Standard-independent estimation of dielectric permittivity with microdielectric fringe-effect sensors

Microdielectric spectroscopy with planar fringe-effect (FE) interdigital sensors is a useful method for noninvasive characterization of the interfacial properties of the materials. Unfortunately, obtaining an accurate dielectric spectrum is difficult because of the complexity of the probing electrical field created by the FE sensor and the contribution of the sensor substrate and stray elements to the overall measurements. Previously, quantitative microdielectric spectroscopy required the calibration of the FE sensor with standard materials that are known to be dielectrically similar to an unknown sample of interest. This limitation complicates the application of microdielectric spectroscopy, particularly in cases where the monitored sample undergoes a transformation that changes its dielectric permittivity. A standard-independent method for quantitative FE microdielectric measurements is proposed in this paper. The developed method is based on comparison of the theoretically predicted admittance of the FE sensor with the sample of known dielectric properties and the measured sensor admittance. Comparison of the theoretical predictions with the admittance measurements reveals the contribution of the unknown stray elements. The measurements with an unknown sample are then adjusted for the strays. The contribution of the sensor substrate to the sensor measurements is removed using the theoretical model derived from the electroquasistatic approximation of Maxwell equations. The dielectric permittivity of the material being tested is calculated by successively solving the system of complex nonlinear equations for each frequency at which the sensor admittance is measured. The developed method is illustrated by applying it to the dielectric measurements of several dissimilar samples. The results are in excellent agreement with those obtained using the gold standard parallel-plate measurement method over the entire range of frequencies.