Optical Absorption Spectra of Charge-Doped ... - ACS Publications

Apr 7, 2009 - ... Beijing 100871, People's Republic of China, and Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0266...
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J. Phys. Chem. C 2009, 113, 7058–7064

Optical Absorption Spectra of Charge-Doped Single-Walled Carbon Nanotubes from First-Principles Calculations Guangfu Luo,†,‡ Jiaxin Zheng,† Jing Lu,*,†,‡ Wai-Ning Mei,*,‡ Lu Wang,† Lin Lai,† Jing Zhou,† Rui Qin,† Hong Li,† and Zhengxiang Gao*,† State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking UniVersity, Beijing 100871, People’s Republic of China, and Department of Physics, UniVersity of Nebraska at Omaha, Omaha, Nebraska 68182-0266 ReceiVed: December 24, 2008; ReVised Manuscript ReceiVed: March 4, 2009

We calculated the optical absorption spectrum response of single-walled carbon nanotubes under charge doping by using density functional theory. We find that the spectrum responses can be generally divided into two categories: one is similar to those obtained from the graphene zone-folding and rigid-band model, while the other deviates from the expectation and shows several special features. Our analysis reveals that the doping type and curvature effects play the primary role. Finally, we argue that the present results will probably prevail in more elaborate methods and other similar nanotubes. I. Introduction As the 1D morphology of graphitic materials, single-walled carbon nanotube (SWCNT) is regarded as a promising building block of the future nanoworld. They are among the stiffest fibers known, and have nanometer cross-section, high conductivity, and other remarkable properties. For the past decade, SWCNTs have attracted enormous interest from both basic research and industrial applications. For example, they have been used in composite materials,1,2 hydrogen and energy storages,3-8 light sources and transistors,9-12 gas and flow sensors,13,14 electromechanical devices,15,16 and various transport studies.17-20 Recently, several technical problems21 which have been setting great hurdles for their extensive applications, such as high product cost, impurities in samples, and difficulties in assembly, are much mitigated. From the production aspect, new techniques such as impurity-free synthesis22 and scalable separation23 methods, nanotube clone route,24 and growth of intramolecular junctions25 render SWCNTs even more feasible, affordable, and controllable materials. From the assembly aspect, newly developed means such as fluidic method,26 nematic nanotube gels,27 and large-scale self-assembly,28 have demonstrated impressive progress. Furthermore, from the device fabrication aspect, the density and amount of SWCNT transistors in the integrated circuits also have reached a record level.29,30 The optical absorption spectrum, together with other techniques such as AFM and Raman spectra, has been demonstrated to be a powerful and widespread tool in the SWCNT studies. To provide a complete picture, extensive theoretical studies have been carried out on the optical spectra of the pristine SWCNTs. At the density functional theory (DFT) level, Barone et al.31,32 successfully calculated optical transitions of series semiconducting and metallic SWCNTs by using the new meta-generalized gradient approximation hybrid functional TPSSh.31 And at the time-dependent DFT level, Marinopoulos et al.33 found that the local-field effects are critical for light polarized perpendicular to the tube axis, while they are negligible for the parallel case. * To whom correspondence should be addressed. E-mail: jinglu@ pku.edu.cn, [email protected], and [email protected]. † Peking University. ‡ University of Nebraska at Omaha.

Furthermore, at the GW-Bethe-Salpeter equation (GW-BSE) level, Louie et al.34-37 showed the important roles of self-energy corrections and electron-hole interaction in SWCNTs. In the SWCNT physics and chemistry, charge transfer between a nanotube and its environment is a problem of major importance.38 Many previous studies on SWCNT involve charge transfer: such as tuning the conductivity39 and band gap,40 enhancing the solubility,41 selectively separating the nanotubes,42-45 and utilizing the SWCNTs as gas sensors,13 actuators,15 and transistor memory.10,12 Nevertheless, most theoretical studies have only performed on the pristine cases, and the optical spectra of charge-doped SWCNTs46-49 are merely interpreted within the graphene zone-folding50 and rigid-band (GZF-RB) scheme, where the band structure is adopted from graphene zone-folding and assumed to be unchanged under the charge dopingsexcept that the Fermi level shifts downward or upward according to the doping type. Such idealization leads to several straightforward conclusions, i.e., the absorption peaks remain unchanged until the band populations of the corresponding transitions change; with increasing doping level, and the absorption peaks disappear sequentially in the order of ascending energy.49,51 On the other hand, two symptoms have clearly demonstrated the incompleteness of the above simplification: first, the hybridization between σ* and π* orbitals52,53 is neglected in the zonefolding model; second, the motion of the nearly free-electron (NFE) bands54 under charge doping is also excluded in the rigidband model. In view of the wide applications of the absorption spectrum, its close relationship with other spectra, such as the resonant Raman spectrum and the resonant Rayleigh spectrum, and the availability of optical experimental techniques on individual SWCNT,55-59 we find that it is important to investigate these issues in depth. In this work, we report the interband vertical optical transition of the charge-doped SWCNTs. In section II, we describe the computational method; in section III, we display the results of our studies and discussions; finally in section IV, we provide the conclusions.

10.1021/jp811392z CCC: $40.75  2009 American Chemical Society Published on Web 04/07/2009

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II. Computational Method All the calculations in this paper are performed in the framework of DFT with the Perdew-Burke-Ernzerhof generalized gradient approximation60,61 (PBE-GGA) realized in the CASTEP code.62 Ultrasoft pseudopotential, which gives almost the same optical spectra as norm-conserving pseudopotential here, is adopted. The plane-wave energy cutoff is 240 eV for full structural optimization and 280 eV for optical calculations (part of the convergency tests are presented in the Supporting Information). Periodic boundary conditions are employed, and the nearest distance between neighbor supercells is about 12 Å to eliminate the direct intertube interaction. For Brillouin zone sampling, a uniform Monkhorst-Pack k-point grid separated by about 0.0469, 0.0078, and 0.0017 Å-1 along the tube axis is used for structural optimization, single-point energy calculations, and optical matrix element integration, respectively. The optical spectrum calculations are based on the DFT random-phase approximation, where both the self-energy corrections and the electron-hole interaction are neglected. The imaginary part of dielectric function is given by the following Fermi’s golden rule in dipole approximation:63

ε2(ω) )

( ) ∑ |〈ψ |e · p|ψ 〉| δ(E

1 2πe 4πε0 mω pω)

2

c k

v 2 k

c k

- Ekv -

k,c,v

(1)

where e is the polarization vector of the incident electric field, p is the momentum operator, and “c” and “v” represent the conduction and valence bands, respectively. Since the local field effects have been proven theoretically35 and experimentally64 to greatly suppress the optical response for e perpendicular to the tube axis, only the parallel polarization is considered here. The real part of the dielectric function ε1(ω) is then obtained from ε2(ω) through the Kramers-Kronig transform.65 We choose the (8,0), (12,0), (16,0), (8,2), (8,4), (10,5), (5,5), and (9,9) tubes as the representatives for SWCNTs. And to further verify our conjecture on the behavior of optical absorption spectra, we study 11 more tubes as shown in the Supporting Information: namely the (10,0), (10,1), (7,1), (14,2), (12,3), (10,4), (6,3), (12,6), (7,4), (6,6), and (7,7) SWCNTs. The extra charges are added to the supercell one by one, and the doping level ranges from 0 to ∼0.14 electrons (or holes) per carbon atom. For brevity, we use e/C (h/C) to represent extra electrons (holes) per carbon atom in the context. The charging issue existing in the periodic systems is dealt with in the jellium model. Comparing with a real system, the main difference originates from the spatial distribution of the counterchargesit is assumed to be isotropic in the jellium model, while it is most likely anisotropic in the experiments.66 The situation in the electromechanical doping experiments67,68 is close to that of the jellum model, where the counterions are movable in the solution and then distribute uniformly on the circumference. However, in the radial direction, probably the distribution is still anisotropic, because the counterions tend to accumulate more near the nanotube surface than far from it. So at the same doping level, the nanotubes experience a stronger electric field in the experiment than in the jellium model. In other words, we anticipate the jellium model would underestimate the spectrum change rate due to charge doping. III. Results and Discussions The absorption spectra can be roughly categorized into two types: the first type can generally be interpreted by using the

GZF-RB model, and the second type exhibits unusual features and has to be analyzed with the first-principles band structures. For convenience, we denote the first and second type as ordinary and unusual spectrum response, respectively. A. Ordinary Spectrum Response. The calculated optical absorption spectra of the (5,5), (9,9), (8,4), and (10,5) SWCNTs are shown in Figure 1. The first feature is that those SWCNTs display distinct optical responses under the same doping level, as expected from the GZF-RB model. Taking the electron doping level at ∼0.100 e/C for example, the (5,5) tube shows only minor spectrum changes (Figure 1a), the (9,9) tube loses the whole first peak (Figure 1b), while the (8,4) and (10,5) tubes lose almost the first two peaks and ∼50% of the third peak (Figure 1c,d). The underlying reason is straightforward: that is the disappearance of absorption peaks depends directly on the number of states to be filled (in electron doping) or depleted (in hole doping) between the Fermi level and van Hove singularities (vHs) that relate to optical transitions. Hence the larger the number of states is, the slower the spectra change. To be more quantitative, we check the density of states (DOS) of the foregoing pristine SWCNTs and find 0.82, 0.64, 0.00, and 0.00 respective electron states between the Fermi level and the first vHs of conduction band, thus explaining their spectra differences in electron doping. On the basis of this idea, we expect that the spectra of semiconducting nanotubes, which have zero states between the Femi level and the first vHs, would show more changes than those of the metallic ones after charge dopingsat least at low charge doping level. The second feature in Figure 1 is the sequential disappearance of the absorption peaks, also expected by the GZF-RB model. We further examine the band structures and their changes under charge doping, thus concluding that under the low doping level, this model is a reasonable good approximation for the SWCNTs considered (see Figure 3 in the Supporting Information). The third feature is that the absorption spectra upon electron doping tend to show many fewer changes than those upon hole doping for the same SWCNTs. Taking the (5,5) tube as an example, though the spectrum remains almost intact at 0.100 e/C, it loses nearly the first peak and ∼12% intensity of the second peak at 0.100 h/C. To explain this issue, it is necessary to consider the NFE bands in a sheet-like system, which was first discovered by Louie et al.69 in the bulk boron nitride and later discussed in other systems.70,71 Particularly, Margine et al.54 have recently revealed that the movement of the lowest NFE bands (moving downward for electron doping and upward for hole doping) actually originates from the simple electrostatic interaction and is universal in the charge-doped SWCNTs. But how do the other NFE bands change and influence the absorption spectra in charge doping? On one hand, since the NFE bands are ∼3 eV above the Fermi level in the pristine and move upward in hole doping,54 they show little influence on the bands and spectra accordingly during hole doping. On the other hand, after separating all the pure NFE bands from the other bands as for the (8,4) SWCNT case shown in Figure 2, we find two notable symptoms in electron doping. First, quite a few NFE bands move downward with respect to the on-tube bands. Quantitatively, while in the pristine there are only 2.69 electron states of pure NFE bands in the range of 0-4 eV, this number increases to 62.5 electron states as shown in Figure 2bsthat is almost the same amount as the other bands (62.8 electron states) in this range (Figure 2c). Second, we observe that while the NFE bands move downward, several original NFE bands hybrid with the on-tube bands. Note that the charge doping process in thisworkcanbeapproximatedasasymmetricperturbationsbecause

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Figure 1. Optical absorption spectra of the electron-doped (a-d) and hole-doped (e-h) (5,5), (9,9), (8,4), and (10,5) SWCNTs. The respective units of charge doping level are % (e/C) and % (h/C). All spectra are broadened with a Gaussian smearing of 0.08 eV.

Figure 2. Band structure analyses of the electron-doped (8,4) SWCNT at 0.0536 e/C. The original band structures (a) are separated into two parts: the pure NFE bands (b) and the rest (c). The short black arrows in panel c indicate the hybridizations between the original NFE bands and the on-tube bands, and the horizontal dotted line represents the Fermi level.

we adopt the jellium model, the geometrical changes are insignificant in our calculations (the tube length changes less than 1%), and the doping levels are not high. Therefore, the above-mentioned hybridizations in electron doping do not significantly affect the optical transitions, but the downwardshift NFE bands greatly increase the DOS and accordingly render fewer spectra changes.

B. Unusual Spectrum Response. In Figure 3, we plot the absorption spectra of the (8,0), (12,0), (16,0), and (8,2) SWCNTs at different charge doping levels, in which the peaks are labeled with A, B, C and so on according to the ascending energy order. Being different from those mentioned in Section IIIA, these spectra exhibit three new behaviors. First, we observe a spectrum merging between peaks A and B of the (8,0) tube under the

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Figure 3. Optical absorption spectra of the electron-doped (a-d) and hole-doped (e-h) (8,0), (12,0), (16,0), and (8,2) SWCNTs. Numbers before the peak letters denote the degeneracy degree of the absorption peaks. The respective units of charge doping level are % (e/C) and % (h/C). All spectra are broadened with a Gaussian smearing of 0.08 eV.

electron doping, as well as peaks C and D of the (8,2) tube under the hole doping. Taking the former, for example, while peaks A and B are ∼0.34 eV apart at the pristine, they get too close to be distinguished at the level of 0.0313 h/C. Second, we also observe spectrum splitting in peak E of the (16,0) tube at 0.0313 e/C, and peak B of the (8,2) tube at 0.0536 h/C. The two new distinct peaks in the (16,0) tube (E- and E+, superscript “-” means a lower energy branch, and vice versa) are separated by ∼0.23 eV, and the B+ and B- in the (8,2) tube by ∼0.28 eV. Third, a more interesting feature is the unusual disappearingorder of the absorption peaks. According to the conventional understanding, with increasing doping level, all the absorption peaks would disappear sequentially in an order of ascending energy. Here we find obvious counterexamples in the electrondoped (8,0) and (12,0) tubes, and the hole-doped (8,2) tube. For the (8,0) tube, peak B is ∼l eV lower than peak C at the pristine, but with increasing extra electrons, peak C declines abruptly: i.e., at a doping level of 0.0313 e/C, it loses ∼56.4% of the original intensity, while peak B loses only ∼6.5%. For the (12,0) tube, the higher peak D also disappears earlier than peak B with increasing electron doping level. In the hole-doped (8,2) tube, the situation becomes more complex: with increasing hole doping level, first peak A disappears, then peak B splits into B- and B+. After that, peak B+ declines much quicker than peak B-: at the level of 0.0893 h/C, peak B+ disappears completely while peak B-remains nearly the same.

To explore the underlying nature, we investigated the energy variation of the vHs involved in optical transitions as a function of doping level, and Figure 4 shows that of the (8,0) tube under electron doping and the (8,2) tube under hole doping. In Figure 4c, we see that the band Ac moves upward since the beginning of electron doping, while band Av remains still, thus causing the upward movement of peak A. The opposite happens in the bands of B transition, and accordingly shift peak B downward. Eventually, the energy difference between the two transitions changes from 0.31 eV at the pristine to 0.005 eV at 0.0313 h/C. From the band structures, we also notice that several seemingly single absorption peaks of the pristine tubes are actually composed of a few nearly energy-degenerate transitions (the degeneracy degree is added before the peak label in Figure 3). And some of them split obviously under charge doping. In the (8,2) tube, peak B is composed of three transitions with energy differences of ∼0.09 eV. As shown in Figure 4d, the component transitions, B+ and B-, move apart with increasing hole doping level, and eventually expand the differences to ∼0.21 eV at 0.0536 h/C. Another notable feature is that the energy order of the conduction band vHs (CvHs) and that of the valence band vHs (VvHs) are asymmetric with respect to the Ef, contrasting to the mirror behavior manifested in the orthogonal tight-binding zone-folding method.72 As in the (8,0) tube, the energy order of the first three pairs of transitions is |EAc| > |EBc| > |ECc| and

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Figure 4. Band structures of pristine SWCNTs and energy variation of the first few optical transitions with doping level: (a, c) for the (8,0) SWCNT and (b, d) for the (8,2) SWCNT. In panels c and d, several data are connected by solid lines to highlight the origin of spectrum splitting or merging. NFE bands are represented by the violet dotted lines, and the origin of the doped band structure is established similarly as the pristine. Superscripts denote the splitting branches in the doped tubes, and subscripted numbers label the energy-degenerate transitions.

|ECv| > |EBv| > |EAv| (subscripts A/B/C represent the transition, and c/v the conduction/valence band). The energy variation in Figure 4c further shows that such order remains unchanged in the whole doping range. Therefore, it is the vHs of the C transition that will be filled first, and accordingly peak C will disappear first during electron doping, whereas in hole doping, since |EAv| is less than |EBv| and |ECv|, peak A will disappear earlier as expected. Similar asymmetry between the B and D transitions of (12,0) tube also explains the unusual disappearingorder there. Unlike the above cases, we hardly expect an unusual disappearing-order would happen at an early hole doping stage of (8,2) tube by its pristine band structure in Figure 4b. But with the increasing extra holes, the three energy-degenerate transitions of peak B degenerate into B- and B+, and the foregoing asymmetry coincidentally exists between them (Figure 4d) and finally causes the unusual disappearing-order. After examining all the spectra, we do not find a direct connection between the spectrum responses and values of mod(m-n, 3) that are often used in SWCNTs classification.73

Actually, we notice that the unusual spectrum response can happen in all three cases, such as the (12,0), (16,0), and (8,0) tubes in Figure 3b,c,a, and similarly for the ordinary spectrum response, such as the (5,5), (8,4), and (10,5) tubes in Figure 1a,c,d. To find out the geometric characters of the SWCNTs with unusual absorption spectra, we compare the pristine band structures calculated from the first-principles method with those from the ab initio zone-folding method. We find that the asymmetry between the energy order of CvHs and VvHs presenting in the former method is absent in the latter. Since the only issue that the latter method ignored is the curvature effects, which are only obvious in the small diameter tubes, we assert that the small diameter must be responsible for the unusual spectra. On the other hand, the small diameter (5,5) tube shows symmetry between the energy order of CvHs and VvHs, so the small diameter is only one necessary condition. Also noting that all our calculated SWCNTs with unusual spectra response have relatively small chirality, we speculate that the small chirality

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J. Phys. Chem. C, Vol. 113, No. 17, 2009 7063 binding energy. Under a further assumption that the charge doping process does not change the above trends, we anticipate the nonsequential disappearing-order occurs at the GW-BSE level. Moreover, for the NFE bands, we expect them to play a similar role at the GW-BSE level as in this paper for their simple electrostatic origin.54 Finally, we would like to address the curvature effects in other SWCNT-like nanotubes. After reexamining our previous work,77 we find the asymmetry between energy order of CvHs and VvHs exists also in certain silicon carbide nanotubes. In light of the above arguments, we expect a direct comparison between our findings and experimental data could be made in the future.

Figure 5. Classification of all the studied SWCNTs according to their absorption spectrum response in the diameter versus chiral-angle graph. Open violet circles and solid red circles represent SWCNTs with ordinary and unusual spectrum response, respectively.

is another necessary condition. In fact, earlier studies74,75 on the band structures and DOS of SWCNTs have shown much larger curvature effects in the zigzag nanotubes than in the others, though a general chiral dependence of the curvature effects is uncertain. To clearly present our results, we map all the studied SWCNTs according to their diameters and chiral angles76 in Figure 5. It seems that those with ordinary spectra are on the upper right part of the figure, whereas those with unusual spectra locate at the lower left regionsa place with relatively small diameter and chiral angle. We expect this trend is generally true for the other SWCNTs in the entire region, yet further detail investigation may be necessary. Finally, we would like to point out that almost all the obviously unusual spectrum responses happen in electron doping. The main cause is that the curvature effects mainly influence the conduction bands75 and thus exhibit in electron doping. The only exception is the (8,2) tube, where the band structure changes after hole doping happen to play a more important role. IV. Conclusions In summary, we have calculated 19 SWCNTs to study the charge doping effects on the optical absorption spectra. According to the spectrum response, we find that SWCNTs can be divided into two categories: (I) one shows relatively rigid on-tube bands, minor spectrum changes under electron doping, and sequential disappearing-order of absorption peaks; (II) the other shows less rigid on-tube bands and several special features, such as peak merging, splitting, and nonsequential disappearingorder. Primarily, these features can be explained from the following band structure behaviors: (1) the NFE bands change rapidly with charge doping and their downward shift in electron doping greatly increases the DOS above the Fermi level; (2) the on-tube bands are much more rigid than the NFE bands, but they display moderate changes for the (II) SWCNTs upon charge doping; (3) the large curvature effects in the smalldiameter and chiral-angle SWCNTs cause the energy order of CvHs and VvHs to be asymmetrical. Although the present optical absorption spectra are carried out at the GGA level and in SWCNTs, we expect the main conclusions should survive qualitatively at the GW-BSE level and in other nanotubes. First, previous GW calculations35,37 on SWCNTs show that the asymmetry between the energy order of CvHs and VvHs exists in certain quasiparticle band structures. Second, the GW-BSE calculations,34-37 which also include the electron-hole interaction, display that the energy order of the quasiparticle absorption peaks is not altered by the exciton

Acknowledgment. This work was supported by the NSFC (Grant nos. 10774003, 10474123, 10434010, 90606023, and 20731160012), National 973 Projects (Nos. 2002CB613505 and 2007CB936200, MOST of China), 211, 985, National Foundation for Fostering Talents of Basic Science (No. J0630311), Program for New Century Excellent Talents in University of MOE of China, China Scholarship Council, and Nebraska Research Initiative (No. 4132050400) of the USA. We also acknowledge the Holland Computer Center at the University of Nebraska at Omaha for providing us the facility and technical support. Supporting Information Available: The convergency tests on energy cutoff, the absorption spectra of other 11 SWCNTs, and the band structure analysis of the (6,6) tube. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Veedu, V. P.; Cao, A. Y.; Li, X. S.; Ma, K. G.; Soldano, C.; Kar, S.; Ajayan, P. M.; Ghasemi-Nejhad, M. N. Nat. Mater. 2006, 5, 457. (2) Mamedov, A. A.; Kotov, N. A.; Prato, M.; Guldi, D. M.; Wicksted, J. P.; Hirsch, A. Nat. Mater. 2002, 1, 190. (3) Guldi, D. M.; Rahman, G. M. A.; Prato, M.; Jux, N.; Qin, S. H.; Ford, W. Angew. Chem., Int. Ed. 2005, 44, 2015. (4) Niu, C. M.; Sichel, E. K.; Hoch, R.; Moy, D.; Tennent, H. Appl. Phys. Lett. 1997, 70, 1480. (5) Frackowiak, E.; Beguin, F. Carbon 2002, 40, 1775. (6) An, K. H.; Kim, W. S.; Park, Y. S.; Choi, Y. C.; Lee, S. M.; Chung, D. C.; Bae, D. J.; Lim, S. C.; Lee, Y. H. AdV. Mater. 2001, 13, 497. (7) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature (London) 1997, 386, 377. (8) Liu, C.; Fan, Y. Y.; Liu, M.; Cong, H. T.; Cheng, H. M.; Dresselhaus, M. S. Science 1999, 286, 1127. (9) Avouris, P.; Freitag, M.; Perebeinos, V. Nat. Photonics 2008, 2, 341. (10) Star, A.; Lu, Y.; Bradley, K.; Gruner, G. Nano Lett. 2004, 4, 1587. (11) Siddons, G. P.; Merchin, D.; Back, J. H.; Jeong, J. K.; Shim, M. Nano Lett. 2004, 4, 927. (12) Fuhrer, M. S.; Kim, B. M.; Durkop, T.; Brintlinger, T. Nano Lett. 2002, 2, 755. (13) Li, J.; Lu, Y. J.; Ye, Q.; Cinke, M.; Han, J.; Meyyappan, M. Nano Lett. 2003, 3, 929. (14) Ghosh, S.; Sood, A. K.; Kumar, N. Science 2003, 299, 1042. (15) Baughman, R. H.; Cui, C. X.; Zakhidov, A. A.; Iqbal, Z.; Barisci, J. N.; Spinks, G. M.; Wallace, G. G.; Mazzoldi, A.; De Rossi, D.; Rinzler, A. G.; Jaschinski, O.; Roth, S.; Kertesz, M. Science 1999, 284, 1340. (16) Sazonova, V.; Yaish, Y.; Ustunel, H.; Roundy, D.; Arias, T. A.; McEuen, P. L. Nature (London) 2004, 431, 284. (17) White, C. T.; Todorov, T. N. Nature (London) 1998, 393, 240. (18) Choi, S. U. S.; Zhang, Z. G.; Yu, W.; Lockwood, F. E.; Grulke, E. A. Appl. Phys. Lett. 2001, 79, 2252. (19) Biercuk, M. J.; Llaguno, M. C.; Radosavljevic, M.; Hyun, J. K.; Johnson, A. T.; Fischer, J. E. Appl. Phys. Lett. 2002, 80, 2767. (20) Holt, J. K.; Park, H. G.; Wang, Y. M.; Stadermann, M.; Artyukhin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O. Science 2006, 312, 1034. (21) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (22) Hata, K.; Futaba, D. N.; Mizuno, K.; Namai, T.; Yumura, M.; Iijima, S. Science 2004, 306, 1362. (23) Rinzler, A. G. Nat. Nanotechnol. 2006, 1, 17. (24) Ren, Z. F. Nat. Nanotechnol. 2007, 2, 17.

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