Combining the Scattering Matrix and Spherical Harmonic Methods for Semiconductor Modeling

Abstract

The spherical harmonics (SH) are applied to realize the scattering matrix method of carrier transport modeling. Using the spherical harmonics has the advantage of reducing the matrix by approximately a factor of 10 less than the previous discrete basis approach[l]. To realize the approach, new spherical-harmonic functions are defined to overcome difficulties associated with orthogonality. The scattering matrix is calculated using Monte-Carlo(MC) techniques to populate the new basis functions. As a initial step towards demonstrating the accuracy of the new mathematical formulation, we calculate the electron energy distribution functions for different homogeneous fields. We also calculate the space-dependent average energy and velocity for a step electrical field, and show agreement with Monte Carlo simulations.