Supercell Approach in Tight-Binding Calculation of Si and Ge Nanowire Bandstructures

Energy bandstructures of 100 oriented Si and Ge quantum nanowires with various cross-sections are calculated by using the sp³d⁵s^* tight-binding model with a supercell approach. Results are compared with those obtained by the first principles method (i.e., density functional theory, or DFT). The differences in the bandstructure between silicon and germanium nanowires are analysed and it is shown that germanium keeps indirect-bandgap and the silicon nanowire along the 100 direction becomes direct-bandgap when the wire diameter shrinks. It is shown in comparison with the available experimental data that the tight-binding method is adequate in predicting the bandstructure parameters relevant to the carrier transport in mesoscopic nanowire devices and is far superior to the DFT method in terms of computational cost.