Genetic algorithms for geometry optimization in lithographic imaging systems
This paper illustrates the use of genetic algorithms (GA) in optimizing mask and illumination source geometries for lithographic imaging systems. The main goal of the proposed optimization process is to find optimum conditions for the generation of certain features like lines and spaces patterns or arrays of contact holes by optical projection lithography. Therefore, different optical resolution enhancement techniques, such as optical proximity correction (OPC) by sub-resolution assists, phase shift masks, and off-axis illumination techniques are combined and mutually optimized. This paper focuses on improving both the genetic algorithm's settings and the representation of the mask and source geometries. It is shown that these two issues have a significant impact on the convergence behavior of the GA. Different representation types for the mask and source geometry are introduced, and their advantages and problems are discussed. One of the most critical tasks in formulating the optimization problem is to set up an appropriate fitness function. In our case, the fitness function consists of five sub-functions, which ensure valid geometries, correct feature dimensions, a stable process for different defocus settings, the mask's manufacturability and inspectability, and that no other features besides the specified target are printed. In order to obtain a stable and fast convergence these criteria have to be assessed. Different weight settings are introduced and their impact on the convergence behavior is discussed. Several results show the potential of the proposed approach and directions for further improvements.