Mask membrane deflection caused by mask tilt during the wafer stepping motion in x-ray steppers

Abstract

A new analysis method for deflection of the mask membrane during the wafer stepping motion in x-ray steppers has been developed. The deflection is caused by the wedge action of the gas film between the mask and the wafer if the mask tilts slightly relative to the plane on which the wafer is traveling. The deflection is not only detrimental to the throughput of x-ray steppers, it may also damage the mask membrane. Lees’ difference approximation method is applied to Reynolds’ equation for the gas film and the equation of motion for the membrane. The results calculated show good agreement with the experimental results (Ref. 1) obtained by Canon Inc. (1) The larger the tilt angle of the mask and the narrower the mask-to-wafer gap, the larger the deflection of the mask membrane. (2) In order to maintain the deflection of the membrane within 1 μm in the calculated mask, the tilt angle of the mask must be within 20 μrad under conditions of a 15 μm mask-to-wafer gap, a 30 mm stepping distance, and a wafer velocity of 100 mm/s. If the stepping distance becomes longer, the tilt angle must be more strictly controlled.