Improved measurement accuracy in optical scatterometry using correction-based library search

Abstract

Library search is one of the most commonly used methods for solving the inverse problem in optical scatterometry. The final measurement accuracy of the conventional library search method highly depends on the grid interval selected for each parameter in the signature library, and the time cost of the parameter extraction increases dramatically when the grid interval is decreasing. In this paper, we propose a correction-based library search method to improve the measurement accuracy for a pregenerated signature library. We derive a formulation to estimate the error between the expected solution of the inverse problem and the actually searched solution obtained by the conventional library search method. Then we use the estimate of the error as a correction term to correct the actually searched solution to improve the measurement accuracy. Experiments performed on a photoresist grating have demonstrated that the proposed correction-based library search method can achieve much more accurate measurement with negligible computational penalty to the conventional library search method in the parameter extraction. It has also been observed that the correction-based library search method has higher measurement accuracy and less time cost than the interpolation-based library search method. The proposed correction-based library search method is expected to provide a more practical means to solve the inverse problem in state-of-the-art optical scatterometry.

Development of a spectroscopic Mueller matrix imaging ellipsometer for nanostructure metrology

“…35 The regression analysis is mostly applied for the analysis of data collected by a single pixel or a number of pixels, while might be unsuitable for data analysis of a large area (usually contain millions of pixels that need to be processed) due to the intensive RCWA calculation. In this case, the library search method can be applied, 36 where a Mueller matrix spectra library is generated prior to the measurement and then the library is searched to find the best match with the measured spectra. Although the offline generation of the spectra library is time-consuming, the search itself during the online measurement can be done quickly with a global solution guaranteed.…”

Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology

“…A weighted least-squares regression analysis (Levenberg-Marquardt algorithm) [10,11] or library search [12][13][14] is then performed, during which the measurands are varied until the calculated and measured data match as much close as possible. The solution of measurandsx can be achieved by minimizing a weighted mean-square error function χ r 2 defined by…”

“…The reconstruction of the structural profile from the measured signature is a typical inverse diffraction problem with an objective of finding a profile whose theoretical signature can best match the measured one. The solution of the inverse problem usually employs two kinds of methods [9], namely the nonlinear regression method [10,11] and the library search method [12][13][14]. Both of these two approaches involve the establishment of a theoretical diffraction model that relates the optical signatures and the structural profiles associated with these signatures.…”

Convergence improvement of the Fourier modal slice absorption method for crossed gratings

“…However, simulation of the crossed grating's 0th diffraction is still time-consuming (e.g., several hours needed in example 3). Therefore, in addition to using the high-performance cluster computer system, the library search method [17] is also widely Page 19 of 21 A c c e p t e d M a n u s c r i p t 19 used in practice to improve the efficiency. But even in the library search method it is still necessary to improve the convergence for these crossed gratings.…”