Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry

Abstract

Critical dimension measurement accuracy in optical scatterometry relies not only on the systematic noise level of instruments and the reliability of forward modeling algorithms, but also heavily on the measurement configuration. To construct a set of potentially high-accuracy configurations, we apply a general measurement configuration optimization method based on error propagation theory and singular value decomposition, by which the measurement accuracy is approximated as a function of a pseudo Jacobian with respect to the measurement configurations. Simulations and experiments for the optical metrology of a sub-wavelength deep-etched multilayer grating establish the feasibility of the proposed method.

Condition-number-based measurement configuration optimization for nanostructure reconstruction by optical scatterometry

“…In particular, we explored the range of incidence angles θ from 60 • to 70 • with an increment of 1 • increment, and azimuthal angles φ from 0 • to 90 • with an increment of 1 • . Compared to previous works [8,[14][15][16], the implementation of this surrogate mode allows us to consider more refined angular step sizes during the optimization process, leading to improved accuracy in identifying optimal configurations. As can be seen from figure 6, the measurement configurations with smaller condition numbers (indicated by the purple region) are distributed within the ranges of 60 • ⩽ θ ⩽ 70 • and 20 • ⩽ φ ⩽ 80 • , as well as within the ranges of 64 • ⩽ θ ⩽ 70 • and 80 • ⩽ φ ⩽ 90 • , predicting that the accuracy of the extracted parameters under these measurement configurations is less susceptible to the errors in measured signatures.…”

“…x WJ x −1 . Several MCO methods, as mentioned in [8,[13][14][15][16], employ this coefficient matrix as a foundation of the optimization objective. In this study, we treat the MCO problem based on the condition-number-based error estimation technique.…”

“…Chen et al also introduced an MCO method based on the theoretical analysis of error propagation and treated the norm of the configuration error propagating matrix as a metric to evaluate the impact of configuration errors on measurement accuracy [15]. Similarly, Zhu et al proposed an MCO method utilizing error propagation theory and singular value decomposition, and the optimal set is determined through the minimization of the Frobenius norm of a pseudo-Jacobian matrix [16]. In summary, MCO methods can be roughly classified into two categories based on their optimization objectives.…”

Optical wafer defect inspection at the 10 nm technology node and beyond

“…However, the defects reported by a standard optical defect inspection tool require a separate SEM review to determine if the defects are patterning defects [124]. Optical scatterometry [125,126], which is also referred to as optical critical dimension metrology, measures profile parameters of periodic nanostructures by leveraging the diffracted polarization properties of light on the wafer [127][128][129][130], i.e. comparing the measured change of polarization state to the simulated one.…”

Optimizing measurement configuration for x-ray critical dimension metrology based on condition number

“…The first group falls under the sensitivity-based MCO method, which assesses the specific impact of an input profile parameter on the output signatures across various measurement configurations [11][12][13]. The second group encompasses the error-based MCO method, which leverages error propagation theory in the context of the inverse problem, with a primary emphasis on optimizing parameters' uncertainties, correlations, or coefficient matrices [14,15]. These methods efficiently optimize measurement configurations, each with its own set of assumptions and advantages.…”