A model of diffusion-controlled annealing of dislocation loops in pre-amorphized silicon

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Abstract
A theoretical model for the process of annealing of a layer of interstitial dislocation loops parallel and close to a planar specimen surface, such as is produced by pre-amorphization of silicon by implantation with germanium, is presented. On the assumption that the kinetics are determined by diffusion of either interstitials or vacancies and using a mean-field approximation, an equation is derived for the rate of change of each loop radius in terms of the size distribution of loops. The results of a numerical solution of this model are compared with transmission electron microscope measurements of mean loop sizes and densities in a set of specimens where the depth of loops from the surface and the annealing time were systematically varied. The results of the model are in reasonable agreement with experiment if a suitable initial loop size distribution is chosen. The model predicts the observation that removal of the loops is easier for smaller loop depths. The combined effects of loop coarsening and loss of interstitial atoms by transport to the surface are reproduced, the latter process being more important for smaller loop depths. The results imply that the initial process of nucleation of the loops has a strong influence on the subsequent behaviour during annealing. Suggestions are made as to how the loops might be avoided in device processes.