Modelling the lattice dynamics in Si(x)Ge(1-x) alloys.

The development of simplified models for the simulation of thermodynamic and thermal transport properties in random alloys is of great importance. In this paper we show how a simple second nearest neighbour model can reliably capture the lattice dynamics of Si(x)Ge(1-x) alloys. The model parameters are extracted from DFT-calculated force constant matrices for pure Si, pure Ge and the Si0.5Ge0.5 ordered alloy. We extract the nearest neighbour contributions directly from density functional theory, whereas effective interactions are obtained for the second nearest neighbour contributions. We demonstrate how the thermal properties, including the expansion coefficient, can be reliably reproduced and that the model is transferable to random Si(x)Ge(1-x) alloys.