Dangling bonds and vacancies in germanium

The quest for metal-oxide-semiconductor field-effect transistors (MOSFETs) with higher carrier mobility has triggered great interest in germanium-based MOSFETs. Still, the performance of germanium-based devices lags significantly behind that of their silicon counterparts, possibly due to the presence of defects such as dangling bonds (DBs) and vacancies. Using screened hybrid functional calculations we investigate the role of DBs and vacancies in germanium. We find that the DB defect in germanium has no levels in the band gap; it acts as a negatively charged acceptor with the (0/$-$1) transition level below the valence-band maximum (VBM). This explains the absence of electron-spin-resonance observations of DBs in germanium. The vacancy in germanium has a much lower formation energy than the vacancy in silicon and is stable in a number of charge states, depending on the position of the Fermi level. We find the (0/$-$1) and ($-$1/$-$2) transition levels at 0.16 and 0.38 eV above the VBM; the spacing of these levels is explained based on the strength of intraorbital repulsion. We compare these results with calculations for silicon, as well as with available experimental data.