Variational formulation of the steady Boltzmann equation forsemiconductors and applications

摘要

We present a variational formulation of the steady Boltzmann equa-tion for semiconductors. In this formulation, the distribution function is replaced bya weighted distribution function, and the symmetry of the drift operator is obtainedby using the parity operator. We show that the solutions of the Boltzmann equationfor the weighted distribution function are stationary functions of a suitable func-tional, which takes into account realistic boundary conditions. After introducing ageneral numerical framework, the proposed approach is tested in the bulk case, bycomputing an approximate expression for carrier mobility in silicon.