Electron Density Measurement with Hairpin Resonator in Low Pressure Plasma

TL;DR

This paper presents a practical method for measuring high electron densities in low-pressure plasma using a hairpin resonator with a simplified, cost-effective microwave electronics setup, extending the technique's range.

Contribution

It introduces a novel implementation of hairpin probes operating at harmonic frequencies to measure higher plasma densities, with detailed correction factors and a reproducible design.

Findings

Successfully measured electron densities up to 10^12 /cm^3

Developed an inexpensive, off-the-shelf electronics setup

Compared results with traditional Langmuir probe measurements

Abstract

Hairpin probes measure electron density in plasmas where other techniques are unsuitable. Previous hairpins were constructed as a quarter-wave resonant structure typically made from a folded piece of wire. The present work conducts the hairpin measurement in high electron density, up to approximately 10^12 / cm3, corresponding to a plasma frequency of about 9 GHz. A series of four probes is described, together with an easily reproducible implementation of the associated microwave electronics using commercial off the shelf components that are inexpensive compared to the network analyzer that is typically required. Measuring higher densities requires increasing the resonant frequency, but we were unable to accurately fabricate the required quarter wavelength structure on the scale of 4 mm. Toward this end we explore operating a larger quarter-wavelength structure at its 3d harmonic (3/4 resonator). Correction coefficients are described for both the plasma sheath effect and the wire coating. Measurements are taken in Argon at pressures below 20 mTorr. Results are compared with Langmuir probe measurements.