We calculate band-to-band radiative transition rate spectra in pure Ge as functions of applied tensile strain, heavy doping, charge injection density, and temperature. Direct and indirect phonon-assisted transitions are considered. Deformation potential theory is adopted to describe the conduction and valence near-gap edges. Biaxial strain has required appropriate treatment of system anisotropy through the evaluation of the mass tensor components for the different bands involved in the studied transitions. Population distribution in the $\Gamma$ and $L$ conduction valleys and in the valence states near $\Gamma$ have been evaluated accordingly considering the degeneracy condition of the sample, induced by high doping and high injection charge density. Also the effect of strain on the dipole matrix elements have been properly taken into account. The energy-resolved near-infrared spontaneous recombination spectra and the TE and TM polarized absorption/gain spectra have been obtained for a broad range of $n$-type doping, strain values, and excitation densities. We conclude that, despite the free carrier losses, net gain values as high as 6000 cm${}^{-1}$, are achievable for doping density and strain values reported in the literature.

• Received 4 March 2013

DOI:https://doi.org/10.1103/PhysRevB.87.235313