Comparative analysis of pseudo-potential and tight-binding band structure calculations with an analytical two-band k.p model: Conduction band of silicon

An analytical two-band k.p model for the conduction band of silicon is compared with the numerical nonlocal empirical pseudo-potential method and the sp(3)d(5)S* nearest-neighbor tight-binding model. The two-band k.p model gives results consistent with the empirical pseudo-potential method and describes the conduction band structure accurately. The tight-binding model overestimates the gap between the two lowest conduction bands at the valley minima, which results in an underestimation of the non-parabolicity effects. When shear strain is introduced, the two-band k.p model predicts an analytical expression for the strain-dependence of the band structure, which is in good agreement with results of pseudo-potential simulations.