Theory of feature broadening in direct-write optical lithography

Abstract

In direct-write optical lithography (DWOL), an intense, nearly-resonant standing light wave of wavelength λ is used to focus a collimated atomic beam. In this way, a grating structure is deposited on the substrate. We argue that during DWOL adatoms move primarily as a result of collisions with incident atoms. The resulting equation of motion for the film surface describes the way in which the features smooth and broaden as the film thickness increases. We find that as the film thickness grows large, the topography tends to a steady state form with amplitude proportional to λ4. No matter how well focused the incident atomic flux is, in the steady state the surface corrugations have a full-width-at-half-maximum that is greater than 45% of the peak-to-peak distance.