Optical gain of germanium infrared lasers on different crystal orientations

We investigate the effects of biaxial tensile stress and n-type doping on the direct-transition optical gain in germanium infrared lasers, in which three differently oriented systems of (0 0 1), (1 1 0) and (1 1 1) Ge are analysed. We show our theoretical model for the strain tensor, strained electronic band structure, carrier occupation, optical gain and free-carrier absorption to evaluate the net optical gain under different strain and n-doping levels. Our analysis shows that for a large strain, (0 0 1) Ge can produce a larger optical gain than the others due to its clear direct-bandgap behaviour for mid-infrared lasers. For a moderate strain combined with the use of n-type doping, (1 1 1) Ge can generate a larger net optical gain than the others for near-infrared lasers. Our modelling results provide an insight into the improvement of optical emission in Ge for lasers.