Magnetic field study of realistic circular wire coils with Comsol Multiphysics

Dr. J. Gospodaric1
1IMS Nanofabrication GmbH, Vienna, Austria
Veröffentlicht in 2024

In the field of electron optics, precise control of magnetic fields is crucial for achieving high-performance outcomes in various applications, particularly in the semiconductor and chip production industry. As the demand for high-precision semiconductor production continues to grow, the need for advanced electron optics elements that provide minimal errors becomes ever more crucial. Constant improvements in these elements are essential to facilitate future semiconductor production, ensuring the highest quality and efficiency in chip manufacturing processes. This study addresses the problem of optimizing the magnetic field distribution generated by realistic electrical circular wire coils. The wire of the coil is wound in a layered fashion, alternating the winding direction with each new layer. This design results in coil defects due to wire crossing with opposite chiralities (coil bulging), with additional imperfections arising from the linking between spirals and the configuration of in/out cables (see example shown in Fig.1). With the help of Comsol Multiphysics we were able to run detailed simulations utilizing magnetic field physics node with cubic discretization. This module allowed us apply current to the wire and investigate the magnetic field along the coil’s central axis, examine how different configurations of input and output cables (Fig.2), layer transitions, and presence of surrounding yoke impact the magnetic field. The primary objective was to maximize the longitudinal magnetic field component Bz while minimizing the transverse components Bx and By, which arise due to coil imperfections. Our results indicate that specific configurations of wire winding and cable connections can significantly influence the magnetic field distribution. This optimization is vital for minimizing aberrations in electron optics systems, which are commonly used in semiconductor manufacturing for tasks such as focusing and defocusing beams, as well as modifying electron beam rotation.

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