Temperature Dependence of the Optical Transition Energies of Carbon Nanotubes: The Role of Electron-Phonon Coupling and Thermal Expansion S. B. Cronin, 1,2, * Y. Yin, 3 A. Walsh, 3 Rodrigo B. Capaz, 4,6 A. Stolyarov, 2 P. Tangney, 5 Marvin L. Cohen, 6 Steven G. Louie, 5,6 A. K. Swan, 3 M. S. U ¨ nlu ¨, 3,7 B. B. Goldberg, 3,7 and M. Tinkham 2 1 Department of Electrical Engineering, University of Southern California, Los Angeles, California 90098, USA 2 Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 3 Department of Physics, Boston University, Boston, Massachusetts 02215, USA 4 Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil 5 The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 6 Department of Physics, University of California at Berkeley, and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 7 Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215, USA (Received 2 August 2005; published 30 March 2006) Tunable Raman spectroscopy is used to measure the optical transition energies E ii of individual single wall carbon nanotubes. E ii is observed to shift down in energy by as much as 50 meV, from 160 to 300  C, in contrast with previous measurements performed on nanotubes in alternate environments, which show upshifts and downshifts in E ii with temperature. We determine that electron-phonon coupling explains our experimental observations of nanotubes suspended in air, neglecting thermal expansion. In contrast, for nanotubes in surfactant or in bundles, thermal expansion of the nanotubes’ environment exerts a nonisotropic pressure on the nanotube that dominates over the effect of electron-phonon coupling. DOI: 10.1103/PhysRevLett.96.127403 PACS numbers: 78.67.Ch, 73.22.f, 78.30.Na The temperature dependence of the electronic band structure of carbon nanotubes is important for many of their practical applications such as field-effect transistors [1] and single nanotube optical emission devices [2]. With a precise understanding of the temperature dependence of nanotubes we are able to use the temperature as a parame- ter to tune the electronic energies of nanotubes in a con- trolled manner, thus providing a more versatile set of devices, as well as a better understanding of the fundamen- tal physics of carbon nanotubes. In earlier work, Raman spectroscopy carried out at a fixed laser energy on large ensembles of nanotubes showed downshifts in the phonon frequencies with increasing tem- perature [3,4]. The results also indicated that the optical transition energies E ii [5] shift with temperature, although they were unable to determine by how much E ii shifted or in which direction. More recently, photoluminescence spectroscopy and tunable Raman spectroscopy have al- lowed the direct measurement of the optical transition energies E ii as a function of temperature [7–14]. These studies show a variety of results ranging in both the mag- nitude and sign of the shift dE ii =dT. Studies on nanotube bundles [13] and nanotubes coated in surfactant [9,13,14] show dE ii =dT to be positive or negative, depending on whether n  mmod3  1 or 2, respectively. In the present work, E ii of individual isolated nanotubes suspended over trenches are measured at various tempera- tures using tunable Raman spectroscopy. By suspending the nanotubes off the substrate we minimize the environ- mental perturbation to the nanotube, and are thus able to observe the theoretically predicted electron-phonon cou- pling behavior in nanotubes [15]. This behavior is not observed in nanotubes in alternate environments, where the thermal effect is dominated by pressures exerted due to the expansion and contraction of the nanotubes’ environment. Individual suspended single wall carbon nanotubes (SWNTs) are prepared by first etching trenches in quartz substrates by reactive ion etching (RIE) in a CF 4 plasma. A chromium film, patterned by electron beam lithography and wet chemical etching, is used to mask the quartz during the RIE process. SWNTs are grown over the trenches by chemical vapor deposition in methane gas at 900  C, using a 1 nm thick film of iron as the catalyst for the nanotube growth. Resonant nanotubes are found by scanning the laser spot along the trench. We typically find 3 to 5 spa- tially separated resonant nanotubes along the 77 m long trench. Once a resonant nanotube is found with an ex- tremely large signal, we record its location. While atomic force microscopy and scanning electron microscopy (SEM) were performed on preliminary samples to optimize the parameters of our growth of individual suspended nanotubes, microscopy was not performed on the samples measured in this work. We found that SEM exposure spoiled the strong resonance we observed in pristine samples. Spectra are measured in a modified Renishaw Raman microprobe RM1000B, with a tunable Ti:sapphire laser and variable angle filters allowing us to tune through the resonance of an individual nanotube between 720 and 830 nm (1.72 to 1.49 eV). For the diameter distribution of these samples we are primarily in resonance with E 11 of metallic nanotubes and E 22 of semiconducting nanotubes. Spectra were taken with a 50 objective (NA  0:75) at a laser power of 1 mW. The sample temperature was con- PRL 96, 127403 (2006) PHYSICAL REVIEW LETTERS week ending 31 MARCH 2006 0031-9007= 06=96(12)=127403(4)$23.00 127403-1  2006 The American Physical Society