Theoretical insights into the amplified optical gain of hexagonal germanium by strain engineering

Strain engineering is a versatile technique used to tune the electronic and optical attributes of a semiconductor. A proper degree of strain can induce the optimum amount of gain necessary for light-emitting applications. Particularly, photonic integrated chips require an efficient light-emitting material that can be easily assimilated into complementary metal-oxide semiconductor (CMOS) technology. Germanium falls in the same group of the periodic table as silicon, and thus, it completely complies with Si technology. Hence, we investigated extensively the electronic and optical properties of hexagonal germanium for both compressive and tensile strains using density functional theory. The electronic bandstructure, dielectric function, absorption, and reflectivity were calculated by employing a modified Becke–Johnson (mBJ) potential including spin–orbit coupling for uniaxial strains ±0.5–5%. We calculated the effective masses at various symmetry points and determined other band parameters, including the crystal field splitting and spin–orbit splitting energies. The partial, projected, and total density of states were discussed in great depth to unveil the characteristics of the energy states that take part in optical transitions. Finally, the optical gain for the semiconductor was calculated as a function of strain. After the band inversion phenomenon, hex-Ge generates a huge increase in the amplification and bandwidth of optical gain. This results from the increased electron concentration in Γ(−)(7c) state and enhanced momentum matrix between the p-character valence states and sp-hybridized states of the conduction band. Conduction band to light hole recombination is observed to improve the light emission to a great extent.