Six Degrees of Freedom Displacement Measurement System for Wafer Stage Composed of Hall Sensors.

Bo Zhao,Xue Qi,Jiubin Tan,Jiawei Zhang,Jiaxin Li,Ming Zhang,Feng Li,Weijia Shi

doi:10.3390/s18072030

Abstract

This paper proposes a decoupled six degrees of freedom (DOF) displacement measurement methodology, which is accomplished by utilizing six pairs of permanent magnets and six Hall sensors. Firstly, the coordinate transformation was mathematically derived, which represented the relationships between the main coordinate system of the motion system and each body coordinate system of the Hall sensors. With the aid of an ellipsoid function and the least squares method, only the output voltages of the six Hall sensors were required to decouple the six-DOF displacement and inclination of the motion platform with high accuracy. Finally, the experimental measurements demonstrate the effectiveness of the six DOF displacement measurement methodology, based on which the maximum errors of displacements can reach 0.23 mm and the maximum errors of inclinations can reach 0.07°.

Highlights

A multiple degree-of-freedom (Multi-degrees of freedom (DOF)) measurement system is the key part in the precision stage, which is playing a critical role in many industrial applications in terms of integrated circuit (IC)
We present a six DOF displacement measurement methodology accomplished by six Hall sensors
The coordinate transformation was mathematically derived, which represented the relationships between the main coordinate system of the system and each body coordinate system of the Hall sensors

Summary

Introduction

A multiple degree-of-freedom (Multi-DOF) measurement system is the key part in the precision stage, which is playing a critical role in many industrial applications in terms of integrated circuit (IC)manufacturing and optical components production. A multiple degree-of-freedom (Multi-DOF) measurement system is the key part in the precision stage, which is playing a critical role in many industrial applications in terms of integrated circuit (IC). The increasing demands of industrial production such as lithography put stricter requirements on the precision stage, especially on the accuracy of its multi-DOF movement [1]. Sensors based on the Hall effect are widely used in different areas [2], including the position, the velocity, and the magnetic fields measurement. Hall-effect sensors can be used as position feedback devices [3]. The different position and direction of Hall effect sensors and permanent magnets generate different Hall effects [4]. A Hall sensor has an offset voltage, such that Petruk [5]

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Conclusion