Analysis of photoluminescence from solubilized single-walled carbon nanotubes

Marcus Jones, Chaiwat Engtrakul, Wyatt K. Metzger, Randy J. Ellingson, Arthur J. Nozik,Michael J. Heben, and Garry Rumbles

Center for Basic Sciences, National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado, 80401-3393, USAsReceived 5 June 2004; revised manuscript received 27 October 2004; published 25 March 2005d

The functional form of the photoluminescencesPLd line shape from individual single-walled carbon nano-tubesSWNTd species is found to contain a significant Lorentzian component and the Stokes shift is observedto be very smalls,8 meVd, which suggests an excitonic dephasing mechanism that is largely decoupled fromsurrounding solvent and surfactant molecules. The PL quantum yieldsPLQYd of two SWNT species is deter-mined to be,5310−4, and it is suggested that this is lower than the “true” value due to quenching of the PLin bundles by metallic tubes. Time-resolved PL measurements reveal a dominant, luminescence lifetime com-ponent of 130 ps that, when combined with a predicted natural radiative lifetime of,20 ns, suggests that thetrue PLQY is,6.5310−3. Finally, deconvoluted PL excitation spectra are produced for eight SWNT species,and the appearance of a higher-energy excitonic subband is discussed.

DOI: 10.1103/PhysRevB.71.115426 PACS numberssd: 73.61.Wp, 71.35.2y, 71.20.Tx

I. INTRODUCTION

Carbon nanotubes were discovered in 19911 and havebeen found to possess a wide variety of remarkablemechanical,2 thermal,3 and electrical4–6 properties and havemany potential practical applications. Recently, however, thediscovery, by O’Connellet al.,7 of structured near-infraredphotoluminescence from suitably isolated semiconductingsingle-walled carbon nanotubessSWNTsd has generated sub-stantial interest in their optical properties. Since that report,steady-state photoluminescence spectra have been measuredon aqueous suspensions of both HiPco SWNTs,7–9 producedby gas-phase chemical vapor deposition in high pressure car-bon monoxide10 and SWNTs produced by pulsed laser va-porization of Ni/Co/carbon targets.11,12 Photoluminescenceefficiencies of HiPco tubes are found to reversibly decreaseas pH is lowered9 and fluorescence energies are changedfwithin a ,25 meV range fors8,3d tubesg when differentsurfactants are used to stabilize the SWNTs in solution.13 Inaddition, SWNTs suspended in air between silicon pillarswere found to exhibit room temperature PL14,15 that wasbroadly similar to the PL from micellar suspensions. Whenindividual nanotubes were probed, at 4 K16 and 300 K,17 adistribution of PL energies was found for tubes with commonchiral symmetry and diameter, which likely arose from tubedefects or variations in the local environment. Cryogenicstudies have also shown the emergence of new PL peaks inthe ensemble spectrum at low temperatures.18

Time-resolved measurements19–26 have also been em-ployed in an attempt to elucidate the carrier dynamics inphotoexcited single-walled carbon nanotubes. Wavelength-dependent pump-probe spectroscopy has revealed a subpico-second intraband relaxation and a longer25 s5-20 psd compo-nent that is attributed to interband carrier recombination.Measurements of SWNT fluorescence decay22,24,26have, un-til now, resulted in PL lifetime estimates of,10–15 ps;however, in this paper we report lifetime values for threedifferent tube species that are approximately 1 order of mag-nitude larger.

One electron band theory was initially used to explainSWNT spectra, but significant deviations were found be-tween theory and experiment. For example, the ratio of theenergy of thesecondpeak in the excitation spectrum to thefluorescence energy was predicted to asymptotically ap-proach 2 in the limit of the large tube radius; experimentally,it instead approaches an asymptotic value nearer to 1.75. Theeffects of electron-hole interactions in SWNTs, identified byAndo,27 have recently been found to resolve the “ratioproblem”28 and the consideration of excitonic states inSWNTs has resulted in a more accurate description ofSWNT electronic structure.29,30

This paper describes the results of a detailed analysis ofthe steady-state and time-resolved PL of aqueous suspen-sions of SWNTs. We illustrate the extraction of spectral in-formation pertaining to a single-tube species within a highlypolydisperse SWNT sample by examination of the two-dimensionals2Dd PL landscape, whose boundaries are de-fined by excitation and emission wavelength vectorsslex andlemd. Absorption data are also presented, and accurate mea-surements of the Stoke’s shift are reported for four-tube spe-cies. An estimate of the PL quantum yieldsPLQYd is madefor two individual SWNT species and this is found to bebroadly in agreement with previous values for the ensemblePL. In addition, time-resolved fluorescence decays have beenmeasured and analyzed, enabling an estimate of the naturalfluorescence lifetime in SWNTs. Single species SWNT exci-tation spectra are generated from the results of the PL analy-sis and the observation of a high-energy excitonic subband isdiscussed.

II. EXPERIMENTAL SECTION

Using a method similar to one previously reported,7

12 mg of as-produced HiPco10 SWNTs sCarbon Nanotech-nologiesd were suspended in 15 ml of aqueous sodium dode-cyl sulfatesSDSd surfactants1 wt %d using a cup-horn soni-cator connected to an ultrasonic processorsCole-Palmer,750 Wd. The mixture was kept in a water bath cooled to

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15 °C during the sonication periods12 mind. The resultingsuspension was centrifugedsBeckman Coulter, Optima XL-100 Kd at 104 000 g for 4 h using a swing bucket rotorsSW-28d. A stable suspension of SWNTs was isolated by decant-ing the upper 75% of the supernatant and used for subse-quent experiments.

PhotoluminescencesPLd spectra were recorded using aFluorolog-3 sJYHoribad spectrometer that utilized a liquid-N2-cooled charge-coupled-devicesCCDd detector. Mono-chromatic excitation light was generated by a xenon arc lampdispersed through a double monochromator. Fluorescencewas collected perpendicular to the excitation beam, passedthrough a single monochromator containing a 300 line/mmgrating and imaged on a cooleds80 Kd CCD array. All PLspectra were corrected for the spectral output intensity of theexcitation source and for the spectral response of the detec-tion system. Linear absorption spectra were recorded on aCary 500 double beam spectrophotometer at 1 nm spectralresolution.

Room-temperature PL decay curves were measured bytime-correlated single-photon countingsTCSPCd.31 Photoex-citation at the desired wavelength was provided by an opticalparametric amplifier pumped by the output of a titanium:sap-phire laser system with a regenerative amplifier. The finallaser output consisted of a 250 kHz pulse train with an aver-age power of 5 mW, a spot size of about 2 mm, and a pulse

width of several hundred femtoseconds. The SWNT PL, de-tected perpendicular to the excitation beam, was passedthrough long pass filters and a spectrometersSpex 320Mdand detected by a cooleds80 Kd, red-sensitive photomulti-plier tube sHamamatsu R5509d. Instrument response func-tions sIRFsd, with a width of,200 ps, were measured usingscattered light from the same samples as those from whichfluorescence was viewed. Analysis of the PL decays wasachieved by nonlinear least squares32 iterative reconvolutionof a model exponential decay function with the IRFs. Thistechnique effectively removed the contribution of the IRF tothe PL decay and resulted in a temporal response of,20 ps,i.e., 10% of the instrument response function width.31

III. RESULTS AND DISCUSSION

Excitation of an SDS-water solution of SWNTs withlexvaried from 300 to 750 nm produced PL spectra that are pre-sented in Fig. 1. Limitations of the sensitivity of the CCDdetector in the near-infraredsnear-IRd enabled only a subsetof the total SWNT fluorescence to be recorded. The PL isassociated with emission from the lowest SWNT electronicexcited state and each peak is assigned ansn,md symmetrylabel by referring to the empirical Kataura plot published byWeisman and Bachilo.33 The two encircled areas, labeled Band C, contain PL peaks that occur after optically allowed

FIG. 1. sColor onlined 2D PL spectrum of aqueous SWNTs. Imagessad and sbd are contiguous, but the intensity scale on imagesbd isenhanced by a factor of 15 compared to that of imagesad. The encircled areas, marked B and C, contain resonant PL peaks from SWNTs thathave been excited to theB0 andC0 excitons, respectively.

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transitions to the second and third lowest excited states, re-spectively. These transitions have often been labeled E22 andE33, denoting the excitation of an electron from the secondsthirdd highest van Hove singularitysvHSd in the valenceband to the secondsthirdd lowest vHS in the conductionband. Recent calculations29 of the density of single particlestates fors8,0d SWNTs has demonstrated that this simplearrangement of vHSs does not always hold and the lowestenergy optically allowed transition may not necessarily occurbetweenn1 andc1. Following Spataruet al.,

29 excited stateswill be denoted, in order of increasing energy, asA0, B0, andC0.

Two streaks associated with Raman lines are clearly vis-ible in the upper right corner of the imagesbd in Fig. 1; theseare 200 and 325 meVs1613 and 2621 cm−1d from the exci-tation line and their intensities can be fitted to Lorentzianfunctions with widths at half maximum of 18±0.5 and23±0.5 meV, respectively. They represent34,35 the tangentialC-C SWNT stretchingG modes and the first overtone,G8,of the disordersDd modes. When the data are plotted with alogarithmic intensity scale another Raman line can be iden-tified at 523 meVs4218 cm−1d, which corresponds to theG8+G combination mode.

Two typical PL slices from the 2D data in Fig. 1 arereplotted for further analysis in Fig. 2. The upper spectrumwas produced by resonant excitation of theB0 exciton in

s6,5d tubes at 565 nm, and the lower spectrum shows a typi-cal nonresonant spectrum after 600 nm excitation. NeitherLorentzian nor Gaussian profiles gave convincing fits to therecorded PL data, indicating that homogeneous and inhomo-geneous broadening mechanisms, which would contributeLorentzian and Gaussian character, respectively, to the PLpeaks, are of roughly the same magnitude. Purely Lorentzianline shapes have been observed in previous PL studies onsingle nanotubes at 4 K16 and at room temperature,17 and, inboth cases, multiple peaks appeared over a spectral rangewhere bands had previously been observed and assigned tonanotubes with common chirality. It therefore seems likelythat, in addition to room-temperature broadening, the Gauss-ian components that appear in our SWNT PL data arise be-cause of local variations in the solvent and/or surfactant en-vironment experienced by tubes with a givensn,mdassignment.sSee e.g. Ref 34d.

The shape of the SWNT PL from each SWNT species wasmodeled using Voigt profiles,36,37 which allowed the relativecontributions of Lorentzian and Gaussian components to beestimated. The Voigt profile is given by

Psx,yd =1

aGÎ ln 2

pKsx,yd, s1d

whereKsx,yd, called the “Voigt function,” is given by

FIG. 2. Resonantsupperd andnonresonantslowerd PL spectrafrom an aqueous suspension ofHiPco SWNTs. Both spectra con-tain transitions from eight SWNTspecies, each of which have beenfitted with Voigt profilessshadeddto illustrate the individual SWNTPL components.

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Ksx,yd =y

pE

−`

` exps− t2dy2 + sx − td2

dt

wherex =n − n0

aGÎln 2, y = aL

aGÎln 2, s2d

and whereaL and aG are the half widths of the Lorentzianand Gaussian components, respectively.

Wheny, proportional to the ratio of Lorentzian to Gauss-ian widths, was assumed to be the same for each peak, thePL profiles of eight nanotube species could be simulta-neously modeled in each of the 450 PL spectra displayed inFig. 1. The shaded peaks in Fig. 2 represent these fitted Voigt

PL profiles. It should be noted that while the amplitudes ofthese functions vary, their positionssn0d and widthssaL andaGd remain essentially unchanged over the entire 2D PLspectrum. From these fits, the full widths at half maximum ofthe SWNT PL were extracted and found to be:10.2±3.2 meV and 19.2±3 meV for the deconvolutedLorentzian and Gaussian components, respectively. The er-rors onaL andaG are 23s, wheres is the standard devia-tion of aL andaG calculated over all 450 PL spectra. By anapproximation given by Whiting,38 the Voigt widths at halfmaximum are calculated to be 30.2±1.4 meV which are con-sistent with previous ensemble measurements.7,39

Photoluminescence from thes11,0d and s7,3d nanotubescontributes shoulders to thes10,2d and s6,5d PL peaks, re-spectively, in Fig. 1; however, their inclusion in the PL fittingprocedure was found to be essential to obtain a consistentlygood fit over the entire excitation wavelength range. Indeed,the PL contribution from thes7,3d tubes was initially ne-glected until the fit residuals dictated that an additional Voigtprofile was required.

The SWNT absorption spectrum is presented in Fig. 3 andthe excitation and emission energy ranges used to producethe PL spectra in Fig. 1 are highlighted. The absorption fea-tures that lie within the PL energy range mirror peaks in thePL data, so by superimposing absorption and PL plots, theStokes shift of emission with respect to absorption energiescan be extracted for the SWNT species whose absorptionlines are narrow and distinct. This process is depicted in Fig.4 and the data are presented in Table I. The Stokes shifts arevery smalls,8 meVd for s10,2d, s7,5d, s6,5d, ands8,3d tubesand are in agreement with previously measured values.7,22,40

This indicates that the distribution of the nuclear coordinatesis little affected by photoexcitation into theA0 state; i.e.,there is very little reorganization of SWNT structure and

FIG. 3. The absorption spectrum of HiPco SWNTs suspended inwater using SDS surfactants1 wt %d. The emission and excitationenergy ranges that define the axes in Fig. 1 are highlighted.

FIG. 4. A comparison of PLand absorption spectra within thePL energy range defined in Fig. 3.Also shown are three of the Voigtprofiles corresponding to the PLcontributions from thes7,5d, s6,5d,and s8,3d tubes. Values of theStokes shifts for these SWNT spe-cies are calculated from the ener-gies of their Voigt PL contribu-tions and the positions of thecorresponding absorption peaks.

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surrounding solvent and/or surfactant molecules. This meansthat the difference in the magnitudes of the coupling betweenelectronic and vibrational statesselectron-lattice couplingdbetween the ground and excited states is small, resulting in aHuang-Rhys parametersSd close to zero. It is not yet clearhow the Stokes shift depends on surfactant; however, a re-cent report by Mooreet al.13 highlighted absolute shifts inboth absorption and emission energies with different surfac-tants. While the Stokes shift values may not be affected bysurfactant, these energy shifts could confirm the effect of thelocal dielectric constant on exciton binding energy reportedby Perebeinoset al.41

The strong Lorentzian component to the line shapes,which is observed in the PL spectra, complements the obser-vation of a small Stokes shift. An electronic system may becoupled to a number of vibrational modes, including in-tramolecular vibrations as well as “bath” modes such as localintermolecular modes and collective solvent modes. Nuclearmotions that couple to an electronic transition can often bemodeled as independent harmonic modes whose equilibriumposition is displaced between the two electronic states. Whennuclear dynamics are fast compared with the couplingstrengthsthe fast modulation limitd42,43 the electronic transi-tion is effectively decoupled from the bathssolvent and sur-factantd, the line shapes of absorption and emission are ex-pected to assume a Lorentzian form, and the Stokes shift willvanish. Moving away from this limit, an electronic systemthat is coupled to just a few independent degrees of freedom,such as the few allowed intermolecular vibrationssratherthan a continuous distribution of oscillatorsd, develops ab-sorption and emission line shapes with Voigt profiles.44 Thisis clearly what is seen in the micellar-suspended SWNT PLand is suggestive of weak coupling of the exciton with sur-rounding molecules and of a prominent intrananotube elec-tronic dephasing mechanism.

Time-resolved PL was measured ins6,5d, s7,5d, ands8,3dSWNTs by settinglex/lem to 565/978, 643/1024, and662/955 nm, respectively. The PL decay of thes7,5d tubes ispresented in Fig. 5 together with the instrument responsefunction sIRFd. The data were analyzed, as described in theprevious section, by convolution of a model decay functionwith the IRF.31 The analysis was performed over the full timerange of the decays0–10 ns in Fig. 5d and the features in the

decay at 5 ns and 9 ns were due to photomultiplier effects.45

Acceptable fits were obtained when a double exponentialmodel decay function,IPLstd=a1 exps−t /t1d+a2 exps−t /t2d,was used, and the resulting fit is shown by the solid line inFig. 5. The fractional contributionYn that each decay timetnconstitutes to the steady-state PL intensity46 is presented,along with values fortn andan in the inset table. The errorsin the values oftn are 23s, wheres is the standard devia-tion of tn. Although the fractional contribution oft2 is only1%, force fitting the data to one exponential decay was foundto add significant uncertainty to the value oft1.

A short lifetime component of,130 ps is found to domi-natesYn=99%d in each of the three tube types. This is con-siderably longer than the 5–15 ps decay times measured inprevious studies,22,26 and Maet al.24 have suggested that astrong dependence of PL lifetime on pump intensity could bedescribed by an exciton-exciton annihilation model. The ex-citation intensity used to generate the data heres1.4–1.731012 photons pulse−1 cm−2d is 102–104 times less intensethan the intensities used by Maet al.24 and, by extrapolatingtheir results, less than one exciton is generated per tube inour experiments. Thus, we expect there to be almost noexciton-exciton annihilation. Any fasts5–15 psd decayswould be readily resolvable in our experiment since the re-convolution procedure reliably extracts features that are5–10% of the instrument response function widths,200 psd.31 The shift between the peaks of the IRF and thePL decay curves arises because the IRF has a finite width,and it is not indicative of a PL rise time.

Natural radiative lifetimes of SWNTs can be obtained ifthe PL lifetime and PL quantum yieldsPLQYd are known.The PLQY,fPL, can be calculated for the ensemble when thefull PL spectrum has been recorded or for individual tubespecies when their individual contributions to the PL andabsorption spectra can be estimated. The former measure-ment, on aqueous solutions of HiPco SWNTs, has been re-ported to be,10−3 by O’Connell et al.7 and 1.7310−4 byWanget al.;26 however, since the data presented in our studycover a subset of the total SWNT population, the calculationof two single-tubefPL values are presented. The method forobtaining the contributions of individual semiconductingtubes to the ensemble PL has already been describedsseeFig. 2d, and a similar fitting method can be used to extract

TABLE I. SWNT PL, absorption, and Stokes shift energies.

SWNTspecies

Diametersd/nmd

PL energyseVd

Stokesshift s±2sd

smeVd

B0 PLEenergy

fEsB0d /eVg

B1 subpeak offset,D=EsB1d−EsB0d

smeVd

C0 PLEenergy

fEsC0d /eVg

s6,4d 0.692 1.4188 2.1361 209 3.815s7,3d 0.706 1.2424 2.4522 234s6,5d 0.757 1.2673 6.9±0.6 2.1887 229 3.606s9,1d 0.757 1.3583 1.7916 3.375s8,3d 0.782 1.2987 7.3±0.4 1.8686 211 3.515s7,5d 0.829 1.2110 5.3±1.0 1.9249 230 3.683s11,0d 0.873 1.1942 1.6693 206 3.281s10,2d 0.884 1.1730 5.2±2.8 1.6894 215 3.358

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their contributions to the absorption spectrum; however, boththe residual carbonaceous impurities and the tail of theSWNT p-plasmon resonance, whose peak lies at around5 eV,47–49 contribute to a significant absorption backgroundthat usually contributes more than 70% of the optical densityat the first absorption band of metallic tubes.20 Figure 6

shows a portion of the % absorption spectrum, containingtransitions to theB0 exciton, which has been fitted with Voigtfunctions offset from zero by a linear background functionthat approximates thep-plasmon tail. The two highlightedVoigt functions in Fig. 6 are located at the energies of theB0exciton photoluminescence excitationsPLEd peaks ofs8,3d

FIG. 5. Instrument response functionsIRFd and luminescence decay profile froms7,5d SWNTs. The solid line corresponds to the IRFconvoluted with a biexponential decay function. The inset table presents the corresponding lifetimes and yields of each function used to fitthe PL from thes6,5d, s7,5d, ands8,3d SWNTs.

FIG. 6. A section of the fitted% absorption spectrum containingtransitions to theB0 states ofsemiconducting SWNTs. TheVoigt profiles that contribute tothe fitted spectrum are offset fromzero by a linear background cor-rection sfreely variable in the fit-ting procedured that estimates thecontribution of both residual car-bonaceous impurities and theSWNT p-plasmon resonance tothe optical density.

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ands7,5d tubesssee Table Id and are therefore assigned to theabsorption contributions of these tubes.

Integrated PL intensities ofs8,3d and s7,5d tubes werecompared to a standard, perylene dye, Lumogen™ F Red300, with a PLQY of 100%. The resulting quantum yieldswere found to be,5310−4 for both s8,3d and s7,5d tubes,about half the ensemble value reported by O’Connellet al.7

In order to make this determination, we assume that theB0exciton relaxed to the emissiveA0 exciton state with unitquantum efficiency. Given the relationship between PLQYand the natural radiative and measured PL lifetimes,tr andtPL sfPL=tPL/trd, we conclude thattr

tains only the emission from the tube type of interest and issuperior to PLE spectra produced by taking vertical slicesdown Fig. 1 since these would contain signals from all tubeswhose PL overlaps those slices. Figure 7 shows the normal-ized excitation spectra of four SWNT species:s7,5d, s6,5d,s8,3d, ands6,4d. In each of the spectra the PL due to excita-tion of the B0 and C0 excitons is clearly observed and ap-pears to be Lorentzian in character.

Associated with theB0 exciton PLE peak is a subpeak,labeledB1, which is shifted by,200 meV from the mainpeak. The energy offset,D, of this peak from its parent peakhas been extracted from these data for seven tube speciesand, as illustrated in Fig. 8, it is found that there is an ap-proximately linear relationship betweenD /EsB0d and d,whereEsB0d is the energy of theB0 exciton PLE peak anddis the SWNT diameter. Values ofEsB0d, EsC0d, and D arepresented in Table I.

The subpeaks,B1, could either constitute a coupling of theelectronic transition with a vibrational mode associated withthe B0 statesa vibronic transitiond or could arise via a tran-sition to an excited excitonic state. Considering the lattercase, an exciton can often exist in a number of nongroundstate configurations that retain a correlatede−h+ pair. Recentcalculations29 have predicted that such states exist in ans8,0dSWNT, although their absorption cross section is likely to bevery low. According to these calculations,D /EsB0d

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