An Efficient Approach to Include Full-Band Effects in Deterministic Boltzmann Equation Solver Based on High-Order Spherical Harmonics Expansion

We present an efficient method to include full-band-structure effects for the case of a silicon conduction band in a deterministic Boltzmann equation solver based on the high-order spherical harmonics expansion method. This method employs the exact density of states and the group velocity obtained from band structure calculations, and it eliminates the modulus of the wave vector in the formulation such that an explicit invertible dispersion relation is not required. While the present method does not require additional central-processing-unit time and memory, compared with the analytic band model, the simulation results are significantly improved and in excellent agreement with those from the full-band Monte Carlo simulations and from an approach based on an invertible anisotropic band that matches several moments of the group velocity of the full band structure.