Deterministic kinetic solvers for charged particle transport in semiconductor devices

Abstract

Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation: (Formula Presented.) where f represents the electron probability density function (pdf) in phase space k at the physical location x and time t. ħ and e are physical constants; the Planck constant divided by 2π and the positive electric charge, respectively. The energy-band function ε is given by the Kane non-parabolic band model, which is a non-negative continuous function of the form (Formula Presented.) where m* is the effective mass and α is the non-parabolicity factor. In this way we observe that setting α = 0 in Equation (7.1.2) the model is reduced to the widely used parabolic approximation.