A self-consistent numerical approach for characterizing the band structures and gain spectrum of tensile-strained and n⁺-doped Ge/GeSi quantum wells

The strain-engineered and n⁺-doped Ge/Ge_x Si_1−x alloy quantum well (QW) has the potential to be light-emitting material for Si-based photonics. Meanwhile, high doping concentration and injection carrier density induce electrostatic potential to the band profile. This effect is known as the carrier screening effect (CSE). So far, the CSE has not been sufficiently investigated in Ge/Ge_x Si_1−x QW. In this work, we analyze the optical gain of a strained Ge/Ge_x Si_1−x QW by means of a Schrödinger–Poisson self-consistent approach. The result shows that the optical gain of the QW is related to the doping profile. The electrostatic potential is important to the optical properties of the indirect-band QW. Without considering the CSE, the optical gain could be underestimated by 22.8%. We designed a doping strategy that alleviates the strain requirement for achieving positive optical gain. For designing Ge/Ge_x Si_1−x alloy material for Si photonics, simulation performed by this method reflects key information for both strain engineering and doping strategy. (paper)