Electrical Resistivity Measurements of Surface-Coated Copper Foils.

Due to the direct contact between the probe and sample, the contact of the four-probe method is important for the structural integrity of the sample and the accuracy of electrical resistivity measurements, especially for surface-coated metal foils with multilayered structures. Here, we analyzed the accuracy and stability of four-probe method probing on different sides of copper (Cu) foils covered with graphene (Gr). Theoretical simulations showed similar potential distributions on the probe tip when probing on the Cu and Gr sides. The resistivity of the Gr/Cu foil was 2.31 ± 0.02 μΩ·cm when measured by probing on the Cu side, and 2.30 ± 0.10 μΩ·cm when measured by probing on the Gr side. The major difference in the mean deviation is attributed to surface damage. In addition, the method of probing on the Cu side was sensitive to the resistivity changes of Gr induced by polymers with a dielectric constant range of 2~12, which is consistent with the calculations based on the random phase approximation theory. Our results demonstrated that the probing position on the metal side in the four-probe method can effectively protect the structural integrity of the functional surface-coated layer and maintain the high sensitivity of the measurement, providing guidance for the resistivity measurements of other similarly heterogeneous materials.