1916 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 5, OCTOBER2005 Differential Open Resonator Method for Permittivity Measurements of Thin Dielectric Film on Substrate SergeyN. Dudorov, Dmitri V. Lioubtchenko, Juha A. Mallat, and Antti V. Räisänen Abstract—A novel differential method based on the open res- onator is developed for permittivity measurement of thin dielectric films on optically dense substrates at millimeter wavelengths. The method is based on measurement of resonant frequency shifts due to appearance of a thin film on upper and lower sides of the sub- strate. The advantages of the method are that there is no need to know the geometry of the open resonator nor the thicknesses of the film and substrate, though one has to measure separately dielectric properties of the substrate. Index Terms—Open resonator, permittivity, substrate, thin film. I. INTRODUCTION T HE OPEN Fabry–Perot resonator is one of the most pre- cise tools for dielectric property measurement of low-loss materials at millimeter wavelengths. The theory of the open res- onator is well developed in, e.g., [1], [2]. Samples consisting of two thick layers are considered in [3]. If one layer is very thin (a few micrometers), the published method is not convenient as it requires quite an accurate knowledge of thicknesses of both layers, permittivity of the substrate, geometry of the resonator, etc. In this paper, we propose a novel method, based on the reso- nant frequency measurements, when the resonator is first loaded with the substrate only, and then with the substrate covered on one side with the film of interest, and finally with that turned up side down. II. THEORY The basic equations for two dielectric layers can be found in [3] (1) (2) where and are the refractive indices of lower and upper layers, respectively, is the resonant wave number, and are the thicknesses of lower and upper layers, respectively, , (see Fig. 1), is the distance between mirrors, and and are phase corrections. Following the Manuscript received March 22, 2004; revised November 9, 2004. The authors are with MilliLab, Radio Laboratory/Smart and Novel Radios Research Unit (SMARAD), Helsinki University of Technology, FI-02015 TKK, Finland (e-mail: sdudorov@cc.hut.fi). Digital Object Identifier 10.1109/TIM.2005.853352 Fig. 1. Hemispherical open resonator containing a bilayer sample. definitions given in [3], phase corrections can be rewritten as (3) (4) (5) where , . From now on, according to Fig. 2, we denote the thicker layer parameters as and , while for the thinner layer, these param- eters are and , . Let us assume that one of the sample layers is very thin com- pared to the wavelength and calculate two resonant frequency shifts. The first shift is the difference of the res- onant frequencies when the resonator is loaded with a sample with a thin film on the upper side of the substrate [Fig. 2(a)] and when it is loaded with the substrate only [Fig. 2(c)]. The second one is the difference of the resonant frequencies when the resonator is loaded with the sample with the film on the lower side of the substrate [Fig. 2(b)] and when it is loaded with the substrate only [Fig. 2(c)]. These frequency shifts will be used in the formulas derived next. 0018-9456/$20.00 © 2005 IEEE Authorized licensed use limited to: COLORADO SCHOOL OF MINES. Downloaded on December 31, 2009 at 12:43 from IEEE Xplore. Restrictions apply.