High-Field Conductivity of the〈111〉Valleys of Ge

We have calculated the distribution function and drift velocity of electrons in the $〈111〉$ valleys of Ge. The model used is essentially a one-valley model for an electric field in the [100] direction and without any electron transfer to higher valleys. The nonparabolicity of the conduction band and the nonclassical occupation of the acoustic modes are taken into account. The coupling constants were obtained from a fit to the low-field mobility, and because of the inclusion of nonparabolicity, the optical-mode coupling was smaller than previously used. The calculated drift velocity is in excellent agreement with the results of Ruch and Kino, and shows a low-temperature negative resistance which vanishes at somewhat above 77 °K. Although the electron energies at an electric field of several thousand V/cm indicate that some electron transfer to higher valleys is probably taking place, it is likely that this transfer is not primarily responsible for the observed negative resistance, but rather results in the resumption of a positive conductivity at still higher electric fields.