Application of Numerical Methods to the Theory of the Periodic Deviations in the Schottky Effect

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Abstract
Results are reported here for a new theoretical calculation of the periodic deviations from the Schottky line. Numerical methods exclusively were used to solve the Schrödinger equation for the emitted electron, to obtain transmission coefficients, and to calculate emitted current by averaging transmission coefficient over an appropriate electron energy distribution. The numerical calculations were carried out both for a simple-image-force potential barrier and for a similar potential differing only in having a small dip at the metal surface. Results for the simple-image-force potential were in complete agreement with previous analytic results, yielding Schottky deviations of approximately the right period and amplitude but shifted in phase by about a quarter-period from experimentally determined deviations. In disagreement with an earlier analytic-numerical study, results for the slightly altered potential were nearly identical to the simple-image-force results and showed the same phase shift.