Vacancy clustering and diffusion in silicon: Kinetic lattice Monte Carlo   simulations
  Diffusion and clustering of lattice vacancies in silicon as a function of temperature, concentration, and interaction range are investigated by Kinetic Lattice Monte Carlo simulations. It is found that higher temperatures lead to larger clusters with shorter lifetimes on average, which grow by attracting free vacancies, while clusters at lower temperatures grow by aggregation of smaller clusters. Long interaction ranges produce enhanced diffusivity and fewer clusters. Greater vacancy concentrations lead to more clusters, with fewer free vacancies, but the size of the clusters is largely independent of concentration. Vacancy diffusivity is shown to obey power law behavior over time, and the exponent of this law is shown to increase with concentration, at fixed temperature, and decrease with temperature, at fixed concentration. 
Benjamin P. Haley and Keith M. Beardmore and Niels Gr{\o}nbech-Jensen