Electronic structure of semiconductor nanowires

We compute the subband structure of several group IV and III-V < 001 >-, < 110 >-, and < 111 >-oriented nanowires using sp(3) and sp(3)d(5)s(*) tight-binding models. In particular, we provide the band gap energy of the nanowires as a function of their radius R in the range R=1-20 nm. We then discuss the self-energy corrections to the tight-binding subband structure, that arise from the dielectric mismatch between the nanowires (with dielectric constant epsilon(in)) and their environment (with dielectric constant epsilon(out)). These self-energy corrections substantially open the band gap of the nanowires when epsilon(in)>epsilon(out), and decrease slower (proportional to 1/R) than quantum confinement with increasing R. They are thus far from negligible in most experimental setups. We introduce a semi-analytical model for practical use. This semianalytical model is found in very good agreement with tight-binding calculations when epsilon(in)>epsilon(out).