A study on the maximum power transfer condition in an inductively coupled plasma using transformer circuit model

Abstract

Correlations between the external discharge parameters (the driving frequency ω and the chamber dimension R) and plasma characteristics (the skin depth δ and the electron-neutral collision frequency νm) are studied using the transformer circuit model [R. B. Piejak et al., Plasma Sources Sci. Technol. 1, 179 (1992)] when the absorbed power is maximized in an inductively coupled plasma. From the analysis of the transformer circuit model, the maximum power transfer conditions, which depend on the external discharge parameters and the internal plasma characteristics, were obtained. It was found that a maximum power transfer occurs when δ≈0.38R for the discharge condition at which νm/ω≪1, while it occurs when δ≈2ω/νmR for the discharge condition at which νm/ω≫1. The results of this circuit analysis are consistent with the stable last inductive mode region of an inductive-to-capacitive mode transition [Lee and Chung, Phys. Plasmas 13, 063510 (2006)], which was theoretically derived from Maxwell's equations. Our results were also in agreement with the experimental results. From this work, we demonstrate that a simple circuit analysis can be applied to explain complex physical phenomena to a certain extent.