Geometric and motion error model of wafer stepper precision motion stages

The precision of wafer stage and mask stage motion is improved by a geometric and motion error model of the wafer stepper motion stages.A lower numbered body array is introduced to describe the wafer stepper topology with a homogeneous coordinate transformation used to model the geometric and motion errors of a typical body in the multi-body system.Multi-body kinematics are employed to derive the structural and motion relations and the corresponding location error equation.The motion error chain for the wafer stepper is analyzed to develop a versatile error model.An entire wafer stepper is analyzed as an example to determine its errors.The method provides a reference for wafer stepper precision design.