Theory and practice of proximity correction by secondary exposure

This article examines the theory and practice of correcting proximity effect in direct write electron beam lithography by the introduction of a second diffuse, image-complement exposure. The common point-spread function for energy deposition in the substrate is used in formulating a solution to the inverse scattering problem, and the solution is expressed as a power series in the backscatter coefficient. The ghost technique is shown to constitute an approximation to this solution. This mathematical exposition clearly indicates the power of the technique for providing very accurate, point-by-point correction of proximity effect. Application of the procedure to nonlinear resists in a shaped-beam exposure tool is given.