Surface conductance of graphene from non-contact resonant cavity

A method is established to reliably determine surface conductance of single-layer or multi-layer atomically thin nano-carbon graphene structures. The measurements are made in an air filled standard R100 rectangular waveguide configuration at one of the resonant frequency modes, typically at TE₁₀₃ mode of 7.4543 GHz. Surface conductance measurement involves monitoring a change in the quality factor of the cavity as the specimen is progressively inserted into the cavity in quantitative correlation with the specimen surface area. The specimen consists of a nano-carbon-layer supported on a low loss dielectric substrate. The thickness of the conducting nano-carbon layer does not need to be explicitly known, but it is assumed that the lateral dimension is uniform over the specimen area. The non-contact surface conductance measurements are illustrated for a typical graphene grown by chemical vapor deposition process, and for a high quality monolayer epitaxial graphene grown on silicon carbide wafers for which we performed non-gated quantum Hall resistance measurements. The sequence of quantized transverse Hall resistance at the Landau filling factors ν = ±6 and ±2, and the absence of the Hall plateau at ν = 4 indicate that the epitaxially grown graphene is a high quality mono-layer. The resonant microwave cavity measurement is sensitive to the surface and bulk conductivity, and since no additional processing is required, it preserves the integrity of the conductive graphene layer. It allows characterization with high speed, precision and efficiency, compared to transport measurements where sample contacts must be defined and applied in multiple processing steps.