A new plasma diagnostic tool called the planar cutoff probe (PCP), recently developed by Kim et al. [Plasma Sources Sci. Technol. 28, 015004(2019)], can be embedded into a chamber wall or wafer chuck electrode for non-invasive electron density measurements. The application feasibility of the probe has so far been demonstrated in terms of signal-to-noise ratio; however, for the successful application of the PCP to real plasma processing, its design should first be optimized based on a comprehensive investigation of its characteristics. Therefore, in this paper, the effects of various parameters on the measurement characteristics of the PCP are investigated and analyzed via 3D full electromagnetic wave simulation. Results show that PCP measurement discrepancies vary by numerous controllable parameters, namely, wafer thickness and relative dielectric constant, antenna distance, input electron density, and chamber pressure. Based on these findings, the condition with the smallest measurement discrepancy and where PCP measurement performance is least affected by the parameters is found and discussed.

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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.