Photoluminescence, recombination rate, and gain spectra in optically excited n-type and tensile strained germanium layers

We theoretically investigate the optical properties of photo-excited biaxially strained intrinsic and n-type doped Ge semi-infinite layers using a multi-valley effective mass model. Spatial inhomogeneity of the excess carrier density generated near the sample surface is considered. Strain effects on the band edges, on the band dispersions, and on the orbital compositions of the near gap states involved in radiative recombinations are fully taken into account. We obtain, as a function of the distance from the sample surface, the energy resolved absorption/gain spectra resulting from the contribution of the radiative direct and phonon-assisted band-to-band transitions and from the intra-band free carrier absorption. Photoluminescence spectra are calculated from the spatially dependent spontaneous radiative recombination rate, taking into account energy-dependent selfabsorption effects. For suitable combinations of doping density, strain magnitude, pump power, and emitted photon polarization, we find gain values up to 5800 cm-1.