Image quality compensation via tolerance sensitivity matrix method in lithography

Abstract

This article introduces an image quality compensation method based on tolerance sensitivity matrix analysis. First, use the optical software CODE V to establish an optical system model, and add tolerances to a set of i-line projection objectives with a numerical aperture of 0.33. Then the singular value decomposition (SVD) is performed on the sensitivity matrix composed of the structural parameters of the system's sensitive components to select the image quality compensator. The image quality is compensated by coupling the determined three compensators to each other. Comparing the performance of the compensated lithography objective lens with the tolerance lithography objective lens, the system wave aberration is converged from 33.5nmRMS to 23.9nmRMS, the wave aberration PV value is reduced from 0.07λ to 0.02λ for the tolerance objective lens, and the distortion is reduced from 491nm to 48.6nm. The rate is reduced from 0.03ppm to 0.01ppm. This study uses fewer compensators to restore the system wave aberration, distortion and magnification to close to the design level, effectively reducing the manufacturing difficulty and cost of the projection lithography objective lens, and verifying the effectiveness of the compensation method and model.