Fast and accurate computation of partially coherent imaging by stacked pupil shift operator

Abstract

In this paper, the stacked pupil shift operator approach to partially coherent imaging as first introduced by Yamazoe1 has been further pursued and investigated with a focus on its practical performances in lithographic simulations.. The stacked pupil shift operator P is a singular matrix obtained by stacking pupil functions that are shifted according to the illumination condition. The transmission cross coefficient (TCC) matrix can then be constructed in an elegant fashion as TCC = P†P. The new development presented in this paper utilizes a matrix multiplication technique to speed up the computation of TCC matrix by tenfolds on average. This enables fast and accurate generation of TCC kernels for complicated illumination source shapes where a large number of source points are required to obtain good accuracy. The eigenvalue decomposition is applied to the TCC matrix instead of the stacked pupil shift operator P so that mask and resist proximity effects can easily be included in the effective TCC kernels.