Straining Ge bulk and nanomembranes for optoelectronic applications: a systematic numerical analysis

Germanium is known to become a direct band gap material when subject to a biaxial tensile strain of 2% (Vogl et al 1993 Phys. Scr. T49B 476) or uniaxial tensile strain of 4% (Aldaghri et al 2012 J. Appl. Phys. 111 053106). This makes it appealing for the integration of optoelectronics into current CMOS technology. It is known that the induced strain is highly dependent on the geometry and composition of the whole system (stressors and substrate), leaving a large number of variables to the experimenters willing to realize this transition and just a trial-and-error procedure. The study in this paper aims at reducing this freedom. We adopt a finite element approach to systematically study the elastic strain induced by different configurations of lithographically-created SiGe nanostructures on a Ge substrate, by focusing on their composition and geometries. We numerically investigate the role played by the Ge substrate by comparing the strain induced on a bulk or on a suspended membrane. These results and their interpretation can provide the community starting guidelines to choose the appropriate subset of parameters to achieve the desired strain. A case of a very large optically active area of a Ge membrane is reported.