Band gap dependence of semiconducting nano-wires on cross-sectional shape and size

Applicability of three different thermodynamic models based on classical (Qi model) as well as quantum approach (Lu et al. and Jiang et al. models) have been discussed to search out the exact description of band gap variation with size in semiconducting nanowires. All considered models showed an increment in the band gap as diametric size of the wire decreases. To study band gap and the band edge shift of nanowires, a novel approach has been proposed by incorporating shape effect with size in Jiang et al. model due to its accuracy or consistency with the experimental results. Hence a unified model without any adjustable parameter has been established for studying the combined effect of size and shape on band edges shift [Delta E-c (D), Delta E-v (D)] and the band gap expansion [Delta E-G (D)] of the semiconducting nanowires. Present study reveals that for small-sized nanowires band gap expansion and edge shift is not only governed by size but also varies with the cross-sectional shape. Band gap expansion and edge shift showed rising behavior due to the enhancement in surface area.