Polygon-based compensation of proximity and density effects in photomask processes

In recent years, mask critical dimension (CD) linearity and uniformity has become increasingly important. The ITRS roadmap shows the mask CD control requirements exceeding those of the wafer side beyond the 45nm node. Measurements show that there are systematic, uncorrected proximity effects even when a state-of-the-art proximity effect correction (PEC) algorithm is used. The uncorrected proximity effect is predictable with a computational model. The model for e-beam lithography and etch process contains terms to model short-range pattern density effects and plasma shadowing effect in Cr-etch. The model is calibrated using CD measurements on a test mask. The model is valid for arbitrary 2-D patterns. We present a model-based mask process compensation (MPC) method which applies geometric changes to polygons as in OPC. We discuss the goodness of model fit to the calibration data; verification of the calibrated model by SEM images; and the improvement obtained by MPC. The mask writing error, i.e. final inspection CD minus incoming database CD, was reduced by a factor of 2 through the use of MPC.