Multi-objective genetic algorithms for reducing mark read-out effort in lithographic tests

This paper describes an application of multi-objective genetic algorithms (MOGA) to an optimization problem in the context of lithographic testing. The overall aim is to find a general procedure for reducing mark read-out effort in lithographic tests with limited degradation of related performance indicators. In these tests, silicon wafers are exposed with marks which are then read-out to determine lithographic performance expressed, for instance, with the 99.7 percentile of the read-out marks. The problem was solved by applying MOGA in two stages. The first stage aims at determining a reduced layout in which for each field the same marks are read-out. In the second stage, the aim is to determine a reduced layout in which different fields have different marks read-out. In both stages the conflicting objectives are two: the number of read-out marks and the chosen performance indicator. The recombination and mutation operators applied in MOGA are different in the two stages and are derived from a statistical analysis of the input data. This approach, when applied to overlay test data, leads to a 50% reduction in read-out marks with 10% degradation range in performance indicators when compared to the full layout.