Model for direct-transition gain in a Ge-on-Si laser

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This paper describes a laser gain model for the direct, Γ-point transition in bulk Ge. The model allows calculation of gain and spontaneous-emission spectra for arbitrary strain, as well as doping and injected carrier densities. Many-body effects are included at the level of the screened Hartree-Fock approximation to account for energy renormalization modifications, especially to the impact of n-doping on magnitude and spectral extension of laser gain. Application of the model is illustrated by predicting the net material peak gain versus injected current density under different combinations of tensile strain and n-doping density.