Modeling Si nanoprecipitate formation in SiO₂ layers with excess Si atoms

Abstract

Computer simulations based on the Monte Carlo method are used to analyze processes leading to the formation of luminescence centers in SiO₂ implanted with Si ions. The simulations, which take place in a two-dimensional space, mimic the growth of silicon nanoprecipitates in layers containing several at.% of excess silicon. It is assumed that percolation clusters made up of neighboring Si atoms form first. As the annealing temperature increases, these clusters grow and compactify into nano-sized inclusions of a well-defined phase. It is shown that a dose dependence arises from an abrupt enhancement of the probability of forming direct Si-Si bonds when the concentration of silicon exceeds ∼1 at. %. Under these conditions, percolation chains and clusters form even before annealing begins. The effect of the temperature of subsequent anneals up to 900 °C is modeled via the well-known temperature dependence of Si diffusion in SiO₂. It is assumed that annealing at moderate temperatures increases the mobility of Si atoms, thereby facilitating percolation and development of clusters due to an increase in the interaction radius. Intrinsic diffusion processes that occur at high temperatures transform branching clusters into nanoprecipitates with well-defined phase boundaries. The dose and temperature intervals for the formation of precipitates obtained from these simulations are in agreement with the experimental intervals of dose and temperatures corresponding to the appearance of and changes in luminescence.