Adjacent Sink Strengths Used in Multiscale Kinetic Rate Equation Simulations of Defects and Impurities in Solids

TL;DR

This paper introduces analytical expressions for adjacent sink strengths in kinetic rate equation models, improving the accuracy of defect and impurity evolution simulations in solids by capturing local retrapping effects.

Contribution

It derives the first analytical expressions for adjacent sink strengths, including finite diffusion jump length correction, enhancing multiscale defect modeling accuracy.

Findings

Adjacent sink strengths dominate retrapping probability.

Inclusion of adjacent sink strengths improves TDS peak temperature predictions.

Models with only random sinks can fit data but yield unphysical parameters.

Abstract

Kinetic Rate Equation (kRE) modeling is widely used to simulate defect and impurity evolution in solids over experimentally relevant time and length scales. However, conventional kRE formulations include only random-position sink strengths, which adequately describe trapping of defects created at random lattice sites but fail to capture the enhanced retrapping of defects released directly adjacent to traps during detrapping or dissociation events. This omission leads to systematic errors, including underestimated thermal desorption (TDS) peak temperatures and incorrect kinetic parameters when fitting to experimental data. In this work, we derive for the first time analytical expressions for the adjacent sink strength, including correction for finite impurity diffusion jump length. We provide a practical implementation strategy for integrating these expressions into kRE simulations. Comparisons with kinetic Monte Carlo (kMC) benchmarks demonstrate that adjacent sink strengths dominate the retrapping probability and are essential for reproducing the correct temperature dependence of TDS release peaks. Simulations that employ only random sink strengths can still be tuned to match TDS spectra; however, the resulting fitted trapping energies, detrapping frequencies, and diffusion parameters are often physically inconsistent. The adjacent sink strength formulation introduced here significantly improves the predictive capability of kRE modeling, enabling accurate multiscale simulations of defect and impurity behavior in materials. This framework also establishes a foundation for future extensions, including adjacent sink strengths associated with extended defects such as dislocations and grain boundaries, offering new opportunities to resolve persistent discrepancies between experimental and simulated trapping energetics.