Approaches to Measure the Resistivity of Grain Boundaries in Metals with High Sensitivity and Spatial Resolution: A Case Study Employing Cu

It is well-known that grain boundaries (GBs) increase the electrical resistivity of metals due to their enhanced electron scattering. The resistivity values of GBs are determined by their atomic structure; therefore, assessing the local resistivity of GBs is highly significant for understanding structure-property relationships. So far, the local electrical characterization of an individual GB has not received much attention, mainly due to the limited accuracy of the applied techniques, which were not sensitive enough to detect the subtle differences in electrical resistivity values of highly symmetric GBs. Here, we introduce a detailed methodology to probe in situ or ex situ the local resistivity of individual GBs in Cu, a metallic model system we choose due to its low resistance. Both bulk Cu samples and thin films are investigated, and different approaches to obtain reliable and accurate resistivity measurements are described, involving the van der Pauw technique for macroscopic measurements as well as two different four-point-probe techniques for local in situ measurements performed inside a scanning electron microscope. The in situ contacts are realized with needles accurately positioned by piezodriven micromanipulators. Resistivity results obtained on coincidence site lattice GBs (incoherent Σ3 and asymmetric Σ5) are reported and discussed. In addition, the key experimental details as well as pitfalls in the measurement of individual GB resistivity are addressed.