Method for measuring thickness of dielectric films using microdielectric fringe-effect sensors.

A method for noninvasive thickness measurements of dielectric films using fringe-effect (FE) sensors is developed and experimentally validated. The fringing electrical field, created by electrodes microfabricated at the film substrate, depends on the film thickness and dielectric permittivity of the film under test (FUT). The unknown film thickness is estimated by matching the theoretical prediction of thickness-dependent sensor admittance with the measured value. In the case of FE sensors with spatially periodic, interdigitated electrode (IDE) configuration, the admittance prediction is simplified, which allows for the real-time measurements of changing thickness. The developed method can be used to continuously measure the changing dielectric permittivity of the FUT material, which makes it possible to determine the thickness of films of changing dielectric properties, caused by chemical or other transformations. The application of the developed method is demonstrated experimentally by measuring the thickness of silicon nitride film deposited in several increments on the quartz substrate of the IDE sensor. In the expected range of sensor sensitivity, the results show an excellent agreement with the independent thickness measurements.

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.

Quantitative measurements of dielectric spectra with microdielectric fringe-effect sensors.

The parallel-plate method is a gold standard for measuring dielectric properties of materials. However, it requires sampling of the material under testing (MUT), which makes it less suitable for real time, dynamic, and in situ measurements. The alternative to the parallel-plate method is to use the microdielectric fringe-effect (FE) sensors, which can be placed inside the process or laboratory equipment to provide rapid, on-line, and noninvasive characterization of the dielectric properties. An additional potential advantage of the FE measurements is the ability to obtain spatially localized and interfacial measurements, which may be important in some applications. Unfortunately, interpretation of the FE sensor measurements is difficult because of the spatial nonuniformity of the electrical excitation field created by the FE sensor and the extraneous contributions from the sensor substrate and unknown stray elements. The objective of this study is to summarize the theoretical basis of the dielectric measurements using planar interdigitated sensors and to use it in the development of a new method for obtaining quantitative measurements with FE sensors. As the first step, the basic correlation between the impedance measurements obtained with the FE sensor and the dielectric properties of the MUT is elucidated. The theoretical results are then used to analyze the contribution of the sensor substrate and unknown stray components to the overall measurements. A novel calibration method to eliminate extraneous contributions is then proposed. The application example demonstrates the application of the developed method to the measurement of the dielectric permittivities of a polydispersed cis-polyisoprene samples. The results are compared with those obtained using the parallel-plate measurements and show excellent agreement. Experimental comparison with the alternative calibration methods is also performed, indicating significant improvement in accuracy of dielectric measurements over a broad range of frequencies.