A numerical method to compute isotropic band models from anisotropic semiconductor band structures

Abstract

A numerical method for the determination of isotropic band models has been developed and applied to silicon. The resulting model accurately approximates both density of states and group velocity of the corresponding anisotropic band structure, thus providing an excellent agreement with both the collision and nonhomogeneous terms of the Boltzmann transport equation. The model, represented by a simple set of energy-wave vector tables, has been implemented in a Monte Carlo device simulator, but can also be extended to alternative methods for solving the Boltzmann equation. Simulation of homogeneous silicon shows a very good agreement with available experimental data. Comparison with results obtained using the complete anisotropic band structure, both in homogeneous and nonhomogeneous silicon devices, confirms the validity of the model. >