Electronic structure and optical properties of silicon nanocrystals

Abstract

We have studied electronic structure and optical properties of Silicon nanocrystals by using density functional theory. The Silicon nanocrystals of diameters 1.0 nanometer up to 4.6 nanometer using the pseudopotential density functional theory were analysed. We have used real space three dimensional grid to approximate the real space integrals, charge densities and potentials, and numerical atomic orbitals allowing for very efficient reliable calculations. The fitness of the grid was governed by the plane wave cutoff. We have used plane wave cur off of 160Ry, which converged energies and density of state for bulk silicon. The basis size for silicon atoms was single with polarization orbitals and for hydrogen double. We have performed bench mark calculations for small silicon clusters. It was found that the cancellation of many body effects and the excitonic effects have given rise to density function theory the highest occupied molecular orbital-the lowest unoccupied molecular orbital gaps comparable with the experimental optical gaps. We have explored three types of structural models for nanocrystals, a spherical model and two polyhedral Wulff type structures and found them equivalent in terms of cohesive energies and density of states. We found that the narrowing of the valence band states contributed to the blue shift of the band gap, as a function of reduced size of the nanocrystals. We found good agreement in theory and experimental results.