IMPACT IONIZATION WITHIN THE HYDRODYNAMIC APPROACH TO SEMICONDUCTOR TRANSPORT

We present a rigorous analytical treatment of band-band impact ionization in semiconductor high-field transport. The microscopic electron impact ionization scattering time is calculated for the general case of three different anisotropic parabolic bands (one for the initial valence electron, the other two for the two final conduction electrons) and an arbitrarily shaped band for the impact-ionizing energetic conduction electron. In this derivation the wave vector dependence of the matrix element is accounted for in contrast to previous calculations. The total impact ionization rate in both direct and indirect semiconductors and the associated energy relaxation rate in direct semiconductors are expressed analytically in a universal scaling form as a function of the electron temperature and a few band-structure parameters like effective masses, energy gap, and the distance in k-space between the band extrema (in case of an indirect semiconductor). Such expressions can be used in the hydrodynamic model as approximations for the collision terms arising in a moment expansion of the Boltzmann equation.