Temperature-dependent transport and $1/f$ noise mechanisms in single-walled carbon nanotube films

The temperature dependence of $1/f$ noise and resistivity in single-walled carbon nanotube (CNT) films are studied. We find that as the temperature decreases, resistivity monotonically increases whereas $1/f$ noise amplitude first decreases, then increases, reaching a minimum at around 40 K. At temperatures considerably smaller than 40 K, the temperature dependence of both resistivity and $1/f$ noise amplitude can be explained by three-dimensional Mott variable-range hopping, which is due to localization effects that result in an insulating behavior in CNT films. At higher temperatures, on the other hand, the dependence of resistivity on temperature can be explained by fluctuation-induced tunneling. In this high-temperature regime, we analyze the temperature dependence of the noise amplitude to extract the density of fluctuators as a function of their energy. Our results show a characteristic peak between 0.3 and 0.6 eV that is responsible for the majority of $1/f$ noise. We also find that, due to its correlation with the number of carriers, the noise amplitude is very sensitive to CNT film device dimensions, especially near the percolation threshold where the resistivity increases. These results not only provide fundamental physical insights about transport and $1/f$ noise mechanisms in CNT films at different temperatures but also help assess the suitability of these films for device applications.

Figure 1

(Color online) Log-log plot of $\rho$ versus $T$ for device D1. Black squares are experimental data points while red (dark) and blue (light) lines are fits to the experimental results based on the VRH and FIT models, respectively. The right inset is a log-log plot of reduced activation energy $\left(W\right)$ versus $T$ for the same device. The solid line in this inset is a power-law fit to the data with an exponent $-0.29$. The left inset is an optical microscope image of a four-point-probe structure with $L=200\mu \text{m}$ and $W=10\mu \text{m}$ etched out of a CNT film with a thickness of 75 nm. Yellow (light) squares labeled from 1 to 4 are Cr/Pd (10 nm/50 nm) metal pads deposited on top of the film contact areas.

Figure 2

(Color online) Log-log plot of $A$ versus $T$ for devices D1 (left $y$ axis) and D2 (right $y$ axis). Due to the high resistance of D2 at low temperatures, noise measurements could be performed only down to 77 K for this device. A power-law fit to the three leftmost D1 data points yields an exponent of 1.53. The black lines are drawn as a guide for the eyes. The inset is a log-log plot of current noise spectral density $\left(S_I\right)$ versus $f$ for a device in set 1 with $L=1000\mu \text{m}$ and $W=50\mu \text{m}$ (open circles), demonstrating the $1/f$-type behavior at low frequencies and saturation of the noise at high frequencies. The black line in this inset is a fit to the low-frequency regime with a slope $\beta$ of 0.99.

Figure 3

(Color online) Log-log plot of $D\left(\eta \right)$ (arbitrary units) versus $\eta$ for devices D1 and D2 directly obtained from $A$ versus $T$ results in Fig. 2. The black lines are drawn as a guide for the eyes. The inset is a linear-log plot of $\beta$ versus $T$ for D1 either experimentally obtained (open circles) or directly calculated from $A$ versus $T$ results in Fig. 2 at 1 Hz.

Figure 4

(a) Log-log plot of measured (filled circles) and simulated (open circles) $A/R$ versus $L$. Measured values are for devices in set 1. The extracted critical exponent from the dashed line power-law fit (i.e., $A/R\propto L^{-\kappa }$) to the simulation dataset is 1.9. (b) Log-log plot of $A\times W$ versus $\rho$ experimentally measured for devices in set 2 (with $L=50\mu \text{m}$ and $W=0.3$, 0.4, 0.7, 1, and $2\mu \text{m}$). The critical exponent extracted from a fit (in the form $A\times W\propto {\rho }^{\delta }$) to the results is 2.5.