Nucleation simulation using a model of hard/soft discs

• Computer study of the nucleation probability is described by different disk models.
• Percolation probability is described as probability of forming a spanning cluster.
• The HCSS model and continuous percolation explain the beginning of the nucleation.

In this paper we present a computer study of the quantum dot (QD) nucleation probability with three possible models of particle interaction; Soft Core (SC), Hard Core (HC) and Hard Core/Soft Shell (HCSS) model. Computer analysis of the nucleation probability is performed on a 500 by 500 lattice with 2000 simulations per event. If a matrix is assumed to represent an SiO2 substrate in which a pure Si quantum dot can grow, it is demonstrated that nucleation centers are more easily distinguished and initially more likely to form in the SC and HCSS models rather than in the HC model. If particles are allowed to move, nucleation centers can appear even in the HC model independent of a preexisting local density. A low probability of nucleation in the HC model and a high probability of nucleation in the SC model are evident from the system entropy curve. The probability of nucleation, therefore, depends on the local density change, percolation probability and system entropy. Low probability of nucleation in the HC model is in accordance with a lower probability of percolating clusters forming in a given model.