Optimum design of a large area, flexure based XY theta mask alignment stage for a 12-inch wafer using grey relation analysis

Abstract

An optimum design methodology for a large area, flexure-based XY theta mask alignment stage, which can be applied to a 12-inch wafer photolithography process, was presented. The XY theta micropositioning stage consisted of a working plate with a 12-inch hole in the center, three piezo actuators, and three displacement amplifiers based on the bridge-type flexure mechanism. Grey relation analysis and orthogonal array were incorporated with finite element analysis to find optimum design conditions. The grey relation grade with weight factors was used to simultaneously optimize three objective characteristics of the micropositioning stage: the maximum stroke, deflection of the working plate, and first natural frequency. The optimally-designed stage was fabricated by wire electrical discharge machining and tested to investigate its performance. The proposed stage showed the first natural frequency of 57 Hz and the maximum stroke of 122.84 mu m, 108.46 mu m, 0.685 mrad in the x-, y-, and theta-direction, respectively. The resolutions in corresponding directions were 11 nm, 10 nm, and 0.5 mu rad. The performance of the stage was improved by optimum design process, and the experimental results were in good agreement with the predicted ones from the finite element analysis.