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 = PP. 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.
An accurately predictive process model is of utmost importance to the traditional Optical Proximity Correction (OPC),
the leading-edge Inverse Lithography Technology (ILT), or other simulation software for IC manufacturing. There are
many parameters and methods in constructing and calibrating a model. But it is difficult to obtain a good empirical
model, partly because the assessment of the final result is lacking in terms of quantitative and objective metrics. We set
out to define certain practical guidelines, e.g. Model Effectiveness Standard Index (MESI), for analyzing parameter
uncertainty and estimating simulation uncertainty of an empirical model, so that we know what to choose among many
similar candidates. The discussion is framed in the estimation theory of statistics.
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