Modelling and Optimisation of a Halbach‐Array Linear Motor for Semiconductor Manufacturing Application

ABSTRACT

This paper presents the analytical modelling and design of a high‐acceleration double‐sided linear motor with an arbitrary Halbach array for lithography machines used in semiconductor manufacturing. The Halbach array, combined with a slotless stator, improves performance in terms of vibration, acoustic noise, and precision compared with slotted motors. Amperian current and magnetic charge models of permanent magnets are integrated into a hybrid analytical framework. Unlike conventional methods that treat magnets as source terms in Poisson's equations, the proposed approach reduces the problem to Laplace's equations by representing the magnets through boundary conditions. The magnetic fields and potentials in the different regions, along with machine quantities such as shear stress, force‐angle characteristics, force profile, attraction force, misalignment force, back‐EMF, and demagnetisation index are derived, comprehensively analysed, and validated against FEM results. To provide a broader modelling framework, two additional analytical models based on the solution of Poisson's equations in terms of scalar and vector potentials are also derived, compared, and analysed. Finally, the design optimisation and sensitivity analysis of a linear stage for lithography applications are discussed.