A novel technique for plasma density measurement using surface-wave transmission spectra

A technique for the measurement of the absolute electron density in low-pressure plasmas using microwaves is described. It is based on observing the propagation of electromagnetic surface waves (SW) at a plasma-sheath boundary, guided by a dielectric cylinder immersed in the plasma. The transmission spectrum is measured between two antennas situated at either end of the dielectric cylinder and connected to a network analyser. Analytical theory based on the Trivelpiece-Gould work (Trivelpiece and Gould 1959 J. Appl. Phys. 30 1784, Trivelpiece 1967 Slow-Wave Propagation in Plasma Waveguides) indicates that the lowest frequency at which the SW can propagate is equal to 1/√2 of the plasma frequency, which is directly related to the electron number density at the plasma-sheath boundary. We call this probe the plasma transmission probe (PTP) in contrast to the plasma absorption probe proposed by Sugai and co-workers (Kokura et al 1999 Japan. J. Appl. Phys. 38 5262). The PTP is promising for the measurement of low densities (≥109 cm-3) at relatively high gas pressure (≤1 Torr). An axi-symmetric finite element model of the probe is presented and used to calculate transmission spectra. Experimental spectra measured in a radio-frequency capacitively coupled discharge in argon at various plasma densities and pressures (40-750 mTorr) are presented and compared with the calculated ones. Plasma densities derived from the transmission spectra were compared with those obtained with a Langmuir probe. The PTP was also compared with a microwave 1/4-wave resonator ('hairpin probe') at low pressure (5-45 mTorr) in an ICP discharge in argon. The densities determined by the PTP were found to be lower by a factor of 0.5-0.7 compared with those obtained with a Langmuir and a hairpin probe. We believe this can be attributed to the pre-sheath plasma density gradient, as the PTP determines the sheath edge electron density, not the bulk value