status solidi Raman spectroscopy of ( n, m )-identified individual single-walled carbon nanotubes

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1 physica pss status solidi basic solid state physics b Raman spectroscopy of ( n, m )-identified individual single-walled carbon nanotubes T. Michel 1, M. Paillet 1, J. C. Meyer 2, V. N. Popov 3, L. Henrard 3, P. Poncharal 1, A. Zahab 1, and J.-L. Sauvajol 1 1 Laboratoire des Colloïdes, Verres et Nanomatériaux, Université Montpellier II, Montpellier cedex 5, France 2 Max Planck Institute for Solid State Research, Stuttgart, Germany 3 Laboratoire de Physique du Solide, Facultés Universitaires Notre-Dame de la Paix, 5000 Namur, Belgium Received 30 April 2007, revised 5 July 2007, accepted 5 July 2007 Published online 2 October 2007 PACS f, Na, Ch The goal of our complete experimental approach was to relate the Raman response of an individual single-walled carbon nanotubes (SWNT) to its (n,m ) structure determined from an independent way. In this aim, a procedure including transmission electronic microscopy (TEM), Raman spectroscopy, and electron diffraction experiments on the same SWNT has been developed. The independent determinations of both structure and Raman features of semiconducting and metallic nanotubes allows to discuss several questions concerning: (i) the relation between diameter of the tubes and the radial breathing mode (RBM) frequency, (ii) the values and the nature of the E and E S 44 optical transition energies. S 33 phys. stat. sol. (b) 244, No. 11, (2007) / DOI /pssb REPRINT

2 phys. stat. sol. (b) 244, No. 11, (2007) / DOI /pssb Raman spectroscopy of (n,m)-identified individual single-walled carbon nanotubes T. Michel 1, M. Paillet **, 1, J. C. Meyer ***, 2, V. N. Popov ****, 3, L. Henrard 3, P. Poncharal 1, A. Zahab 1, and J.-L. Sauvajol *, 1 1 Laboratoire des Colloïdes, Verres et Nanomatériaux, Université Montpellier II, Montpellier cedex 5, France 2 Max Planck Institute for Solid State Research, Stuttgart, Germany 3 Laboratoire de Physique du Solide, Facultés Universitaires Notre-Dame de la Paix, 5000 Namur, Belgium Received 30 April 2007, revised 5 July 2007, accepted 5 July 2007 Published online 2 October 2007 PACS f, Na, Ch The goal of our complete experimental approach was to relate the Raman response of an individual single-walled carbon nanotubes (SWNT) to its (n,m) structure determined from an independent way. In this aim, a procedure including transmission electronic microscopy (TEM), Raman spectroscopy, and electron diffraction experiments on the same SWNT has been developed. The independent determinations of both structure and Raman features of semiconducting and metallic nanotubes allows to discuss several questions concerning: (i) the relation between diameter of the tubes and the radial breathing mode (RBM) frequency, (ii) the values and the nature of the E and E optical transition energies. S 33 S 44 1 Introduction For long time, the identification of the (n,m) indices of the tubes was mainly done from the comparison between the experimental transition energies, derived from the measurement by Raman spectroscopy of the excitation profile of the radial breathing modes (RBM), and the calculated transition energies obtained in the framework of different tight binding approaches [1, 2]. Obviously, this identification requires an accurate knowledge of the dependence on diameter and helicity of the electronic transitions (the so-called Kataura plot ) and of the RBM frequency. The first (E11) S and second transition (E S 22) display a strong dependence with the diameter and chirality. Consequently, comparison between experimental and calculated Kataura plot allows this identification and gives in addition the ω RBM vs. d relation. By contrast, for higher optical transitions (E S 33, E S 44 for instance) this method of identification is not so easy because of the large number of electronic transitions in a reduced energy/diameter range. Recently, in the aim to obtain an independent determination of the carbon nanotube atomic structure in combination with its Raman spectrum, a new procedure has been developed. It must be emphasized * Corresponding author: sauva@lcvn.univ-montp2.fr, Phone: , Fax: ** Present address: Université de Montréal, Canada *** Present address: Department of Physics, University of California, Berkeley, CA , USA **** Permanent address: Faculty of Physics, University of Sofia, 1164 Sofia, Bulgaria

3 Original Paper phys. stat. sol. (b) 244, No. 11 (2007) 3987 that this approach allows to minimize environmental effects and to ensure that the measurements have been performed on individual SWNTs. Indeed, for nanotubes wrapped in surfactant, it is very difficult to distinguish between an individual SWNT and a small SWNT bundle. In this paper, we discuss the diameter dependence of the RBM frequency on (n,m)-identified freestanding SWNTs. In a second part, we focus on higher energy optical transitions, namely the third (E S 33) and fourth (E S 44) transitions. Especially, the excitonic nature of these transitions are discussed. 2 Experimental methods Our experimental procedure consists of the preparation of SWNTs as freestanding objects on a metallic grid and the localization of these SWNTs by transmission electron microscopy with respect to the lithographic pattern. Then we perform Raman experiments and the identification of the structure [i.e. (n,m) indices] of the same SWNTs by electron diffraction (for details see Ref. [3]). The main problem of this procedure is that the identification of the structure of the tubes was done after measuring the Raman spectra because the electron beam damages the tubes. Consequently, we do not have an estimate of the resonance conditions of the tubes investigated before Raman experiments. To measure the Raman spectrum, we use the following procedure: (i) at a fixed laser energy excitation (power impinging on the sample of about 200 µw) we localize the laser spot on a particular tube. In addition, the tube axis is oriented parallel to the polarization of the incident laser light. In these conditions we try to detect a signal by using a short counting time (typically 10 seconds). (ii) if a signal is detected, the spectrum is measured by using a long counting time (typically 10 minutes). (iii) if not, we change the excitation energy and try again by using a short counting time, and so on. In these experimental conditions, when a signal is detected in few seconds (step i), we assume that, for each tube detected, the laser excitation energy (E L ) and the transition energy (E ii ) are close. This assumption will be discussed in thefollowing. Five laser excitation energies were used: E L = 1.70 ev, E L = 1.57 ev, E L = 1.64 ev from a Ti:Sapphire laser, and E L = 1.92 ev and E L = 2.41 ev from an Ar/Kr mixed gas laser. 3 Results and discussion 3.1 RBM frequency versus tube diameter The Raman spectra of eight different (n,m)-identified individual SWNTs have been recorded: five semiconducting and three metallic nanotubes. The diameters of these tubes were derived by using the usual relation: 2 2 3( n + m + nm) d = ac - c, (1) π where a c c = nm. In Fig. 1(a) are compared the diameter dependence of the RBM frequency performed on (n,m)- identified freestanding SWNTs (solid dots) with those measured in the same diameter range on SWNTs grown on two different substrates: SiO 2 [4] (Fig. 1(a), open black square), and on the top of a quartz substrate [5] (Fig. 1(a), open blue triangles). For tubes in the nm diameter range, a reasonable agreement between the different set of data is found. For instance, the semiconducting (11,10) tube is measured at cm 1 in Ref. [5] against cm 1 in this work [3], and the metallic (16,7) is found at 154 cm 1 in Refs. [4, 3]. The RBMs of these two later tubes are shown in Fig. 1(b). Above 1.6 nm, the RBM performed on freestanding SWNTs are at higher frequency than the RBM measured on tubes grown at the top of a quartz substrate [5]. These results suggest that the environment more affects the RBM frequency of large tubes compared to the small ones. A similar conclusion was found by Zhang et al. [6] from comparison between the Raman spectra of the same nanotube taken on a substrate or suspended over a trenche. However, in this later work, the frequency is found smaller for suspended tube

4 3988 T. Michel et al.: Spectroscopy of SWNTs RBM Frequencies (cm -1 ) HWHM (cm -1 ) (23,21) d (nm) (27,4) (15,14) (a) (17,9) (15,6) (16,7) (12,12) /d (nm -1 ) (11,10) (b) (16,7) 1.57 ev (11,10) 2.41 ev Raman shift (cm -1 ) Fig. 1 (online colour at: ) (a) Dependence of the RBM frequency with the inverse of diameter. Red circles are from this work [3], the best fit (ω = 204/d + 27) is indicated by the red solid line. Open blue triangles are data from Araujo et al., the best fit (ω = 217.8/d ) is indicated by the blue line [5]. Open black squares are data from Jorio et al., the best fit (ω = 244.5/d) is indicated by the dark line [4]. (b) RBM of the (16,7) (up) and (11,10) (down). The laser excitation energies are 1.57 ev and 2.41 ev respectively. Intensity (Arb. Units) than for the same tube interacting with the substrate. The ensemble of these results suggest that, for large tubes, the shift of the RBM depends on the kind of environment. On the other hand, since most of the environmental effects are minimized for freestanding SWNTs, a linear RBM frequency vs. d relationship is expected (for a review, see Ref. [7]). It is striking to note that the RBM frequencies measured on (n,m) freestanding SWNTs well agree with a line obeying the relation (Fig. 1, red solid line): ωrbm = + 27 cm. (2) d(nm) The strong value of the non-zero limit of this relation for an infinite diameter, usually assigned to environmental effects, is an open question. Some explanations can be suggested. (i) It must be emphasized that with regards to the small number of data available on identified freestanding SWNTs, the value of this limit strongly depends on the accuracy of the measurements of the two large diameters, namely the (23,21) and (27,4) SWNTs. Errors in the measurement of their RBM frequency significantly change the slope of the RBM vs. d relationship. However, to vanish the additional term, we must assume an error on the RBM frequency of about 10 cm 1 or more for the (27,4) and (23,21) SWNTs which is very unlikely. (ii) Because our experiments are performed at ambiant conditions the effect of the gases adsorbed at the surface of the tubes could be an extrinsic factor which affects the RBM frequency. This effect would be more pronounced for the large diameters because of their large surface. Additional data obtained on freestanding SWNTs for diameters above 1.6 nm, in air and under vacuum, are necessary in order to light definitely this point. (iii) Finally, it is also striking to observe that the linewidth of the RBM measured at the resonance conditions (see below), increases with the tube diameter (Fig. 1, inset) unambigously confirming previous behavior found in Ref. [8]. It is tempting to relate this broadening at a blueshift of the RBM frequency, or in other words: larger the diameter larger the deviation from the linear law. However, no theoretical calculations predicts such behavior.

5 Original Paper phys. stat. sol. (b) 244, No. 11 (2007) 3989 Fig. 2 (online colour at: ) Experimental Kataura plot displaying normalized energy transitions, E N ii, on the Raman data from this work. Black open stars, open (filled) squares are for E M 11, E S 33 (E S 44) calculations, respectively. Red triangles (circles) are for tubes measured by Raman (Rayleigh) spectroscopy. Blue squares and blue stars are for calculations of the tubes measured by Rayleigh or Raman spectroscopy. 3.2 The E M 11, E S 33 and E S 44 transitions for SWNTs in the nm diameter range As recalled previously, when a RBM signal is detected in few seconds, it is reasonable to assume that the laser excitation energy (E L ) and the transition energy (E ii ) of the tube investigated are close. More precisely, we assume E RRS ii = EL ± Γ /2 where Γ is the broadening (FWHM) of the resonance window. For individual tubes, Γ values from 10 mev to 60 mev were found [9, 10]. In the framework of this assumption we can compare the values of the excitation energy for which a RBM was measured in few seconds with calculations of the energy transitions performed by using a non-orthogonal tight-binding (NTB) approach (E NTB ii ) [11]. We found that a rigid shift of 0.32 ev of the calculated first transition for the metallic tubes (E11), M and a rigid shift of about 0.44 ev of the calculated third (E S 33) and fourth (E S 44) transitions for the semiconducting tubes leads to a very good agreement between experimental (Fig. 2, red triangles) and calculated transitions energies (Fig. 2, blue symbols) for tubes in the nm diameter range. The value of our experimental uncertainty (the resonance window) is then ten times lower than the rigid shifts. The shifted E NTB ii are called normalized optical transitions, E N ii. Recently, the optical energy transitions of several well-identified metallic and semiconducting SWNTs have been measured by combining electron diffraction and Rayleigh scattering on the same individual freestanding SWNTs [12]. The Rayleigh data are in good agreement with the calculations normalized on our Raman results (Fig. 2, red circles). The agreement between the data obtained independently on freestanding SWNTs by using two different experimental techniques and samples, must be emphasized. It validates our assumption about the closeness of the laser excitation energy (E L ) and transition energy (E ii ) when a RBM signal is measured in few seconds in our experimental conditions. This agreement further supports our conclusion that a rigid shift is needed for matching the calculated E11, M E S 33 and E S 44 with the corresponding experimental transitions for SWNTs in the nm diameter range. 3.3 On the nature of the E S 33 and E S 44 transitions An important question remains: why a rigid shift of the calculated transition energies by non-orthogonal tight-binding model gives the good experimental E M 11, E S 33 and E S 44 transitions in this diameter range?

6 3990 T. Michel et al.: Spectroscopy of SWNTs Fig. 3 (online colour at: ) Deviation of D Eii from the KM correction vs. 1/d for the third semiconducting (green symbols), fourth semiconducting (blue symbols), and first metallic transitions (black symbols). Open squares are the Raman data from Ref. [5], filled circles are Rayleigh data from Ref. [12] and filled triangles are Raman data from this work (see also [15]). The black solid line is the exciton binding energy dependence: 0.34 ev nm (from Ref. [16]). Horizontal black dotted line is the expected zero deviation for metallic SWNTs. Indeed, the difference between the experimental and calculated transition energies (DE ii ), results from two opposite many-body effects: an increase of the single-particle transition energy due to the electron electron correlation and a decrease of the same transition energy due to the excitonic effect. Few years RRS NTB ago, Kane and Mele have proposed that E ii = E ii - E ii followed a diameter-dependent logarithmic law, referred to as the KM correction [13] in the following: RRS NTB 2p Ê 2Λ ˆ Eii - Eii = α log, 3d Á Ë2p/ 3d (3) where p = 1 for E M 11, p = 2 for E S 22, p = 3 for E M 11, p = 4 for E S 33..., respectively, and the ultraviolet cutoff Λ is equal to 1.5 nm 1 [14]. The parameter α is equal to 0.67 ev nm [15]. The ability of the KM correction to fit the E M 11 and E S 22 transitions was previously found [14]. To analyze the data reported in Fig. 2, we compare the diameter dependence of the DE ii deviation for the E M 11, E S 33 and E S 44 transitions with respect to the KM correction (Fig. 3). As expected and found previously, the deviation for E M 11 is close to zero. By contrast, the deviations for E S 33 and E S 44 transitions show a linear dependence with respect of the inverse tube diameter. Especially, it must be pointed out that the deviation for the E S 44 transition (Fig. 3, blue symbols) shows the same linear dependence as the exciton binding energy, 0.34 ev nm/d [16]. For the E S 33 transition a slightly different scaling law is observed (Fig. 3, green symbols). In the same plot (Fig. 3, squares) we have reported the deviations of the E M 11, E S 33 and E S 44 transitions measured on tubes grown on the top of a quartz substrate by Araujo et al. [5]. Same behaviors as those observed on freestanding SWNTs are found meaning that this deviation slightly depends on the tube environment. In the framework of the Kane and Mele approach, these data mean that the KM correction is underestimated for the E S 33 and E S 44 transitions. Because the energy in excess for E S 33 and E S 44 follows diameter dependences close to the exciton binding energy, these results suggest that the exciton binding energy is very small or missing for these transitions. Further theoretical investigations are necessary to probe this conclusion or to propose another way to explain these well-established results.

7 Original Paper phys. stat. sol. (b) 244, No. 11 (2007) Conclusion In this paper, we have reported a review of recent results obtained by Raman spectroscopy on freestanding SWNTs. Comparison with other data obtained in the same diameter range on tubes grown on substrates allows us to state the following conclusions: (i) in the nm diameter range, the RBM frequency slightly depends on the tube environment. (ii) Comparing the diameter dependence of the DE ii deviation for the optical transitions with respect to the KM correction suggest that the processes involved in E S 33 and E S 44 and in the E M 11, E S 11 and E S 22 transitions are different and gives new insight about the nature of the E S 33 and E S 44 transitions. Acknowledgements The authors warmly acknowledge Prof. S. Roth and Prof. Ph. Lambin for their support during this work. One of us (L.H.) is supported by the Belgian F.N.R.S. This work has been done in the framework of the GDRE n 2756 Sciences and applications of the nanotubes-nano-e. References [1] C. Fantini et al., Phys. Rev. Lett. 93, (2004). [2] H. Telg et al., Phys. Rev. Lett. 93, (2004). [3] J. C. Meyer et al., Phys. Rev. Lett. 95, (2005). [4] A. Jorio et al., Phys. Rev. Lett. 86, 1118 (2001). [5] P. T. Araujo et al., Phys. Rev. Lett. 98, (2007). [6] Y. Zhang et al., J. Am. Chem. Soc. 127, (2005). [7] S. Reich, C. Thomsen, and J. Maultzsch, Carbon Nanotubes. Basic Concepts and Physical Properties (Wiley- VCH, Weinheim, Germany, 2004). [8] A. Jorio et al., Phys. Rev. B 66, (2002). [9] C. Fantini, A. Jorio, M. Souza, M. S. Strano, M. S. Dresselhaus, and M. A. Pimenta, Phys. Rev. Lett. 93, (2004). [10] A. Jorio, A. G. Souza Fihlo, G. Dresselhaus, M. S. Dresselhaus, R. Saito, J. H. Hafner, C. M. Lieber, F. M. Matinaga, M. S. S. Dantas, and M. A. Pimenta, Phys. Rev. B 63, (2001). [11] V. N. Popov and L. Henrard, Phys. Rev. B 70, (2004). [12] M. Y. Sfeir et al., Science 312, 554 (2006). [13] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 93, (2004). [14] A. Jorio et al., Phys. Rev. B 71, (2005). [15] T. Michel et al., Phys. Rev. B 75, (2007). [16] G. Dukovic et al., Nano Lett. 5, 2314 (2005).