Hybrid functional study of point defects in germanium

Abstract

Germanium exhibits electron and hole mobilities that are higher than silicon. These unique properties make Ge a promising material for the development of metal-oxide semiconductor eld e ect transistors (MOSFETs). Point defects in semiconductors in uence the electronic structure as well as the thermodynamic and optical properties of the material. Well-known defects in Ge have been intensively studied experimentally and results reported. In the past, defects in Ge were di cult to study theoretically, since the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals in the framework of density functional theory (DFT) incorrectly predict Ge to be a metal. However, the screened hybrid functional developed by Heyd, Scuseria, and Ernzerhof (HSE) accurately predicts the band gap and gives better estimates of the charge state transition levels of point defects in semiconductors. This thesis reports the results of DFT calculations using the HSE06 functional to predict the structural, electronic and charge state thermodynamic properties of Ge di-interstitials, rare earth (RE) substitutional and interstitial impurities as well as vacancy-RE impurity complexes in Ge. Results obtained showed that the Ge di-interstitial could exist in three con gurations with formation energies between 6.53 and 7.63 eV. The lowest energy con guration was the double tetrahedral con guration with a binding energy of 1.24 eV. This con guration induced only a shallow donor level at an energy of 0.04 eV below the conduction band minimum. Other con gurations of the Ge di-interstitial exhibited negative-U ordering. RE interstitials in Ge formed with formation energies between −4.76 and 6.71 eV, with the Pr interstitial in Ge having the lowest formation energy at −4.76 eV for the neutral charge state in the tetrahedral con guration. The tetrahedral con guration was the most stable con guration for the Ce, Pr, Eu and Tm, while the Er interstitial showed charge state controlled metastability. While the Ce interstitial induced a shallow donor level in the band gap, the Eu and Er interstitials induced deep levels within the band gap of Ge. The Pr interstitial in Ge did not induce any charge state transition levels, with the neutral charge state stable for all Fermi energies in the band gap. Tm3+ defects in Ge formed with formation energies between 1.81 and 5.31 eV for the neutral charge state. Of all the Tm3+ related defects in Ge studied, the Tm3+ i in the tetrahedral con guration formed with the lowest formation energy of 1.81 eV. Tm3+ i induced a shallow donor level, while Tm3+ Ge and Tm3+ i -VGe induced both acceptor and donor levels that were deep and shallow. Tm3+ substitutional and vacancy complex (Tm3+ Ge-VGe) in Ge exhibited charge state controlled metastability and negative-U ordering. The role of the di-interstitial, vacancy related defects, substitutional impurities and vacancy-interstitial complexes in Ge were pointed out and it is expected that the data and information presented will be useful in the process modelling of Ge-based devices for industrial, laboratory applications and for comparison to experimental results.