Monte Carlo Analysis of the Evolution from Point to Extended Interstitial Type Defects in Crystalline Silicon
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Monte Carlo Analysis of the Evolution from Point to Extended Interstitial Type Defects in Crystalline Silicon Antonino La Magna, Salvatore Coffa and Sebania Libertino CNR-IMETEM Stradale Primosole 50, I95121 Catania Italy ABSTRACT We present a Lattice Kinetic Monte Carlo study of the atomic evolution leading to {311} defects formation upon annealing of a damaged Si-crystal. Self-interstitial (I) agglomeration is modeled by using local interaction and considering the energetic cost to under/over coordinate the Si atoms belonging to an I-complex. The static properties of the I aggregates as derived by molecular dynamics calculations, in the two extreme regimes of very small and very large clusters, have been mapped in the model. The typical evolution of an excess of Si ions is characterized by three distinct stages: (1) the formation of clusters consisting of few interstitials in a over-coordination state, (2) their redistribution in larger agglomerates containing a few of these small I clusters all preserving their original structure, (3) a transition leading to Is rearrangement along the chains, which are the structural units of {311} defects. The duration of the preliminary stages critically depends on temperature and density of the added atoms. INTRODUCTION One major challenge for the applied theoretical research is to achieve a deep comprehension of the non-equilibrium phenomena involving damage evolution in c-Si undergoing to thermal process steps. This field conjugates uniquely the technological relevance with the frontiers of fundamental investigations on the kinetics of complex systems. In this respect, a paradigmatic specific argument is the pathway leading to the rod-like {311} formation or, more generally, the evolution of an excess of Si ions in a Si crystal matrix. In these last years many works have been devoted to investigate the precursor complexes which should store interstitials in the early stages of their evolution upon annealing, i.e. before {311} formation [1,2]. However a definitive comprehension of the experimental findings in terms of microstructural evolution is still lacking. Indeed, the studies on the stability of I-type complexes performed using quantum mechanical calculations (QMC) [3,4] are not able per se to predict the behavior of any evolving system. Statistical methods could satisfy the demand for an atomic level investigation of the system evolution, if the relations between structure and stability, derived by QMC, were correctly recovered in such codes. In the case of a vacancy (V) systems in c-Si, it has been shown [5] that Lattice Kinetic Monte Carlo (LKMC) constitutes a suitable framework to recover the statics derived by QMC. In this code defect-defect effective interaction models are used instead of fixed form for the aggregate binding energy. In the V case new insights in the mechanism ruling the ripening were derived [5,6]. In this work LKMC is applied to investigate the evolution of an I super-saturation in cSi. The model implemented allows one to map the results of QMC, u
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