A Deterministic Boltzmann Equation Solver Based on a Higher Order Spherical Harmonics Expansion With Full-Band Effects

In this paper, a deterministic Boltzmann equation solver based on a higher order spherical harmonics expansion, including full-band (FB) effects, is presented. An anisotropic band structure for the conduction band with an invertible energy/wave vector relation has been generated by matching several moments of the group velocity of the silicon FB structure. A generalized formulation of the free-streaming operator is presented, which is stabilized according to the maximum entropy dissipation scheme. From the numerical results for various systems such as silicon bulk, an n⁺-n-n⁺ structure, and SiGe heterojunction bipolar transistors, it can be concluded that the new model improves significantly the accuracy of the Boltzmann solver compared to previous band models without degrading the numerical stability.