By means of density functional theory (DFT), using the screened Heyd,
Scuseria, and Ernzerhof (HSE06) hybrid functional we present results of the Tm3+Ge-VGe defect complexes in germanium (Ge). The formation energies of the rst (fnn), second (snn), third (tnn) and fourth (ftnn) nearest neighbour con gurations of Tm3+Ge-VGe were examined. The charge state transition levels for all these con gurations were examined as well. The Tm3+Ge-VGe complexes
were found to have a positive binding energies for the neutral charge
state in the fnn and ftnn con gurations. The thermodynamic transition levels revealed that the Tm3+Ge-VGe induced shallow levels in the band gap for the fnn, tnn and ftnn con gurations and deep level for the tnn con guration.The snn con guration showed no charge state transition level, the -2 charge state was stable for all Fermi energies in the band gap . The Tm3+Ge-VGe displayed
evidence of a single donor level (+1=0) and an acceptor level (-1=-2) within the band gap. Charge state controlled metastability was exhibited by the Tm3+Ge-VGe.