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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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