Tight-binding calculation of optical gain in tensile strained [001]-Ge/SiGe quantum wells

It is known that under a tensile strain of about 2% of the lattice constant, the energy of the bottom conduction state of bulk Ge at the Gamma point falls below the minimum at the L point, leading to a direct gap material. In this paper we investigate how the same condition is realized in tensile strained Ge quantum wells. By means of a tight-binding sp(3)d(5)s(*) model, we study tensile strained Ge/Si(0.2)Ge(0.8) multiple quantum well (MQW) heterostructures grown on a relaxed SiGeSn alloy buffer along the [001] direction. We focus on values of the strain fields at the crossover between the indirect and direct gap regime of the MQWs, and calculate band edge alignments, electronic band structures, and density of states. We also provide a numerical evaluation of the MQW material gain spectra for TE and TM polarization under realistic carrier injection levels, taking into account the leakages related to the occupation of the electronic states at the L point. The analysis of the different orbital contributions to the near-gap states of the complete structure allows us to give a clear interpretation of the numerical results for the strain-dependent TM/TE gain ratio. Our calculations demonstrate the effectiveness of the structures under consideration for light amplification.