THE POTENTIAL DEPENDENCE OF THE RATE-CONSTANT FOR CHARGE-TRANSFER AT THE SEMICONDUCTOR-REDOX ELECTROLYTE INTERFACE

The kinetics of charge transfer at the semiconductor-redox electrolyte interface is described in terms of the Gurney-Gerischer-Marcus (GGM) model(1) by using nuclear configuration potential energy diagrams, ele ctronic configuration potential energy diagrams, density of state dist ributions and rate constant distributions. The model of identical para bolas for the nuclear configuration diagrams is used; this leads to Ga ussian oxidant and reductant distribution functions, g(E), where E is the vertical transition (Franck-Condon) energy.(1) The rate constant d istribution, k(E), is obtained from the overlap between occupied and u noccupied state distribution functions of the semiconductor and redox electrolyte. Integration of k(E) gives the rate constant which is calc ulated as a function of the Helmholtz potential, V-H, for various valu es of the reorganization energy, E(reorg). Three types of semiconducto r are considered: intrinsic, doped and highly doped. For intrinsic sem iconductors the charge transfer rate constant is relatively small and involves both the conduction and valence bands. For symmetric charge t ransfer (zero energy change, E(0,0), for the reaction) both oxidation and reduction occur between the redox electrolyte and both bands of th e semiconductor. For unsymmetrical reactions, charge transfer tends to involve only one of the bands; for net reduction, the valence band is involved, whereas for net oxidation the conduction band is involved. For doped semiconductors the rate constant is larger and only one band is involved; for n-type it is the conduction band, and for p-type it is the valence band. For highly doped semiconductors with the Fermi le vel in either the conduction or valence bands, the rate constant is ev en larger and only one band is involved. Changes in Helmholtz potentia l affect k(E) in a similar way to that for metals. However, unlike for metals,(1) the calculated Tafel plots for highly doped n-type semicon ductors are shown to exhibit a Marcus inversion region. This is a cons equence of the energy gap between conduction and valence bands of the semiconductor. For doped semiconductors, changes in the Helmholtz pote ntial also produce a maximum in the Tafel plot and because of the rela tively low currents involved this maximum should be experimentally obs ervable. For intrinsic semiconductors, variation of Helmholtz potentia l without inclusion of band bending in the semiconductor produces unex pectedly low Tafel slopes which are related to the ratio of the band g ap to the reorganization energy, so that the larger the ratio the smal ler the Tafel slope. This unexpected result, which amounts to an assum ption of band edge unpinning, is shown to; accurately account for the experimentally observed Tafel slopes for reduction at n-WSe2 of the di methylferrocenium ion in acetonitrile.(2)