The role of grain boundary and alloy scattering within the Callaway model to calculate lattice thermal conductivity in GaN/AlN superlattice

The grain boundary and alloy scattering within the Debye-Callaway model were introduced to calculate the temperature-dependent lattice thermal conductivity (LTC) in the GaN/AlN superlattice. The superlattice layers are assumed to be grains, and the sample is then treated as a multigrain material. The computations include various physical parameters related to Aluminum alloy compositions, such as Debye temperature, atomic mass, lattice volume, density, alloy scattering factor and deformation energy. In general, the sample size effect on LTC in this superlattice structure was similar to any single component solids, but it has a significant influence from the grain boundaries represented by the thickness of layers in the form of ${LTC}_{Peakpoint.}=5.9925e^{0.0005L^2}$ at the peak point maximum and $LTC\left(600K\right)=0.344L$ at 600K, $L$ is the sample size. The dislocations in these samples are controlled by the inbuilt AlN layers with the dependence of $N_{Disl.}=-0.542L_{AlN}+7.4$.