A combination of library search and Levenberg-Marquardt algorithm in optical scatterometry

Abstract

Optical scatterometry has been widely used for nanostructure metrology in integrated circuit (IC) given the fast, low-cost, non-contact, non-destructive, and in-line technique. Library search is a common solution for optical scatterometry, but the deterministic error in this method is hard to be eliminated due to the limitation of the grid interval in the spectral library. Another solution is the nonlinear regression algorithm, which faces difficulty in practical applications in meeting the in-line real-time requirements as it involves the time-consuming rigorous coupled-wave analysis (RCWA) calculations in the forward modeling. In this paper, we propose a combination of library search and Levenberg-Marquardt (LSLM) algorithm to solve the problem. We apply a presorted K-dimensional tree (KD-tree) algorithm to speed up searching the initial parameters in the spectral library and replace the time-consuming RCWA calculations with the Taylor expansion in the spectral library to compute the Jacobian matrix in the Levenberg-Marquardt (LM) procedure. Simulations and experiments demonstrate that the results in the proposed method are accurate, and in particular, the speed is much faster than that in previous methods.