True process variation aware optical proximity correction with variational lithography modeling and model calibration

Optical proximity correction (OPC) is one of the most widely used resolution enhancement techniques (RET) in nanometer designs to improve subwavelength printability. Conventional model-based OPC assumes nominal process conditions without considering process variations because of the lack of variational lithography models. A simple method to improve OPC results under process variations is to sample multiple process conditions across the process window, which requires long run times. We derive a variational lithography model (VLIM) that can simulate across the process window without much run-time overhead compared to the conventional lithography models. To match the model to experimental data, we demonstrate a VLIM calibration method. The calibrated model has accuracy comparable to nonvariational models, but has the advantage of taking process variations into consideration. We introduce the variational edge placement error (VEPE) metrics based on the model, a natural extension to the edge placement error (EPE) used in conventional OPC algorithms. A true process-variation aware OPC (PVOPC) framework is proposed used the VEPE metric. Due to the analytical nature of VLIM, our PVOPC is only about 2 to 3× slower than the conventional OPC, but it explicitly considers the two main sources of process variations (exposure dose and focus variations) during OPC. Thus our post-PVOPC results are much more robust than the conventional OPC ones, in terms of both geometric printability and electrical characterization under process variations.