Valence band properties of relaxed Ge 1− xC x alloys

Abstract

We report hole effective mass calculations of Ge 1− x C x alloys. A 16 × 16 Hamiltonian matrix constructed from the linear combination of atomic orbitals with spin-orbit interaction terms is used for the calculations. The properties of alloys are calculated under the virtual crystal approximation. The 1 meV constant energy surface below the valence band edge is used to determine the nominal hole effective masses. Calculations are carried out by taking the diamond split-off energy Δ E s − o(C) as 0 and 6 meV, respectively. In both cases, the light hole band results of Ge 1− x C x alloys agree to within less than 1%. The effective masses of light hole increase monotonically from 0.078 m 0 (for pure Ge) to 0.19 m 0 (for pure C) while the non-parabolicity drops rather monotonically. The heavy hole effective masses of the alloys show a highly non-linear dependence on the carbon content ( x). The results in both cases are indistinguishable from x = 0.0 to about x = 0.9; it decreases slightly from x = 0.0 to x = 0.5 and increases slowly from x = 0.5 to x = 0.9. The values increase for x > 0.9. With Δ E s − o(C) = 0 meV, there is an abrupt increase by a factor of two from x = 0.97 to x = 1.0 to a value of 0.89 m 0. For Δ E s − o(C) = 0 meV, a similar trend is found with a lower value of 0.45 m 0 at x = 1.0. The non-parabolicity of the heavy hole masses increases monotonically from x = 0.0 to x = 0.99, and nearly disappears for pure diamond for Δ E s − o(C) = 0 meV, while a monotonie increase of non-parabolicity is found for Δ E s − o (C) = 0 meV from pure Ge to pure C. The interaction between the split-off hole band and the heavy hole band is proposed for the anomalous behavior of the heavy hole effective masses of GeC alloys.