Probing porosity in metals by electrical conductivity: Nanoscale experiments and multiscale simulations

Motivated by the significant influence of the underlying microstructure on the effective electrical properties of a material system and the desire to monitor defect evolution through non-destructive electrical characterisation, this contribution is concerned with a detailed study of conductivity changes caused by the presence of sub-microscale pores. Reducing the complexity of the material system, geometrically well-defined pore arrays are created by focused ion beam (FIB) milling in Cu thin films and characterised by 4-point probe electrical measurements. The experiment is designed such that it reduces to a (quasi-)one-dimensional electrical problem which is amenable to analytical techniques when invoking a computational homogenisation scheme to approximate the effective electrical properties of a given microstructure. The applicability of the proposed approach is shown in a first step by comparing simulation results for different pore volume fractions and pore shapes against their experimental counterparts. In a second step, a sensitivity analysis of the experimental data is carried out and the usefulness of the proposed modelling approach in interpreting the experimental data is demonstrated. In particular, the findings suggest that the proposed experimental method allows (at best) the determination of pore volume fractions with an accuracy of ±0.5%.