Publications
Quantitative imaging of graphene impedance with the near-field scanning microwave microscope
Gin, Aaron G.; Shaner, Eric A.
Graphene has emerged as a promising material for high speed nano-electronics due to the relatively high carrier mobility that can be achieved. To further investigate electronic transport in graphene and reveal its potential for microwave applications, we employed a near-field scanning microwave microscope with the probe formed by an electrically open end of a 4 GHz half-lambda parallel-strip transmission line resonator. Because of the balanced probe geometry, our microscope allows for truly localized quantitative characterization of various bulk and low-dimensional materials, with the response region defined by the one micron spacing between the two metallic strips at the probe tip. The single- and few-layer graphene flakes were fabricated by a mechanical cleavage method on 300-nm-thick silicon dioxide grown on low resistivity Si wafer. The flake thickness was determined using both AFM and Raman microscopies. We observe clear correlation between the near-field microwave and far-field optical images of graphene produced by the probe resonant frequency shift and thickness-defined color gradation, respectively. We show that the microwave response of graphene flakes is determined by the local sheet impedance, which is found to be predominantly active. Furthermore, we apply a quantitative electrodynamic model relating the probe resonant frequency shift to 2D conductivity of single- and few-layer graphene. From fitting a model to the experimental data we evaluate graphene sheet resistance as a function of thickness. Near-field scanning microwave microscopy can simultaneously image location, geometry, thickness, and distribution of electrical properties of graphene without a need for device fabrication. The approach may be useful for design of graphene-based microwave transistors, quality control of large area graphene sheets, or investigation of chemical and electrical doping effects on graphene transport properties. We acknowledge support from the DOE Center for Integrated Nanotechnologies user support program (grant No.U2008A061), from the NASA NM Space Grant Consortium program, and from the LANL-NMT MOU program supported by UCDRD.