Analysis of deformation of X-ray mask membrane in aligner motion

Deformation of X-ray mask membrane is analysed theoretically based on the viscous fluid dynamics in the case where a solid boundary (wafer) placed adjacent to the membrane moved perpendicular to the membrane, It is assumed that the membrane and its support are axisymmetric and the gap between the membrane and the wafer is so thin that the Hele-Shaw flow theory can be applied. It is shown that the center of the membrane is deflected in the same direction as the wafer motion and that the maximum deflection depends on the membrane tension and the final gap. The results of analysis agree well with the experiment.