Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A front-tracking method for dendritic solidification
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
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The development of new semiconductor-device materials is currently dominated by costly and time-consuming experimental investigations in which growth parameters are varied and correlated, ex situ, to device characteristics. Model-based process development has the potential to assist greatly in optimizing growth parameters and providing models suitable for use in in situ process control. Researchers have not used this approach, however, because robust, predictive models that describe the growth of semiconductor materials are neither well-developed nor validated. This situation is changing, however, due to the availability of high-resolution microscopy and improved modeling capabilities resulting from greatly increased computer power and more efficient numerical algorithms.