Statistical studies of random silicon-germanium alloys using electronic structure calculations

Random alloys are relevant for many applications. One example is silicon-germanium which is used for high frequency devices like heterojunction-bipolar transistors. We therefore investigate the electronic structure of Si1−xGex alloys in the entire composition range 0≤ x≤ 1. For our study we use density functional theory in combination with bulk models of the alloys. To describe the band gap precisely we use the pseudopotential projector shift method as implemented in QuantumATK 18.06. We perform a random generation of Si1−xGex structures to get statistical distributions of the electronic properties. After optimizing the structure we evaluate the band structure by averaging equivalent directions in the Brillouin zone. The mean of the band gap is in good agreement with experimental reference data. We also demonstrate wide variations of the band gap, which are in the range of about 10 %. Further properties, such as the lattice constant and the formation energy are studied as well. Finally, we investigated also the impact of additional carbon dopants in the silicon-germanium alloy.