Resonant and Broadband Microwave Permittivity ...

Mater. Res. Soc. Symp. Proc. Vol. 1057 © 2008 Materials Research Society

1057-II15-61

Resonant and Broadband Microwave Permittivity Measurements of Single-walled Carbon Nanotubes Chinmay D. Darne1,2, Lei-Ming Xie2, Divya Padmaraj1,2, Paul Cherukuri3, Wanda ZagozdzonWosik1,2, and Jarek Wosik1,2 1 Department of Electrical and Computer Engineering, University of Houston, Houston, TX, 77204 2 Texas Center for Superconductivity, University of Houston, Houston, TX, 77204 3 Department of Chemistry, Rice University, Houston, TX, 77005 ABSTRACT We report on complex permittivity measurements of single-walled carbon nanotubes (SWNTs) over the microwave frequency range. The SWNT samples contained a mixture of semiconducting and metallic nanotubes and were homogeneously suspended using surfactant (Pluronic, F108). Other samples that were characterized included a Pluronic powder and a carpet of oriented multi-walled nanotubes (MWNT). Shielded open-circuited transmission line technique was used for broadband frequency measurements. Single frequency (resonant) measurements for SWNT samples were carried out by using two specially designed microwave dielectric resonators (DR). The first DR, with an axial cylindrical hole in the dielectric disk, could excite either TE011 or TM011 mode (3.4 GHz and 6 GHz) and was designed for liquid/powder sample characterization. The second DR used was split-post dielectric resonator (12 GHz). At 3.4 GHz, the real and imaginary parts of permittivity for Pluronic only suspended SWNTs were experimentally found to be 3.5 and 0.72, respectively. From our calculations conductivity of SWNT mixture was 1.16x105 (S/m) and for Pluronic it was 1.6587x10-2 (S/m). INTRODUCTION In the last few years carbon nanotubes emerged as one of the highly investigated materials, primarily due to their quasi-one dimensional structure, superior mechanical and chemical properties and most importantly their tunable electronic nature (by altering their chirality and diameter). Properties of single-walled carbon nanotubes (SWNTs) are of special interest and great consequence because of their potential applications in various microwave frequency ranges as microwave lenses, high-speed nanoelectronic devices, antennas, waveguides, nano-electromechanical systems (NEMS), etc. [1]. Recent studies have shown that high current density combined with flat conductivity response (from dc to 10 GHz) for SWNTs make them an ideal candidate for high-speed transistor applications [2]. Due to their superior conductivity, efforts are being made to incorporate nanotubes as interconnects in future microelectronic devices. SWNTs can also be used as electromagnetic interference (EMI) shields in high-frequency circuits and as low-reflectivity materials for military applications. The excellent conductivity of the nanotubes coupled with their high aspect ratio helps to drastically reduce their loading density in composites and thus make them a very good alternative to the currently employed carbon black [1,3,4]. Theoretical calculations performed for static polarizabilities of metallic SWNTs have shown that the polarizability component along the

nanotube axis is much stronger than that normal to their axis because of their high aspect ratio [5]. This gives rise to different permittivities for nanotubes along their longitudinal and radial directions not only for quasi-static case but also for high frequency ranges. Therefore, to completely understand the behavior of nanotubes at high frequencies we need to study their complex dielectric permittivity response over a broad microwave frequency range. Differentiation of such responses between semiconducting and metallic nanotubes as well as their respective frequency behavior originating from their orientations should be the ultimate goal, which is important both for basic knowledge of SWNTs and for their applications. This work is an experimental step towards understanding the complex permittivity response of carbon nanotubes over a selected microwave frequency range. EXPERIMENT We used liquid-suspended SWNT samples as well as highly oriented multi-walled nanotubes (MWNT) carpet for our dielectric characterization study. The SWNT suspension comprised of SWNTs suspended in water (30mg/L) through surfactant (1 % weight/volume). Surfactant (Pluronic) was used to stabilize the inherently hydrophobic SWNTs in water and hence to obtain a homogeneously suspended water-based SWNT solution. Pluronic solution measurement without SWNT was also performed over the broad frequency range (50 MHz to 7 GHz) as a reference run. Broadband measurements were also carried out on Pluronic powder to measure its permittivity over the frequency range of interest. SWNTs suspended in low permittivity liquid surfactant (X10) were also measured for reasons explained later. Shielded open-circuited Coaxial Probe Shielded open-circuited coaxial probe based on transmission-line model was used for broadband frequency measurements of SWNTs. We have designed and analyzed the probe based on a model of a similar structure proposed by J. Baker-Jarvis et. al from NIST [6]. A sketch of the coaxial sample probe is shown in Figure 1. Figure 1. Shielded open-circuited sample holder for broadband frequency measurements of SWNTs.

The coaxial probe design consists of a section of coaxial transmission line with an inner conductor of shorter length. This design helps to increase the measurement sensitivity of the probe by confining the electromagnetic (EM) signal to the inside of the probe. The maximum operating frequency of the probe is limited by the cut-off frequency for the circular waveguide (length L3). Azimuthal symmetry of the probe makes TEM the dominant mode in the probe apart

from evanescent TM0n modes (due to sample discontinuity). Exact solution of Maxwell’s equation is very difficult to obtain for such a complex probe design and hence a rigorous EM analysis was performed (see Ref. 6) to establish a relationship between the measured one-port reflection parameters and the complex permittivity of the dielectric sample. HP8720 vector network analyzer was used for measurements of the one-port reflection parameters from the sample. LABVIEW interface was used for communication and data acquisition from the analyzer. Inverse problem solving technique was used to evaluate the complex permittivity of the sample from the measured single port reflection data. Dielectric Resonators Resonators, in general are useful not only for high sensitivity measurements of complex dielectric permittivity but also for anisotropic measurements of the samples. TE011/TM011 mode dielectric resonator (DR) was used in this study to cross-verify the measurements obtained from the coaxial probe. Perturbation caused in the resonator field upon introducing a sample was used for studying the dielectric properties of the sample. Shift in the resonant frequency and Q-factor due to field perturbation were indicative of the dielectric constant and loss occurring in the sample. The TE/TM mode DR design included a dielectric cylinder with a central hole (for holding the sample) and metal plates terminating each side (Figure 2) [7]. TE011 mode was excited inductively using coupling loops while antennas were used to excite the TM011 mode. Negligible conductor losses associated with these resonators ensured a very high Q-factor thus improving the measurement accuracy. Figure 2. A TE011/TM011 mode dielectric resonator used for studying the SWNT dielectric response.

Maximum measurement sensitivity was achieved by selecting the sample diameter to coincide with the region of high E-field. In the TE011 mode, an in-plane ϕ-component of the Efield was increasing away from the center and so it was necessary to use a large sample diameter for this mode. However, losses associated with the large samples severely affected the accuracy of Q-measurements. Therefore, it was imperative to select a sample diameter that would balance the loss related to the sample volume with high enough sensitivity required for measuring the frequency shift. For the TM011 mode, the magnitude of out-of-plane z-component of the E-field was at maximum in the resonator center. Therefore, the sample diameter for the TM011 mode could be very small. Teflon (inherent low loss) tubes, sealed at one end were used to hold the SWNT samples. We have measured the liquid-based SWNT response at two microwave frequencies- 3.4 GHz using the TE011 mode and 6 GHz using the TM011 mode. We also used a split post dielectric resonator (TE01δ mode) [8,9] operating at 12 GHz to study the response of the aligned MWNT carpet grown using Chemical Vapor Deposition (CVD) technique.

RESULTS AND DISCUSSION The SWNT sample response was measured over a broad frequency range from 50 MHz to 7 GHz using the coaxial probe. The Pluronic powder measurements gave a flat response with a very low dielectric constant (< 2), while water suspension of Pluronic has the dielectric constant similar to that of water. The measured loss for Pluronic was also very small and hence its contribution towards the measurements of Pluronic suspended SWNTs was quite negligible. Figure 3 shows only a selected region of the whole frequency range scanned using the coaxial probe. Figure 3. A zoomed-in region for a selected frequency range shows coaxial probe measurements for Pluronic and SWNT solutions.

No visible difference was observed in the dielectric constants for the SWNT suspension and blank Pluronic solution (Figure 3 (a)). One of the possible reasons for this behavior may be the relatively large dielectric constant of water that screens the response from low concentration SWNT suspension. Dielectric loss for the SWNT solution is however considerably higher than that of Pluronic solution (Figure 3 (b)). To further investigate whether this observed loss was a measurement artifact or was actually contributed by the presence of SWNTs, the original SWNT solution was diluted with surfactant. Figure 4 (a) shows the imaginary part of permittivity for original (with its concentration (x) normalized to unity) and diluted SWNT solutions. It can be observed that with every dilution step, the measured imaginary permittivity decreases, indicating that the presence of SWNTs is responsible for the observed dielectric loss. Thus, the presence of SWNTs was found to increase the loss of the overall suspension without altering its dielectric constant. Sample conductivity was extracted from the measured dielectric loss for the sample. The measured dielectric loss, in general, is given by: '' '' = ε suspension + ε measured

σ ωε 0

'' '' where ε measured is the total dielectric loss measured from the sample, ε suspension is the actual

(1)

dielectric loss, σ is the sample conductivity, ω is the angular frequency and ε0 is the permittivity of vacuum. Data fitting was performed for the above equation for each of the original and diluted SWNT solutions to compute the sample conductivity over the frequency range of 50 MHz2GHz, where the influence of conductivity on sample measurements was high. The calculated

conductivity as a function of normalized sample concentration is shown in Figure 4 (b). A linear fit for the experimental plots gave us the conductivity of the Pluronic solution (1.6587x10-2 (S/m)). At the same time, the average conductivity of nanotube mixture was computed from the slope of the graph knowing the SWNT volume fraction in the suspension. An average SWNT conductivity of 1.16x105 (S/m) was obtained from our calculations, similar to reported data [3]. To successfully identify the response of dielectric constant for SWNTs from its suspension over the wide frequency range, we used a low permittivity liquid surfactant (X10) to suspend the SWNTs. The surfactant retained the homogeneity of the suspended SWNTs. The coaxial probe measurements were repeated with this new suspension. A reference run with only X10 solvent was also measured over the same frequency range. Figure 4. Plots showing changes in the imaginary part of permittivity versus frequency (a) and conductivity as a function of the normalized SWNT concentration (b).

The solution containing the suspended SWNTs exhibited not only a higher dielectric constant as compared to the stand-alone X10 solution (Figure 5 (a)), but also an increased loss over the X10 solution (Figure 5 (b)). Thus, the coaxial probe was now able to differentiate the response coming from the SWNT suspension and X10 solution. Figure 5. Plots show good correlation between measured results obtained using a coaxial probe and dielectric resonators.

To verify the results obtained using the coaxial probe and to further measure the same sample responses with much better sensitivity, we used DR with TE011/TM011 modes. The resonators were first calibrated at their respective operating frequencies by measuring a reference sample (water) with known complex permittivity. For the actual experiments we again used a

low permittivity liquid surfactant (X10) based SWNT samples and measured them using TE011 mode (3.4 GHz) and TM011 mode (6 GHz). Two samples were measured for each of the resonator: SWNTs suspended in X10 and X10 alone. The results are shown in Figure 5. Good agreement can be observed between the measurements from the resonators and the coaxial probe. Additional modeling needs to be performed to extract the stand-alone dielectric response of SWNTs from the suspension for both coaxial probe and TE011/TM011 mode DR. A carpet of well aligned multi-walled nanotubes (MWNT) was also measured as part of this work. Split post dielectric resonator measurements (at 12 GHz) employing TE01δ mode was used for measuring this sample. The MWNT sample consisted of a mixture of semiconducting (response to in-plane E-field) and metallic (response to out-of-plane H-field) nanotubes (Figure 6). The strong metallic response can be attributed to the presence of iron nano-catalyst particles used to grow the nanotubes. Theoretical modeling of the field distribution within the split post dielectric resonator is also required to extract the dielectric permittivity of MWNTs. Figure 6. 3D response obtained from scanning of an oriented MWNT carpet using split post dielectric resonator (12 GHz).

CONCLUSIONS Measurements were performed on liquid-based SWNT samples using a coaxial probe (50 MHz to 7 GHz) and DR (TE011 at 3.4 GHz and TM011 at 6 GHz) including a split post dielectric resonator (12 GHz). The results from the transmission-line-based and resonance-based techniques showed very good correlation for the measured SWNT samples. Since the dielectric constant for water-based SWNT samples was not discernible from its suspending solution (due to large dielectric constant of the water) the experiments were repeated using SWNTs suspended in a low-permittivity (X10) surfactant. The dielectric constant was now successfully measured over the complete frequency range. Significant conductivity was however observed for both water-based and X10-based SWNT samples. The average conductivity of SWNT mixture was extracted from the dilution experiments and was found to be 1.16x105 (S/m). ACKNOWLEDGEMENTS The research was supported by Texas Center for Superconductivity and Institute for Space Systems Operations (ISSO) at University of Houston (TcSUH) and Strategic Partnership for Research in Nanotechnology (SPRING). We are grateful to Dr. Q. Yu for providing us with aligned MWNT samples.

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