Electronic structure of semiconductor nanowires

We compute the subband structure of several group IV and III-V $⟨001⟩$-, $⟨110⟩$-, and $⟨111⟩$-oriented nanowires using sp³ and sp³d⁵s* 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--200.3em0exnm. 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 εᵢₙ) and their environment (with dielectric constant εₒᵤₜ). These self-energy corrections substantially open the band gap of the nanowires when εᵢₙ>εₒᵤₜ, and decrease slower (∝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 εᵢₙ>εₒᵤₜ.