1530 Broadband Permittivity Measurements of High Dielectric Constant Films J. Obrzut 1 , A. Anopchenko 1 and R. Nozaki 2 1 Polymers Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. 2 Division of Physics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan. Abstract - Our investigation concerns measuring broadband dielectric permittivity and loss tangent of thin film high dielectric constant dielectric materials at microwave frequencies. The measurements are made in an APC-7 coaxial configuration where the test specimen represents a load terminating an air-filled coaxial transmission line. In contrast to conventional lumped capacitance approximations, the parallel plate capacitor filled with a dielectric film is treated as a distributed component consisting of a depressive, transmission line with a capacitance. The model expression for input impedance takes into consideration the wave propagation within the dielectric specimen section and correlates the network parameters with the relative complex permittivity of the specimen. The method is suitable for testing high-k polymer- composite materials having nominal thickness of 1 µm to 300 µm at frequencies of 100 MHz to 12 GHz. With proper calibration and computation the frequency range can be extended to 18 GHz . Index Terms - dielectric materials, high frequency measurements, coaxial discontinuity I. INTRODUCTION Broadband dielectric spectroscopy allows direct insight into molecular dynamics of materials. It covers a broad frequency range and therefore can be employed to study fast and slow molecular motions [1]. Broadband permittivity measurements of film dielectrics are also important in practical applications because the wide frequency range information is essential for many different industrial requirements. Among them, high permittivity films (high-k) are being developed for electronic applications operating at microwave frequencies [2] at which the existing broadband testing procedures frequently fail to produce meaningful results. A parallel plate capacitor terminating a coaxial waveguide (transmission line) has been widely used in the broadband complex permittivity measurements. In this configuration, often referred to as a lumped capacitance method, a dielectric disk or rod sample of the diameter of the center conductor is placed at the end of coaxial waveguide as a capacitive termination [3]. Iskander and Stuchly proposed a highly refined technique for measuring the broadband dielectric properties of such materials utilizing the reflection coefficient. As a sample holder, they used a small-gap shunt capacitor terminating a coaxial line [4]. This technique is accurate at frequencies where the sample holder can be treated as a lumped capacitance. They empirically determined that this technique is accurate up to a frequency at which input impedance of the specimen decreases to one tenth (0.1) of the characteristic impedance of the coaxial line. This frequency limit is lower for thinner specimens that have a higher dielectric constant. For a 100 µm thick specimen with a dielectric constant of about 60, measured in the APC-7 configuration, the upper frequency limit falls to within 85 MHz. This is well below the desirable frequency range of about 10 GHz to 20 GHz. Marcuvitz analyzed an equivalent circuit of a coaxial line, terminated by a small gap capacitance, treating it as a quasi- electrostatic problem. His analysis assumes a principal propagating mode in the coaxial line and no propagation in the gap [5]. A more fundamental analysis of TEM wave scattering in a coaxial line terminated by a gap was performed by Eom et al, using a Fourier transform and mode matching technique [6]. The results agreed with the Marcuvitz model up to frequencies of 12 GHz, but no satisfactory physical solution was obtained for gaps thinner than 100 µm and a dielectric constant larger than 10. In our earlier work we analyzed in detail the wave propagation in the film specimen terminating a coaxial line. We considered it as a distributed component having complex capacitance with residual inductance, for which we formulated an expression for the input impedance [7, 8]. In this paper, we present an application of this expression to measure complex permittivity of high-k film materials. II. ANALYSIS At frequencies where the specimen may be treated as a lumped capacitance, the input impedance, in Z , is given by expression (1a) and the real (ε’) and imaginary (ε”) component of the dielectric permittivity can be obtained from equations (1b) and (1c) respectively [3, 4]: * 1 r p in C j ε ω = Z (1a) ( ) 2 11 11 0 11 cos 2 1 sin 2 ' S S S + + − = φ ω φ ε p C Z (1b) φ ε ε δ sin 2 1 ' " tan 11 2 11 S S − − = = (1c) Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States 0-7803-8879-8/05/$20.00 ©2005 IEEE