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

Abstract

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 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.