Models for characterizing phase-shift defects in optical projectionprinting

An algebraic model is developed for characterizing the printability, inspection, and repair of phase-shift defects in optical projection printing. Phase-shift defects are particularly difficult to characterize because of the many parameters associated with the exposure tool and with the attenuating phase shift mask (PSM) pattern. Furthermore, the parameters change during inspection of the attenuating PSM because the mask is examined under illumination conditions which differ from the exposure illumination. An algebraic model which encompasses this large set of variables is derived by considering the electric fields under the mask to be a combination of the electric fields from the feature and defect. These fields are then combined according to the mutual coherence function for the mask illumination. A notable difficulty is the relative phase shift due to defocus between large and small features. The model is shown to be valid for defects up to 0.35 λ/NA by comparison to SPLAT. Experimental verification is made for defects impacting a 6% transmitting PSM for 0.35-μm features at i-line. The reliability of the model is illustrated by giving rules of thumb for defect printing in attenuating PSM's