Kinematic analysis of the reticle stage for lithography with gamma ratio mapping method

This paper presents kinematic analysis of a vertical type 6 DOF reticle stage for lithography process and a novel mapping method using a ratio of input-output relationship. The vertical type reticle stage system was designed for installing masks in photo-lithography process, and controlled using six precise gap sensors. As the stage is directly actuated by voice coil motors (VCM) and supported by plate springs, it has no mechanical contact or bearings those make mechanical wear and hysteresis effect in nano-level actuating. Meanwhile, the stage has cross coupled kinematics between each axes, so in this paper, the forward and inverse kinematics were solved to get an accurate reference position. In addition, a novel mapping method that reduces overall error using a ratio between command and output is proposed. The proposed mapping method needs only one measurement process to get the equal accuracy that obtained by two or three times measurement iterations in conventional mapping process. The mapping process was modeled and analyzed by input-output relation named as gamma ratio in this paper.