Analysis of temperature dependency of the resonant frequency for electron density measurement with curling probe

We developed a curling probe, one of the plasma diagnostic probes, to find electron density using electrical resonance in the microwave range.  The probe utilizes a slot antenna to get the resonance, and the antenna forms a spiral shape on a top surface plane.   Because the probe is operated in the high-frequency range, the probe realizes the density measurement even when a film deposition occurs. Furthermore, the probe treats plasma as a dielectric material for measuring principle so that the probe can be utilized at any pressure.  Even with the versatility of the probe, we have noticed that a resonant frequency depends on the probe temperature.  Unfortunately, we do not know the main cause of the frequency shift due to the temperature. Still, the dependency is observed even with the probe temperature rising by 10 degrees C. This presentation will show our recent analysis of the temperature dependence of the resonant frequency from the curling probe by conducting in-situ monitoring of the temperature and the resonant frequency during plasma exposure.  After a careful analysis, we found that the shift has a certain regularity, and we finally have developed a technique to calibrate the temperature-dependent frequency.