Carbon nanotube population analysis from Ramanand photoluminescence intensitiesA. Jorio, C. Fantini, and M. A. PimentaDepartamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais,30123-970 BrazilD. A. Heller and M. S. StranoDepartment of Chemistry, Department of Chemical and Biomolecular Engineering, University of Illinois atUrbana/Champaign, 118 Roger Adams Laboratory, Box C-3 600 South Mathews Avenue,Urbana, Illinois 61801-3602M. S. DresselhausDepartment of Physics and Department of Electrical Engineering and Computer Science,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307Y. Oyama, J. Jiang, and R. SaitoDepartment of Physics, Tohoku University and CREST JST, Aoba Sendai 980-8578, Japan共Received 25 July 2005; accepted 11 November 2005; published online 11 January 2006兲In the absence of standard single-wall carbon nanotube samples with a well-known 共n ,m兲population, we provide both a photoluminescence excitation 共PLE兲 and resonance Raman scattering共RRS兲 analysis that together can be used to check the calculations for PLE and RRS intensities forcarbon nanotubes. We compare our results with available models and show that they describe wellthe chirality dependence of the intensity ratio, confirming the differences between type 1 and type2 semiconducting tubes 关共2n +m兲 mod 3兴 = 1 and 2, respectively, and the existence of a node in theradial breathing mode intensity for type 2 carbon nanotubes with chiral angles between 20° and25°. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2162688兴Large efforts are now being directed to developing syn-thesis or manipulation processes able to generate single-wallcarbon nanotubes 共SWNTs兲 with well-defined geometricstructure, i.e., diameter 共dt兲 and chiral angle 共␪兲, or equiva-lently their 共 n , m兲 indices.1–3Photoluminescence excitation2,4共PLE兲 and resonance Raman spectroscopy5–7共RRS兲 are twotechniques able to nondestructively probe isolated tubes andlarge ensembles, characterizing the result of a given synthe-sis or separation process, giving the 共n ,m兲 values of thesamples using optical techniques. Since the RRS and PLEintensities depend on the number of scatterers in the sample,intensity analysis provides the population of specific 共n ,m兲SWNTs in the sample.8–10However, since the efficiency forthe RRS and PLE processes should also depend on 共n , m兲,the population information cannot be extracted directly fromthe measured intensities, but should firstly be corrected toaccount for the 共n ,m兲 dependence of the RRS and PLEefficiencies.9,10To make such corrections for the 共n,m兲 dependence ofthe RRS and PLE intensities, different calculations havebeen performed.11–15However, due to the lack of a samplewith a well-known 共n, m兲 population, there is no experimen-tal evaluation of the accuracy of the proposed models. In thispaper we provide experimental results that can be used toevaluate the RRS and PLE intensity calculations. We mea-sure both RRS and PLE on a SWNT sample and we proposethat the experimental intensity ratio IExpPLE/IExpRRSshould be in-dependent of the 共n ,m兲 population. This ratio can, therefore,be used to test the validity and accuracy of the calculatedintensity ratio ICalcPLE/ICalcRRS.The RRS and PLE experiments were performed at roomtemperature on HiPco SWNTs in SDS suspended aqueoussolution, prepared as described in Ref. 16. For the RRS ex-periments, a Dilor XY triple monochromator equipped with aN2-cooled charge-coupled device 共CCD兲 was used and ex-cited by ArKr, Ti:Sapphire and dye lasers in the range1.6 to 2.7 eV. The reported data for RRS intensities 共IExpRRS兲are related to resonances with the E22Snanotube levels.6ForPLE experiments, we used a home-built n-IR fluorescencespectrometer, coupled to a nitrogen-cooled germanium detec-tor 共Edinburgh Instruments兲. The excitation ranged between1.55 to 3.10 eV, and nanotube emission was measured be-tween 0.89 to 1.38 eV. The reported data for PLE intensities共IExpPLE兲 are related to absorption at E22Sand emission at E11Slevels.4The spectral intensities 关IExpRRSfor RRS and IExpPLEforPLE 共see Table I兲兴 were evaluated from the radial breathingmode 共RBM兲 RRS profile6and from the PLE resonanceprofile4,8for each 共 n , m兲 tube. The RRS intensities are cali-brated by measuring the signal of nonresonant CCl4underthe same conditions. The PLE intensities are calibrated bydividing the nanotube signal over the relative lamp power atall excitation wavelengths and by considering the blackbodyspectrum.A given PLE or RRS experimental intensity accuracy isbasically related to the strength of the signal and the numberof different excitation laser lines close enough in energy sothat the resonance profile can be well evaluated. This profilecan change from tube to tube and, in our case, the accuracy isbetter than 20%. When comparing the 共n,m兲 dependence forthe IExpPLEdata obtained in this paper with published data forHiPco SWNTs 共e.g., by Bachilo et al.8兲, the overall 共n , m 兲dependence is similar. Some intensity differences go up to30% of the values and these differences can be related toAPPLIED PHYSICS LETTERS 88, 023109 共2006兲0003-6951/2006/88共2兲/023109/3/$23.00 © 2006 American Institute of Physics88, 023109-1Downloaded 16 Jan 2006 to 130.126.226.153. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jspdifferences in sample population due to different samplepreparation procedures.The experimental results will be here compared to theo-retical calculations. The PLE theoretical intensities 关ICalcPLE共seeTable I兲兴 are calculated by the product of the E22Sinducedabsorption probability, the electron relaxation rate from E22Sstate to any other state satisfying energy-momentum conser-vation by emitting or absorbing one phonon at 300 K, andthe E11spontaneous emission probability, as described inRef. 14. Reich et al.15used a different model to calculate PLintensities, but the general 共n ,m兲 dependence is similar towhat is shown here and does not change the conclusions, asdiscussed later. The RRS theoretical intensities 关ICalcRRS共seeTable I兲兴 were calculated using the procedure discussed inRefs. 11 and 12, making use of the symmetry-adapted non-orthogonal tight-binding model and considering resonancewith E22Slevels. The results used here are in good