Formation of dopant-pair defects and doping efficiency in B- and P-doped silicon nanowires

First-principles calculations are performed to investigate the stability of dopant-related defects and the dependence of doping efficiency on wire diameter and orientation in hydrogen-passivated silicon nanowires doped with B and P dopants. As the diameter decreases below a critical value, it is energetically more favorable for donor atoms to form donor-pair defects, which consist of two donors separated at the nearest-neighbor distance. While donor-pair defects are unstable in bulk Si, the stability of these defects is greatly enhanced because of the confinement effect in nanostructures, which leads to the increase of band gap and thereby the shallow level of a substitutional donor. As donor-pair defects are electrically inactive defects, the doping efficiency is expected to be suppressed in small-diameter wires, regardless of the presence of surface or interface dangling-bond defects which were previously proposed to be the compensating defects. In the case of B dopants, the formation of pair defects is unfavorable against shallow acceptor levels, in contrast to n-type dopants, without affecting the doping efficiency.