Direct probing of imperfection-induced electrical degradation in millimeter-scale graphene on SiO2 substrates

In large-scale electronic applications of graphene, imperfections play a key role in controlling the electrical properties. Here we directly probe the electrical-degradation effects induced by wrinkles, grain boundaries, multilayered islands, cracks, holes, and adsorbates on millimeter-scale graphene on a SiO2/Si substrate using a four-probe scanning tunneling microscope. By comparing the local measurements near and far away from these imperfections, we quantify their impact on the most important figures of merit including sheet resistance, carrier mobility, and residual carrier-density variations in the vicinity of the imperfections. Angle-dependent measurements via a van der Pauw geometry are then performed to determine the influence of imperfections on the whole graphene flake. A key result is that, as long as the imperfections do not extend continuously over the entire flake, the overall electrical properties of a graphene flake are not distinctly impacted by the imperfections because carriers find the paths of least resistance. The four-probe method can also be extended to evaluate the degradation effects on electrical-transport properties in other two-dimensional (2D) materials.