Interrelationship between the saturated drift velocity and impact ionization of electrons in silicon

Abstract

The saturated drift velocity of electrons in silicon is explained in terms of a tight coupling between electrons and optical phonons with an energy of 46.8 meV. In the saturated regime the scattering time is inversely proportional to the electric field, which results in a spread of carrier energies increasing with the electric field. The field dependence of the ionization coefficient may be explained if a drifted Maxwellian distribution is assumed. In this field range the electron temperature T* is due to randomized motion in the plane perpendicular to the electric field direction and is related to the scattering time τ through the relationship kT*=h/τ, where h is Planck's constant. Excellent numerical agreement is found between the theoretical predictions and all experimentally observable quantities.