Because the effects of diffraction during proximity-print x-ray lithography are of critical importance, a number of previous researchers have attempted to calculate the diffraction patterns and minimum achievable feature sizes as a function of wavelength and gap. Work to date has assumed that scalar diffraction theory is applicable—as calculated, e.g., by the Rayleigh–Sommerfeld formulation—and that Kirchhoff boundary conditions (KBC) can be applied. KBC assume that the fields (amplitude and phase) are constant in the open regions between absorbers, and a different constant in regions just under the absorbers (i.e., that there are no fringing fields). An x-ray absorber is, however, best described as a lossy dielectric that is tens or hundreds of wavelengths tall, and hence KBC are unsuitable. In this report we use two numerical techniques to calculate (on a Cray 2 supercomputer) accurate diffracted fields from gold absorbers for two cases: a 30-nm-wide line at λ=4.5 nm, and a 100-nm-wide line at λ=1.3 nm. We show that the use of KBC introduces unphysically high spatial frequencies into the diffracted fields. The suppression of these frequencies—which occurs naturally without the need to introduce an extended source or broad spectrum—tremendously improves exposure latitude for mask features near 0.1 μm and below. In particular, we show that KBC should not be applied to 0.1-μm features and wavelengths near 1.3 nm for gaps below 11 μm.
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Schattenburg et al. (1991) studied this question.