Microwave (8–50 GHz) Characterization of Multiwalled Carbon Nanotube Papers Using Rectangular Waveguides

Multiwalled carbon nanotubes (MWNTs) are characterized at X-, Ku-, Ka-, and Q-bands by rectangular waveguide measurements. The scattering parameters (S-parameters) of thin MWNT papers containing a large ensemble of randomly oriented nanotubes are measured by a vector network analyzer from 8 to 50 GHz. A rigorous extraction algorithm has been developed to compute the effective complex permittivity ( epsiv = epsiv'- jepsiv") and permeability ( mu = mu' - jmu") of the nanotube papers from the measured -parameters. The extracted effective medium parameters are verified by finite-element simulations using Ansoft's High Frequency Structure Simulator (HFSS). The uncertainties for this characterization method are analyzed. The systematic uncertainties are found larger at lower frequencies than at higher frequencies. The extracted conductivity of the nanotube papers is in the range of 810-1500 S/m and the dielectric constant is from 250 to 700. The extracted complex permittivity can be fitted with the Drude-Lorentz model for the 8-50-GHz frequency range. The effective medium theory is then applied to remove the impact of air in the nanotube paper.

I. Introduction

Carbon nanotubes are in the form of cylinders rolled up with graphene sheets. A carbon nanotube may be single walled if the tube is a one-atom-thick layer, or multiwalled if the tube consists of more than one layer of graphene sheets. Single-walled carbon nanotubes, depending on the different ways that the graphene sheets are rolled up, can be either metallic or semiconducting [1]. Carbon nanotubes have been extensively studied since they were discovered and are considered as potential building blocks for nanoscale circuits in virtue of their unique mechanical and electrical properties [1], [2]. Recently, many microwave and terahertz applications have been suggested as well [3]–[5], including nanoantennas, nanointerconnects, etc. Since a multiwalled carbon nanotube (MWNT) has multilayers and the layers can be considered as parallel, most of multiwalled tubes are metallic, compared to single-walled tubes, only around 30% of which are metallic [1]. Therefore, MWNTs may be more applicable for microwave applications, as there is not yet an effective way to control the properties of single-walled tubes. However, most of the measurements of carbon nanotubes are done at dc, low frequencies, and optical frequencies. Over the microwave regime, carbon nanotubes' electrical properties have not yet been well studied. The most intuitive method to study the microwave properties of carbon nanotubes is to characterize individual tubes. However, it is very difficult to conduct these types of measurements due to the nanotubes' high intrinsic impedance ( to ), which is incompatible with typical 50- microwave testing systems. In addition, at microwave frequencies, parasitics of testing structures often dominate over the intrinsic properties of carbon-nanotube devices-under-test [6]. An alternative approach is to characterize a large ensemble of nanotubes, e.g., a coplanar waveguide (CPW) filled with carbon nanotubes [7], carbon-nanotube films [8]–[12], or arrays, to obtain the relevant material properties. When a microwave signal impinges upon a nanotube ensemble, at the interface, part of the signal is reflected and part of it is transmitted. The magnitude and phase of the reflection and transmission depend on the sample's properties and can be measured and used to extract the complex permittivity and permeability of the sample.