TCAD Modeling of High-Field Electron Transport in Bulk Wurtzite GaN: The Full-Band SHE-BTE

Gallium Nitride (GaN) High-Electron Mobility Transistors (HEMTs) actually represent one of the best candidates for medium-high power and radio frequency applications. As they operate at large bias and electric fields, a comprehensive analysis of the high-field transport properties is fundamentals, as hot electrons are expected to play a relevant role for the device reliability. In this perspective, Technology Computer-Aided Design (TCAD) simulations can be a very useful tool for the understanding of the phenomena dominating hot-electron degradation mechanisms. The most-accurate modeling approaches are based on the direct solution of the Boltzmann equation, which is not actually available for the GaN material. In this work, the deterministic solution of the Boltzmann transport equation via the spherical-harmonics expansion (SHE-BTE), as incorporated in a commercial TCAD tool, has been extended to the analysis of GaN electrons. To this purpose, the details of the full-band structure has been derived from DFT calculations as in state-of-art literature works, and the electron density of states,
$g(E)$
, and group velocity
$u_{g}(E)$
, have been calculated for the SHE-BTE for the first time. In addition to this, an accurate calibration of the total scattering rate accounting for nonpolar acoustic and optical carrier-phonon interaction, Coulomb scattering and impact ionization has been carried out against available Monte Carlo data and experiments. The proposed model is also shown to correctly predict the temperature dependence of the electron impact-ionization coefficient and current density up to breakdown.