Studies of Charge Transfer at Semiconductor/Liquid Junctions Citation Pomykal, Katherine Elizabeth (1998) Studies of Charge Transfer at Semiconductor/Liquid Junctions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/v5ck-gf39. https://resolver.caltech.edu/CaltechTHESIS:08112025-204826614 Abstract Steady-state current-voltage measurements on two types of semiconductor/liquid junction solar cells are presented. Results of these and other experiments on single-crystal electrodes are discussed in terms of present kinetic theory on charge transfer at these junctions. Nanoporous titanium dioxide electrodes have been sensitized with a series of dyes with varying ground state reduction potentials. The spectral response and current-voltage properties of these electrodes have been measured. The trends can be explained by the differences in absorption spectra and ground state potentials. The effect of pH on the conduction band edge position of nanoporous titanium dioxide has been examined through current-voltage measurements and luminescence studies on dye-sensitized electrodes. The results are discussed in the framework of current theories on increasing efficiency of these electrodes. Studies involving charge separation at the back electrode contact were also performed. Predictions of the Marcus/Gerischer theory for photoelectrode stability have been investigated experimentally for n-Si/CH 3 OH photoelectrochemical cells. Specifically, a semiconductor electrode is predicted to be more stable if the reorganization energy of the stabilizing agent is decreased (in the normal region of the Marcus behavior), thereby increasing the rate of minority carrier capture by the stabilizer. This prediction was quantified experimentally by monitoring the branching ratio between two competing reactions at a semiconductor/liquid interface. The experimental observations can be consistently explained through this predicted influence of the minority carrier acceptor reorganization energy on the interfacial charge transfer rate constant. Interfacial charge transfer rate constants at indium phosphide/liquid junctions were investigated using current density-potential and differential capacitance-potential methods. The measured electron transfer rate constants, k et , for these systems were ≈10 -16 cm 4 s -1 , in excellent agreement with previous theoretical predictions. Contacts which did not display bimolecular kinetic behavior still yielded upper bounds on the charge transfer rate constants, which were also consistent with limits predicted by theory. The current density potential behavior of n-InP and p-InP/Fe(CN) 6 3-/4- (aq) junctions was also examined in order to assess the validity of prior kinetic measurements on these interfaces. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Lewis, Nathan Saul Thesis Committee: Gray, Harry B. (chair) Lewis, Nathan Saul Marcus, Rudolph A. Okumura, Mitchio Defense Date: 23 September 1997 Record Number: CaltechTHESIS:08112025-204826614 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08112025-204826614 DOI: 10.7907/v5ck-gf39 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17608 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 12 Aug 2025 16:46 Last Modified: 12 Aug 2025 16:46 Thesis Files PDF - Final Version See Usage Policy. 53MB Repository Staff Only: item control page

STUDIES OF CHARGE TRANSFER AT SEMICONDUCTOR/LIQUID JUNCTIONS Thesis by Katherine Elizabeth Pomykal In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1998 (Submitted September 23, 1997) ll Acknowledgements Acknowledgement #1: There is no possible way I will remember everyone I should thank for getting me through the last four years, so I apologize in advance to anyone I forgot in the list below. I'm sure you all remember or will experience the feeling, as Janet once told me, that you "don't have two brain cells left to rub together" while finishing your degree, so I'm sure you will forgive the omission. Caltech should have people send in their acknowledgements a year after they graduate so these things don't happen. Acknowledgement #2: Even if I do remember all you that you did for me, if I put everyone's name in here, the acknowledgements will be longer than my thesis. So just because your name became part of "... and others," doesn't mean I appreciate what you did for me any less. Thanks. Now to get (somewhat) more serious, I'll start by thanking people who helped me on a professional level. First and foremost, without Dr. John Reynolds at Lawrence Livermore National Laboratory I never would have ended up doing chemistry research, and without Dr. Michael Sailor at UC San Diego I never would have ended up in Nate's group at Caltech. Therefore, Mike and John deserve all the credit (or blame, depending on my mood) for getting me here in the first place. Both of them were great and caring advisors, and Mike especially has continued to give me helpful advice on dealing with various aspects of life. Working (and playing) with the Sailor group has been one of the most fun periods of time in my life. This is not to say I haven't also worked with a terrific bunch of people in the Lewis group. I've always been thankful that we have maintained a good group dynamic throughout the coming and goings of postdocs and graduate students, and I have interacted with many intelligent, creative, and fun people during my time here. Special thanks go to Amel Fajardo, who co-authored two papers with me, and to Genevieve Sauve and George Coia, my present collaborators. These people helped tremendously with constructive 111 criticism, experimental data, and useful discussion. Although many people have offered good insights and helped in revising proposals and manuscripts, I'd like to also single out Gary Shreve and Rob Rossi as two people I could always count on to look at my work thoroughly and gently but honestly point out all the strengths and weaknesses. I'd also like to especially thank William Royea for always keeping us entertained with stories of his exploits--there's never a dull moment when Will is around. One of the hardest parts in writing one's acknowledgements seems to be what to say about your thesis advisor. For me, no matter how frustrated I get with Nate sometimes, he has always come through when I really needed him to. I'd also like to echo the sentiment of many former students that working in this group definitely teaches one how to be a good scientist. Any paper coming out of this group is written to withstand the highest standards of scientific rigor, and most of the time we are more critical of ourselves than anyone else would be, which is as I think things should be. Of course, most of us need to get out of the lab sometimes to keep our sanity (or at least find insanity in other ways). Fortunately, I have had many people throughout the years who have helped me keep perspective. Thanks to all who have pounded the pavement with me, especially my fellow marathon training partners Dave Liberles, Aimee Wyatt, and Doug Sutton. A special thanks to Michelle Parks, who not only dragged me on enough long runs to eventually convince me to try marathoning, but was also a good friend and confidante during the long hours on the roads as well as at other times. A special thanks also to "honorary runner" Tom Dakan, who provided music and entertainment while biking with us and kept Michelle and me going on those 26-milers. The Caltech Masters Swim Team has also provided some much-needed diversion from graduate school, and I'd like to thank all of the members. Before mentioning any teammates names, however, I have to thank Chris Kenyon for getting me riled up enough to get back in swimming shape in the first place. If he hadn't insulted me that day, I might IV have never gotten to know a great group of people. I especially want to express my gratitude to my coach, Kenny Grace, for his caring, and to Dan and Lori Stein, without whom I might have been homeless my last month of graduate school. Kenny can put a smile on anyone's face no matter how bad one's mood is, and I can't express my thanks enough to Dan and Lori for letting me impose on them. Thanks also to Jordan Kaplan, who was an inspiration to us all and whose life inspires me still. Last, but certainly not least, I want to thank my friends and family not already mentioned above. Along with Michelle, Janet Kesselman was one of my best friends in graduate school, as well as a fellow UCSD and Lewis group alumna. Thanks for all the lunchtime talks and weekend expeditions. Andy and I were also lucky enough to have several family friends in the So. Cal. area; thanks to them for providing a "home away from home" several times a year. I have also been incredibly fortunate to be blessed with two wonderful and supportive sets of parents; my own, Tom and Karen Nelson, as well as my in-laws Glenn and Glynice Pomykal who treat me like their own daughter. I'd also like to thank my little sister Carolyn for entertaining me with her various trials and tribulations; even though she has had almost as many exploits as Will, I'm still proud of her. My sisters-in-law and their families also treat me like one of the family, and thanks to Susan and Carey for being "big sisters." Most importantly, a million thanks to the most vital person in my life, my husband Andy, without whom I would be completely lost. His love and support has meant everything to me. V Abstract Steady-state current-voltage measurements on two types of semiconductor/liquid junction solar cells are presented. Results of these and other experiments on single-crystal electrodes are discussed in terms of present kinetic theory on charge transfer at these junctions. Nanoporous titanium dioxide electrodes have been sensitized with a series of dyes with varying ground state reduction potentials. The spectral response and current-voltage properties of these electrodes have been measured. The trends can be explained by the differences in absorption spectra and ground state potentials. The effect of pH on the conduction band edge position of nanoporous titanium dioxide has been examined through current-voltage measurements and luminescence studies on dye-sensitized electrodes. The results are discussed in the framework of current theories on increasing efficiency of these electrodes. Studies involving charge separation at the back electrode contact were also performed. Predictions of the Marcus/Gerischer theory for photoelectrode stability have been investigated experimentally for n-Si/CH 3OH photoelectrochemical cells. Specifically, a semiconductor electrode is predicted to be more stable if the reorganization energy of the stabilizing agent is decreased (in the normal region of the Marcus behavior), thereby increasing the rate of minority carrier capture by the stabilizer. This prediction was quantified experimentally by monitoring the branching ratio between two competing reactions at a semiconductor/liquid interface. The experimental observations can be consistently explained through this predicted influence of the minority carrier acceptor reorganization energy on the interfacial charge transfer rate constant. Interfacial charge transfer rate constants at indium phosphide/liquid junctions were investigated using current density-potential and differential capacitance-potential methods. The measured electron transfer rate constants, ket, for these systems were ""IQ-16 cm4 s-1, VI in excellent agreement with previous theoretical predictions. Contacts which did not display bimolecular kinetic behavior still yielded upper bounds on the charge transfer rate constants, which were also consistent with limits predicted by theory. The current densitypotential behavior of n-InP and p-InP/Fe(CN)6 3-14-(aq) junctions was also examined in order to assess the validity of prior kinetic measurements on these interfaces. Table of Contents Acknowledgments 11 Abstract V Table of Contents Vil List of Schemes and Figures Xl List of Tables XIV Summary 1 Chapter 1 5 Basics of Semiconductor/Liquid Junctions I. Introduction 6 Il. Theory 8 III. References 17 Chapter 2 21 Steady-State Current-Voltage Characteristics of Dye-Sensitized Titanium Dioxide Electrodes: pH Dependence and Spectral Response I. Introduction 22 II. Experimental Section 26 A. Materials 26 l. Dye Characterization 26 2. Electrodes 26 3. Redox Couples and Electrolytes 28 B. Electrochemical Methods 36 C. Luminescence Studies 37 Vlll III. Results 38 A. Characterization of Unsensitized Electrodes 38 B. Spectral Response 44 C. Current-Voltage Curves 55 D. Effect of pH on I-V Curves--TiO2/RuL'2(NCS)2 Electrodes 73 E. Effect of pH on Luminescence of the Adsorbed Dye--TiO2/RuL'3 Electrodes 83 IV. Discussion 91 V. References 92 Chapter 3 93 Stability of n-Si/CH30H Contacts as a Function of the Reorganization Energy of the Electron Donor I. Introduction 94 II. Theory 94 III. Experimental Section 99 A. Electrodes 99 B. Redox Couples and Electrolytes 99 C. Electrochemical Methods 108 D. Barrier Height Measurements 110 IV. Results A. Electrode Stability and Current Density vs. Voltage (J-V) Behavior as a 112 112 Function of the Solvent Reorganization Energy of the Electron Donor B. XPS Investigations of Electrochemical Oxide Growth 122 C. Barrier Height Determination for n-Si/CH 3OH-Me2Fc+/O and 134 n-Si/CH 3OH-Co(bipy) 33+/2+ Contacts V. Discussion 139 VI. References 142 IX Chapter 4 144 Theoretical and Experimental Upper Bounds on Interfacial Charge Transfer Rate Constants Between Semiconducting Solids and Outer-Sphere Redox Couples I. Introduction 145 II. Theory 145 A. Abiabaticity and Finite Ion Size Effects on ket,max 148 B. Establishing an Upper Bound for Majority Carrier Charge Transfer 153 Rate Constants at Semiconductor/Liquid Contacts III. Experimental 159 A. Electrodes and Materials 159 B. Electrochemical Cells and Instrumentation 160 C. Built-in Voltage Measurements and Rate Constant Calculations 161 D. Passivation/Corrosion Measurements of InP/Liquid Contacts 163 IV. Results A. Barrier Height Measurements and Upper Bounds on ketlkht for 165 165 Semiconductors in Contact with Nonaqueous Solvents B. Steady-State J-E Behavior of n-InP/H2O-Fe(CN)63-/4- Contacts 173 1. 1-E Data for n-InP Electrodes in KCl(aq)-Fe(CN)63-14- Solutions 173 2. Effects of Exposure to KCl(aq)-Fe(CN)63-14-Solutions on the 173 Behavior of n-InP/CH30H-Me2Fc+IO Contacts 3. 1-E Data for n-InP Electrodes in HCl( aq)-Fe( CN)63-14 - Solutions 174 4. XPS Studies of Oxide Formation and Estimates ofket for n-InPI 175 KCl(aq)-Fe(CN)63-l4 - and n-InPIHCl(aq)-Fe(CN)63-l4 - Interfaces C. Steady-State J-E Behavior of p-lnP/H2O-Fe(CN)6 3-14- Contacts 194 V. Discussion 200 VI. References and Notes 205 X Chapter 5 211 Measurement of Interfacial Charge Transfer Rate Constants at n-type InP/CH30H Junctions I. Introduction 212 II. Experimental Section 213 A Electrodes and Materials 213 B. Electrochemical Cells and Instrumentation 214 C. Current Density vs. Potential and Built-in Voltage Measurements 215 III. Results 218 A Rate Constant Measurements for n-lnP/CH3OH-Me2Fc+/O Contacts 218 B. Rate Constant Measurements for n-InP/CH3OH(25%)-THF(75%) 224 -Me10Fc+/0 Contacts C. Rate Constant Data for n-InP/CH3OH-PV 2+/+• Contacts 228 D. n-InP/CH3OH-Fc+/O Contacts 233 IV. Discussion 240 V. References 246 Xl List of Schemes and Figures Chapter 1. Scheme 1.1 Charge separation at a semiconductor/liquid junction. 13 Scheme 1.2 The Gratzel cell. 15 Scheme 2.1 The Gratzel cell. 24 Figure 2.1 Absorption spectra of the 8 dyes used in this work. 31 Figure 2.2 Current-potential behavior for unsensitized electrodes in 40 Chapter 2. CH3CN/0.040 M l2/0.500 M Lil in the dark. Figure 2.3 Current-potential behavior for unsensitized electrodes in 40 CH3CN/(0.l00 M/0.100 M) Me2Fc+IOJ1.00 M LiClO4 in the dark. Figure 2.4 Average spectral response for TiO2 electrodes sensitized with one 45 of the 8 dyes charcterized above in CH3CN/0.040 M l2/0.500 M Lil/(0.001 M/0.001 M) py/pyH+. Figure 2.5 Spectral response data normalized for dye absorption. 50 Figure 2.6 Current-potential curves for a representative TiO2 electrode for each 57 of the 8 dyes characterized above at a light intensity of 1 Sun in CH3CN/0.040 M l2/0.500 M Lil/(0.001 M/0.001 M) py/pyH+. Figure 2.7 Current-potential data taken in the dark for the electrodes represented 66 in Figure 2.6. Figure 2.8 Current-potential curves for a RuL'2(NCS)2-sensitized TiO2 75 electrode at a light intensity of 1 Sun. Figure 2.9 Current-potential curves for solutions containing various Proton Sponge concentrations. 78 Xll Figure 2.10 Luminescence data for a RuL'3-sensitized TiO2 electrode immersed 85 in a CH3CN solution buffered with 0.001 M/0.001 M py/pyH+. Figure 2.11 Current-potential data for a RuL'3-sensitized TiO2 electrode in 88 CH3CN/0.040 M h/0.500 M Lil/(0.001 M/0.001 M) py/pyH+. Chapter 3. Figure 3.1 Pathways for hole transfer at the Si/liquid interface. 97 Figure 3.2 Cyclic voltammograms for the redox couples used in this work. 102 Figure 3.3 J-V curves for untreated electrodes in CH3OH. 114 Figure 3.4 J-V curves for treated electrodes in CH3OH. 118 Figure 3.5 XP Spectra of Si photoelectrodes. 125 Figure 3.6 J-V curves, treated electrodes, Co(2,2'-bipy))3+/2+. 130 Figure 3.7 Summary of XPS data; oxide growth over time. 132 Figure 3.8 c- 2 vs. V data for Si electrodes immersed in various redox couples. 136 Calculated values for the maximum possible charge transfer rate 151 Chapter 4. Figure 4.1 constant ket, max at semiconductor/liquid junctions. Figure 4.2 Recombination mechanisms at the semiconductor/liquid interface. 157 Figure 4.3 Current density vs. voltage data for a p-InP/CH3CN-Co(Cp)2+/0 169 (0.025 MI 0.0010 M) junction. Figure 4.4 Cctiff 2 vs. applied de potential for the p-InP/CH3CN-Co(Cp)2+/0 171 junction in Figure 3. Figure 4.5 J vs. E data for n-InP/CH3OH-Me2Fc+IO(0.lO0 M / 0.0100 M) vs. 177 n-InP/H2O-Fe(CN)6 3-14-(0.100 MI 0.100 M)-KCI(l .00 M) junctions. Figure 4.6 J vs. E data for n-InP/CH3OH-Me2Fc+IO(0.lO0 M / 0.0100 M) vs. n-InP/H2O-Fe(CN)6 3-14-(0.100 MI 0.100 M)-HCl(l .00 M) junctions. 181 Xlll Figure 4.7 Phosphorus (2p) region of XP spectra of electrodes after treatments 185 described in Figures 4.5 and 4.6. Figure 4.8 Bode plot for impedance data taken at 0.25 V de bias for the 190 n-InP/H2O/Fe(CN)6 3-14-(0.100 M I 0.100 M)-KCl( 1.00 M) junction. Figure 4.9 c- 2 vs. applied de potential for the n-InP/H2O-Fe(CN)6 3-14- 192 junction in Figure 8. Figure 4.10 J vs. E data for p-InP/CH3CN-Co(Cp)2+10(0.025 MI 0.0010 M) vs. 196 p-InP/H2O-Fe(CN)6 3-14-(0.100 MI 0.100 M)-KCl(l .00 M) junctions. Chapter 5. Figure 5.1 Current density-potential and differential capacitance-potential 221 data for n-type InP/CH3OH-Me2Fc+/O contacts. Figure 5.2 Data for n-InP/CH3OH-THF-Me 10Fc+/O contacts. 226 Figure 5.3 Data for n-InP/CH3OH-l.00 M LiCl-PV 2+/+• contacts. 230 Figure 5.4 Data for n-InP/CH3OH-Fc+/O contacts. 235 Figure 5.5 Dependence of the built-in voltage of n-InP electrodes on the 244 Nernstian potential, E(A/A-), of various contacts having outer-sphere redox systems dissolved in the solution phase. XIV List of Tables Chapter 2. Table 2.1 Ground state reduction potentials for the dyes used in this work. 29 Table 2.2 Open Circuit Voltages (V0c) and Short-Circuit Current Densities 62 CJsc) as a Function of Sensitizer at 1 Sun illumination. Table 2.3 Predicted short circuit current densities at 100 mW cm- 2 incident 64 illumination based on integrated spectral response data. Table 2.4 Applied potential required to sustain 2.0 mA cm- 2 of reductive current 71 in the dark for TiO2 electrodes sensitized with each dye. Table 2.5 Open circuit voltages and short-circuit current densities for 81 RuL'2(NCS)2-TiO2 electrodes as a function of Proton Sponge concentration at 1 Sun illumination. Chapter 3. Table 3.1 Standard reduction potentials and self-exchange rates for the 106 redox couples used in this work. Chapter 4. Table 4.1 Summary of built-in voltages and upper limits on the rate constants 167 for n-type semiconductors in contact with nonaqueous electrolytes. Chapter 5. Table 5.1 Summary of electron transfer rate constants. 238 1 Summary Since Fujishima and Honda published their work on titanium dioxide as a photoanode in water in 1975, much interest has been generated in the field of semiconductor/liquid junctions as a useful source of energy. Semiconductor/liquid junction technology is also important in the electronics industry in terms of etching and other chemical processing steps. These junctions have also shown promise in photocatalytic applications such as toxic waste remediation and in sensor applications. A fundamental understanding of the chemistry at these junctions is thus vital for a number of technological areas. This thesis examines steady-state charge transfer at semiconductor/liquid junctions and uses experimental data to evaluate existing theory on charge transfer rate constants. Chapter 1 will present a general overview of semiconductor/liquid junction technology and some background on electron transfer theory at these junctions. The basic organization of this thesis was developed to move from more qualitative studies to quantitative measurements of charge transfer rate constants. One fairly new approach to solar energy conversion is the use of highly porous, dye-sensitized electrodes. Gratzel and others have reported efficiencies of up to 10% with titanium dioxide electrodes of this type. However, this field is still in comparatively early stages and many gaps remain in understanding the behavior of these cells. Due to the complexity of this system, many of its properties cannot be directly correlated to those of the more typical singlecrystal semiconductor/liquid junctions and must be looked at separately. Some of these characteristics will be examined in Chapter 2. Systematic studies are described regarding changing the ground state reduction potential and central metal of the dye molecule, as well as examining the pH dependence of the current-voltage behavior of the cells. The spectral response and current-voltage properties of electrodes modified with a series of dyes are compared. The trends can be explained by the differences in absorption spectra and ground state potentials. The effect of pH on the conduction band edge position of nanoporous 2 titanium dioxide has been examined through current-voltage measurements and luminescence studies on dye-sensitized electrodes. The results are discussed in the framework of current theories on increasing efficiency of these electrodes. Studies involving charge separation at the back electrode contact were also performed. Chapters 3-5 involve single crystal electrodes in contact with non-aqueous solutions. Theoretical analyses of charge transfer rates have been published on these systems, but until recently little experimental data was available to evaluate the theory. In Chapter 3, the dependence of the hole transfer rate constant from the semiconductor to the liquid is examined as a function of the reorganization energy of the electron donor in solution. An n-type semiconductor electrode is predicted to be more stable to passivation or corrosion reactions if the reorganization energy of the electron donor is decreased (in the normal region of the Marcus behavior) because the rate constant for hole transfer to the desired electron donor is increased. This prediction was quantified experimentally by monitoring the branching ratio between two competing reactions at a semiconductor/liquid interface: hole transfer from a Si photoanode to the electron donor in solution vs. passivation of the Si photoanode through hole transfer to water. Dimethylferrocene (Me2Fc), ruthenium(II) pentaammine 4,4'-bipyridine (Ru(NH 3) 5(4,4'-bipy) 2+), and cobalt(II) tris(2,2'-bipyridine) (Co(2,2'-bipy)/+) were used as electron donors because of their very similar standard electrochemical potentials but varying solvent reorganization energies. Also, charge transfer with these species is known to proceed by an outer-sphere mechanism and none of these donors adsorb to the electrode surface. At constant electron donor concentration, constant driving force for reaction, constant photocurrent density, and constant water concentration in CH3OH, the stability of n-Si photoelectrodes decreased in the order Me2Fc+/O>Ru(NH 3) 5(4,4'-bipy) 3+/2+>Co(2,2'-bipyh 3+/l+_ This observation can be consistently explained through the theoretically predicted influence of the minority carrier acceptor reorganization energy on the interfacial charge transfer rate constant. 3 In Chapters 4 and 5, electron transfer rate constants are compared with the maximum possible rate constant predicted by theory. Chapter 4 contains some modifications of the original theory and upper limits on the electron transfer rate constant measured experimentally. Theoretical expressions for the charge transfer rate constant at a semiconductor/liquid junction have been modified to include the effects of adiabaticity and the existence of a Helmholtz layer at the solid/liquid interface. These expressions have yielded an estimate of the maximum interfacial charge transfer rate constant, at optimal exoergicity, for a semiconductor in contact with a random distribution of non-adsorbing, outer-sphere redox species. An experimental upper bound on this interfacial charge transfer rate constant has been obtained through the determination of key energetic and kinetic measurements for stable semiconductor electrodes in contact with outer-sphere redox species. The upper limits for the interfacial charge transfer rate constant at several semiconductor/liquid contacts were found to be consistent with the upper limits predicted by theory. The current density-potential behavior of n-InP and p-InP/Fe(CN)63-/4-(aq) junctions was also examined and compared to the behavior of stable, non-aqueous InP photocells in order to assess the validity of prior kinetic measurements on these interfaces. Chapter 5 describes quantitative measurements of electron transfer rate constants at n-type indium phosphide/methanol junctions and relates these results to the theory. Steady-state methods are used to measure interfacial electron transfer rate constants at ntype indium phosphide/liquid junctions which displayed bimolecular kinetic behavior in which the observed current density was first order in the concentration of electrons at the semiconductor surface and in the concentration of acceptors in the solution. Differential capacitance-potential measurements were used to determine the energetics for the charge transfer process as well as to determine the concentration of electrons at the semiconductor surface as a function of applied potential. These measurements also indicated that the voltage dropped across the semiconductor space charge region varied ideally with the 4 change in cell potential. The measured charge transfer rate constants, ket, for these systems were zlQ-16 cm4 s-1, in excellent agreement with previous theoretical predictions. 5 Chapter 1: Basics of Semiconductor/Liquid Junctions 6 I. Introduction Charge transfer processes at semiconductor/liquid interfaces are the fundamental steps in developing efficient photoelectrochemical energy storage systems, 1-5 chemical sensors, 6,7 selective photoelectrochemical etching systems, 8,9 and photocatalytic degradation processes for toxic waste remediation. 10- 15 Although electron transfer between fixed donor-acceptor species in solution 16- 19 and at metal electrodes 20-24 has been well-characterized, relatively little comparison between theory and experiment is available for charge transfer processes involving semiconductor electrode surfaces. 25 -32 This lack of information can largely be ascribed to difficulties involved in rigorously controlling the chemical composition of semiconductor electrode surfaces, difficulties in developing measurement methods that are sensitive to the desired interfacial charge transfer kinetic processes, and difficulties in identifying electrode/electrolyte combinations that would allow an unambiguous comparison between experimental measurements and theoretical predictions. 1-4 ,25 -44 Despite these problems, this area has attracted considerable attention by both theoretical and experimental chemists 26 ,29 ,3o,32 A5-5o because of the importance of understanding these processes, and because understanding how different variables affect the charge transfer rate constant could also provide insight into solid-state semiconductor contacts. This chapter will provide a background in current theory on semiconductor-liquid interfaces in the context of solar energy conversion. Since Chapters 3-5 deal with predictions involving charge transfer rate constants, a general discussion of theoretical treatments of the rate constant will also be included here. Specific aspects of such theories will be left to the chapters pertaining to them. An alternate approach to solar energy conversion which will be introduced here will be more thoroughly examined in Chapter 2. The basic problem in semiconductor/liquid junction solar cell technology is the trade-off between stability and conversion efficiency. Semiconductors such as silicon, indium phosphide, and gallium arsenide have small bandgaps which overlap well with the 7 terrestrial solar spectrum but are unstable in water. Wide bandgap semiconductors such as titanium dioxide are stable in aqueous solutions but do not absorb visible light, resulting in very low terrestrial conversion efficiencies. There are two approaches to overcoming these problems: extending the absorption spectrum of semiconductors such as titanium dioxide to better match the terrestrial solar spectrum, or finding a way to stabilize semiconductors such as silicon in solution. This thesis examines aspects of both approaches to semiconductor/liquid junction energy conversion. One approach to solar energy conversion is to sensitize wide bandgap semiconductors with dyes which absorb visible light. Early attempts to do this with singlecrystal electrodes were not very successful because one monolayer of dye proved insufficient to absorb much of the incident light,51 ,52 while multiple layers of dye resulted in self-quenching of the dye and inefficient injection. 53 To overcome these problems, high-surface area electrodes were used instead of single-crystals. In this way, one monolayer of dye can absorb most of the incident light while still achieving efficient electron injection. Gratzel and others have had a great deal of success in this area using high-surface area titanium dioxide electrodes. 54 Using nanoporous TiO2 electrodes in conjunction with ruthenium-based dyes, efficiencies of up to 10% have been reported.55 Although many papers have been published investigating such systems, answers to some fundamental questions remain unclear. Chapter 2 will address some of these issues. One solution to the problem of stabilizing solar cells fabricated with small-bandgap semiconductors is to use non-aqueous electrolyte solutions. Although initial papers reported high resistive losses and low efficiencies,56 -58 optimizing solvent-electrolyte combinations and electrode configurations resulted in stable, efficient cells. Efficiencies of up to 14% have been reported for silicon electrodes in contact with methanolic solutions. 59 This approach is still not commercially viable due to the toxicity and cost of the solvents and electrolyte combinations used; however, these systems are ideal for study due to their simplicity. Single crystal electrodes can be manufactured with very low surface defect 8 densities and nearly perfect junctions with liquids are easily obtained, in contrast with solid-state junctions which are very difficult to make atomically perfect. Chapters 3, 4 and 5 discuss various aspects of charge transfer across these types of semiconductor/liquid junctions. II. Theory Many review articles 5,26 ,60-62 have been written on charge separation and recombination mechanisms at single-crystal semiconductor/liquid junctions; therefore this topic will be only briefly described here to clarify other areas of the theory. The traditional method by which semiconductor/liquid junctions create electrical power from light is illustrated in Scheme 1.1 . Although this scheme and the following discussion describe the case of an n-type semiconductor, an analogous model is readily derived for p-type semiconductors. The electrochemical potential of the semiconductor before immersion is known as its Fermi level, Ef, and is a function of the dopant density Nd. When the semiconductor is placed in contact with a liquid containing a redox-active species of Nemstian potential E(A!A-), the electrochemical potentials of the two phases must equilibrate. The potential drop required to attain this equilibrium develops primarily across the semiconductor, in which dopant atoms are ionized. The resulting electric field separates photogenerated carriers, directing charges of opposite sign in opposite directions . Although photogenerated electrons are driven away from the surface by the electric field described above, there are always a finite concentration of electrons at the surface of the semiconductor, given by a Boltzmann exponential term. These electrons have sufficient driving force to cross the interface into the solution despite the electric field present; thus, the rate constant for this process is very important to the overall efficiency of the junction. Very rapid majority carrier charge transfer is undesirable for photoelectrochemical devices, since rapid collection of majority carriers (electrons in the case of n-type semiconductors) by species in solution would result in significant recombination of charge carriers and would thus limit the efficiency of a photoelectrochemical energy conversion device. 9 However, very slow capture of minority carriers (holes) is also undesirable, because any appreciable current would require a large overpotential and would result in wasteful voltage losses in the cell. For these reasons, an understanding of both majority and minority charge transfer rate constants at these interfaces is essential. An understanding of the factors affecting interfacial charge transport processes should also allow design of systems that kinetically direct charge carriers in the solid to react with the desired redox molecules in the solution, thereby improving electrode stability and decreasing deleterious electrode passivation or corrosion reactions. For charge transfer processes between molecular donor and molecular acceptor reagents in homogeneous solution, the theoretical behavior predicted by Marcus has been widely verified by experiment. 16- 19 In addition, data on metal electrodes have yielded insight into heterogeneous charge transfer processes.20-24 In contrast, relatively little linkage between theory and experiment has been attained for delocalized carriers in a semiconducting solid transferring into localized, molecular acceptors in a liquid electrolyte. 25 -32 Recent theoretical treatments of charge transfer processes at semiconductor/liquid interfaces have yielded expressions for the electron transfer rate constant, ket, between a charge carrier in the semiconductor and an outer-sphere redox species in the electrolyte. 29 ,46 Starting with Marcus' treatment of liquid-liquid interfaces, 63 and modifying the result to describe the situation in which one species is a delocalized electron in the semiconducting solid and the other is an electron acceptor dissolved in homogeneous solution, yields: 29 ket = Vn Kel Kn (1. 1) with (1.2) 10 and (1.3) In this transition state theory description of the interfacial rate constant the attempt frequency, Vn, is the relevant nuclear vibrational frequency, taken to be approximately 10 13 s-1. Ke! and Kn are the electronic and nuclear factors, respectively. In the expression for Ke!, rA and re are the effective radii of the acceptor in solution and of the electron in the solid, respectively, and~ is the electronic coupling decay constant. In the nuclear term, AA is the total reorganization energy of the acceptor molecule, ~G 0 ' is the free energy of reaction for the electron transfer, k is the Boltzmann constant, and T is the temperature. Similar expressions can be derived for hole transfer rate constants. Some authors have criticized this approach and the upper limit on the charge transfer rate constant predicted by this theory. 64 A theoretical treatment which accurately predicts the rate constant is important due to interest in "hot" charge carrier transfer processes. Normally, even when an n-type semiconducting crystal is irradiated with light above the bandgap energy, the excited electrons thermalize to the energy of the conduction band edge before charge transfer can occur, resulting in a constant driving force for charge transfer with respect to the incident wavelength. "Hot" electrons would be able to transfer into solution before complete thermalization, potentially resulting in higher energy efficiencies. Experiments are needed to test the predictive power of the Marcus theory approach as well as to validate or disprove any other theoretical treatments. Due to the difficulty in measuring these rate constants directly, many of the conclusions reached from earlier data in the literature are strongly dependent on interpretation. In the work described in this thesis, experiments were carefully designed to avoid the possibility of misinterpretation of the data. For the rate constant studies described in Chapters 3-5, single crystal electrodes 11 with very few surface defects were used in cells which were known to be stable over long time periods. An alternate approach to solar energy conversion, developed by Griitzel, 54 is illustrated in Scheme 1.2. Unlike the systems described above, in which the photon absorption and charge separation all occur within the semiconductor, Griitzel's approach to the conversion of photons into electrical energy involves two distinct materials. An adsorbed dye absorbs photons to create electron-hole pairs, while titanium dioxide nanoparticles accept the excited state electron and separate them from the holes. Normally the counter electrode would be unable to efficiently regenerate the dye due to diffusion problems, so a redox couple is added to the solution to accept electrons from the counter electrode and reduce the dye to complete the circuit. Many aspects of the cell must be considered in order to optimize its performance. The dye's excited state must be sufficiently energetic to efficiently inject an electron into the Ti02 conduction band, while the reduction potential of the solution species must be energetic enough to efficiently reduce the dye. Simultaneously, the dye must overlap closely with the solar spectrum, and the potential difference between the solution redox potential and the conduction band edge should be maximized for greater photovoltages. A complicating aspect in studying these films is that due to the nanocrystalline character of the semiconducting electrodes, many of the equations used to describe singlecrystal electrode systems are not easily applied to dye-sensitized Ti02 systems. In a singlecrystal system, the interface is clearly defined and is only two-dimensional. In contrast, the titanium dioxide/liquid junction is a randomly twisting, three-dimensional interface. The presence of two redox-active species, the dye and the redox couple in solution, also complicate kinetic analyses of these systems. Finally, the nanocrystals which make up the Ti02 electrode are probably not large enough to support an electric field, so it is likely that transport of electrons through the film is driven by a concentration gradient. Due to the complex nature of these films, a detailed rate constant analysis will not be presented here, 12 but rather a more basic approach will be used to qualitatively describe charge transfer processes at the electrode surface. Although the body of literature on dye-sensitized, nanocrystalline titanium dioxide is immense, many fundamental questions remain unanswered. The characteristics of the semiconductor/liquid junction can vary with the preparation of the Ti02 colloids, the dye used, the pH of the electrolyte solution, humidity, and countless other details. Systematic changes in the dye and solution pH will be examined, while other variables such as water content and colloid preparation will be held as constant as possible. 13 Scheme 1.1: Charge separation at a semiconductor/liquid junction. Integrating the charge distribution caused by the ionization of dopant atoms with respect to position yields the electric field strength. integration yields the electric potential difference. A second 14 Equilibrium Char1:e Distribution Initial Electric Potential - - -.. E cb ,-.__ I<'----- 09 -qE(AJA) semiconductor ++++ = & - - --FFI-T· : qE(AJA) - solution ++++ ++++ - ++++ ~b integrate twice with respect to position Scheme 1.1 15 Scheme 1.2: The Gratzel cell. All of the energy levels (Dye, Dye*, E(A/A-)) must be carefully chosen in order for energy to be obtained from the cell. The Pt counter electrode is not efficient at directly regenerating the dye, most likely due to diffusional problems in getting an electron from the counter electrode across the solution to the dye, so a redox active molecule is needed in solution to act as an electron shuttle, accepting the electron from the counter electrode and regenerating the dye. 16 ------- ------- ------ ------- ------ Dye·◄~-------qE(AI Ti0 2 electrode Scheme 1.2 ...J_-_·_·_1·_·;~=:::::gy A-) _ _ _ Pt electrod~--------- 17 III. References (1) Wrighton, M. S. Acc. Chem. Res. 1979, 12, 303. (2) Rajeshwar, K. J. Appl. Electrochem. 1985, 15, 1. (3) Parkinson, B. Acc. Chem. Res. 1984, 17, 431. (4) Finklea, H. 0. Semiconductor Electrodes; Elsevier: New York, 1988. (5) Tan, M. X.; Laibinis, P. E.; Nguyen, S. T.; Kesselman, J.M.; Stanton, C. E.; Lewis, N. S. Prog. Inorg. Chem. 1994, 41, 21. (6) Hafeman, D. G.; Paree, J. W.; McConnell, H. M. Science 1988, 240, 1182. (7) de Rooij, N. F.; van de Vlekkert, H. H. In Chemical Sensor Technology; N. Yamazoe, Ed.; Kodansha, Ltd.: Tokyo, 1991 ; Vol. 3; 213. (8) Elliott, D. J. Integrated Circuit Fabrication Technology; Mc-Graw Hill: New York, 1989. (9) Kohl, P. A.; Ostermayer, F. W. Ann. Rev. Mat. Sci. 1989, 19, 379. (10) Kormann, C.; Bahnemann, D. W.; Hoffmann, M. R. Environ. Sci. Technol. 1991, 25, 494. (11) Pruden, A. L.; Ollis, D. F. Environ. Sci. Technol. 1983, 17, 628. (12) Draper, R. B.; Fox, M. A. Langmuir 1990, 6, 1396. (13) Fox, M.A. In Photocatalysis and Environment: Trends and Applications; M. Schiavello, Ed.; Kluwer Academic Publishers: Dordrecht, 1988; Vol. 237; 445. (14) Minero, C.; Aliberti, C.; Pelizzetti, E.; Terzian, R.; Serpone, N. Langmuir 1991, 7,928. (15) Hidaka, H.; Nohara, K.; Zhao, J.; Serpone, N.; Pelizzetti, E. J. Photochem. Photobiol. A: Chem. 1992, 64, 247. (16) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J. Phys. Chem. 1986 , 90, 3673. (17) McClendon, G.; Miller, J. R. J. Am. Chem. Soc. 1985, 107, 7811. (18) Fox, L. S.; Kozik, M.; Winkler, J. R.; Gray, H.B. Science 1990, 247, 1069. 18 (19) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (20) Saji, T. ; Yamada, T.; Aoyagui, S. J. Electroanal. Chem. lnte,facial Electrochem. 1975 , 61, 147. (21) Saji, T.; Maruyama, Y.; Aoyagui, S. J. Electroanal. Chem. 1978, 86, 219. (22) Miller, C.; Gditzel, M. J. Phys. Chem. 1991, 95, 5225 . (23) Chidsey, C. E. D.; Bertozzi, C. R.; Putvinski, T. M.; Mujsce, A. M. J. Am. Chem. Soc. 1990, ll2, 4301. (24) Ravenscroft, M. S.; Finklea, H. 0. J. Phys. Chem. 1994, 98, 3843. (25) Morrison, S. R. Electrochemistry at Semiconductor and Oxidized Metal Electrodes; Plenum: New York, 1980. (26) Koval, C. A.; Howard, J. N. Chem. Rev. 1992, 92, 411. (27) Memming, R. Ber. Bunsenges. Phys. Chem. 1987, 91 , 353. (28) Gerischer, H. In Physical Chemistry: An Advanced Treatise; H. Eyring; D. Henderson and W. Yost, Ed.; Academic: New York, 1970; Vol. 9A; 463. (29) Lewis, N. S. Ann. Rev. Phys. Chem. 1991, 42, 543. (30) Bard, A. J.; Mirkin, M. V.; Horrocks , B. R. J. Phys. Chem. 1994, 98, 2739. (31) Miller, B.; Menezes, S.; Heller, A. J. Electrochem. Soc. 1979, 126, 1483. (32) Rosenwaks, Y.; Thacker, B. R.; Nozik, A. J.; Ellingson, R. J.; Burr, K. C.; Tang, C. L. J. Phys. Chem. 1994, 98, 2739. (33) Colell, H.; Alonsovante, N.; Tributsch, H.J. Electroanal. Chem. 1992, 324, 127. (34) Willig, F.; Eichengerger, R.; Sundaresan, N. S.; Parkinson, B. A. J. Am. Chem. Soc. 1990, ll 2, 2702. (35) Albery, W. J.; Bartlett, P. N. J. Electrochem. Soc. 1981, 128, 1492. (36) Ellis, A. B.; Bolts, J.M.; Kaiser, S. W.; Wrighton, M. S. J. Am. Chem. Soc. 1977, 99, 2848. (37) Miller, R. J. D.; Kasinski , J. J.; Gomez-Jahn, L.A. ; Min , L. Springer Ser. Chem. Phys. 1988, 48, 424. 19 (38) Heller, A. Acc. Chem. Res. 1981, 14, 154. (39) Bard, A. J. J. Phys. Chem. 1982, 86, 172. (40) Frank, S. N.; Bard, A. J. J. Am. Chem. Soc. 1975, 97, 7427. (41) Rosenbluth, M. L.; Lewis, N. S. J. Am. Chem. Soc. 1986, 108, 4689. (42) Lantz, J.M.; Corn, R. M. J. Phys. Chem. 1994, 98, 4899. (43) Fischer, P.R.; Daschbach, J. L.; Richmond, G. L. Chem. Phys. Lett. 1994, 218, 200. (44) Moser, J.E.; Gratzel, M. Chem. Phys. 1993, 176, 493. (45) Marcus, R. A. J. Phys. Chem. 1990, 94, 1050. (46) Gerischer, H. J. Phys. Chem. 1991, 95, 1356. (47) Pomykal, K. E.; Fajardo, A. M.; Lewis, N. S. J. Phys. Chem. 1996, JOO, 3652. (48) Fajardo, A. M.; Lewis, N. S. Science 1996, 274, 969. (49) Smith, B. B.; Nozik, A. J. Chem. Phys. 1996, 205, 47. (50) Uhlendorf, I.; Reinekekoch, R.; Memming, R. J. Phys. Chem. 1996, 100, 4930. (51) Matsumura, M.; Nomura, Y.; Tsubomura, H. Bull. Chem. Soc. Jpn. 1977, 50, 2533. (52) Alonso, N.; Beley, V. M.; Chartier, P.; Ern, V. Rev. Phys. Appl. 1981, 16, 5. (53) Eichberger, R.; Willig, F. Chem. Phys. 1990, 141, 159. (54) O'Regan, B.; Gratzel, M. Nature 1991, 353, 737. (55) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphry-Baker, R.; Mi.iller, E.; Liska, P.; Vlachopoulos, N.; Gratzel, M. J. Am. Chem. Soc. 1993, 115, 6382. (56) Legg, K. D.; Ellis, A. B.; Bolts, J. M.; Wrighton, M. S. Proc. Natl. Acad. Sci. 1977, 74, 4116. (57) Kohl, P. A.; Bard, A. J. J. Am. Chem. Soc. 1977, 99, 7531. (58) Langmuir, M. E.; Hoenig, P.; Rauh, R. D. J. Electrochem. Soc. 1981, 128, 2357. 20 (59) Gibbons , J. F. ; Cogan, G. W. ; Gronet, C. M.; Lewis, N. S. Appl. Phys. Lett. 1984, 45, 1095. (60) Lewis, N. S. Acc. Chem. Res. 1990, 23, 176. (61) Lewis, N. S.; Rosenbluth, M. In Photocatalysis: Fundamentals and Applications; N. Serpone and E. Pelizzetti, Ed.; John Wiley & Sons: New York, 1989; pp 45. (62) Nozik, A. J. Ann. Rev. Phys. Chem. 1978, 29, 189. (63) Marcus, R. A. J. Phys. Chem. 1991, 95, 2010. (64) Smith, B. B.; Halley, J. W.; Nozik, A. J. Chem. Phys. 1996, 205, 245. 21 Chapter 2: Steady-State Current-Voltage Characteristics of Dye-Sensitized Titanium Dioxide Electrodes: pH Dependence and Spectral Response 22 I. Introduction One approach to the useful conversion of light into electrical energy is the use of wide bandgap semiconductors. These compounds tend to be more stable to air and water oxidation than small bandgap semiconductors such as Si, InP, and GaAs. 1 However, to overcome the poor overlap of wide bandgap semiconductors with the solar spectrum, electrodes made with these materials must be coated with dyes which absorb light in the visible region. Gratzel and others have had a great deal of success in this area using highsurface area titanium dioxide electrodes. 2-5 These systems consist of nanocrystalline titanium dioxide coated onto a conducting glass substrate, the adsorbed dye, a sacrificial electron donor to regenerate the dye, and a platinum counter electrode to reduce the electron donor (Scheme 2.1 ). When these nanoporous electrodes are sensitized with rutheniumbased dyes, efficiencies of up to 10% have been reported. 6 Although many papers have been published on various aspects of these systems, 5,7-9 answers to some fundamental questions remain unclear. One possible complication arising from using particulate systems as electrodes is that the individual particles are too small to support an electric field. 5 Since this electric field provides the mechanism for charge separation in traditional solar cells, the high photocurrents and photovoltages observed in the dye-sensitized TiO2 electrodes were initially surprising. As described in this work, studies were undertaken to determine why the electrons injected from the dye travel towards the conducting glass substrate to be collected. The current-voltage properties of the conducting glass substrate as well as of unsensitized TiO2 electrodes were characterized in both Lil/12 and Me2Fc+/O in an effort to explain the mechanism for charge separation in these systems. Next, the synthesis of a series of dyes with varying ground state reduction potentials is reported. The choice of this particular series of dyes serves two purposes. First, by varying the ground state potential, a threshold value for the driving force necessary for the electron donor to regenerate the dye can be obtained. Also, by 23 synthesizing both the ruthenium and osmium analogs of each dye the effect of changing the metal can be examined. Since the singlet-triplet transition is not as forbidden in osmium complexes as in ruthenium, the osmium dyes have additional absorption bands at higher wavelengths. 10 If the excited electrons produced from these absorbed photons are still sufficiently energetic to inject into the Ti02, higher photocurrents will be observed. This prediction will be explored through photocurrent-voltage measurements and spectral response data. A third issue which will be addressed in this work is the effect of various additives on the current-voltage properties of these cells. Additives such as 4-methylmorpholine Noxide (NMO) and t-butyl pyridine have been found to increase the open-circuit voltages and efficiencies of these electrodes. 6 One hypothesis put forward is that these compounds passivate surface states on the electrode, so that the dark current is decreased and electrode performance is enhanced. 6•1I Another explanation is that since both NMO and t-butyl pyridine can act as bases, these compounds change the effective pH of the solution, moving the band edges of the Ti02 and changing the energetics of the junction. The present work attempts to differentiate between these two explanations by creating the same improvement using a non-coordinating base. Using Proton Sponge, a non-nucleophilic base, to control the solution pH, any change in the open circuit voltage should be solely the result of the change in pH, since it is unlikely that the Proton Sponge could passivate any surface states. 24 Scheme 2.1: The Gratzel cell. All of the energy levels (Dye, Dye*, E(NA-)) must be carefully chosen in relation to Ecb so that energy can be obtained from the cell. It has been shown that the Pt counter electrode is not efficient at directly regenerating the dye, most likely due to diffusional problems in getting an electron from the counter electrode across the solution to the dye, so a redox active molecule is needed in solution to act as an electron shuttle, accepting the electron from the counter electrode and regenerating the dye. 25 e- Dye* E c b - - - • ..~----------------------- Dye ....... ..._____ E(A/k Ti02 electrode Evb Scheme 2.1 \ - - - _ . _ ... J. ava~:;::~;gy Pt electrode 26 II. Experimental Section A. Materials The performance of the nanoporous dye-sensitized electrodes has been found to be highly dependent on the method of preparation of the titanium dioxide as well as on the methods of synthesis and purification of the dyes. Therefore, although the electrode preparation used here is similar to that described elsewhere, 6,8 the procedure will be described in detail. 1. Dye Characterization The synthesis and purification of the 8 dyes listed in Table 2.1 is described elsewhere. 12 These organometallic complexes were found to be pure by NMR analysis and elemental analyses for C, H, and N were within 0.4% for all dyes except Ru(4,4'(dicarboxy)-2,2'-bipyridine)2(CN)2 for which the elemental analysis deviated from the calculated values by 0.6%. Absorption spectra of the dyes were obtained on a HewlettPackard Model 8452A Diode Array Spectrophotometer and are shown in Figure 2.1 . The spectra for all dyes except the tris-[4,4'-(dicarboxy)-2,2'-bipyridine] (L') complexes were taken in ethanolic solutions containing 0.001 M/0.001 M pyridine/pyridinium triflate (py/pyH+). Due to solubility constraints, the spectra for the OsL'3 and RuL'3 were obtained in ethanolic solutions of 0.010 M py+. 2. Electrodes The nanoporous electrodes consist of three distinct layers, where most of the thickness of the film resides in the middle layer, consisting of the TiO2 colloid. For the other two layers, stock solutions were prepared by adding 0.100 M TiCl4 to isopropanol or 2.00 M TiCl4 to water with vigorous stirring. Once the initial fuming had stopped, these preparations resulted in clear solutions. The isopropanol solution was used as prepared, but immediately before use, an aliquot of the aqueous solution was diluted to 0.20 M . The preparation of titanium dioxide colloidal solutions was based on the procedure of Smetana. First, 2.6 mL of concentrated nitric acid was added to 375 mL deionized 27 water. With vigorous stirring, 62.5 rnL Ti(OCH(CH3)2)4 was added slowly ( ~30 mL/min.), and a white precipitate formed. This solution was then stirred for 2 hours at room temperature and 8 hours at 80 °C to evaporate the propanol. The resulting sol was suction filtered through fine filter paper and then autoclaved at 200 °C for 12 hours in a sealed pressure vessel. The final solution was evaporated to a concentration of 160 g L-1 in TiO2. To maintain porosity in the final film, Carbowax 20000 was added to a concentration of 40% weight equivalent of TiO2 and the sol was stirred overnight. This colloid solution was stored and used as a stock solution for up to 2 months without significant change in electrode properties. Electrodes were prepared by first depositing a layer of the isopropanol solution onto 3-mm thick glass coated with a conducting layer of F-doped SnO2 (8-10 Wsquare, L.O.F.). The layer was evenly spread by pulling a glass slide across the surface of the electrode, where Scotch tape on either side of the electrode region acted as a spacer for the slide. After the isopropanol had evaporated, the colloid solution was spread onto the conducting glass in a similar fashion . Once this layer had dried, the electrodes were fired in a tube furnace under flowing air at 450 °C for 30 minutes. Once the electrodes had cooled, 100 rnL of the freshly made aqueous solution was deposited on each electrode. After the electrodes were covered and allowed to sit overnight, the electrodes were rinsed with isopropanol. Sample electrode thicknesses were approximately 5 µm as measured by profilometry. Immediately before dye adsorption, each electrode was fired a second time at 450 °C for 30 minutes. The electrodes were cooled to 100 °C and then were immersed in an ethanolic solution containing 0.0001-0.0005 M of the desired dye. The dye solution was buffered with 0.001 mM pyridine/pyridinium triflate (py/pyH+). The electrodes were immersed in the dye for at least 4 hours before use in electrolyte solution. An absorption spectrum of each electrode was taken prior to use to quantify the amount of dye adsorbed. 28 3. Redox Couples and Electrolytes Lithium iodide, iodine, Proton Sponge and pyridinium triflate were purchased from Aldrich. Pyridinium triflate was also synthesized from pyridine by acidification of a solution of pyridine in diethyl ether with triflic acid, and was dried under vacuum before use. Proton Sponge was stored in a nitrogen-purged drybox and was used as received. Lil was dried at 200 °C before use. Iodine and dimethylferrocene were sublimed under vacuum before use. Dimethylferrocenium was synthesized using the method of Hendrickson et al. and was dried under vacuum before use. Absolute ethanol was purchased from EM Science and used as received. Pyridine and acetonitrile were purchased from EM Science and distilled before use. The CH3CN was distilled first over CaH2 and then over P2O5. Stock solutions containing 0.500 M Lil/0.040 M 12/0.001 M py/pyH+ in CH 3CN were prepared for use with the TiO2 electrodes. For pH studies, aliquots of this solution were added to solid Proton Sponge to yield the desired concentrations. Initial experiments with TiO2 electrodes showed poor reproducibility. It was hypothesized that variables such as water concentration and solution pH were affecting the current-voltage behavior of these electrodes, so care was taken to control these variables. All reagents and solutions listed above were stored in a nitrogen-purged box after purification. The pyridinium triflate and pyridinium were added to both the dye and electrolyte solutions in 0.001 M concentrations to maintain a constant initial pH. In pH studies, these buffered solutions were made more basic by adding Proton Sponge. Enough Proton Sponge was added so that the pyridine/pyridinium could no longer act as a buffer. All cells were constructed inside the nitrogen-purged box and sealed to avoid water contamination before being brought out of the box. These precautions led to greatly improved reproducibility. 29 Table 2.1: Ground state reduction potentials for the dyes used in this work. All values are referenced to a methanol SCE. Abbreviations for the dyes are as follows: RuL' 3=tris(4,4'-( dicarboxy)-2,2'-bipyridy l)ruthenium(II) (hexafluorophosphate salt) OsL' 3=tris(4,4'-( dicarboxy )-2,2 '-bipyridy l)osmium(II) (hexafluorophosphate salt) RuL2L '=bis(2,2'-bipyridyl)( 4,4'-( dicarboxy )-2,2'bipyridyl)ruthenium(II) OsL2L' =bis(2,2'-bipyridy 1)(4,4'-( dicarboxy )-2,2'bipyridyl)osmium(II) RuL' 2(CN)z=cis-dicyanobis( 4,4'-( dicarboxy)-2,2'bipyridyl)ruthenium(II) OsL' 2( CN)z=cis-dicyanobis( 4,4'-( dicarboxy )-2,2'bipyridyl)osmium(II) RuL' 2(NCS)z=cis-di(isothiocyanato )bis(4,4'-( dicarboxy )-2,2'bipyridyl)ruthenium(II) OsL' 2(N CS)z=cis-di(isothiocyanato )bis( 4,4'-( dicarboxy )-2,2'bipyridyl)osmium(II) a: from ref. 13 b: from ref. 10 30 Dye Reduction Potential (V vs. SCE) RuL'3 1.32a OsL'3 1.01 RuL2L' 1.24 OsL2L' 0.84 RuL'2(CNh l.04b OsL'2(CNh 0.78 RuL'2(NCSh 0.80 OsL'2(NCS)2 0.42 Table 2.1 31 Figure 2.la-h: Absorption spectra of the 8 dyes used in this work, in ethanolic solution. 32 2.5 2 la) RuL' 3 ,,-.._ -~ 1.5 """'0 ~ "-" 1 w 0.5 0 400 500 600 700 800 900 700 800 900 wavelength (nm) 2.5 2 lb) OsL' 3 ,,-.._ -~ 1.5 """'0 ~ "-" 1 w 0.5 0 400 500 600 wavelength (nm) 33 2.5 .......-r-,r"""""""T"""""".......-r-,.---.......-r-,.---.......-r-,.---.......-r-,.---.........--~ 2 0.5 0 ...............___.___.____.___._____.___._____.__.___._...............................................................___............... 400 500 600 700 800 900 600 700 800 900 wavelength (nm) 2.5 2 ld) OsL2L' ,-._ ...... I ~ ""0 ~ '-" 1.5 1 w 0.5 0 400 500 wavelength (nm) 34 2.5 .....-r-....--r-....--r-....--r-....--r-.-----....--r-....--r-....--r-....--r-....--r-...........---r--, 0.5 0 ........__.................................................._._......__._...............__.__._...__.__.__............._............._............... 400 2.5 500 600 700 800 wavelength (nm) 900 .---,.......-,.-.---.----r--r_____...---,---r-.......................................-...........-.........-T"""_____, Cl) 0.5 0 ..........___............__..........._..........._.....__._....___._.............................................____.___.____.__..........._............... 400 500 600 700 800 wavelength (nm) 900 35 2.5 ....--r-...--r-....--r-...--r-r--r---...--r-r--r---...--r-r--r---....--r-r--r---..--.-T""""""1 2 0.5 0 .........___............_............._..,___,__.__._...._................._.__._-=---___.___.___.___.'---'--.&..-..L.....J 400 500 600 700 800 900 wavelength (nm) 2.5 .........,......,.............---.---,.---.---,.---.---.----.---,-.....,...................................,..............,..........---.--~ 0.5 0 ............._..___.__............._..___.__............._..___.__............._.............__............._.............__............._............_.......... 400 500 600 700 wavelength (nm) 800 900 36 B. Electrochemical Methods The ground state reduction potentials of the 8 dyes, shown in Table 2.1, were obtained by cyclic voltametry. All measurements performed in this laboratory were done using an EG&G Princeton Applied Research (PAR) Model 172 Potentiostat in conjunction with a Houston Instruments Omnigraphic 2000 recorder. The cyclic voltametric experiments were done in methanol solutions containing 0.0005-0.001 Min the dye of interest except for the two dyes listed below. The ground state reduction potential of the RuL'L2 dye was measured in acetonitrile. The reduction potential of the fully protonated RuL'3 was measured by Spitler in aqueous solution. 13 All reduction potentials were referenced to a saturated calomel electrode (SCE). Current density vs. potential experiments were performed using an EG&G Princeton Applied Research (PAR) Model 362 Potential Controller in conjunction with a Houston Instrument Omnigraphic 2000 recorder. Light intensities were controlled by the use of an ELH W-halogen bulb and were determined by use of a calibrated silicon photodiode (Solarex). A UV cutoff filter was used to avoid direct excitation of electrons in the titanium dioxide. All measurements were performed in a three-electrode potentiostatic set-up, with a Pt wire reference and Pt gauze counter electrode. The distance between the working and counter electrodes was approximately 2 mm and no stirring was performed. Some dye-electrolyte combinations were found to require some equilibration time to reach a stable open-circuit voltage; therefore, all cells were allowed to equilibrate for at least 30 minutes after exposure to a new solution before data reported here were recorded. After exposure to Proton Sponge, electrodes were allowed to reequilibrate with the buffered I-/h solution for at least 2 hours. Although the current-voltage properties of these junctions remained stable while the cell was assembled, once the electrodes were removed from the iodine solution they tended to degrade. For this reason, fresh electrodes were used in all experiments. 37 Spectral response data was obtained by biasing the cell to short circuit and measuring the voltage output from the current monitor on the potentiostat. Monochromatic light was obtained from a Spex 1682A tungsten lamp in conjunction with a Spex 1681 B monochromator with 1.25 mm slits. For the TiO2 electrodes, the dark current tended to drift slightly over time, so the dark current was measured at each wavelength and subtracted from the photocurrent at that wavelength. The light intensity from a beam-split portion of the monochromator output was measured by monitoring the photocurrent at a Si photodiode from United Detector Technology. This diode thus served as a calibration of the lamp intensity. Quantum yields were obtained by placing a calibrated Si photodiode in the same position as the TiO2 working electrode and measuring the photocurrent at short circuit, then correcting the data from the TiO2. Current-voltage data at AM 1.0 illumination was obtained before and after each run. Electrodes which showed significant decreases in photocurrent (~ 5%) were viewed to be defective and were not included in the final analysis. C. Luminescence Studies Luminescence data was obtained from dye-sensitized electrodes immersed in a solution of CH3CN containing 0.0010 M py/pyH+ and 0 or 0.010 M Proton Sponge. Spectra were collected using a spectrofluorimeter consisting of a 150-watt xenon continuous-arc excitation source, two Spex 1618B Minimate monochromators, a Hamamatsu R955 photomultiplier detector and appropriate collecting and focusing optics. The excitation beam was pulsed at 1.0 kHz using a mechanical chopper, which allowed phase-sensitive detection of the PMT response. A National Instruments PC-LPM-16 interface card was used to provide AID conversion and monochromator control via an Intel 80386-based computer. The slit widths of the excitation and emission monochromators were set to 2.5 and 1.5 mm, respectively. Electrodes were positioned in the cell containing the solution, and the cell was rotated approximately 45 ° relative to both monochromators. The cell was then rotated 38 slightly away from 45 ° to avoid deflecting light from the excitation source directly into the PMT. Emission spectra were obtained first in solutions containing no Proton Sponge. First, one scan was taken and the peak intensity was noted. Ten scans were then signal averaged to reduce noise in the spectrum. A final scan was taken and the peak intensity was compared to the initial value to make sure there was no change over the course of the experiment. Then the solution was removed by pipette, taking care not to change the electrode position, and solution containing 0.010 M Proton Sponge was added. The electrode was allowed to equilibrate for 30 minutes and the above procedure was repeated. Finally, the Proton Sponge solution was removed and a new aliquot of the initial solution was added. The electrode was allowed to equilibrate for 2 hours and a third set of emission spectra was taken. III. Results A. Characterization of Unsensitized Electrodes Current-voltage behavior in the dark for a nanoporous titanium dioxide electrode was first compared to the current-voltage behavior for a conducting glass electrode in a solution of Lil/I2. As seen in Figure 2.2, both reduction and oxidation of the l2/J- couple require high overpotentials at the conducting glass electrode and very low currents are observed in either potential direction. In contrast, the TiO2 electrode shows rectifying behavior and yields much higher dark currents in forward bias than the conducting glass alone. This behavior indicates that the success of this system may be due to the slow kinetics of electron transfer for iodine at the conducting glass surface. Because reduction and oxidation of iodine/iodide is sluggish at the back contact, negligible recombination losses are suffered. Then, since the titanium dioxide is rectifying at the IiJI- junction, a large photovoltage is attainable. To further support this explanation for the success of these electrodes, a similar experiment was performed with Me2Fc+/O as the redox couple in solution. This redox couple was chosen because the reduction potential of this couple is reasonably close to that 39 of the l2/I-. In this case, very high currents were observed in both potential directions at the conducting glass electrode, as seen in Figure 2.3. At the titanium dioxide electrode, similar behavior was observed. Although data is not shown here, dye-sensitized electrodes immersed in solutions of Me2Fc+/O developed only low photovoltages and showed little photocurrent at short circuit. This behavior results because in this case, high recombination losses are present at the back contact. Therefore, the ideal redox couple in these cells must not only have the correct reduction potential for efficient regeneration of the dye, but also have slow kinetics at the conducting glass substrate. 40 Figure 2.2: Current-potential behavior for unsensitized electrodes in CH3CN/0.040 M Ji!0.500 M Lil in the dark. Filled circles represent the data for the conducting glass used as a substrate for the TiO2. Open circles show the data for a nanoporous TiO2 electrode with no dye sensitizer. 41 2 ........,..""l"""'T"_,.....__ _ _ _ _ _ _ _.,.........._................._.._.,.._ ~ 1.5 su 1 @ '-' 0.5 c 0 "uj ~ (l) 0 -0.5 -+-I ~ ~ -1 ::::3 u -1.5 -2 ~..,__,_....i......i_._.,__._....._._.........,j................................._ _....__................... -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) Figure 2.2 0.6 42 Figure 2.3: Current-potential behavior for unsensitized electrodes in CH3CN/(0.100 M/0.100 M) Me2Fc+10/1 .00 M LiClO4 in the dark. Filled circles represent the data for the conducting glass used as a substrate for the TiO2. Open circles show the data for a nanoporous TiO2 electrode with no dye sensitizer. 43 2 ,--. ~ s () r""'T"'...,....,--,-"T"-r-r-l"""T'""T"""T.....,-T"""T'~r-T"""T"""T'~T"""T"...,...., 1.5 1 1o.s 0 .(/j i::::: 0 Q.) 0 -0.5 +-,I 0 ~ ::::s -1 U-1.5 -2-0.6 - --0.4 -------0.2 0.2- -0.4 0.6 0 -Applied Potential vs. Cell (V) Figure 2.3 44 B. Spectral Response Spectral response data for electrodes sensitized with the eight dyes characterized above are shown in Figure 2.4. These results can be explained fully by three coinciding factors. First, as expected, the spectral response roughly correlates with the absorption spectrum of each dye. Dyes which adsorb in lower concentrations such as the RuL'3 and OsL'3 showed lower current responses. The wavelength at which the maximum photocurrent was observed corresponded to the absorption maximum for each dye. To correct for differences in dye absorption, the spectral response data was divided by the absorption spectrum of the electrode used. The results are shown in Figure 2.5. In most cases, this procedure makes the response much more similar from dye to dye. Second, within a given set of ligands, the osmium dyes showed much more photocurrent at higher wavelengths. This phenomenon is due to the weak band present in the absorption spectra of the osmium dyes which is not present in the ruthenium dyes and which likely arises due to the direct excitation of photons to triplet states in the osmium dyes. These transitions are more forbidden in the ruthenium analogs and thus low photocurrent is seen at these wavelengths. The only response which cannot be explained by a combination of these two effects is that of electrodes sensitized with the OsL'2(NCS)2 dye. Electrodes sensitized with this dye show very high light absorption, yet these electrodes show very poor energy conversion. However, this effect can be explained by examining the ground state reduction potentials of the dyes. Of the dyes examined in this work, the OsL'2(NCS)2 has the least positive reduction potential and in fact is only 0.18 V positive of the h/1- redox couple. It is likely, therefore, that the smaller driving force for regeneration of the dye limits the efficiency of this dye. 45 Figure 2.4a-h: Average spectral response for TiO2 electrodes sensitized with one of the 8 dyes characterized above in CH3CN/0.040 M l2/0.500 M Lil/(0.001 M/0.001 M) py/pyH+. IPCE represents the incident photon-toelectron conversion efficiency and is equivalent to the external quantum yield of the cell. 46 14 4a) RuL' 3 12 ,,__ 10 ~ '-' ~ u~ ~ 8 6 4 2 0 400 500 700 600 800 wavelength (nm) 900 5 4b) OsL' 3 4 ,-_ ~ '-' 3 ~ u~ ~ 2 1 0 ...........__....................................___.___.___.__.__.__..................................._,___.___.___.__.__...........__.........., 400 500 600 700 wavelength (nm) 800 900 47 30 4c) RuL 2L' 25 ~ 20 '-' ~ u~ 15 ~ 10 5 0 400 500 600 0 800 900 800 900 wavelength (nm) 25 4d) OsL2L' 20 ,,-._ ~ 15 ~ u~ ~ 10 5 0 400 500 600 700 wavelength (nm) 48 70 ...--,-,......,-...--,-,......,-,.........-,......,-,.........-,......,-..........-,......,-~~.,........, 60 ,-.._ 50 ~ 40 ~ ~ 30 ~ 20 10 0 L...J.._.L.....J.....L.....l......J.......J.......L......L.....l......J......J.....lll!~.---1-.1.--1.......1_!,_L-L.-'---1......J 400 500 600 700 800 900 wavelength (nm) 40 10 0 ~~~~~-----~~400 • 500 600 700 800 900 wavelength (nm) 49 80 ..........-..--r-..........-..--r-.-,--..--r-.-,--..--r-.-,--..--r-~~-r--, 4g) RuL'/SCN) 2 70 60 ~ 50 .c..a-.ar-..__,,, ~ 40 ,___ u ~ 30 20 10 0 t......i..._.L...J......L....L..L......L....J.......L...l...L...J........L....L....l.......1.-.1.....J:::ll~~L......J......' 400 500 600 700 800 900 wavelength (nm) 12 4h) OsL' 2 (SCN) 2 10 ,___ ~ -..__,,, ~ u~ ~ 8 6 4 2 0 400 500 700 600 wavelength (nm) 800 900 50 Figure 2.Sa-h: Spectral response data normalized for dye absorption. 51 40 ,-._ 35 ~ "-' 30 "'O .-e0 25 20 ~ ~ 15 10 u~ ~ 5 5a) RuL' 3 (l) VJ ~ ioo 500 700 800 600 wavelength (nm) 900 10 5b) OsL' 3 ,-._ ~ "-' 8 0 0 •...-1 -+-I ..D ~ 6 0 VJ ~ ~ -.. ~ u~ 4 2 ~ 0 400 500 700 800 600 wavelength (nm) 900 52 30 ~ ~ ...._,, 25 "'O 20 a) -B0 r./J ~ ~ ..._ ~ u~ ~ 5c) RuL 2L' 15 10 5 0 400 500 600 700 wavelength (nrn) 800 900 25 5d) OsL2L' ~ ~ ...._,, 20 "'O a) ..0 I-; 0 15 r./J ~ ~ ..._ 10 ~ u~ ~ 5 0 400 500 600 700 wavelength (nrn) 800 900 53 70 ~ ~ '-" "'O (1) ..0 ;.... 0 VJ ~ ~ ..._ 5e) RuL' 2(CN) 2 60 50 40 30 u~ 20 ~ 1---1 10 0 400 500 700 800 600 wavelength (nm) 900 50 5f) OsL' 2(CN\ ~ ~ '-" 40 "'O (1) ..0 ;.... 0 30 VJ ~ ~ ..._ 20 u~ 10 ~ 1---1 ~00 500 600 700 800 wavelength (nm) 900 54 ,,-._ ~ ...__, "d (l.) .-e0 VJ ~ ~ ~ u~ ~ 80 70 60 50 40 30 20 10 0 400 5g) RuL' 2(NCS) 2 500 600 700 800 wavelength (nm) 900 500 600 700 800 wavelength (nm) 900 12 ~ 10 ...__, "d (l.) .-e0 8 ~ 6 ~ ...._ 4 VJ ro ~ u~ ~ 2 0 400 55 C. Current-Voltage Curves Current-voltage behavior for sample electrodes are shown in Figure 2.6. The range of open circuit voltages and short circuit current densities for a series of electrodes are listed in Table 2.2. In each case, the light intensity corresponded to the photon flux present at AM 1.0 illumination as monitored by the calibrated photodiode. As depicted in Figure 2.6, these electrodes showed little degradation in current after being held at short circuit under low light intensity for approximately 30 minutes (the duration of the spectral response measurements). As predicted by Grl:itzel et al., 5 electrodes sensitized with the RuL'2(NCS)2 complex exhibited the highest efficiencies. Table 2.3 shows the relative short circuit current densities predicted by the spectral response for a cell illuminated with 100 mW cm-2 of light. In most cases, the trend in the short-circuit current densities corresponded to the trend in photon-to-current efficiencies. However, some electrodes deviated significantly from the expected behavior. The electrodes sensitized with the OsL'3 dye exhibited much higher short circuit current densities than would be predicted from the spectral response data. With this dye the spectral response was particularly slow to stabilize; however, the cause of the discrepancy is still unknown. One question which arises from the data is whether the differences in the open circuit voltages at AM 1.0 illumination between electrodes sensitized with different dyes is due to a difference in the junction energetics or is merely a reflection of the difference in injection efficiency. Since the maximum free energy obtainable from the cell should only be dependent on the difference between the TiO2 conduction band edge and the redox couple in solution (Scheme 2.1 ), the open-circuit voltage should not be a function of the dye at a given current density. Assuming the principle of superposition holds, the currentvoltage behavior of these cells in the dark should yield information regarding this issue. Figure 2.7 shows the dark current-voltage behavior of the electrodes depicted in Figure 2.6. The curves do not appear to deviate from each other by more than 100 mV, supporting the hypothesis that the differences in the cells in the light are only due to 56 differences in the number of electrons injected into the Ti 02. Table 2.4 shows the potential required to pass 2.0 mA cm- 2 of reductive current in the dark and further illustrates the similarities in the electrode behavior. Only the electrodes sensitized with RuL'2(NCS)2 and RuL'2(CN)2 require significantly higher voltages than other electrodes. In fact, electrodes sensitized with RuL'2(CN)2 show the highest voltages, so at a given photocurrent, electrodes sensitized with this dye should exhibit the highest photovoltages. 57 Figure 2.6a-h: Current-potential curves for a representative TiO2 electrode for each of the 8 dyes characterized above at a light intensity of AM 1.0 in CH3CN/0.040 M l2/0.500 M Lil/(0.001 M/0.001 M) py/pyH+. Filled circles represent data collected before measuring the spectral response of the electrode while open circles represent data taken after the spectral response measurements. 58 2.5 ______.._____________.._ __....._______ 6a) RuL' 3 ~ 0 ~ 0.5 :::s u 0 ..........___,__........,.,..,._..........,,__,__......_...............,__...........,__,__.........,,.__._____. -0.6 ~ () 0.4 3.5 ___________.,...__ _ ___ N S -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 3 6b) OsL' 3 ~ S 2.5 ___., o 2 .,...; r:.r., 0 Q) 1.5 ~ 1 Q Q) t:::::s 0.5 u 0 ..........,__,__...........,...,_..........,,__,__......_..........,....,__...........,__,__.........,,.__._____. -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 59 ,-__ N S 2.5 C) +,J 0 a) t:: 0.5 ~ u 0 -0. 6 __,_....,___,.....I ,-__ ------------------------ -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 6 N s 5 ~ s 4 I 6d) OsL2L' C) ~ >--. -~ +,J [/J 0 3 a) Q +,J 2 0 a) t:: ~ 1 u 0 -0.6 -0.4 -0.2 0.2 0 Applied Potential vs. Cell (V) 0.4 60 10 - - - - - - - - - - - - - - - - - - - - - 0 ................it _ _ _ _ _ _ _ _.........._........._...................._...................._____......._. -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 10 __.....,........___.,.............,........__________________ 0 ___.___,__.....,.........___,_........_..........,_.__..........__.__.......................................... -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 61 20 ____________,_________ 0 ~ -0.6 ..........................................___. . .___._____...........,_ _ _...,,___. -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 1.2 _ _ _..,..._.___________ ,...........-.---i~ ~ 01 9u 1 6h) OsL' 2(NCS) 2 ~ 0.8 '-' ~ -~ 0.6 ~ a) Q 0.4 ~ a) ~ u 0.2 0 ....................................................----............__,__--..........,,.................___. -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 62 Table 2.2: Open Circuit Voltages (V oc) and Short-Circuit Current Densities CJsc) as a Function of Sensitizer at AM 1.0 illumination. V oc values are listed vs. the cell potential. 63 Dye Voc (average, mV) Isc (average, rnA cm-2) Voc (range, mV) Isc (range, rnA cm-2) RuL'3 370 2.0 365-380 1.3-2.6 OsL'3 360 4.6 345-375 2.4-5.8 RuL2L' 390 3.2 385-405 2.7-3.7 OsL2L' 390 5.4 350-450 4.7-6.2 RuL'2(CN)2 490 8.4 470-500 8.3-8.5 OsL'2(CN)2 410 8.2 410 7.5-9 .0 RuL'2(NCS)2 520 17 495-570 15-20 OsL'2(NCS)2 330 2.1 310-375 2.0-2.2 Table 2.2 64 Table 2.3: Predicted short circuit current densities at 100 mW cm- 2 incident illumination based on integrated spectral response data. a: Calculated using solar spectrum. b: Calculated using spectrum of Sylvania ELH bulbs used in this work. 65 Dye RuL'3 OsL'3 RuL2L' OsL2L' RuL'2(CN)2 OsL'2(CN)2 RuL'2(NCS)2 OsL'2(NCS)2 Current Density (mA cm-2? Current Density (mA cm-2)b .96 .62 1.6 2.8 5.6 7.6 11 2.0 Table 2.3 1.1 .78 1.7 3.5 7.0 9.7 16 2.4 66 Figure 2.7a-h: Current-potential data taken in the dark for the electrodes represented in Figure 2.6. 67 ,__ NI s (.) 0.5 7a) RuL' 3 0 --< s -0.5 "-' ~ ~ •...-1 r:/J ~ -1 a) Q ~ -1.5 ~ a) ~ ;:::$ u -2 -2.5 -0.6 -0.2 0.2 -0.4 0 Applied Potential vs. Cell (V) 0.4 0.5 0 7b) OsL' 3 -0.5 -1 -1.5 -2 -2 .5 . . . . . . . . . . . . . . . _...__.........._. . . . . . . .____.__....__.__. . . . . . . .____.__. . . . . . . _. . .___.__. . .___. -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) 68 ---- 0.5 7c) RuL 2L' N su 0 ~___, -0.5 c -1 -~ I r:r:, 0 (1.) 0 -+-I -1.5 0 (1.) ~ :::s u -2 -2.5 . . . . . . ._. . . . . . . .___._............._. . . . . . . .____.___. . . . . . _. . . . . . . .___._............._. . . . . . . .____.___. -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) 0.5 ~"""T"'"""""'T~..------r-"""T"'"""""'T~~"""T"'"""""'T~T""""""'T""""""T"'"""""'T___, 0 ~___, -0.5 c -~ 0 -1 (1.) 0-+-I -1.5 0 (1.) ~ :::s u -2 -2.5 -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 69 ,,,-.._ NI s () 0.5 0 7e) RuL' 2(CN) 2 ~ -0.5 '-' ~ -+-I ...... rfJ -1 0 (I.) Q -+-I -1.5 0 (I.) t:~ -2 u -2.5 .____._. . . . . . . .___.__...__.___.__............__ ___.__~__.__............__ _ -0.6 ,,,-.._ NI s () -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 0.5 0 7f) OsL' 2(CN) 2 <t: s -0.5 '-' ~ -+-I ...... rfJ 0 -1 (I.) Q -+-I -1.5 0 (I.) t:~ u -2 -2. 5 ..........._. . . . . . . .___.__............_.......__.___.__............._.......__.____._____. . . .__.____.____. -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) 70 ~ -~ ~ -1 Q.) 0+-- -1.5 ~ Q.) ~ -2 u -2.5 . . . . . . . . . . . . . . . _.__. . . . . . . . . . . . . . . ____._____. . . . . . . _. . . . . . . ._._.............._. . . . . . . ._.______. -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 0.5 N,-..._ . I su 0 7h) OsL' 2 (SCN) 2 ~ s -0.5 ---~ ~ +-rJ.J -1 ~ Q.) 0 +-~ Q.) t:: -1.5 -2 :::::s u -2. 5 . . . . . . . . . . . . . . . _.__~~---~-~....___._. . . . . . . .____.____. -0.4 -0.2 0 0.2 -0.6 0.4 Applied Potential vs. Cell (V) 71 Table 2.4: Applied potential required to sustain 2.0 mA cm- 2 of reductive current in the dark for TiO2 electrodes sensitized with each dye. 72 Dye Potential vs. Cell (V) RuL'3 -0.43 OsL'3 -0.40 RuL2L' -0.41 OsL2L' -0.38 RuL'2(CN)2 -0.50 OsL'2(CN)2 -0.41 RuL'2(NCS)2 -0.47 OsL'2(NCS)2 -0.39 Table 2.4 73 D. Effect of pH on 1-V Curves--Ti02/RuL'2(NCS)2 Electrodes Ti02/RuL'2(NCS)2 electrodes were characterized as a function of Proton Sponge concentration to determine whether improvements seen in cells with special additives were due to surface state passivation or some other mechanism or if the effect could be explained solely on the basis of pH change. In initial sets of experiments, each electrode was first characterized in a solution containing only buffered Lil/I2. As depicted in Figure 2.8a, when Proton Sponge was added, the open circuit voltages increased dramatically and the short circuit currents dropped. This effect is believed to be due to a shifting in the band edge position of the Ti02 with pH. As the difference between the conduction band edge position of the Ti02 and the reduction potential of the Lil/I2 is increased, the open circuit voltage gets larger. If the conduction band edge becomes so negative that the excited dye cannot inject electrons efficiently, the short-circuit current density decreases. However, as shown in Figure 2.8b, when the electrode was reintroduced to the buffered solution, the open-circuit voltages decreased as expected, but the short-circuit current densities did not recover. As mentioned earlier, once the electrodes were exposed to iodine solution, the removal of the iodine contact caused some irreversible degradation of the electrode which could account for the change between the first and last potential scan. To determine whether the decrease in current upon exposure to Proton Sponge was completely due to emptying the cell and refilling it, current-voltage curves of fresh Ti02/RuL'2(NCS)2 electrodes in solutions containing various concentrations of Proton Sponge were examined (Figure 2.9). As seen in the figure, the results for the 10 rnM Proton Sponge solution were almost identical to those of electrodes first exposed to buffered solution. Since the dyes are known to desorb in aqueous base, the more basic solutions could cause some loss of dye even in non-aqueous solutions, resulting in lower currents when the electrodes are reimmersed in buffered solution. Although this effect may also account for part of the current decrease, the voltage increases in basic solution cannot be explained by a loss of 74 dye, thus a band edge shift seems likely. The dark curves for this dye-electrode system show a similar shift in the voltage, further supporting the presence of a band edge shift. Table 2.5 summarizes the open circuit voltages and short circuit current densities as a function of Proton Sponge concentration. 75 Figure 2.8: Current-potential curves for a RuL'2(NCS)2-sensitized TiO2 electrode at a light intensity of AM 1.0. (a) Filled circles represent data for the electrode immersed in a CH3CN solution containing 0.040 M l2/0.500 M Lil/(0.001 M/0.001 M) py/pyH+. Open circles represent data for the same electrode in a solution similar to the initial solution but containing 0.010 M Proton Sponge. (b) Filled squares represent data for a second TiO2 electrode immersed in the 0.010 Proton Sponge solution. Open triangles represent data for this electrode in CH3CN/0.040 M h/0.500 M Lil/(0.001 M/0.001 M) py/pyH+ after exposure to the Proton Sponge solution. 76 25 _,.....,............,...._________.....___________....._ ••• -5 .._._.........._._.............................................................................................................................. -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) 77 10 ______________....._.,...._.._______~---- ■ ■ ■ ■ ■ ■ ■ ■ ■ I -5 ........................................................................................______......______...................... 0.2 -0.8 -0.6 -0.4 -0.2 0 0.4 Applied Potential vs. Cell (V) 78 Figure 2.9: (a) Photocurrent-potential curves for solutions containing various Proton Sponge concentrations. All light intensities were AM 1.0. Filled squares represent data taken in a solution containing 0.001 M Proton Sponge, open circles represent data taken in a solution containing 0.003 M Proton Sponge, and filled triangles represent data taken in a solution containing 0.010 M Proton Sponge. (b) Dark current-potential curves for an electrode before (filled squares) and after (open squares) exposure to Proton Sponge. Squares represent data taken in the buffered CH3CN solution while triangles represent data in a solution containing 0.010 M Proton Sponge. 79 20 ......,.........,~------------------- ;'--- ~ oO cP O ~ 0C0000 0 OOD ~ 10 ..._,, 0 .uj 5 i::: (1.) 0 'E(1.)= 0 U -5 t::;::s -10 .........-.................................................................._.__......................................................................... -0.8 -0.6 -0.4 -0.2 0.2 0.4 0 Applied Potential vs. Cell (V) 80 0.5 - - - - - - - - - - - - - - ~ - - -2.5 ________________..........._____________________ -0.8 -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 81 Table 2.5: Open circuit voltages and short-circuit current densities for RuL'2(NCS)2-TiO2 electrodes as a function of Proton Sponge concentration at AM 1.0 illumination. 82 Proton S onge Concentration Yoe (average, mV) lsc (average, mA cm-2) 0rnM 520 ± 20 17 ± 2 1 rnM 550 ± 20 18 ± 2 3rnM 590 ± 20 15 ± 1 lOrnM 700 ± 20 7.2 ± 1 Table 2.5 83 E. Effect of pH on luminescence of the adsorbed dye--Ti02/RuL'3 electrodes The effect of pH on the TiO2 band edge positions was further examined through luminescence studies of the adsorbed dye. The quantum yield for luminescence (<I>) of the dye is given by eq. 2.1, where krad is the rate constant for radiative decay, knrad is the rate constant for non-radiative decay, and kinj is the injection rate constant: krad <I> = - - - - - = -="---- (2.1) krad + knrad + kinj If a shift in the band edge position causes a decrease in the injection rate constant, resulting in a decrease in photocurrent increase, the quantum yield for luminescence should increase, and thus luminescence intensity should increase as the pH is increased. If the decrease in current observed above was solely due to a loss of dye, the luminescence intensity should decrease due to the smaller amount of dye on the surface of the electrode. Luminescence studies were first attempted on TiO2/RuL'2(NCS)2 electrodes, but the luminescence intensity was very low and the peak was at a wavelength too high to detect with the system available. TiO2/RuL'3 electrodes were chosen as an alternate because of the strong luminescence of the L'3 dyes. The luminescence results are shown in Figure 2.10a. When Proton Sponge is present, the luminescence intensity increases as expected. After 2 hours of immersion in the buffered solution after exposure to the Proton Sponge solution, the luminescence drops back down near the initial value. To minimize the effects of changing solutions, the luminescence experiment was repeated with a new electrode in a CH3CN solution containing 0.001 M/0.001 M py/pyH+. In this case, a few drops of glacial acetic acid were then added to the solution to neutralize the Proton Sponge. As shown in Figure 2.10b, an immediate decrease in the luminescence intensity was observed, consistent with an increased dye injection efficiency and a positive conduction band edge shift due to the decreased pH. To make sure the effect of pH on the current-voltage characteristics was not limited to the RuL'2(NCS)2 system, J-E curves of the TiO2/RuL'3 electrodes were examined as a 84 function of pH. The results are shown in Figure 2.11. The photocurrents drop significantly when the Proton Sponge concentration is changed from Oto 0.010 M. The large amount of hysteresis present makes it difficult to quantify the open-circuit voltage change although it appears to increase slightly. As in the previous case, the photocurrents decrease from their initial value on reimmersion and equilibration with the buffered solution. The dark curves show a large negative shift in the voltage when the electrode is exposed to Proton Sponge, similar to the behavior observed with the TiO2/RuL'2(NCS)2 electrodes. The dark curves return to their previous position when the electrode is reimmersed in the buffered solution. 85 Figure 2.10: Luminescence data for a RuL'3-sensitized TiO2 electrode immersed in a CH3CN solution buffered with 0.001 M/0.001 M py/pyH+. Spectra are corrected for instrument response. (a) Open symbols represent data taken in the buffered solution, while the filled squares represent data taken in a solution with 0.010 M Proton Sponge added. Diamonds represent data taken before exposure to Proton Sponge; circles represent data taken after exposure to Proton Sponge. (b) Open squares represent data taken in a solution with 0.010 M Proton Sponge added; filled circles represent data taken in the same solution with a few drops of glacial acetic acid added. 86 3 _......_ _,........______,..._____,..._ _......___ 10a) RuL' 3 0 _____.__........,.____.___________.........._ 600 650 700 750 wavelength (nm) 800 87 2 10b) RuL' 3 ,__ r:/J -~0 ,I-I :::s . 1.5 ,,r) ~ "-" >-. -~ ,I-I r:/J 0 1 (l) ,I-I -~0 (l) -~> 0.5 ,I-I ro ,....... (l) ;... 0 -....................................................__._.........__._..........................................................- 600 650 700 wavelength (nm) 750 800 88 Figure 2.11: Current-potential data for a RuL'3-sensitized TiO2 electrode in CH3CN/0.040 M 12/0.500 M Lil/(0.001 M/0.001 M) py/pyH+. Triangles represent data taken in solutions containing only the buffer, while circles represent data taken in a solution with 0.010 M Proton Sponge added. Filled triangles represent data taken before exposure to Proton Sponge ; open triangles represent data taken after exposure to Proton Sponge. (a) Photocurrent-potential data. (b) Dark current-potential data. 89 1.5 ___________....._____.,...._.__________ 1 .....>-. .j,,,j 1 la) RuL' 3-light 0 r:r.i = -0.5 Q = -1 .j,,,j Q.) ~ u -1.5 I -2-0.8 ---- - - -0.4 - - - --0.2 - - - - -0- - - 0.2 - - - - 0.4 -0.6 Applied Potential vs. Cell (V) 90 0.5 _____________......,._ _ _ __ 11 b) RuL'rdark ~ su 0 @-0.5 '-' ·vsc:= -1 (]) Q 'E= -1.5 (]) t:: :::s U -2 I -2.5 ........................_._...._._..............................................._._.....__..............................................._ -0.8 -0.6 -0.4 -0.2 0.2 0.4 0 Applied Potential vs. Cell (V) 91 IV. Discussion The data presented here provide a rational approach for design of more efficient nanoporous electrodes. As discussed above, the first requirement for this type of system is slow charge transfer kinetics between the back contact of the electrode and the sacrificial electron donor/acceptor in solution. This condition allows the separation of charge by a diffusion gradient rather than drift. A similar approach has been used in single crystal systems such as Si, in which ohmic selective back contacts were used in conjunction with Si electrodes with very high carrier lifetimes to produce efficient solar cells. 14 The exploration of alternate dyes also seems promising. As expected, moving down the periodic table from ruthenium to osmium results in a second band in the absorption spectrum. Spectral response data shows that these excess photons absorbed also result in electron injection into the Ti 02. In theory, this effect would result in higher photocurrents from a continuous wavelength source such as the sun. Unfortunately, the effect of changing the metal on the ground state reduction potential must also be considered. The osmium dyes are less easily reduced and thus in certain cases are not efficiently regenerated by the iodine/iodide redox couple. However, careful design of the ligands or changing the solution redox species could improve the photoproperties of these solar cells. Finally, the effect of solution pH on the interfacial energetics of the junction should be considered. The data demonstrates that changing the solution pH can have a profound effect on the current-voltage properties of the cell even in nonaqueous solutions. Increasing the pH has been shown to result in photovoltage increases of up to 200 m V. Again, though, this parameter needs to be optimized for the system studied. If the conduction band edge moves too negative as a result of changing the pH, the dye excited state may no longer be energetically capable of injecting an electron, and photocurrents will decrease. Another consideration is the stability of the dye adsorption at high pH. Design of a more robust linker on the dye ligands would alleviate this problem. 92 V. (1) References Tan, M. X.; Laibinis, P. E.; Nguyen, S. T.; Kesselman, J.M.; Stanton, C. E.; Lewis, N. S. Prag. Inorg. Chem. 1994, 41, 21. (2) O'Regan, B.; Gratzel, M. Nature 1991, 353, 737. (3) Smestad, G.; Bignozzi, C.; Argazzi, R. Solar Energy Mater. Solar Cells 1994, 32, 259. (4) Argazzi, R.; Bignozzi, C. A.; Heimer, T. A.; Castellano, F. N.; Meyer, G. J. Inorg. Chem. 1994, 33, 5741. (5) Hagfeldt, A.; Gratzel, M. Chem. Rev. 1995, 95, 49; and references therein. (6) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphry-Baker, R.; Muller, E.; Liska, P.; Vlachopoulos, N.; Gratzel, M. J. Am. Chem. Soc. 1993, 115, 6382. (7) Vinodgopal, K.; Hua, X.; Dahlgren, R. L.; Lappin, A.G.; Patterson, L. K.; Kamat, P. V. Journal Of Physical Chemistry 1995, 99, 10883. (8) Lindstrom, H.; Rensmo, H.; Sodergren, S.; Solbrand, A.; Lindquist, S. E. Journal Of Physical Chemistry 1996, 100, 3084. (9) Fitzmaurice, D. J.; Eschle, M.; Frei, H.; Moser, J. Journal Of Physical Chemistry 1993, 97, 3806. (10) Heimer, T. A.; Bignozzi, C. A.; Meyer, G. J. Journal Of Physical Chemistry 1993, 97, 11987. (11) Huang, S. Y.; Schlichthorl, G.; Nozik, A. J.; Gratzel, M.; Frank, A. J. Journal Of Physical Chemistry B 1997, 101, 2576. (12) Sauve, G.; Cass, M. E.; Lewis, N. S. to be submitted. (13) Spitler, M. T. J. Electroanal. Chem. 1987, 228, 69. (14) Tan, M. X.; Kenyon, C. N.; Wilisch, W. C. A.; Lewis, N. S. J. Electrochem. Soc. 1995, 142, L62. 93 Chapter 3: Stability of n-Si/CH30H Contacts as a Function of the Reorganization Energy of the Electron Donor All or part of this text originally appeared in : Pomykal, K. E., Fajardo, A. M., and Lewis, N. S., J. Phys. Chem., 1995, 99(20), pp. 8302-8310. 94 I. Introduction In this chapter and those following, experiments are conducted with single crystal electrodes and a more quantitative approach to analysis of semiconductor/liquid junction kinetics is used. This chapter addresses the experimental validation of one key aspect of the Marcus/Gerischer model for charge transfer at semiconductor/liquid contacts as first presented in Chapter 1. Based on the expression for Kn (Equation 3.2 below), it is obvious that the interfacial charge capture rate of a photogenerated charge carrier in the semiconductor should be highly dependent on A, the reorganization energy of the molecular reagent in the electrolyte solution. 1-6 Such a correlation is especially important for photogenerated minority carriers in n-type semiconductors because, as discussed earlier, many photoanodes are unstable in the presence of water and undergo deleterious photocorrosion or photopassivation reactions. 7-9 An improved understanding of the factors involved in determining interfacial charge transfer rate constants at semiconducting electrodes should allow more efficient scavenging of photogenerated charge carriers and should thereby enable the construction of more stable, efficient photoelectrochemical cells. II. Theory As discussed in Chapter 1, the interfacial charge transfer rate constant for hole transfer to an electron donor, kht, can be broken down into a vibrational term, Yn, a nuclear term, Kn, and an electronic term, Ke1: (3.1) Only Kn contains a term that is strongly dependent on the reorganization energy, A: (3.2) where ~G 0 ' equals the driving force of the elementary charge transfer step at the semiconductor/liquid contact, T is the temperature, and k is the Boltzmann constant. Thus, the interfacial charge capture rate of a delocalized, photogenerated charge carrier in the 95 semiconductor should be highly dependent on A, the reorganization energy of the molecular reagent in the electrolyte solution. 1-6 Such a correlation is especially important for photogenerated minority carriers in n-type semiconductors because most photoanodes are unstable in the presence of water and undergo deleterious photocorrosion or photopassivation reactions. 7-9 For hole transfer at an n-type semiconductor/liquid interface, ~G 0 '=E0 '(A/A-)-Evb• where E 0 '(A/A-) is the standard electrochemical potential of the redox couple in solution, and Evb is the energy of the valence band edge at the semiconductor surface.5 At constant driving force with Evb-E0 '(A/A-)<A, the interfacial charge transfer rate constant for capture of minority carriers should therefore decrease as A mcreases. Due to the difficulty in directly measuring kht for photogenerated minority carriers at an n-type semiconducting photoelectrode,3•10- 12 the approach used here was to evaluate the kinetic competition between passivation and stabilization reactions for a given semiconductor/solvent-electrolyte combination. Three different outer-sphere electron donors, with nearly constant electrochemical potentials but widely varying electron selfexchange rate constants (and thus widely varying A values) (Table 3.1), 13•14 were used as stabilizing agents for n-Si/CH3OH-electrolyte interfaces. Water was then deliberately introduced into the dried solvent to provide a controlled, known concentration of passivating agent against which kinetic competition by the various stabilizers could be measured (Figure 3.1). The concentration of redox stabilizer and the light intensity were also maintained constant throughout the photoelectrode experiments, and the driving force for charge transfer was determined to be essentially identical for all three contacts. Under these conditions, the Marcus/Gerischer theory predicts that stabilizers with smaller A values should possess larger kht values and therefore should produce improved photoanode stability and increased solar energy conversion efficiency. Prior work has investigated the electrode stability of some semiconductor/liquid contacts in the presence of redox stabilizers, but has produced mixed results when 96 compared to theoretical predictions. Gomes and coworkers have studied the stabilization of GaP by Fe(CN) 64- and by Fe(II) (EDTA) using rotating ring-disk electrode methods. 15 However, comparisons between the two redox couples were performed at different pH values, resulting in a shift of the band edge positions that changed the driving force for charge transfer in the two systems. 16 Schneemeyer and Wrighton examined the efficiencies of MoSe 2 electrodes in contact with various halide ions in acetonitrile, 17 but charge transfer processes to the halide redox systems generally involve inner-sphere redox steps and/or multi-step pathways which are not amenable to straightforward comparisons with theory. Here these problems were minimized by use of simple outer-sphere oneelectron transfer reagents with nearly identical redox potentials, and controlled amounts of passivation in non-aqueous solvents. 97 Figure 3.1: Pathways for hole transfer at the Si/liquid interface. E(NA-) is the electrochemical potential of the redox couple in solution, q V n is defined as the difference in the bulk of the semiconductor between the conduction band energy, Ecb, and the Fermi level, Ef, and Vbi is the built-in voltage of the junction, which is equal in magnitude to the flat-band potential measured relative to the equilibrium potential of the solution. The barrier height, <h, is defined as the sum of V bi and V n- As the selfexchange rate constant of the redox couple NA- decreases, kht decreases, and the corrosion reaction becomes a viable pathway. 98 ,,....__ I ..__, qVbi t ... q<!>b Ecb qVn ; ~ (1) 'Ef 1--< - - - - - E(A/A-) izi > > >-. bJ) 1--< (1) i::: ~ kht Evb A-+ h+ ---> A h+ ,,....__ Si + 4h+ + 2H20 ---> Si02 + 4H+ kcorr + ..__, I solution semiconductor Figure 3.1 99 III. Experimental Section A. Electrodes Single-crystal wafers of (100)-oriented n-type Si (2-6 n-cm resistivity, phosphorus-doped, obtained from Silicon Sense Inc., Nashua NH) were cut into squares approximately 4 mm on each side to provide specimens suitable for use as Si electrodes. Ohmic contacts were then formed by scratching Ga:In eutectic into the back (unpolished) side of the Si squares. The samples were attached to a Cu wire with Ag print (GC Electronics), and all metal contacts were insulated from the solutions through the use of white epoxy (lC; Dexter Corp.). The area of each electrode was determined by photographing the electrodes and their insulating epoxy, magnifying the pictures by a known amount, and using a digitizing program to determine the exposed geometric areas. The magnification factor was determined through simultaneous photographs of a microruler. B. Redox Couples and Electrolytes Purification of the solvents and electrolytes has been described previously. 18 All electrolytes were dried through heating under vacuum in a Schlenk tube, and methanol was dried over Mg methoxide and then distilled under nitrogen. The trifluoromethanesulfonate (TFMS) salt of ruthenium(II) pentaammine 4,4'bipyridine (Ru(NH 3) 5(4,4'-bipy) 2+) was prepared according to the method of Fleischer and Lavallee, 19 with minor modifications to obtain the TFMS salt instead of the chloride salt. One equivalent of [Ru(NH 3) 5Cl]Cl 2 (Strem Chemical Co.) was dissolved in H20 at 80 °C and two equivalents of AgTFMS (Aldrich) were added to precipitate two equivalents of AgCl. The solution was filtered and the filtrate was then degassed with argon. Zinc amalgam was added to the filtrate to reduce the ruthenium ion, forming Ru(NH 3) 5H 20 2+(aq). In another flask, 4 equivalents of 4,4'-dipyridyl hydrate (Aldrich) were dissolved in hot H20 . To avoid formation of the unwanted dimeric compound (Ru(NH 3) 5)i(4,4'-bipy) 4+, the Ru(NH 3) 5H2o2+(aq) solution was slowly added to the 100 dipyridyl solution through a cannula. The solvent was removed by vacuum distillation, and the resulting solid was dissolved in hot ethanol. Diethyl ether was added to precipitate (Ru(NH 3) 5(4,4'-bipy)(TFMS)i, which was isolated by filtration and was dried under vacuum. The chloride salt of cobalt (II) tris(2,2'-bipyridine) (Co(2,2'-bipyh 2+) was prepared by dissolving one equivalent of anhydrous cobalt(II) chloride in dry CH 3OH followed by addition of a solution that contained three equivalents of 2,2'-dipyridyl dissolved in dry CH 3 OH. 20 The solvent was removed by vacuum distillation and the product was dried under vacuum. 1, 1'-Dimethylferrocene Me2Fc (Strem Chemical Co.) was purified by sublimation under vacuum. 1,1'-Dimethylferricenium (Me 2Fc+) was available from previous experiments in this laboratory 18 or was generated in situ using controlled potential electrolysis in a three compartment cell. The oxidized forms of the Ru and Co redox couples, Ru(NH 3) 5(4,4'-bipy) 3+ and Co(2,2'-bipyh 3+, were produced electrochemically from the corresponding reduced Ru(II) and Co(II) complexes that were prepared as described above. Electrolysis was monitored both by counting the number of coulombs passed through the cell and by checking the cell potential and comparing it to the value expected from the Nemst equation, E(A/A-)=E0 '(AJA-)+(RT/F)ln([A]/[A-]). In this equation, E(AJA-) represents the redox potential of the solution, £0°(AJA-) is the standard potential for reaction between A and A-, R is the gas constant, and Fis Faraday's constant. Values of E 0 '(AJA-) were measured using cyclic voltammetry at a 0.50 cm long, 0.5 mm diameter platinum wire in methanolic solutions of 1.00 M electrolyte and 0.00100.0015 M [A-] (Figure 3.2). A platinum foil was used as a counter electrode, and a CH 3OH SCE, consisting of mercury and mercurous chloride in a saturated methanolic solution of Li Cl, was used as the reference electrode. This CH 3OH SCE had a potential of 0.0500 ± 0.0005 V vs. a normal SCE when measured in saturated aqueous KCI. Note that all potentials are referenced against this CH 3OH SCE unless noted otherwise. The 101 voltamrnetry experiments showed quasi-reversible behavior for all three redox couples, although the peak-to-peak separation was largest for Co(2,2'-bipy) 3 3 +12 +. E 0 '(AJA-) was determined by estimating the mean of the anodic and cathodic peak positions (Table 3.1). 102 Figure 3.2: Cyclic voltammograms for the redox couples used in this work. (a) 0.0010 M Me 2Fc-l.00 M LiCIO 4 , scan rate= 50 mV s- 1; (b) 0.0010 M Ru(NH 3) 5(4,4'-bipy) 2+-I.00 M LiTFMS, scan rate= 20 mV s-1; (c) 0.0015 M Co(2,2'-bipyh 2+-I.00 M LiCI, scan rate= 50 mV s- 1. The reference electrode in (a) and (b) was a methanol SCE; the reference electrode in (c) was a standard SCE. Anodic currents are positive in sign. 103 2a) Me Fc+io 2 0.01 -0.01 0 0.2 0.4 0.6 Applied Voltage vs. CH 3OH SCE (V) 104 0.004 b) Ru(NH 3)/4,4'-bipy)3+12+ -0.004 0 0.2 0.4 0.6 Applied Voltage vs. CH3OH SCE (V) 105 0.002 c) Co(2,2'-bipy\ 3+12+ -0.002 0 0.2 0.4 Applied Voltage vs. SCE (V) 0.6 • 106 Table 3.1. Standard reduction potentials and self-exchange rates for the redox couples used in this work. a Co(2,2'-bipy)3+/2+ = cobalt(III/II) tris(2,2'-bipyridine); Ru(NH 3)5 (4,4'bipy) 3+12 + = rutheniurn(III/II) pentaamrnine 4,4'-bipyridine; Me2Fc+/0 = 1, 1'-dimethylferricenium/1, 1'-dimethylferrocene. b The values for E(NA-) have been corrected for the differences between the CH 30H SCEs and a standard SCE to give approximate values vs. SCE. The values for the 3+/2+ redox couples have been corrected for charge effects not present in the Me 2Fc+/O redox couple using the correction to infinite ionic strength described by Gray et aI. 31 ,32 c from ref 53. The measurements of self-exchange rates were done in aqueous solutions; the self-exchange rate for Ru(NH 3)5 ( 4,4'-bipy) 3+12 + was estimated by the self-exchange rate for Ru(NH 3)5(py) 3+12 +, where py = pyridine. d from ref 54. The self-exchange rate was measured in methanol; the selfexchange rate for Me 2Fc+/O was estimated by the self-exchange rate of ferrocene/ferrocenium. 107 Redox Couplesa Self-Exchange Rate Eo'(AJA-),b V vs. SCE Co(2,2'-bipy)3 3+12 + 50 M- 1s- 1 c 0.32 Ru(NH3)5( 4,4'-bipy)3+/2+ 1 x 106 M- 1s-l d 0.26 Me2Fc+/O 1 x IQ7 M-ls-1 d 0.20 Table3.l 108 C. Electrochemical Methods All electrochemical experiments were performed using a Model 173 potentiostat from EG&G Princeton Applied Research (PAR) with a Houston Ornnigraphic 2000 recorder and an EG&G PAR Model 175 Universal Programmer. Data were collected in a three-electrode set-up that consisted of a Si working electrode, a Pt foil counter electrode, and a Pt wire reference electrode. The concentrations of the various components of the cell were 1.00 M electrolyte, 0.0010 M of the oxidized form of the redox couple (A), and 0.0240 M of the reduced form of the redox couple (A-), unless otherwise specified. LiC1O4 , LiTFMS, and LiCl were the electrolytes for the redox couples Me 2Fc+IO, Ru(NH 3) 5(4,4'-bipy)3+/2+, and Co(2,2'-bipyh3+/2+, respectively. An electrochemical cell was typically prepared by loading 5.00 x 1o-4 moles of the reduced form of the desired redox couple and 2.00 x 1o- 2 moles of the electrolyte into the cell in an inert atmosphere drybox. The cell was then removed from the box and 20.0 mL of CH3OH were added by syringe while purging the cell with nitrogen. All electrodes were also added and removed while purging the cell with nitrogen. To produce the oxidized form of the redox couple, a Pt foil working electrode and a CH 3OH SCE were immersed in the main solution. A smaller compartment that was separated from the main cell by a Nafion frit and that contained a Pt foil counter electrode was then filled with a 1.00 M solution of electrolyte in methanol. Voltages of 0.20-0.30 V vs. CH3OH SCE were applied to produce anodic current until the oxidized form of the redox couple reached 0.0010 M, as monitored by the cell potential and by the number of coulombs passed through the cell. A controlled amount of water was then added to the cell, and the potential was allowed to stabilize. It was found that 5-10%(v/v) H 2O (2.8-5.6 M) was the optimal amount for the measurements described herein. At lower H2O concentrations, the best stabilizing agents prevented essentially all electrode passivation for exposure times up to 60 min, while at higher H2O concentrations, the poorest stabilizing agents were not able to 109 compete effectively enough with passivation to obtain meaningful current density vs. voltage curves. To examine the current density vs. voltage (J-V) behavior of the silicon electrodes as a function of time, the CH 3OH SCE was replaced by a Pt wire, and the Pt foil was removed from the auxiliary electrode compartment and placed into the main cell compartment with the Si working electrode and the Pt wire reference electrode. The potential of the Si electrode was then continuously scanned from -0.500 V to +0.200 V vs. E(A!A-) at a rate of 50 mV s- 1, and the J-V curves were then recorded at predetermined time intervals. A constant light intensity from an ELH-type W-halogen bulb, 21 corresponding to an initial light-limited photocurrent density of""' 100 µA cm- 2, was maintained throughout the J-V scans. Through the course of these experiments, it was discovered that Si electrodes yielded much more stable J-V behavior if they were first immersed into CH 3OH-1.00 M LiC1O4-0.15 M Me2Fc-0.002 M Me2Fc+ solutions with the potential being scanned from -0.500 V to +0.200 V vs. E(AJA-) at a photocurrent density of 100200 µA cm- 2 for 5 minutes. For consistency, all measurements were therefore made after electrodes had undergone this J-V scanning procedure, and fresh electrodes were used for measurements in each new redox couple-electrolyte solution. The rate of electrochemically-induced oxide growth was measured by X-ray photoelectron spectroscopy (XPS). At the beginning of each experiment, an HF-etched Si electrode was placed into a nitrogen-purged Schlenk tube and was then isolated from nominally identical Si samples that were to be used in the electrochemical measurements. A second HF-etched, Me2Fc+/O treated Si electrode was then immersed into the electrolyteredox couple solution for 10 seconds at open circuit and then was also placed into this Schlenk tube. A third, HF-etched, Me2Fc+10-treated Si electrode was then placed into a solution containing the redox couple of interest. The potential of the working electrode was set to be equal to the redox potential of the cell, and the light intensity was periodically adjusted to maintain a constant photocurrent density of 100 µA-cm- 2, except when the 110 photocurrents became so low due to electrode passivation that the lamp could not be moved closer towards the cell without producing significant heating of the sample. J-V curves were taken at the beginning of each experiment and were also collected after a specified amount of time at short circuit. After sufficient passivation had occurred, the Si electrode was removed from the electrolyte solution and was rinsed with CH3OH. The electrode was then placed into the Schlenk tube that contained the original control specimens. A series of experiments consisted of repeating this passivation procedure with fresh electrodes, all exposed to the electrolyte solution for a different amount of time. At the end of a series, the Schlenk tube was introduced into a nitrogen flushbox, and the electrodes were mounted onto UHV (ultra-high vacuum) sample studs for XPS measurements. The electrodes were transferred to vacuum through a load-lock that connected directly to the flushbox. A Varian V-200 Turbo Pump was used to evacuate the load-lock to approximately 1o- 7 torr prior to introduction of the samples into the UHV system. The XPS experiments were conducted in an M-Probe Surface Spectrometer (Surface Science Instruments (Fisons)) that was pumped by a CTI-Cryogenics 8 cryo pump. The instrument was maintained at a base pressure of 5 x 10- 10 torr, although the operating pressure was slightly higher (5 x 10-9 to 2 x 10-8 torr) due to slow outgassing of the epoxy around the sample. XP spectra were taken by exciting electrons with Al Ka (1486.6 eV) X-rays and collecting data with a hemispherical analyzer. The detector was positioned at an angle of 35° from the plane of the sample surface. Data collection and analysis were done with the M-Probe package software, version 3.4. This instrument has a sensitivity of approximately 0.1 monolayers and a resolution (full width at half maximum for the Au (4f)7/2 peak) of 0.88 ± 0.01 eV. 18 Spectra were taken for three different areas on each electrode surface to verify the uniformity of the oxide layer. D. Barrier Height Measurements The barrier heights of the various n-Si/CH 3OH junctions were calculated from the dependence of the differential capacitance of the semiconductor/liquid contact on the 111 potential applied to the electrode. In a conventional equivalent circuit for the semiconductor/liquid junction,2 three capacitances are connected in series: the space-charge region capacitance (C 5c), the Helmholtz layer capacitance (C8 ), and the diffuse layer capacitance (Cct)- Since C5c<<C8 and C5c<<Cct, the junction may be described as a single capacitor (C 5c) in parallel with a resistor, R5c, where Rsc represents the voltage-dependent resistance to faradaic charge transfer. A resistor, R 5 , in series with these two elements accounted for any resistances in the cell and completed the electrical circuit . The C 5c values could then be determined from experimental impedance data through the equation: (3.3) where Zim is the imaginary part of the impedance for a given frequency f, where the angular frequency co= 21tf. Impedance spectra were obtained on a computer-controlled Schlumberger Model 1260 frequency response analyzer equipped with a Model 1286 Electrochemical Interface. An impedance measurement consisted of 11 frequency sweeps from 106 to 103 Hz, each with a 10 m V peak amplitude ac voltage. Each sweep was performed using a different de reverse bias relative to short circuit, with the de bias increasing in 50 mV increments from 0.000 to 0.500 V. Results were obtained at seven frequencies between 5.012 kHz and 100 kHz. For each de bias, the Nyquist plot of the real part of the impedance versus the imaginary part of the impedance was fit to a semicircle, and the diameter of this semicircle was taken to be Rsc· The C5c values were then extracted and plotted vs. the applied de bias, using the well-known Mott-Schottky relationship of Csc-2 vs. V for a depleted semiconductor/liquid contact. 22 ,23 These Mott-Schottky plots were extrapolated to infinite Csc (Csc- 2=0) to obtain the flat-band potential, and thus the barrier height, <l>b, of the 112 solid/liquid contact. The desired driving force for minority carrier transfer was then calculated using the known value of the band gap, Eg, of Si: (3.4) Frequency dispersion in the capacitance-voltage data was observed when the concentration of acceptor species was 0.0010 M, so the concentrations of both forms of the redox couple were increased to 0.175 M in donor species and 0.009 M in acceptor species for all impedance measurements. This higher redox concentration produced minimal frequency dispersion and indicated that at low redox concentrations, effects of polarization at the counter electrode were important over this frequency range even under potentiostatic control. The final, higher concentration ratios produced approximately the same solution potential as that used in the J-V and stability experiments. A large (0.8-0.9 cm2) Si electrode area was also required for impedance measurements in order to eliminate errors in the dopant densities calculated from the c- 2 vs . V plots. Reliable Mott-Schottky plots could not be obtained for Ru(NH 3)5(4,4'-bipy) 3+12 + because the redox system was not sufficiently soluble in CH3OH, and the Csc vs. V data obtained at the solubility limit of the redox couple were dependent on the ac measurement frequency . IV. Results A. Electrode Stability and Current Density vs. Voltage (J-V) Behavior as a Function of the Solvent Reorganization Energy of the Electron Donor Figure 3.3 presents the J-V data for n-Si/CH 3OH-Me2Fc+IO, n-Si/CH 3OHRu(NH 3)5(4,4'-bipy)3+/2+, and n-Si/CH 3OH-Co(2,2'-bipyh3+/2+ contacts. All three redox couples have very similar standard electrochemical potentials, and the concentration of the oxidized form of the redox pair was adjusted to produce identical Nemstian potentials for the three solutions of concern. n-Si/CH 3OH-Me2Fc+/O contacts (Figure 113 3.3e) displayed J-V behavior in accord with that reported previously for this well-studied semiconductor/liquid contact. As expected from the similar redox potentials of Ru(NH 3)5(4,4'-bipy) 3+12 + and Me2Fc+IO, very similar open circuit voltages (V oc) and J-V characteristics were observed for these two redox couples. Use of Co(2,2'-bipyh3+/2+ yielded similar V oc values but produced a somewhat lower fill factor than was observed for n-Si/CH 3OH-Me 2Fc+/O or n-Si/CH3OH-Ru(NH3)5(4,4'-bipy) 3+12 + contacts. Pre-treating electrodes in the Me2Fc+/O solutions 18 improved the fill factors as well as the stability of electrodes in contact with Co(2,2'-bipyh 3+12 + solutions (Figure 3.4). n-Si/CH 3OH-Me2Fc+/O and n-Si/CH 3OH-Ru(NH 3)5(4,4'-bipy)3+/2+ contacts exhibited stable J-V behavior over 20 min time scales, but n-Si/CH 3OH-Co(2,2'bipyh3+/2+ contacts were unstable even over these short time periods. Repeated attempts to thoroughly purify the solvent and to exclude water from the cells did not produce stability of n-Si/CH 3OH-Co(2,2'-bipyh 3+12 + contacts over 20 min time scales. As seen in Figure 3.3, Si electrodes became very resistive after 20 minutes of continuous scanning in the light in Co(2,2'-bipy) 33+12+. After 60 minutes, even electrodes cycled in CH 3OHRu(NH 3) 5(4,4'-bipy)3+/2+-2.8 M H 2O began to fail (Figure 3.3d). In contrast, nSi/CH 3OH-Me2Fc+/O junctions were stable for much longer periods even when no precautions were taken to exclude air or water from the components of the cell (Figure 3.3e, f). These observations qualitatively suggested that the three different redox systems had greatly different stabilities towards photopassivation reactions due to oxide growth. 114 Figure 3.3: J-V curves for untreated electrodes in CH 3OH. The electrolyte concentration was 1.00 M, the concentration of the reduced form of the redox couple was 0.0240 M, and the concentration of the oxidized form of the redox couple was 0.0010 M. All redox potentials are measured vs. a CH 3OH SCE: (a) Co(2,2'-bipy)} 3+12+-LiCl (E(NA-) = 300 ± 2 mV); (b) Co(2,2'-bipy)}3+/2+_LiCl, 2.8 M H2O; (c) Ru(NH 3)5(4,4'-bipy)3+/2+_ LiTFMS (E(A/A-) = 225 ± 2 mV); (d) Ru(NH 3)5(4,4'-bipy) 3+12+-LiTFMS, 2.8 M H 2O; (e) Me 2Fc+IO_LiC1O 4 (E(A/A-) = 180 ± 2 mV); (f) Me 2Fc+/O_ LiC1O 4 , 2.8 M H2O. (a)-(f): solid line= start. (a), (b): dashed line= after 20 minutes of continuous scanning. (c)-(f): dashed line= after 60 minutes. 115 3a) Co(2,2'-bipy\ 3+12+ -0.6 -0.3 0 Applied Potential vs. Cell (V) 0.3 3b) Co(2,2'-bipy \ 3+12+ ~ ...... r:r.:, ~ ~ a) Q ~ ~ 0 a) ~ ::::s u -0.6 -0.3 0 Applied Potential vs. Cell (V) 0.3 116 -0.6 -0.3 0 Applied Potential vs. Cell (V) 0.3 12 3d) Ru(NH 3)/ 4,4'-bipy )3+___.+---~-"'~" ,_ ~ .,. {, -, I , ;; r I ,, , , J .,,,,,,,. ~--~------0.6 -0.3 / / 0 Applied Potential vs. Cell (V) 0.3 117 ~ I 3e) Me Fc+io su 2 ~ 0.1 '-' c ..... r;/J = <l) 0 -0.6 -0.3 0 Applied Potential vs. Cell (V) 0.3 -0.3 0 Applied Potential vs. Cell (V) 0.3 su ~ 0.1 s '-' ~ ..... -,j,..j r;/J = <l) 0 0 -0.6 118 Figure 3.4: J-V curves for treated electrodes in CH 3OH. The electrolyte concentration was 1.00 M, the concentration of the reduced form of the redox couple was 0.0240 M, and the concentration of the oxidized form of the redox couple was 0.0010 M: (a) Co(2,2'-bipyh3+/2+_LiCl (E(AJA-) = 300 ± 2 mV); (b) Co(2,2'-bipyh 3+12 +-LiC1, 2.8 M H 2O; (c) Co(2,2'bipy)3 3+12 +-LiCl, 5.6 M H2O; (d) Ru(NH3)5(4,4'-bipy) 3+12 +-LiTFMS (E(A/A-) = 225 ± 2 mV); (e) Ru(NH 3)5(4,4'-bipy) 3+12 +-LiTFMS, 2.8 M H 2O; (f) Ru(NH 3)5(4,4'-bipy) 3+12+-LiTFMS, 5.6 M H2O; (g) Me 2Fc+/O_ LiCIO 4 (E(A/A-) = 180 ± 2 mV); (h) Me2Fc+/O_LiC1O 4 , 2.8 M H 2O; (i) Me 2Fc+10 -LiCIO 4 , 5.6 M H 2O. (a)-(i): solid line= start. (a)-(c): dashed line= after 45 minutes of continuous scanning. (d)-(i): dashed line= after 60 minutes. 119 0.1 4a) no H 2 O 0 -0.6 . .., - -0.3 0 0.3 0 0.3 ,-._ NI su <s 0.1 4b) 2.8 M H 2O "-' / ~ -~ ~ = Q 0 = t:: [/J (1.) J, r' _.,,. .,, - '' ~ (1.) ;:::l u -0.6 0.1 -0.3 4c) 5.6 M H 2O .......-..-- ~:,--~~ 0 -0.6 -0.3 0 Applied Potential vs. Cell (V) 0.3 120 0.1 0 -0.6 -0.3 0 0.3 0 0.3 ,-._ N I su <s 0.1 4e) 2.8 M H 2O '-" ~ +,j ,,...; rJJ = Q = 0 u -0.6 C) +,j C) t::;::s -0.3 4f) 5.6 M H 2O 0.1 --=--,-=-~-=-~ 0 -0.6 -0.3 0 Applied Potential vs. Cell (V) 0.3 121 0.1 4g) no H 2O 0 ,-._ -0.6 -0.3 0 0.3 0 0.3 NI s ~ 0.1 s ...._, () 4h) 2.8 M H 2O ~ -~r.r:, ,+.J ~ (1) Q ,+.J ~ 0 (1) t=~ u -0.6 0.1 -0.3 4i) 5.6 M H 2O - -- 0 -0.6 -0.3 0 Applied Potential vs. Cell (V) 0.3 122 B. XPS Investigations of Electrochemical Oxide Growth A more quantitative measure of the relative photoanode stability was obtained by examining the rate of silicon oxide formation for the three various n-Si/CH 3OH contacts. These investigations were performed using a high-resolution X-ray photoelectron spectrometer that was interlocked to an anaerobic transfer system. This system allowed manipulation of samples, and their subsequent introduction into a UHV chamber, without significant oxide growth during the handling and analysis steps. To minimize variations in stability that might have resulted from variations in the amount of uncontrolled, adventitious water in the solvent, the water concentration was deliberately increased to 2.8 M (5 % by volume) in each system. This decreased the stability of the n-Si/CH 3OH-Me2Fc+/O contact, but produced conditions under which the oxide growth rate could be evaluated and compared for all three redox couples. To minimize possible errors due to the increased resistance of the passivated electrode surface, stability measurements were restricted to time scales that produced relatively thin (<15 A) oxide layers. During oxide growth, the electrode potential was maintained at short circuit vs. the Nernstian potential of the cell to ensure similar driving forces and similar photogenerated hole concentrations at the electrode surface for all three redox systems. Survey scans to determine the elemental composition of the surface were taken before focusing on the Si region to determine the amount of oxide growth. These survey scans typically showed peaks corresponding to Si, 0, and C. No Fe, Ru, or Co was detected on the surface within the instrument sensitivity limit of less than 0.1 monolayers. Figure 3.5 shows representative XPS data of the Si 2p region for Me 2Fc+10-treated Si electrode surfaces that had been exposed to CH 3OH-2.8 M H2 O solutions, each containing 0.0240 M of one of the three redox couple donors and 0.0010 M of the corresponding acceptor. Also included in Figure 3.5 are XPS data for n-Si/CH 3OH-2.8 M H 2 O-0.0960 M Co(2,2'-bipy)3 2+-0.0040 M Co(2,2'-bipy)33+ contacts. Samples that had been reserved as controls, or had only been immersed at open circuit into the electrolyte 123 solutions, showed no detectable oxide and only displayed the characteristic Si 2p doublet at a binding energy of 99.7 ± 0.2 eV (Figure 3.5, dashed lines). In contrast, after passage of anodic photocurrent in the three solutions, all XP spectra showed a new peak with a binding energy approximately 3.7 eV larger than the substrate Si 2p peak (Figure 3.5). Since these electrodes were held at short circuit instead of continuously scanned, the current decayed more quickly, especially for electrodes in contact with the Co(2,2'bipy))3+/2+ redox couple, than it did in the J-V experiments described above. J-V curves for the Co(2,2'-bipy)J3+/2+ redox couple are shown in Figure 3.6 for both n-Si/CH 3OH2.8 M H 2O-0.0240 M Co(2,2'-bipy)) 2+-0.0010 M Co(2,2'-bipy)) 3+ and n-Si/CH 3OH2.8 M H2O-0.0960 M Co(2,2'-bipy)) 2+-0.0040 M Co(2,2'-bipy)) 3+ cells. The peak position of the higher binding energy signal of Si in the XPS data has been well-documented to be characteristic of SiO2. Using a peak fitting program to determine the relative areas of the Si 2p substrate and SiO 2 peaks, the thickness of the oxide was calculated as: I° I d = (Aes x cos S)[ln(l + (~)(_A))] rA Is (3.5) where d is the oxide thickness, Aes is a tabulated attenuation factor based on the escape depth of the photoelectrons produced in the material of study, and 8 is the angle from the surface of the sample to the detector relative to normal incidence. 24 •25 rs/ r A is an instrument normalization factor related to the ratio of the signals expected for pure Si vs. pure SiO 2, and IA and Is are the measured areas of the SiO2 and Si peaks, respectively. Inserting the known parameters for the instrument and samples used in these experiments (A=26A, 26 l°s/1°A=l.3, 27 and 8=55 °) allowed calculation of the equivalent thickness of the oxide overlayer. This value is designated as an equivalent thickness because use of 124 Equation 3.5 implicitly assumes that the overlayer is homogeneous and uniform over the electrode surface. 24 •25 Figure 3.7 shows a summary of the oxide thickness data deduced from application of Equation 3.6 to the XPS data. Contact with CH 3OH-H 2O-Co(2,2'-bipy)} 3+12 + clearly produced the most rapid Si oxide growth, while CH 3OH-H2O-Me2Fc+/O and CH 3OHH 20-Ru(NH 3) 5(4,4'-bipy) 3+12+ contacts were similar to each other and produced significantly less oxide over the same time period. The error bars in the plot are representative of both the variation between the measurements for the three areas of each electrode and the possible change in 8 due to difficulties in mounting the electrodes perfectly parallel to the sample studs. Although not pictured in Figure 3.7, the line representing XPS data for n-Si/CH 3OH-2.8 M H 2O-0.0040 M Co(2,2'-bipy)} 3+-0.0960M Co(2,2'-bipy)} 2+ contacts fell between the line for CH 3OH-2.8 M H 2O-0.0010 M Ru(NH 3)5 (4,4'-bipy) 3+-0.024 M Ru(NH 3)5(4,4'-bipy) 2+ contacts and CH 3OH-2.8 M H 2O-0.0010 M Co(2,2'-bipy)}3+-0.0240M Co(2,2'-bipy)} 2+ contacts. These oxide formation data were therefore in accord with the stability trends deduced from the timedependence of the J-V data, and indicated that the Me 2Fc+/O and Ru(NH 3)5 (4,4'bipy) 3+12 + redox systems significantly improved the electrode stability relative to the Co(2,2'-bipy) 33+/2+ redox system. 125 Figure 3.5: XP Spectra of Si photoelectrodes. (a) electrode cycled in Me 2Fc+/O solution (0.0010 MI 0.0240 M), 100 min.; (b) electrode cycled in Ru(NH 3 ) 5 ( 4,4'-bipy) 3 +12 + (0.0010 M I 0.0240 M) , 60 min.; (c) electrode cycled in Co(2,2-bipyh 3+12 + (0.0010 MI 0.0240 M), 20 min.; (d) electrode cycled in Co(2,2-bipyh 3+12+ (0.0040 MI 0.0960 M), 30 min. The XP spectrum of a freshly etched n-Si electrode is included as a dashed line in panel. 126 5a) 1000 0 l-.L..-..L.,_...a........L.....1.........L...---L......L----L..::l~==--I 100 108 104 96 Binding Energy (eV) 127 5b) I I 0 L-L--L-L-.JL....JL....-L-L-.JL....J~~-108 104 100 96 Binding Energy (eV) 128 Sc) 1000 0 L..:...i:..:..l----L---1........L.....L....&...-..L......=:!:!!:!t:d 108 104 100 96 Binding Energy (eV) 129 5d) ,-__ 1000 I I rr.; -~0 I I I I I I I I I I I I I I I I ~ :::s ~ ~ -~b t '-' ~ -~ ~ rr.; 0 Q.) ~ 0 ~ '" 0 108 104 100 Binding Energy (eV) 96 130 Figure 3.6: J-V curves, treated electrodes. (a) Co(2,2'-bipyh3+/2+ (0.0010 MI 0.0240 M), solid line= start, dashed line= after 20 minutes at short circuit; (b) Co(2,2'-bipyh 3+12 + (0.0040 MI 0.0960 M), solid line= start, dashed line = after 30 minutes at short circuit. 131 6a) -0.60 ~ -0.30 0 Applied Potential vs. Cell (V) 0.30 6b) s ~ 0.1 s '-" ;;>-.. .,.... ~ r/) i::::: Q.) Q E: Q.) 0 t::: u::::3 -0.60 -0.30 0 Applied Potential vs. Cell (V) 0.30 132 Figure 3.7: Summary of XPS data; oxide growth over time. (a) Me 2Fc+IO, 0.0010 M/0.0240 M (solid squares); (b) Ru(NH 3) 5 (4,4'bipy)3+12+, 0.0010 M/0.0240 M (open squares); (c) Co(2,2-bipy) 33+/2+, 0.0010 M/0.0240 M (diamonds). 133 8 ,-.._ o<t: '-' rJJ rJJ (].) ] () •...-1 ...c:: ~ (].) "'Cl • ...-1 >< 0 7 c) 6 5 4 b) 3 a) 2 1 00 20 40 60 Time (min) 80 100 120 134 C. Barrier Height Determination for n-Si/CH 30H-Me 2 Fc+/O and n- Si/CH 30H-Co(bipyh3+/ 2 + Contacts An important component of Kn as expressed in the Marcus/Gerischer formalism (Equation 3.2) is the driving force for hole transfer from the valence band of the semiconductor to the stabilizing agent, E 0 '(A!A-)-Evb· This energetic quantity can be determined if the band edge positions of the semiconductor can be assigned relative to the redox potential of the solution. Differential capacitance vs. voltage (Mott-Schottky) analysis was performed to independently determine E(A/A-)-Evb, and ~G0 '=E0 '(AfA-)Evb, for the redox couples of concern. Figure 3.8 shows the results of the Mott-Schottky measurements of Me2Fc+/O_ treated Si electrodes in contact with CH 3OH-Co(2,2'-bipyh 3+12 + and CH 3OH-Me2Fc+/0 solutions. The flat-band potential, Vfb , for each system was obtained from the x-intercept (as (Csc)- 2-->0) of such plots. Values for Vtb were identical within experimental error when measured for n-Si/CH 3OH-Me 2Fc+/0 and n-Si/CH 3OH-Co(2,2'-bipy) 33+/2+ contacts, with V tb=0.637 ± 0.007 V. Correction of these results for the difference between the Fermi level and conduction band edge in the bulk of the sample, V n (Figure 3.1), yielded barrier heights of <l>b=0.93±0.007 V. Using this value for <l>b in Equation 3.4 resulted in a driving force ~G 0 '=-0.25 eV for hole transfer at both of these solid/liquid contacts. The quality of each Mott-Schottky plot was evaluated by three criteria: linearity, lack of frequency dispersion, and accuracy of the slope. Excellent linearity of c-2 vs. V was achieved with the linear regressions typically yielding R2 values of 1.00, where R is the correlation coefficient for the line fit. A measure of the frequency independence was obtained by comparing the extrapolated x-intercepts for a single electrode, which fell within a range of 5 to 30 mV. Slope accuracy was determined by calculating a dopant density and comparing it to the measured dopant density of the sample. According to the MottSchottky equation: 135 (3.6) where VA represents the applied potential, £, the dielectric constant of the semiconductor, Nn, the dopant density of the semiconductor, and As, the geometric area of the electrode. 2 Therefore, plotting (CscY 2 versus VA should yield a line of slope (2/(q££oNnAs2)). Independent measurements of Nn (from four-point probe conductivity data) yielded values for the dopant density of the sample that were within 2-4% of those calculated from the slope of the Mott-Schottky plots, thereby lending confidence to the validity of the driving force values obtained herein. 136 Figure 3.8: c- 2 vs. V data for Si electrodes immersed in various redox couples. (a) Co(2,2'-bipyh 3+12 +; (b) same plot as in (a), extrapolated to c- 2 equals 0; (c) Me2Fc+10; (d) same plot as inc), extrapolated to c-2 equals 0. Results are given for 7 frequencies between 5 and 100 kHz. Note that the x-axis in (b) and (d) has been greatly expanded to show the lack of frequency dependence on the x-intercept. 137 1.8 8a) 1.6 \0 .....-1 I 0 ~ ~ 1.4- ,-. N I ~ '-' N I u 1.2 - i t i i I I I i i I 1.0li I 0.8 0 I 0.20 0.40 0.60 Applied Potential vs. Cell (V) 10.0 8b) 8.0 ("<") .....-1 I 0 ~ 6.0 ~ ,-. N I ~ '-' 4.0 N I u 2.0 0.0-__.______._..LII.L...L..._ ____.__........___...________. -0.65 -0.63 -0.62 -0.64 Applied Potential vs. Cell (V) 138 2.0 . 8c) 1.8 - . \0 ....-I I ~ 0 ~ ~ 1.6- I ,___ N I ~ '-" N i i i 1.4 - I i u I i 1.2- i I i.d .. I 0 I 0.40 0.20 0.60 Applied Potential vs. Cell (V) 10.0 8d) 8.0 ('<) ....-I I 0 ~ 6.0 ~ ,___ N I ~ '-" 4.0 N I u 2.0 o.o-----------0.65 -0.64 -0.63 -0.62 Applied Potential vs. Cell (mV) 139 V. Discussion The results obtained above clearly demonstrate the dependence of the stability of a silicon photoelectrochernical cell on the reorganization energy of the redox couple. As the reorganization energy of the stabilizing agent increased, the donor molecule did not compete as effectively with the water for the photogenerated holes, and the electrode passivated more rapidly. Note that the Me2Fc+/O and Ru(NH 3)5(4,4'-bipy)3+/2+ redox couples displayed approximately equal stabilization efficiencies, in accord with the observation that the self-exchange rate constants, k 5e, for these redox couples only differ by about an order of magnitude (Table 3.1 ). In contrast, electrodes immersed in Co(2,2'bipy) 33+12+, which has a self-exchange rate that is several orders of magnitude lower than the rate for the other two redox couples, exhibited very poor stability towards passivation. Increases in the concentration of the Co(2,2'-bipyh3+/2+ stabilizer did improve the electrode stability, as expected from the rate law governing competition for photogenerated holes at an n-type semiconductor/liquid contact. 5,22 ,28 However, even a four-fold increase in the Co(2,2'-bipyh 3+12+ concentration was not sufficient to yield passivation protection that was comparable to that of the other redox systems (with smaller 'A values) at lower donor concentrations. Ideally, more redox couples with electrochemical potentials in this range would have been used in this study, especially ones with self-exchange rate constants on the order of 1Q3-1Q4 M-1 s-1 . However, it was very difficult to identify such systems, especially with the constraint that the redox couples must be outer-sphere, one-electron donors/acceptors that are reasonably soluble in methanol. The Marcus equations can be utilized to compare the stability ratios observed experimentally to those expected theoretically. The reorganization energies can be estimated by the equation: (3 .7) 140 where Zbi:::::1O 11 M- 1s- 1 is the normal collisional vibration frequency for bimolecular reactions at room temperature.29 This treatment yields values of A=O.96 eV, 1.2 eV, and 2.2 eV for Me 2Fc+I0, Ru(NH 3)5(4,4'-bipy)3+12+, and Co(2,2'-bipy))3+/2+, respectively . Using Equations 3.1 and 3.2 and assuming vn =10 13 sec- 1 and Kei=l allows calculation of the relative rate constant ratios for hole capture for the three semiconductor/liquid contacts under study. Using the experimental value of ~G 0 ' = -0.25 eV and the values calculated above for A implies that kht(Ru(NH3) 5(4,4'-bipy) 2+) = 0.4 kht(Me 2Fc) and kht(Co(2,2'bipy)) 2+)= 0.005 kht(Me 2Fc). As depicted above, these relative rate constant ratios are in good agreement with the observed stabilization ratios for these three redox couples at nSi/CH 30H-H20 interfaces. The excellent stability of n-Si/CH 30H-Me2Fc+/O interfaces can therefore be ascribed in part to the low reorganization energy and in part to the relatively large hole capture rate constant at this solid/liquid interface. Additional increases in stability for redox systems involving the Co(2,2'-bipy)) 3+12 + system could be achieved, in principle, through changes in the complex to decrease E(AIA-) and thus increase ~G 0 '. However, such an approach would produce a decrease in the overall energy conversion efficiency of the resulting photoelectrochernical cell because the free energy used to accelerate the hole capture process would not be available for collection from photogenerated carriers in the external circuit. In this respect, the n-Si/CH 30H-Me2Fc+/O interface 30 is seen to be nearly ideal for protection against Si passivation without sacrificing excessive amounts of free energy to achieve the desired faradaic stabilization process. In summary, the predictions of the Marcus/Gerischer theory have been semiquantitatively verified for n-Si/CH 30H photoelectrochernical cells. By holding the electron donor concentration, the reaction driving force, and the photocurrent density constant for each cell, the effect of changing the reorganization energy of the electron donor could be isolated. Charge transfer rates from the semiconductor electrode to the electron donor are predicted to decrease as this reorganization energy is increased. This effect was investigated by adding a constant amount of water to each cell and monitoring the 141 competition between hole transfer to the electron donor and passivation due to hole transfer to the water. Current-voltage behavior qualitatively showed a correlation between the reorganization of the redox couple and stability of the cell. XP spectra of electrodes gave a more quantitative measure of the rates of passivation, which gave reasonable correlations with calculated rates of hole transfer to the redox stabilizer. 142 VI. References (1) Memming, R. In Electroanalytical Chemistry; A. J. Bard, Ed.; Marcel Dekker, Inc.: New York, 1979; Vol. 11; pp 1. (2) Morrison, S. R. Electrochemistry at Semiconductor and Oxidized Metal Electrodes; Plenum: New York, 1980. (3) Koval, C. A.; Howard, J. N. Chem. Rev. 1992, 92, 411. (4) Gerischer, H. J. Phys. Chem. 1991, 95, 1356. (5) Lewis, N. S. Ann. Rev. Phys. Chem. 1991, 42, 543. (6) Marcus, R. A J. Phys. Chem. 1990, 94, 1050. (7) Gerischer, H.J. Electroanal. Chem. 1977, 82, 133. (8) Bard, A J.; Wrighton, M. S. J. Electrochem. Soc. 1977, 124, 1706. (9) Rajeshwar, K. J. Appl. Electrochem. 1985, 15, I. (10) Kenyon, C. N.; Ryba, G. N.; Lewis, N. S. J. Phys. Chem. 1993, 97, 12928. (11) Rosenwaks, Y.; Thacker, B. R.; Nozik, A J.; Ellingson, R. J.; Burr, K. C.; Tang, C. L. J. Phys. Chem. 1994, 98, 2739. (12) Peter, L. M. Chem. Rev. 1990, 90, 753. (13) Yang, E. S.; Chan, M.; Wahl, A: C. J. Phys. Chem. 1975, 79, 2049. (14) Weaver, M. J.; Yee, E. L. lnorg. Chem. 1980, 19, 1936. (15) Gomes, W. P.; Van Overmeire, F.; Vanmaekelbergh, D.; Vanden Kerchove, F. ACS Proc. 1981, 119. (16) Ginley, D.S.; Butler, M. A In Semiconductor Electrodes; H. 0. Finklea, Ed.; Elsevier: New York, 1988; pp 329. (17) Schneemeyer, L. F.; Wrighton, M. S. J. Am. Chem. Soc. 1980, 102, 6964. (18) Tufts, B. J.; Kumar, A; Bansal, A; Lewis, N. S. J. Phys. Chem. 1992, 96, 4581. (19) Fleischer, E. B.; Lavallee, D. K. J. Am. Chem. Soc. 1972, 94, 2583. (20) Burstall, F. H.; Nyholm, R. S. J. Chem. Soc. 1952, 3570. 143 (21) Gronet, C. M.; Lewis, N. S. J. Phys. Chem. 1984, 88, 1310. (22) Gerischer, H. In Physical Chemistry: An Advanced Treatise; H. Eyring; D. Henderson and W. Yost, Ed.; Academic: New York, 1970; Vol. 9A; pp 463. (23) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley & Sons: New York, 1980, pp 629. (24) Fadley, C. S. Prag. Solid State Chem. 1976, 11, 265. (25) Briggs, D.; Seah, M. P. Auger and X-ray Photoelectron Spectroscopy; 2nd ed.; John Wiley & Sons, Inc.: New York, 1990; Vol. 1. (26) Rochella, M. F., Jr.; Carim, A.H. Surf Sci. Lett. 1988, 197, L260. (27) Lauermann, I.; Lewis, N. S. unpublished results. (28) Marcus, R. A. J. Phys. Chem. 1991, 95, 2010. (29) Marcus, R. A. J. Phys. Chem. 1963, 67, 853. (30) Rosenbluth, M. L.; Lieber, C. M.; Lewis, N. S. Appl. Phys. Lett. 1984, 45, 423. (31) Wherland, S.; Gray, H.B. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 2950. (32) Cummins, D.; Gray, H.B. J. Am. Chem. Soc. 1977, 99, 5158. 144 Chapter 4: Theoretical and Experimental Upper Bounds on Interfacial Charge Transfer Rate Constants Between Semiconducting Solids and Outer-Sphere Redox Couples All or part of this text originally appeared in: Pomykal, K. E., Fajardo, A. M., and Lewis, N. S., J. Phys. Chem. , 1996, 100(9), pp. 3652-3664. 145 I. Introduction In this section, experimental results are presented that have been designed to investigate whether ket values in the range ket"" 10- 13-10-12 cm4 s-1 are generally characteristic of semiconductor/liquid contacts. Specifically, charge transfer processes involving non-adsorbing, outer-sphere redox reagents in semiconductor/liquid contacts that provide efficient energy conversion systems are investigated. These types of interfaces are the ones for which the modified Marcus theory outlined in Chapter 1 was developed and for which experimental validation is required. In many of these systems, interfacial charge transfer is not the rate-determining recombination step, so the observed steady-state interfacial current density cannot yield a direct value for ket• However, for these types of junctions, measurements of the total interfacial recombination flux at a specific potential, combined with energetic information on the barrier height of the semiconductor/liquid contact, can yield an experimentally rigorous upper bound for ket for the contact of concern. The measurements in this work have been performed on semiconductor/liquid junctions with Kn "" 1.0 (See Equation 4.1 ), so any upper bounds on ket should also establish upper bounds on ket,max at these types of contacts. This chapter also explores analytically the implications of ket values far larger than ket = 10-16 cm4 s-1 for the construction of efficient photoelectrochemical energy conversion devices. In addition, slight modifications of the previous theoretical model are described herein, in which adiabaticity is explicitly incorporated into the theoretical treatment of ketWe also evaluate the effects of a finite distance of approach of the ion to the electrode surface on theoretical values for ket,max· II. Theory As described in Chapter 1, the Marcus treatment of electron transfer at semiconductor/liquid junctions predicts a theoretical maximum for the value of the charge transfer rate constant ket, where ket = Vn Kn KeJ• This plateau arises from the expression for the nuclear term, Kn: 1 146 (4.1) In this term, AA is the total reorganization energy of the acceptor molecule, ~G0 ' is the free energy of reaction for the electron transfer, k is the Boltzmann constant, and T is the temperature. An estimate for the upper limit on the value of the rate constant, ket,max, can be obtained by setting the total reorganization energy equal to -~G0 ', so Kn= 1.0 in Equation 4.1 and the condition of optimal exoergicity for ket is attained. In the expression for ket, the attempt frequency, Vn, is the relevant nuclear vibrational frequency, with v 0 taken to be approximately 10 13 s- 1. The numerical value of ket,max thus depends on the value of the electronic factor, Ke!: (4.2) In the expression for Kel, rA and re are the effective radii of the acceptor in solution and the electron in the solid, respectively, and pis the electronic coupling decay constant. To arrive at the expression in Equation 4.2 for Ke!, the distance dependence of the electronic coupling term was taken to be: -rA) = KeJ ,O e _A(R-r I-' e (4.3) where Kel,O is the electronic term at the closest approach distance of the reactants and R is the distance between the electron in the solid and the acceptor in solution. 2 Integration of Ke1(R) was then performed over the relevant distances and angles to describe properly a random distribution of acceptors confined to the liquid phase and a random distribution of electrons confined to the semiconducting phase. 1,2 147 In the semiquantitative treatment of such processes presented previously in the literature, re was approximated to be the Bohr radius of an electron in the solid, and p was assumed to be::::: 1 x 10-8 cm-1. The value for the Bohr radius is well-documented from theory and experiment on Si, GaAs and other semiconducting solids, 3 while the assumed value for p is consistent with values reported previously for the experimentally-determined distance dependence of Ke1(R) through hydrocarbon glasses4,5 as well as through proteins 6-9 and other non-conjugated chemical linkages. 10-21 Inserting p = 1 x 10-8 cm-I and re = 2 x 1o- 7 cm for Si into Equation 4.2 and using this value for Kel in Equation 4.1 yields an estimate of ket,max = 1o- 17 cm4 s- 1. Although ket is theoretically sensitive to the third power of the decay constant p, the assumed value for Pis unlikely to be in error by an order of magnitude, so the uncertainty in ket,max is estimated to be less than a factor of 102. A somewhat different derivation, which used an effective reaction zone for the charge transfer process and assumed that the process proceeded with an averaged, single rate constant for all pairs that were in the zone of reaction, yielded similar values for the upper limit of the rate constant, specifically, ket,max = 10- 16 cm 4 s-1.22 Some data on charge transfer rate constants at semiconductor/liquid interfaces seem to support this theoretical model. In the few systems amenable to experimental investigation to date, measured ket values, or upper limits on ket, have been established as ket ~ 10-14 cm4-s-1, 23 with more typical values for ket < 10-16 cm4 s-1. 24-26 However, it has been suggested recently that the prior theoretical treatments may underestimate ket,max by as much as 4-5 orders of magnitude.27 This suggestion was based on experimental data that have been interpreted to indicate that ket values exceeded 10- 12 cm4 s-1 for p-InP/liquid and p-GaAs/liquid contacts. 27 In addition, it has been suggested that significant increases in ket,max would be obtained theoretically if adiabaticity in the electron transfer process were explicitly included into the pair-weighted averaging procedure that was used to calculate Kel from the functional form for Ke1(R) (Equation 4.3). 28 148 A. Abiabaticity and Finite Ion Size Effects on ket,max Adiabaticity of the interfacial charge transfer process is readily included into the treatment of ket within the framework of the previous theoretical model. Adiabaticity can be included semi-quantitatively merely by adjusting the apparent radius of the electron in the solid to account for the effective distance of adiabaticity, b. Assuming a typical Bohr radius for an electron in a semiconducting solid, re= 2 x 10-7 cm, an additional adiabatic reaction distance of 5 x 10- 8 cm would only increase ket,max by a value of 2.5/2.0 relative to the prediction of Equation 4.2 for re = 2 x 10-7 cm. In other words, this effect would constitute a correction of less than a factor of 2 in the estimated upper limit of ket,max· A more rigorous treatment of adiabaticity can be obtained by re-evaluating the limits of integration in the pair-weighted calculation of Kel used to obtain Equation 4.2. Modification of the integral to accommodate the possibility that Kel = 1.0 for electron-ion distances R ~ (re+ fA + <>) yields: re+rA+8 R-rA J J R=re+rA r=re 0max J 21t 2 (4.4) J R sin 0 d0 de)> dr dR + 0=0 q>=O Integration of this function yields Kel as a function of re, ra, and <5: 2 6 (2re + 2r A + 6<5) <5 + + + ~4 ~3 ~2 Ket (re, r A,<>) = 7t (re+rA+8)8 ~ 2 + (re + r A)83 3 84 + 4 (4.5) 149 For the chosen values of re= 2 x 1o- 7 cm and rA= 3 x I o- 8 cm, ket,max for 8 = 5 x 1o- 8 cm exceeds the value of ket,max for 8 = 0 by a factor of 37 (Figure 4.1, dH = 0). In addition to adiabaticity, the issue of a finite, non-zero distance of approach between the redox-active ion and the electrode surface must be considered. This effect will counteract the predicted increase in ket,max by tending to lower the predicted value of the optimum charge transfer rate constant. Equations 4.2-4.5 considered the ions in solution to be distributed randomly at all distances from infinity to a position of direct contact with the electrode surface. Assuming that the outer-sphere redox ion cannot penetrate the inner Helmholtz layer (of thickness dH) ,29 the value of the integral will be reduced from that calculated in Equation 4.5. Evaluation of the limits of integration with a finite dH, assuming adiabaticity over a distance 8, yields: = 7t 6 ~4 + (4.6) The interplay between finite values of 8 and dH is graphically displayed in Figure 4.1. From this figure, it is evident that for reasonable values of 8 and dH, ket,max is expected to reach a maximum of approximately 10- 16 to 10- 15 cm4 s-1. Thus, when effects of adiabaticity and finite ion approach distances are simultaneously taken into account, the theoretical value of ket,max is similar to, but might exceed slightly, that obtained from the simple treatment presented previously. 1,30 Further improvements in the theoretical treatment of delocalized charge carriers in the semiconducting solid will require a more sophisticated treatment of the electron in the solid as well as the extension of its wave function across the solid/liquid interface. Because of the counteracting effects of adiabatic and finite approach distance modifications to the original theory of ket,max, upper bounds of ket,max = 10- 16 to 10- 15 cm4 s- 1 are thus taken 150 as reasonable working models until a more sophisticated theoretical treatment is available in the literature. In the results and discussion sections below, we explore the reasonableness of this upper limit for ket of approximately 10- 16 to 10- 15 cm4 s- 1 in the context of experimental data for semiconductor/liquid interfaces. 151 Figure 4.1: Calculated values for the maximum possible charge transfer rate constant ket, max at semiconductor/liquid junctions. The various lines represent values calculated at a fixed Helmholtz layer distance dtt while varying the distance 8 over which adiabatic electron transfer is allowed. The various lines are merely interpolations between the calculated points and are not intended as fits to Equation 4.6. 152 0 • dH=0A - -El- - dH = 2 A _. -dH=4A ~- -dH = 6 A --.---dH = 8 A 0 0 0 :::-' 10-15 0 I (/) 0 'tj" 0 s ...._, dH = 10 A I ii (.) ~ s ~'i 10-16 1o-17~_ 0 ____._......____.__ _........._ _...a..,__ ___J 2 4 6 8 (A) 8 10 153 B. Establishing an Upper Bound for Majority Carrier Charge Transfer Rate Constants at Semiconductor/Liquid Contacts Current density vs. potential measurements, in conjunction with energetic information obtained from differential capacitance vs. potential measurements, can provide useful information on the value of ket for various semiconductor/liquid contacts. For specificity, the theoretical discussion will focus on interfacial charge transfer processes for an n-type semiconductor/liquid contact under illumination. Similar expressions for p-type semiconductor/liquid contacts can be derived in terms of hole transfer rate constants, with appropriate changes in sign due to the change in direction of rectification at the semiconductor/liquid contact. In general , the interfacial current density can be separated into a photocurrent density, Jph(E), and a recombination current density, Irec(E): 31 -33 J(E)= Irec(E) + Jph(E) (4.7) The potential, E, is measured relative to the Nernstian potential of the cell. The sign convention in Equation 4.7 arises because the photocurrent density Jph(E) produces a net flow of electrons from the liquid into the solid, whereas Irec(E) represents all processes that produce a net flow of electrons from the solid into the liquid (resulting from the voltage developed by illumination of the solid). The charge transfer process related to ket involves transfer of electrons from the conduction band of the n-type semiconductor into the acceptor ions of the liquid electrolyte. At an applied potential E, the expression for the current density resulting from this kinetic process is: 1•31 l et(E) = -q ket ns(E) [A] (4.8) 154 where [A] is the concentration of acceptors in the interfacial region. The negative sign appears in Equation 4.8 because cathodic current flow through the interface is assigned as a negative current density by convention. If the built-in voltage, Vbi, of the semiconductor/liquid contact is known experimentally, ns(E) can be computed from the dopant density, Nct, of the semiconductor:34 (4.9) Thus, (4.10) where (4.11) In general, other kinetic processes will also contribute to the interfacial current flow. These processes include tunneling of majority carriers through the depletion region, with a current density ltun(E). 32 In addition, several processes resulting from interfacial transfer of minority carriers, including surface recombination, with a current density Jss(E), recombination in the depletion region, with a current density Jdr(E), and bulk recombination/diffusion, with a current density Jbr(E), must all be considered as possible rate-determining recombination processes (Figure 4.2).32 •34-36 The total interfacial recombination current density can then be written as: (4.12) 155 If the total measured recombination current density is dominated by ler(E) (i.e., ler(E)"" lree(E)), then measurement of lree(E) provides a direct measurement of ket through use of Equation 4.8, provided that n5 (E) (i.e., either Vbi or the barrier height <l>b =Vbi + (kT/q)(ln Ne!Nct), 34 where Ne is the effective density of states in the conduction band) is known. Otherwise, if it can be shown that lree(E) is not limited by ler(E) (i.e., llree(E)I >> ller(E)I), then measurement of lree(E) can be used with Equations 4.8 and 4.9 to establish an upper limit on the value of ler(E). Under these conditions, use of Equations 4.8 and 4.9 allows establishment of an upper bound for ket of the semiconductor/liquid interface of concern. Prior work from several laboratories has shown that, in contrast to directly measuring lree(E), it is experimentally advantageous to measure the magnitude of the voltage at open circuit, Voe, developed by a cell at a given photocurrent density. 37 ,38 Measurement of Voe is advantageous because negligible net current flows through the interface during the measurement, so effects of uncompensated ohmic resistance losses, mass transport overpotentials, kinetic overpotentials, and other significant corrections to J ree(E) are minimized at J =0 (i.e., at E =-Voe for an n-type semiconductor). 39 When J = 0 and lree(E) ""ler(E) (and Voe>> kT/q), Equations 4.8 and 10 yield: 1 V oe -(kTJ[l ( q n -JetrhCO) J] (4.13) or equivalently, (4.14) Under these condition·s, measurement of Voe at a known value of Jph directly yields a value for ket if Nct and Vbi are known. 156 Alternatively, if it can be established that llet(E)I << IIrec(E)I, then the inequality in Equation 4.15 must hold: (4.15) In other words, when another recombination mechanism dominates Voc, the experimentally determined open-circuit voltage allows establishment of an upper limit on the magnitude of the direct interfacial charge transfer current density, IJet(E)I. This upper limit of IJet(E)I then provides an upper limit on ket, if Vbi is known. Measurement of V 0c at a known cell temperature and photocurrent density can therefore be used to either establish ket directly (Equation 4.14) or can be used to establish an upper bound on the possible value of ket (Equation 4.15). Although all equations in this thesis are derived for n-type semiconductors, equivalent expressions are easily obtained for p-type semiconductors, substituting kht, Na, and [A-] for ket, Nct, and [A] respectively and making the appropriate sign changes. 157 Figure 4.2: Recombination currents present at the semiconductor/liquid interface. The majority carrier processes let and ltu represent the current density due to electron transfer to solution acceptor ions from the conduction band edge and via partial tunneling through electric potential barrier present in the depletion layer, respectively. l ss, Jbu , and lctr represent current density due to recombination via surface-states, bulk recombination, and depletion region recombination , respectively. l ss, Jbu , and lctr result from minority carrier processes and are not expected to depend on the solution acceptor concentration. 158 . C/'J > > C) ~ solid Figure 4.2 liquid --➔- 159 III. Experimental A. Electrodes and Materials All semiconductor electrodes were fashioned using the general procedure described below. After making an ohmic contact, each sample was attached to a Sn:Cu wire with Ag print (GC Electronics). The wire was enclosed in glass tubing, and after mounting the sample onto the wire, the back and edges of the electrode assembly were insulated from the solution by white epoxy (Dexter Corp.). Electrode areas were quantified by photographing the electrodes concurrently with a microruler, followed by magnifying the images and digitizing them. Both n-type (nominally undoped, dopant density= 5.5 x 1Q15 cm-3, (100)orientation) and p-type (sulfur-doped, dopant density= 1.1 x 1017 cm-3, (100)-oriented) indium phosphide wafers were obtained from Crysta-Comm, Inc. The n-type samples were contacted with a Ga:In eutectic, while p-type samples were contacted by sequential evaporation of 100 AAu, 1000 AZn, and 700 AAu 40 followed by annealing at 500 QC for 5 min under N2(g) . Indium phosphide electrodes were etched by alternately dipping the sample in solutions of 0.05 % Br2 (v/v) in CH3OH and 4.0 M NH3 in CH3OH for 30 sec, with rinses of CH3OH between immersions. This procedure was repeated twice before the electrodes were used in electrochemical experiments. CH3OH and CH3CN were dried before use and were distilled under N2(g). CH3OH was dried over magnesium methoxide, while CH3CN was predried over CaH2 and then dried over P2O5. Dimethylferrocene (Me2Fc, Strem) and cobaltocene (Co(Cph, Aldrich) were purified by sublimation before use. Me2FcBF4 was prepared as previously described41 and was dried in vacuo. Co(Cp )2PF6 (Aldrich) was recrystallized from CH3CN and dried in vacuo. LiClO4 (Aldrich) was dried by fusing at 240 QC under vacuum. All of the redox couples and electrolytes described above were stored in a N2(g)purged drybox until use. Potassium ferrocyanide, potassium ferricyanide, and potassium chloride were obtained from Aldrich and were used as received. 160 B. Electrochemical Cells and Instrumentation For nonaqueous electrochemical cells, all solids were introduced into the cell inside the drybox. InP cells were sufficiently sensitive to air that standard Schlenk techniques for transferring solvents and introduction of electrodes yielded poor current density vs. potential stability. The solids and solvents for these cells were instead separately transferred into a nitrogen flushbox that contained less than 10 ppm of 02 (as monitored by the fuming of (CH3CH2)2Zn). The solids were dissolved in an appropriate solvent, and the electrodes were etched within the flushbox and added to the cell. All electrochemical experiments with these systems were then conducted within the flushbox. All cells utilized a three-electrode potentiostatic setup, with a Pt wire reference electrode poised at the Nernstian solution potential and a Pt foil or Pt gauze counter electrode. The area of the counter electrode was at least ten times larger than that of the working electrode, to minimize any set-up related impedance losses and to minimize mass transport overpotentials at the counterelectrode. For nonaqueous junctions with n-type InP, the concentrations of the cell components were typically 0.100 M of the reduced form of the redox couple (A-), 0.010 M of the oxidized form of the redox couple (A), and 1.00 M of electrolyte. These precautions (large counterelectrode, high concentrations of both forms of the redox couple, large working electrode areas, etc.) were essential to obtaining highly reproducible, minimal frequency dispersion of the differential capacitance of the semiconductor/liquid contacts studied in this work. This minimal frequency dispersion contrasts with prior reports of the impedance properties of many of these same photoelectrode systems, which apparently contained frequency-dependent features that arose from an unoptimized experimental configuration of the cells and measurement apparatus and/or unoptimal electrode etching and surface preparation. The InP/KCl(aq)Fe(CN)63-/4- cells consisted of 0.100 M Fe(CN)6 3-, 0.100 M Fe(CN)64-, and 1.00 M KCl, while p-InP/CH3CN-Co(Cp)2+/0 cells consisted of 0.0010 M Co(Cp)2, 0.020 M Co(Cp)2+, and 0.70 M to 1.00 M LiClO4. 161 All current density vs. potential experiments were performed using an EG&G Princeton Applied Research (PAR) Model 173 potentiostat in conjunction with a Houston Instruments Omnigraphic 2000 recorder and an EG&G PAR Model 175 Universal Programmer. Light intensities were controlled by the use of an ENH-type W-halogen bulb in conjunction with neutral density filters . X-ray photoelectron spectroscopy (XPS) measurements were conducted in an apparatus that has been described previously, and which consisted of an ultra-high vacuum (UHV) surface science instrument interfaced to a drybox.42 Impedance spectra were obtained on a computer-controlled Schlumberger Model 1260 Frequency Response Analyzer equipped with a Model 1286 Electrochemical Interface. C. Built-in Voltage Measurements and Rate Constant Calculations For experiments with semiconductors in nonaqueous electrolytes, the current density vs. potential (J-E) behavior of each electrode was initially measured as a function of the incident light intensity. The J-E data were obtained at a scan rate of 50 mV s-1, and direct measurements of Voe and lsc (where lsc is the current density at short circuit and is assumed to be equal to Jph) were taken at each light intensity by reading the appropriate quantities through a digital multimeter that had been connected to the electrochemical cell. These J-E measurements were repeated after each set of impedance measurements to verify that the properties of the electrode remained constant over the time scale of the impedance measurements. The built-in voltages, V bi, of the various semiconductor/liquid junctions were calculated from electrochemical impedance data. An impedance measurement consisted of 11 or 13 frequency sweeps, each with an ac voltage of 10 m V rms amplitude. Each sweep was performed at a different de potential in reverse bias. The ac frequency range was varied for each semiconductor/liquid system in order to identify the region of purely capacitive behavior of the semiconductor/liquid contact. Impedance data were fit to an equivalent circuit consisting of a resistor Rsc (representing the resistance to Faradaic charge 162 transfer) in parallel with a capacitor Csc (representing the differential capacitance of the semiconductor space charge region), both of which were in series with a resistance Rs (representing resistive losses through the solution, leads, etc.). This model assumes that the measured differential capacitance (C) equals Csc• The differential space-charge capacitance was computed from the impedance data using the equation:29 21tfC . d1ff 2 1/2 =1+(1-4(Zim/Rsc)) 2 z.I l l (4.16) where f is the frequency of the ac voltage and Zim is the imaginary part of the measured impedance, Z, at the de bias of interest. Rsc values were taken as the diameter of a semicircular fit to a Nyquist plot (Zim vs. Zreal as a function off, where Zreal is the real part of the measured impedance) at each de bias. The differential capacitance was then related to the built-in voltage of the semiconductor/liquid junction by the Mott-Schottky equation: (4.17) Here£ is the dielectric constant of the semiconductor, £0 is the permittivity of free space, and As is the area of the semiconductor electrode. A plot of E vs. c- 2, followed by extrapolation of the data to infinite capacitance and application of the correction factor (kT/q) (Equation 4.17), yielded the built-in voltage of the solid/liquid contact. The validity of the equivalent circuit model used in this work was assessed by computing the slopes of the lines of Csc- 2 vs. Eat each frequency of the ac voltage and comparing these slopes to those expected from the known dopant density, area, and dielectric constant of the electrode in question. Within a data set, only data which exhibited linear c-2 vs. E (R2 ~ 0.999, where R is the correlation coefficient) plots having slopes which corresponded to the measured dopant density to within 50% were considered. Electrodes that yielded non- 163 linear or frequency-dependent plots for all frequency values were considered defective and were not included in the analysis. D. Passivation/Corrosion Measurements of InP/Liquid Contacts Unlike the other cells studied in this work, lnP/Fe(CN)6 3-14-(aq) contacts were observed to undergo rapid passivation or corrosion processes. A series of measurements was performed to investigate these phenomena in some detail. To assess electrode stability, lnP electrodes were first contacted with a redox couple/electrolyte solution known to display stable J-E properties, and the J-E behavior was measured in the presence of band gap illumination of the solid. The electrodes were then immersed into a KCl(aq)Fe(CN)6 3-14- solution, and J-E measurements were performed. In an attempt to minimize electrode oxidation, data in aqueous solutions were obtained in the dark for n-type electrodes and in the light for p-type electrodes. Finally, the electrodes were reimmersed into the first (stable) redox couple-electrolyte solution and the resulting J-E behavior was measured. For example, in the case of p-type InP electrodes, J-E curves were measured in the light in CH3CN-0.70 M LiClO4-0.l00 M Co(Cp)i+-0.0010 M Co(Cp)2 solutions before and after J-E curves were measured in the light in a 1.00 M KCl(aq)-0.100 M Fe(CN)6 3--0.100 M Fe(CN)64- electrolyte. Surface science techniques were used to determine the oxide levels on various InP electrodes. The J-E data for a freshly etched n-type InP electrode were first obtained under band gap illumination in a N2(g)-purged CH3OH-l.00 M LiClO4-0. lOO M Me2Fc-0.0l0 M Me2FcBF4 solution. This n-type InP electrode was then rinsed and immediately placed into a nitrogen-purged Schlenk tube as a control. Another freshly-etched electrode was also placed in this Schlenk tube as a second control. A third electrode was etched and immersed into the CH3OH-Me2Fc+/O solution, and J-E data were collected on this specimen in the presence of band gap illumination. This electrode was then rinsed with CH3OH and was immediately immersed into a nitrogen-purged 1.00 M KCl(aq)-0.100 M Fe(CN)6 3--0.100 M Fe(CN)64- solution. The J-E behavior of this contact was then 164 determined in the dark. The electrode was then rinsed and was immediately reimmersed into the CH3OH-Me2Fc+/O solution. J-E data were collected (again in the presence of band gap illumination) to assess the stability of the electrode in the KCl(aq)-Fe(CN)63-/4solution. This InP electrode was then rinsed and placed in the Schlenk tube. This series of experiments was then repeated with a fourth electrode, except that instead of 1.00 M KCl(aq) as the electrolyte in the Fe(CN)63-/4- solution, 1.00 M HCl(aq) was used. The Schlenk tube containing the four electrodes was then introduced into a nitrogen flushbox equipped with a load-lock into the UHV chamber. The electrodes were removed from the Schlenk tube, mounted onto UHV sample studs, and introduced into the UHV chamber for XPS studies. Impedance measurements as described above were also attempted for both the neutral and acidic solutions. The thicknesses of any oxide layers resulting from the procedure described above were determined using standard overlayer models. 43 The thickness of an overlayer, d, on the InP sample is related to the XPS signals for the overlayer and the substrate by: (4.18) where I0 and Is are the areas under the peaks for the overlayer and the substrate, respectively. Here A is the electron escape depth from the material (23 A for InP 43 ,44 ), ~ is the angle of the detector from the substrate (35 °), and n0 and ns are the number of P atoms per unit volume in the overlayer and substrate, respectively. The ratio nsfn 0 thus corrects for the difference between the densities of the substrate and overlayer, with nsfn 0 = 1.42 for pure InP referenced to oxidized InP. This model assumes that the sensitivity factors and escape depths are the same for the overlayer and substrate, which is reasonable since both the overlayer and substrate signals originate from the same type of atom. 165 IV. Results A. Barrier Height Measurements and Upper Bounds on ketlkht for Semiconductors in Contact with Nonaqueous Solvents In conjunction with the work described below for InP, built-in voltages were measured for two other efficient, stable, n-type semiconductor/electrolyte combinations, and upper limits on the rate constant were calculated. Differential capacitance vs. potential data were used to measure Vbi for these contacts. In conjunction with Equation 4.15, these Vbi values allow establishment of upper bounds on ket for then-type semiconductor/liquid interfaces. The barrier height of the junction, <l>b, is related to the built-in voltage by the equation: 34 (4.19) for an n-type semiconductor. Combination of Equation 4.19 with Equations 4.8 and 9 yields the expression: (4.20) The results of these experiments are summarized in Table 1. Note that in both cases it has been shown that electron transfer from the conduction band edge is not the rate-limiting recombination mechanism in these systems, and thus the values in Table 1 represent upper limits on the electron transfer rate constant. p-InP photoelectrodes also provide well-behaved, efficient energy conversion systems in nonaqueous solvents. 45 The p-type InP/CH3CN-Co(Cp)2+/0 junction thus provided a semiconductor/liquid contact that was suitable for investigation of interfacial charge transfer rate constants. This system is valuable in that it provides an upper bound 166 on the charge transfer rate constant for hole transfer, kht, as opposed to the upper bounds on ket that were obtained from the studies of n-type photoanodes described above. Figure 4.3 displays the current density-potential data at varying light intensities for a p-InP/CH3CN-Co(Cp)2+/0 junction. The J-E curves were rectifying and displayed high photovoltages (Figure 4.3), consistent with prior cyclic voltammetry studies of p-InP photocathodes in contact with outer-sphere redox couples in CH3CN. 45 ,46 Figure 4.4 displays the c- 2 vs. E data for the p-InP/CH3CN-Co(Cp)2+/0 system. The plots were linear and were in good agreement with each other for 1 x 1Q3 < f < 1 x 1Q5 Hz. The slopes were within 25% of the manufacturer-quoted values for the dopant density of the samples, and the intercepts yielded Vbi = 1.04±0.02 V for these contacts. Use of the manufacturer-reported dopant density NA= 1. 1 x 10 17 cm-3 to calculate a barrier height for this system yielded <l>b = 1.16 V. This value is in reasonable agreement with previous capacitance vs. potential measurements on p-InP samples of slightly different dopant densities. These previous measurements yielded <l>b = 1.23 V (NA= 1.86 x 1Q18 cm- 3) or <l>b = 1.03 V (NA= 1.87 x 1Q16 cm-3).47 Use of Equation 4.15, modified for a p-type semiconductor, yielded an upper bound for kht~l0- 13 cm4 s- 1 for this system. The limited solubility of Co(Cph in most solvents precluded determination of whether the recombination rate was limited by hole (majority carrier) transfer to the Co(Cp )2 donor species. If the donor concentration could have been increased further, a more rigorous upper limit could be placed on the charge transfer rate constant for this system. 167 Table 4.1 Summary of built-in voltages and upper limits on the rate constants for n-type semiconductors in contact with nonaqueous electrolytes. Data is taken from Pomykal, K. E., Fajardo, A. M., and Lewis, N. S., J. Phys. Chem., 1996, 100(9), pp. 3652-3664. Me2Fc+/O = 1, 1'-dimethy lferrocenium/ 1, 1'-dimethy lferrocene; Fc+IO = ferrocenium/ferrocene. 168 ket max (cm4 s- 1) System n-Si/CH30H-Me2Fc+/O 0.884±0.014 n-GaAs/CH3CN-Fc+/O 1.053±0.023 Table 4.1 1.03 10-15 10-14 169 Figure 4.3: (a) Current density vs. voltage data for a p-InP/CH3CN- Co(Cp)2+f0(0.025 MI 0.0010 M) junction at various light intensities. The scan rate was 50 mV s- 1. (b) Natural logarithm of the photocurrent density vs. the open circuit voltage for the junction represented in (a). The line is a fit to the equation: ln(Jph) = ln(llet(0)I) + (qV 0c/AkT). The diode quality factor, A, is calculated to be 1.2 from this plot. 170 -8 N 0 0.4 0.2 3a) p-InP/Co(Cp)2+10 0 1 -0.2 ..._ ~ •.-I ~ <l) 0 -0.4 -0.6 -0.8 = § -1 u -1. 2 ._____._______.____,_____._____.______._____.____.,___._______._______.______. -0.4 -0.2 0 0.2 0.4 0.6 0.8 Applied Potential vs. E(A/A-) (V) -6.5 -7 - - y = -27.923 + 32.258x R= 0.9987 .-----r------r----r-----r------r---,,---r--~~--, 3b) p-InP/Co(Cp) 2+10 -7.5 u O"l ~ Cl -8 -8.5 -9 -9.5 ...__.....____._____._______._______._____._ _.___.....______.______. 0.56 0.58 0.6 0.62 0.64 0.66 Applied Potential vs. E(A/A-) (V) 171 Figure 4.4: (a) c- 2 vs. applied de potential for the p-InP/CH3CNCo(Cp)2+/0 junction in Figure 3. The points represent data taken at seven frequencies between 0.5 and 15 kHz. (b) The extrapolation of the data points in (a). 172 2.8 2.6 ....-. N I ~ '-" tr) ...... I 0 2.4 2.2 0 ,........i >< N u I s 4a) p-InP/Co(Cp)2+/0 II I I II 2 0 I 1.8 I I ft I 1.6 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 Applied Potential vs. Cell (V) 0.1 10 8 ....-. N I ~ '-" 6 4b) p-InP/Co(Cp )2+10 ("(') ...... I 0 ,........i >< 4 NI u 2 o.___---~~~-~~~ 1.00 1.05 1.10 0.90 0.95 Applied Potential vs. Cell (V) 173 B. Steady-State J-E Behavior of n-InP/H20-Fe(CN)6 3 •14 • Contacts 1. J-E Data for n-InP Electrodes in KCl(aq)-Fe(CN)63-14 - Solutions Figure 4.5 displays the J-E data for n-InP anodes in contact with KCl(aq)-0.100 M Fe(CN)64- 0.100 M Fe(CN)63-. When compared to data on n-InP/CH3OH-Me2Fc+/O contacts studied previously48 and re-evaluated in the course of this work (Figure 4.5a), the current densities in Figure 4.5b were extremely small at low forward bias. Even at an electrode potential of -1.0 V vs. E(A/A-), the current density at the n-InP/KCl(aq)Fe(CN)63-/4- junction was only on the order of IQ-3 A cm- 2. The low current densities indicated that the electron transfer rate was very small for n-InP/KCl(aq)-Fe(CN)6 3-14contacts. Although the short-circuit current density was zero at n-InP/CH3OH/Me2Fc+/O contacts, a non-zero short-circuit current density of 0.5 µA cm- 2 was observed for nInP/KCl(aq)-Fe(CN)63-/4-junctions. The presence of a finite current density at short circuit indicated the presence of a chemical passivation or corrosion reaction at the nInP/KCl(aq)-Fe(CN)6 3-14- contact. Consistently, the open-circuit voltage of this interface was "" 350 m V even in the absence of illumination. 2. Effects of Exposure to KCl(aq)-Fe(CN)63-14 -Solutions on the Behavior ofnInP/CH30H-Me2Fc+IO Contacts Since the oxides of InP are insoluble at near-neutral pH in H2O, 49 corrosion of the InP induced by the presence of Fe(CN)6 3- should produce an insoluble oxide overlayer on the electrode surface. The formation of such an overlayer was investigated by evaluation of the J-E properties of the n-InP/CH3OH-Me2Fc+/O interface. Figure 4.5a displays the J-E behavior of a freshly etched n-InP electrode in contact with the CH3OH/Me2Fc+/O solution. Consistent with prior work, 48 the J-E curves in this electrolyte were stable and reproducible, exhibiting large V oc values and excellent fill factors. In contrast, Figure 4.5c displays the J-E behavior of the same n-InP/CH3OH-Me2Fc+/O junction in Figure 4.5a after the electrode had been exposed to the pote~tial scans in the dark shown in Figure 174 4.5b. After exposure to the KCl(aq)-Fe(CN)63-/4 - electrolyte, the open-circuit voltage of the n-InP/CH3OH-Me2Fc+/O junction decreased by 100 mV, the fill factor decreased from 0.7 to 0.2, and the forward bias current density decreased significantly at all potentials. This behavior indicated that exposure to the KCl(aq)-Fe(CN)63-14- electrolyte was deleterious to the performance of n-InP photoanodes, causing J-E properties characteristic of electrodes possessing electrically insulating overlayers on their surfaces. 3. J-E Data for n-InP Electrodes in HCl(aq)-Fe(CN)63-14 - Solutions Further evidence for the presence of a chemical reaction between InP and KCl(aq)Fe(CN)63-/4- was obtained by investigation of the J-E properties of n-InP electrodes in contact with acidic HCl(aq)-Fe(CN)63-/4- electrolytes (Figure 4.6). In and P oxides are soluble in strongly acidic solutions of HCl(aq), 47 .49-51 implying that active etching, as opposed to formation of an insoluble insulating oxide overlayer, should occur under these acidic conditions. In accord with these predictions, the J-E behavior of n-InP/HCl(aq)Fe(CN)63-14- junctions at pH=0 showed a significant open-circuit voltage, with V oc "" 400 mV (Figure 4.6b). A non-zero short-circuit current density was also observed for this system, and its value was much larger than that for n-InP/KCl(aq)-Fe(CN)6 3-14- contacts measured at neutral pH values (Figures 4.5b, 4.6b). These observations signaled that the InP was undergoing a corrosion reaction with the acidic electrolyte. However, as displayed in Figure 4.6c, the chemical reaction did not induce significant changes in the J-E behavior of subsequently formed n-InP/CH3OH-Me2Fc+/O contacts. Additionally, the J-E behavior in the aqueous acidic medium was much less resistive than was observed at neutral pH (Figures 5b, 6b), indicating the absence of insulating oxide overlayers on InP surfaces in contact with the acidic solutions. The non-zero short-circuit current densities, finite open-circuit voltages, and absence of an insulating overlayer on the InP during immersion into acidic HCl(aq)-Fe(CN)6 3-14- solutions (Figure 4.6) are precisely the behaviors expected for an etching reaction that yields a soluble oxide product. 175 4. XPS Studies of Oxide Formation and Estimates of ket for n-InP/KCl(aq)-Fe(CN)63-l4 and n-InP/HCl(aq)-Fe(CN)63-l4 - Interfaces XPS studies were performed to confirm further the presence of corrosion reactions at n-lnP/KCl(aq)-Fe(CN)6 3-l4- contacts. Figure 4.7 shows XP spectra of the phosphorus region for electrodes that had been etched (4.7a), etched and exposed to CH3OH-Me2Fc+/O (4.7b), etched and exposed to KCl(aq)-Fe(CN)63-/4- at neutral pH (4.7c), and etched and exposed to HCl(aq)-Fe(CN)6 3-14- at acidic pH (4.7d). All electrodes except those that had been exposed to KCl(aq)-Fe(CN)6 3-14- at neutral pH exhibited negligible oxide signals in the phosphorus region. Figures 4.7a-c show only the XPS signal expected for pure InP, at a binding energy of about 129-130 eV. 52 In contrast, the electrodes that had been exposed to neutral pH solutions of KCl(aq)-Fe(CN)63-/4- showed an additional signal at 134 eV, whose area indicated the presence of 7.5 A. of phosphate (phosphorus oxide) on the electrode surface (Equation 4.18). 52 Despite the presence of the oxide overlayer on n-InP/KCl(aq)-Fe(CN)63-/4contacts, impedance measurements were performed to provide an estimate of ket through use of Equations 4.10 and 4.11. Although this analysis will clearly underestimate the actual ket value relevant to the contact in the absence of the insulating oxide overlayer, such a calculation was of interest with respect to the value of ket reported from luminescence decay data that have been collected on InP surfaces in this same redox system. 27 Figure 4.8 displays a Bode plot for an n-type InP electrode at E=+0.25 V vs. E(A!A-) in contact with a 1.00 M KCl -0.100 M Fe(CN)6 3--0.100 M Fe(CN)6 4- solution. Even though oxidation of the InP was probably occurring on the time scale of these measurements, the Bode plot (log IZI vs. log f, where IZI is the magnitude of the impedance vector) showed ideal behavior, with a slope of 0.97±0.01 for frequencies of 0.01 kHz< f < 100 kHz. The c- 2 vs. E data for this system are shown in Figure 4.9. The plots were linear for 400 < f < 1 x 104 Hz, and the slopes of the lines agreed to within 50% of those expected from the manufacturer's specified dopant densities of the samples. 53 176 Extrapolation of the Mott-Schottky data of Figure 4.9 to c- 2 = 0 yielded Vbi = 0.97 ± 0.02 V. For n-InP/KCl(aq)-Fe(CN)63-/4- contacts, J = 0.17 rnA cm-2 at E= -0.8 V vs. E(AIA-) , so Equations 4.10 and 4.11 yielded an upper limit on ket of 10- 18 cm4 s-1. Because the 1-E data were so resistive for the oxide-coated n-InP electrodes, the apparent rate constants were a function of the applied potential. At potentials more negative than -0.8 V vs. E(A!A-), the apparent rate constant was even smaller; using the value of J = 2 rnA cm- 2 at E=-1.0 V in Equations 4.10 and 4.11 yielded a maximum value for ket of 1o-20 cm4 s- 1. These bounds on ket were directly obtained from the steady-state 1-E data and therefore are essentially independent of kinetic models for the actual charge transfer process; in this regard, it is notable that the bounds on ket determined herein are significantly smaller than the values of ket (lQ-15 to 10-1 2 cm4 s-1, at various potentials) that were obtained from a model-dependent (oxide-free, defect-free surface) interpretation of the luminescence decay data for p-InP cathodes in contact with this same redox system. 27 Impedance plots for n-InP/HCl(aq)-Fe(CN)6 3-14- contacts were non-ideal, possibly due to the higher faradaic current at these electrodes. No useful information about the builtin voltage for this system could be obtained from a conventional Mott-Schottky analysis of the impedance data. However, assuming a similar value of Vbi for n-InP/KCl(aq)Fe(CN)6 3-14- contacts at neutral and acidic pH, an upper bound for ket in acidic media can be estimated from the data of Figure 4.6b. Taking a value of 1.2 rnA cm- 2 at E = 0.70 V vs. E(AIA-) from the data of Figure 4.6b and making the same assumptions as above, ket was bounded at< lQ-15 cm4 s-1 for this system. 177 Figure 4.5: (a) J vs. E data for a n-lnP/CH3OH-Me2Fc+IO(0.lO0 M / 0.0100 M) junction in the light at two different light intensities. (b) J vs. E data for the same n-InP electrode contacting a H2O-Fe(CN)6 3-14-(0.100 M / 0.100 M)-KCl(l.00 M) solution in the dark. Note that ideal diode behavior is not observed for this system; i.e., the curves for the two current scales do not show the ideal 0.059 V separation in voltage. (c) J vs. E data for the same n-InP/CH3OH-Me2Fc+/O junction in the light after this electrode had been cycled in the H2O-Fe(CN)63-/4--KCI solution in the dark. Although the photocurrent densities are the same as in (a), the open circuit voltages are much lower and the curves are more resistive. In all cases the scan rate was 50 mV s-1. 178 1.5 ,-._ N su I 5a) n- InP/Me2Fc+IO 1 ~ s 0.5 "-' ~ ~ -~ C/.l 0 ~ Q.) 0 ~ ~ -0.5 Q.) t=:::s u -1 -1.5 -1.0 L - - - . _ _ _ L - - - . _ _ __ _ _ _. _ _ _ . . _ _ _ . _ _ _ . . _ _ _ . . _ _ _ . . _ _ _ _ . . . _ _ _ _ . -0.8 -0.6 -0.4 -0.2 0.0 Applied Potential vs. Cell (V) 0.2 179 1.5 N,__ 1 Is 5b) n-InP/Fe(CN) 3-/4--KCl 6 () I - • • ...- . I - 'I ....... ' . . . . . JxlO - - J x 1000 I 1 - -~1 ' -0.8 -0.6 -0.4 -0.2 0 Applied Potential vs. Cell (V) 0.2 180 1.5 ~ 5c) n-InP/Me 2Fc+io I -~ 0.5 r:/J $=:l Q.) Q 'EQ.)= 0 t:: :::s u -0.5 -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 181 Figure 4.6: (a) J vs. E data for a n-InP/CH3OH-Me2Fc+IO(0.lO0 MI 0.0100 M) junction in the light at two different light intensities. (b) J vs. E data for the same n-InP electrode contacting a H2O-Fe(CN)6 3-14-(0.100 MI 0.100 M)-HCl(l.00 M) solution in the dark. In this case, the curves for the two current scales show a much lower separation in voltage, closer to ideal diode behavior. (c) J vs. E data for the same n-InP/CH3OH-Me2Fc+/O junction in the light after this electrode had been cycled in the H2OFe(CN)6 3-14--HC1 solution in the dark. Note that here the curves in (a) and (c) are nearly superimposable. In all cases the scan rate was 50 mV s-1 . 182 1.5 ~ N I su 1 ~ 0.5 '-" >--. -~r:/J +.J 0 = 0 -0.5 = (l) +.J (l) t:::::s u -1 -1.5 -1 -0.8 -0.6 -0.4 -0.2 0 Applied Potential vs. Cell (V) 0.2 183 1.5 .----.------,,-------,-----,-------r---.---'T'"------r------r------r------r---. 6b) n-InP/Fe(CN) 3-14--HCl ,,-._ N I S 1 ~ 0.5 (.) "-' 6 --J I ,I I ,I • • • • • J X 10 - - J x 1000 I I -1.5 -1 -0.8 -0.6 -0.4 -0.2 0 Applied Potential vs. Cell (V) 0.2 184 1.5 1 § 0.5 '-" 0 .(/j i::: 0 Q.) Q ~ -0.5 i::: Q.) ~ :::s u -1 - 1.5 .....____......_____._____,,_____._..,_____.______.______.__.___.____.,______.______. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 185 Figure 4.7: Phosphorus (2p) region of XP spectra of electrodes after treatments described in Figures 4.5 and 4.6. The normal, unoxidized P(2p) signal for InP occurs at about 130.5 eV. (a) control 1: n-InP electrode etched in Br2/CH3OH and NH3/CH3OH (vide infra). (b) control 2: n-InP electrode cycled in a CH3OH-Me2Fc+I0(0.100 MI 0.0100 M) solution in the light. (c) n-InP electrode cycled in a H2O/Fe(CN)63-l4-(0.100 MI 0.100 M)-HCl(l.00 M) solution in the dark (Figure 4.6). (d) n-InP electrode cycled in a H2O/Fe(CN)6 3-14 -(0.100 MI 0.0100 M)-KCl(l.00 M) solution in the dark (Figure 4.5). Of the four spectra, only Figure 4.7d shows a significant signal at 134.5 eV, evidence of a thick oxide layer on the surface of the electrode. 186 12 7a) ,-._ rzi ~ •...-1 ~ 10 :=I ;>-.. ~ ,ij 8 •...-1 ~ "-" ;>-.. 6 ~ •...-1 rzi ~ Q.) ~ ~ 4 ~ 2 128 130 132 134 136 Binding Energy (eV) 138 187 12 7b) ,,-.__ rzi -~0 10 :::s ~ ~ ro l::J -~ ..0 ~ -.._, ~ -~ 8 6 ..,_j rzi 0 C) ..,_j 0 4 ~ 2 128 130 132 134 136 Binding Energy (eV) 138 188 12 7c) ,-._ r:r., -~ 10 .j,,,j ~ :::s ~ .j,,,j ro 8 b -~ t 6 ...._, ~ -~r:r., .j,,,j 4 ~ a) .j,,,j ~ ~ 2 0 128 130 132 134 Binding Energy (eV) 136 138 189 12 ~ 10 -~ i= 7d) ~ ~ >-... ~ 8 -~b 6 ..0 ~ '-' >-... -~ 4 ~ (/'l i= (].) ~ i= 2 ~ 0 128 130 132 134 136 Binding Energy (eV) 138 190 Figure 4.8: Bode plot for impedance data taken at 0.25 V de bias for the n-InP/H2O/Fe(CN)63-l4 -(0.100 M I 0.100 M)-KCl(l.00 M) junction. Fitting the curve to a power law shows the ideal dependence of impedance on frequency, with an exponent of 0.97, where the slope of a log IZI vs. log f plot should be 1.0. 191 n-InP/Fe(CN) 3-14--KCI 6 105 N 10 1 ...........----_.._........ua--......-...-.............---.-.......... 10 1 102 103 104 Frequency (Hz) Figure 4.8 105 106 192 Figure 4.9: (a) c- 2 vs . applied de potential for the n-InP/H2OFe(CN)6 3-14- junction in Figure 4.8. The points represent data taken at six frequencies between 0.1 and 1.2 kHz. (b) Extrapolation of the data points in (a). 193 1.6 ,-._ N 0 ~ '-' NI • i □ • 1.4 □ □ "& 0.4 0.5 • i i • i □ I ~ t.n ,....... • 9a) n-InP/Fe(CN) 63-/4- 1.5 1.3 • • t • i □ u 1.1 • i 1 • i 0.9 -0.1 0 A • f A □ 1.2 □ ◊ 0.1 0.2 0.3 0.6 Applied Potential vs. Cell (V) 1.2 . 9b) 1 - n-InP/Fe(CN) 63-/4- . ,-._ N I ~ ~ ,....... 0 0.8 . 0.6 - . ~ '-' N I u 0.4 .0.2 • 0 -1.1 I I -1.05 I I -1 I -0.95 Applied Potential vs. Cell (V) I -0.9 194 C. Steady-State J-E Behavior of p-InP/H20-Fe(CN)6 3 -14 - Contacts Since anodic oxidation can be minimized on photocathodes that are continuously illuminated with band gap light and maintained in depletion, 54 ,55 the 1-E behavior of p-InP electrodes was investigated directly in contact with KCl(aq)-Fe(CN)6 3-14- solutions in the light. The goal of these studies was to evaluate whether the results obtained above, indicating the presence of irreversible chemical reactions on InP surfaces in contact with KCl(aq)-Fe(CN)63-/4-, were applicable to illuminated p-type InP photocathode surfaces. 27 A protocol established previously, 56 and utilized in the studies of the electrochemistry of nInP described above, was also used to evaluate the chemical reactivity of p-type InP surfaces. In this method, the 1-E properties of an inert, stable, semiconductor/liquid contact are used to evaluate whether deleterious chemical reactions have occurred upon immersion and subsequent electrochemical experiments of the semiconductor surface with the electrolyte of interest. 56 CH3CN-Co(Cp)2+/0 solutions were used as the test electrolyte in this work, since p-InP electrodes were found to yield stable J-E curves and ideal Mott-Schottky plots in contact with these solutions. Figure 4.10a shows the J-E data for electrodes illuminated in contact with CH3CN-0.100 M Co(Cp)2+-0.0010 M Co(Cp)2 solutions. For such surfaces, V oc values of 690 m V were obtained at lsc = 1.1 mA cm- 2 at T =300 K. This JE behavior is consistent with prior cyclic voltammetry studies on p-InP surfaces 45 A6 in that large Voc values are expected in contact with the Co(Cp )2+/0 redox couple. In addition, the p-InP photoelectrode of Figure 4.10a yielded significant optical-to-electrical energy conversion, displaying stable light-limited photocurrents in forward bias. In contrast, the current density vs. potential properties of p-InP/1.00 M KCl(aq)Fe(CN)63-/4-- contacts were very poor (Figure 4.10b). This J-E behavior is in qualitative accord with that described in a prior report of the behavior of p-InP/1.00 M KCl(aq)Fe(CN)63-/4- contacts at neutral pH. 27 In Figure 4.1 Ob, negligible cathodic current densities were observed in forward bias, and applied voltages >0.5 V into reverse bias 195 were required in order to achieve a significant photocurrent density. Comparison of Figures 1Oa and 1Ob indicates that an overpotential of > 1 V relative to V oc was required on the p-InP/1.OO M KCl(aq)-Fe(CN)6 3-14- contact to produce photocurrent densities that were comparable to those of the p-InP/CH3CN-Co(Cp)2+/0 contact. When the p-InP photocathode of Figure 4.1Ob was reimmersed, without etching, into the CH3CN-Co(Cp)2+/0 electrolyte, significant changes were observed in the J-E properties of this system. Comparison of Figures 10a and 10c illustrates that immersion of the p-InP electrode into the 1.00 M KCl(aq)-Fe(CN)6 3-14- electrolyte produced irreversible changes in the photoelectrode properties, and converted an efficient, energy-storing photoelectrode into a photoelectrode that required both illumination and an applied bias relative to the equilibrium solution potential in order to sustain significant interfacial photocurrent. This behavior is consistent with the formation of an insulating oxide overlayer on the p-InP surface in contact with 1.00 M KCl(aq)-Fe(CN)63-/4- solutions, as was identified above for n-InP electrodes. The use of CH3CN-Co(Cp)2+/0 as a test electrolyte thus clearly revealed that the p-InP/1.OO M KCl(aq)-Fe(CN)63-/4--system is unstable and produces irreversible changes in the surface electrical properties of the p-InP photocathode. 196 Figure 4.10: (a) J vs. E data for a p-InP/CH3CN-Co(Cp)2+10(0.025 M / 0.0010 M) junction in the light at three different light intensities. (b) J vs. E data for the same p-InP electrode contacting a H2O-Fe(CN)63-14-(0.100 M / 0.100 M)-KCl( 1.00 M) solution at approximately identical light intensities. The photovoltages are extremely low in comparison with (a), and the curves are very resistive. (c) J vs. E data for the same p-InP/CH3CN-Co(Cp)2 junction at the same light intensities in (a) and (b) after this electrode had been cycled in the H2O-Fe(CN)6 3-14--KCI solution. In all cases the scan rate was 50 mV s-1 . 197 0.5 ..----------,,-------,----,,------..------r-~------.------r------r------r---r----, 10a) p-InP/Co(Cp) +to 2 - 1. 5 ....____......_____._____._____.______.______.______._____.______.______._______._____. -0.4 -0.2 0 0.2 0.4 0.6 0.8 Applied Potential vs. Cell (V) 198 0.5 .....----,....----,-----.,---.------.-------,-------.-----.------,------.------10b) p-InP/Fe(CN) 3-/46 -1.5 ~~~~~~~-~~--------- -0.8 -0.6 -0.4 -0.2 0 0.2 Applied Potential vs. Cell (V) 0.4 199 0.5 10c) p-InP/Co(Cp) +lo 2 -1.5 -0.4 -0.2 0.2 0.4 0 Applied Potential vs. Cell (V) 0.6 200 V. Discussion Although the data described herein do not establish absolute values for ket, they do allow definition of upper bounds on ket of less than 1o-13 cm4 s- 1 for the entire collection of semiconductor/liquid contacts and upper bounds on ket of less than 10- 14 cm4 s-1 for the n-Si and n-GaAs semiconductor/liquid interfaces that have been investigated. The approach used herein also extends a previously proposed protocol for establishing which interfaces are suitable for use in a comparison between the theoretical predictions and the experimental data. 56 Estimates of A and measurements of Vbi for these well-behaved semiconductor/liquid junctions indicate that Kn is on the order of 1o-1-1 oo for the contacts discussed herein. These data therefore serve to establish semi-quantitative upper bounds on ket,max for these systems. The measurements and calculations discussed above are also in agreement with recent determinations of ket for p-WS2/H2O-Ru(NH3)6 3+12+ contacts, 24 with measurements of ket for n-WSe2/CH3CN-Me2Fc+/O contacts, 57 and with upper limits on ket that have been estimated previously for n-Si/liquid contacts.1,26 ,33 ,39 The maximum possible value of the bimolecular interfacial charge transfer rate constant is pertinent to optimal efficiencies for photoelectrochemical solar energy conversion devices. Specifically, a large majority carrier charge transfer rate constant is undesirable for the construction of efficient photoelectrochemical energy conversion devices. For example, from Equation 4.11, with ket = 10- 12 cm4 s- 1, Nct = 1Q16 cm-3 and [A]= 0.10 M, llet(0)I = (1 x 105) exp(-qVbj/kT). Setting lree = let in Equation 4.12, and taking Jph = 20 mA cm- 2 (Equation 4.15) allows calculation of the maximum possible Voe under these conditions. Such a calculation implies that V0e - Vbi = -0.40 V, and that the difference between <l>b and V0e is 0.55-0.65 V. Thus, even in the optimized situation of extremely high barrier heights, with <l>b ~ Eg/q, Voe would be much less than (Eg/q) due to efficient majority carrier capture process. Losses in quantum yield would also be observed in the short-wavelength spectral response of such semiconductor/liquid contacts, 58 due to the efficient competition between drift-induced charge separation and concentration-gradient 201 driven charge recombination processes that would occur with such a large majority carrier collection velocity. 58 The construction of efficient photoelectrochemical cells, such as those reported in the literature using n-Si/CH3OH-Me2Fc+10, 38 ,59 ,60 n-GaAs/CH3CNFc+I0, 61 ,62 p-Si/CH3CN-cobaltocene+I0,63 and other semiconductor/liquid contacts 48 would not appear to be possible with this value of the bimolecular rate constant for interfacial majority carrier charge transfer. 64 It is also interesting to explore the implications of rate constants greater than the upper bounds established in the systems studied herein with respect to the physical behavior of semiconductor/liquid contacts. A value of ket= 1o- 12 cm4 s- 1 was assigned to a luminescence decay time of -1 ps for InP cathodes injected with 10 12 carriers cm-3 in contact with 0.10 M Fe(CN)6 3--0.10 M Fe(CN)64-. 27 A bimolecular rate law interpretation of this data would therefore predict a luminescence decay time of"'" 100 ps at 1.0 mM of acceptor species. At [A]= 1.0 mM = lQ17 cm-3, the volume defined by a 1 cm x 1 cm area of solution extending 10-7 cm from the electrode surface contains 1010 molecules. Because the large scale ion movements are essentially frozen on short timescales, in order to collect 101 2 charge carriers cm- 2 through interfacial charge transfer in 100 ps, a significant fraction of the photogenerated charge carriers would have to be injected 0.1 µm into the solution during this 100 ps time period. Such rates have no precedent in molecular charge transfer systems; 65 -68 thus, a bimolecular charge transfer rate constant of 10-12 cm4-s-1 would require that the semiconductor electrode drastically modify the electron tunneling properties of the solvent in order for the electron transfer to occur over such large distances on such short timescales. The unusual electrical junction properties predicted at very large interfacial charge transfer rate constants are underscored by comparison of the predicted recombination current density at semiconductor/liquid interfaces with various values of ket to the recombination current density observed for semiconductor/metal Schottky barriers.34 For semiconductor/metal contacts, essentially every carrier that reaches the semiconductor/metal 202 junction is captured by the metal phase.34 The thermionic emission-diffusion current density for semiconductor/metal contacts, which describes this charge carrier capture process, is: 34 (4.21) where A* is the effective Richardson constant for thermionic emission. Combining Equations 4.10 and 21 therefore yields the ratio between the charge transfer current densities for semiconductor/metal and semiconductor/liquid contacts of identical barrier heights: (4.22) With ket = 10-12 cm4 s-1 and [A]= 0.10 M = 6 x 1019 cm-3 (a typical value for operating photoelectrochemical cells), Equation 4.22 predicts that let z Ith· In other words, with such a large bimolecular charge transfer rate constant, the steady-state majority carrier recombination losses from an interfacial electron transfer process would be as severe as those for semiconductor/metal contacts, in which essentially every majority carrier that reaches the surface is collected in a deleterious recombination event. This efficient capture by the redox ions in the solution would be occurring at only [A] = 0.10 M, i.e., under conditions when > 99% of the volume of the solution, and > 99% of the geometric cross sectional area presented to the electron, was occupied by inert, spectator species such as the electrolyte ions and the solvent molecules. Smaller values of ket, such as those established in this work, therefore correspond more closely to the expected situation in which the capture cross section of the acceptor species is approximately its geometric cross section.69 203 Small majority carrier interfacial rate constants are thus desirable for the construction of efficient photoelectrochemical cells. The system in which bias-dependent luminescence decay dynamics have been reported and interpreted in terms of field-dependent charge transfer velocities is the pInP/KCl( aq)-Fe(CN)6 3 -14- interface. 27 In the present work, InP/KCl(aq)-Fe(CN)6 3-14interfaces have been shown to be unstable to passivation and corrosion processes both in the dark and under illumination. The presence of an insulating oxide would require the application of large reverse bias potentials in order to obtain significant photocurrent flow through the layer. The presence of such an oxide would thus provide a consistent explanation of the high overpotential J-E behavior observed in this work and in prior work for p-InP/KCl(aq)-Fe(CN)63-/4- contacts 27 and would explain the poor J-E behavior observed for p-InP photocathodes in contact with CH3CN-Co(Cp)2+/0 contacts after exposure to the passivating KCl(aq)-Fe(CN)6 3-14- solution. A quantitative analysis of the behavior of the charge transfer dynamics in the p-InP/KCl-Fe(CN)6 3-14- system would therefore require rigorous inclusion of the transmission coefficients and voltage drops across the insulating oxide overlayer as a function of the applied potential. Notably, the field-dependent minority carrier charge transfer effects identified to date, if validated experimentally while accounting for the presence of the InP oxide overlayer, would not appear to be of concern in efficient energy conversion systems, for which the band bending under illumination must be minimized in order to obtain maximal photovoltages from the semiconductor/liquid contact. Another contributing factor to produce apparently large ket values in transient relaxation processes of semiconductor/liquid contacts involves adsorption of the redox ions on the semiconductor surface. Strong adsorption increases the effective surface concentration of acceptor species above that calculated for a random distribution of acceptors, thereby facilitating increased charge carrier capture rates. Additionally, intermediate capture of charge carriers by surface states prior to subsequent transfer into the 204 acceptor ion, 22 •25 ,57 inner sphere bridges to the redox center from the electrode, and other such processes might also be important in producing very high apparent ket values.70 ,71 Experiments conducted under such situations do not measure the rate constant for transfer to outer-sphere, non-adsorbed, randomly distributed acceptors at inert semiconductor surfaces, but measure the capture velocity for a fundamentally different charge transfer process. Adsorption appears to be of concern in a previously investigated system for which real-time luminescence quenching measurements of the charge carrier decay dynamics had been interpreted as exhibiting ket values larger than theoretically expected, 56 ,72 and possibly could affect rate constants for InP/KCl(aq)Fe(CN)63-/4contacts in the absence of an oxide overlayer or could establish the upper limit for charge transport through the InP oxide overlayer. The direct steady-state methods employed herein place an upper bound on the charge transfer rate constant that is z8 orders of magnitude lower than those obtained from an interpretation of transient luminescence decay experiments, underscoring the difficulty in interpreting transient luminescence decay data in the absence of well-defined, oxide-free and defect-free surfaces with defined band bending and carrier injection levels. In summary, upper limits on ket or kht have been experimentally determined for three semiconductor/solution systems which have been shown to exhibit stable, nonresistive, diode behavior. The limits on bimolecular interfacial charge transfer rate constants determined for these systems are consistent with theoretical expectations. In contrast, it has been shown that n- and p-type lnP/KCl(aq)-Fe(CN)63-14- contacts are unstable and thus unsuitable for these types of measurements. Further quantitative study involving charge transfer rate constants requires identification of systems in which the recombination current is dominated by charge transfer across the barrier or demands exploiting another reliable technique by which these rate constants can be measured. 205 VI. References and Notes (1) Lewis, N. S. Ann. Rev. Phys. Chem. 1991, 42, 543. (2) Marcus, R. A. J. Phys. Chem. 1991, 95, 2010. (3) Ibach, H.; Luth, H. Solid-State Physics; Springer Verlag: Berlin, 1990. (4) Miller, J. R.; Beitz, J. V.; Huddleston, R. K. J. Am. Chem. Soc. 1984, 106, 5057. (5) Domingue, R. P.; Fayer, M. D. J. Chem. Phys. 1985, 83, 2242. (6) Bowler, B. E.; Raphael, A. L.; Gray, H. B. Prag. Inorg. Chem. 1990, 38, 259. (7) Axup, A. W.; Albin, M.; Mayo, S. L.; Crutchley, R. J.; Gray, H.B. J. Am. Chem. Soc. 1988, 110, 435. (8) Elias, H.; Chou, M. H.; Winkler, J. R. J. Am. Chem. Soc. 1988, 110, 429. (9) Mayo, S. L.; Ellis, W. R.; Crutchley, R. J.; Gray, H. B. Science 1986, 233, 948. (10) Oevering, H.; Paddon-Row, M. N.; Heppener, M.; Oliver, A. M.; Cotsaris, E.; Verhoeven, J. W.; Hush, N. S. J. Am. Chem. Soc. 1987, 109, 3258. (11) Paddon-Row, M. N.; Oliver, A. M.; Warman, J.M.; Smit, K. J.; de Haas, M. P.; Oevering, H.; Verhoevern, J. W. Phys. Chem. 1988, 92, 6958. (12) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (13) Penfield, K. W.; Miller, J. R.; Paddon-Row, M. N.; Cotsaris, E.; Oliver, A. M.; Hush, N. S. J. Am. Chem. Soc. 1987, 109, 5061. (14) Isied, S. S.; Vassilian, A.; Wishart, J. F.; Creutz, C.; Schwarz, H. A.; Sutin, N. J. Am. Chem. Soc. 1988, 110, 635. (15) Schanze, K. S.; Sauer, K. J. Am. Chem. Soc. 1988, 110, 1180. (16) Leland, B. A.; Joran, A. D.; Felker, P. M.; Hopfield, J. J.; Zewail, A.H.; Dervan, P. B. J. Phys. Chem. 1985, 89, 5571. (17) Geno, M. J. K.; Dawson, J. H. Inorg. Chem. 1984, 23, 1182. (18) Finckh, P.; Heitele, H.; Volk, M.; Michelbeyerle, M. E. J. Phys. Chem. 1988, 92, 6584. 206 (19) Woitellier, S.; Launay, J.P.; Spangler, C. W. Inorg. Chem. 1989, 28, 758 . (20) Finklea, H. O.; Hanshew, D. D. J. Am. Chem. Soc. 1992, 114, 3173. (21) Carter, M. T.; Rowe, G. K.; Richardson, J. N.; Tender, L. M.; Terrill, R.H.; Murray, R. W. J. Am. Chem. Soc. 1995, 117, 2896. (22) Gerischer, H. J. Phys. Chem. 1991, 95 , 1356. (23) Shreve, G. A. Thesis, California Institute of Technology, 1994. (24) Bard, A. J.; Mirkin, M. V.; Horrocks, B. R. J. Phys. Chem. 1994, 98, 2739. (25) Morrison, S. R. Su,face Science 1969, 15, 363. (26) Forbes, M. D. E.; Lewis, N. S. J. Am. Chem. Soc. 1990, 112, 3682. (27) Rosenwaks, Y. ; Thacker, B. R.; Nozik, A. J.; Ellingson, R. J.; Burr, K. C.; Tang, C. L. J. Phys. Chem. 1994, 98 , 2739. (28) Smith, B. B.; Nozik, A. J. In 19th D. 0. E. Solar Photochemistry Research Conference; Washington, D. C., 1995. (29) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley & Sons: New York, 1980, pp 629. (30) Kesselman, J.; Hoffman, M. R.; Shreve, G. A.; Lewis, N. S. J. Phys. Chem. 1995, 98, 13385. (31) Morrison, S. R. Electrochemistry at Semiconductor and Oxidized Metal Electrodes; Plenum: New Yark, 1980. (32) Fonash, S. J. Solar Cell Device Physics; Academic: New York, 1981. (33) Laibinis, P. E.; Stanton, C. E.; Lewis, N. S. J. Phys. Chem. 1994, 98, 8765 . (34) Sze, S. M. The Physics of Semiconductor Devices; 2nd ed.; Wiley: New York, 1981. (35) Lewis, N. S. J. Electrochem. Soc. 1984, 131, 2496. (36) Lewis, N. S. Acc. Chem. Res. 1990, 23, 176. (37) Rosenbluth, M. L. ; Lewis, N. S. J. Am. Chem. Soc. 1986, 108, 4689. 207 (38) Kobayashi, H.; Chigami, A.; Takeda, N.; Tsubomura, H.J. Electroanal. Chem. 1990, 287, 239. (39) Kumar, A.; Lewis, N. S. J. Phys. Chem. 1991, 95, 7021. (40) Kuphal, E. Sol. St. Electron. 1981, 24, 69. (41) Hendrickson, D. H.; Sohn, Y. S.; Gray, H. B. Inorg. Chem. 1971, 10, 1559. (42) Pomykal, K. E.; Fajardo, A. M.; Lewis, N. S. J. Phys. Chem. 1995, 99, 8302. (43) Briggs, D.; Seah, M. P. Auger and X-ray Photoelectron Spectroscopy; 2nd ed.; John Wiley & Sons, Inc.: New York, 1990; Vol. 1. (44) Tanuma, S.; Powell, C. J.; Penn, D.R. Surf Interface Anal. 1991, 17, 927. (45) Dominey, R. N.; Lewis, N. S.; Wrighton, M. S. J. Am. Chem. Soc. 1981, 103, 1261. (46) Koval, C. A.; Austermann, R. L.; Turner, J. A.; Parkinson, B. A. J. Electrochem. Soc. 1985, 132, 613. (47) Segar, P. R.; Koval, C. A.; Koel, B. E.; Gebhard, S. C. J. Electrochem. Soc. 1990, 137, 544. (48) Heben, M. J.; Kumar, A.; Zheng, C.; Lewis, N. S. Nature 1989, 340, 621. (49) Pourbaix, M. Atlas of Electrochemical Equilibria in Aqueous Solution; Pergammon: New York, 1966. (50) Aspnes, D. E.; Studna, A. A. Appl. Phys. Lett. 1981, 39, 316. (51) Kobayashi, H.; Mizuno, F.; Nakato, Y.; Tsubomura, H. J. Phys. Chem. 1991, 95, 819. (52) Massies, J.; Turco, F.; Contour, J.-P. Jpn. J. Appl. Phys. 1986, 25, L664. (53) The poorer agreement of the slopes of the lines with those calculated using the dopant density specified by the manufacturer may be partially due to the concurrent passivation of the electrode with the impedance measurements. As the electrode is oxidized, less of the applied voltage will be dropped across the semiconductor depletion region, so the calculated Vbi may be even higher than the actual Vbi· Due to the problems 208 inherent in this system, these values should be viewed as only rough estimates, where the parameters have been chosen to yield the highest rate constant estimates that are consistent with the data. (54) Heller, A.; Miller, B.; Lewerenz, H.J.; Bachmann, K. J. J. Am. Chem. Soc. 1980, 102, 6555 . (55) Finklea, H. 0. Semiconductor Electrodes; Elsevier: New York, 1988. (56) Bansal, A.; Tan, M. X.; Tufts, B. J.; Lewis, N. S. J. Phys. Chem. 1993, 97, 7309. (57) Howard, J. N.; Koval, C. A. Anal. Chem. 1994, 66, 4525 . (58) Kumar, A.; Lewis, N. S. J. Phys. Chem. 1990, 94, 6002. (59) Rosenbluth, M. L.; Lieber, C. M.; Lewis, N. S. Appl. Phys. Lett. 1984, 45, 423 . (60) Gibbons, J. F.; Cogan, G. W.; Grenet, C. M.; Lewis, N. S. Appl. Phys. Lett. 1984, 45, 1095. (61) Kohl, P. A.; Bard, A. J. J. Electrochem. Soc. 1979, 126, 603. (62) Grenet, C. M.; Lewis, N. S. Appl. Phys. Lett. 1983, 43, 115. (63) Lieber, C. M.; Grenet, C. M.; Lewis, N. S. Nature 1984, 307, 533 . (64) These upper bounds on ket, max are conservative because effects of band edge movement under illumination, which would tend to yield lower barrier heights and thus even smaller upper bounds on ket,max, have not been included in computing this ket,max value. For the outer sphere redox couples used in this work, band edge movement is expected to be minimal, as shown by a direct measurement on the illuminated nSi/CH3OH-Me2Fc+/O contact, for which the quasi-Fermi level of holes was equal, within experimental error, to the Nernstian potential of the solution.73 A differential capacitance measurement on an illuminated (J5c=20 mA/cm2) n-Si/CH3OH-Me2Fc+/O contact yielded a barrier height of 0.89 V; using this value yields an upper bound on ket,max that is on the same order of magnitude as that determined from use of <l>b value determined for this system in the dark. 2 0 9 ( 6 5 ) Closs, G. L.; Calcaterra, L. T.; Green, N. Phys. Chem. 1986, 90, ( 6 6 ) ( 6 7 ) J . ; Penfield, K. W .; Miller, J . R . J. 3 6 7 3 . McClendon, G. ; Miller, J . R . J. Am. Chem. Soc. 1985, 107, Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 7 8 1 1 . 2 6 5 . Gray, H.B . Science 1990, 247, 1069. (68) Fox, L. S.; Kozik, M. ; Winkler, (69) It is possible to speculate that effects of an extremely strong interfacial electric field J . R . ; could increase ket for minority carriers above those described herein while not affecting the interfacial rate constant for majority carriers. There appears to date to be no theoretical or experimental support for a process in which interfacial electric fields would accelerate the electron into a liquid sufficiently rapidly to produce a significant increase in the capture cross section from ions that are generally at distances in excess of the electron mean free path in the liquid phase. A semiclassical collision theory approach to estimate ket yields: ket = cr v 8 (4.23) where cr is the cross section for reaction, v is the relative velocity of the reactants, and dis the effective zone of reaction. For a typical molecular dimension of 3 x 10-8 cm, with a relative velocity of 107 cm s- 1 (dominated by the thermal velocity of the charge carrier in the solid) and an effective distance for electron transfer of 10-7 cm, ket = 10-12 cm4-s-1 implies a value for the cross section of cr = 10- 12 cm2. Thus, ket = 10-1 2 cm4 s-1 implies that ions which participate in the charge transfer process (presumably proceeding off-resonance) would exhibit the curious behavior of possessing capture cross sections that far exceeded their geometric cross sections. "Giant" cross sections for carrier capture of this magnitude have been reported for the solid state, but such processes are dominated by Coulombic attraction effects. 74 Coulombic attractions will be minimized in interfacial charge transfer processes by the presence of the electrolyte and the correspondingly small Debye screening lengths in the liquid phase. 210 (70) Gronet, C. M.; Lewis, N. S. J. Phys. Chem. 1984, 88 , 1310. (71) Ryba, G. N.; Kenyon, C. N.; Lewis, N. S. J. Phys. Chem. 1993, 97, 13814. (72) Rosenwaks, Y.; Thacker, B. R.; Ahrenkiel, R. K.; Nozik, A. J. J. Phys. Chem. 1992, 96, 10096. (73) Tan, M. X.; Kenyon, C. N.; Lewis, N. S. J. Phys. Chem. 1994, 98, 4959. (74) Fahrenbruch, A. L.; Bube, R.H. Fundamentals of Solar Cells: Photovoltaic Solar Energy Conversion; Academic: New York, 1983. 211 Chapter 5: Measurement of Interfacial Charge Transfer Rate Constants at n-type InP/CH30H Junctions All or part of this text originally appeared in Pomykal, K. E., and Lewis, N. S., J. Phys. Chem., 1997, 101( 14), pp 2476-2484. 212 I. Introduction In this chapter, experimental measurements of interfacial charge transfer rate constants for n-type InP electrodes in contact with a series of one electron, outer-sphere redox reagents are reported. These reagents have been chosen because they allow variation in the driving force for the interfacial charge transfer process while controlling variation in other solvent-related reorganization parameters. In addition, many of these redox couples have been used in efficient InP-based photoelectrochemical cells, 1-3 so understanding the factors that control the interfacial rates at these contacts provides a direct understanding of the factors that control the efficiency losses in such photoelectrochemical energy conversion devices. As described in the preceding chapter, a model based on an adaptation of Marcus' theory for liquid/liquid interfaces has recently been used to estimate values of the electron transfer rate constant, ket, for semiconductor/liquid contacts. 4•5 Although upper limits on ket have been established experimentally 5-7 and are consistent with estimates of ket produced by the available theories, 4,5 the use of any approach currently available in the literature to estimate ket for such systems has recently been criticized. 8•9 To date, there appears to be little direct experimental data on values of ket at well-defined semiconductor/liquid interfaces. 4 ,10- 12 We describe such measurements, using n-InP electrodes and a series of outer-sphere redox couples, in this chapter. The flux of electrons from the conduction band edge of a semiconductor to a molecular electron acceptor species dissolved in the solution is given by: 13 Jet(E) = qk etn s (E)[A] (5.1) where Jet (A cm- 2) is the current density due to the direct charge transfer process, E (V) is the applied potential, q (C) is the elementary charge, ns (cm- 3) is the electron concentration at the surface of the semiconductor, and [A] (cm-3) is the concentration of acceptors that participate in the electron transfer process. The surface electron concentration is measured 213 in units of cm-3 rather than cm- 2, because it is related to the electron concentration in the bulk, %, through a Boltzmann relationship: 14 n/E) = Nde -q(E+Vb)/(kT) (5.2) In Equation 5.1, Vbi is the built-in voltage developed across the space charge layer in the semiconductor at charge transfer equilibrium of the semiconductor/liquid contact and °b is taken to be equal to the dopant density of the semiconductor, Nd. Thus, the two variables in a semiconductor/liquid system that must be measured in order to evaluate the electron transfer rate constant using steady-state methods are Vbi and JetCE). As outlined in Chapter 4, only Jet varies linearly with n5 (i.e., exponentially with E, under forward bias) and varies linearly with [A]. Only a system in which direct-electron transfer is the dominant recombination current exhibits both of these characteristics. When these criteria are obeyed, Equations 5.2 and 5.3 can be used to determine the value of ket, provided that Vbi can be determined experimentally. Measurements of ket for solid/liquid contacts having various values of .1.G0 ' can then yield a value for ket,max and, in turn, can allow estimation of Kel- li. Experimental Section A. Electrodes and Materials Nominally undoped (Nd= 6.4 x 1Ql5 cm-3) (100)-oriented, n-type InP wafers were obtained from Crysta-Comm, Inc., and Sumitomo Electric Industries, LTD. The samples were sliced into pieces ranging from 0.1 to 0.3 cm2 in area, and were fashioned into electrodes using procedures that have been described previously in the literature. 5 Crosssectional areas of the electrodes were determined photographically, and the roughness factor of these electrodes was assumed to be negligible. Electrodes were etched by alternately immersing the sample two times each for 30 s into solutions of 0.05% Br2 (v/v) in CH3OH and 4.0 M NH3 in CH3OH, followed by rinsing with CH3OH after each immersion.15 Each electrode was etched immediately before use in electrochemical experiments. 214 All solvents were dried and distilled under N2(g) and were then stored under an anaerobic atmosphere. CH3OH (EM Science) was dried over magnesium methoxide. Tetrahydrofuran (THF) (EM Science) was pre-dried over KOH pellets, then transferred to the solvent still, dried over sodium metal (with benzophenone as an indicator), and distilled. The ferrocenes (ferrocene, Fe; 1, l '-dimethylferrocene, Me2Fc; and decamethylferrocene, Me10Fc) were obtained from Strem or Aldrich and were purified by sublimation. The tetrafluoroborate salts of each ferrocene (FcBF4, Me2FcBF4, and Me10FcBF4) were prepared using the method of Hendrickson et al. 16 The dichloride salt of 1, l '-diphenyl-4,4'-dipyridinium (PVCl2) was prepared using the synthesis of Kamogawa et al. 17 1, 1'-diphenyl-4,4'-dipyridinium radical cation (PV+") was produced by electrolysis (vide infra). LiClO4 was dried by fusion at 240 °C in vacuo, and LiCl was dried by heating at 220 °C for at least 6 hours in vacuo. All redox couples and electrolytes were stored in a nitrogen-purged drybox until use. B. Electrochemical Cells and Instrumentation Electrochemical cells were prepared inside a nitrogen-purged drybox by introducing the solid components of the solution into the cell. The cells were then transferred to the anaerobic atmosphere and the appropriate solvent was introduced. CH3OH was used as the solvent for all redox systems except Me10Fc+IO, for which a solution of 25% CH3OH75 % THF (v/v) was required to dissolve the redox species at the desired concentrations. LiC1O4 was used as the electrolyte in all solutions except in CH3OH-PV2+/+• cells, where Li Cl was required in order to avoid precipitation of the redox species. In all cases, 1.00 M electrolyte was used. All experiments were conducted within the anaerobic atmosphere, which contained less than 10 ppm of 02 as monitored by the lack of any visibly detectable fumes arising from diethyl zinc. In the CH3OH-PV 2+1+• cells, the reduced form of the redox couple was generated electrochemically. A platinum gauze electrode was used as the working electrode and a second platinum gauze electrode, separated from the main solution by a glass frit, was used 215 as the counter electrode. A reference electrode (a methanolic saturated calomel electrode, MSCE) with a potential of -50.0 mV vs. SCE was made according to conventional SCE fabrication procedures, except that CH3OH saturated with LiCl was substituted for the more conventional saturated KCl(aq) solution. 18 The py+• was generated by applying a potential of -100 to -200 m V vs. MSCE across the cell (more negative potentials produced some PVO). The progress of the electrolysis was monitored both by counting the number of coulombs passed through the cell and by periodically checking the cell potential vs. the MSCE reference electrode. In all electrochemical experiments, after the desired ratio of the oxidized to reduced forms of the redox couple was obtained, the n-InP electrode was etched and immersed into the electrolyte. All electrochemical experiments with semiconducting electrodes were conducted in a three-electrode set-up, with a Pt gauze counter electrode and a Pt wire reference. An EG&G Princeton Applied Research (PAR) Model 173 potentiostat in conjunction with an EG&G PAR Model 175 Universal Programmer was used for all current density vs. potential measurements. The data were collected on a Houston Instruments Omnigraphic 2000 recorder and in some cases were also fed directly into a computer. Data acquisition and analysis were performed using Lab View software (National Instruments, Inc.). Impedance spectra were obtained on a computer-controlled Schlumberger Model 1260 frequency response analyzer equipped with a Model 1286 electrochemical interface. After each set of experiments, the solution potential was measured to insure that the cell composition had not changed significantly during the course of the experiment. C. Current Density vs. Potential and Built-in Voltage Measurements For kinetic studies, the current density vs. potential (J-E) behavior of each electrode was measured in the dark in a cell containing the desired concentration of the redox acceptor species. The J-E data were collected at a scan rate of 50 mV s- 1. Each electrode was then re-etched and the series of experiments was repeated, changing the redox acceptor 216 concentration by tenfold. In some cases, instead of just lowering the acceptor concentration by a factor of ten, the entire solution was diluted with solvent containing 1.00 M electrolyte in order to maintain a constant cell potential. This procedure was necessary for PV2+1+• cells because changing only the acceptor concentration made the cell potential sufficiently negative to form an ohmic contact to the n-InP. Also, in the case of nInPfFc+/O contacts, the band edges were found to shift upon increasing the acceptor concentration, so the dilution method was used to examine the concentration dependence of the interfacial kinetics at fixed Vbi values. For some experiments, the electrodes were not etched between J-E experiments; in such instances, after running J-E curve~ in the second solution, the electrodes were returned to the original solution, again without etching, and a third set of J-E data was obtained. The purpose of these experiments was to determine whether a shift in the J-E behavior was due to the changing acceptor concentration or to some irreversible reaction occurring at the electrode surface. All J-E curves were corrected for the series resistance present in the cell, with the series resistance either determined from impedance measurements (vide infra) or from the J-E behavior of a platinum electrode of similar size and shape to that of the n-InP electrode positioned in the same cell geometry. The built-in voltage of each n-InP/liquid junction was calculated from the electrochemical impedance data. Data were only collected for cells containing at least 0.010 M of both the oxidized and reduced forms of the redox couple and which contained a counter electrode having at least ten times the surface area of the working electrode. These precautions were necessary to obtain reliable impedance data. 5 Impedance data were fit to an equivalent circuit consisting of a resistor Rsc (representing the resistance to Faradaic charge transfer) in parallel with a capacitor Csc (representing the differential capacitance of the semiconductor space charge region), both in series with a resistance R 5 (representing the series resistance due to resistive losses through the cell, leads, etc.). The differential capacitance of the space charge layer is related to the built-in voltage of the junction through the Mott-Schottky equation: 13 , 14 217 (5.4) where Eo is the permittivity of free space, £ is the dielectric constant, and As is the area of the semiconductor electrode. Thus, by measuring the impedance data at several different potentials, V bi was determined for the semiconductor/liquid interface of interest. For each de bias, the impedance, Z, of the cell was measured by superimposing an ac signal of 10 m V rms amplitude on the applied de potential. The ac frequency was varied from 0.1 to IQ3 kHz, but only data which were almost purely capacitive in nature (phase angle> 80°) were used in the Mott-Schottky analyses. The differential capacitance, assumed in this equivalent circuit model to be equal to the differential space-charge capacitance of the semiconductor, Csc, was extracted from Zim, the imaginary part of the measured Z, from the equation: 19 2 1/2 = 1 + (1-4(Zim I Rsc) ) 21tfC SC 2Z·lffi (5.5) In the above expression, f is the frequency of the ac voltage and Rsc was taken as the diameter of the semicircle formed by plotting Zim vs. Zreal for the whole frequency range, where Zreal is the real component of the measured impedance. The equivalent circuit used to model the data was validated by two methods. First, since the Mott-Schottky expression should be independent of the measurement frequency, electrodes which did not show measured capacitances that were independent of frequency (over at least one order of magnitude in frequency) were considered defective and were discarded. Second, the slope of the Mott-Schottky plot should be dependent only on the properties of the semiconductor itself (Equation 5.4). The validity of the equivalent circuit model was thus assessed by extracting the dopant density from the slope of the MottSchottky plot and comparing it to the value reported by the manufacturer. Only data which showed linear Mott-Schottky plots (R2 ~ 0.999, where R is the correlation coefficient) with calculated dopant densities within 50% of the reported dopant density were considered valid. 218 III. Results A. Rate Constant Measurements for n-InP/CH30H-Me2Fc+/O Contacts Figure 5. la shows the 1-E behavior of several n-InP/CH3OH-Me2Fc+/O contacts in the absence of illumination. In this series of experiments, the concentration of Me2Fc was held constant at 0.100 M while the concentration of Me2Fc+ was either 0.100, 0.010, or 0.001 M. The data were corrected for series resistance and referenced to MSCE for all three concentrations of Me2Fc+. The data of Figure 5. la can be fit to the diode equation: 20 (5.6) where A is the diode quality factor and J0 is the exchange current density of the semiconductor/liquid contact. In sufficiently far forward bias (-E>>AkT/q), the exponential term dominates the right-hand side of Equation 5.6, and the expression can be rewritten as: lnJ = lnJ 0 - qE AkT (5.7) Fitting the data of Figure 5. la to Equation 5.7 yielded diode quality factors of 1. 15, 1.28, and 1.34 for Me2Fc+ concentrations of 0.001 M, 0.010 Mand 0.100 M, respectively. The deviation from the ideally expected value of A= 1.0 for these junctions may arise from a different recombination mechanism contributing to the current density at lower potentials, but the general behavior was in accord with the first-order kinetic dependence of Jon the concentration of electrons at the surface of the semiconductor. For the two higher concentrations of Me2Fc+, the separation of the data along the abscissa was 75 ± 5 mV, which is close to the ideally expected 59 mV value derived from Equations 5.2 and 5.3. 21 Changing the acceptor concentration by two orders of magnitude resulted in a potential difference in the 1-E data of 125 ± 5 mV relative to a MSCE reference, compared to the ideal shift of 118 mV. These data verify a first-order dependence of J on the concentration of acceptors in the solution, thus the interfacial flux at 219 this solid/liquid contact was dominated by electron transfer from the conduction band to the redox acceptor in the solution phase. Figure 5.lb displays the Csc- 2 -E data for an n-InP/CH3OH-0.lO0 M Me2Fc-0.0l0 M Me2Fc+ contact. In this plot, Csc was extracted from the impedance data obtained at f = 100 kHz and f = 10 kHz. The Csc- 2-E data were linear and essentially independent of frequency over the measurement range. The calculated dopant density was 8.7 x 1015 cm- 3 while that reported by the supplier of this wafer was 6.4 x 10 15 cm-3. Use of Equation 5.4 yielded a built-in voltage of V bi =0.64±0.01 V for the solid/liquid contact of Figure 5.1 b. The impedance analysis was also performed for solutions having a higher concentration of Me2Fc+/O in order to insure that the band edge positions of the semiconductor were relatively fixed as the solution acceptor concentration was changed. Figure 5. lc displays the results of a c- 2-E plot for an n-lnP/CH 3OH-0.100 M Me2Fc0.100 M Me2Fc+ contact. These data yielded Vbi = 0.69 ± 0.01 V. These Mott-Schottky plots also were in good agreement with the reported dopant density and were independent of frequency over the range of frequencies probed in this work. Since the Nernstian potential of the cell, E(A/A-), in Figure 5.lc was more positive than that of Figure 5.lb by 59 m V, the built-in voltage of the contact of Figure 5. lc was expected to be 59 mV greater than that of Figure 5.1 b. The actual difference was just slightly less than this ideal separation, but was in the correct direction, so that a positive shift in £(AJA-) led to an increase in the built-in voltage of the semiconductor/liquid contact. The energetic information from the c- 2-E analysis of Figures 5.1 band 5. lc was then combined with the kinetic information from the J-E data of Figure 5. la to evaluate the value of ket for this system. To perform this computation, the built-in voltage obtained from the Mott-Schottky plots was used with Equation 5.3 to compute the surface electron concentration at a given potential in forward bias. Using Equation 5.2, a rate constant value was then computed from the current density observed at the chosen potential. The 220 potentials chosen for evaluation of ket were all ones for which the J-E data were linearly dependent on the acceptor concentration. For the n-InP-CH3OH-0. l00 M Me2Fc -0.100 M Me2Fc+ interface of Figure 5.1 , this procedure yielded ket = 6.2 x 10-17 cm4 s-1 at E =-0.45 V vs. £(AJA-). Since the diode quality factors for these junctions were not exactly unity, the calculated values of ket depended slightly on the potential chosen for the kinetic measurements. For instance, a value of ket = 1.7 x lQ-16 cm4 s-1 was obtained for the same electrode at a potential of -0.25 V vs. £(AJA-). Since kinetic processes with diode quality factors of 1.0 tend to dominate the interfacial flux further into forward bias, the charge transfer rate constants calculated at the more negative potentials are more likely to reflect the true rate constant. 22 For the n-InP/CH3OH-0. lO0 M Me2Fc-0.010 M Me2Fc+ contact, the computed electron transfer rate constant varied from 2.2 x 10- 17 cm4 s-1 to 1.2 x lQ-16 cm4 s-1 over a potential range of E = -0.45 to -0.25 V vs. £(AJA-). Thus, these ket values were consistent with the ones derived for the higher Me2Fc+ acceptor concentration, confirming the bimolecular nature of the observed interfacial kinetic process. At any individual potential, repeated determinations of J-E and Csc- 2-E were performed, and the resulting values for ket were analyzed using conventional statistical procedures. Results from many different electrodes yielded an average charge transfer rate constant of (8.5 ± 7.7) x 10- 17 cm4 s- 1 for n-lnP/CH3OH-0.l00 M Me2Fc- 0.100 M Me2Fc+ contacts and yielded ket = 1.1 x 10- 16 cm4 s- 1 for InP/CH3OH-0. lO0 M Me2Fc0.0l 00 M Me2Fc+ contacts. The standard deviation in the case of the InP/CH3OH-0. l 00 M Me2Fc- 0.0100 M Me2Fc+ system was slightly larger than the mean, with individual ket values ranging from 1.5 x lQ-18 cm4 s-1 to 9.9 x 10- 16 cm4 s-1. The second highest (of 24 values) calculated rate constant was 3.6 x 10- 16 cm4 s- 1. Given the error present in the measurements, ket for the n-InP/CH3OH-Me2Fc+/O junction was estimated to be between (1-10) x 10- 17 cm4 s-1. 221 Figure 5.1: Current density-potential and differential capacitancepotential data for n-type InP/CH3OH-Me 2Fc+/O contacts. (a) ln J vs. E for n-InP/CH3OH-l.00 M LiClO4-0. lO0 M Me2Fc interfaces having Me2Fc+ (electron acceptor) concentrations of: (i) 0.001 M (E(A/A-) = 0.130 V vs. MSCE), (ii) 0.010 M (E(A!A-) = 0.192 V vs. MSCE), and (iii) 0.100 M (E(A/A-) = 0.252 V vs. MSCE). The diode quality factor, A, was extracted from linear fits of these data to Equation 5.7. (b) Mott-Schottky plots taken at two ac measuring frequencies, 10 kHz (dashed line, solid squares) and 100 kHz (solid line, open circles) , for an n-InP/CH3OH-l.00 M LiClO40.lO0 M Me2Fc-0.0l0 M Me 2Fc+ contact. The potentials are referenced to the Nernstian potential of the cell, E(A/A-). The average dopant density extracted from the slopes of these lines was 8.7 x 10 15 cm-3, compared to the reported dopant density of 6.4 x 10 15 cm-3. The built-in voltages, Vbi, are listed for each frequency. (c) Mott-Schottky plots for two ac measuring frequencies, 10 kHz (dashed line, solid squares) and 100 kHz (solid line, open circles), for an n-InP/CH3OH-l.00 M LiClO4-0.lO0 M Me2Fc-0.100 M Me2Fc+ contact. The average dopant density extracted from the slopes of these lines was 8.7 x 1Q15 cm-3. 222 la) " VMe2Fc+ 1 o -12 -~ rfJ (iii) A=l.15, • 0 1 0, •05 •• ~ LJ o◄ \ 0 •075 V ~'• --♦ $'.:l Q) 0 (i) A=l.34,,.,,,.,.,.,.. -+-I $'.:l Q) ~ u 1........1 $'.:l -14 0.001 M Me2Fc+ \ •• ~\ •• ~ D □ • • □ (ii) A=l .28, 0.010 M Me2Fc+ -16-------------0.3 -0.2 -0.1 0 Applied Potential vs. CH30H SCE (V) 223 10.0 - - - - - - - - - - - lb) 8.0 ~ N I t::, 6.0 \0 ,....., 10 kHz, Vbi = 0.64 V I 0 ~ 4.0 N u 2.0 I 100 kHz, Vbi =0.65 V 0 ..........~.......... ----1,----1,-,1,,_,1,,---,1,,___._.....a.........a...-1-......1 -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) 0.6 10.0 le) ~8.0 N I ~ '-' ~ I 6.0 0 ~ 10 kHz, Vbi = 0.69 V ~ 4.0 I u 2.0 0 100 kHz, Vbi = 0.67 V -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) 0.6 224 B. Rate Constant Measurements for n-InP/CH30H(25%)-THF(75%)Me10Fc+/O Contacts Analogous experiments were performed for n-InP/Me10Fc+/O contacts. In this system, due to the poor solubility of Me10Fc in pure CH3OH, the solvent was 25% CH3OH/75% THF (v/v). J-E data were collected for [Me10Fc] = 0.025 M with the acceptor concentration adjusted to produce [Me10Fc+]=0.025 Mor [Me10Fc+] = 0.0025 M (Figure 5.2a). Although the diode quality factors of these contacts deviated somewhat from unity, the data for the two Me10Fc+ concentrations were separated by the expected 60 m V relative to MSCE. Thus, the reaction was kinetically first order in the concentration of solution acceptors and in the electron concentration at the semiconductor surface, as predicted by the rate law of Equation 5.2. Figure 5.2b displays the Mott-Schottky plots for n-lnP/CH3OH-THF-0.025 M Me2Fc-0.025 M Me10Fc+ contacts at f = 39.811 kHz and f = 3.981 kHz. For these contacts, the range over which the impedance data were independent of frequency was somewhat smaller than that observed for n-InP/CH3OH-Me2Fc+/O contacts, but the impedance data were nevertheless essentially independent of frequency over an order of magnitude off. Over this frequency range, the dopant density computed from the c-2-£ data was in good agreement with the known dopant density of the sample. The built-in voltage obtained from the c- 2-E analysis of this sample was 0.49 ± 0.01 V. 23 The same procedure as described in section IV.A above, in which the analyses of c- 2-E and J-E data were combined, was used to compute the value of ket for thenInP/CH3OH-THF-Me10Fc+/O contacts. For the data shown in Figure 5.2, ket = 1.2 x 1017 cm4 s- 1 at E = -0.35 V vs . E(A/A-) and ket = 4.9 x 10-17 cm4 s-1 at E = -0.15 V vs. E(AIA-) . Over several trials, the average electron transfer rate constant for this system was found to be 5.3 x 10-17 cm4 s-1, but individual values ranged from 9.3 x 10-18 cm4 s-1 to 6.6 x 10- 17 cm4 s-1 . Within the experimental error afforded by the relatively small uncertainties in V bi (propagating into larger uncertainties in n5), along with differences in 225 ket determined at different measurement potentials (due to the deviation of A from the ideal value of A = 1.0), these ket values were indistinguishable from those reported above for nInP/CH3OH- Me2Fc+/O contacts. 226 Figure 5.2: Data for n-InP/CH3OH-THF-Me 10Fc+/O contacts. (a) ln J vs. E data for n-lnP/CH3OH-THF-l.00 M LiClO4-0.025 M Me10Fc contacts having Me 10Fc+ concentrations of: (i) 0.0025 M (E(NA-) = -0.042 V vs. MSCE), and (ii) 0.025 M (E(NA-) =0.010 V vs. MSCE). The diode quality factor, A, was extracted from linear fits of these data to Equation 5.7. (b) Mott-Schottky plots for two ac measuring frequencies, 3.981 kHz (dashed line, solid squares) and 39.811 kHz (solid line, open circles), for an n-InP/CH3OH-THF-l.00 M LiClO4-0.025 M MeioFc-0.025 M Me 10Fc+ contact. The average dopant density extracted from the slopes of these lines was 9.5 x 1Q15 cm-3. The built-in voltages, Vbi, are listed for each frequency. 227 -8 - - - - - - - - - - - - - - - - - - - , (ii) A=l.23, 2a) • 0.025 M Me10Fc+ ,__ l"'"""""1 N ·,. ·v S u -10 < '-' •• •• (i) A=l.42, 0.0025 M Me10Fc+ • • • • • • -18 ...__ __.__ __.___ ____,__ _ _ ___ -0.4 -0.2 0 Applied Potential vs. CH30H SCE (V) 4.0 2b) ,__ 3.0 N I ~ '-' \0 ,.....; I 0 2.0 3.981 kHz, Vbi = 0.49 V ~ ~ N u 1.0 I 39.811 kHz, Vbi = 0.48 V 0 -0.6 -0.4 -0.2 0 0.2 0.4 Applied Potential vs. Cell (V) 0.6 228 C. Rate Constant Data for n-InP/CH30H-PV 2 +1+• Contacts Cyclic voltamrnetric data showed that PV 2+/+• exhibited reversible, one electron redox behavior in CH3OH at a Pt electrode. This redox couple displayed a formal potential, E 0 '(NA-), of-180 mV vs. MSCE, which was >200 mV more negative than E 0 '(NA-) for Me10Fc+/O (in CH3OH-THF). Consequently, the more negative value of E 0 '(NA-) for PV2+1+• should produce smaller built-in voltages, and therefore lower values of ~G 0 ', for n-InP/CH3OH-PV 2+/+• contacts relative to those of n-InP/CH3OH-Me2Fc+/O or n-InP/CH3OH-THF-Me10Fc+/O junctions. Figure 5.3a shows the J-E data for an n-InP electrode in contact with CH3OH-l .00 M LiCl-0.050 M PV2+-0.010 M py+•. In this system, J0 was sufficiently large that the condition -E>AkT/q was not satisfied over the entire potential range of interest. Thus, the simplifications that allow Equation 5.6 to be transformed into Equation 5.7 were not appropriate for this system. The kinetic data of Figure 5.3a were therefore fit to Equation 5.6 to yield J 0 , and then ket was computed using Equation 5.2, with n5 (E) = n5 (0). Since the redox potential of the solution was near the InP conduction band edge energy at the semiconductor surface, the J-E behavior for this n-InP/liquid contact was very sensitive to the value of E(NA-). For example, at even slightly more negative potentials than E(NA-) = -0.150 mV vs. MSCE, the n-lnP/liquid contact exhibited nonrectifying, near-ohmic behavior. It was therefore not possible to perform an experiment analogous to that described in Figure 5.1 with the n-InPIPV 2+1+• contacts, in which the acceptor concentration was decreased in order to reveal the kinetic dependence of Jon [A] while [A-] was held constant. Instead, the J-E properties of an n-InP electrode were recorded in contact with a CH3OH-l.00 M LiCl-0.010 M PV2+-0.050 M py+• solution and then in contact with a CH3OH-l.00 M LiCl-0.0010 M PV2+-0.0050 M py+• solution. The latter solution was prepared by diluting part of the more concentrated solution with 1.00 M Li Cl in CH3OH. This procedure allowed investigation of the desired kinetic behavior but required a slightly different analysis of the data, as described below. 229 The results of this experiment are shown in Figure 5.3b. In this figure, the current scale for the electrode in the more dilute solution is multiplied by a factor of ten. These data clearly show the first-order dependence of the current density on the concentration of acceptor species dissolved in the solution, as expected from Equation 5.2. The Mott-Schottky plots for two ac frequencies applied to the CH3OH-l.00 M LiCl-0.010 M PV2+-0.050 M py+· interface are shown in Figure 5.3c. The impedance data for this junction exhibited more frequency dispersion than is evident in Figures 5. lc-d or 2c, possibly due to the large Faradaic current that was present during the impedance measurements of this low barrier height system. Despite this complication, the dopant density obtained from the c- 2 -E plots over the frequency range 158.489 kHz to 15.849 kHz was within 30% of the value specified by the manufacturer. Additionally, although the slopes varied slightly over this range of frequencies, the x-intercepts of the c-2-E plots were in agreement to within± 15 mV. The built-in voltage of this junction was calculated to be 0.28 V, yielding an electron transfer rate constant of 3.3 x lQ-16 cm4 s-1. Over many measurements of this system, the average electron transfer rate constant was ket = (3.3 ± 2.4) x 10-16 cm4 s- I. In this case, the range of values for the electron transfer rate constant was higher than those reported for the n-InP/CH3OH-Me2Fc+/O and n-InP/CH 3OH-THFMe 10Fc+/O interfaces, with ket ranging from 1 x 10-16 cm4 s-1 to 9 x 10-16 cm4 s-1. It should be noted, however, that the reorganization energies for the viologens in homogeneous solution are significantly lower than those of the ferrocenes, 24-26 hence the decreased outer-sphere reorganization energies of this redox system somewhat counteracted the effects of the lower driving force at the n-InP/PV 2+1+• contact. 230 Figure 5.3: Data for n-InP/CH3OH-l.00 M LiCl-PV 2 +1+• contacts. (a) J-E data for an n-InP/CH3OH-l.00 M LiCl-0.050 M PV 2+- 0.010 M py+· contact (E(A/A-) = -0.146 V vs. MSCE). The data were fit to Equation 5.8 and yielded a diode quality factor of 1.1. (b) J-E data for n-InP/CH3OHl.00 M LiCl-0.050 M PV2 +- 0.010 M py+• and n-InP/CH3OH-l.00 M LiCl-0.0050 M PV2+- 0.0010 M py+• contacts. The current density data for the n-InP/CH3OH-l.00 M LiCl-0.0050 M PV 2 +- 0.0010 M py+• contact (triangles) has been multiplied by ten for better comparison to the data for the CH3OH-l.00 M LiCl-0.050 M PV2+- 0.010 M py+• solution (open squares). (c) Mott-Schottky plots for the system in (a) at two ac measuring frequencies, 15.849 kHz (dashed line, open circles) and 158.489 kHz (solid line, filled circles). The dopant density predicted from the slope of the 15.849 kHz line was 9.9 x lQ15 cm-3, while the dopant density extracted from the slope of the I 58.489 kHz line was 8.9 x 1Ql5 cm-3 . The built-in voltages, Vbi, are listed for each frequency . 231 ,-. N 0 3a) A=l.11 s ~ -1 I () '-' ~ ~ -~ r:fj ~ Q) Q ~ ~ -2 Q) ~ ;:::t u -3 -0.1 0.1 0 0.2 Applied Potential vs. Cell (V) 3b) 0 -1 □ J (0.050 M pv2+-0.010 M pv+•) • J x 10 (0.0050 M pv2+-0.0010 M pv+•) -0.1 0.1 0 0.2 0.3 Applied Potential vs. Cell (V) 232 3.0r-----------------,..---, 3c) 2.5 \0 ,-..-1 6 1.5 158.489 kHz, Vbi = 0.28 V :r (/° ~ ~ u 1.0 N 0.5 O -0.2 ~ 15.849 kHz, Vbi = 0.27 V 0.2 0.4 0.6 0 Applied Potential vs. Cell (V) 0.8 233 D. n-InP/CH30H-Fc+IO Contacts Figure 5.4a depicts the J-E characteristics of n-InP/CH3OH-0.0lO M Fc-0.100 M Fe+ and n-lnP/CH3OH-0.0lO M Fc-0.010 M Fe+ contacts. In contrast to the behavior of the n-lnP/CH3OH interfaces described above, the n-InP/CH3OH-Fc+/O junction showed a shift in its J-E properties of 120 mV vs. MSCE upon increasing the acceptor concentration by an order of magnitude. This shift was approximately twice as large as the ::::::60 mV shift that was observed for the other redox systems (Figures 5.1-5.2), and is twice as large as that expected from the rate law of Equation 5.2. This J-E behavior indicated a shift in the band edge positions of the semiconductor as the Nemstian potential of the Fc+IO solution increased, and precluded a straightforward justification of the second-order rate law by variation of [A] with constant [A-]. This band edge movement may arise from a number of sources, including surface state charging or carrier inversion, and does not necessarily indicate any adsorption of the Fe+ ion on the electrode surface. To minimize such band-edge shifts, the concentrations of Fe+ and Fe were changed simultaneously but the [A]/[A-] ratio was held fixed, so that Nemstian potential of the solution was held constant. To implement this process, part of a CH3OH-l .00 M LiClO40.0lO M Fc-0.100 M Fe+ solution was diluted with sufficient CH3OH-l.00 M LiClO4 to form a CH3OH-l.00 M LiClO4-0.00lO M Fc-0.010 M Fe+ solution. This method is identical to the one used to prove second-order kinetics for the n-InP/CH3OH-PV 2+/+• system (vide supra). Figure 5.4b shows the J-E behavior for an n-InP electrode in contact with each solution, and illustrates the 70 mV potential shift of the J-E behavior, relative to a MSCE reference, that was observed when this experimental protocol was used. Impedance data were again used to obtain the energetics for the n-lnP/CH3OHFc+/O interface. Figures 5.4c and d display the impedance data for representative nlnP/CH3OH-0.0lO M Fc-0.100 M Fe+ and n-lnP/CH3OH-0.0l0 M Fc-0.010 M Fe+ contacts, respectively, in the form of Mott-Schottky plots. These c- 2 -E plots showed little frequency dispersion and had slopes that were consistent with those computed from the 234 dopant density reported by the manufacturer of the InP samples. In addition, the built-in voltages of these two n-InP/CH3OH-Fc+/O contacts were essentially indistinguishable from each other. This effect was observed for several different electrodes; in fact, the mean value of Vbi for the n-InP/CH3OH-0.0l0 M Fc-0.100 M Fe+ contact, Vbi = 0.78 V, was slightly lower than the mean value of Vbi = 0.81 V measured for the n-InP/CH3OH-0.0lO M Fc-0.010 M Fe+ contact. The 120 mV shift observed in the J-E data when [Fe+] was varied but [Fe] was held constant is thus readily understood in the context of the band edge movement revealed by the c- 2-E data. As displayed in Figures 5.4c-d, the built-in voltage of the more concentrated Fe+ solution is lower than expected by ""'60 m V, due to a band edge shift that is consistent with prior studies of n-InP/nonaqueous liquid contacts having such positive Nemstian solution potentials.3 This band edge movement results in an additional 60 mV shift in the J-E curves for these solutions relative to that expected from the rate law of Equation 5.2 assuming fixed band edge positions, thus resulting in the 120 mV shift in J-E behavior (vs. the MSCE reference) observed in Figure 5.4a. With the energetics available from the impedance analysis, ket could be computed for each n-InP/CH3OH-Fc+/O solution from the combined analysis of c- 2-E and J-E data. For the n-InP/CH3OH-0.0lO M Fc-0.100 M Fe+ contact, the average electron transfer rate constant was found to be (5.3 ± 3.2) x lQ-17 cm4 s-1, while for the n-InP/CH3OH-0.0lO M Fc-0.010 M Fe+ contact, the average ket value was (1.6 ± 1.1) x 10-16 cm4 s-1. Table 1 summarizes the kinetic data for all of the InP/liquid contacts studied in this work. 235 Figure 5.4: Data for n-InP/CH3OH-Fc+/O contacts. (a) J-E data for n- InP/CH3OH-l.00 M LiCIO4-0.0lO M Fe contacts having Fe+ concentrations of: (i) 0.010 M (E(A/A-) = 0.350 V vs. MSCE), and (ii) 0.100 M (E(A/A-) = 0.407 V vs. MSCE). (b) In J vs. E data for an nInP/CH3OH-l.00 M LiCIO4-0.0lO M Fc-0.100 M Fe+ contact (filled circles) and for an n-InP/CH3OH-l.00 M LiCIO4-0.00lO M Fc-0.010 M Fe+ contact (open circles). (c) Mott-Schottky plots for two ac measuring frequencies, 10 kHz (dashed line, open squares) and 100 kHz (solid line, filled circles), for an n-InP/CH3OH-l.00 M LiCIO4-0.0lO M Fc-0.010 M Fe+ interface. The average dopant density extracted from the slopes of these lines was 8.1 x 1Q15 cm-3. The built-in voltages, Vbi, are listed for each frequency . (d) Mott-Schottky plots for two ac measuring frequencies, 3.981 kHz (dashed line, filled circles) and 39.811 kHz (solid line, open circles), for an n-InP/CH3OH-l.00 M LiCIO4-0.0lO M Fc-0.100 M Fe+ contact. The average dopant density extracted from the slopes of these lines was 8.2 x 1Q15 cm-3. 236 -4 -,----........r----------4a) r--, ,-._ N (ii) A=l.10, 0.100 M Fe+ S -6 u I ~ '-' o -8 ...... rJJ 0 (l) 0 -10 ~ 0 (l) ~ 8 -12 1........1 - (i) A=l.19, 0.010 M Fe+ 0 -0.3 -0.2 -0.1 0 Applied Potential vs. CH3OH SCE (V) ~ -6 ~ -8 su N '-' 0 ...... rJJ 0 (l) Q -10 ~ 0 (l) ~ :::s u -12 1........1 0 ,. . . . -14 ..____.__ __.....___________.__.....___. -0.7 -0.6 -0.5 -0.4 -0.3 Applied Potential vs. Cell (V) 237 5.0 4c) □ 4.0 ,-.._ N I ~ 3.0 l,O 10 kHz, Vbi = 0.80 V □ rh ~ ~ □~ ~ I 0 ~ 2.0 >< '° N I u 1.0 100 kHz, Vbi = 0.76 V 0 ...___________.____________.___________ -0.8 -0.4 0 0.4 Applied Potential vs. Cell (V) 0.8 5.0 4d) 4.0 ~ ~ 3.o 39.81 kHz, Vbi = 0.79 V l,O ~ I 0 ~ 2.0 N I u 1.0 3.981 kHz, Vbi = 0.78 V 0 -------------0.8 -0.4 0 0.4 0.8 Applied Potential vs. Cell (V) 238 Table 5.1. Summary of electron transfer rate constants. Values listed for ket are averages obtained for each redox couple at each electron acceptor concentration. The error present in each average is listed in the text. 239 Redox Cou le [A] (M) ket (cm4 s- 1) Me2Fc+I0 0.100 8.5 X lQ-l 7 Me2Fc+I0 0.010 1.1 X lQ-l 6 Me10Fc+/O 0.025 5.3 X lQ-l7 py2+/+• 0.050 3.3 X lQ-l 6 Fc+IO 0.100 5.3 X 10-l 7 Fc+IO 0.010 1.6 X IQ-16 Table 5.1 240 IV. Discussion The most significant feature of the n-InP/liquid contacts discussed herein is that they exhibited not only nearly-ideal energetic but also nearly-ideal kinetic behavior. Ideal energetic behavior, in which the c-2-E plots are well-behaved and the resulting band edge positions are invariant for a wide range of redox potentials, has been observed previously for some n-InP/CH3CN contacts. 3 The above data document this behavior in detail for a series of outer-sphere redox couples and extend these observations to CH3OH as the solvent. In addition, the n-InP contacts studied in this work exhibited nearly ideal kinetic behavior in that their current density-potential relationships were observed to obey the rate law behavior expected from Equation 5.2 for a simple interfacial electron transfer event acting as dominant recombination rate to produce current flow through the semiconductor/liquid interface. Such behavior has not been reported previously for a series of outer-sphere, one-electron redox couples at a semiconductor surface except in a very few cases, 27 yet this combination of behaviors is required in order to determine directly the values of the heterogeneous charge transfer rate constants for semiconductor electrodes from steady-state J-E data. The ideal energetic behavior reported herein is significant in view of prior hypotheses that n-type InP surfaces exhibit Fermi level pinning in contact with nonaqueous electrolytes. 1•28 In the absence of Fermi-level pinning, the difference in the built-in voltage of two semiconductor/liquid junctions should be equal to the difference in the Nemstian potentials of the two electrolyte solutions. Figure 5.5 shows the built-in voltage as a function of E(AJA-) for the junctions examined in this work. The points define a straight line, with the exception of those for the CH3OH-l.00 M LiClO4-0.0lO M Fc-0.100 M Fe+ solution, where the junction is no longer sensitive to the cell potential, and the Me 10Fc+/O solution, where a different solvent system was used because of solubility constraints. Fitting the remaining points to a line yielded a slope of 1.1, indicating that these junctions behave nearly ideally over this potential range. Thus, for this series of contacts, the 241 equilibrium band bending and equilibrium electric field strength in the n-InP are not dominated by surface states, but instead respond completely to variation of the thermodynamic properties of the redox species in the liquid phase. This conclusion is in agreement with the photovoltage behavior of n-InP/CH3CN contacts,2 but contrasts with earlier, nonideal c- 2-E data that were interpreted within a complex equivalent circuit model to indicate nearly complete Fermi level pinning for n-type InP electrodes in contact wth CH3CN solvent. 28 It also contrasts with the well-documented Fermi level pinning behavior of metal-semiconductor Schottky contacts formed on n-type InP surfaces. 29 ,30 The kinetic behavior of these n-InP/CH3OH contacts is also significant in the context of theoretical expectations for heterogeneous charge transfer rate constants at semiconductor/liquid interfaces. Since the ~G 0 ' values for the reported contacts were between -0.4 and -0.9 eV, and the reorganization energies of the redox couples used in this work were ::::0.5-1.0 eV, 24-26 the value of ket is expected to be dominated by the electronic terms of the rate constant expression, as opposed to the nuclear (Franck-Condon) factors. For example, for the Me 10Fc+/O redox couple, the reorganization energy is predicted to be about 0.80 eV, 26 ,31 while n-InP in contact with this redox system yielded ~G 0 ' = -0.6 eV. Substituting these numbers into Equation 5.1 yields Kn= 0.52, indicating ket for this system is only expected to be about a factor of 2 lower than ket, max. Performing a similar calculation for the n-InP/CH3OH-PV2+/+• system using A= 0.5 eV 25 ,31 and ~Go'= 0.4 e V yields Kn = 0.82. The value of KeJ has been previously estimated to be 10-30 cm4 for a typical semiconductor,4 •5 which yields a value of ket,max = 1o- 17 cm4 s- 1 at optimal exoergicity, assuming that Vn =10 13 s- 1. The expectations for ket,max and KeJ are thus in excellent agreement with the kinetic behavior observed for the n-InP/liquid contacts investigated in this work. Considering the theoretical prediction in more detail, the value of Kel has been related to the Bohr radius of the electron in the solid. In this approach, the Bohr radius was taken as a qualitative measure of the delocalization length of the wavefunction for the 242 electron in the conduction band of the semiconductor. Due to the very low effective mass of electrons in the conduction band of n-InP, 14 the Bohr radius of electrons in InP is a factor of 10 larger than that of electrons in Si (or than that of carriers in most other common semiconductors), 32 so the existing model implies that the ket values for n-InP/liquid contacts should be larger, by about an order of magnitude, than those for otherwise identical contacts using other types of semiconductor electrodes. This prediction seems to be borne out experimentally from the available data, because recent steady-state kinetic data obtained on n-type Si/CH3OH interfaces has yielded ket,max values of ~sx 10- 17 cm4 s- 1 for a series of viologen acceptors. 27 Due to the significant error of these types of J-E and c- 2 - E kinetic measurements at present, which limits the precision of the determination of ket,max to factors of 5-10, further work would be required to evaluate definitively any experimental relationship between the Bohr radius of the carrier in the solid and the charge transfer rate constant at the semiconductor/liquid contact. Nevertheless, the data available to date seem to be in qualitative agreement with this prediction of the model for interfacial charge transfer at semiconductor/liquid junctions. 4 In summary, a combination of energetic and kinetic measurements has been used to determine values of the interfacial charge rate constants for a series of n-InP/liquid contacts. In all cases, the J-E behavior was in accord with the ideally expected rate law for interfacial charge transfer, being first order in the concentration of acceptors in the solution and first order in the concentration of electrons at the surface of the semiconductor. Mott-Schottky plots derived from impedance measurements were essentially independent of frequency, yielded the theoretically expected slopes, and produced reliable measurements of the builtin voltages and band edge positions of the solid/liquid contacts. The built-in voltages of nInP/CH3OH interfaces were found to be controlled by the Nemstian potential of the solution, indicating a lack of Fermi level pinning over most of the potential range investigated. Electron transfer rate constants for these semiconductor/liquid junctions were determined to be on the order of 1Q-17 -1 Q-16 cm4 s-1. These values are in excellent 243 agreement with theoretical models available in the literature for such charge transfer processes. Taken together with upper limits on ket,max that have been established recently for a wide range of semiconductor/liquid junctions, these data therefore strongly support the theoretical prediction that optimally exoergic steady-state interfacial charge transfer rate constants are in the range 10-17- 10-16 cm4 s- 1 for semiconductor surfaces in contact with randomly dissolved, nonadsorbing, outer-sphere redox couples. 244 Figure 5.5: Dependence of the built-in voltage of n-InP electrodes on the Nernstian potential, E(AJA-) , of various contacts having outer-sphere redox systems dissolved in the solution phase. The Nernstian potentials are referenced vs. SCE and differ from the MSCE values by 50.0 mV. The equation for the best fit line (omitting the point for Me 10Fc+IO, which was obtained in a different solvent system) yields a slope of 1.09. Extrapolating the graph to V bi = 0 V and correcting for the difference between the potential of the conduction band edge, Ecb, and the Fermi level in the semiconductor yields Ecb = -0.52 V relative to SCE. However, since the slope is not exactly 1.0, at higher built-in voltages the apparent conduction band edge position is slightly different; for example, taking the specific point determined for n-lnP/CH3OH--l.00 M LiClO4-0. lO0 M Me2Fc-0.l 00 M Me2Fc+ of Vbi =0.69 Vat E(AJA-) = 0.19 V vs. SCE, Ecb = -0.62 V. 245 0.9 0.8 0.7 --> 0.6 '-' (solvent= THF/CH30H) ..... ~ ~I > 0.5 0.4 0.3 0.2 -0.2 -0.1 0.0 0.1 0.2 E(A/A-) vs. SCE (V) Figure 5.5 0.3 246 V. References (1) Dominey, R. N.; Lewis, N. S.; Wrighton, M. S. J. Am. Chem. Soc. 1981, 103, 1261. (2) Heben, M. J.; Kumar, A.; Zheng, C.; Lewis, N. S. Nature 1989, 340, 621. (3) Koval, C.; Austermann, R. J. Electrochem. Soc. 1985, 132, 2656. (4) Lewis, N. S. Ann. Rev. Phys. Chem. 1991, 42, 543. (5) Pomykal, K. E.; Fajardo, A. M.; Lewis, N. S. J. Phys. Chem. 1996, 100, 3652. (6) Forbes, M. D. E.; Lewis, N. S. J. Am. Chem. Soc. 1990, 112, 3682. (7) Howard, J. N.; Koval, C. A. Anal. Chem. 1994, 66, 4525. (8) Rosenwaks, Y.; Thacker, B. R.; Nozik, A. J.; Ellingson, R. J.; Burr, K. C.; Tang, C. L. J. Phys. Chem. 1994, 98, 2739. (9) Smith, B. B.; Nozik, A. J. Chem. Phys. 1996, 205, 47. (10) Koval, C. A.; Howard, J. N. Chem. Rev. 1992, 92, 411. (11) Horrocks, B. R.; Mirkin, M. V.; Bard, A. J. J. Phys. Chem. 1994, 98, 9106. (12) Uhlendorf, I.; Reinekekoch, R.; Memming, R. J. Phys. Chem. 1996, 100, 4930. (13) Morrison, S. R. Electrochemistry at Semiconductor and Oxidized Metal Electrodes; Plenum: New York, 1980. (14) Sze, S. M. The Physics of Semiconductor Devices; 2nd ed.; Wiley: New York, 1981. (15) Aspnes, D. E.; Studna, A. A. Appl. Phys. Lett. 1981, 39, 316. (16) Hendrickson, D. H.; Sohn, Y. S.; Gray, H.B. Inorg. Chem. 1971, 10, 1559. (17) Kamogawa, H.; Sato, S. Bull. Chem. Soc. Jpn. 1991, 64, 321. (18) Pomykal, K. E.; Fajardo, A. M.; Lewis, N. S. J. Phys. Chem. 1995, 99, 8302. (19) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley & Sons: New York, 1980, pp 629. (20) Tan, M. X.; Laibinis, P. E.; Nguyen, S. T.; Kesselman, J.M.; Stanton, C. E.; Lewis, N. S. Prag. Inorg. Chem. 1994, 41, 21. 247 (21) Rosenbluth, M. L.; Lewis, N. S. J. Phys. Chem. 1989, 93, 3735. (22) The observed current at the semiconductor interface is given by the sum of the currents for all possible processes. Since the diode quality factor, A, appears in the denominator of the exponential in Equation 6, at sufficiently large potentials a process with a smaller value of A can dominate the total interfacial flux even if the exchange current density, J0 , is larger for other parallel kinetic processes having larger A values. (23) The cell potential was 20 mV vs. MSCE, nearly 200 mV more negative than that of the Me2Fc+/O system, but the built-in voltage was only 150 mV smaller for thenlnP/CH3OH-THF-Me10Fc+/O contact than for the n-InP/CH3OH-Me2Fc+/O contact. This is likely due to the slight difference in the apparent band edge positions between the two different solvent systems that were required for these measurements. (24) Yang, E. S.; Chan, M.; Wahl, A. C. J. Phys. Chem. 1975, 79, 2049. (25) Dai, S. Thesis, University of Tennessee, 1990. (26) Nielson, R. M.; McManis, G. E.; Safford, L. K.; Weaver, M. J. J. Phys. Chem. 1989, 93, 2152. In this work, the self-exchange rate constant, kse, for Me 10Fc+/O was not reported in methanol. However, kse for Fc+IO was reported in methanol as well as in some solvents for which kse for Me 10Fc+/O was also reported. In most cases, kse of Me 10Fc+/O exceeded that of Fc+/O by about a factor of three. To arrive at a reorganization energy for Me 10Fc+/O in methanol, kse of Fc+IO in methanol was multiplied by three and converted to a reorganization energy by the equation: kse = Zbi e-(Al4kT) where Zbi ::::: 1011 M-1 s-1 is the normal collisional vibration frequency for bimolecular reactions at room temperature. 31 (27) Fajardo, A. M.; Lewis, N. S. Science 1996, 274, 969. (28) Nagasubramanian, G.; Wheeler, B. L.; Bard, A. J. J. Electrochem. Soc. 1983, 130, 1680. (29) Mead, C. A.; Spitzer, W. G. Phys. Rev. 1964, 134, A713. 248 (30) Newman, N.; Kendelewicz, T.; Bowman, L.; Spicer, W. E. Appl. Phys. Lett. 1985, 46, 1176. (31) Marcus, R. A. J. Phys. Chem. 1963, 67, 853. (32) Ibach, H.; Luth, H. Solid-State Physics; Springer Verlag: Berlin, 1990.