Source mask optimization using real-coded genetic algorithms

Source mask optimization (SMO) is considered to be one of the technologies to push conventional 193nm lithography to its ultimate limits. In comparison with other SMO methods that use an inverse problem formulation, SMO based on genetic algorithm (GA) requires very little knowledge of the process, and has the advantage of flexible problem formulation. Recent publications on SMO using a GA employ a binary-coded GA. In general, the performance of a GA depends not only on the merit or fitness function, but also on the parameters, operators and their algorithmic implementation. In this paper, we propose a SMO method using real-coded GA where the source and mask solutions are represented by floating point strings instead of bit strings. Besides from that, the selection, crossover, and mutation operators are replaced by corresponding floating-point versions. Both binary-coded and real-coded genetic algorithms were implemented in two versions of SMO and compared in numerical e xperiments, where the target patterns are staggered contact holes and a logic pattern with critical dimensions of 100 nm, respectively. The results demonstrate the performance improvement of the real-coded GA in comparison to the binary-coded version. Specifically, these improvements can be seen in a better convergence behavior. For example, the numerical experiments for the logic pattern showed that the average number of generations to converge to a proper fitness of 6.0 using the real-coded method is 61.8% (100 generations) less than that using binary-coded method.