Theory of Optical Gain of Ge-SixGeySn1−x−y Quantum-Well Lasers

We develop a theoretical model for optical gain of a strained Ge--Si_xGe_ySn_1-x-y quantum-well (QW) structure. By using a ternary Si_xGe_ySn_1-x-y material system as the barriers, a tensile strained germanium QW with a direct band gap for the electron and hole confinements can be realized. We show our theoretical model for the strained band structure and the polarization dependent optical gain spectrum of the tensile strained germanium QW laser taking into account the carrier occupations in both the Gamma- and L-valleys of the conduction band. Reasonable material parameters are used to estimate the transition energy, optical gain spectrum, and effects of the carrier leakage in presence of the quantized subbands