Comparative Study on Microwave Probes for Plasma Density Measurement by FDTD Simulations

In order to measure the absolute plasma density, various probes are proposed and investigated and microwave probes are widely used for its advantages (Insensitivity to thin non-conducting material deposited by processing plasmas, High reliability, Simple process for determination of plasma density, no complicate assumptions and so forth). There are representative microwave probes such as the cutoff probe, the hairpin probe, the impedance probe, the absorption probe and the plasma transmission probe. These probes utilize the microwave interactions with the plasma-sheath and inserted structure (probe), but frequency range used by each probe and specific mechanisms for determining the plasma density for each probe are different. In the recent studies, behaviors of each microwave probe with respect to the plasma parameters of the plasma density, the pressure (the collision frequency), and the sheath width is abundant and reasonably investigated, whereas relative diagnostic characteristics of the probes by a comparative study is insufficient in spite of importance for comprehensive applications of the probes. However, experimental comparative study suffers from spatially different plasma characteristics in the same discharge chamber, a low-reproducibility of ignited plasma for an uncertainty in external discharge parameters (the power, the pressure, the flow rate and so forth), impossibility of independently control of the density, the pressure, and the sheath width as well as expensive and complicate experimental setup. In this paper, various microwave probes are simulated by finite-different time-domain simulation and the error between the input plasma density in FDTD simulations and the measured that by the unique microwave spectrums of each probe is obtained under possible conditions of plasma density, pressure, and sheath width for general low-temperature plasmas. This result shows that the each probe has an optimum applicable plasma condition and reliability of plasma density measurement using the microwave probes can be improved by the complementary use of each probe.