Multilayer-coating-induced aberrations in extreme-ultraviolet lithography optics

A multilayer coating alters the amplitude and phase of a reflected wave fro nt. The amplitude effects are multiplicative and well understood. We presen t a mathematical formalism that can be used to describe the phase effects o f coating in a general case. On the basis of this formalism we have develop ed an analytical method of estimating the wave-front aberrations introduced by the multilayer coating. For the case of field-independent aberrations, we studied both uniform and graded multilayer coatings. For the case of fie ld-dependent aberrations, we studied only the effects of a uniform multilay er coating. Our analysis is based on a coated plane mirror tilted with resp ect to an incident converging beam. Altogether we have found, up to the sec ond order, the following aberrations: a field-dependent piston, a field-squ ared-dependent piston, defocus, field-independent tilt, field-independent a stigmatism, and anamorphic magnification. To obtain numerical results we ap ply our analysis to the specific case of a plane mirror tilted 8.2 deg with respect to an incident converging beam with a numerical aperture of 0.1. W e find that the magnitudes of the field-independent aberration coefficients for the graded coating are approximately ten times smaller than those for the uniform coating. We show that a coating can introduce anamorphic magnif ication. (C) 2001 Optical Society of America OCIS codes: 310.1620, 310.6860 , 230.4170, 220.3740, 110.3960.