Band Structure, Deformation Potentials, and Carrier Mobility in Strained Si, Ge, and SiGe Alloys

Using nonlocal empirical pseudopotentials, we compute the band structure and shear deformation potentials of strained Si, Ge, and SiGe alloys. Fitting the theoretical results to experimental data on the phonon-limited carri er mobilities in bulk Si and Ge, the dilatation deformation potential $\Xi_{d}$ is found to be 1.1 eV for the Si $\Delta$-minima, -4.4 eV for the Ge $L$-minima, corresponding to a value for the valence band dilatation deformation potential $a$ of approximately 2 eV for both Si and Ge. The optical deformation potential $d_{0}$ is found to be 41.45 and 41.75 eV for Si and Ge, respectively. Carrier mobilities in strained Si and Ge are then evaluate d. The results show a large enhancement of the hole mobility for both tensile and compressive strain along the [001] direction, but only a modest enhancement (approximately 60\%) of the electron mobility for tensile biaxial strain in Si. Finally, from a fit to carrier mobilities in relaxed SiGe alloys, the effective alloy scattering potential is determined to be about 0.5 eV for electrons, 0.9 $\pm$ 0.1 eV for holes, and the low-field mobilities in strained alloys can be evaluated. The results show that alloy scattering completely cancels any gain expected from the lifting of the valleys/bands degeneracy caused by the strain.