Assist features for modeling three-dimensional mask effects in optical proximity correction

Liberal use of assist features of both tones is an important component of the 45nm lithography strategy for many layers. These features are often sized at λ/4 on the mask or smaller. Under these conditions, formerly successful approximations of the mask near field using boundary layer methods or domain decomposition methods break down. Rigorous simulations of the mask near field must include a three-dimensional (3D) Maxwell's equation analysis, but these computations are cost-prohibitive for full-chip OPC, RET, and lithographic compliance checking applications. The purpose of this paper is to describe a simple and computationally efficient method that can improve model fidelity for 45nm assist features of either tone, while still retaining computational simplicity. While the model lacks the generality of a rigorous solution of Maxwell' sequations, it can be well-anchored to the real physics by calibrating its performance to a lithographic TCAD mask simulator. The approach provides a balanced tradeo. between speed and accuracy that makes it a superior approach to boundary layer and domain decomposition methods, while retaining the capability to realistically be deployed on a full-chip lithography simulation.