Variational formulation of the steady Boltzmann equation for semiconductors and applications

摘要

We present a variational formulation of the steady Boltzmann equation for semiconductors. In this formulation, the distribution function is replaced by a weighted distribution function, and the symmetry of the drift operator is obtained by using the parity operator We show that the solutions of the Boltzmann equation for the weighted distribution function are stationary functions of a suitable functional, which takes into account realistic boundary conditions. After introducing a general numerical framework, the proposed approach is tested in the bulk case, by computing an approximate expression for carrier mobility in silicon.