Accurate and efficient modeling of nucleation and growth processes

Abstract

We have developed an efficient approach for modeling of nucleation and growth processes in nonhomogeneous systems, by considering the evolution of the moments of the precipitate size distribution at each point on a spatial grid. Through the use of an energy-minimizing closure assumption, the size distribution can be reproduced from the moments and thus the evolution of the moments can be derived directly from the full set of discrete rate equations describing the size evolution. The model has been implemented in a general reaction/diffusion simulator using a table look-up scheme for computational efficiency. We have tested the moment-based approach and found that it accurately reproduces the results of the full model over a range of processing conditions. The model has been applied with excellent results to processes occurring during VSLI fabrication (e.g. dopant precipitation, evolution of point defect clusters and dislocation loops following ion implantation), reproducing behavior such as Ostwald ripening and nucleation rates, as well as more complex phenomena such as reverse annealing and recovery following temperature steps. The modeling approach is general enough to apply to a large range of processes and materials systems and has been extended to consider the formation of aggregates with varying composition.