Morphology effects on the bandgap of silicon nanocrystals - Numerically modelled by a full multi-grid method

Silicon nanocrystals embedded in a dielectric matrix have been considered a potential candidate for many optoelectronic and photovoltaic applications and have been under vigorous study in recent years. One of the main properties of interest in this application is the absorption bandgap, which is determined by the quantum confinement of silicon nanocrystals. The ability to predict the absorption bandgap is a key step in designing an optimum solar cell using this material. Although several higher level algorithms are available to predict the electronic confinement in these nanocrystals, most of them make regular-shape assumptions for the ease of computation. In this work, we present a model for the accurate prediction of the quantum confinement in silicon nanocrystals of non-regular shape by employing an efficient, self-consistent Full-Multi-Grid method. Confined energies in spherical, elongated, and arbitrarily shaped nanocrystals are calculated. The excited level calculations quantify the wavefunction coupling and energy level splitting arising due to the proximity of dots. The splitting magnitude was found to be as high as 0.1 eV for the 2 nm size silicon quantum dots. The decrease in confinement energy due to the elongation of dots was found to be more than 0.2 eV, and the trend was similar for different dielectric materials. Theoretical predictions were compared to the results from optical and structural characterisation and found to be in agreement. The loss of degeneracy in highly asymmetric quantum dots, such as a “horse-shoe” shaped quantum dot, significantly affects the excited state energies.