Optimizing Silicon Oxide Embedded Silicon Nanocrystal Inter-particle Distances.

We demonstrate an analytical method to optimize the stoichiometry and thickness of multilayer silicon oxide films in order to achieve the highest density of non-touching and closely spaced silicon nanocrystals after annealing. The probability of a nanocrystal nearest-neighbor distance within a limited range is calculated using the stoichiometry of the as-deposited film and the crystallinity of the annealed film as input parameters. Multiplying this probability with the nanocrystal density results in the density of non-touching and closely spaced silicon nanocrystals. This method can be used to estimate the best as-deposited stoichiometry in order to achieve optimal nanocrystal density and spacing after a subsequent annealing step.