Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy.

The importance of high dielectric constant materials in the development of high frequency nano-electronic devices is undeniable. Their polarization properties are directly dependent on the value of their relative permittivity. We report here on the nanoscale metrological quantification of the dielectric constants of two high-κ materials, lead zirconate titanate (PZT) and lead magnesium niobate-lead titanate (PMN-PT), in the GHz range using scanning microwave microscopy (SMM). We demonstrate the importance of the capacitance calibration procedure and dimensional measurements on the weight of the combined relative uncertainties. A novel approach is proposed to correct lateral dimension measurements of micro-capacitive structures using the microwave electrical signatures, especially for rough surfaces of high-κ materials. A new analytical expression is also given for the capacitance calculations, taking into account the contribution of fringing electric fields. We determine the dielectric constant values εPZT = 445 and εPMN-PT = 641 at the frequency around 3.6 GHz, with combined relative uncertainties of 3.5% and 6.9% for PZT and PMN-PT, respectively. This work provides a general description of the metrological path for a quantified measurement of high dielectric constants with well-controlled low uncertainty levels.

Reply to "Comment on Liu et al. 'Discrepancies of Measured SAR between Traditional and Fast Measuring Systems' Int. J. Environ. Res. Public Health, 2020, 17, 2111".

The authors of this reply published an article in International Journal of Environmental Research and Public Health and received comments from Douglas and Kuster. Responses are made to these comments with complementary explanations and numerical results.

Validation of a Broadband Tissue-Equivalent Liquid for SAR Measurement and Monitoring of Its Dielectric Properties for Use in a Sealed Phantom.

We report on the development of a method for measuring the permittivity and conductivity of fluids inside a sealed tank (or a pipe) by using an embedded coaxial probe. Permittivity and conductivity in the frequency range 600 MHz to 6 GHz are determined from measurements of a complex reflection coefficient by using a vector network analyser (VNA) that is connected to the embedded probe via a coaxial cable. Substitution methods for calibration of an inaccessible probe are studied in this paper. These require the VNA with attached cable to be calibrated prior to connecting the cable to the embedded coaxial probe. Measurement of permittivity and conductivity of fluids inside sealed tanks and pipes is needed for monitoring industrial processes, such as fermentation. The authors' requirement, however, was to allow monitoring of a tissue-equivalent liquid that is contained inside a sealed tank. This tank is a component of a commercial system for rapid, multiple-band measurement of the specific absorption rate (SAR) of mobile phone handsets. Monitoring of permittivity and conductivity is needed to ensure compliance with international standards for SAR measurement. The paper also presents data for a new broadband (600 MHz to 6 GHz) tissue-equivalent liquid that is based on an oil-in-water emulsion. It is demonstrated that over an extended period of time, the liquid is stable, and an embedded coaxial probe enables its properties to be monitored with the required accuracy.

Discrepancies of Measured SAR between Traditional and Fast Measuring Systems.

Human exposure to mobile devices is traditionally measured by a system in which the human body (or head) is modelled by a phantom and the energy absorbed from the device is estimated based on the electric fields measured with a single probe. Such a system suffers from low efficiency due to repeated volumetric scanning within the phantom needed to capture the absorbed energy throughout the volume. To speed up the measurement, fast SAR (specific absorption rate) measuring systems have been developed. However, discrepancies of measured results are observed between traditional and fast measuring systems. In this paper, the discrepancies in terms of post-processing procedures after the measurement of electric field (or its amplitude) are investigated. Here, the concerned fast measuring system estimates SAR based on the reconstructed field of the region of interest while the amplitude and phase of the electric field are measured on a single plane with a probe array. The numerical results presented indicate that the fast SAR measuring system has the potential to yield more accurate estimations than the traditional system, but no conclusion can be made on which kind of system is superior without knowledge of the field-reconstruction algorithms and the emitting source.