Optical proximity correction (OPC)-friendly maze routing

As the technology migrates into the deep submicron manufacturing (DSM) era, the critical dimension of the circuits is getting smaller than the lithographic wavelength. The unavoidable light diffraction phenomena in the sub-wavelength technologies have become one of the major factors in the yield rate. Optical proximity correction (OPC) is one of the methods adopted to compensate for the light diffraction effect as a post layout process. However, the process is time-consuming and the results are still limited by the original layout quality. In this paper, we propose a maze routing method that considers the optical effect in the routing algorithm. By utilizing the symmetrical property of the optical system, the light diffraction is efficiently calculated and stored in tables. The costs that guide the router to minimize the optical interferences are obtained from these look-up tables. The problem is first formulated as a constrained maze routing problem, then it is shown to be a multiple constrained shortest path problem. Based on the Lagrangian relaxation method, an effective algorithm is designed to solve the problem.