Theory of near infra-red germanium lasers

Due to major advances in silicon photonics technology and the importance of having a silicon-compatible laser operating in the 1.3 - 1.55 micron communications wavelength window. There is currently an intense interest in the optical properties of germanium, which has a direct band gap transition in this wavelength range. The Ge band structure can be engineered using biaxial or uniaxial strain in order to achieve optical gain. Recently, both optically pumped and electrical injection pumped lasing have been reported in Ge-on-Si devices. This work aims to perform gain modeling in a germanium laser grown on a silicon substrate which operates in the near infrared wavelength communications band.
A description of the background theory of the variation of the relevant electronic band structure properties of Ge with the applied strain is given. Shifts of the conduction and valence band edges with strain (biaxial and uniaxial) applied to Ge grown on substrates of different orientations has been investigated using the linear deformation potential and k.p methods.
In order to make Ge behave as a direct band gap material, and to have a good electron injection efficiency, an investigation of the combination of the applied strain and doping density on direct band gap and injected carrier efficiency were carried out at 0 K, for both bulk Ge and Ge quantum wells.
At finite temperatures, the k.p method and effective mass approximation were used to calculate the energy bands for [001] bulk Ge, the quasi-Fermi levels for given values of carrier densities, and then the interband gain and IVBA were calculated for biaxially tensile strained [001] bulk Ge. Furthermore, a detailed description of the free carrier absorption coefficient calculation, accounting for both intervalley and intravalley scattering in strained [001] Ge is given. The effect of unequal electron and hole densities, which are required to achieve the interband gain and reduce the absorption coefficient due to IVBA and FCA in order to obtain the net gain, has been investigated for strained bulk n+ Ge at room and typical device temperatures.