Dynamic motion of mask membrane in x-ray stepper

This article presents a new analysis method and experimental results for the deflection and vibration of x-ray masks, which are caused by the squeeze effect of the gas film between a mask and a wafer in x-ray steppers. The deflection and vibration occur when a mask-to-wafer gap setting is executed or if the wafer vibrates in the mask direction during stepping motion with a narrow gap. They are not only detrimental to the throughput, but may also damage the mask membrane. Lees' difference approximation method is applied to a compressible Reynolds' equation and the equation of motion for the mask membrane. The main results of calculations and experiments, which showed good agreement with each other, are outlined below. (1) When the wafer approaches the mash: at a constant velocity, the mask deflection increases in proportion to the velocity, and the mask deflection is larger for a smaller mask tensile stress. (2) When the wafer vibrates in the mask direction, the amplitude of the mask vibration increases with increasing the wafer frequency, and reaches a maximum value at a frequency that depends on the gap size. The maximum amplitude of a tested mask becomes 4 times as large as the wafer amplitude. (3) For a high frequency and narrow gap, the mask vibrates while deflecting convexly in the direction opposite to that of the wafer. (C) 1996 American Vacuum Society.