Two theories are developed to quantify image skew of photomask features caused by aberrations. In one formulation, the extent of image distortion can be described by the image asymmetry (Δxasymmetry) ,which captures both image shift and sidelobe intensity imbalance. This quantity is equivalent to the shift of the image centroid. In situations where one is more concerned with placement error than centroid shift, the change in the location of the intensity extremum (Δxshift) can be expressed as functions of the mask spectrum and the wave aberration. This theory on image shift is applied to the study of enhanced alternating PSMs. Although the optimal mask pattern is aberration-function-specific, mask spectra with gradual variations have lower placement sensitivity in general. These theories are applicable to all mask technologies and patterns.
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