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The electronic structure of silicon rods has been studied by means of the tight-binding recursion method to investigate the dependence of the energy gap (E g ) on a rod length and the direction of the rod axis. An empirical expression for E g is derived from numerical results for the rods in ͗100͘, ͗110͘, and ͗111͘ directions. This expression is applicable to the energy gaps of wires and crystallites, which can be regarded as limiting cases of rods.

Photoluminescence spectra of porous silicon prepared with electro-chemical etching, were analyzed using a simple model based on a statistical distribution of particle size. It was found that the size of nanoparticles, obeys the logarithmic normal distribution in all the porous silicon investigated here. This model also explains the dependence of the photoluminescence spectrum on the excitation energy.

The electronic band structure as well as the crystal structure of the BiI 3 semiconductor is investigated by performing first-principles pseudopotential calculations for the space group D 1 3d or C 2 3i . The optimized structures were determined through total-energy calculations. The calculated results indicate that a rhombohedral structure (C 2 3i ) forms a flatter band at the bottom of the conduction bands as compared to a hexagonal structure (D 1 3d ). The lattice relaxation of the iodine atoms around a vacant site on the atomic plane of bismuth is found to play an important role on the conduction band bottom. It is proved that the rhombohedral BiI 3 is an indirect semiconductor, while the hexagonal BiI 3 has a direct band gap.

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