  To investigate the transport properties in random alloys, it is important to
model the alloy disorder using supercells. Though traditional methods like
Virtual Crystal Approximation (VCA) are computationally efficient, the local
disorder in the system is not accurately captured as artificial translational
symmetry is imposed on the system. However, in the case of supercells, the
error introduced by self-image interaction between the impurities is reduced
and translational symmetry is explicitly imposed over larger length scales. In
this work, we have investigated the Effective Phonon Dispersion (EPD) and
transport properties, from first principle calculations using supercells in
AlxGa1-xN alloy systems. Using our in-house developed code, the EPD of AlGaN is
obtained and the individual modes are identified. Next, we discuss our in-house
developed method to calculate low-field transport properties in supercells.
First to validate our methods we have solved the Boltzmann Transport Equation
using Rode method to compare the phonon limited mobility in the 4 atom GaN
primitive cell and 12 atom GaN supercell. Using the same technique, we have
investigated the low field transport in random AlxGa1-xN alloy systems. Our
calculations show that along with alloy scattering, electron-phonon scattering
may also play an important role at room temperature and high-temperature device
operation. This technique opens up the path for calculating phonon-limited
transport properties in random alloy systems.
