A deterministic Boltzmann solver for GaAs devices based on the spherical harmonics expansion

Abstract

A deterministic Boltzmann solver has been developed using a spherical harmonics expansion and is applied to gallium arsenide. The Newton-Raphson scheme is used to solve the nonlinear Boltzmann and Poisson equations. Inclusion of polar optical phonons and their projection onto spherical harmonics is performed. The Pauli exclusion principle is included with the assumption of an isotropic band structure for GaAs. Results are shown for a bulk system and n + -ni-n + structures, which emphasize the impact of the Pauli principle. AC simulations show plasma oscillations of the GaAs devices.

Inclusion of the Pauli principle in a deterministic Boltzmann equation solver based on a spherical harmonics expansion

“…Note that the polar optical phonon scattering, which is important for III-V materials, cannot be properly treated as a velocity-randomizing one. In this case, higher-order expansions of the transition rate should be considered in the simulation, as shown in [15]. Instead, in [15], another simplification is obtained using the assumption of an isotropic band structure for GaAs material.…”

“…In this case, higher-order expansions of the transition rate should be considered in the simulation, as shown in [15]. Instead, in [15], another simplification is obtained using the assumption of an isotropic band structure for GaAs material. Screening of impurity scattering is calculated based on Fermi-Dirac statistics [1].…”