Two formulations of semiconductor transport equations based on spherical harmonic expansion of the Boltzmann transport equation

Two different formulations of semiconductor transport models based on the spherical harmonic expansion of the Boltzmann transport equation are presented. In the one-dimensional (1-D) case, macroscopic transport coefficients are defined through Legendre components of the distribution function. Although either formulation is permissible, the modeling of transport coefficients in one of the formulations is more tractable than the other. The validity of the Einstein and other relations are also examined. The two different transport formulations are then applied to the hydrodynamic simulation of an n⁺-n-n⁺ structure and results are compared with the Monte Carlo simulation data