The effects of uniaxial and biaxial strain on the electronic structure of germanium

Abstract

The effects of uniaxial and biaxial strain on the electronic structure of bulk germanium are investigated using density functional theory in conjunction with four approximations for the exchange correlation interaction: the local density approximation (LDA) and generalized gradient approximation (GGA) with on-site Hubbard corrections (LDA+U, GGA+U), the meta-GGA (MGGA), and the screened hybrid functional (HSE06). The band structure and, especially, the band gap of unstrained Ge are well reproduced by these methods. The results of LDA+U/GGA+U and MGGA show that a biaxial tensile strain above 1.5% turns Ge into a direct-gap (Γ–Γ) semiconductor, whereas the indirect Γ–L gap is maintained for uniaxial strain up to 3%. The HSE06 results confirm a similar trend, although the predicted critical strain is lower. The effective masses were also calculated and they were found to be in good agreement with experiments for bulk Ge. It is predicted that the masses at Γ can be tuned to be smaller/larger by tensile/compressive strain in all directions.