Electronic band structure of semiconductor alloys: From ab initio to k.p via computational alchemy, on example of Ge1-xSnx alloy

First principles calculations are increasingly often used in device modelling. However, due to their complexity and high computational costs, simplified but reliable models are of great value. In this work, we present an original method of finding the 30-band k.p parameters on an example of Ge1-xSnx alloy. It allows to reproduce the electronic band structure in the full BZ and in the full composition range. The method uses the state-of-the-art supercell based ab initio calculations as the reference. A direct fitting of the k.p parameters from ab initio supercell band structures is difficult since the assignment of the k.p bands to correct eigenvalues of the reference band structures may be ambiguous. For this reason, the ab initio computational alchemy is used as an intermediate step. Owing to its properties, the supercell unfolded eigenvalues are approximated with continuous curves, which enables a straigthforward way to fit the 30-band k.p parameters. As an example of application, the optical gain in bulk Ge0.91Sn0.09 has been calculated. The advantage of using the 30-band over the often used 8-band k.p approach is clearly seen. The presented method can be applied to any mixed, isovalent and isostructural system, eg. III-V, or II-VI alloys.