Modifications to the spreading resistance equation when using micro-contact impedance spectroscopy to measure resistive surface layers.

Micro-contact impedance spectroscopy (mcIS) is a powerful tool that can allow local features such as grain boundaries and surfaces in electro-ceramics to be directly interrogated. Typical macroscopic electrodes fully cover the specimen surfaces and data are converted from resistance into conductivity using a geometric correction factor based on the surface area of the electrodes and thickness of the sample. For mcIS measurements this requires a different approach. The conversion factor required in this case is that for a spreading resistance and the correction factor depends on the radius (r) and separation of the micro-contacts. When dealing with conversions for samples with a resistive surface layer, two extreme scenarios exist depending on the thickness of the surface layer (T) and the arrangement and size of the contacts. When the resistive layer is thin (T/r < 10) the geometric correction factor provides accurate conductivities but for thick layers (T/r > 10) the spreading resistance correction equation is required. When the surface layer is an intermediate thickness however neither provides a good estimate for conductivity. Using finite element modelling we simulate resistive surface layer systems using a top-top micro-contact arrangement and show that instead of using either of the two separate correction equations, a single modified spreading resistance equation can be used on the resulting impedance data to provide greater accuracy and simplicity in the extraction of conductivity. With this modified correction factor, when the ratio of bulk material conductivity versus surface layer conductivity (σb/σs) is ≥100, σs can be calculated for any surface layer thickness. When the ratio is <100, only when (T/r) is >3 can σs be accurately estimated.