Model for the Surface Potential Barrier and the Periodic Deviations in the Schottky Effect

Abstract

Although most of the features of the observed periodic deviations in the Schottky effect are in good agreement with predicted behavior, there is still disagreement between theory and experiment in the phase and amplitude of the deviations. It has been suggested that a possible origin of this difficulty is the use of the simple image force barrier at the surface of the metal. In this paper a model for the surface potential barrier is developed which is based on the quantum-mechanical calculation made by Bardeen on the form of the potential at the surface of a sodium-like metal, and the analysis of Sachs and Dexter on the quantum limits of the image-force theory. Employing this model, the periodic deviations are recalculated using essentially the mathematical formalism developed by Juenker and his co-workers. Certain computational refinements are introduced in the averaging of the transmission coefficient. The results are compared with previous theory and experiment in terms of two parameters which characterize the form of the surface potential; the surface reflection coefficient $\left|\mu \right|$ which appears as a factor in the amplitude, and the phase factor $\delta$. These computed values are 0.6 and 2.6 respectively, as compared to single mean experimental values of 0.4 and 2.2 for the highly refractory metals, and to previous theoretical values of 0.2 and 3.7. The surface reflection coefficient calculated for the present model is in satisfactory agreement with recent experiments on the elastic scattering of slow electrons from the surface of a metal.