Hole mobility in SiGe alloys from first principles.

First principles density functional theory is used to calculate the mobility of holes in Si$_{1-x}$Ge$_{x}$ alloys as a function of alloy composition. The alloy host is modelled within the virtual crystal approximation (VCA) using supercell techniques. The scattering matrix for carrier scattering in the presence of a Ge or Si substitutional atom in the VCA lattice is determined from the resultant energy splitting in the valence bands. The effect of the spin-orbit interaction is included in these calculations. The mobility is obtained from the scattering rate using the Boltzmann transport equation in the relaxation time approximation.