Recent advances in computational technology and algorithms have made it feasible to accurately model the electronic structures of solids by means of density functional theory. The development of hybrid functionals have improved the accuracy of band gap calculations and made it possible to make qualitative predictions regarding the charge transition energy levels of defects in semiconductors. The Sb-V defect (also known as the E-center) in germanium is a well-known defect, which have been the subject of many experimental and some theoretical studies. It has been found to have interesting annealing properties and the aim of this study is to investigate the electronic properties of the Sb-V defect theoretically. The vacancy defect in germanium (VGe), the antimony substitutional (SbGe) defect in germanium and the defect complex (Sb-V) arising from the combination of these two defects is explored in great detail and how they interact in proximity to one another is presented here. In addition, this work can be seen as a test for the effectiveness of the technique to model defects in semiconductors correctly. The E-center defect was investigated using the HSE06 hybrid functional as implemented in the VASP code. A positive binding energy of 1.5 eV, 1.02 eV and 0.88 eV was found for the first, second and third nearest neighbor configurations respectively, between the Sb and the vacancy was predicted. No metastability was detected and the nearest-neighbor configuration had the lowest energy for all charge states. Four transition levels in the band gap were predicted, with energy level relative to the valence band maximum, lying at 0.52 eV (-2/-1), 0.40 eV (-1/0), 0.44 eV (0/+1) and 0.02 eV (+1/+2). The two mid-gap levels (-1/0) and (0/+1) had negative-U ordering with U= -0.04 eV. iv These findings were consistent with the current experimental model of the Sb-V complex in germanium whereby no metastability has been observed experimentally. The energy level of the (-2/-1) corresponded well with the experimental DLTS level in n-type material at 0.37 eV, though the correspondence for the other levels was not as good. Experimentally, no negative-U behavior was observed, but the predicted negative-U behavior was rather small and no deliberate experiments have been performed to investigate the presence of negative-U behavior in the Sb-V complex. / Dissertation (MSc)--University of Pretoria, 2016. / National Research Foundation (NRF) / Physics / MSc / Unrestricted