Inspired by the novel properties of a newly predicted two-dimensional (2D) tetragonal allotrope of Ge called 2D tetragonal Ge, first-principles calculations have been performed to explore the stability, and structural and electronic properties of 2D tetragonal Ge via hydrogenation, and the effect of external strain on structural and electronic properties of hydrogenated 2D tetragonal Ge is considered. Our calculations reveal that the hydrogenated 2D tetragonal Ge, α-GeH and β-GeH, are proved to be dynamically and thermally stable. Both α-GeH and β-GeH are semiconductors with a direct band gap of 0.953 eV and indirect band gap of 2.616 eV, respectively. When applying external strain from ?7% to 7%, α-GeH is more energetically stable than β-GeH around the equilibrium geometry, β-GeH is more stable than α-GeH when external strains exceed a certain critical value, respectively. The direct band gap of α-GeH reduces rapidly from 2.008 eV to 0.036 eV as external strain increases from ?7% to 7%, while the indirect band gap of β-GeH is changed slightly. Our results reveal that α-GeH and β-GeH can offer an intriguing platform for nanoscale device applications and spintronics.
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