Hybrid-Functional Calculations of the Copper Impurity in Silicon

We calculate formation energies and transition levels for copper-related defects in silicon using the screened hybrid functional of Heyd, Scuseria, and Ernzerhof HSE06. We consider Cu siting on interstitial sites (Cu-i), a substitutional site (Cu-Si), a Cu-Si-Cu-i pair, a complex formed from substitutional Cu and interstitial hydrogen (Cu-Si-H-i), and a complex formed from a substitutional Cu and three interstitial Cu atoms (Cu-Si-3Cu(i)). We find that Cu-i is a fast diffuser, with a migration barrier of only 0.19 eV, in good agreement with experimental values. Cu-i is a shallow donor and its formation energy is lower than that of CuSi for all Fermi-level positions in the band gap. Cu-Si, on the other hand, induces levels in the gap which are related to the occupation of antibonding states originating from the coupling between the Cu 3d states (t(2)((d))), resonant in the valence band, and the vacancy-induced gap states (t(2)((p))). The stable charge states of Cu-Si in the gap are +1, 0, -1, and -2. The transition levels of CuSi-Cui and Cu-Si-H-i are closely related to the levels of isolated Cu-Si: a donor level (+/0) near the valence band, an acceptor level near midgap, and a double-acceptor level in the upper part of the gap. The calculated transition levels are in good agreement with experimental results, and the formation energies explain the observed solubility.