Tight-binding versus effective mass approximation calculation of electronic structures of semiconductor nanocrystals and nanowires

We study the electronic structure of semiconductor nanocrystals and nanowires using the tight-binding sp3d5s∗ model with all semiconductor atoms dangling bonds passivated by hydrogen atoms. In particular, we show the effect of confinement on the band gap energy of the nanocrystals and nanowires as a function of their radius R. Quantum confinement becomes significant for small nanowires with diameter less than 10 nm. We also show the confinement-dependence of the position of the energy minimum in the band structure of nanowires. We present the full band structure of Ge and Si nanowires, showing their similarity that the [1 1 1] wires exhibit a transition from an indirect gap in large wires to a direct one in small wires. We compare the electron band structure calculated using the effective mass approximation with the results obtained by tight-binding method, and we introduce for practical use a semi-analytical model for both the electron effective mass and effective band gap in nanocrystals and nanowires.