A systems-based approach for generating quantitative models of microstructural evolution in silicon materials processing

A systematic approach based on multiple model regression to several distinct types of experimental data is used to create a robust modeling framework for defect and impurity evolution during crystalline silicon processing. The three experimental systems considered here are Czochralski single-crystal growth, zinc diffusion, and oxide precipitation during wafer thermal annealing. All three systems are intimately connected at the atomistic level by the thermodynamic and transport properties of single point defects. The present work demonstrates how this microscopic overlap in these macroscopically distinct systems can substantially reduce uncertainty in model regression to experimental data, leading to strict bounds on the transport, reaction, and thermodynamic properties of the various species present. The resulting parameters lead to a solid, quantitative basis for modeling a wide variety of technologically important defect-related phenomena in silicon processing. Several different stochastic global optimization methods are employed to perform the computationally expensive multi-objective function minimization, namely simulated annealing, genetic algorithms, Tabu search and particle swarm optimization. These methods are compared and contrasted as part of the investigation and it is shown that a hybrid genetic algorithm that periodically incorporates a local search is the most robust approach for the types of problems considered in this work.