NANO LETTERS
Optical Phonon Lifetimes in Single-Walled Carbon Nanotubes by Time-Resolved Raman Scattering
2008 Vol. 8, No. 12 4642-4647
Kwangu Kang,*,† Taner Ozel,‡ David G. Cahill,† and Moonsub Shim† Frederick Seitz Materials Research Laboratory, and Department of Materials Science and Engineering, UniVersity of Illinois, Urbana, Illinois 61801, and Department of Physics, UniVersity of Illinois, Urbana, Illinois 61801 Received August 12, 2008; Revised Manuscript Received September 22, 2008
ABSTRACT The lifetimes of optical phonons (OPs) in single-walled carbon nanotubes are determined by time-resolved incoherent anti-Stokes Raman scattering using a subpicosecond pump-probe method. Lifetimes in semiconducting and metallic nanotubes at room temperature are similar, 1.2 and 0.9 ps, respectively. The OP lifetimes decrease with increasing temperature, approximately scaling as ∼1/T, consistent with anharmonic processes being the dominant decay mechanism for both semiconducting and metallic nanotubes.
Single-walled carbon nanotubes (SWNTs) have attracted considerable attention as novel nanoelectronic materials1-3 because of their ballistic electron transport and high current densities. Recent studies4-7 show that ballistic transport over a few hundred nanometers is possible at low bias ( 70 µJ cm-2, we kept the average laser power on the sample constant and varied the fluence by varying the repetition rate of optical pulses using an electro-optic modulator, i.e., by pulse picking. The high thermal conductivity of the sapphire substrate is also critical for minimizing heating of the sample by the absorbed laser power. The OP lifetime in HiPCO and arc-discharge nanotubes at room temperature are similar, ≈1.2 and ≈0.9 ps, respectively, and independent of pump fluence; see Figure 4a. This time scale is much smaller than the ≈40 ps time scale we have previously measured for heat dissipation between a nanotube and a surrounding surfactant;30 computational work suggests that exchange of thermal energy between adjacent, bundled, nanotubes should be similar.31 Absorption of the laser light produces some steady-state heating of the nanotube samples. To estimate the size of this steady-state heating, we used the temperature dependence of the G+ mode frequencies measured by a continuous-wave 785 nm laser as an internal thermometer. At a laser intensity of 40 times larger than the highest average intensity used in the time-resolved measurements, the estimated steady-state temperature rises for HiPCO and arc-discharge nanotubes are 125 and 80 K, respectively. Thus, at the maximum laser Nano Lett., Vol. 8, No. 12, 2008
Figure 4. Lifetimes of OPs in HiPCO (open triangles) and arcdischarge nanotubes (filled circles) as functions of (a) the pump fluence at room temperature and (b) temperature of the substrate at a pump fluence of 35 µJ cm-2. Error bars denote the uncertainty in the fit between the model and the data.
power used in the time-resolved measurement, the steadystate temperature rise is 500 K. We can now compare our experimental results for T1 to prior studies of the width of the Raman lines measured by conventional spectroscopy. In semiconducting nanotubes, the smallest observed Raman linewidths34 are ΓG+ ≈ ΓG- ≈ 5 4645
cm-1. If we ignore the pure dephasing term in eq 1 and estimate the OP lifetimes from this Raman line width, T2/2 ≈ T1 ≈ 1.06 ps, comparable to the OP lifetime of T1 ) 1.2 ps measured directly by TRIARS. We conclude that pure dephasing processes are negligible in semiconducting nanotubes. We cannot, unfortunately, draw definitive conclusions about the presence or absence of intrinsic dephasing processes in metallic nanotubes because (i) we cannot be sure which of the G mode phonons are contributing to the signals measured by TRIARS; (ii) reactions with the ambient may shift the Fermi-level significantly and therefore modify the strength of electron-phonon coupling;26 and (iii) we cannot easily rule out that our experiments are performed at too high of a fluence to observe an intrinsic decay process that might be easily saturated. The effect is close to the size of the error bars, but we note that OP lifetimes in the arc-discharge samples appear to decrease with decreasing fluence; see Figure 3a. In metallic nanotubes, ΓG+ ≈ 5 cm-1, comparable to ΓG+ in semiconducting nanotubes;34 on the other hand, ΓG- is dependent on the chiral index and diameter.22,27 Previous studies of isolated metallic tubes27,34,35 with diameters in the range 1.35 nm < d < 1.60 nm show ΓG- ≈ 60 cm-1, which translates to T2/2 ≈ 0.1 ps. Due to Kohn anomalies in metallic nanotubes, electron/LO-phonon coupling is strong, while electron/TO-phonon coupling is absent.22,26,27 We cannot, however, distinguish between the G+ and G- OPs in the TRIARS measurements because of the large bandwidth of the probe: a quickly decaying population of G- OPs might not be visible in our experiments if this decay was superimposed on a slowly decaying population of G+ OPs. Furthermore, the width and position of the G- peak in the Stokes spectrum of the arc-discharge sample, see Figure 1, suggest the Kohn anomaly is not fully manifested in our arcdischarge sample, presumably because of the adsorption of oxygen that shifts the Fermi-level away from the band crossing.26 Finally, we note that our data and comparison to ref 21 suggest that the OP lifetimes in semiconducting nanotubes are not strongly dependent on either the nanotube diameter d or the environment of nanotube. Our measurement of T1 ) 1.2 ps for semiconducting nanotubes with d ≈ 1 nm is in close agreement with T1 ) 1.1 ps measured on (6,5) semiconducting nanotubes with a d ) 0.76 nm. This lack of variation with diameter is consistent with prior studies that showed that the Raman linewidths ΓG+ of semiconducting nanotubes are independent of diameter.34,36 Furthermore, our results are obtained on samples that are best described as bundles of nanotubes while the results of ref 21 are for nanotubes surrounded by a surfactant and suspended in water. We therefore also conclude that the lifetimes of OPs in semiconducting nanotubes are not strongly dependent on their environment. In summary, we restate our most significant results: the OP lifetimes in semiconducting and metallic nanotubes are similar, T1 ≈ 1 ps; T1 decreases with increasing temperature 4646
in a manner that is consistent with anharmonic processes being the dominant decay mechanism. Acknowledgment. We thank Professor T. Heinz for helpful discussion on the physics of electrons and phonons in nanotubes and graphite. This material is based upon work supported by the U.S. Department of Energy, Division of Materials Sciences under Award No. DE-FG02-07ER46459, through the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana-Champaign. Experiments were carried out in part in the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois, which are partially supported by the U.S. Department of Energy under Grants DE-FG02-07ER46453 and DE-FG0207ER46471. This material is also based in part upon work supported by the National Science Foundation under Grant No. DMR-0348585. References (1) Javey, A.; Guo, J.; Wang, Q.; Lundstrom, M.; Dai, H. Nature 2003, 424, 654. (2) White, C. T.; Todorov, T. N. Nature 1998, 393, 240. (3) Liang, W.; Bockrath, M.; Bozovic, D.; Hafner, J. H.; Tinkham, M; Park, H. Nature 2001, 411, 665. (4) Yao, Z.; Kane, C. L.; Dekker, C. Phys. ReV. Lett. 2000, 84, 2941. (5) Javey, A.; Guo, J.; Paulsson, M.; Wang, Q.; Mann, D.; Lundstrom, M.; Dai, H. Phys. ReV. Lett. 2004, 92, 106804. ¨ stu¨nel, H.; Braig, (6) Park, J. Y.; Rosenblatt, S.; Yaish, Y.; Sazonova, V.; U S.; Arias, T. A.; Brouwer, P. W.; McEuen, P. L. Nano Lett. 2004, 4, 517. (7) Perebeinos, V.; Tersoff, J.; Avouris, P. Nano Lett. 2006, 6, 205. (8) Pop, E.; Mann, D.; Cao, J.; Wang, Q.; Goodson, K.; Dai, H. Phys. ReV. Lett. 2005, 95, 155505. (9) Mann, D.; Pop, E.; Cao, J.; Wang, Q.; Goodson, K; Dai, H. J. Phys. Chem. B 2006, 110, 1502. (10) Auer, C.; Schu¨rrer, F.; Ertler, C. Phys. ReV. B 2006, 74, 165409. (11) Lazzeri, M.; Mauri, F. Phys. ReV. B 2006, 73, 165419. (12) Letcher, J. J.; Kang, K.; Cahill, D. G.; Dlott, D. D. Appl. Phys. Lett. 2007, 90, 252104. (13) Laubereau, A.; Kaiser, W. ReV. Mod. Phys. 1978, 50, 607. (14) Fischer, S. F.; Laubereau, A. Chem. Phys. Lett. 1975, 35, 6. (15) Califano, S.; Schettino, V. Int. ReV. Phys. Chem. 1988, 7, 19. (16) Fatti, N. D.; Ganikhanov, F.; Langot, P.; Tommasi, R.; Valle´e, F. J. Nonlinear Opt. Phys. Mater. 1998, 7, 271. (17) von der Linde, D.; Kuhl, J.; Klingenberg, H. Phys. ReV. Lett. 1980, 44, 1505. (18) Grann, E. D.; Tsen, K. T.; Ferry, D. K. Phys. ReV. B 1996, 53, 9847. (19) Kash, J. A.; Jha, S. S.; Tsang, J. C. Phys. ReV. Lett. 1987, 58, 1869. (20) Tsen, K. T.; Kiang, J. G.; Ferry, D. K.; Morkoc, H. Appl. Phys. Lett. 2006, 89, 112111. (21) Song, D.; Wang, F.; Dukovic, G.; Zheng, M.; Semke, E. D.; Brus, L. E.; Heinz, T. F. Phys. ReV. Lett. 2008, 100, 225503. (22) Wu, Y.; Maultzsch, J.; Knoesel, E; Chandra, B.; Huang, M.; Sfeir, M. Y.; Brus, L. E.; Hone, J.; Heinz, T. F. Phys. ReV. Lett. 2007, 99, 027402. (23) Tchoul, M. N.; Ford, W. T.; Lolli, G.; Resasco, D. E.; Arepalli, S. Chem. Mater. 2007, 19, 5765. (24) Araujo, P. T.; Doorn, S. K.; Kilina, S.; Tretiak, S.; Einarsson, E.; Maruyama, S.; Chacham, H.; Pimenta, M. A.; Jorio, A. Phys. ReV. Lett. 2007, 98, 067401. (25) Kataura, H.; Kumazawa, Y.; Maniwa, Y.; Umezu, I.; Suzuki, S.; Ohtsuka, Y.; Achiba, Y. Synth. Met. 1999, 103, 2555. (26) Nguyen, K. T.; Gaur, A.; Shim, M. Phys. ReV. Lett. 2007, 98, 145504. (27) Lazzeri, M.; Piscanec, S.; Mauri, F.; Ferrari, A. C.; Robertson, J. Phys. ReV. B 2006, 73, 155426. (28) Kamaraju, N.; Kumar, S.; Sood, A. K.; Guha, S.; Krishnamurthy, S.; Rao, C. N. R. Appl. Phys. Lett. 2007, 91, 251103. (29) Ma, Y. Z.; Stenger, J.; Zimmermann, J.; Bachilo, S. M.; Smalley, R. E.; Weisman, R. B.; Fleming, G. R. J. Chem. Phys. 2004, 120, 3368. Nano Lett., Vol. 8, No. 12, 2008
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