Analytical expressions for spreading resistance in lossy media and their application to the calibration of scanning microwave microscopy

Abstract

This paper presents the analytical derivation of spreading resistance expressions for diverse geometries of a conducting probe submerged in a lossy medium. Resulting equations can be used to calibrate scanning impedance/scanning microwave microscopes operating in liquid. The expressions are systematically validated through numerical and experimental methods for the calibration of an inverted Scanning Microwave Microscope (iSMM) when operating in a lossy saline medium, such as Dulbecco's Modified Eagle Medium (DMEM), a widely used medium for supporting the growth of biological cells. The calibration process within DMEM plays an important role in the quantitative local evaluation of electromagnetic properties of biological samples under physiological conditions. Additionally, measurements are performed in distilled water for comparative analysis.