Finite element modeling of resistive surface layers by micro-contact impedance spectroscopy

Micro-contact impedance spectroscopy (MCIS) is potentially a powerful tool for the exploration of resistive surface layers on top of a conductive bulk or substrate material. MCIS employs micro-contacts in contrast to conventional IS where macroscopic electrodes are used. To extract the conductivity of each region accurately using MCIS requires the data to be corrected for geometry. Using finite element modeling on a system where the resistivity of the surface layer is at least a factor of ten greater than the bulk/substrate, we show how current flows through the two layers using two typical micro-contact configurations. This allows us to establish if and what is the most accurate and reliable method for extracting conductivity values for both regions. For a top circular micro-contact and a full bottom counter electrode, the surface layer conductivity (sigma(s)) can be accurately extracted using a spreading resistance equation if the thickness is similar to 10 times the micro-contact radius; however, bulk conductivity (sigma(b)) values can not be accurately determined. If the contact radius is 10 times the thickness of the resistive surface, a geometrical factor using the micro-contact area provides accurate sigma(s) values. In this case, a spreading resistance equation also provides a good approximation for sigma(b). For two top circular micro-contacts on thin resistive surface layers, the MCIS response from the surface layer is independent of the contact separation; however, the bulk response is dependent on the contact separation and at small separations contact interference occurs. As a consequence, there is not a single ideal experimental setup that works; to obtain accurate sigma(s) and sigma(b) values the micro-contact radius, surface layer thickness and the contact separation must all be considered together. Here we provide scenarios where accurate sigma(s) and sigma(b) values can be obtained that highlight the importance of experimental design and where appropriate equations can be employed for thin and thick resistive surface layers.