Modeling and Design Optimization of a Linear Motor with Halbach Array for Semiconductor Manufacturing Technology

Abstract: This paper presents analytical modeling and design of a high-acceleration, low-vibration slotless double-sided linear motor with an arbitrary Halbach array for lithography machines used in semiconductor manufacturing technology. Amperian current and magnetic charge models of permanent magnets are integrated into a hybrid approach to develop comprehensive analytical modeling. Unlike conventional methods that treat magnets as sources for Poisson's equations, the solution is reduced to Laplace's equations, with magnets being represented as boundary conditions. The magnetic fields and potentials within distinct regions, along with machine quantities such as shear stress, force-angle characteristics, torque profile, attraction force, misalignment force, and back-EMF, are derived, comprehensively analyzed, and compared to FEM results for accuracy validation. In addition, two models based on Poisson's equations in terms of scalar and vector potentials are derived, compared, and analyzed. Finally, design optimization and sensitivity analysis of a linear stage for lithography applications are discussed.