Fast synthesis of topographic mask effects based on rigorous solutions

Topographic mask effects can no longer be ignored at technology nodes of 45 nm, 32 nm and beyond. As feature sizes become comparable to the mask topographic dimensions and the exposure wavelength, the popular thin mask model breaks down, because the mask transmission no longer follows the layout. A reliable mask transmission function has to be derived from Maxwell equations. Unfortunately, rigorous solutions of Maxwell equations are only manageable for limited field sizes, but impractical for full-chip optical proximity corrections (OPC) due to the prohibitive runtime. Approximation algorithms are in demand to achieve a balance between acceptable computation time and tolerable errors. In this paper, a fast algorithm is proposed and demonstrated to model topographic mask effects for OPC applications. The P r o Gen To pographic Ma s k (POTOMAC) model synthesizes the mask transmission functions out of small-sized Maxwell solutions from a finite-difference-in-time-domain (FDTD) engine, an industry leading rigorous simulator of topographic mask effect from SOLID-E. The integral framework presents a seamless solution to the end user. Preliminary results indicate the overhead introduced by POTOMAC is contained within the same order of magnitude in comparison to the thin mask approach.