Simulation of Indirect-Direct transformation phenomenon of germanium under uniaxial and biaxial strain along arbitrary orientations

Germanium can be transformed from an indirect bandgap material to a direct bandgap material by applying strain. Unstrained Ge has an indirect bandgap of 0.66eV (at L point) and a direct bandgap of 0.8eV [1]. When strain is applied, the band structure of germanium will be altered. When the strain is tensile, both the indirect and the direct bandgaps tend to decrease. Under certain strains, the direct bandgap will be pushed even below the indirect bandgap, at which point, germanium becomes a direct bandgap material. The value of the bandgap when Ge transforms from an indirect to direct semiconductor upon the application of strain is named the Bandgap Transition Point (BTP), and the required strain is named STP (Strain at Transition Point). Previous research has been done on uniaxial and biaxial strained germanium on the conventional orientations. In this work, calculations are made on the effect of applying tensile stress in arbitrary orientations based on nonlocal empirical pseudopotential method (EPM) [2] [3]. We also use cubic spline interpolation of the atomic form factors [4] [5], as well as the rules for strain translation [6], to determine how the Indirect-Direct transformation phenomenon of germanium changes with respect to virtually any orientation of the crystal planes. In addition, we calculated the optimal orientation and the effect that departure from this optimal orientation has on the bandgap.