Dopant states ina-Si: H. I. Tight-binding-model results

The gap states of substitutional dopants in $a$-Si: H are studied with the use of tight-binding models. Within its 1.8-eV-wide gap, N is found to be the only truly shallow donor, and P is borderline deep, with As, Sb, and Bi deeper still. For acceptors, only B is found to be shallow because of its small atomic radius. It is argued that bond-length disorder at substitutional impurity sites is small, as elsewhere in $a$-Si. The remaining forms of disorder are calculated to cause only a small ±0.05-eV broadening of donor levels but a dramatic ±0.2-eV broadening of any deep acceptor levels. Pairing of dopant sites is found to cause a small broadening of levels, but donor-acceptor pairing is shown to give shallower levels.