Measuring aberrations in lithographic projection systems with phase wheel targets

A significant factor in the degradation of nanolithographic image fidelity is optical wavefront aberration. Aerial image sensitivity to aberrations is currently much greater than in earlier lithographic technologies, a consequence of increased resolution requirements. Optical wavefront tolerances are dictated by the dimensional tolerances of features printed, which require lens designs with a high degree of aberration correction. In order to increase lithographic resolution, lens numerical aperture (NA) must continue to increase and imaging wavelength must decrease. Not only do aberration magnitudes scale inversely with wavelength, but high-order aberrations increase at a rate proportional to NA2 or greater, as do aberrations across the image field. Achieving lithographic-quality diffraction limited performance from an optical system, where the relatively low image contrast is further reduced by aberrations, requires the development of highly accurate in situ aberration measurement. In this work, phase wheel targets are used to generate an optical image, which can then be used to both describe and monitor aberrations in lithographic projection systems. The use of lithographic images is critical in this approach, since it ensures that optical system measurements are obtained during the system\u27s standard operation. A mathematical framework is developed that translates image errors into the Zernike polynomial representation, commonly used in the description of optical aberrations. The wavefront is decomposed into a set of orthogonal basis functions, and coefficients for the set are estimated from image-based measurements. A solution is deduced from multiple image measurements by using a combination of different image sets. Correlations between aberrations and phase wheel image characteristics are modeled based on physical simulation and statistical analysis. The approach uses a well-developed rigorous simulation tool to model significant aspects of lithography processes to assess how aberrations affect the final image. The aberration impact on resulting image shapes is then examined and approximations identified so the aberration computation can be made into a fast compact model form. Wavefront reconstruction examples are presented together with corresponding numerical results. The detailed analysis is given along with empirical measurements and a discussion of measurement capabilities. Finally, the impact of systematic errors in exposure tool parameters is measureable from empirical data and can be removed in the calibration stage of wavefront analysis