Brillouin zone unfolding method for effective phonon spectra

Thermal properties are of great interest in modern electronic devices and nanostructures. Calculating these properties is straightforward when the device is made from a pure material, but problems arise when alloys are used. Specifically, only approximate bandstructures can be computed for random alloys and most often the Virtual Crystal Approximation (VCA) is used. Unfolding methods [T. B. Boykin, N. Kharche, G. Klimeck, and M. Korkusinski, J. Phys.: Condens. Matt. 19, 036203 (2007).] have proven very useful for tight-binding calculations of alloy electronic structure without the problems in the VCA, and the mathematical analogy between tight-binding and valence-force-field approaches to the phonon problem suggest they be employed here as well. However, there are some differences in the physics of the two problems requiring modifications to the electronic structure approach. We therefore derive a phonon alloy bandstructure (vibrational mode) approach based on our tight-binding electronic structure method, modifying the band-determination method to accommodate the different physical situation. Using the method, we study In$_x$Ga$_{1-x}$As alloys and find very good agreement with available experiments.