The Electronic Structure of One-Dimensional (1-D), 2-D, and 3-D Silicon Clusters

The electronic structure of one-dimensional (1-D), 2-D, and 3-D silicon clusters have been calculated using the Discrete Variational (DV)-Xalpha Molecular-Orbital method. The calculated results are discussed with respect to the effect of the size of the cluster on the energy level of molecular orbitals. The energy-gap (E(g)) between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) decreases with the increase of cluster size and the number of dimensions. It is found that including silicon 3d orbitals as basis sets decreases the E(g) value. The results also show that the components of silicon 3d orbitals in the unoccupied levels near LUMO are over 50 per cent. The calculated results predict that the E(g) value will be close to the band gap of crystalline silicon when a 3-D cluster contains more than 1000 silicon atoms.