Correction on the effect of numerical aperture in optical scatterometry

Optical scatterometry, also referred to as optical critical dimension (OCD) metrology, has been introduced for critical dimension (CD) monitoring and overlay metrology with great success in recent years. Forward modeling to calculate the optical signature from the measured diffractive structure is one of the most important issues in OCD metrology. To simplify the forward modeling approach, such as rigorous coupled-wave analysis (RCWA), the incidence and azimuthal angles are usually assumed to be constant. However, since some focusing elements, such as focusing lens or parabolic mirrors with finite numerical aperture (NA), are always used to gain a sufficient small spot size onto the sample, this assumption is not true in the whole exit pupil of the focusing elements, leading to a modeling error in forward modeling, and finally leading to a fitting error in OCD metrology. In this paper, we propose a correction method with consideration of the effect of NA to decrease the modeling error in the forward modeling. The correction method is an average integral method based on Gaussian quadrature in two dimensions inside a circle, and is performed on forward modeling with varied incidence and azimuthal angles over the exit pupil. Experiments performed on silicon gratings with a Mueller matrix polarimeter have demonstrated that the proposed correction method achieves a higher accuracy in OCD metrology.