Analysis of Lasing From Direct Transition in Ge-on-Si

This paper describes a theoretical investigation of lasing from the direct, Γ-point transition in bulk germanium grown on silicon substrate. Relationships between desired gain and required current density are computed using a screened Hartree- Fock gain model for structures of different tensile strains and n-doping densities. The calculations indicate that for unstrained Ge, high free-carrier absorption and gain saturation may lead to no positive net gain regardless of excitation. With 0.2% tensile strain, the theory predicts possible lasing under laboratory conditions, but uncertainties in free-carrier absorption and Auger losses make difficult definitive predictions for a practical device. Results for 0.6% tensile strain and > 10¹⁹ cm^-3 n-doping gives a more definitive prediction of constant wave lasing with threshold current density of ~1 kA/cm².