SPIE - Education Optimization Methods for Lithographers SC1159

Mathematical Optimization is an empowering and indispensable tool in productive engineering practices. A variety of lithographical applications rely on optimization methods to deliver efficient engineering solutions: Process engineers routinely tune the number of films and optical properties of resist stacks, while lithographers subject the projection illuminator towards a laborious perfection by using Source-Mask Optimization (SMO). The spectrum of methods, which are used in the aforementioned (and numerous other) everyday practices, is broad. Finding a suitable algorithm for a given problem is not always easy. This course classifies lithography-related optimization problems, scrutinizes state-of-the-art optimization algorithms, and then makes recommendations on how to properly match these problems with effective and practical optimization methods. We will start by working with unconstrained and constrained one-dimensional problems, move on to consider linear programming, and then address special types of high-dimensional problems, all illustrated with lithographical examples, including mask-inverse lithography (ILT) and SMO. The course will continue with an outline of modern optimization algorithms and explanation of their properties, strengths, weaknesses, and limitations.