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

Abstract

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.

Accounting for the resistivity contribution of grain boundaries in metals: critical analysis of reported experimental and theoretical data for Ni and Cu

“…By averaging over seven measurements in different wires, they obtained a grain-boundary resistivity value ρ SGBR 1.06(10) × 10 -16 m 2 for the incoherent 3 {211} grain boundary. In view of the < ρ SGBR (Cu) >~3 × 10 -16 m 2 value for average random grain boundaries (see Table 2), the result of Bishara et al [53] is very reasonable (we will later compare it also to available theoretical values).…”

“…The physical picture behind the Andrews approach [15] is that we can assign a definite resistivity value to the unit surface area of a grain boundary, the latter considered as a wall of finite thickness. As discussed above, delicate measurements [43,[51][52][53] have demonstrated that, indeed, there is a definite resistivity increment when measuring the resistivity of a thin strip specimen containing a single grain boundary in comparison with an identical strip without grain boundary.…”

“…1.06(10) × 10 -16 m 2 ) of Bishara et al [53] obtained by averaging data measured for seven single incoherent 3 boundaries in Cu. This value is significantly larger (by about a factor of 5) than the reported theoretical and experimental data for the coherent 3 boundary which is certainly mainly due to the much larger atomic disorder in an incoherent 3 boundary with respect to the coherent counterpart.…”

“…In a very recent paper, Bishara et al [53] reported on a new experimental setup for measuring the resistivity of single grain boundaries with the help of four independent micromanipulator tips inside a scanning electron microscope. By FIB milling, narrow wires with 600 nm width and typically 50 mm length were cut from sputtered high-purity Cu films with a thickness of 500 nm on an insulating substrate and the grain boundaries were located and identified by EBSD in the wires.…”

“…9 Results of theoretical calculations of ρ SGBR for various CSL boundary types for Cu metal from reports as indicated in the legend. Experimental results for coherent (♦ [58]) and incoherent (˛ [53]) 3 boundaries are also included parameters are to be derived as noted already in Sect. 2.2.1 in connection with the results of Chawla et al [44].…”