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)- X α 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 3 d orbitals as basis sets decreases the E g value. The results also show that the components of silicon 3 d 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.