Characterization and Modeling of Low Frequency Noise in Single-walled Carbon Nanotube Film-based Devices Ashkan Behnam, Gijs Bosman, and Ant Ural

Electrical and Computer Engineering, University of Florida, Gainesville, 32611, Florida Email: abehnam@ufl.edu Phone: +1(352)392-8411 Fax: +1(352)392-8381

Single-walled carbon nanotube (CNT) films are a new class of transparent, conductive, and flexible materials, and they exhibit uniform physical and electronic properties1. Several promising device applications of CNT films have recently been demonstrated, such as thin film transistors, optoelectronic devices, and chemical sensors2. For many of these applications, intrinsic noise level and its scaling with device parameters is undoubtedly one of the most important figures of merit; hence they are the focus of this study. For our experiments, CNT films were fabricated using a vacuum filtration approach1 (Fig. 1a) and then patterned into four point probe structures (Fig. 1b) using photo/e-beam lithography and O2 plasma etching3. Noise measurements depict dominant 1/f type behavior at low frequencies (Fig. 1c). For computational analysis, stacked networks of nanotubes with random origin and direction were generated using a Monte Carlo approach4 (Fig. 1d). Equivalent resistance and noise amplitude of the whole device was calculated based on the resistance and noise amplitude of the individual elements in the film (nanotubes and tube-tube junctions)5.

The simulation results for the noise amplitude normalized to resistance (A/R) versus device length (L) of a single-layer nanotube network are in excellent agreement with the experimental data6, clearly indicating that A/R is a strong function of L (Fig. 2). The dashed line is a power-law fit to the experimental data, yielding αLRA ∝/ with a critical exponent α = -1.3. The decrease in the noise amplitude A with device length is consistent with 1/N type dependence where N is the number of carriers, although theoretically, α = -2 is expected for bulk devices6. Our results suggest that the observed exponent is due to the effect of other device parameters on the 1/f noise amplitude. To illustrate this point further, Fig. 3 shows how the film thickness (t) affects the scaling of A/R with L. The extracted critical exponents from the power-law fits to the simulation data are α= -1.9 and α = -0.8 for 8 and 3 layer devices, respectively. As its thickness is reduced, the 3D CNT film becomes like a 2D network and approaches the percolation threshold7, therefore α decreases significantly. The simulation results for the 8 layer (i.e. t = 16 nm) device are in excellent agreement with our experimental data, and both exhibit a critical exponent very close to the theoretical value of α = -2. Figs. 2 and 3 show that the simulation data starts to increase from the dashed line fits for small values of L. This increase is a result of the change in the resistivity (ρ) of the CNT film. As L approaches the length of an individual nanotube (lCNT), the statistical distribution of nanotubes in the device can result in short conduction paths consisting of only a few nanotubes connecting source to drain, decreasing the total ρ of the device8 (Fig. 4a). The effect of the change in ρ at small L (due to percolation) on the noise amplitude A can be illustrated further by plotting the data for t = 16 nm as A ×L vs. ρ (Fig. 4b), thereby removing6 the direct effect of L on A. Then the data can be fit by a power-law relationship given by βρ∝×LA with an extracted critical exponent of β = 0.4. This observed power law behavior is a direct manifestation of percolation affecting the 1/f noise in the CNT film.

Thickness and width also have strong effects on ρ. While ρ is almost constant for wide and thick films (inset in Fig. 5a and left inset in Fig. 6), strong inverse power law dependence of resistivity on t and W exists for thin/narrow devices. We find that the thickness normalized noise A × t has a strong dependence on ρ in the form νρ∝× tA , where the extracted critical exponent is ν = 1.8 (Fig. 5a). These results match previous experimental observations7. As a confirmation of how the two possible noise sources (nanotube and junction) affect the results, A × t versus ρ is calculated for the same device, but with tube-tube junction noise set to zero (Fig. 5b). In this case, not only A drops by orders of magnitude, but also ν becomes negative, both in sharp opposition to experimental observations and theoretical expectations7. These results imply that the tube-tube junctions dominate the 1/f noise in CNT film devices. We obtain similar results for the effect of W on A both experimentally (right inset in Fig. 6) and computationally (main panel of Fig. 6) with critical exponents of 2.3 and 1.8, respectively, for the power law dependencies of A × W on ρ. Our results provide fundamental insights into the complex interdependencies associated with percolation transport in nanotube film devices and help understand and improve the performance of these nanomaterials in potential device applications. [1] Z. Wu, et al., Science 305, 1273 (2004). [2] T. Ozel, et al., Nano Lett. 5, 905 (2005); K. Bradley, et al., Nano Lett. 3, 1353 (2003); G. Esen, et al., Appl. Phys. Lett. 90, 123510 (2007). [3] A. Behnam, et al., Appl. Phys. Lett. 89, 093107 (2006).

[4] A. Behnam et al., Phys. Rev. B 75, 125432 (2007). [5] A. A. Snarskii, et al., Phys. Rev. E 53, 5596 (1996). [6] E. S. Snow, et al., Appl.Phys. Lett. 85, 4172 (2004). [7] S. Soliveres, Appl. Phys. Lett. 90, 082107 (2007). [8] S. Kumar, et al., Phys. Rev. Lett. 95, 066802 (2005).

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Figure 6. Log-log plot of A × W versus ρ for the nominal device. Left inset is a log-log plot of ρ versus W for the same device. Right inset shows log-log plot of A × W versus ρ experimentally measured for devices all with L = 50 µm and t = 75 nm and widths of 0.3, 0.4, 0.7, 1 and 2 µm.

Figure 3. Log-log plot of A/R versus L for multi-layer CNT films. Experimental data points are for CNT film devices with t ~15 nm and W ranging from 2 to 50 µm. Simulation data points are for nominal devices (i.e. device width W = 2 µm, nanotube length lCNT = 2 µm, nanotube density per layer n = 1.25 µm-2), but with t = 16 nm and t = 6 nm (8 and 3 layers).

Figure 2. Log-log plot of A/R, vs. L for a single-layer nanotube network. Experimental data points are from 2D nanotube networks of Snow et al.6. Simulation data points are for single-layer devices with W = 2 µm, lCNT = 2 µm, and n = 5 µm-2.

Figure 1. (a) AFM image of a CNT film with t ~ 15 nm. (b) Optical microscope image of a four point probe structure fabricated from CNT film with L = 200 µm, W = 5 µm, and t = 75 nm. Thin Cr/Pd layers were deposited on top of the contacts using e-beam evaporation. (c) Log-log plot of experimental current noise spectral density (SI) versus f for a device with L = 1000 µm, W = 25 µm, and t = 75 nm under 75 µA current bias. The line is a fit to the 1/f dominated noise data (less than ~100 Hz) with an exponent of β ≈ -0.99. (d) A 2D CNT network generated using a Monte Carlo approach for a device with L = 4 µm, W = 4 µm, lCNT = 2 µm and n = 10 µm-2. Semiconducting and metallic nanotubes are shown in cyan and blue color (light and dark) respectively.

Figure 4. (a) Log-log plot of ρ versus L for the nominal device (same as Fig. 3) with t = 16 nm. (b) Log-log plot of A × L versus ρ for the same device. The change in resistivity is a result of the change in device length.

Figure 5. (a) Log-log plot of A × t versus ρ for the nominal device. The inset is a log-log plot of ρ versus t. (b) Log-log plot of A × t versus ρ for the same device without any noise sources at the tube-tube junctions.

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