Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys

TLDR

The authors employed nonlocal empirical pseudopotentials to calculate band structures and deformation potentials of strained Si, Ge, and SiGe alloys, then used these results to evaluate carrier mobilities under strain and to fit relaxed SiGe data, yielding effective alloy scattering potentials and low‑field mobilities. The study determined dilatation deformation potentials of 1.1 eV (Si Δ) and –4.4 eV (Ge L), optical deformation potentials of ~41.5 eV, and showed that strain markedly boosts hole mobility but only modestly improves electron mobility, while alloy scattering negates any strain‑induced mobility gains.

Abstract

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 carrier mobilities in bulk Si and Ge, the dilatation deformation potential Ξd is found to be 1.1 eV for the Si Δ 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 d0 is found to be 41.45 and 41.75 eV for Si and Ge, respectively. Carrier mobilities in strained Si and Ge are then evaluated. 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 0.7 eV for electrons, 0.9±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.