Internally consistent approach for modeling solid-state aggregation. II. Mean-field representation of atomistic processes

Abstract

A detailed continuum (mean-field) model is presented that captures quantitatively the evolution of a vacancy cluster size distribution in crystalline silicon simulated directly by large-scale parallel molecular dynamics. The continuum model is parameterized entirely using the results of atomistic simulations based on the same empirical potential used to perform the atomistic aggregation simulation, leading to an internally consistent comparison across the two scales. It is found that an excellent representation of all measured components of the cluster size distribution can be obtained with consistent parameters only if the assumed physical mechanisms are captured correctly. In particular, the inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Dynamic clusters with large capture volumes at high temperature, which are the result of rapid cluster shape fluctuations, are shown to be larger than would be expected from static analyses, leading to substantial enhancement of the nucleation rate. Based on these results, it is shown that a parametrically consistent atomistic-continuum comparison can be used as a sensitive framework for formulating accurate continuum models of complex phenomena such as defect aggregation in solids. ABSTRACT A detailed continuum (mean-field) model is presented that captures quantitatively the evolution of a vacancy cluster size distribution in crystalline silicon simulated directly by large-scale parallel molecular dynamics. The continuum model is parameterized entirely using the results of atomistic simulations based on the same empirical potential used to perform the atomistic aggregation simulation, leading to an internally consistent comparison across the two scales. It is found that an excellent representation of all measured components of the cluster size distribution can be obtained with consistent parameters only if the assumed physical mechanisms are captured correctly. In particular, the inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Dynamic clusters with large capture volumes at high temperature, which are the result of rapid cluster shape fluctuations, are shown to be larger than would be expected from static analyses, leading to substantial enhancement of the nucleation rate. Based on these results, it is shown that a parametrically consistent atomistic-continuum comparison can be used as a sensitive framework for formulating accurate continuum models of complex phenomena such as defect aggregation in solids.

Detailed microscopic analysis of self-interstitial aggregation in silicon. II. Thermodynamic analysis of single clusters

“…This conclusion can be contrasted starkly with the more common case of energetic stabilization of "magic" cluster sizes, such as for vacancy clusters. 49,50 In the energetic stabilization case, clusters of particular sizes are favored relative to others at low temperature because certain configurations minimize the formation energy ͑e.g., by the minimization of dangling bonds͒. However, at elevated temperature, this effect is obscured by entropic contributions and the formation free energy per vacancy is found to decrease almost monotonically with cluster size.…”

“…[38][39][40][41][42] Configurational entropy arises from the presence of numerous mechanically stable configurations that a defect cluster can assume within the lattice. Each of these configurations, ␣, ͑so called inherent structures͒ can be identified by a local energy minimum, V ␣ , in the multidimensional potential-energy landscape ͑PEL͒ that defines the overall system.…”

On-lattice kinetic Monte Carlo simulations of point defect aggregation in entropically influenced crystalline systems

“…In fact, MD simulations with various potentials 17,18 indicate that the interaction extends up to the 4NN distance along the ͑110͒ direction, and somewhat less along other directions. Assuming that the vacancy-vacancy interaction is approximately isotropic, the interaction distance therefore can extend up to the 8NN interaction shell!…”

“…Assuming that the vacancy-vacancy interaction is approximately isotropic, the interaction distance therefore can extend up to the 8NN interaction shell! In our previous work, 11 it was further shown that this interaction distance was essentially independent of the local environment, and can be assumed to be constant.…”

“…This particular system choice is based on the fact that vacancy aggregation is a technologically important pro-cess that has been characterized in detail with experiments 8,9 and detailed continuum models, [10][11][12] and also because accurate empirical interatomic potentials are readily available. [13][14][15] Vacancy aggregation is also often assumed to be a prototypical "on-lattice system," an assumption that we show here to be invalid, particularly at elevated temperature.…”