Electronic structure of semiconductor nanowires

Abstract

We compute the subband structure of several group IV and III-V $⟨001⟩$-, $⟨110⟩$-, and $⟨111⟩$-oriented nanowires using $s{p}^{3}$ and $s{p}^{3}{d}^{5}{s}^{*}$ tight-binding models. In particular, we provide the band gap energy of the nanowires as a function of their radius $R$ in the range $R=1--20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. 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 ${\ensuremath{\epsilon}}_{\mathrm{in}}$) and their environment (with dielectric constant ${\ensuremath{\epsilon}}_{\mathrm{out}}$). These self-energy corrections substantially open the band gap of the nanowires when ${\ensuremath{\epsilon}}_{\mathrm{in}}>{\ensuremath{\epsilon}}_{\mathrm{out}}$, and decrease slower $(\ensuremath{\propto}1∕R)$ 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 ${\ensuremath{\epsilon}}_{\mathrm{in}}>{\ensuremath{\epsilon}}_{\mathrm{out}}$.