Improvement of thermoelectric performance of single-wall carbon nanotubes by heavy doping: Effect of one-dimensional band multiplicity

Doped single-wall carbon nanotube (SWCNT) films were prepared and their Seebeck coefficient (S) and electrical resistivity (ρ) were investigated as functions of carrier density. For heavy doping, a second maximum of S (S = 35 µV/K) was discovered, with its corresponding power factor, P = 85 µW/(m·K2), 6 times that of the first maximum for lightly doped films. Calculations for zigzag SWCNTs suggest that the thermoelectric performance can be effectively improved by controlling the multiplicity of the one-dimensional band and tuning the carrier density. This provides a new strategy for achieving higher performance at a lower cost than using high-purity semiconducting SWCNTs.

S ingle-wall carbon nanotubes (SWCNTs) 1) have great potential as flexible thermoelectric films. [2][3][4][5][6][7][8][9] Highpurity and high-quality semiconducting SWCNTs exhibit a large Seebeck coefficient S of 170 µV=K and a potential power factor P > 1200 µW=(m·K 2 ). 2,3) Zhou et al. 4) reported that P was >2000 µW=(m·K 2 ) for films and fibers that were mixtures of metallic (m-) and semiconducting (s-) SWCNTs, a value almost the same as that for commercial Bi-Te materials. However, the reported figure of merit ZT values ranged from <0.01 to 0.2, [4][5][6][7][8] while the estimated potential ZT ranged from 0.4 to 1.2. 10) The scatter in ZT, in addition to other thermoelectric properties, is partly due to variations in characteristics such as the carrier density, inhomogeneous carrier doping, film morphology, and structural distribution of SWCNTs in the film. Therefore, further systematic studies on the relationships between each characteristic and the thermoelectric properties are required. With respect to the carrier density, a lightly doped region has been reported, 2,3,9) while a heavily doped region has been investigated only in electric double-layer transistor arrangements based on s-and m-SWCNT films. 11) Here, we discuss the effect of heavy acceptor doping on S and the electrical resistivity ρ for mixed SWCNT films that consist of m-and s-SWCNTs with the goal of obtaining high-performance thermoelectric films.
S and ρ were measured for SWCNT films that were heavily doped with HNO 3 and H 2 O as acceptors, although the mechanism of carrier doping with H 2 O has not been clarified. 3) Using the starting SWCNTs (ArcSO grade) purchased from Meijo-Nanocarbon, 12) a film was prepared using a procedure similar to that reported previously. 13) Briefly, pristine SWCNTs were dispersed in a sodium deoxycholate solution and centrifuged, after which the upper 90% of the supernatant was collected. The supernatant was then vacuum-filtered to prepare a SWCNT film. The prepared film, which consisted of SWCNTs (mean diameter: 1.45 nm) with different chirality values, was a mixture of m-and s-SWCNTs with a nominal ratio of 2 : 1. Before measurements, the film was annealed at 500°C for 10 min in vacuum to remove absorbed molecules such as alcohol and oxygen. The detailed doping and de-doping procedures, as well as the measurement systems, have been described in our previous reports. 2,3) First, the film was acceptor-doped in humid air and then heavily doped with 13.1 M HNO 3 . The film was subsequently de-doped by heating under a dynamic vacuum. HNO 3 facilitates hole doping with Fermi level shifts of 0.2-0.5 eV for SWCNTs produced using an arc-discharge method. 14,15) X-ray diffraction measurements suggested that the doping was homogeneous over the entire region of the SWCNT film. Figure 1 shows the S-ρ and P-ρ relationships for the lightly doped region ( ρ > 10 mΩ·cm) of the SWCNT film along with previously reported data. 3) Two distinct maxima, S 1 and S 2 , were observed in the S-ρ relationship at ρ ≈ 1.5 and 30 mΩ·cm, respectively. The moderately large S 2 = 35 µV=K peak at ρ ≈ 1.5 mΩ·cm was observed for the first time in a mixed film, and the obtained power factor of P = 85 µW=(m·K 2 ) was six times larger than that of the S 1 peak due to the low resistivity and large S 2 . This P value of 85 µW=(m·K 2 ) corresponds to approximately 70% of that for a highly concentrated s-SWCNT film. 2) Considering the high cost of preparing s-SWCNT films using current technology such as density gradient ultracentrifugation, 16,17) these results demonstrate that heavy doping of a mixed film of m-and s-SWCNTs is a useful method for fabricating high-performance films at a much lower cost.
A systematic model calculation of S and the electrical conductance G was conducted for zigzag SWCNTs that have a chiral index of ðn; 0Þ, where n = 9-38, to understand the cause of the observed multiple peaks for S and P. Zigzag SWCNTs were used for the calculation because their use is less expensive than chiral-type SWCNTs. Although SWCNTs for which n is a multiple of 3 are classified as m-SWCNTs, there is a small gap at the Fermi level, 18) which also occurred in the present calculation (see Fig. 2). The other zigzag SWCNTs are s-SWCNTS. The SWCNTs were modeled as rollup structures of graphene nanoribbons (GNRs) with a C-C bond length of a CC = 0.142 nm.
The electronic states were calculated using a semiempirical (extended Hückel) theory with the Hoffmann carbon potential. The transport calculation details were essentially the same as those reported previously for GNRs. 19) The transmission function ζ(ε) of a carrier with energy ε was calculated on the basis of the nonequilibrium Green's function method using the Atomistix ToolKit (ATK-SE 12.2.0). 20) S and G are given by where q is the charge of a carrier, T is the temperature, and K n is the intermediate function where h is Planck's constant, f is the Fermi-Dirac distribution function, and μ is the chemical potential. We assumed that μ could be tuned by carrier doping within a rigid band model. Although the present method should be used in the coherent extreme, the results semiquantitatively explain the experimental results obtained in previous studies. 2,3) This may be because tunneling effects at SWCNT-SWCNT junctions play a major role in determining film properties. Figure 2 shows typical results for the electronic density of states (DOS) and ζ(ε), along with S and P at 300 K. Here, P = S 2 =R using the SWCNT resistance R = 1=G, instead of P = S 2 =ρ because ρ is not defined without the cross section of the SWCNTs. Even in m-SWCNTs with ð3m; 0Þ, a small gap exists at the center ( μ ≈ 0), unlike metallic armchair SWCNTs with ðn; nÞ. This gap leads to the S and P peaks S M,max and P M,max , respectively, around μ ≈ 0. Similarly, for μ < 0 within the band gap E g in s-SWCNTs, S increases linearly with μ from the band edge μ ∼ −E g =2, as shown in the bottom panels of Fig. 2, to reach a maximum value, S 1,max , around μ ≈ 0. 2,3) In ð25; 0Þ and ð26; 0Þ s-SWCNTs, the maximum value of P in the gap, P 1,max , appears just below (above) the conduction (valance) band edges μ = ±E g =2, rather than at μ ≈ 0 (see bottom panels of Fig. 2). This is because R inside the band  gap increases exponentially from the band edge to the center of the gap at finite temperatures, which is indicated by the transmission function shown in the center panels of Fig. 2 and Eqs. (1) and (2). The experimentally observed peaks in the high-resistivity region (ρ > 10 mΩ·cm in Fig. 1) should correspond to the S 1,max and P 1,max peaks in Fig. 2. The magnitude of the observed S peak is substantially reduced and its position has shifted from μ ∼ 0 toward the band edges μ ∼ ±E g =2 because of the presence of m-SWCNTs in the film. 2,3) Figure 3 presents S 1,max and P 1,max as functions of SWCNT diameter D and E g , in addition to the E g -D relationship in the inset in Fig. 3(a). Although the magnitude of E g is dependent on the calculation method and parameters used, the S max -E g and P max -E g relationships obtained are quantitatively identical, 21,22) even for GNRs, 19) because of the same one-dimensional (1D) nature. Figure 3(a) shows that S max , i.e., S 1,max or S M,max (in units of µV=K), increases with an increase in E g (in units of eV) for both m-and s-SWCNTs. A polynomial fit of the data (solid line) is given by S max ¼ À11:6 þ 1221E g þ 658E 2 g À 356E 3 g at 300 K. Instead of using E g obtained by the present calculations, a more practical estimate of S max would be obtained using E g calculated via more sophisticated methods that involve DOS (e.g., see Refs. 23 and 24). In contrast, as shown in Fig. 3(b), P 1,max is almost independent of D in s-SWCNTs, while P M,max for m-SWCNTs increases toward that for s-SWCNTs with a decrease in D.
On the other hand, Figs. 3(c) and 3(d) show that S 2,max and P 2,max are quite sensitive to the chiral index ðn; 0Þ, where S 2,max is in the range of 40-90 µV=K and P 2,max is 0.5-2 times larger than P 1,max ≈ 1.5 pW=K 2 . Note that P 2,max can be greater than P 1,max . For example, the ð24; 0Þ SWCNT exhibits the largest peak for P > 3 pW=K 2 with a moderately large S 2,max in this region [Figs. 3(c) and 3(d)].
These peaks are related to the DOS, which is sensitive to n, as seen in the top panels of Fig. 2. The DOS is composed of several contributions from 1D π-bands, and many spikelike peaks in the DOS emerge because these bands have van Hove singularities (VHSs). The S and P peaks can arise from these 1D bands. 11) However, in contrast to S and P related to the band edge (the first VHS around μ ∼ ±E g =2), a significant enhancement of S and P is generally not expected for VHSs inside the valence bands, as indicated by the vertical red dashed line in the middle bottom panel of However, a moderately large S is obtained when the M bands (M is the number of 1D bands) are successively superimposed in a narrow energy region, as shown by the red arrow in the left middle panel in Fig. 2 for ð24; 0Þ m-SWCNTs. Each band exhibits stepwise conductance, which is characteristic of a 1D system, as demonstrated by Fig. 3. Maximum values of (a) S (S max ) and (b) P (P max ) within the band gap E g . The inset in (a) shows the relationship between E g and the chiral index n.
Second maximum values of (c) S (S 2,max ) and (d) P (P 2,max ) in the valence band (see arrows in the bottom panels of Fig. 2). The SWCNT diameter is given by D ¼ ffiffiffi 3 p a cc n=. Red circles indicate the results for n = 3m (m-SWCNTs), blue squares for n = 3m + 1 (s-SWCNT), and black circles for n = 3m + 2 (s-SWCNT), where m is an integer. ζ(ε) in Fig. 2; therefore, S forms peaks around VHSs, as already mentioned. In addition, band multiplicity, if present, can substantially enhance the slope of ln G( μ) with respect to μ, which leads to a larger S, even within the band. This is seen with the ð24; 0Þ m-SWCNT; it has the largest S 2,max around μ = −0.5 eV [see Fig. 3(c)], based on the steepest slope in ln ζ(ε), or the largest value for d ln G( μ)=dμ (see the online supplementary data at http://stacks.iop.org/APEX/9/ 125103/mmedia) due to band multiplicity.
Finally, the experimental data are compared with the calculated results in Fig. 1. Calculations were not performed for general ðn; mÞ SWCNTs; therefore, the following comparison is only tentative; future studies with more sophisticated calculations are needed. A parallel network model of ð19; 0Þ s-SWCNTs and ð11; 11Þ m-SWCNTs (see the online supplementary data at http://stacks.iop.org/APEX/9/125103/ mmedia) was used for the calculations because the measured samples were films of mixtures of s-SWCNTs and m-SWCNTs. The content of m-SWCNTs was set to 30% for the calculation. S and R were calculated as functions of μ and the S vs R relationship was plotted. However, the calculated R was scaled as R 1.6 to fit the experimental data because the observed R was not identical to the calculated R. Electrons (holes) tend to become localized or trapped at the shallow levels of films. This effect is more marked at low carrier densities, so R increased as the carrier density decreased in the present experiment, which is consistent with our current understanding. Figure 1(b) [and Fig. S2(b) in the online supplementary data at http://stacks.iop.org/APEX/9/125103/ mmedia] shows that the second peak, S 2,max ≈ 50 µV=K, is almost unaffected by the mixing of m-SWCNTs, while the first peak for s-SWCNTs, S 1,max ≈ 600 µV=K, is reduced to 75 µV=K. On the other hand, Fig. 1 shows that P 2,max is substantially improved through a reduction of R by heavy doping.
In practice, the advantage of heavy doping to achieve highperformance films is twofold. First, the relative contribution of phonons to the thermal conductivity, κ p =κ e , decreases with increased doping, which leads to an improvement in the ZT value. This can be understood by considering that ZT = S 2 Tρ −1 (κ p + κ e ) −1 = S 2 L −1 (κ p =κ e + 1) −1 , where κ p and κ e are the phonon and electron contributions to the thermal conductivity, respectively, and L = ρκ e =T is the Lorentz number. Here, it is expected that κ p =κ e decreases with heavy doping because κ p is presumably almost constant while κ e increases with carrier density. Second, the presence of m-SWCNTs does not significantly reduce S and P in the heavily doped region, unlike the case for high-purity s-SWCNTs. The large S value, S 1,max , for pure s-SWCNTs that appears within the band gap is significantly suppressed by the presence of highly conductive m-SWCNTs through electrical shorting effects. In contrast, electrical shorting is less important in heavily doped films because s-SWCNTs become metallic and the observed S is a conductivity-weighted average. 2,3,25) In the present study, heavy doping of films composed of mixtures of m-and s-SWCNTs was shown to substantially improve electrical resistivity while the Seebeck coefficient S was moderately large. This leads to a significant enhancement of the power factor P, without the use of high purity s-SWCNTs. The 1D nature of SWCNTs, which results in a stepwise increase of electrical conductance, could be responsible for the observed behavior. The present results suggest that the thermoelectric performance of SWCNT films can be further improved by controlling the multiplicity of 1D bands and tuning the chemical potential by carrier doping. In the present work, simple calculations on the electronic states of SWCNTs were employed to obtain insight into the cause of the observed thermoelectric properties. Calculations that are more sophisticated are needed to determine SWCNTs with the appropriate chirality and to design new SWCNT complexes, such as SWCNTs that encapsulate guest molecules.