The kinetic Monte Carlo method (KMC) is an efficient approach for simulating dynamical evolution in microscopic systems such as microstructural evolution in crystals because it overcomes the primary temporal bottleneck in molecular dynamics simulations – the vibrational frequency. On the other hand, full atomic resolution KMC, i.e. one lattice site per KMC degree-of-freedom is still highly constrained in scope and is limited to about the micron scale for many problems of interest [1,2]. Recently, there has been much interest in the development of coarse-grained KMC simulations in which multiple lattice sites are spatially grouped together into coarse-grained cells, which in turn evolve via a series of coarse-grained hops [1,2]. A key step in formulating such approaches is the closure rule, which dictates how all the single-atom events are averaged within a coarse-grained cell.

In this paper we apply the lattice KMC coarse-graining framework proposed recently by Vlachos and coworkers [1,2] to a model for vacancy aggregation in crystalline silicon. The underlying microscopic KMC model is based on a bond counting approach with long-range interactions [3,4]. The bond energies are computed using a global regression approach in which the KMC model output is compared to molecular dynamics-generated data. We have shown previously that this approach allows us to capture off-lattice configurational entropic effects that substantially alter the evolution dynamics at the elevated temperatures relevant to point defect aggregation in crystalline semiconductors.

Several mean-field approximations and the quasi-chemical approximation are used to compute averaged KMC potentials for the coarse-grained systems. The application of these strategies to coarse-graining in the diamond lattice is investigated in detail and the different closure rules are compared and contrasted. We also study the application of coarse-graining to complex KMC interactions. The KMC interaction model in refs. [3,4] includes screening effects in which particles can obstruct bonding interactions between other pairs, effectively leading to a many-body potential. We begin by considering simplified interaction models and then investigate coarse-graining approaches to correctly capture the screening (many-body) component of our microscopic KMC potential.

[1] M. A. Katsoulakis and D. G. Vlachos, Coarse-grained stochastic processes and kinetic Monte Carlo simulations for the diffusion of interacting particles. J. Chem. Phys., 119 (2003) 9412. [2] A. Chatterjee and D. G. Vlachos, Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules. J. Chem. Phys., 121 (2004) 11420. [3] J. Dai, J. M. Kanter, S. S. Kapur, W. D. Seider and T. Sinno, On-lattice kinetic Monte Carlo simulations of point defect aggregation in entropically influenced crystalline systems. Phys. Rev. B, 72 (2005) 134102.