IMPACT IONIZATION WITHIN THE HYDRODYNAMIC APPROACH TO SEMICONDUCTOR TRANSPORT

We present a rigorous analytical treatment of band-band impact ionizat ion in semiconductor high-field transport. The microscopic electron im pact ionization scattering time is calculated for the general case of three different anisotropic parabolic bands (one for the initial valen ce electron, the other two for the two final conduction electrons) and an arbitrarily shaped band for the impact-ionizing energetic conducti on electron. In this derivation the wave vector dependence of the matr ix element is accounted for in contrast to previous calculations. The total impact ionization rate in both direct and indirect semiconductor s and the associated energy relaxation rate in direct semiconductors a re expressed analytically in a universal scaling form as a function of the electron temperature and a few band-structure parameters like eff ective masses, energy gap, and the distance in k-space between the ban d 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.