Stability of donor-pair defects in Si_1-xGe_x alloy nanowires

We perform density-functional calculations to investigate the defect properties of group-V elements (P, As, Sb) in Si, Ge, and Si _1-xGe_x alloy nanowires. In all nanowires, P dopants have a tendency to form donor-pair defects, which consist of two dopants at the first nearest distance, when the wire diameter decreases below a critical value. The quantum confinement and chemical bonding effects play a role in stabilizing donor-pair defects against isolated substitutional donors. As the donor-pair defect has a deep level in the band gap, which is electrically inactive, the doping efficiency is reduced in small-diameter nanowires. As the Ge concentration increases, the formation of the donor-pair defect becomes more favorable, lowering further the doping efficiency. On the other hand, with As and Sb dopants, which have the larger atomic radii, the formation of donor-pair defects is suppressed due to large strain energies. Uniaxial compressive strain also reduces the stability of donor-pair defects and thereby increases the doping efficiency.