In modern industry, there usually exist high-precision stages, such as reticle stages and wafer stages in VLSI lithography tools, metrology stages in coordinate measurement machines, motion stages in CNC machine tools, etc. These stages need high-precision measurement/metrology systems for monitoring its XY movement. As the metrology systems are quite accurate, we often cannot find a standard tool with better accuracy to implement a traditional calibration process for systematic measurement error (i.e., stage error) determination and measurement accuracy compensation. Subsequently, self-calibration technology is developed to meet this challenge and to solve the calibration problem. In this chapter, we study the self-calibration of two-dimensional precision metrology systems and present a holistic self-calibration strategy. This strategy utilizes three measurement views of an artifact plate with mark positions not precisely known on the un-calibrated two-dimensional metrology stage and constructs relevant symmetry, transitivity, and redundancy of the stage error of the metrology stage. The misalignment errors of all measurement views, especially including those of the translation view, are totally determined by detailed mathematical manipulations. Then, a redundant equation group is synthesized, and a least-square–based robust estimation law is employed to calculate out the stage error even under the existence of random measurement noise. Furthermore, as the determination of the misalignment error components of the measurement views is rather complicated but important in previous and the proposed methods, this chapter also significantly analyzes the necessity of this costly computation. The proposed approach is investigated by simulation computation, and the simulation results prove that the proposed determination scheme can calculate out the stage error rather exactly without random measurement noise. Furthermore, when there exist various random measurement noises, the calibration accuracy of the proposed strategy is also investigated, and the results illustrate that the standard deviations of the calibration error are consistently with the same level of those of the random measurement noises. All these results verify that the proposed scheme can realize the stage error rather accurately even under the existence of random measurement noise. The practical procedure for performing a standard self-calibration is also introduced for engineers to facilitate actual implementation.
Part of the book: New Trends and Developments in Metrology