Double-exposure mask synthesis using inverse lithography

Abstract

Inverse lithography mask design and double-exposure lithog- raphy are two technologies that have gained a lot of attention in the recent past. Inverse lithography consists of synthesizing the input mask that leads to the desired output wafer pattern by inverting the mathemati- cal forward model from mask to wafer. Double-exposure lithography uses two pairs of mask and exposure to print a single desired wafer pattern. It usually involves splitting the latter into two parts. In this work, we present some preliminary results in our unique effort to combine the previous two powerful techniques. The goal is to use the inverse imaging approach to automatically synthesize the masks required to print the desired wafer pattern employing double-exposure lithography. We em- ploy the pixel-based mask representation, analytically calculate the gra- dient, and use a cyclic coordinate descent optimization algorithm to syn- thesize the two masks. We present results for chromeless phase-shift masks for an idealized case of a coherent imaging system =0 using the Kirchhoff approximation. The results indicate that our algorithm au- tomatically splits the target pattern into two overlapping parts, which are used separately during the individual exposures. Furthermore, the proposed approach is also capable of resolving the phase conflicts. The comparison with a single-exposure case indicates a superior contrast and no hot-spots. © 2007 Society of Photo-Optical Instrumentation Engineers.