The revised Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE06) was used for calculating the formation and migration energies of the vacancy in Ge, and the results were compared with those previously obtained using the local density approximation with the on-site Coulomb interaction U (LDA+U) approach and with other published results. It was demonstrated that using HSE06 gave a much more accurate electronic description of the vacancy and yields an excellent estimate of the activation energy of self-diffusion in Ge consistent with experimental data. The migration energies of the vacancy in different charge states calculated with the HSE06 approach agreed well with the results of low-temperature infrared-absorption measurements. In contrast to previous results, the HSE06 calculations suggested that vacancies in Ge were multiple-level acceptors with levels located in the upper half of the band-gap. This could explain the observed high density of acceptor-like interface traps near the conduction band, pinning the Fermi level and inhibiting the formation of an inversion layer in n-channel devices in Ge.

Improved Calculation of Vacancy Properties in Ge using the Heyd-Scuseria-Ernzerhof Range-Separated Hybrid Functional. P.Śpiewak, J.Vanhellemont, K.J.Kurzydłowski: Journal of Applied Physics, 2011, 110[6], 063534