  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 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-principle 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
0.34% triaxial tensile strain (negative pressure) and without the challenges
associated with Sn doping. At the same time a significant increase in
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 - in order to optimize their properties.
