ELECTROMAGNETIC CALCULATION OF SOFT-X-RAY DIFFRACTION FROM 0.1-MU-M SCALE GOLD STRUCTURES

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 lambda = 4.5 nm, and a 100-nm-wide line at lambda = 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-mu-m and below. In particular, we show that KBC should not be applied to 0.1-mu-m features and wavelengths near 1.3 nm for gaps below 11-mu-m.