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

In X-ray critical dimension metrology (XCD), it is a common practice to select an appropriate measurement configuration, including incidence angle, azimuth angle, exposure time, etc., to improve measurement results. This is crucial as the quality of the obtained signature is impacted not just by the instrument's precision, but also by the specific chosen measurement configuration. This is known as the measurement configuration optimization (MCO) problem. This paper proposes a general MCO method based on the theory of error propagation and error estimation techniques using condition numbers. Finally, the MCO problem in XCD is framed as optimizing the "max-min" condition number of the coefficient matrix within the context of linear error estimation. The proposed method is showcased on "virtual experiments" conducted via simulations to determine the optimal combinations of rotation angles along two coordinate axes. The method's feasibility is substantiated through a comparison with the distributions of parameter uncertainty. The results suggest that the proposed method holds promise as an alternative approach for comprehensive evaluation in the context of the MCO problem in XCD and various measurement scenarios.