Exciton energy transfer in nanotube bundles
P. H. Tan, A. G. Rozhin, T. Hasan, P. Hu, V. Scardaci, W. I. Milne, A. C. Ferrari
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A p r Exciton energy transfer in nanotube bundles
P. H. Tan, A. G. Rozhin, T. Hasan, P. Hu, V. Scardaci,W. I. Milne and A. C. Ferrari ∗ Department of Engineering, University of Cambridge, Cambridge CB3 0FA, UK (Dated: January 15, 2007)Photoluminescence is commonly used to identify the electronic structure of individual nanotubes.But, nanotubes naturally occur in bundles. Thus, we investigate photoluminescence of nanotubebundles. We show that their complex spectra are simply explained by exciton energy transferbetween adjacent tubes, whereby excitation of large gap tubes induces emission from smaller gapones via F¨ o rster interaction between excitons. The consequent relaxation rate is faster than non-radiative recombination, leading to enhanced photoluminescence of acceptor tubes. This fingerprintsbundles with different compositions and opens opportunities to optimize them for opto-electronics. PACS numbers: 78.67.Ch, 71.35.-y, 78.55.-m, 71.35.Cc, 73.22.-f
Carbon nanotubes are rolled graphene sheets [1]. Onedimensional quantum confinement makes their bandstructure fundamentally different from graphene, withsub-bands and singularities in the density of states [1].These are fully determined by their chiral indexes (n,m),which specify how graphene is folded into each nanotube.Thus, measuring the optical transitions allows in princi-ple to determine the chiral indexes, and fully identify ananotube sample. For this reason, a massive effort wasput to measure photoluminescence in nanotubes sincetheir discovery. However, it took more than ten yearsto unambiguously detect and identify photoluminescenceemission from single wall nanotubes (SWNT)[2, 3]. In-deed, SWNT naturally occur in bundles, due to Van-der-Waals interactions [4], but a significant intensity was onlymeasured when efficient de-bundling was achieved[2, 3].This paved the way to the interpretation of their complexabsorption and emission spectra[2, 3]. The discrepancybetween single-particle theory and experiments, pointedto the major role of electron-electron and electron-holeinteractions in shaping their band-structure[5, 6]. Theexciton binding energies were recently measured[5, 6].These are very large, from tens meV to 1 eV, dependingon diameter, chirality, and dielectric screening [5, 6, 7].Thus, excitons dominate even at room temperature.The investigation of the optical properties of nan-otubes is now a most pursued research area[2, 3, 5, 6,7, 8, 9, 10], however this still focuses on individual tubes,in contrast with their natural occurrence in bundles. Fur-thermore, the luminescence quantum yield of individ-ual SWNTs is very low and this hinders their applica-tions in optoelectronics [3, 9, 10]. Here we present athorough investigation of absorption and emission spec-tra of nanotube bundles. We show that their appar-ently complex spectra can be simply interpreted con-sidering exciton energy transfer between tubes. This isa well known phenomenon in biological systems, conju-gated polymers, quantum wires, dots, and other low-dimensional systems[11, 12, 13, 14, 15], which we nowclearly identify in nanotubes. We find that energy trans-fer is a major non-radiative relaxation channel for large
FIG. 1: PLE map for (a) as-prepared suspensions and (b)after two months. Solid lines at upper left corners representresonances with same excitation and recombination energies.The dashed-dotted lines are associated with G and 2D side-bands. Circles mark emission from (8, 4), (7, 6) and (9, 4)SWNTs, with excitation matching eh , eh , eh of (6, 5). gap tubes, strongly enhancing the photoluminescence ofthe acceptor tubes. Thus, contrary to what usually as-sumed, nanotube bundles could be ideal for high yieldoptoelectronics applications, far surpassing the poor per-formance of individual tubes [9, 10]. Furthermore, energytransfer fingerprints bundles with different nanotube con-centrations, finally offering a quantitative means to mon-itor the composition of bundles in solution, a key require-ment for research and applications[2, 3].We measure absorption on CoMoCAT SWNT(SouthWest Nanotechnologies) [16] suspensions in D O withsodium dodecylbenzene sulfonate (SDBS) surfactant[2],using a Perkin-Elmer 950 spectrometer. A JY Fluorolog-3 is used for Photoluminescence Excitation (PLE).Figure 1a plots PLE maps from the as-prepared so-lution. Each spot can be labeled as ( λ ex , λ em ), where Emission wavelength (nm)
800 900 1000 1100 1200 1300 E xc i t a t i on w a v e l eng t h ( n m ) (5,4) (6,4)(9,1)(8,3)(6,5) (7,5)(10,2) (9,4)(7,6)(8,4) (8,6)(11,3) (8,7)(9,5)(5,4)(6,4)(9,1) (9,2) G2D (6,5)(8,3) (7,6)(6,4) (9,1) (8,3)(6,5) (7,5)(10,2)(8,3) (7,5) (7,6)(8,4)(8,4) (10,5)
FIG. 2: Main features in the PLE spectra of as-prepared sus-pension. Solid circles, diamonds and triangles represent eh emission of SWNTs for which excitation matches their eh , eh , eh and eh transitions. Each peak is labeled with thechiral index of the corresponding SWNT. Open circles anddiamonds are phonon sidebands. Solid crosses are assignedto EET between s-SWNTs. Gray contour patterns compriseboth exciton-related resonances and EET spectral features. λ ex , λ em are, respectively, the excitation and emissionwavelengths. Several high intensity peaks in Fig.1a areexciton-exciton resonances [3, 17]. In this case λ ex cor-responds to the energy of the excitonic states eh ii asso-ciated with the i th electronic interband transitions E ii ( i =1, 2, 3, 4) in the single particle picture [3, 17], while λ em is the emission energy of the lowest exciton transi-tion eh . Other spots in Fig.1a are related to exciton-phonon sidebands [18, 19, 20]. The spectral features inFig.1a are summarized in Fig.2. We identify 16 differentSWNT species in the range 800nm-1300nm, and assigntheir chiral indexes in Fig. 2, as for Ref. 3. The phononsidebands for the eh and eh excitons are shown in Fig.2 with open circles and diamonds. The eh ii wavelengthsof most SWNT here are 3-10 nm larger than Ref. 3. Thisred-shift is expected in the presence of bundling [21, 22].Fig.2 has some interesting features compared with pre-vious data on isolated SWNT suspensions [3, 17]: 1)the spectral profile of exciton resonances significantlyelongates in the horizontal and vertical directions; 2)new peaks appear, such as, e.g., (645nm, 1265nm) and(568nm, 1250nm), with intensity much stronger than the( eh , eh ) peaks of (10, 5), (8, 7) and (9, 5) SWNTs; 3)a strong broad band near (980nm, 1118nm) is observed.To clarify the origin of these bands, we check PLE fromthe same solution after two months (Fig. 1b). Figs. 1a,bhave similar features. However, the eh emission wave- lengths of most SWNTs in Fig. 1b redshift ∼ eh ii , eh )( i =2, 3, 4) bands of (8, 4) and (7, 6) tubes,which shadowed them in the pristine solution. Notably,these three peaks do not correspond to any of the knownexciton-exciton resonances of SWNTs in this spectralrange [3, 17]. The (980nm, 1118nm) peak is not as-signed to a D phonon sideband of (8, 4), (7, 6) or (9,4) tubes, due to the lack of such sideband in previousinvestigations of these and other tubes [18, 19, 23, 24].Indeed, the excitation energies of the (980nm, 1118nm),(568nm, 1118nm) and (346nm, 1118nm) bands match,respectively, the eh , eh and eh transitions of (6, 5)tubes[3], whereas their emission around 1118 nm is con-sistent with (8, 4), (7, 6), (9, 4) eh . Thus, resonant ex-citation of large gap donors tubes induces emission fromsmaller gap acceptors. This implies energy transfer be-tween SWNT in bundles. Due to the large exciton bind-ing energies[5, 6, 7], this happens mainly via excitons,not via intertube electron or hole migration [25].A thorough examination of all peaks in Figs. 1a,b, al-lows us to identify several other exciton energy transfer(EET) features (solid crosses in Fig. 2). The peaks notattributable to known exciton-exciton resonances alongeach horizontal dashed-dotted line in Fig.2 are assignedto eh ii excitation of donor tubes, inducing eh emis-sion from acceptors. Vice-versa, the crosses along eachvertical dashed-dotted line are eh emission of an ac-ceptor, following EET from eh ii excitation of donors.Broad/elongated patterns of Fig.1, shown by grey con-tours in Fig.2, contain overlapping peaks from tubes withsimilar excitation or emission energies. Size, concentra-tion and distribution of nanotube species within a bundlewill determine the EET-induced intensities. The higherthe concentration of semiconducting tubes, the higher theprobability of them being adjacent, the higher the chanceof EET-induced emission. Thus, the strongest peaks willappear around eh ii transitions of semiconducting tubeswith highest concentration, such as (6, 5), (7, 5), (8, 4)in our CoMoCAT solutions [16, 17].Fig.3 compares the absorption of the as-prepared solu-tion with its photoluminescence emission and excitationspectra. The ( eh ii , eh ) peaks are marked by crosses.We assign most of the other bands to energy transferfrom donor to acceptors within bundles. The ( eh , eh )peak is the strongest amongst all possible ( eh ii , eh ) fora given (n, m), as, e.g., in the (6, 5) tube of Fig. 3b. Thisis because eh excitons have higher density of states than eh , eh [26]. Thus more photons are absorbed by eh states. Then, as shown in Fig. 3a, the eh excitation of Wavelength (nm)
300 400 500 600 700 800 900 1000 1100 1200 1300 A b s o r ban c e ( a r b . un i t s ) .25.40.55 P L I n t en s i t y ( a r b . un i t s ) ( , )( , )( , )( , )( , )( , ) ( , ) ( , ) ( , ) ( , )( , )( , )( , ) ( , )( , ) ( , ) ( , ) ( , )( , ) x2 ( , )( , ) x1/10 Excitation wavelength (nm)
300 400 500 600 700 800 900 1000 1100 1200 13000400800 ( , )( , ) (a)(b)(c) eh (6,5) eh (7,5)(6,5) eh (10,2) eh (9,5)346nm PLEPLAbsorption eh (6,5)981nm eh (5,4)831nm ( , ) FIG. 3: (a) PLE spectra, (b) emission spectra and (c) absorp-tion spectrum. Arrows indicate detection wavelengths in PLEand excitation in emission. Exciton resonances and associated(n, m) are also shown. Crosses in (a,b) mark exciton-excitonresonances in emission and excitation. Dashed lines in (b) arefits of the ( eh , eh ) resonances. These fits are done aftersubtracting the fitted Rayleigh peaks of the SWNT solutionfrom that of a D O/SDBS solution without SWNTs. large gap donors is a more efficient way to enhance emis-sion of smaller gap acceptors than the direct eh and eh excitation of the acceptors, despite the low photo-luminescence quantum efficiency of individual tubes [2].We can estimate the exciton energy transfer efficiencyin bundles as follows. Let us consider the exciton relax-ation of two adjacent tubes with different gaps, followingthe resonant eh excitation of the larger gap tube. Therate equations of the donor-acceptor system are: ∂n D /∂t = G pe − n D (1 /τ nrD + 1 /τ rD ) − n D /τ DA (1) ∂n A /∂t = n D /τ DA − n A (1 /τ nrA + 1 /τ rA ) (2)where τ DA is the energy transfer lifetime between donorand acceptor, n D is the population of excitons in thedonor and n A in the acceptor, τ nrD , τ rD , τ nrA and τ rA are the radiative (r) and non-radiative (nr) lifetimes, G pe the exciton density in the donor created by photo-excitation. An estimation of the EET efficiency is theratio of acceptor eh emission intensity ( I A = n A /τ rA ) tothat of the donor ( I D = n D /τ rD ). Then, deriving n A /n D from Eqs. (1,2) at steady state, we get: I A /I D = 1 /τ DA /τ rA + 1 /τ nrA τ rD τ rA (3) Emission wavelength (nm)900 950 1000 1050 E xc i t a t i on w ave l e ng t h ( n m ) FIG. 4: Some features in the two-photon map of Ref. 6. Opencircles: two-photon peaks. Solid circles, squares: EET peaks.
The eh radiative lifetime is reported ∼ ∼ ∼ ∼
10 ns)[29]. Thus, the observed lifetimes are de-termined by non-radiative recombination. Eq. (3) canthen be simplified as I A /I D ≈ τ nrA /τ DA .We measure a very high I A /I D in bundles. E.g., under eh excitation of the (5, 4) tubes in Fig. 3b, the ra-tio of photoluminescence intensity of all acceptor tubeswith emission above 900 nm [such as (6, 5), (7, 5), (8,4),(7,6)] to that at ∼
831 nm of the (5, 4) donor tubes isat least ∼
75. This indicates that most resonantly-excited(5, 4) eh excitons transfer their energy to the accep-tors, rather than recombine. Thus, in bundles exciton re-laxation is comparable or even faster than non-radiativerecombination. This fast relaxation suppresses emissionfrom donors. But it significantly increases the acceptorsluminescence. This suggests that small bundles entirelyformed of semiconducting tubes can be ideal for opto-electronics, such as in light-emitting devices[9, 10].Two-photon excitation is used to derive exciton bind-ing energies[5, 6]. Fig.4 summarizes the two-photon mapof Ref.6. The open circles are two-photon exciton reso-nances. These are slightly shifted with respect to thoseof Ref.5 due to the presence of small bundles[6]. Beloweach two-photon band, Ref.[6] reported a set of peaks,indicated by solid squares and circles in Fig.4. These ap-pear like a Rydberg series of states, each matching theexcitation energy of a larger gap tube, as indicated byhorizonal dashed lines in Fig. 4. These are analogous tothe energy transfer-induced peaks along each horizonaldashed-dotted line in Fig. 2. We attribute them to emis-sion of small gap tubes due to exciton energy transferfrom larger gap tubes in bundles. We assign the four fea-tures in Fig. 4 with ∼ FIG. 5: (Left) Schematic EET from a large gap donor (D) toa small gap acceptor (A).( a → b ) exciton absorption at eh D ;( b → c ) fast relaxation to eh D within the donor; ( c → d ) FRETfrom donor eh D to acceptor exciton states; ( d → e ) fast inter-band relaxation down to eh A of acceptor; ( e → f ) radiativerecombination at eh A .(Right) Recombination mechanism fortwo-photon excitation in bundles adapted from Ref.6, where1g, 1u, 2u and 2g are the even (g) and odd (u) exciton statesassociated with E . photon-exchange and F¨ o rster Resonance EnergyTransfer (FRET) are efficient exciton energy transfermechanisms [11, 12, 13, 14, 15, 30]. We attribute energytransfer in bundles to FRET. Indeed, tunneling requirescoupling of exciton wavefunctions. Its rate decaysrapidly with donor-acceptor distance ( R DA ) and is verysensitive to the eh energy difference [30]. The 16 tubespecies in our experiment have diameters ∼ eh ∼ ∼ o [3, 17]. Therefore, the efficiency should stronglydepend on specific donor and acceptor couples. How-ever, the spectrum in Fig. 3b excited at (5, 4) eh ,reproduces the profile of the absorption in Fig.3c above850nm, with no (n,m) preference. This suggests that thefactor dominating exciton energy transfer in bundles istube concentration, not symmetry, diameter or bandgapdifference, thus exciton tunneling is not the dominantmechanism.Photon-exchange is exciton-photon coupling with nodirect donor-acceptor interaction. It has a smaller de-pendence on R DA than FRET, thus it can become sig-nificant for much longer distances than FRET. However,the lack of significant EET features in isolated tube solu-tions [3, 17] combined with the low quantum efficiency [2]suggest that even if photon-exchange might exist betweenbundles or between isolated SWNTs, it is not dominantbetween adjacent tubes in a given bundle.FRET is a very efficient exciton energy transfermechanism via a resonant, near-field, dipole-dipoleinteraction[11, 12, 13, 14, 15]. It is commonly ob-served in biological systems, conjugated polymers, wires,dots[11, 12, 13, 14, 15], where it dominates at short andintermediate distances (0.5-10nm) [11, 12, 13, 14, 15].Its efficiency is determined by the spectral overlap ofdonor emission and acceptor absorption, by R DA , andby the relative orientation of emission and absorption dipoles [11]. The rate of energy transfer is proportionalto R − DA [11]. The FRET efficiency in bundles is expectedto be high. Indeed, there is a large overlap betweenemission of large gap tubes and absorption of small gaptubes. SWNTs in bundles are parallel, giving a max-imum dipole orientation factor. They aggregate withsmall wall-to-wall distance [4, 21]. This makes highermultipolar contributions possible as well [11, 12]. Indeed,considerable luminesce quenching of CdSe-ZnS dots con-jugated to SWNTs was reported due to FRET from dotsto tubes [15]. This further suggests FRET to be dom-inant in bundles. This process is schematized in Figs.5a,b for both one and two-photon spectroscopies.In summary, we presented a thorough investigation ofphotoluminescence in nanotube bundles. We have shownthat the apparently complex absorption and emissionspectra can be simply explained by exciton energy trans-fer between adjacent semiconducting tubes. By study-ing the spectral evolution for increasing bundle size, weassigned all the excition energy transfer peaks. We ar-gue that F¨ o rster interaction between excitons dominatesthe transfer process. This is highly efficient in nanotubebundles, adding a major relaxation channel for excitons,explaining the low luminescence yield of large gap nan-otubes. Thus, contrary to what usually assumed, bundlescould be ideal for high yield optoelectronics applications,far surpassing the poor performance of individual tubes.Furthermore, energy transfer fingerprints bundles withdifferent tube concentrations, finally offering a quantita-tive means to monitor the composition of solutions andfilms, a key requirement for research and applications.We acknowledge D. Prezzi, A. Rubio, A. Hartschuhfor useful discussions; funding from EPSRC GR/S97613and Ministry of Information and Communication, Re-public of Korea (No. A1100-0501-0073). PHT and ACFacknowledge funding from the Royal Society. ACF fromthe Leverhulme Trust. ∗ Electronic address: [email protected][1] S. Reich, C. Thomsen, J. Maultzsch,
Carbon nanotubes (Wiley, Weinheim),(2004).[2] M. J. O’Connell et al., Science 297, 593 (2002).[3] S. M. Bachilo et al., Science 298, 2361 (2002).[4] T. Hertel, R. E. Walkup, P. Avouris, Phys. Rev. B 58,13870 (1998).[5] F. Wang et al., Science 308, 838 (2005).[6] J. Maultzsch et al., Phys. Rev. B 72, 241402(R) (2005).[7] V. Perebeinos, J. Tersoff, P. Avouris, Phys. Rev. Lett.92, 257402 (2004).[8] Y. Z. Ma et al., Phys. Rev. Lett. 94, 157402 (2005).[9] J. A. Misewich et al., Science 300, 783 (2003).[10] J. Chen et al., Science 301, 1171(2005).[11] T. F¨ o rster, Discuss. Faraday Soc. 27, 7 (1959).[12] C. R. Kagan et al., Phys. Rev. Lett. 76, 1517 (1996).[13] S. R. Adams et al, Nature 349, 694 (1991).rster, Discuss. Faraday Soc. 27, 7 (1959).[12] C. R. Kagan et al., Phys. Rev. Lett. 76, 1517 (1996).[13] S. R. Adams et al, Nature 349, 694 (1991).