Non-contact characterization of graphene surface impedance at micro and millimeter waves

The experimental characterization of the surface impedance of monolayer graphene at micro and millimeter wave frequencies is addressed. Monolayer graphene is transferred on a substrate stack, which is placed in the cross-section of a rectangular waveguide. In the fundamental mode, this setup is equivalent to a TE-polarized plane wave impinging under oblique incidence on an infinite graphene sheet, and similarly, the surface impedance of the graphene is a simple lumped element in a transmission-line model, that exactly represents the electromagnetic problem under study. Using this model, we propose a technique based on transmission matrices to accurately extract the surface impedance. The method is able to relax the influence of the substrates tolerances by taking advantage of the graphene infinitesimally small electrical thickness. It can also account for any gap between the sample and the test waveguide, thereby allowing to disregard graphene-metal contact resistance issues. The approach has been successfully applied to characterize graphene samples at X and K-a bands. The extracted surface impedances fit the Drude conductivity model in the absence of interband transitions, and provides a wideband frequency independent resistance (in the range of K Omega s) and a weak inductive behavior (in the range of pHs). (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4728183]