Germanium under High Tensile Stress: Nonlinear Dependence of Direct Band Gap vs Strain

Abstract : Germanium is a strong candidate as a laser source for silicon photonics. It is widely accepted that the band structure of germanium can be altered by tensile strain so as to reduce the energy difference between its direct and indirect band gaps. However, the conventional gap deformation potential model most widely adopted to describe this transition happens to have been investigated only up to 1% uniaxially loaded strains. In this work, we use a microbridge geometry to uniaxially stress germanium along [100] up to epsilon(100) = 3.3% longitudinal strain and then perform electroabsorption spectroscopy. We accurately measure the energy gap between the conduction band at the Gamma point and the light- and heavy-hole valence bands and calculate the theoretical dependency using a tight-binding model. We measure the hydrostatic and tetragonal shear deformation potential of germanium to be a = -9.1 +/- 0.3 eV and b = -2.32 +/- 0.06 eV and introduce a second-order deformation potential that provides a better fit for both experimental and theoretical relations. These new high-strain coefficients will be suitable for the design of future CMOS-compatible lasers and optoelectronic devices based on highly strained germanium.