In this paper, we present a new “hybrid” method for on-wafer dielectric measurements of nanolitre fluid samples. The first part of the hybrid method uses a technique that extracts the complex relative permittivity of the material used to make microfluidic channels. The extraction is performed with an empty channel measurement, and thus requires no extra deembedding structures. The second part of the hybrid method involves an accurate extraction of the complex relative permittivity of dielectric fluids. The hybrid method uses three different extraction algorithms and calculates their Type B uncertainties within the NIST Microwave Uncertainty Framework. By choosing the calculation algorithm with the smallest uncertainty at each frequency, the hybrid method can achieve accurate measurements of the fluids' permittivity over a broad bandwidth. One of the three algorithms is a new algorithm based on closed-form equations. A trace-based algorithm is also applied to fluids measurements, for the first time to our knowledge. Through the uncertainty analysis, we found out that these two algorithms should be favored over a traditional least-squares optimization-based algorithm at millimeter wave frequencies, due to their lower sensitivities to probe-placement errors.

With emerging medical, chemical, and biological applications of microwave-microfluidic devices, many researchers desire a fast and accurate calibration that can be achieved in a single connection. However, traditional on-wafer or coaxial calibrations require measurements of several different artifacts to the data prior to measuring the microwave-microfluidic device. Ideally, a single artifact would be able to present different impedance states to correct the vector network analyzer data, minimizing drift and eliminating artifact-to-artifact connection errors. Here, we developed a multistate single-connection calibration that used a coplanar waveguide loaded with a microfluidic channel. We then used measurements of the uncorrected scattering parameters of the coplanar waveguide with the channel empty, filled with deionized water, and filled with 30 w% (30 grams per liter) of saline to construct an eight-term error model and switch-term correction. After correction, the residuals between measured scattering parameters and with the literature-based finite-element simulations were below -40 dB from 100 MHz to 110 GHz. This multistate single-connection calibration is compatible with both wafer-probed and connectorized microwave-microfluidic devices for accurate impedance spectroscopy and materials characterization without the need for multiple device measurements.

The dielectric spectroscopy (DS) measurement is an attractive noninvasive method to reveal the intrinsic information of biological materials and cell cultures. However, the presence of a double layer due to electrode polarization within the lower RF and microwave range significantly affects the accurate analysis of dielectric properties of ionic liquids. In this paper, we measure the broadband DS of five saline solutions with a microfluidic coplanar waveguide (CPW) transmission line sensor across the frequency range from 40 kHz to 110 GHz. Derived from a parallel-plate structure that is transformed from the quasi-TEM CPW sensor through a conformal mapping technique, a broadband spectroscopy modeling method is proposed, where a Cole-Cole function or a constant phase element formula is used depending on the ionic concentrations and the measurement window. Validation analysis on the five saline solutions demonstrates the capability of the modeling method in separating relaxation properties of the bulk sample from the double-layer effects.

We present two new methods to perform series-resistor calibrations on substrates with losses. Lossless calibration substrates, which are required by the traditional calibration comparison technique, are not needed. The proposed methods rely on multiline thru-reflect-line-calibrated series-resistor and series-capacitor data. The first method uses closed-form equations and the second method is based on multifrequency optimization. The proposed methods are based on a fundamental assumption that the resistance and the inductance of series-resistor standards fabricated with thin-film technologies are frequency-independent. In addition, an improved version of the traditional calibration comparison technique is proposed and is used as the benchmark technique. By measurement results on a high-resistivity silicon substrate up to 110 GHz, the validity of the proposed approaches is demonstrated.

A simplified dielectric material characterization technique that combines an equivalent impedance algorithm and a general “line–line” trace method is introduced. The technique is applicable to every type of transmission lines. Due to the convenient fabrication and the allowance of integration with various polymers, coplanar waveguide transmission lines integrated with an SU-8 microfluidic channel is primarily used in this study. The conformal mapping method, an efficient and straightforward way, is introduced to build the foundation of dielectric material characterization and to optimize the sensor design. A validation measurement of the proposed technique is performed on deionized water, and show valuable consistency with previous reliable data presented in the literature. Next, the technique is applied on solid SU-8 characterization with four groups of on-wafer measurements. SU-8 measurement results and the related uncertainty analysis are demonstrated subsequently.

This paper investigates a unified theory to derive vector network analyzer calibration algorithms based on the T-matrix representation, by which means the line-reflect-match (LRM), line-reflect-match-match (LRMM), and the line-reflect-reflect-match (LRRM) calibrations are formulated. The proposed calibration theory is more general than other versions of LRM, LRMM, and LRRM in that an arbitrary known two-port device can be used as the line standard L, rather than a perfect thru or transmission line. Experimental verifications of the proposed theory using on-wafer calibrations from 0.5 GHz to 110 GHz are given.