Thermodynamic and morphological analysis of large silicon self-interstitial clusters using atomistic simulations

Abstract

We study computationally the formation of thermodynamics and morphology of silicon self-interstitial clusters using a suite of methods driven by a recent parameterization of the Tersoff empirical potential. Formation free energies and cluster capture zones are computed across a wide range of cluster sizes (2 < Ni < 150) and temperatures (0.65 < T/Tm < 1). Self-interstitial clusters above a critical size (Ni ∼ 25) are found to exhibit complex morphological behavior in which clusters can assume either a variety of disordered, three-dimensional configurations, or one of two macroscopically distinct planar configurations. The latter correspond to the well-known Frank and perfect dislocation loops observed experimentally in ion-implanted silicon. The relative importance of the different cluster morphologies is a function of cluster size and temperature and is dictated by a balance between energetic and entropic forces. The competition between these thermodynamic forces produces a sharp transition between the three-dimensional and planar configurations, and represents a type of order-disorder transition. By contrast, the smaller state space available to smaller clusters restricts the diversity of possible structures and inhibits this morphological transition.