A 2D semi-analytical model for Faraday shield in ICP source

• In this paper, a 2D model of ICP with faraday shield is proposed considering the complex structure of the Faraday shield.
• Analytical solution is found to evaluate the electromagnetic field in the ICP source with Faraday shield.
• The collision-free motion of electrons in the source is investigated and the results show that the electrons will oscillate along the radial direction, which brings insight into how the RF power couple to the plasma.

Faraday shield is a thin copper structure with a large number of slits which is usually used in inductive coupled plasma (ICP) sources. RF power is coupled into the plasma through these slits, therefore Faraday shield plays an important role in ICP discharge. However, due to the complex structure of the Faraday shield, the resulted electromagnetic field is quite hard to evaluate. In this paper, a 2D model is proposed on the assumption that the Faraday shield is sufficiently long and the RF coil is uniformly distributed, and the copper is considered as ideal conductor. Under these conditions, the magnetic field inside the source is uniform with only the axial component, while the electric field can be decomposed into a vortex field generated by changing magnetic field together with a gradient field generated by electric charge accumulated on the Faraday shield surface, which can be easily found by solving Laplace's equation. The motion of the electrons in the electromagnetic field is investigated and the results show that the electrons will oscillate along the radial direction when taking no account of collision. This interesting result brings insight into how the RF power couples into the plasma.