Servo system design of a high-resolution piezo-driven fine stage for step-and-repeat microlithography systems

Most microlithographic steppers use a dual stage design to achieve both large stroke and high precision motion. The fine-stage of the stepper compensates for the insufficient resolution of the coarse stage. In this design, the stepper fine-stage adjusts the semiconductor wafer position and orientation to a close to 10-nm positioning accuracy with a 10-micron motion stroke. The stage uses three sets of piezoelectric actuators to adjust the X, Y positioning and θ orientation. The servo controller positions and orients the stage to meet the specification. A multivariable system identification process indicates that there is a serious coupling among the system dynamics in different degrees of freedom. In addition, the actuators possess a non-linear hysteresis effect. A diagonal controller, based upon the linear-quadratic Gaussian algorithm, is designed to overcome the actuators´ hysteresis effect, and decouple the plant at steady state. The experimental results show that the resultant control achieves a satisfactory performance