Frumkin corrections for heterogeneous rate constants at semiconducting electrodes

Abstract

Frumkin corrections for semiconductor electrodes have been evaluated in both depletion and accumulation conditions. In conjunction with the Gouy-Chapman-Stern model, a finite difference approach was used to calculate the potential drop in a depleted semiconductor and in the compact and diffuse layers of the contacting solution as a function of the potential applied to the solid/liquid interface. At potentials greater than 30 mV positive of the flat-band potential E_(fb) the potential drop across the solution accounts for less than 3% of the total potential drop across an n-type semiconductor of dopant density 1 × 10¹⁵ cm⁻³ in a methanolic solution of 1.0 M LiCl. Under these conditions, the concentration of a non-adsorbing, dipositively-charged redox species at the outer Helmholtz plane does not vary from its concentration in the bulk of the solution by more than 2%. This relatively small concentration gradient and potential drop across the Helmholtz layer combine to produce negligible Frumkin correction terms for kinetic data at depleted semiconductor electrodes compared to those for metallic electrodes at the same applied potential relative to the potential of zero charge. Under accumulation conditions, the potential drop across the solution is more significant, and the concentration of redox species at the surface can be as much as twice as great as that in the bulk of the solution. However, these conditions require an applied potential of −1 V relative to E_(fb). Additionally, under all conditions that were simulated, the correction to the driving force used to evaluate the heterogeneous rate constant does not exceed 2% of the uncorrected heterogeneous rate constant.

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