Fast synthesis of topographic mask effects based on rigorous solutions

Abstract

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 roGen Topographic Mask (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.

General imaging of advanced 3D mask objects based on the fully-vectorial extended Nijboer-Zernike (ENZ) theory

“…Although, the most appropriate way to deal with this issue would be to replace the Kirchhoff boundary conditions approach by a rigorous treatment of the electromagnetic boundary problem, there remains a large threshold in applying this approach due to the large computational implications. As a result, many alternative model-based methods have been proposed that try to include the main topography effects 19,20 . Although these methods have proven to be sufficient for the time being, we see them merely as temporary solutions as the ongoing shrinkage of mask features demands for more and more topography effects to be included.…”