A simple model of solenoidal inductively coupled plasma sources considering finite size

Abstract

This paper proposes an updated transformer model for solenoidal inductively coupled plasma sources that can be applied even in low electron density regions. The proposed model can handle plasma in a finite geometry where the electric fields propagating from each boundary overlap, employing a simple analytic expression of the electric field, a one-dimensional (1D) sine hyperbolic function. Based on this field expression, all circuit elements of the transformer model that depend on the electron density, namely, plasma resistance, magnetic inductance, and mutual inductance, can now be obtained. Comparison of absorbed power as well as the circuit elements calculated using the proposed model, named here as the 1D transformer model, shows good agreement with the electromagnetic model, which is known for being quite accurate for cold plasma not only in high but also in low electron density regions. Results also indicate that the 1D transformer model is not limited to a specific setup but rather can be applied in a wide range of discharge conditions.