Modeling interface roughness scattering with incorporation of potential energy and wave-function fluctuations: Enhancing mobility in AlN/GaN digital alloys

Interface roughness (IFR) scattering significantly impacts the mobility of two-dimensional electron gases (2DEGs) in heterostructures. While existing models for IFR scattering have advanced our understanding, they have notable limitations. The model developed by Jin et al. in 2007, while incorporating a realistic barrier height and roughness-induced changes in potential and subband wave-functions, employs a first-order roughness expansion. The formulation introduced by Lizzit et al. in 2014, although avoiding the first-order approximation for better higher-order effect modeling, omits IFR-induced change in electron density distribution. To address these limitations, we introduce a novel model that comprehensively accounts for all IFR-induced effects while avoiding any expansion approximations, by incorporating IFR-modified subband energies and wave-functions obtained from the numerical solution of the Schrödinger equation during the calculation of IFR scattering matrix elements. In addition, we have included models for other relevant scattering mechanisms, including charged dislocation lines, ionized impurities, acoustic phonons, and polar optical phonons. A comprehensive numerical analysis of carrier mobility has been performed for an AlN/GaN high electron mobility transistor, yielding results consistent with experimental data. Furthermore, to investigate the impact of device architecture on 2DEG mobility, we study the effects of layer thickness and modulation doping profiles in AlN/GaN digital alloys. Our findings reveal strategies for engineering high mobility at elevated 2DEG concentrations, potentially advancing the development of high-performance semiconductor devices.