Mode-matching analysis of a spit-circular cavity resonator for measurement of the dielectric constant for film on a substrate

In this paper, we apply the mode-matching technique (eigenmode expansion) to formulate an analytical model for a split cylindrical cavity resonator with a thick ceramic film layer sandwiched between two-layer alumina substrates. We then compute the resonant frequencies with the TE011 mode with an eigenvalue problem approach using the model formula. The quality factor (Q-factor) of the resonator is also calculated by applying the perturbation method to the analytical model. The validity of the proposed analytical technique is confirmed by applying this method to the estimation of permittivity of thick films as an inverse problem. Ceramic films (2 µm thickness) were synthesized using a chemical solution method onto 200-µm-thick, 50-mm-diameter alumina substrates. The complex permittivity of the films was then determined using the TE011 mode split cylindrical cavity resonator in the 10-GHz band. The extent of the edge effect at a sample insertion space was evaluated by comparing the estimated results through TE wave analysis using the mode-matching method when the transverse resonance technique and the perturbation method were applied to calculate the resonant frequency and the dielectric Q-factor. The results obtained indicate that a difference of 0.153% in the permittivity of the alumina substrate causes differences of 6.10 and 3.75% in the measured permittivity and loss tangent, respectively, of 2-µm-thick ceramic film with a permittivity of ∼50. Differences in permittivity and loss tangent were more pronounced with thinner films. It was also confirmed that the estimated results for permittivity and the loss tangent values of these ceramic films were affected by the estimated permittivity value of the alumina substrate. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.