Effects of defects on thermoelectric properties of carbon nanotubes

Carbon nanotubes (CNTs) have recently attracted attention as materials for flexible thermoelectric devices. To provide a theoretical guideline of how defects influence the thermoelectric performance of CNTs, we theoretically studied the effects of defects (vacancies and Stone-Wales defects) on their thermoelectric properties; thermal conductance, electrical conductance, and Seebeck coefficient. The results revealed that the defects most strongly suppress the electron conductance, and deteriorate the thermoelectric performance of a CNT. By plugging in the results and the intertube-junction properties into the network model, we further show that the defects with realistic concentrations can significantly degrade the thermoelectric performance of CNT-based networks. Our findings indicate the importance of the improvement of crystallinity of CNTs for improving CNT-based thermoelectrics.

Figure 1

Schematic of a CNT with defects: vacancy and SW defect. The defective region connects with pristine CNT leads at both ends. For the NEMD simulation, the length of the leads is half of that of the defective region ($L_{\mathrm{def}}/2$) and are terminated by fixed layers. For the Green's function method, on the other hand, the leads are defined to be semi-infinite and periodic. Dashed circles in the bottom panels show the region in which atoms are displaced over 0.15 nm due to the introduction of defects.

Figure 2

Change in thermal conductivity of (10, 0) CNTs due to (a) vacancy and (b) SW defect. The symbols, black circle, blue square, and orange triangle, represent different CNT lengths, 10, 50, and 100 nm, respectively. The solid line in (a) shows the fitting line for vacancy and the broken line in (a) and (b) for SW defect. The inset in (a) shows a closeup at high defect concentration ($0.5\%\le \sigma \le 1.0\%$), the marked region.

Figure 3

Transmission function of 100-nm CNTs with (a) vacancies and (b) SW defects. The bottom panels show the transmission of low-energy electrons (closeups of the marked areas). The defect concentration varies from 0.0% (blue) to 0.1% (red) ($N_{\mathrm{def}}=0\mathrm{to}9$) with the equal interval.

Figure 4

Thermoelectric properties of 100-nm CNTs with vacancies (top) and SW defect (bottom): (a) Seebeck coefficient, (b) electron conductance, (c) electron thermal conductance, and (d) power factor. Color identification is the same as in Fig. 3. Broken lines denote the peak chemical potentials for $P, {\mu }_{p/n,\mathrm{opt}}=-/+0.38\mathrm{eV}$. Insets of (a), (b), and (d) show closeups of the marked region while those of (d) show the Wiedemann-Franz law.

Figure 5

Peak chemical potential for $P$ shifts with increasing the defect concentration. (a) Fluctuation of the optimized chemical potential for $P$ of $p$-type CNTs with (top) vacancy and (bottom) SW defect. (b) Change in different electron transport properties for $p$-type CNTs with vacancies of $\sigma =0.00,0.02$, and 0.04% ($N_{\mathrm{def}}=0,3$, and 6). The units for $\left|S\right|, G_{\mathrm{el}}, P$, and $\mathrm{\Theta }\left(E\right)$ are V/(5000 K), $S$/5000, $\mathrm{pW}/{\mathrm{K}}^2$, and dimensionless, respectively. The competing behavior of $G_{\mathrm{el}}$ and $S$ with the introduction of vacancies, the decrease in $G_{\mathrm{el}}$, and increase in $S$ causes the shift of the peak chemical potential for $P$ toward high doping level.

Figure 6

Thermoelectric properties of CNTs with vacancies (left) and SW defects (right): (a) $\left|S\right|$, (b) $G_{\mathrm{el}}$, and (c) $P$. $P$ and $G_{\mathrm{el}}$ are plotted on a logarithmic scale. Solid and broken lines show data at ${\mu }_{\mathrm{opt}}$ and ${\mu }_0$, respectively. Orders of reduction of $G_{\mathrm{el}}$ are a dominant factor of the reduction of $P$ due to defects.

Figure 7

Figure of merit of CNTs with (a) vacancies and (b) SW defects. Insets show the data at low $\sigma (<0.25\%)$, denoted by broken lines in the main figure, with linear scale. Solid and broken lines show data at ${\mu }_{\mathrm{opt}}$ and ${\mu }_0$, respectively, the same as in Fig. 6.

Figure 8

Fitting results: (a) electron transmission function $\mathrm{\Theta }(E,L_{\mathrm{def}},\sigma )$ of CNTs with $\sigma =0.02\%$ at different energy levels and (b) thermal conductivity of CNTs with different σ.

Figure 9

Figure of merit of CNT-based networks. (a) Figure of merit of individual CNTs (black) and corresponding two- (green) and three- (blue) dimensional CNT networks. Bold and thin lines indicate data for pristine ($\sigma =0\%$) and defective ($\sigma =0.02\%$) CNTs, respectively. (b) Figure of merit of CNT-based three-dimensional networks composed of defective CNTs with different lengths. The data are normalized by values for pristine systems shown in (a).