We present a new method to extract resistivity and doping concentration of semiconductor materials from Scanning Microwave Microscopy (SMM) S₁₁ reflection measurements. Using a three error parameters de-embedding workflow, the S₁₁ raw data are converted into calibrated capacitance and resistance images where no calibration sample is required. The SMM capacitance and resistance values were measured at 18 GHz and ranged from 0 to 100 aF and from 0 to 1 MΩ, respectively. A tip–sample analytical model that includes tip radius, microwave penetration skin depth, and semiconductor depletion layer width has been applied to extract resistivity and doping concentration from the calibrated SMM resistance. The method has been tested on two doped silicon samples and in both cases the resistivity and doping concentration are in quantitative agreement with the data-sheet values over a range of 10⁻³ Ω cm to 10¹ Ω cm, and 10¹⁴ atoms per cm³ to 10²⁰ atoms per cm³, respectively. The measured dopant density values, with related uncertainties, are [1.1 ± 0.6] × 10¹⁸ atoms per cm³, [2.2 ± 0.4] × 10¹⁷ atoms per cm³, [4.5 ± 0.2] × 10¹⁶ atoms per cm³, [4.5 ± 1.3] × 10¹⁵ atoms per cm³, [4.5 ± 1.7] × 10¹⁴ atoms per cm³. The method does not require sample treatment like cleavage and cross-sectioning, and high contact imaging forces are not necessary, thus it is easily applicable to various semiconductor and materials science investigations.

The application of scanning microwave microscopy (SMM) to extract calibrated electrical properties of cells and bacteria in air is presented. From the S ₁₁ images, after calibration, complex impedance and admittance images of Chinese hamster ovary cells and E. coli bacteria deposited on a silicon substrate have been obtained. The broadband capabilities of SMM have been used to characterize the bio-samples between 2 GHz and 20 GHz. The resulting calibrated cell and bacteria admittance at 19 GHz were Y _cell = 185 μS + j285 μS and Y _bacteria = 3 μS + j20 μS, respectively. A combined circuitry-3D finite element method EMPro model has been developed and used to investigate the frequency response of the complex impedance and admittance of the SMM setup. Based on a proposed parallel resistance–capacitance model, the equivalent conductance and parallel capacitance of the cells and bacteria were obtained from the SMM images. The influence of humidity and frequency on the cell conductance was experimentally studied. To compare the cell conductance with bulk water properties, we measured the imaginary part of the bulk water loss with a dielectric probe kit in the same frequency range resulting in a high level of agreement.

Electrochemical impedance spectroscopy (EIS) is a widely used method for battery tests in manufacturing and automotive field applications. As such, accurate measurement of the impedance over a broad frequency spectrum is of high relevance, also requiring specific calibration methods and evaluation of error bounds. Here, we report for the first time a comprehensive uncertainty analysis of calibrated EIS for batteries. We aim to identify two uncertainty sources, the fixture repeatability and measurement noise, and evaluate their effect on the measured impedances. To this end, an error model assigned to each of them and the real and imaginary parts of the model parameters are characterized in the frequency range of 100 mHz–5 kHz by performing specific impedance measurements on a shunt resistor and a short standard. We demonstrate how different uncertainties are combined with the measured impedances, incorporating also the impedance calibration procedure. The errors are propagated through the calibration and correction functions by applying the linear error propagation method provided by the UncLib package from METAS. The error bounds are derived from uncertainty propagation in the shunt standard and the prismatic battery cell EIS and verified by conducting a series of measurements. Thereby, the uncertainty is shown as ellipsoids in every frequency point of the Nyquist plot. For instance, at 1 Hz, the 34-Ah prismatic cell shows a calibrated real-part impedance and two standard deviation error bounds of 1.07 $\text{m}\Omega $ ± $26~ \mu \Omega $ .

Lithium-ion batteries are a key technology for electromobility; thus, quality control in cell production is a central aspect for the success of electric vehicles. The detection of defects and poor insulation behavior of the separator is essential for high-quality batteries. Optical quality control methods in cell production are unable to detect small but still relevant defects in the separator layer, e.g., pinholes or particle contaminations. This gap can be closed by executing high-potential testing to analyze the insulation performance of the electrically insulating separator layer in a pouch cell. Here, we present an experimental study to identify different separator defects on dry cell stacks on the basis of electric voltage stress and mechanical pressure. In addition, finite element modeling (FEM) is used to generate physical insights into the partial discharge by examining the defect structures and the corresponding electric fields, including topographical electrode roughness, impurity particles, and voids in the separator. The test results show that hard discharges are associated with significant separator defects. Based on the study, a voltage of 350 to 450 V and a pressure of 0.3 to 0.6 N/mm² are identified as optimum ranges for the test methodology, resulting in failure detection rates of up to 85%.