Electron transport and ionization in silicon at high fields

Abstract

The saturated drift velocity measured for electrons at high fields is inconsistent with Shockley's model for impact ionization in silicon. It is explained in terms of a field-dependent mean free path for high energy phonon creation in the electric field direction, electrons creating a high energy phonon as soon as they have acquired sufficient energy from the field. Assuming that the electron wavepacket travels at the saturated drift velocity without dispersion, it can be shown that the increased scattering rate at high fields must result in a large spread in the carrier energy. If a drifted Maxwellian distribution is assumed, a unique expression can be obtained for the carrier temperature T * which is in good agreement with the measured field dependence of the ionization coefficient. In this model, a cylindrical hot carrier distribution must be assumed with the hot carrier energy in a plane perpendicular to the applied field. Exact calculations of the magneto-resistance of such a distribution can be made verifying that the drift velocity is indeed saturated.