Ion beam synthesis (IBS) is a technologically important method to fabricate nanocrystals inside a solid environment. The process involves firing high energy ions into the host matrix well beyond the solubility limit such that the implanted atoms segregate into clusters. This technique offers precise control of the quantity and depth of the injected species and has the benefit of seamless integration with industrial fabrication. The width of the size distributions is important for applications of such nanostructured materials. However, there is little understanding of what governs the size distribution of these nanoclusters.

Experimental results of ions implanted into amorphous silica have suggested the presence of as-imlanted clusters, which seed later thermal processing steps with an initial distribution. In this work, we explore the various parameters that govern the as-implanted size profile of IBS of various materials in silica, using both stochastic (kinetic Monte Carlo) and mean-field (rate equations) schemes. Agreement between the two methods renders a predictive, quantitative model describing IBS in an amorphous silica matrix.