Simulation of x-ray mask distortion

X-ray mask distortion caused by membrane and absorber stresses is investigated by computer simulation using differential equations derived from thermal stress theory. A frame supporting the membrane is stretched toward its center by the membrane tension, and the amount of displacement increases with membrane size and depends on the uniformity of the stress. Distortion is also caused by frame bowing resulting from the membrane and the absorber stresses. These distortions can be reduced by using a thick frame. Stress variation in the membrane causes in-plane distortion of the membrane. To suppress the maximum displacement to less than 0.02 μm, this stress uniformity must be less than 1%. Out-of-plane distortion of the membrane caused by the absorber stress is very sensitive to pattern size.