Resolution limits in x-ray lithography

Abstract

During an x-ray lithography proximity exposure x rays generate electrons in the resist which deposit energy along a finite range. This range combines with diffraction spreading to degrade the image resolution. The component of resolution arising from electron range is often taken as the Grun range of the most copiously generated photoelectrons, about 0.1 μm at an exposure wavelength of 10 Å. Although some experiments have shown much better resolutions, there is a widespread belief that photoelectron range limits resolution to about 0.1 μm. We have analytically modeled the distribution of energy deposited by Auger and photoelectrons. Near an edge the distribution is well-fit by an error function. The standard deviation of this error function, which we define as the ‘‘effective range,’’ is about 0.01 μm at 10 Å in poly(methylmethacrylate) (PMMA) resist. For all energies of interest to x-ray lithography the effective range of the electrons is much smaller than the Grun range, explaining the high-resolution results. It is diffraction which dominates the resolution of conventional x-ray lithography. Consequently, reducing the gap in proximity printing should produce resolutions far below 0.1 μm, while retaining all the latitude inherent in the x-ray lithography process.