MECHANICAL DISTORTIONS OF SUPPORT FRAMES FOR X-RAY-LITHOGRAPHY MASKS

The stringent requirements for low-distortion x-ray lithography masks make it essential to minimize the mechanical displacements of the supporting structure. Basic axisymmetric models of a mask frame are investigated to determine the out-of-plane deflection (or bow) induced in the support structure by the tension in the membrane. Circular rings with both rectangular and nonrectangular cross sections are evaluated by finite elements. A theoretical analysis verifies the finite element models and also provides analytical expressions for determining the bow as a function of the membrane stress. In-plane distortions created by the effects of gravity on a vertically supported mask blank are also considered. Two- and three-dimensional finite element models are developed for mapping the membrane distortions resulting from the gravitational loads. Results show that in-plane displacements can be minimized by optimizing the type of mount and actual mounting position for the specific mask considered.