Electrochemistry at Metal and Semiconductor Electrodes This Page Intentionally Left Blank Electrochemistry at Metal and Semiconductor Electrodes by Norio Sato Emeritus Professor, Graduate School of Engineering, Hokkaido University, Sapporo, Japan ELSEVIER Amsterdam - Boston - London - New York - Oxford ~ Paris - San Diego San Francisco - Singapore - Sydney - Tokyo ELSEVffiR SCIENCE B.V Sara Burgerhartstraat 25 P.O Box 211, 1000 AE Amsterdam, The Netherlands © 1998 Elsevier Science B.V All rights reserved This work is protected under copyright by Elsevier Science, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery Special rates are available for 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contained in the material herein Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and dmg dosages should be made First edition 1998 Second impression 2(X)3 Library of Congrsss C«ta1og1ng-tn^ X X Xad Xj Xp ^ x J XRED /i ^«d ^j \Ji[ ^f Pi pf Vi 395 Fermi level of standard redox electrons in complexed redox particles Fermi level of standard redox electrons in adsorbed redox particles Fermi level of n-type or p-tyi)e semiconductor electrodes quasi-Fermi level of electrons in semiconductor electrodes quasi-Fermi level of holes in semiconductor electrodes energy of a particle i mobility g a p in amorphous semiconductors rnost probable electron level of oxidant or reductant particles standard gaseous electron level (t^^-O) electron level of the surface state on semiconductors reaction order with respect to a particle k in a reaction rate of increase in electric field across the inner Helmholtz layer overvoltage of an electrode reaction overvoltage across a compact la3^r at electrodes interfacial overvoltage a t photoexcited semiconductor electrodes overvoltage across a space charge layer in semiconductors overvoltage for transport of charge carriers in semiconductors overvoltage for generation and transport of electrons i n semiconductors overvoltage for generation and transport of holes in semiconductors adsorption coverage adsorption coverage of a pauiicle i relative dielectric constant a kinetic parameter wave l e n g t h of photons reorganization energy of redox particles, oxidants or reductants reorganization energy of adsorbed redox particles absolute activity of a particle i Fermi w a v e length of electrons reorganization energy of oxidant or reductant particles dipole m o m e n t adsorption-induced dipole m o m e n t chemical potential of a particle i imitary chemical potential of a particle i stand£ird chemical potential of a particle i electrochemical potential of a charged particle i standard electrochemical potential of a charged particle i stoichiometrical coefficient of a particle i in a reaction 396 V* o o^ a^ Og Osc o« MH ^sc X O UST OF SYMBOLS stoichiometric nxunber of an elementary step, r, in a reaction electric charge for unit area electric charge due to surface adsorption for unit area electric charge on the metal side of metal electrodes for unit area electric charge on the solution side of electrodes for unit area electric charge in a space charge layer for imit area of semiconductors electric charge of the surface states for unit area electrostatic inner potential potential across a compact layer (Helmholtz layer) potential across a space charge layer in semiconductor electrostatic outer potential surface potential (difference in potential across a surface) work function INDEX absolute activity absolute electrode potential 99 acceptor 25 acceptor level 27 accumulation layer 42, 175, 177 add site 181,189 addic proton hydration 78 addic proton level 78, 320 addic proton transfer 82 activated flow 224 activated state 290 activation energy 73, 222 active state 382 activity 5, 33 activity coeffident 5, 33 adsorbed intermediate 294 adsorbed redox particle 165 adsorption 121,138,158 adsorption e n e i ^ 123 adsorption isotherm 143 adsorption of redox particle 274 adsorption-induced dipole moment 155 adsorption-induced surface state 41 amorphous semiconductor 44 anion 88 anode 201, 213 anodic polarization 219 anodic reaction 213 antibonding band 24, 35 band edge level pinning 171, 252 band edge potential 195 band gap 24, 37 band model 19, 24, 32 base site 181, 189 basic proton h3rdration 79 basic proton level 78,320 Boltzmann factor Boltzmann function bonding band 24, 36 Bose particle Bose-Einstein function Bose-Einstein level capadty of space charge layer 177 cathode 201, 213 cathodic hole ii\jection 347, 355 cathodic polarization 219 cathodic reaction 213 cation 88 cation-anion vacancy pair formation 73 cell diagram 203 cell reaction 202 charge transfer coefSdent 155, 167 chemical cell 202 chemical potential chemical potential of electron 8,22 chemisorption 121 dathrate hydrates 162 dean surface 119 cluster-like network structure 159 coadsorption 122 communal energy compact layer 128, 132,148, 150,154,156, 181,184 compact layer capadty 148 complexation 274 conduction band 24 conduction band mechanism 251 contact adsorption 140,142,153, 155,163, 278 contact potential 92, 99 corrosion potential 377 covalent adsorption 125 covalent semiconductor 298,302 cratic energy Debye length 130.132,169,176 deep depletion layer 175,179 degeneracy 44,174 depletion layer 42,175,178 diftoe charge layer 129 398 diffuse layer 130 diffusion overvoltage 246 direct band gap 24, 36 direct electron transfer 281 donor 25 donor level 27 effective Debye length 177 effective excess charge plane 146 effective image plane 144 effective state density 27, 28, 251 electric double layer 127,168 electromotive force 110 electrocapillary curve 139 electrochemical cell 201 electrochemical potential electrochemical potential of electron 8, 20 electrochemical potential of ion 64 electrode 87 electrode potential 96, 99, 104,105, 108,109 electrode reaction 213 electrolytic cell 202 electromotive force 110, 205, 367, 369 electron accepting reaction 47 electron donating reaction 47 electron transfer 213, 214, 235, 237, 249 electron-hole pair formation 72 electronic electrode 88 electronic electrode potential 102 emersed electrode 112 energy band 16 equilibrium electrode potential 206 equivalent Fermi level 107, 311 exchange reaction current 240, 254 exponential kinetics 218 extrinsic semiconductor 25 F faradaic current 90 Fermi e n e i ^ Fermi function Fermi level 2, 5,172 Fermi level of intrinsic semiconductor 29 Fermi level of metal 19 Fermi level of n-type semiconductor 31 Fermi level of p-t3i>e semiconductor 31 Fermi level of redox electron 239 Fermi level pinning 42, 252 Fermi partide Fermi temperature Fermi wave length 21 fermion flat band potential 185, 192, 337,344 INDEX fluctuation band 54 fluctuation of electron energy level 51 Franck-Condon level splitting 50 free energy free enthalpy Frenkel defect 74 frontier band 19 Frumkin's adsorption isotherm 143 Galvani potential difference 92 Galvanic cell 201 gap state 45 gas electrode 108 Gibbs adsorption equation 138 H Henry's law hole 24, 27 hopping model 32 hydrogen electrode 108 hydrogen-oxygen fuel cell 202 hydroxyl radical 160 hydroxylation 181 IHP (inner Hehnholtz plane) 141 indirect band gap 24, 36 indirect electron transfer 281 inner Hehnholtz layer 141,156,157 inner potential 9,10, 90 inner potential difference 92, 95 inner-sphere electron transfer 215, 278, 283 interfadal charge 92 interfadal complex 182 interfadal dipole 92 interfadal ion pair 182 interfadal lattice transformation 162 interfadal overvoltage 246, 350 interfadal potential 95 interfadal redox electron 315 interfadal redox reaction 317 interfadal state 39 intrinsic semiconductor 25, 27 inverse overvoltage 349, 363, 363, 365, 368 inversion layer 175,179 ion adsorption 314, 317 ion transfer 213, 289, 302, 306, 314, 317 ionic electrode 88 ionic electrode potential 102 ionic semiconductor 306,309 iso-electric point 183, 321 INDEX jelliiim model of metal 21 Kelvin's method 114 kink site 66, 69 Langmuir's adsorption isotherm 143, 296 Lewis acid 158 Lewis base 158 linear kinetics 218 localized electron level 29, 38,45, 47, 51 M mcgority charge carrier 32 mean stoichiometric number 230 metal ion level 63 metal oxide 35 metallic adsorption 125 minority charge carrier 32 mixed electrode 373 mixed electrode potential 377 mobihty edge level 45 mobility gap 45 molality 76 molar fraction 4, 77 most probable electron level 52, 55, 238 Mott-Schottky plot 178 N nonfaradaic current 90 nonpolarizable electrode 89 normal hydrogen electrode 55,110 n-type semiconductor 25, 29 occupied proton level 78 OHP (outer Hehnholtz plane) 128 operation potential 363 outer Hehnholtz layer 141,156 outer potential 10, 90 outer potential difference 92,95 outer-sphere electron transfer 215, 235, 249, 283,285 overvoltage 220, 258, 348 overvoltage for hole generation and transport 349 oxidant 47 oxidation 47 oxidative dissolution 309 passivation 382 399 passivation potential 382 passive state 382 Peltier effect 206 photocurrent 334 photoelectrochemical semiconductor cell 357 photoelectrode reaction 334 photoelectrolytic cell 357, 364 photoelectron 325 photoexcitation 325 photopotential 330 photo-shift of flat band potential 344 photostationary state 325 photovoltaic cell 357, 367 physisorption 121 polarizable electrode 89 polarization 89, 219 polarization curve 218 polarization resistance 292,379 potential of space charge layer 43 potential of zero charge 130,135,139 proton level 62 proton level on electrode surface 319 p-type semiconductor 25, 29 Q quasi-Fermi level 326,348 quasi-metaUization of semiconductor surface 44,171 R Raoult*slaw5 rate-determining multiple steps 230 ratio of afifinity distribution 231 reaction afi&nity 216 reaction current 242, 259 reaction order 225 reaction rate 217 reaction resistance 292 real potential 12 real potential of electron 21,97 real potential of hydrated ion 76 recombination current 268 recombination of photoexcited electron-hole pair 352 redox electron 47, 53,105 redox electron level 54 redox electron transfer 268 redox particle 48, 88, 235 redox reaction 47 reductant 47 reduction 47 reductive dissolution 311 relative electrode potential 112 reorganization energy 48, 51, 279 400 S Schottky barrier 181 Schottky defect 74 self-passivation 388 single electrode 373 single rate-determining step 228 space charge layer 42, 129,174,176 specific adsorption 140 spontaneous passivation 388 standard electrochemical potential of electron 33 standard equilibrium potential 208 standard Fermi level of redox electron 238, 255 standard gaseous electron 56 standard gaseous electron level 9, 48 standard ion level 77 standard real potential of ion 77 standard redox electrode potential 105, 207 state density 6,18 stoichiometric number 220 surface atom ionization 298 surface dangling state 40 surface degeneracy 44 surface Fermi level 42 surface ion level 74 surface ion-induced state 41 surface lattice transformation 120,162 surface metal ion level 65 surface potential 10, 21, 46, 90 surface radical 298 surface reconstruction 119 surface relaxation 119 surface state 39,188,272 surface state capacity 191 symmetry factor 223, 239, 290 Tafel constant 225, 264, 293 Tafel equation 245 Tafel plot 220 Tafel slope 220 Temkin's adsorption isotherm 296 thermodynamic potential transpassivation 382 transfer coefficient 225 transition metal oxide 36 transpassivation potential 382 transpassive state 382 transport coefficient 247 transport overvoltage 266 tunneling transfer 223 INDEX U undervoltage 349 unitary electrochemical potential of electron 32 imitary energy level unitary ion level 61 unitary real potential of ion 68 unitary surface ion level 63, 65, 67, 71 vacant proton level 78 vacuvun electron level valence band 24 valence band mechanism 251 Volta potential difference 92 W work function 21, 23 zero charge interface 93 .. .Electrochemistry at Metal and Semiconductor Electrodes This Page Intentionally Left Blank Electrochemistry at Metal and Semiconductor Electrodes by Norio Sato Emeritus Professor, Graduate... standard gaseous state and that of the standard stable state can be derived thermodynamically (4) The state of unit activity of hydrated proton at the standard temperature 25X! and pressure atm.:... polarization 8.1.5 Diffusion and reaction rate 8.2 Electron Transfer at Semiconductor Electrodes 8.2.1 Semiconductor electrodes compared with metal electrodes 8.2.2 The conduction band and the