Tensile-strain effect of inducing the indirect-to-direct band-gap transition and reducing the band-gap energy of Ge

Abstract

By means of a hybrid density-functional method, we investigate the tensile-strain effect of inducing the indirect-to-direct band-gap transition and reducing the band-gap energy of Ge. We consider [001], [111], and [110] uniaxial tensility and (001), (111), and (110) biaxial tensility. Under the condition of no normal stress, we determine both normal compression and internal strain, namely, relative displacement of two atoms in the primitive unit cell, by minimizing the total energy. We identify those strain types which can induce the band-gap transition, and evaluate the critical strain coefficient where the gap transition occurs. Either normal compression or internal strain operates unfavorably to induce the gap transition, which raises the critical strain coefficient or even blocks the transition. We also examine how each type of tensile strain decreases the band-gap energy, depending on its orientation. Our analysis clearly shows that synergistic operation of strain orientation and band anisotropy has a great influence on the gap transition and the gap energy.