Verification of partially coherent light diffraction models in x-ray lithography

Abstract

The image formed in proximity x-ray lithography is normally computed using a physical optics model that takes in explicit account diffraction processes. It is important to understand the assumption implicit in the various models and the effects that they have on the image formation. We concentrate, in particular, on the effect of the type of illumination on the quality of the image that can be obtained in proximity x-ray lithography. In this paper, different methods of calculating the diffraction of partially coherent light are compared and the approximations implicit in each discussed. In a partially coherent system, the properties of the source play an intrinsic role in image formation, so they must be treated together with the imaging process. The full detailed calculations are too complex for implementation on even a supercomputer but, for some types of sources and optical systems it is possible to simplify the problem. Particularly important is the issue of the validity of the linear shift-invariant system approximation, since it allows great improvements in computational time. We prove the validity of the approximation and verify it using a full 4D numerical integration, based on the Rayleigh–Sommerfeld theory and realized on a Cray YMP8 supercomputer. Application of the results to some physical cases of 0.25 and 0.1 μm features is presented and discussed, illustrating the wide process latitude and resolution of x-ray lithography.