90 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 12, NO. 3, MARCH 2002 A CPW T-Resonator Technique for Electrical Characterization of Microwave Substrates Rebecca Lorenz Peterson, Student Member, IEEE and Rhonda Franklin Drayton, Member, IEEE Abstract—An impedance independent method is proposed using a finite ground coplanar waveguide (CPW) T-resonator to electri- cally characterize microwave materials. Silicon-based CPW T-res- onators are designed and measured, with calibrated data agreeing well with other methods up to 30 GHz. Uncalibrated measurements produce dielectric constant and attenuation results within 3.7% and 25%, respectively, of those obtained with calibration. Hence, the CPW T-resonator can be used to provide rapid and accurate characterization of microwave substrates with unknown dielectric properties. Index Terms—Coplanar waveguide, dielectric constant, res- onators, semiconductor material measurements. I. INTRODUCTION T HE MICROSTRIP T-resonator technique [1] allows quick and accurate electrical characterization of microwave sub- strates up to 20 GHz [2]. The primary advantages of this tech- nique over others are a) easy implementation and testing, b) broadband results, and c) calibration independence of data. Two important factors, however, limit the applicability of the microstrip T-resonator to novel substrates. First, effective di- electric constant is a strong function of line impedance and thus of line dimensions and substrate height. Hence, its use is hindered on substrates with unknown dielectric constant. Second, the microstrip configuration cannot be easily imple- mented on all substrates since via holes may be necessary to transfer ground signals to the lower substrate surface. This is particularly true in assessment of novel materials such as porous silicon [3], [4] that form an integrated layer on the host substrate, silicon. A coplanar waveguide (CPW) T-resonator approach can be used to overcome both of these issues since the effective di- electric constant has weak impedance dependence and all con- ductors are printed on one surface. II. DESIGN AND FABRICATION At odd quarter-wavelengths, a standing wave distribution ex- ists along the open-circuited T-resonator stub (see Fig. 1) and Manuscript received August 11, 2001; revised December 13, 2001. This work was supported by fellowships from the National Science Foundation (NSF) and Automatic RF Techniques Group (ARFTG) and by the NSF (ECS 9996017) and Dupont Educational Aid Grants. The review of this letter was arranged by Associate Editor Dr. Shigeo Kawasaki. R. L. Peterson was with the Electrical and Computer Engineering Depart- ment, University of Minnesota, Minneapolis, MN 55455 USA. She is now with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA. R. F. Drayton is with the Electrical and Computer Engineering Depart- ment, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: drayton@ece.umn.edu). Publisher Item Identifier S 1531-1309(02)02278-X. Fig. 1. Layout of a CPW T-resonator (not to scale). presents well-defined resonances. Under low loss conditions, the resonant frequency and 3 dB bandwidth around each resonance point can be used to extract effective dielectric constant and total attenuation , according to (1) dB (2) where is the resonance index ( 1, 3, 5, ...), is the speed of light in vacuum and is the effective physical length of the resonating stub. Using Hoffman’s equations [5] and finite ground coplanar waveguide techniques [6], 50 test circuits are designed with signal line , gap , and ground plane widths of 94, 53, and 400 m, respectively, on silicon ( ). Gap spacing at the stub open end and feed line ends is also 53 m. The T-resonator layout, shown in Fig. 1, has stub and feed lengths of 1.0 cm and 0.2 cm, respectively. All circuits are printed on high resistivity silicon wafers [n-type (100), 2000 -cm, 525 m thick] with an evaporated Ti/Au (400/1500 Å) layer that is gold electroplated to 4 m. III. EXPERIMENTAL RESULTS Scattering parameter data are measured on an HP8510C automatic network analyzer using a Cascade Microtech/Alessi RF1 microwave probe station with Cascade Microtech GSG150 probes. In this work, a probe-tip calibration, based on the LRM (Line–Reflect–Match) technique, is performed on an ISS alumina substrate. 1531–1309/02$17.00 © 2002 IEEE