Efficient Direct Band-Gap Transition in Germanium by Three-Dimensional Strain

Complementary to the development of highly three-dimensional (3D) integrated circuits in the continuation of Moore's law, there has been a growing interest in new 3D deformation strategies to improve the device performance. To continue this search for new 3D deformation techniques, it is essential to explore beforehand, using computational predictive methods, which strain tensor leads to the desired properties. In this work, we study germanium (Ge) under an isotropic 3D strain on the basis of first-principles methods. The transport and optical properties are studied by a fully ab initio Boltzmann transport equation and many-body Bethe-Salpeter equation (BSE) approach, respectively. Our findings show that a direct band gap in Ge could be realized with only 0.70% triaxial tensile strain (negative pressure) and without the challenges associated with Sn doping. At the same time, a significant increase in the refractive index and carrier mobility, particularly for electrons, is observed. These results demonstrate that there is a huge potential in exploring the 3D deformation space for semiconductors, and potentially many other materials, to optimize their properties.