Mask shops typically use carbon to repair any clear defects identified on
a mask, irrespective of the type of mask. However, carbon can have
different characteristics than the original patterning material on the
mask. Therefore, a mask that is repaired using carbon may not optically
perform as if it were defect-free. An automated method of repairing a
clear defect on an attenuated phase shifting mask (PSM) provides an
optimized plug size/shape. In this method, a repair solution to the clear
defect can be simulated, thereby allowing the repair decision for an
attenuated PSM to be advantageously made at the same time that inspection
is done and before actual repair. Simulation can include performing
model-based OPC on the repair solution.