NANO LETTERS
On the Electron−Phonon Coupling of Individual Single-Walled Carbon Nanotubes
2005 Vol. 5, No. 9 1761-1767
Matti Oron-Carl,†,‡ Frank Hennrich,‡ Manfred M. Kappes,†,‡ Hilbert v. Lo1 hneysen,§,| and Ralph Krupke*,‡ Institut fu¨r Physikalische Chemie, UniVersita¨t Karlsruhe, D-76128 Karlsruhe, Germany, Institut fu¨r Nanotechnologie, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany, Physikalisches Institut, UniVersita¨t Karlsruhe, D-76128 Karlsruhe, Germany, and Institut fu¨r Festko¨rperphysik, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany Received June 12, 2005; Revised Manuscript Received July 25, 2005
ABSTRACT We show that the phonon coupling to the electronic system in individual metallic single-walled carbon nanotubes is not due to coupling to low-energy plasmons. The evidence stems from the measured Raman-Stokes G-mode, which for metallic and semiconducting tubes could be fitted well by the superposition of only two Lorentzian lines associated with vibrational modes along the nanotube axis and the nanotube circumference. In the case of metallic tubes the lower-energy G mode is significantly broadened, however maintaining the Lorentzian line shape, in contrast to the theoretically expected asymmetric Breit−Wigner−Fano line shape from phonon-plasmon coupling. The results were obtained by studying 25 individual metallic and semiconducting single-walled carbon nanotubes with atomic force microscopy, electron transport measurements, and resonant Raman spectroscopy.
Electron-phonon coupling in carbon nanotubes is an important mechanism which has major impact on the electronic transport properties. For instance the ballistic electron transport in metallic single-walled carbon nanotubes (SWNTs) over a distance of micrometers is limited to the low bias region due to optical phonon emission and thereby sets constraints on the applicability of SWNTs as low-dissipative interconnects.1 A good starting point to understand the electron-phonon coupling in SWNTs is to study graphite in the first place. Recently, a high-precision inelastic X-ray scattering measurement on a graphite single crystal has unraveled a pathological linear dispersion for the highest optical phonon branches together with a discontinuity of the phonon frequency derivative at the phonon wave vectors q ) Γ and K.2 The data have been reproduced by the calculation of Piscanec et al.,3 who demonstrated that the electron-phonon coupling is particularly strong for the Γ-E2g and the K-A1′ modes. It is anticipated that the strong electron-phonon coupling in graphite is relevant in SWNTs as well, and in particular for metallic SWNTs. The Γ-centered phonons are directly measured in Raman spectroscopy,4-6 * Corresponding author. E-mail:
[email protected]. † Institut fu ¨ r Physikalische Chemie, Universita¨t Karlsruhe. ‡ Institut fu ¨ r Nanotechnologie, Forschungszentrum Karlsruhe. § Physikalisches Institut, Universita ¨ t Karlsruhe. | Institut fu ¨ r Festko¨rperphysik, Forschungszentrum Karlsruhe. 10.1021/nl051107t CCC: $30.25 Published on Web 08/19/2005
© 2005 American Chemical Society
and therefore Raman-mode broadening due to strong electronphonon coupling should be observable. Indeed the G mode in SWNTs occasionally exhibits an asymmetric BreitWigner-Fano (BWF) line shape, which is usually an indication of a coupling to continuum states.7,8 Hence the broadening has been assigned to metallic tubes and used as a tool to identify by Raman spectroscopy whether a SWNT is metallic or semiconducting.9,10 Yet in most of the studies, no additional electrical transport measurements have been performed to support the interpretation of the Raman data, except for several tubes as in the work of Balasubramanian et al. and Cronin et al.11,12 To address the question whether the metallic or the semiconducting character of a SWNT, as derived from electron-transport measurements, indeed correlates with a type specific Raman spectrum, we have studied 25 individual metallic and semiconducting tubes with atomic force microscopy, electron-transport measurements, and resonant Raman spectroscopy. In addition we have analyzed the Raman G mode line shapes, which allows to test the actual electron-phonon coupling model for SWNTs. Single-walled carbon nanotubes were synthesized using the pulsed laser vaporization (PLV) technique with Ni and Co as catalysts. According to our Raman measurements (Tables 1 and 2), the tubes exhibit a diameter distribution of ∼1.0-1.5 nm for both metallic and semiconducting
Table 1. Raman Data Analysis of Individual Metallic SWNTs: Width of Fitted G- Mode (∆G-), fwhm of the G Mode, and RBM Frequencya experimental sample no. (w118c)
gate dependence
1 (75p3e) 2 (103p2c) 3 (106p1c) 4 (66p1f)
comparison
∆G- (cm-1)
fwhm (cm-1)
ωRBM (cm-1)
ωRBM (cm-1)
no no no no
43.7 ( 2.3 52.1 ( 7.0 74.8 ( 2.0 61.8 ( 1.8
47.0 ( 1 56.0 ( 5 99.0 ( 1 83.0 ( 1
5 (06p2e) 6 (09p1b)
no no
50.2 ( 1.8 42.0 ( 1.5
68.0 ( 1 56.0 ( 1
202.1 ( 1.8 202.1 ( 1.2 194.9 ( 1.1 161.0 ( 1.1 178.2 ( 1.2 194.9 ( 1.2 200.0 ( 1.3
204.024
7 (09p3e) 8 (09p1f) 9 (45p2e)
no no no
58.5 ( 2.8 41.4 ( 1.2 54.5 ( 1.7
85.0 ( 2 57.0 ( 1 69.0 ( 2
10 (09p3b)
no
56.9 ( 2.4
72.0 ( 1
(n, m) (10,7) (10,7) (13,4) (11,11) (14,5) (13,4) (15,0) (14,2) (11,8) (13,4) (15,6) (12,6) (17,2)
204.024 195.324 160.3b 179.928 195.324 201.524 200.525 185.425 196.525 164.928 189.624 170.428
185.6 ( 1.4 196.0 ( 1.3 162.6 ( 1.3 187.6 ( 1.3 168.0 ( 1.1
EM 11 (eV) 2.0724 2.0724 1.9324 1.83b 1.9324 1.8624 1.9225 1.9025 1.9325 1.9424
The data are compared with referenced experimental data, and the tubes were assigned accordingly. Note the spectral resolution of 6 cm-1. b Extrapolated from ref 25, see Figure 1. a
Table 2. Raman Data Analysis of Individual Semiconducting SWNTs: Width of Fitted G- Mode (∆G-), fwhm of the G Mode, and RBM Frequencya experimental
comparison
gate dependence
∆G- (cm-1)
fwhm (cm-1)
ωRBM (cm-1)
ωRBM28 (cm-1)
1 (93p1e)
yes
17.0 ( 6.1
20.2 ( 1
2 (95p2c) 3 (108p2b)
yes yes
24.7 ( 2.3 20.6 ( 2.4
27.7 ( 1 24.5 ( 1
198.5 ( 1.3 193.0 ( 1.5 197.9 ( 2.3 187.5 ( 1.2
4 (113p1f) 5 (103p1a) 6 (103p3c) 7 (110p1e)
yes yes yes yes
21.8 ( 1.5 18.1 ( 3.3 19.6 ( 2.2 20.8 ( 1.7
21.0 ( 1 18.0 ( 1 20.0 ( 1 23.0 ( 1
193.3 ( 1.8 195.2 ( 1.2 194.1 ( 1.2 191.5 ( 1.1
8 (119p3a) 9 (114p2a) 10 (126p3f)
yes yes yes
37.9 ( 4.4 20.0 ( 2.4 30.1 ( 2.7
42.0 ( 1 20.0 ( 1 34.0 ( 1
178.8 ( 1.1 196.5 ( 1.4 180.8 ( 1.2
11 (136p2e)
yes
23.0 ( 1.5
20.0 ( 1
190.6 ( 1.1
12 (04p1f) 13 (84p2d) 14 (75p2e) 15 (95p2f)
yes yes yes yes
21.6 ( 3.6 24.1 ( 5.9 17.3 ( 2.3 38.0 ( 3.1
19.0 ( 1 32.0 ( 1 20.0 ( 1 29.0 ( 1
193.7 ( 1.1 230.4 ( 1.1 231.1 ( 1.1 166.8 ( 1.1
198.5 192.7 198.5 187.4 187.4 192.7 193.8 193.8 191.6 191.6 178.1 198.5 179.8 181.6 191.6 191.6 192.7 229.1 229.1 165.9
sample no. (w118c)
(n, m)
ES33 27 (eV)
(n - m) mod 3 )
(12,5) (10,8) (12,5) (15,2) (13,5) (10,8) (15,1) (15,1) (14,3) (11,7) (17,0) (12,5) (13,6) (12,7) (14,3) (11,7) (10,8) (13,0) (13,0) (13,8)
2.49 2.59 2.49 2.35 2.70 2.59 2.78 2.78 2.77 2.47 2.62 2.49 2.32 2.54 2.77 2.47 2.59 2.70 2.70 2.35
+1 -1 +1 +1 -1 -1 -1 -1 -1 +1 -1 +1 +1 -1 -1 +1 -1 +1 +1 -1
a The data are compared with referenced theoretical data and the tubes were assigned accordingly. Calculated excitation energies for most tubes with (n - m) mod 3 ) -1 exceed the resonance window of Elaser ) 2.41 ( 0.1 eV. Note the spectral resolution of 6 cm-1.
SWNTs, in agreement with the fluorescence measurements on the same kind of material.13 Of the as-grown SWNTs, 0.02 mg/mL was suspended in D2O with 0.5 wt % sodium dodecylbenzenesulfonate. The suspension was centrifuged at 154000g for 2 h with the upper 50% of the supernatant carefully decanted and then diluted with D2O by a factor of 100 to a concentration of a few ng/mL of individual SWNTs. Multiple submicrometer electrode pairs with 1 µm gap were prepared on p-type silicon substrates with 800 nm thermal oxide, using standard electron-beam lithography and lift-off technique. Approximately 40 nm thick Pd or Au was used 1762
as the top-electrode material with ∼2-3 nm titanium as an adhesion layer. For the tube deposition, we have used low-frequency dielectrophoresis.14 The simultaneous deposition of SWNT on several contacts has been described in detail elsewhere.15 The deposition was typically performed with an applied voltage Vpp ) 2 V at a frequency f ) 300 kHz for 6-7 min, with a 30 µL drop of the SWNTs suspension applied to the chip immediately after switching on the rf generator. Under these conditions, individual SWNTs are trapped between the electrodes with reproducible alignment.15,16 We emphasize Nano Lett., Vol. 5, No. 9, 2005
Figure 1. Experimental and theoretical excitation energies of SWNTs versus the inverse RBM frequency ωRBM based on the experimental data of Fantini et al.25 (red crosses), Telg et al.24 (blue pluses), and calculations of Reich et al.27 (triangle and square for ES33 and ES44 transitions, respectively). The dashed lines indicate the resonance windows Elaser ( 0.1 eV (Elaser ) 1.96 and 2.41 eV). The excitation energy of the (11,11) tube was derived by extrapolating the experimental (n,n) values of ref 25 (dotted line). On the basis of our Raman and transport measurements in combination with the above data, we have identified the labeled tubes in our experiment. The identified tubes, highlighted with a star, which belong to the (n - m) mod 3 ) -1 family, must have significantly lower excitation energies than theoretically predicted in order to be detected at Elaser ) 2.41 eV. No experimental excitation-energy reference data available for tubes (14,5), (15,6), (17,2).
that the frequency used in our experiments is much smaller than the one reported for tube separation.17 At low frequencies (ω , ωC), with ωC defined as the surfactant-concentration-dependent crossover frequency, both metallic and semiconducting tubes experience a positive dielectrophoretic force and are thus attracted toward the electrodes.14 After deposition the sample was rinsed with methanol and dried with a stream of nitrogen gas before turning off the generator. All samples were annealed for 2 h at 200 °C in air and subjected to scanning electron microscopy (SEM) and atomic force microscopy (AFM) characterizations to ensure the presence of an individual tube. Typically 3 out of 18 contact pairs are bridged by one individual SWNT, as a result of the suspended nanotube length variations and the residual bundle content.18 The individual tubes were finally characterized by electron transport measurements and resonant Raman spectroscopy. Transport measurements were done with a Keithley 6430 and 2400 SourceMeter at a constant source-drain voltage, where the source-drain current, ISD, was measured while changing the gate voltage applied to the Si substrate. All the transport measurements were done at room temperature under vacuum (10-5 mbar). For the Raman measurements, we used a confocal Raman microscope, Witec CRM 200, excited with an Ar+ ion laser at 2.41 eV or Ne/He laser at 1.96 eV, a laser spot diameter of ∼500 nm, and a power density of ∼1.4 MW/cm2 at the sample. Raman spectra were recorded under ambient conditions with the polarization of the incident light parallel to the long axis of the electrodes. Our total spectral resolution is ∼6 cm-1, as measured with a spectral calibration lamp. The chosen setup enables a fast measurement of the high- and low-energy Raman modes on Nano Lett., Vol. 5, No. 9, 2005
Figure 2. Example of an individual SWNT, imaged by scanning electron microscopy (left) and atomic force microscopy (right). The tube was trapped between Au/Ti electrodes via low-frequency dielectrophoresis. The measured height of the tube has been used to exclude the presence of a bundle with three or more tubes. Dimers remain unresolved. Dots in the AFM topography image reveal residual surfactant molecules, on and in the vicinity of the tube. The AFM cross section was taken at a surfactant-free tube segment. 1763
Figure 3. Electrical transport measurements (left) and the corresponding Raman spectra (right) of an individual semiconducting SWNT (a) and an individual metallic SWNT (b). The type of tube is identified by the specific gate-voltage dependence of the source-drain current (ISD) and the spectral shape of the G mode. For semiconducting SWNTs, the typical hysteretic gate dependence appears in combination with a narrow G mode. In contrast, for metallic SWNTs, showing no gate dependence, the G mode is broad. For most metallic or semiconducting tubes, the peak intensity of the G mode appears rather weak or strong compared to the RBM, respectively. Laser excitation energies Elaser, RBM frequencies, and source drain voltages VSD are indicated. Contribution from the Si substrate is indicated by an asterisk. The room-temperature Raman and transport measurement data were recorded in air and vacuum, respectively.
the level of individual tubes at limited spectral resolution. The calibration error is less than 1 cm-1. According to Figure 1, we excite metallic SWNTs at 1.96 eV through the first pair of van Hove singularities (EM 11) and semiconducting SWNTs at 2.41 eV through the third pair for optical transition (ES33). Figure 2 shows an example of a wired individual tube using the experimental setup described above. Following the cross section along the tube, the thickness varies smoothly. We attribute this observation to residual surfactant molecules adsorbed on the tube surface, similar to the dots formed on the substrate surface. Therefore surfactant-free tube sections were used to determine the tube diameter. We have thus identified a tube to be individual if the determined diameter was smaller than 1.7 nm. More specifically, the vertical resolution of our AFM allows an individual tube or a twotube bundle to be distinguished from a closed packed threetube bundle, which for our range of tube diameters yields heights of 1.9-2.8 nm. Thus we have assigned a tube to be individual when its diameter was e1.7 nm, taking into account an error of (0.2 nm. Individual tubes, characterized by transport measurements and showing a radial breathing mode (RBM) Raman signal, were studied in this work. Figure 3 shows transport measurements and the corresponding Raman signals of two representative individual SWNTs. Figure 3a (left) represents a typical gate dependence as observed on 15 individual tubes, 1764
where the source-drain current, ISD, strongly depends on the applied gate voltage, VG. Switching between the on and off states is accompanied by a rather strong hysteresis, originating from the reorientation of dipolar surfactant or water molecules,19 or alternatively from trapped charges in the gate oxide.20 The result is typical for a Schottky-barrier type field effect transistor (SB-FET) based on a semiconducting tube, which exhibits p-type behavior due to oxygen exposure.21,22 The corresponding Raman spectrum (3a, right) shows a RBM peak at 193.7 cm-1, a disorder D mode peak at 1348 cm-1, and a narrow G mode peak at around 1590 cm-1. Figure 3b (left) represents another type of gate dependence as observed on 10 individual tubes. The device cannot be switched off at any gate voltage and exhibits a nearly constant ISD for any VG applied. This behavior is typical for a wired metallic tube, where the gate potential does not change the number of conduction channels. The corresponding Raman spectrum (3b, right) reveals a sharp RBM peak at 194.9 cm-1, a D mode peak at 1310 cm-1, and a wide G mode peak ranging between 1500 and 1600 cm-1. Figure 4 shows the Raman G mode region for all measured nanotubes. It is obvious that all nanotubes, identified by transport measurements as semiconducting or metallic, exhibit a narrow or a wide G mode, respectively. This observation seems to be in general agreement with the theory of phonon-plasmon coupling, which predicts narrow G modes, G+ and G-, for semiconducting tubes and a broad Nano Lett., Vol. 5, No. 9, 2005
Figure 4. Comparison between the Raman G modes of individual semiconducting (a) and individual metallic (b) SWNTs. The data have been fitted with two Lorentzian high- and low-energy components G+ and G-, corresponding to the circumferential and longitudinal vibrational modes, respectively (red line). After background subtraction a least-squares fit was obtained with the G-mode positions and widths as free parameters (green line). Semiconducting tubes have a measured G- width, ∆G-, of typically 20 cm-1. For metallic tubes, ∆G- is between 40 and 60 cm-1. The G+ width, ∆G+, is for both tube types 20 cm-1 wide, a value which has been used to derive ∆G- in cases where the double peak structure was not resolved. Note that the G modes are extrinsically broadened due to the spectral resolution of ∼6 cm-1. The spectra were shifted vertically for clarity. The numbering relates to Tables 1 and 2. More details are available in the Supporting Information.
BWF line shaped G- mode for metallic tubes.8,23 Yet within this theory, the G- broadening is expected to be strong only in bundled metallic tubes and weak in individual metallic tubes. Our data on individual metallic tubes show however that the G mode is dominated by a broadened G- mode rather than showing a weak G- shoulder. Moreover, the G mode of individual metallic SWNTs could be fitted well with two Lorentzians, taking into account the vibrational modes along the nanotube axis and the nanotube circumference. These findings are important, since the scenario, that phonon coupling to low-frequency plasmons is responsible for the G-mode broadening in metallic tubes, seems not to apply on the level of individual metallic nanotubes. The broad Lorentzian-type line shape of the lower-energy G mode rather points to a more simple electron-phonon coupling mechanism. Indeed electron-phonon coupling has been recently shown to be strong in graphite and is anticipated to be relevant in SWNTs as well.3 Despite lacking a theoretical description of the observed G-mode line shape for individual metallic SWNTs, we nevertheless conclude on the basis of our combined Raman and transport measurements that it is Nano Lett., Vol. 5, No. 9, 2005
possible to identify individual metallic and semiconducting tubes via the measured width of the lower-energy G mode, ∆G-, as demonstrated in Figure 5. ∆G- in our experiment is between 40 and 60 cm-1 for metallic tubes and around 20 cm-1 for semiconducting tubes. Taking into account the spectral resolution of 6 cm-1, we derive 34-54 and 14 cm-1 for the intrinsic line width of the lower-energy G mode of metallic and semiconducting tubes, respectively. Within the small nanotube diameter range of our samples we do not observe a significant diameter dependence of ∆G- or of the G--mode position. Note that we used for this study only tubes, which showed a RBM signal, thereby indicating that an optical transition is resonant with either an incident or a scattered photon.4 Within both the single resonance and the double resonance Raman theory, the shape of the G mode should then be a characteristic feature of the tube type.9 To assign (n,m) values to our measured tubes, we compared the RBM frequencies of our individual metallic tubes with measured values from Telg et al.24 and Fantini et al.,25 taking into account an excitation resonance window of 1765
Figure 5. Width of the G- modes from Figure 4, ∆G-, plotted versus the inverse measured RBM frequency ωRBM. ∆G- for individual metallic SWNTs (green squares) is significantly larger than values for individual semiconducting SWNTs (red triangles). Intrinsic ∆Gdenotes the values corrected for the spectral resolution.
Elaser ) 1.96 ( 0.1 eV (Table 1). In agreement with Hennrich et al.26 we have identified tubes which belong to the lower and upper branches of EM 11. The data from our individual semiconducting tubes we compared with excitation energy calculations of Reich et al.,27 taking into account an excitation resonance window of Elaser ) 2.41 ( 0.1 eV. Good agreement is observed for tubes with (n - m) mod 3 ) +1 (Table 2). The identified tubes are labeled in Figure 1. In conclusion, we have presented Raman spectra of individual single-walled carbon nanotubes, where the tube type, whether metallic or semiconducting, has been determined independently by electron transport measurements, and the presence of individual tubes has been tested by atomic force microscopy. The data show the expected systematic correlation of transport measurements and resonant Raman spectroscopy, with a narrow or wide G mode for semiconducting or metallic tubes, respectively. However the broad G mode, observed for our metallic SWNTs, is not in agreement with the phonon-plasmon coupling theory. We anticipate, that the recently observed strong electron-phonon coupling in graphite, once used to calculate the electronphonon coupling in SWNTs, will explain the broad G mode observed for individual metallic SWNTs. Acknowledgment. The authors acknowledge S. Lebedkin, S. Reich, A. Ferrari, and O. Kiowski for discussions and D. Beckmann for transport measurement assistance. M.O.C. acknowledges funding by the Deutsche Forschungsgemeinschaft within the Center of Functional Nanostructures and R.K. by the Initiative and Networking Fund of the Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF). 1766
Supporting Information Available: Figures showing correlation between transport measurements and resonant Raman spectroscopy on individual tubes, atomic force images, and Raman G mode analysis. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Yao, Z.; Kane, C. L.; Dekker, C. Phys. ReV. Lett. 2000, 84, 29412944. (2) Maultzsch, J.; Reich, S.; Thomsen, C.; Requardt, H.; Ordejon, P. Phys. ReV. Lett. 2004, 92, 075501-1. (3) Piscanec, S.; Lazzeri, M.; Mauri, F.; Ferrari, A. C.; Robertson, J. Phys. ReV. Lett. 2004, 93, 185503-1. (4) Dresselhaus, M. S.; Dresselhaus, G.; Jorio, A.; Souza Filho, A. G.; Saito, R. Carbon 2002, 40, 2043-2061. (5) Pimenta, M. A.; Marucci, A.; Empedocles, S. A.; Bawendi, M. G.; Hanlon, E. B.; Rao, A. M.; Eklund, P. C.; Smalley, R. E.; Dresselhaus, G.; Dresselhaus, M. S. Phys. ReV. B 1998, 58, 1601616019. (6) Dresselhaus, M. S.; Eklund, P. C. AdV. Phys. 2000, 49, 705-814. (7) Kempa, K. Phys. ReV. B 2002, 66, 195406. (8) Chaoyang, J.; Kempa, K.; Zhao, J.; Schlecht, U.; Kolb, U.; Basche´, T.; Burghard, M.; Mews, A. Phys. ReV. B 2002, 66, 161404-1. (9) Maultzsch, J.; Reich, S.; Schlecht, U.; Thomsen, C. Phys. ReV. Lett. 2003, 91, 87402-1. (10) Jorio, A.; Souza Filho, A. G.; Dresselhaus, G.; Dresselhaus, M. S.; Swan, A. K.; U ¨ nlu¨, M. S.; Goldberg, B. B.; Pimenta, M. A.; Hafner, J. H.; Lieber, C. M.; Saito, R. Phys. ReV. B 2002, 65, 155412. (11) Balasubramanian, K.; Fan, Y.; Burghard, M.; Kern, K. Appl. Phys. Lett. 2004, 84, 2400-2402. (12) Cronin, S. B.; Barnett, R.; Tinkham, M.; Chou, S. G.; Rabin, O.; Dresselhaus, M. S.; Swan, A. K.; U ¨ nlu¨, M. S.; Goldberg, B. B. Appl. Phys. Lett. 2004, 84, 2052-2054. (13) Lebedkin, S.; Hennrich, F.; Skipa, T.; Kappes, M. M. J. Phys. Chem. B 2003, 107, 1949-1956. (14) Krupke, R.; Hennrich, F.; Kappes, M. M.; Lo¨hneysen, H. v. Nano Lett. 2004, 4, 1395-1399. (15) Krupke, R.; Hennrich, F.; Weber, H. B.; Kappes, M. M.; Lo¨hneysen, H. v. Nano Lett. 2003, 3, 1019-1023.
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(16) Oron, M.; Krupke, R.; Hennrich, F.; Weber, H. B.; Beckmann, D.; Lo¨hneysen, H. v.; Kappes, M. M. AIP Conference Proceedings 2004, 723, 561-564. (17) Krupke, R.; Hennrich, F.; Lo¨hneysen, H. v.; Kappes, M. M. Science 2003, 301, 344-347. (18) Most of the remaining contacts are not fully bridged due to short tube segments, and rarely by bundles. (19) Woong, K.; Javey, A.; Vermesh, O.; Wang, Q.; Li, Y.; Dai, H. Nano Lett. 2003, 3, 193-198. (20) Fuhrer, M. S.; Kim, B. M.; Du¨rkop, T.; Brintlinger, T. Nano Lett. 2002, 2, 755-759. (21) Xiaodong, C.; Freitag, M.; Martel, R.; Brus, L.; Avouris, Ph. Nano Lett. 2003, 3, 783-787. (22) Derycke, V.; Martel, R.; Appenzeller, J.; Avouris, Ph. Appl. Phys. Lett. 2002, 80, 2773-2775.
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(23) Brown, S. D. M.; Jorio, A.; Corio, P.; Dresselhaus, M. S.; Dresselhaus, G.; Saito, R.; Kneipp, K. Phys. ReV. B 2001, 63, 155414-1. (24) Telg, H.; Maultzsch, J.; Reich, S.; Hennrich, F.; Thomsen, C. Phys. ReV. Lett. 2004, 93, 177401-1. (25) Fantini, C.; Jorio, A.; Souza, M.; Strano, M. S.; Dresselhaus, M. S.; Pimenta, M. A. Phys. ReV. Lett. 2004, 93, 147406-1. (26) Hennrich, F.; Krupke, R.; Lebedkin, S.; Arnold, K.; Fischer, R.; Resasco, D. E.; Kappes, M. M. J. Phys. Chem. B 2005, 109, 1056710573. (27) Reich, S.; Maultzsch, J.; Thomsen, C.; Ordejon, P. Phys. ReV. B 2002, 66, 035412-1. (28) Bachilo, S. M.; Strano, M. S.; Kittrell, C.; Hauge, R. H.; Smalley, R. E.; Weisman, R. B. Science 2002, 298, 2361-2366.
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