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This paper presents analytical modeling and design of a high-acceleration,low-vibration slotless double-sided linear motor with an arbitrary Halbacharray for lithography machines used in semiconductor manufacturing technology.Amperian current and magnetic charge models of permanent magnets are integratedinto a hybrid approach to develop comprehensive analytical modeling. Unlikeconventional methods that treat magnets as sources for Poisson's equations, thesolution is reduced to Laplace's equations, with magnets being represented asboundary conditions. The magnetic fields and potentials within distinctregions, along with machine quantities such as shear stress, force-anglecharacteristics, torque profile, attraction force, misalignment force, andback-EMF, are derived, comprehensively analyzed, and compared to FEM resultsfor accuracy validation. In addition, two models based on Poisson's equationsin terms of scalar and vector potentials are derived, compared, and analyzed.Finally, design optimization and sensitivity analysis of a linear stage forlithography applications are discussed.

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