Dynamic motion of mask membrane in x-ray stepper

Abstract

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 mask 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.

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

“…3 In this article, a new analysis method for case ͑c͒, in which the deflection is caused by the wedge action of the gas film between the mask and the wafer, is described and the calculation results, which show good agreement with the experimental data 1 obtained by Canon Inc., are discussed. 3 In this article, a new analysis method for case ͑c͒, in which the deflection is caused by the wedge action of the gas film between the mask and the wafer, is described and the calculation results, which show good agreement with the experimental data 1 obtained by Canon Inc., are discussed.…”

Motion error correction for non-contact ultrasonic motor driven by multi-layered piezoelectric actuators

“…A unique feature of the squeeze effect is that it provides load carrying capacities without a supply of compressed air or relative slide motion, whereas aerostatic and the hydrodynamic guideways based on wedge effects have additional requirements. These factors are utilized for analysis of the squeeze film damper (Lin et al 2002), silicon accelerometer, quartz resonators (Veijola et al 1995;Andrews et al 1995), and deflection of a mask membrane when a wafer approaches (Uchida et al 1996). A research study was conducted in order to further explore practical applications of squeeze gas bearings in the 1960s.…”