Theoretical Models of Hot Carrier Effects at Metal‐Semiconductor Electrodes

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© 1992 ECS - The Electrochemical Society
, , Citation Karl W. Frese Jr. and C. Chen 1992 J. Electrochem. Soc. 139 3234 DOI 10.1149/1.2069059

1945-7111/139/11/3234

Abstract

The physical and electrochemical properties of hot carriers at metallized semiconductor electrodes in contact with a redox electrolyte are described. Theoretical ballistic mean‐free paths, , for hot carriers in Ag, Cu, Au, Al, Ru, Pd, and Pt, were calculated as a function of excess energy above the Fermi energy. At 0.5 eV hot, was 580 Å for Ag, 420 Å for Cu and Au, 90 to 130 Å for the remaining metals, with Pt having the lowest value. Using the Marcus‐Gerischer model, currents at the equilibrium potential were calculated as a function of built‐in barrier, film thickness, and reorganization energy for Au and Pt. The current for a simple outer sphere electron transfer reaction is predicted to be enhanced when the film thickness becomes . For Au/n‐Si diodes, the enhancement for reorganization energy, , 100 Å Au and built‐in barriers of 0.4 to 0.6 eV are predicted to be 60 to 10 times. Larger enhancements are predicted for larger reorganization energies, the maximum effect being predicted for . The stage most likely to limit observation of hot carriers effects is slow vibrational or vibrational‐rotational relaxation of the redox acceptor or donor. By a combination of theoretical calculations and empirical data, we conclude that it is possible to observe hot carrier effects under real conditions. Experimental data that support the theoretical development and the hot carriers concept are presented in the following paper.

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