Free-Energy Dependence of Electron-Transfer Rate Constants at Si/Liquid Interfaces

Abstract

Differential capacitance vs potential and current density vs potential measurements have been used to characterize the interfacial energetics and kinetics, respectively, of n-type Si electrodes in contact with a series of one-electron, outer-sphere redox couples. The differential capacitance data yielded values for the electron concentration at the surface of the semiconductor as well as values for the driving force of the interfacial electron-transfer event at Si/CH₃OH−viologen^(2+/+) junctions. The differential capacitance vs potential measurements were essentially independent of the ac frequency imposed on the interface, with linear Bode plots (log|impedance| vs log frequency, at a fixed potential) between ≈10³ and ≈10⁵ Hz, with slopes typically between −0.99 and −1.00. The slopes of C²−E (Mott−Schottky) plots were in excellent agreement with theory, and little frequency dispersion was observed in the x-intercepts of such plots. The conduction band edge of the n-type Si anodes was invariant to within ±40 mV in response to a variation in the redox potential of the solution of greater than 400 mV, indicating "ideal" interfacial energetic behavior of this system with no evidence for Fermi level pinning. From these measurements, the surface-state density of the Si/CH₃OH contact can be estimated as <10¹¹ cm², i.e., less than 1 defect for 10⁴ surface atoms. The current density vs potential plots exhibited a first-order kinetic dependence on the concentration of electrons at the semiconductor surface and a first-order kinetic dependence on the concentration of acceptors in the solution. Rate constants for transfer of charge from the semiconductor to the acceptor were determined as a function of the driving force for the interfacial charge-transfer event. The rate constants varied from 4 × 10⁻¹⁸ cm⁴ s⁻¹ to 6 × 10⁻¹⁷ cm⁴ s⁻¹ and were well fit to Marcus-type behavior, with a reorganization energy of 0.7 eV and a maximum rate constant at optimal exoergicity of 6 × 10⁻¹⁷ cm⁴ s⁻¹. This maximum rate constant value is in excellent agreement with theoretical expectations for transfer of charge from a delocalized carrier in a semiconductor to a one-electron, outer-sphere redox acceptor dissolved in the electrolyte solution.

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