Lattice kinetic Monte Carlo modeling and simulation of atomic aggregation in crystals
The control of microstructural evolution during semiconductor and metallic materials processing is increasingly challenging because of more stringent design specifications. An important example is the control of defect aggregation in crystalline semiconductor silicon which is used widely as a substrate for microelectronic device fabrication. As device feature lengths shrink, so do the maximum allowable defect cluster sizes. At the nanometer scale, the use of atomistically resolved simulation tools becomes a requirement for process design. In this thesis we apply a bond-counting variant of the lattice kinetic Monte Carlo (LKMC) method to the study of vacancy aggregation in bulk crystalline silicon. The process of vacancy aggregation leads to harmful nanovoids that continue to impact device yield and performance in polished silicon wafers. In the first part of the thesis, we address the development of a quantitatively accurate LKMC simulator using a database generated by molecular dynamics simulations for model regression and validation. We find that lattice models such as LKMC, which by definition do not explicitly accommodate off-lattice degrees-of-freedom, are unable to properly describe aggregation dynamics unless special care is applied to include the effects of off-lattice relaxations, especially at elevated temperatures. We show that the developed LKMC model is quantitatively in agreement with the predictions of MD simulations. In the next area of work, we extend the LKMC model to probe the effect of a common impurity in commercial crystalline silicon, namely interstitial oxygen, on the void morphology which is surprisingly rich. A simple trapping model is used to represent the reversible binding between oxygen atoms and vacancies. The resulting LKMC model is able to describe the diverse void morphology that is observed in experimental measurements, further demonstrating the predictive power of the LKMC model developed in this work. In the final section of the thesis, a novel spatial coarse-graining approach is presented which is aimed at greatly extending the scope of the LKMC simulations. While previous approaches for spatial coarse-graining have focused on weakly interacting systems, we develop numerical closure rules that allow for the consideration of strong interactions between particles, which are generally present in aggregating systems. A detailed comparison between the approach developed here and previous literature methods is presented. Although the present coarse-graining work is aimed at an idealized two-dimensional square lattice, our approach should be readily generalizable to more complex lattice structures in three-dimensions.
Dai, Jianguo, "Lattice kinetic Monte Carlo modeling and simulation of atomic aggregation in crystals" (2008). Dissertations available from ProQuest. AAI3309420.