Band structure and optical gain of tensile-strained germanium based on a 30 band k⋅p formalism

Abstract

We have investigated the band structure of tensile-strained germanium using a 30 band k⋅p formalism. This multiband formalism allows to simultaneously describe the valence and conduction bands, including the L, Δ, and Γ valleys. We calculate the energy band variation as a function of strain and obtain that the crossover from indirect to direct band gap occurs for a tensile in-plane strain of 1.9%. The effective masses of density of states are deduced from the calculated conduction and valence band density of states. Significant deviations are observed as compared to the effective masses of density of states values of unstrained bulk germanium. We finally calculate the optical gain that can be achieved with tensile-strained bulk germanium. An optical gain larger than 3000 cm−1 is predicted for a carrier density of 1×1018 cm−3 and a 3% in-plane biaxial strain. This optical gain is larger than the one of GaAs calculated with the same formalism and is much larger than the experimental free-carrier absorption losses. This gain should be sufficient to achieve lasing in these structures.