Germanium is a strong candidate as a laser source for silicon photonics. Despite the indirect nature of its bandgap, the application of several percent of tensile strain reduces the energy difference between its direct and indirect bandgaps . It has been predicted that above a certain strain threshold, germanium transforms into an actual direct bandgap material . However, the properties of this material at unprecedented levels of strain still raise issues. A recently introduced strain technology based on prestressed germanium layers  enables to fabricate micro-membranes at such high strain. We present here both a theoretical and experimental study of the band edge and Raman shift at such high strain level.
For above reasons, we start from slightly tensile-strained germanium-on-insulator (GeOI) substrates obtained by the Smart CutTM technology . By etching adequate pattern in the germanium layer, both uniaxial and biaxial stress conditions were obtained after etching away the sacrificial buried oxide underneath the germanium layer. We performed x-ray diffraction measurements at the ESRF synchrotron using Laue in combinations with rainbow filtering techniques on the micro-membranes revealing strain values of 4.9 % for the uniaxial strain and 1.9 % for the biaxial strain [5-6]. We then studied the relationship between strain and Raman shift. While the relationship remained linear for biaxial stress condition, a significant deviation from the linear behavior behavior was observed above 2.5 % uniaxial strain. Such nonlinearity becomes dominant at very high strain levels; indeed a 9.9 cm-1 Raman shift corresponds to 4.9 % strain instead of the 6.5 % predicted by the linear extrapolation .
We performed simulations of the band structure of germanium under various stress conditions using a tight-binding model. For uniaxial stress, the relation between the energy positions of the band edges differed significantly from the deformation potential models in . Finally, we performed electro-absorption measurements on micro-membranes to determine the energy of the direct transitions (conduction band to light and heavy holes) in uniaxially stressed germanium. The relationship between strain and direct bandgap became nonlinear above 2.5 %, in agreement with our theoretical models.
In conclusion, we show that under uniaxial strain level above 2 %, germanium exhibits significant nonlinear behaviors which have to be taken into consideration for the design and fabrication of future on-chip germanium laser sources compatible with CMOS technologies.
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 Gassenq et al., submitted
 Gassenq et al., submitted