Percolation transition from germanium quantum dots to a monolayer in the heteroepitaxy growth model

Abstract

We developed a kinetic Monte Carlo method to investigate the heteroepitaxial growth of Ge/Si(001) quantum dots under varying temperatures and fluxes. Our results show that increasing the flux rate of impinging atoms and raising the temperature promotes the coalescence of quantum dots on the surface within the heteroepitaxial Volmer-Weber growth regime, ultimately driving a transition from quantum dots to a continuous monolayer. Using percolation theory, we estimate the transition threshold from quantum dots to a monolayer at different fluxes and temperatures. Additionally, we determine the critical percolation exponents by applying the finite-size scaling method. Our findings reveal that variations in flux and temperature significantly influence the size, distribution of formed islands, and the percolation threshold from quantum dots to the monolayer within the Volmer-Weber growth regime.