Investigation of electron mobility and saturation velocity limits in gallium nitride using uniaxial dielectric continuum model

Abstract

Here we introduce a uniaxial dielectric continuum model with temperature-dependent phonon mode frequencies to study temperature- and orientation-dependent polar-optical-phonon limited electron mobility and saturation velocity in uniaxial semiconductors. The formalism for calculating electron scattering rates, momentum relaxation rates, and rate of energy change as a function of the electron kinetic energy and incident electron angle with respect to the c-axis are presented and evaluated numerically. Electron–longitudinal-optical-phonon interactions are shown to depend weakly on the electron incident angle, whereas the electron–transverse-optical-phonon interactions around the emission threshold energy are observed to depend strongest on the electron incident angle when varied from π/4 to π/2 (with respect to the c-axis). We provide electron mobility and saturation velocity limits in different GaN crystal orientations as a function of temperature and electron concentration. At room temperature and for an electron density of 5 × 1018 cm−3, electron mobility limit of ∼3200 cm2/V s and electron saturation velocity limit of 3.15 × 107 cm/s are calculated. Both GaN electron mobility and saturation velocity are observed to be governed by the longitudinal-optical-phonon interaction, and their directional anisotropy is shown to vary less than 5% as the electron incident angle with respect to the c-axis is varied from 0 to π/2. Overall, we develop a theoretical formalism for calculating anisotropic properties of uniaxial wurtzite semiconductors.