Schottky plot is visible at two locations in the case of the uncorrected

Mott-Schottky plot. As discussed earlier, the first flattening around a voltage of 0.6 V – 0.8 V

is related to r-SS and the second flattening which is observed at a voltage higher than 1.0 V (in

the bold line) is related to the potential drop over 𝑅s. This second flattening is not visible when

correction is applied to the voltage axis (dotted line). The flattening observed around 0.6 V -

0.8 V remains unchanged in both cases as the Fermi level pinning due to r-SS is independent

of 𝑅s. The corrected plot shows only Fermi-level pinning due to the surface states, omitting

the potential drop across 𝑅s. Hence, the correction for the potential drop over 𝑅s enables

accurate identification of surface state phenomena from the Mott-Shottky plot.

Chapter 4 173

Figure 9 The simulated value of 1/(𝐶𝑠𝑐)2 as a function of voltage, where voltage is 𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑(solid line) and

𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑 − 𝑗 ⋅ 𝑅𝑠 (dotted line) for 𝑅𝑠 = 100 Ωcm2. The dotted line shows only one flattening which is the Fermi

level pinning due to r-SS.

We show that the data obtained from equivalent circuit fitting can be corrected for the effects

of 𝑅s by plotting vs. 𝑉applied − 𝑗. 𝑅s. Such a correction will lead to a characterization of the

photoanode material independent of the contribution from series resistance. For instance, in

the case of an annealing experiment, the corrected data will give information about the

performance of the functional layer, irrespective of variations in back contact during

annealing.

4 Summary and conclusions

The series resistance (𝑅s) is related to the back contact resistance of the photoanode and the

electrolyte resistance. Since the magnitude of 𝑅s is relatively small compared to the other

resistive components in the EIS, 𝑅s is generally assumed to have no impact on PEC

measurement data. However, certain electrode treatments aimed at performance

enhancement are reported to result in a significant increase in 𝑅s. We have investigated in

this chapter, the impact of 𝑅s on typical electrochemical data, such as j-V curves and EIS, using

a microkinetic model of OER. The model can simulate the current density and typical data

from EIS analysis, like surface state capacitance, the capacitance of the space charge layer,

and charge transfer resistance, directly based on the processes occurring at the interface.

From the simulated data, we find that 𝑅s has an impact on the electrochemical data at applied


potentials higher than the onset potential. The significance of the impact increases with an

increase in 𝑅s and the magnitude of current density due to OER.

In the case of j-V data, the saturation current density and the slope of the j-V ramp decrease

with an increase in 𝑅s as shown in Figure 10a. Thus, 𝑅s has an impact on the j-V curve and the

perceived OER performance. Additionally, a decrease in the slope of the j-V ramp can be an

indication of an increase in 𝑅s. The simulated scenario of annealing shows that an increase in

𝑅s can mask the increase in photocurrent resulting from the passivation of surface states. We

find that the OER onset potential is unaffected by the series resistance, as the potential drop

over 𝑅s becomes significant only after the onset of current.

Figure 10 Representative plots summarizing the impact of 𝑅𝑠 on a) j-V plot; b) surface state capacitance (𝐶𝑠𝑠); c)

Mott-Schottky plot and d) charge transfer resistance (𝑅𝑠𝑠). The blue curves represent the case with 𝑅𝑠 = 0 Ωcm2,

the dashed red curve represents the case for the typical value of 𝑅𝑠 = 30 Ωcm2 and bold red curves represent the

case with 𝑅𝑠 = 200 Ωcm2. The grey dashed lines mark the onset potential.

The impact of 𝑅s on the impedance contributions, like surface state capacitance, the

capacitance of the space charge layer, and the charge transfer resistance, are simulated. It is

𝑪𝒔𝒔

Mott-Schottky plot

j-V plot a b

c 𝑹𝒔𝒔 d

𝑉onset

Chapter 4 175

found that the large peak in the surface state capacitance observed around the onset potential

is marginally affected by the change in 𝑅s as shown in Figure 10b. However, for the smaller

second peak visible after the onset potential (show in the inset), the spread of the peak

increases and the maximum of the peak decreases with an increase in 𝑅s. Thus, in general,

those parts of the surface state capacitance data, observed at potentials higher than the onset

potential are affected by an increase in 𝑅s.

The impact of 𝑅s on the capacitance of the space charge layer is observed as a flattening in

the Mott-Schottky plot around the onset potential as shown in Figure 10c. This flattening can

be misinterpreted as Fermi level pinning due to surface states as the surface state capacitance

is usually observed around the same potential. The flattening increases with an increase in 𝑅s

due to the associated increase in potential drop. The charge transfer resistance of the

photoanode is also observed to increases with an increase in 𝑅s. The increase in charge

transfer resistance is significant directly after the onset potential as shown in Figure 10d.

The variation in the above-mentioned impedance elements affects the EIS of the photoanode.

We found – in contrast to the typical assumption that an increase in 𝑅s merely shifts the

Nyquist plot along the x-axis – that an increase in 𝑅s increases the polarization resistance and

decreases the time constants of the processes represented in the EIS. The potential drop over

𝑅s reduces the potential across the space charge region, which reduces the hole flux and the

rate of OER. This explains how the increase in 𝑅s leads to an increase in polarization resistance

and an increase in time constants of the arc in the EIS.

We can, therefore, state that 𝑅s has an impact on PEC data and becomes significant with the

increase in magnitude of 𝑅𝑠. It is necessary to correct these data for a potential drop over 𝑅s

to avoid underestimation of the OER performance of the semiconductor material. A list

showing, PEC analysis data with corresponding 𝑅s correction requirement is given in Table 3.

Table 3. Typical PEC analysis data and corresponding 𝑅𝑠 correction requirement

Typical data from PEC analysis 𝑹𝐬 correction required

Onset potential No

Current density after onset potential Yes

Data from EIS analysis

Mott-Schottky plot Yes

Surface state capacitance Yes

Charge transfer resistance Yes

It should be noted that the correction mentioned here is different from the IR drop correction

done in the experimental setup. The IR drop correction usually done in the experimental setup

account for the IR drop over the resistance of the electrolyte between the working electrode


(photoanode in this case) and the reference electrode in the setup.48 This usual IR correction

done in the experimental setup does not include the back contact resistance.

In the literature, the magnitude of 𝑅s and change in 𝑅s, if any, are not always reported along

with the experimental data of photoanodes. Based on the results, it is important to quantify

and report 𝑅s along with the PEC measurements. Once 𝑅s is available, the j-V data and the

data obtained from the equivalent circuit fitting can be corrected for the potential drop over

𝑅s by plotting against 𝑉applied − 𝑗. 𝑅s. This corrected data will aid in drawing conclusions about

the OER performance of the functional layer irrespective of the effects of 𝑅s. As the potential

drop increases with an increase in current density, these observations are highly relevant in

the case of high-performing photoanodes with high current density. Additionally, from the

modeling point of view, it is necessary to include 𝑅s in models aimed at performing

comparisons with experiments.

Acknowledgments

George acknowledges funding from the Shell-NWO/FOM “Computational Sciences for Energy

Research” PhD program (CSER-PhD; nr. i32; project number 15CSER021). Bieberle-Hütter

acknowledges the financial support from NWO (FOM program nr. 147 “CO2 neutral fuels”) and

M-ERA. NET (project “MuMo4PEC” no. 4089). Supercomputing facilities of the Dutch national

supercomputers SURFsara/Lisa and Cartesius are acknowledged.

Chapter 4 177

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Chapter 4 181

Supporting information

S1. Series resistance and polarization resistance

An example of a Nyquist representation of an electrochemical impedance spectrum showing

series resistance (𝑅s) and polarization resistance (𝑅pol) is given in Figure S1.

Figure S1 A Nyquist representation of EIS showing 𝑅𝑠 and 𝑅𝑝𝑜𝑙. The direction of the increase in frequency is

shown by the arrow.

S2. Hole flux to the surface

The photocurrent depends on the rate of OER at the semiconductor-electrolyte interface

which depends on the hole density at the semiconductor surface. The hole density at the

surface under illumination depends on 𝑢sc. This is explained as follows. Under illumination,

electron-hole pairs are generated within the semiconductor. Under a positive bias, the holes

move towards the semiconductor surface where it oxidizes water. According to the Gartner

equation, the flux of holes to the surface (𝐽G) under illumination is given by1

𝐽G = 𝐼0(1 −

exp(−𝛼𝑊sc)

1 + 𝛼𝐿p)

(S. 1)

where 𝐼0 is the illumination intensity, 𝛼 represents the absorption coefficient for a given

wavelength of the incident light, 𝑊sc represents the width of the space charge region, and 𝐿p

represents the minority carrier diffusion length. 𝑊sc is given by2

𝑊sc = √2𝜖r𝜖0𝑒𝑁d

(𝑢sc − 𝑘B𝑇/𝑒)

(S. 2)


𝑁d is the doping density, 𝑒 is the charge of an electron, 𝑘B is the Boltzmann constant, and 𝑇

is the temperature.


S3. Constants used in the simulation

Simulation in this chapter is performed using the model developed in George et al.3. The

constants used and their descriptions are given in Table S1.

Table S1 Model parameters, their descriptions, and values used in the simulations.

Parameter Description Value Reference

𝐸V Val. band energy level for hematite 2.4 4

𝐸C Cond. band energy level for hematite 0.3 4

𝐸T Trap state energy level 𝐸C+ 0.4

𝑛s0 Electron density under zero bias 𝑁d

𝑝s0 Hole density in the dark under zero

bias

1 cm-3

𝑅s Series resistance 30 Ω ⋅cm2

𝛼 Absorption coefficient 1.5 X 105 cm-1 5

𝐿D Hole diffusion length 4 X 10-7 cm 6

𝜖 Relative permittivity of hematite 38 7

𝑉fb Flat band potential 0.4 V 7

𝐼0 Illumination intensity 1 X 1016 cm2 5

𝜎p Electron capture cross section of

holes

1 X 10-16 cm2 5

𝑣th Thermal velocity of electrons 1 X 105 cm/s 5

𝑘n, 𝑘p Electron and hole trapping rates 𝜎p ⋅ 𝑣th (cm3/s) 5

𝑘rec Direct recombination rate within SCR 1 X 10-6 cm3/s

𝑑 Thickness of hole accumulation layer 1 X 10-7 cm 5,8

𝐶H Helmholtz layer capacitance 20 X 10-6 F/ cm2 9

𝑁d Doping density 3 X 1018 cm-3 7

𝑁0,ideal No. of. ads site on ideal hematite

surface

2.9 X 1014 cm-2 10

𝑁T Surface state density of r-SS 1 X 1013 cm-2

𝑁0 No. of. ads sites on surface in the

presence of r-SS

𝑁0,ideal − 𝑁T

𝐾B Boltzmann constant 8.61733 X 10-5 eV/K

𝑒 Charge of electron 1.60217662 X 10-19 C

𝜖0 Permittivity of free space 8.8541878128 X 10-14 F

cm-2

𝑆𝑟 Scan rate 5 mV/s


pH pH of the electrolyte 13.6

Chapter 4 183

pOH pOH of the electrolyte 14-pH

𝑥OH Mole fraction of hydroxyl ions 10-pOH/(molar conc. of

water)

𝑥H2O Mole fraction of water 1- 𝑥OH

𝑘v,max,f, 𝑘v,max,b Max. rate constants via val. band 3 X 10-16 cm4/s 11

𝑘c,max,f, 𝑘c,max,b Max. rate constants via cond. band 3 X 10-16 cm4/s 11

𝑘𝑡,max,f, 𝑘𝑡,max,b Max. rate constants via trap state 3 X 10-16 cm4/s 11

𝜆 Solvent reorganization energy 1 eV 12

𝑁C Density of state of cond. band 4 X 1022 cm-3 13

𝑁V Density of state of val. band 1 X 1022 cm-3 13

𝐾𝑓5 Desorption rate of oxygen 8 X 105 cm-1 14

Δ 𝐺1 Gibbs free energy for step 1 in OER 1.87 eV 3




S4. Surface coverage

The surface state capacitance is calculated based on the change in coverage of OER

intermediates with respect to the change in the applied voltage (Eq. (1)). The surface

coverages of OER intermediates for 𝑅s = 0 Ωcm2 are shown in Figure S2 (bold lines). The green

line represents the fraction of free sites at the surface. The coverage of OH shows a sharp

increase between 0.8 V and 1.0 V. This explains the main peak in the 𝐶ss plot as shown in

Figure 6a in the main text. There is a small variation in coverage between 1.0 V and 1.2 V

which explains the second smaller peak in the 𝐶ss plot as shown in Figure 6b in the main text.

The increase in 𝑅s decreases the rate of the intermediate reactions and affects the coverage

of intermediate species as shown in the figure (dashed line). The effect of 𝑅s is visible at

applied voltages higher than 1.0 V, which explains the variation in the smaller peak in the 𝐶ss

plot as shown in Figure 6b in the main text.


Figure S2 Change in surface coverage with a change in 𝑅𝑠. Bold lines represent the surface coverage for 𝑅𝑠 = 0

Ωcm2 and the dashed lines represents the surface coverage with 𝑅𝑠 = 200 Ωcm2. ‘*’ represents the fraction of

free sites at the surface.

S5. Capacitance due to r-SS simulated for different 𝑹𝐬

The capacitance due to r-SS is calculated using Eq. (2). Figure S3 shows the capacitance due to

r-SS simulate for different 𝑅s. Since the potential range of the capacitance is at applied

voltages lower than the onset potential, it is unaffected by a change in 𝑅s.

Figure S3 Capacitance due to r-SS simulated for different 𝑅𝑠.The simulated capacitance due to r-SS is unaffected

by the change in 𝑅𝑠

Chapter 4 185

S6. Enlarged plots for 𝑹𝐬𝐬

The simulated curves for 𝑅ss from Figure 7b enlarged for applied potential higher than the

onset is shown in Figure S4. The 𝑅ss around the OER onset is higher when 𝑅s is high. 𝑅ss shows

a decrease in magnitude around the end of the j-V ramp and then starts increasing again. The

plot of 𝑅ss in Figure S4 might give a notion that an increase in 𝑅s leads to a decrease in 𝑅ss at

higher potentials. This is due to the delayed minima and concomitant delay in the increase in

𝑅ss with increase in 𝑅s.

Figure S4 Charge transfer resistance (𝑅𝑠𝑠) enlarged for applied potentials after OER onset. The charge transfer

resistance reaches a minimum around the applied potential of 1.2 V and then increases upon a further increase

in applied voltage.


S7. EIS simulated for different applied potentials

Nyquist plots simulated for different applied potentials (1.0 V, 1.05 V, 1.1 V, and 1.15 V)

around the onset potential are shown in Figure S5. The Bode phase plot of the same data is

also shown. In all the cases, the polarization resistance increase with an increase in 𝑅s. The

frequency corresponding to the peaks in the phase plots also changes with the change in 𝑅s.

Figure S5 The Nyquist representation of EIS and Bode phase plots simulated at different applied potentials (a)

1.0 V (b) 1.05 V (c) 1.1 V and (d) 1.15 V. The polarization resistance increases with 𝑅𝑠 in all the cases. The phase

plot shows that the peak of the phase plot and the frequency corresponding to the phase peak changes with an

increase in 𝑅𝑠.

a

c

d

b

Chapter 4 187

References

(1) Peter, L. M.; Wijayantha, K. G. U.; Tahir, A. A. Kinetics of Light-Driven Oxygen Evolution at α-Fe 2 O 3 Electrodes. Faraday Discuss. 2012, 155 (0), 309–322. https://doi.org/10.1039/C1FD00079A.


(3) Kiran George, Tigran Khachatrjan, Matthijs van Berkel, Vivek Sinha, and A. B.-H. Microkinetic Modeling at the Surface Combined with Charge Carrier Dynamics in the Bulk: A New Approach to Investigate the Impact of Surface States in Water Oxidation on Experimental Data. To be Submitt.











Summary 189

Summary

Modeling water oxidation at photoanodes: A multiscale approach

Water splitting using sunlight is a promising path for storing solar energy in chemical bonds. A

potential cost-effective method to do this is by using a photoelectrochemical (PEC) cell. In a

PEC cell, the hydrogen evolution reaction takes place at the cathode and the oxygen evolution

reaction (OER) takes place at the anode. Depending on the configuration, a PEC cell has at

least one of the electrodes made of a semiconductor with a suitable bandgap to absorb energy

from sunlight. The semiconductor materials should also be able to catalyze the water-splitting

reactions. Even though theoretical solar-to-hydrogen conversion efficiencies of PEC cells are

promising, the practical efficiencies are quite low for commercialization. The OER occurring at

photoanodes is identified to be one of the performance-limiting processes in PEC water

splitting. Therefore, improving the efficiency of OER at the photoanode is necessary to

improve the overall efficiency of water splitting.

The OER is generally assumed to take place via four steps with different intermediates. The

kinetics and thermodynamics of these intermediate steps in OER at the semiconductor surface

affect the catalytic efficiency of OER. The charge carrier dynamics within the semiconductor

affect the availability of charge carriers at the semiconductor surface which in turn influences

the OER. Conclusively, the interplay between thermodynamics and kinetics of the

intermediate steps in OER, and the charge carrier dynamics within the semiconductor have a

critical impact on the overall performance and electrochemical characteristics of the cell.

However, limited tools are available to analyze the interplay between multistep OER and the

semiconductor properties.

The aim of this dissertation is therefore to develop an approach that allows for simulating the

semiconductor-electrolyte interface (SEI) under realistic conditions and for comparing the

simulated data with experiments. The approach takes into account the interplay between

thermodynamics and kinetics of the intermediate steps in OER and the charge carrier

dynamics within the semiconductor. For this, a new computational approach is developed that

brings together density functional theory (DFT), microkinetic modeling, and charge carrier

dynamics within the photoanode. The thermodynamics of the four-step OER on the

semiconductor surface is investigated using DFT calculations. The reaction kinetics of the

intermediate steps are represented by a microkinetic model of OER, and the charge carrier

dynamics are modeled based on the processes occurring within the semiconductor under

illumination. The material-specific rate constants used in the microkinetic model are

estimated using the free energies calculated by DFT. The charge carrier concentration at the

semiconductor surface is calculated from the material properties, rate constants for the

190 Summary

processes within the semiconductor, and the rate constants of the multiple steps in OER. Thus,

for the first time, a model is developed which takes into account the combined effect of four-

step OER at the SEI and the charge carrier dynamics in the semiconductor. Electrochemical

data, such as j-V characteristics, impedance spectra, chopped light measurements, are

simulated from the model. This is the same data that is measured experimentally to

characterize the SEI. Hence, simulations and experimental data can be directly compared

which enables mechanistic interpretation of experimental data. Hematite (Fe2O3) is used as

the model system throughout the dissertation.

In Chapter 1, DFT calculations are carried out to investigate the effect of thermodynamics

of intermediate steps in OER on the overpotential. In specific, the impact of adding a co-

catalyst layer of NiOOH on hematite is investigated. Experimental studies in the literature have

shown that such catalysts improve OER performance. The reason behind this increase in

performance is investigated. The free energies of the formation of OER intermediates on

NiOOH/Fe2O3 surface and ultimately the overpotentials are calculated. It is found that the

improvement in overpotential results from the higher catalytic activity of Ni sites which are in

close vicinity of the Fe atoms. Based on these results it is concluded that depositing NiOOH as

nano-islands on the hematite surface is preferable compared to the deposition of a uniform

layer of NiOOH. From the modeling perspective, the co-catalyst layer should be implemented

as a continuous strip in order to give a stable and computationally efficient geometry.

In Chapter 2, a microkinetic model of OER on the SEI is developed which can simulate the

same data that is usually measured experimentally to characterize the SEI, i.e. current-voltage

curves and electrochemical impedance spectra (EIS). Microkinetic rate equations for the four

steps in OER are formulated as a non-linear state-space model. Charge carrier density at the

semiconductor surface is assumed to be a function of applied potential. The theoretical

reaction rates used in the model are estimated from DFT calculations as introduced in Chapter

1, in combination with Gerischer theory. For the first time, the EIS for a semiconductor

photoanode interface is simulated from first principles in combination with a microkinetic

model. A relation between EIS and rate constants of the four OER steps is derived. The

simulated curves are directly compared to experimental measurements. Apart from the

current density and the EIS, the model can simulate the coverage of intermediate species as a

function of applied potential which is experimentally very challenging but highly sought after

for identifying the limiting processes at the interface.

In Chapter 3, the charge carrier dynamics within the semiconductor under illumination is

added to the microkinetic model of OER developed in Chapter 2. The extended model takes

into account illumination as well as charge carrier trapping at different types of surface states,

i.e. recombining surface states (r-SS) and surface states due to OER intermediates (i-SS). The

impact of these surface states on the PEC measurements and how they affect OER are still a

Summary 191

topic of debate in the literature. Using the model, the impact of r-SS and i-SS on the PEC data,

such as j-V curves, hole flux, surface state capacitance, Mott-Schottky plot, and current density

under chopped light are elucidated. It is found that r-SS results in a capacitance before the

OER onset potential and leads to an increase in the onset potential and a decrease in

saturation current density. i-SS, in contrast, results in a capacitance around the onset

potential; the onset potential is increased by an increase in the capacitance corresponding to

i-SS while the maximum current density is not changed. A decrease in the capacitance peak

corresponding to i-SS can be an indication of lower catalytic performance of the

semiconductor surface. Regarding the potential distribution within the space charge layer

investigated by Mott-Schottky analysis, it is observed that r-SS leads to Fermi level pinning

before the onset potential whereas i-SS does not result in Fermi level pinning. We conclude

that r-SS reduces OER performance and i-SS mediates OER. The results from the model allow

separating the impact of r-SS and i-SS in PEC data.

In Chapter 4, the impact of the series resistance (𝑅𝑠) on the OER performance perceived from

electrochemical data is investigated using the same model as in Chapter 3. 𝑅𝑠 refers to the

back-contact resistance of the photoanode and any uncorrected change in the resistance of

the electrolyte. From the simulated j-V plots, it is observed that the saturation current density

and the slope of the j-V ramp decrease with an increase in 𝑅𝑠. However, the OER onset

potential is not affected by 𝑅𝑠. The impact of 𝑅𝑠 on the impedance components like surface

state capacitance, the capacitance of the space charge layer, and the total resistance is

simulated using the model. In contrast to the typical assumption that 𝑅𝑠 only leads to a linear

shift of the Nyquist plot along the x-axis, it is found that both the polarization resistance and

the time constants of the processes increase with 𝑅𝑠. It is therefore important to quantify and

report 𝑅𝑠 along with PEC data and we suggest a way to correct for 𝑅𝑠 and plot the data

appropriately. Such corrected data will give information about the performance of the

functional layer irrespective of contributions from 𝑅𝑠.

In summary, the models developed in the dissertation aid in gathering mechanistic

information about OER occurring at photoanodes by enabling theory-experiment comparison.

The individual and combined impact of thermodynamics of the multiple reaction steps in OER,

the reaction kinetics, and charge carrier dynamics within the semiconductor, on OER at the

SEI are elucidated by the simulations. Some of the intriguing questions about the SEI, such as

the impact of different types of surface states on OER, are answered based on the comparison

of simulation and experiment. Further development of the multiscale modeling in

combination with experiments will deliver a clear understanding of the SEI which will aid in

devising strategies to develop high-performance PEC cells.

192 Summary

Publications and presentations 193

Publications and presentations

List of Publications (First author)

1. K. George, X. Zhang, A. Bieberle-Hütter, Why does NiOOH cocatalyst increase the oxygen

evolution activity of alpha-Fe2O3? J. Chem. Phys. 150 (2019) 041729.

2. K. George, M. van Berkel, X. Zhang, R. Sinha, A. Bieberle-Hütter, Impedance spectra and surface

coverages simulated directly from the electrochemical reaction mechanism: A nonlinear state-

space approach, J. Phys. Chem. C 123 (15) (2019) 9981-92.

3. K. George, T. Khachatrjan, M. van Berkel, V. Sinha, A. Bieberle-Hütter, Understanding the

impact of different types of surface states on photoelectrochemical water oxidation: A

microkinetic modeling approach. Submitted, 2020.

4. K. George, M. van Berkel, A. Bieberle-Hütter, The critical role of the series resistance in

impedance measurements of photoelectrodes. In preparation, 2020.

Oral presentations (Presenting author in bold)

1. K. George, X. Zhang, A. Bieberle-Hütter, Origin of enhanced Oxygen Evolution Reaction

performance of NiOOH-hematite photoanodes: A DFT study, Computational Sciences for

Future Energy conference 2017, 2017/09/19 - 2017/09/20, Eindhoven, Netherlands.

2. K. George, M. van Berkel, X. Zhang, A. Bieberle-Hütter, Integrated modeling of multistep

reactions at photo-electrochemical interfaces by combining DFT and non-linear state-space

modeling, International Workshop on Computational Electrochemistry IWCE 2018, Helsinki,

Finland.

3. K. George, M. van Berkel, X.Q. Zhang, R. Sinha, A. Bieberle-Hütter, Modeling Impedance

Spectra at Semiconductor-Electrolyte Interface - A Multiscale Approach, MRS Spring 2019,

Phoenix, Arizona.

4. K. George, T. Khachatrjan, M. van Berkel, and A. Bieberle-Hütter, Linear sweep voltammetry

and impedance spectra simulated directly from the electrochemical mechanism, E-MRS Fall

Meeting 2019, Warsaw, Poland.

5. K. George, M. van Berkel, X. Zhang, V. Sinha, R. Sinha, Y. Zhao, A. Bronneberg, and Anja

Bieberle-Hütter, Identifying the Limiting Processes at Electrochemical Interfaces: From

Experimental Data to Multi-scale Modeling, MRS Fall 2019, Boston.

194 Publications and presentations

Poster presentations

1. K. George, T. Khachatrjan, M. van Berkel, V. Sinha, A. Bieberle-Hütter, Simulating surface states

in water oxidation directly from the electrochemical mechanism, Accepted for Faraday

Discussions 2020 (postponed to 2021).

2. K. George, M. van Berkel, X. Zhang, A. Bieberle-Hütter, Microkinetic Modeling of Water

Oxidation in Photoelectrochemical Cells: The Impact of Surface States on the Electrochemistry,

MRS Fall Meeting 2019, 2019/12/01 - 2019/12/06, Boston, MA, USA.

3. K. George, T. Khachatrjan, M. van Berkel, A. Bieberle-Hütter, Linear sweep voltammetry curves

simulated directly from the electrochemical reaction mechanism, Applied Computational

Sciences (ACOS) symposium 2019, 2019/10/30, Eindhoven, Netherlands.

4. K. George, X. Zhang, A. Bieberle-Hütter, Increased oxygen evolution activity on NiOOH/a-

Fe2O3: a DFT study, Physics Veldhoven 2019, 2019/01/22 - 2019/01/23, Veldhoven,

Netherlands.

5. K. George, M. van Berkel, X.Q. Zhang, R. Sinha, A. Bieberle-Hütter, Modeling electrochemical

impedance spectra by combining DFT and non-linear state space approach, CHAINS: Chemistry

matters for the future, 2018/12/03 - 2018/12/05, Veldhoven, Netherlands.

6. K. George, M. van Berkel, X.Q. Zhang, A. Bieberle-Hütter, Simulating photo-electrochemical

interface data by combining DFT and state-space modeling, Applied Computational Sciences

(ACOS) symposium 2018, 2018/10/10, Eindhoven, Netherlands.

7. K. George, M. van Berkel, X. Zhang, A. Bieberle-Hütter, Modeling oxygen evolution: state-space

modeling in combination with density functional theory, Physics Veldhoven 2018, 2018/01/23

- 2018/01/24, Veldhoven, Netherlands.

8. K. George, X. Zhang, A. Bieberle-Hütter, Enhanced Oxygen Evolution Reaction performance of

NiOOH-hematite photoanodes: A DFT study, CHAINS: Chemistry matters for the future,

2017/12/05 - 2017/12/07, Veldhoven, Netherlands.

9. K. George, X. Zhang, M. van Berkel, A. Bieberle-Hütter, New method of Modeling Oxygen

Evolution in Solar Water Splitting: Density Functional Theory based State-Space Modeling,

Renewable Energy Driven Chemistry Workshop, 2017/04/05, Eindhoven, Netherlands.

10. K. George, X. Zhang, A. Bieberle-Hütter, Modeling of Oxygen Evolution in Solar Water Splitting

by Density Function Theory based State-Space Modeling, CSER conference Computational

Sciences for Future Energy 2016, 2016/10/11, Utrecht, Netherlands

Acknowledgments 195

Acknowledgments

When I look back to my journey so far, I see the faces of many people who have shaped me

into the individual I am right now. I would like to thank all of them for being a part of my story.

Without their support and encouragement, this thesis would not have been possible.

First of all, I would like to thank my supervisor Anja Bieberle-Hütter for guidance and support

throughout the past four years. I have always valued the way you make yourselves available -

your promptness in responding to emails, openness to discussions, and quick and meticulous

feedback on documents. I admire how you positively adapt your supervision style to be apt

for the individual in front of you. Your constructive criticisms motivated me to push my limits.

Whenever I had doubts, the discussions with you were very enriching and helped me arrive at

the right answers. During tough times you identified the positives and more importantly

communicated those to me. It was very encouraging and it played a huge role in keeping my

morale up throughout the project. Thank you for the patience you have shown and the belief

you had in me during the project.

I would like to thank my co-supervisor Matthijs van Berkel for guidance and support. Matthijs,

you have helped me a lot during these four years. Your critical thinking and clarity in work are

admirable. Thank you for introducing me to the system identification course in Brussels. I

remember you came to Brussels and stayed there for a week during the course so that I could

clear the doubts easily with you. Thank you for all the scientific and non-scientific discussions

and the support you have given during the project.

Special thanks to my promoter Richard van de Sanden, whose support and guidance have

been invaluable for this PhD project. You always posted the right questions during our

meetings. Your questions positively influenced my thought process and helped me to come

up with new ideas. The support and appreciation you have given inspired me to elevate my

work. Thank you for the time you have invested in me out of your busy schedule.

Thanks to Xueqing Zhang for your guidance especially during my initial days at DIFFER. I am

indebted to you for the knowledge you shared regarding catalysis and DFT. You were so kind

and helpful and never showed any signs of impatience when I used to approach you frequently

for clearing my doubts in the beginning of my project.

I would like to thank Marco de Baar for the motivating discussions. You have inspired me a lot

and I always enjoyed the conversations with you. I admire the way you took an interest in

asking me about the developments in the project and appreciating the efforts. Thank you.

196 Acknowledgments

I would like to thank my thesis committee members Sophia Haussener, Roel van de Krol, Marc

Koper, and Siep Weiland for the time and effort put in reading my thesis and giving valuable

comments.

Thanks to all the DIFFER group leaders, especially Andrea Baldi, Shuxia Tao, Michail Tsampas,

Gerard van Rooi, Michael Gleeson, Stefan Welsel, and Suleyman Er for the scientific insights.

Thanks to my colleagues in the EMI group Rochan, Yihui, Quihua, Nitin, Vivek, Aafke, and

Christian. It was a pleasure working with you all. Rochan, special thanks for sharing your

knowledge in semiconductor physics during my initial days. Yihui, I admired the way you

approached problems and I have learned a lot from your smart-working methods. Qihua,

thanks for all the conversations we had and keep going with the positive energy you spread

around you! Nitin, thank you for the scientific discussions and fun chats. Vivek, thanks for all

the support you have given for my project especially with the DFT calculations. Aafke, your

experimental works on the identification of intermediates and the discussions inspired me in

my modeling efforts.

Thanks to my students Qinyi, Sem, and Tigran. I am happy that I got the opportunity to work

with you and thank you for the hard work you have delivered.

I was fortunate to get selected to attend the system identification workshop at Vrije University

Brussels, organized by the ELEC department. This was a great learning opportunity and I would

like to thank the organizers of the workshop and special thanks to Dr. John Lattire and prof.

dr. ir. Gerd Vandersteen for the fruitful discussions. Thanks to all the fellow workshop

attendees for making the time at VUB enjoyable.

Tesfaye, Yihui, thank you for being amazing office mates, and thank you for making the office

such a fun place. Tesfaye, your 6 pm after-work funny video sessions brought joy at the end

of the day. Yihui, our trip to Ghent and the Glow trip were awesome and to date, you are my

best gym buddy with exceptional dedication. After you two finished your PhD, it was hard to

be alone in the office.

I got the opportunity to be the Sinterklaas for the DIFFER Cabaret 2017. Thanks to Muhammed

for choosing me to be the Sinterklaas. Thanks to all the members of DIFFER Cabaret 2017,

Adelbert, Martijn, Sander, Bram, Stein, Tom, Qin, George, Alex, Bob, and Bobby for the

amazing experience. I had so much fun acting, singing, filming, and writing sketches with you

guys. For me, the Cabaret is one of the best memories during the past four years at DIFFER.

I would like to thank Henk, Jolanda, Erik, Maarja, Wilko, Ed, Ans, Jaqueline, Jan-Willem, Albert,

Fred, and Miranda for the support and making things easier for me. Thanks to Pieter Willem,

Han, Erwin, and Aron for the discussions and friendly conversations.

Acknowledgments 197

There are many people who have helped to make DIFFER a jovial workplace and made the

past four years a memorable one for me. Dozie, Shih-Chi, Sofia, Haibo, Jose, the lunch table

conversations with you guys were something I looked forward to every day. Thanks for the

fun chats and coffee corner talks which covered history, current affairs, science, TV series, and

more. Those moments were really fun, refreshing, and informative. Georgios, I enjoyed our

conversations especially based on the shared interest in football. The champions league game

at the PSV stadium we attended with the last-minute ticket was fun. Matteo, thank you for

the company during the EMRS conference in Warsaw. I enjoyed the conversations and the city

tour during the stay in Warsaw. Also thanks for the excellent suggestions during my trip to

Rome. Bram, thanks for all the tips during the thesis writing days.

Thanks to all my friends at DIFFER from the past and present - Dirk, Teo, Nicola, Srinath, Tom,

Aron, Fiona, Anna, Yaoge, Vladimir, Muhammed, Gilson, Damien, Stein, Renato, Karel, Dani,

Devyani, Wei, Junke, Quhua, Zehua, Min, Isabel, Ray, Pedro, Luca, Michele, Aaron, Timo,

Rickey, Eloy, Karol, Jonathan, Mojgan, Ana, Alex, Floran, Johannes, Tim, Tiny, Ilker, Murat,

Abhishek, Xi, Xuan, Tibout, Vaselius, Paola, Usman, Arun, Satyaraj, Rakesh, Hrishikesh, Ruben,

and Gayatri. Life at DIFFER would not have been fun without you guys.

There are many friends outside work who added fun and meaning to my life in Eindhoven.

Special thanks to Anna, Rianne, Enrico, Erasmus, Jude, Florian, Prince, Clint, Piyush, Fajo,

Deepti, Abraam, Richie, Cindy, Anisha, Stallone, Limi, Winston, Andrea, Jimmy, Shikha,

Sidharth, Alina, Joe, Aelikkutty, Sherin, Prima, Jijo, Shubha, Jofin, and Anju. Thanks for the

encouragement and support you have provided.

Eindhoven would not have been this enjoyable for me without the company of the Malayali

friends. Thanks to Rifat, Subin, Subhash, Sangeeth, Ayushi, Vishnu, Arunitha, Amal,

Narasimhan, Nitin, Justin, Jyolsana, Emi, Mabel, Babu, Indu, Shaneesh, Rishija, Sreekanth,

Sruthi, Abhilash, and Sreenish. The lunches, dinners, games, and trips we had together were

valuable to me and helped me keep my life balanced. Rifat, thanks for organizing the get-

togethers, the conversations during the bike rides back home, and the occasional calls during

the lockdown period. Special thanks to you for all the tips during the thesis writing time,

suggestions with the cover design, and being the voice of reason during tough times. Subin,

conversations with you always lighten the situation. Sangeeth, thanks for being a great friend.

You are so dedicated that even after you moved to Tilburg you made sure that you were there

for all our gatherings. Subash, thanks for the company during our trips, and especially during

the everyday lunch at DIFFER. Vishnu, I admire the way you handle even the worst situations

and carry yourself without any worry. I had so much fun during the trip we had with Sreenish

and it was one of the best trips I ever had. Babu, Shaneesh, thanks for the invaluable advice

regarding PhD and life. Justin and Jyolsana, you are like family to me. I always enjoyed our

gatherings and the time we spent together. Emi and Mabel, you have helped me a lot during

198 Acknowledgments

my time in Eindhoven. Whenever I needed help, you always made time out of your busy

schedule.

My family has been a huge support for me during my journey so far. I would like to thank my

brother Unni for the consistent support and advice. Unni, I could talk to you about anything

anytime and you found time during your busy work schedule to listen and talk to me. During

tough times, your advice and kind words helped me to keep going. Thanks to Teslin for all the

support. Chachan and Amma, no words are enough for the support and encouragement you

have given. You listened to my concerns patiently and assured me whenever I felt low. Thank

you for everything! Special thanks to Appa, Amma, Roy, and Anetta for the kind support,

understanding, and encouragement. Thanks to all my cousins, uncles, and aunts who have

encouraged me throughout my journey. I am lucky to have you all in my life.

Last but not least, I would like to thank my wife Shilpa for the consistent support,

understanding, and encouragement throughout the PhD and especially during the thesis

writing phase. Most of the thesis writing happened at home due to COVID-19 and you were

my ‘home office mate’. You actively listened to my concerns and gave me support and advice

which helped me a lot. When I had difficult deadlines you sat with me to breakdown the to-

do list and made an hour-wise plan which helped me finish on time. Thanks for proofreading

my thesis and investing time out of your busy work schedule to give corrections. Thank you,

Shilpa!

The road to PhD is a very long one. I believe it is more than the four years spent on the PhD

project. Many people have directly and indirectly contributed to my journey so far. I might

have failed to mention certain names. To all of them, I would like to say from the bottom of

my heart, “Without your help, support, and encouragement I wouldn’t have been here, thank

you”.

Curriculum Vitae 199

Curriculum Vitae

Kiran George was born on 19th October 1988 in Thrissur, India. After completing his secondary

school education in Thrissur in 2006, he enrolled for a Bachelor's program in Mechanical

Engineering at College of Engineering Thiruvananthapuram, India. Following graduation in

2010, he started working as a mechanical engineer at Saint-Gobain Glass, Chennai, India. In

June 2012 he joined a Master’s program in Mechanical engineering at the Indian Institute of

Technology (IIT) Madras, India. His Master's thesis was on the modeling of the electrochemical

response of graphite anodes in Li-ion batteries during charge-discharge cycles. After

graduating from IIT Madras in 2014, he joined GE India technology center at Bangalore as a

mechanical design engineer. During the two years at GE, he worked on computational

modeling and analysis of gas turbines used for power generation. Along with the job he

successfully graduated from the Edison engineering development program (EEDP) at GE. In

2016 he got selected for the CSER scholarship from Shell and NWO to pursue a PhD in

computational energy research. He started his PhD in the Electrochemical Materials and

Interfaces (EMI) group at DIFFER Eindhoven in July 2016. The results of his PhD work are

presented in this dissertation.

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