A universal expression of band gap for silicon nanowires of different cross-section geometries.

We use the first-principles tight binding method to investigate the electronic structure and band gap of [110] oriented hydrogen-passivated silicon nanowires (SiNWs) of different cross-sectional geometries. A quantitative universal band gap expression for [110] SiNWs is obtained, which shows a linear dependence of band gap on the surface area to volume ratio (SVR), and it is independent of the cross-sectional geometry. In contrast to the ambiguity in the definition of the SINW transverse dimension, using of SVR has the advantage to readily predict band gap for SiNWs with any cross-sectional shapes. Our results demonstrate that the SVR is an ideal "gauge" to describe the band gap of SiNWs.