Mask Design for Optical Microlithography—An Inverse Imaging Problem

In all imaging systems, the forward process introduces undesirable effects that cause the output signal to be a distorted version of the input. A typical example is of course the blur introduced by the aperture. When the input to such systems can be controlled, prewarping techniques can be employed which consist of systematically modifying the input such that it (at least approximately) cancels out (or compensates for) the process losses. In this paper, we focus on the optical proximity correction mask design problem for "optical microlithography," a process similar to photographic printing used for transferring binary circuit patterns onto silicon wafers. We consider the idealized case of an incoherent imaging system and solve an inverse problem which is an approximation of the real-world optical lithography problem. Our algorithm is based on pixel-based mask representation and uses a continuous function formulation. We also employ the regularization framework to control the tone and complexity of the synthesized masks. Finally, we discuss the extension of our framework to coherent and (the more practical) partially coherent imaging systems.