The effect of sheath dielectric on the inferred plasma parameters of a DC biased hairpin resonator probe

A hairpin resonator probe (HP) measures absolute electron density in a plasma. It is primarily based on the resonance principle of a parallel wire transmission line, where the quarter-wavelength of the characteristic resonance frequency equals the physical length of the HP [1]. However, owing to the finite sheath width formed around its pins, its accuracy is compromised. As a consequence, the resonance frequency is underestimated, and the electron density is inferred incorrectly. This limitation may be resolved by introducing sheath correction based on a capacitive model in which the series combination of sheath and plasma capacitances is compared to the effective capacitance of the area between the pins, with the sheath dielectric equal to the constant vacuum value. While the sheath width is calculated analytically by calculating the Poisson's equation, along with the continuity and momentum equations, under the assumption of an electron free sheath [2]. In this work, the impact of electron and ion sheath surrounding the cylindrical pins of the HP on the inferred plasma characteristics in a 13.56 MHz CCRF argon and oxygen discharge is studied using a DC biased HP. The capacitance model is addressed by applying a bias-dependent sheath dielectric value surrounding the probe pins [3]. It is found that the peak in the resonance frequency corresponds to a relatively higher value of the applied bias than the plasma potential. Furthermore, its impact on estimating the plasma parameters, including plasma potential, electron temperature, and electronegativity, is discussed with a plausible explanation.