Stability Analysis of a Multigroup Model for the Boltzmann Transport Equations of Carriers and Phonons

We present a direct solution method to the Bloch‐Boltzmann‐Peierls equations governing the transport of carriers and optical phonons in semiconductors. This approach is based on a multigroup formulation of the original equations, which still contains both the full quantum statistics of carriers and phonons and a very general description of the carrier band structure. It allows the investigation of the particle distributions of arbitrary anisotropies with respect to a main direction. Concerning the mathematical properties of the deduced transport model, we prove a Boltzmann H‐theorem for the obtained evolution equations. The equilibrium solution of the multigroup model is compared with that of the original Bloch‐Boltzmann‐Peierls equations. Numerical results are given for relaxation processes of hot electrons and hot phonons.