Effect of an inhomogeneous electron density profile on the transmission microwave frequency spectrum of the cutoff probe

Abstract

The cutoff probe (CP), which precisely measures electron density from a microwave transmission (S 21) spectrum, has been successfully developed through physical models under the assumption of homogeneous plasma between the probe tips. In practice, however, the chamber and sheath structure, flow effects, and the probe insertion itself produce plasma inhomogeneity between the probe tips, which necessitates the study of any related effects on the CP measurement results. This paper investigated the effect of inhomogeneous plasma on the S 21 of the CP through a three-dimensional E/M wave simulation with various density gradient directions. The simulations found, notably, double cutoff peaks and a cutoff frequency shift in the S 21 that depend on the gradient direction. These results are analyzed via a simple circuit model of the CP, and their origins are elucidated at the end of this paper.

Computational Study on the Parallel Double-Curling Probe for Multi-Site Electron Density Measurement in Low-Temperature Plasma

“…It is based on the Maxwellian distribution of electrons, and is valid within the electron temperature range of 1-7 eV. Here, we assumed an electron temperature of 3 eV, which is a common discharge condition used in previous studies of microwave probes [12,30,31]. Then, the calculated 𝜈 𝑚 is 2.26×𝑝 in MHz, where 𝑝 is the gas pressure in mTorr.…”

Science-based, data-driven developments in plasma processing for material synthesis and device-integration technologies

“…37) The hairpin resonator has also been used to measure the electron temperature. 38) The spatial distribution of plasma density in a chamber was revealed by the cutoff probe 39,40) and the surface-wave probe. 41,42) Optical diagnostics are categorized into passive and active methodologies.…”

Development of the Measurement of Lateral Electron Density (MOLE) Probe Applicable to Low-Pressure Plasma Diagnostics

“…The cutoff probe was connected to vector network analyzer 2 (S3601B 100 kHz–8.5 GHz, SALUKI Inc., Taipei, Taiwan) via two SMA cables. The cutoff probe can precisely measure the electron density by measuring the cutoff frequency in S ; details can be found elsewhere [ 9 , 46 , 47 , 48 , 49 ]. In the next section, operation of the MOLE probe at the center of the chamber is first demonstrated compared to the cutoff probe.…”

“…The SWR frequency is proportional to the rf power, and as the pressure increases, the Q-factor of the peak abruptly decreases. As shown in Figure 8 d–g, the cutoff frequency ( ) in S , which is marked with an arrow at each rf power condition, is proportional to the rf power [ 47 , 48 , 49 ]. This implies that the electron density is also proportional to the rf power.…”