Influence of Ellipsoidal Energy Surfaces on the Differential Resistance of Schottky Barriers

The tunneling probability has been derived for arbitrary orientations of the ellipsoids with respect to the plane of the barrier. The results are used to calculate the voltage current characteristics for multivalley semiconductors and, in particular, the differential resistivity for the $〈100〉$, $〈110〉$, and $〈111〉$ directions of $n$-type germanium. For the particular cases studied, only a weak dependence of the tunneling current on orientation is predicted. The discrepancy between theory and the experimental results of Conley et al. is still unresolved.