A Novel Approach to Spherical Harmonics Expansion for Electron Transport in Semiconductors

TL;DR

This paper develops a new spherical harmonics expansion method for modeling charge transport in semiconductors, incorporating non-parabolic band effects and providing explicit solutions for stationary, homogeneous cases.

Contribution

It introduces a novel approach to spherical harmonics expansion that accurately models electron transport with detailed treatment of band structures and energy range modifications.

Findings

Derived equations from Boltzmann kinetic equation for charge transport.

Explicit solutions for stationary and homogeneous cases.

Validated asymptotic solutions against numerical results.

Abstract

A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic band approximation are treated in detail. In these cases, the set of equations is equivalent to those obtained in the spherical-harmonics expansion. Stationary and homogeneous solutions are explicitly treated. In order to solve numerically the equations, a cut in the energy range is introduced. The modified model maintains the physical characteristics of the original equations. The solution of an asymptotic equation is found and compared to the numerical solutions.