Fast and accurate solution of inverse problem in optical scatterometry using heuristic search and robust correction

Abstract

Library search is one of the most commonly used methods in optical scatterometry, which consists of the beforehand construction of a signature library and the grid search. The efficiency of existing search algorithms such as k-dimensional tree method and locality-sensitive hashing heavily depends on the size of the signature library and usually is inversely proportional to the library scale. Additionally, since the two-norm based objective function is quite sensitive to the outliers, the abnormally distributed measurement errors will bias the solution of the traditional chi-square or maximum likelihood function. In the present paper, the authors propose a heuristic search algorithm and a robust correction method to realize the fast library search and to achieve the more accurate results, respectively. Instead of searching in the signature library, the authors perform the search procedure in an extra constructed Jacobian library using the principle of gradient-based iteration algorithms, by which the fast search speed can be achieved for an arbitrary scale library. After the search, a robust correction procedure is performed on the basis of the searched optimal parameter set to obtain the more accurate results. Simulations and experiments performed on an etched silicon grating have demonstrated the feasibility of the proposed heuristic search algorithm and robust correction method.