Conformal mapping in microlithography: Theory & Application

It is shown that imaging with a quasi Gaussian beam (electron or laser microlithography) in thin resist layers is equivalent to a diffusion process. Therefore when the spot size is of the order of the dimension of the sought feature, the image rendered by the convolution of the beam with the said feature obeys the steady state Laplace equation. Hence, we investigate the use of harmonic functions in an attempt to increase the acuity of the image. Working through the mathematical analysis and simulations we show that a certain mapping reminiscent of a 'conformal mapping' improves the acuity of the image in the corners. Experimental results support our conjecture.