Determination of Electron Temperature and Density Using Complex Impedance Measurements

We present on an electron temperature (T_e) and density (n_e) diagnostic that utilizes measurements from a Vector Network Analyzer (VNA) to infer the plasma impedance (Z_p). This diagnostic is non-invasive and uses the relations between Z_p, T_e, and n_e that are obtained from a plasma circuit model[1][2][3]. Our VNA centric approach further assists in design and characterization of the matching network to Z_p for both high efficiency (>90%) and reduced risk of damage-causing reflected waves. We validate the VNA measurements and matching network through SPICE and SimNEC simulations. For a cylindrical, capacitively coupled Argon plasma (13.56MHz, 50V_pp push/pull, 15 Pa, A_elec = 0.009 m^-2 , d= 0.06 m) , we obtain n_e ≈ 2E+14 m^-3 and T_e ≈ 1.69 eV. These results agree with computational results from a method similar to that of Lieberman and Lichtenberg[3], and they will soon be verified against Langmuir probe measurements. Our computational results indicate a strong correlation between applied RF voltage and Z_p , which we look to investigate in future work. The relationship with neutral gas pressure shall also be investigated. We aim to provide a framework for both plasma analysis and matching network design. Our non-invasive plasma impedance diagnostic shows strong promise towards being a useful tool for plasma analysis and RF power optimization.

[1] https://doi.org/10.1063/1.4927780

[2] https://doi.org/10.1109/TPS.2021.3121999

[3] https://doi.org/10.1002/0471724254