Evaluation of energy barriers for topological transitions of Si self-interstitial clusters by classical molecular dynamics and the kinetic activation-relaxation technique

Abstract

The modeling of self-interstitial defects evolution is key for process and device optimization. For a self-interstitial cluster of a given size, several configurations or topologies exist, but conventional models assume that the minimum energy one is instantaneously reached. The existence of significant energy barriers for configurational transitions may change the picture of defect evolution in non-equilibrium processes (such as ion implantation), and contribute to explain anomalous defect observations. In this work, we present a method to determine the energy barriers for topological transitions among small self-interstitial defects, which is applied to characterize the Si self-interstitial and the di-interstitial cluster. Keywords-silicon; self-interstitial cluster; configurational transition; energy barrier I. INTRODUCTION Self-interstitial defects are commonly formed in Si as a consequence of fabrication processes, and may range from small selfinterstitial clusters (I-clusters) to extended defects, such as rod-like defects and dislocation loops. For I-clusters several configurations have been reported, each one characterized by a specific topology and a formation enthalpy [1]. Traditional defect evolution models only consider the minimum energy configuration for each cluster size, by assuming that there are no barriers among them. These models successfully describe defect kinetics [2], but they fail to explain some experimental observations, like the growth of dislocation loops in shallow Ge implanted Si, without the previous formation of rod-like defects [3]. The relevance of higher energy I-clusters configurations depends to a large extent on the existence and height of energy barriers for configurational transitions. The Nudged Elastic Band Method (NEBM) can be used to calculate energy barriers in a static way, by considering the initial, final, and at least one intermediate position of all moving atoms. As a predefined atomic position along the pathway for a configurational transition is considered, calculated energy barriers may be overestimated, if the pathway followed is not the lowest energy one. Classical molecular dynamics (CMD) uses a semi-empirical potential to simulate the vibration and movements of atoms, can provide the energetic and topological description of I-clusters, and simulate their dynamics. However, the determination of energy barriers for configurational transitions with CMD may be very time consuming, as these transitions are usually infrequent events compared to the fast vibrational movement of atoms.