Tensile-strained, n-type Ge as a gain medium for monolithic laser integration on Si

We analyze the optical gain of tensile-strained, n-type Ge material for Si-compatible laser applications. The band structure of unstrained Ge exhibits indirect conduction band valleys (L) lower than the direct valley (F) by 136 meV. Adequate strain and n-type doping engineering can effectively provide population inversion in the direct bandgap of Ge. The tensile strain decreases the difference between the L valleys and the T valley, while the extrinsic electrons from n-type doping fill the L valleys to the level of the T valley to compensate for the remaining energy difference. Our modeling shows that with a combination of 0.25% tensile strain and an extrinsic electron density of 7.6×10¹⁹/cm³ by n-type doping, a net material gain of ∼400 cm^-1 can be obtained from the direct gap transition of Ge despite of the free carrier absorption loss. The threshold current density for lasing is estimated to be ∼6kA cm^-2 for a typical edge-emitting double heterojunction structure. These results indicate that tensile strained n-type Ge is a good candidate for Si integrated lasers.