Zernike coefficients: Are they really enough?

Abstract

Zernike aberration coefficients are routinely used in simulation exercises for lithographic printing and the discovery of Zernike values is considered strategic for many lithographic process engineers. Thanks to progress in actinic interferometry and resist base evaluation techniques, reliable estimates of Zernike component magnitudes are possible in many cases. It is expected that wavelength reductions from 248 nm and 193 nm to 157 nm along with continued use of aspheric elements in high NA designs will lead to an increase in the component of wavefront aberration that is not adequately characterized by a 36 term Zernike polynomial. Wavefront errors not well characterized by a conventional Zernike fit are variously termed mid-spatial frequency errors, lack of fit, residuals, flare, scatter etc. This paper explores the importance, characterization and analysis of these residual errors and attempts to clarify the boundaries between the various classes of wavefront error. We find that an accurate assessment and model of lens performance requires the inclusion of both residual wavefront errors and flare effects in addition to the customary 36 term Zernike expansion.