Electronic properties and defect levels induced by group III substitution–interstitial complexes in Ge

In this report, we used the hybrid density functional theory to systematically investigate the formation of substitution–interstitial complex defects formed by group III (B, Al, Ga and In) atoms in Ge for charge states − 2, − 1, 0, + 1 and + 2 as a function of the Fermi level. Under equilibrium conditions, the substitution–interstitial complexes in Ge formation energies were found to be relatively lower than 7.00 eV and stable with respect to their binding energies. For the neutral charge state, the Al $$_{\mathrm {Ge}}$$ Ga $$_i$$ complex (where Al $$_{\mathrm {Ge}}$$ and Ga $$_i$$ represent Al substitution in Ge and Ga interstitial, respectively) is the most stable defect with a binding and formation energies of 2.41 and 4.14 eV, respectively. Substitution–interstitial complexes induced defect levels in the band gap of Ge. Whereas the shallow donor defects are the B $$_{\mathrm {Ge}}$$ Al $$_i$$ and In $$_{\mathrm {Ge}}$$ Ga $$_i$$ , the deep acceptor defects are Ga $$_{\mathrm {Ge}}$$ B $$_i$$ , B $$_{\mathrm {Ge}}$$ Ga $$_i$$ , Al $$_{\mathrm {Ge}}$$ B $$_i$$ and B $$_{\mathrm {Ge}}$$ Al $$_i$$ . The In $$_{\mathrm {Ge}}$$ Ga $$_i$$ acts as a shallow single donor defect, the In $$_{\mathrm {Ge}}$$ Al $$_i$$ and Al $$_{\mathrm {Ge}}$$ In $$_i$$ induced only donor levels. The substitution–interstitial defects do not only alter the known electronic properties of the pristine host but also provide a new interesting character.