Ab-Initio calculated Low field transport properties in Supercells and its application to Alloys

To investigate the transport properties in random alloys, it is important to capture the alloy disorder using supercells. In case of supercells, the self-image interaction error between the impurities is reduced and translational symmetry is explicitly imposed over larger length scales which traditional methods like Virtual Crystal Approximation fails to capture. In this work, we have investigated the polar optical phonon (POP) limited transport properties from first-principles calculations using supercells without unfolding the phonon dispersion. First, the phonon properties of GaN supercells are calculated and verified by comparing with the primitive cell. To validate our methods of supercell based mobility calculations, the Boltzmann Transport Equation is solved using Rode’s method to compare the POP and IIP limited mobility in the 4 atom GaN primitive cell and 12,40,32 atom GaN supercell. For random Al_xGa_1-xN alloy systems, the phonon dispersion properties are calculated using Density Functional Perturbation Theory on a 40-atom random Al_xGa_1-xN system. Solving the Boltzmann Transport Equation iteratively our calculations predict a room temperature mobility of 189 cm²/V-s at x=0.25 and 149 cm²/V-s at x=0.5 Al fractions at n=1e18cm^-3 electron concentration which show that along with alloy scattering, electron-phonon scattering also plays an important role at room temperature. This technique opens the path for calculating phonon limited transport properties in random alloy systems.