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

Abstract

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.