Modeling phase-shifting masks

An algebraic image perturbation model is introduced which used the point spread function of the lens and the mutual coherence of the illumination to give insight into the interactions of auxiliary patterns with features for the phase shifting mask technology. The model is based on adding electric field contributions and the cross term is shown to characterize the dominant interaction as a function of the number of auxiliary features, the relative coherence of the illumination, and the spreading of the image of the auxiliary pattern toward the feature. Data on the point/line spread functions and the mutual coherence are given and used to verify the accuracy of quantitative predictions of the change in peak intensity for lines and contacts when nonprinting phase shifting auxiliary patterns are added.