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Ultrafast Optical Spectroscopy of Micelle-Suspended Single-Walled Carbon Nanotubes

a r X i v :c o n d -m a t /0308233v 2 [c o n d -m a t .m e s -h a l l ] 4 M a r 2004

myjournal manuscript No.(will be inserted by the editor)

J.Kono 1?,G.N.Ostojic 1,S.Zaric 1,M.S.Strano 2??,V.C.Moore 2,J.Shaver 2,R.H.Hauge 2,and R.E.Smalley 2

Department of Electrical and Computer Engineering,Rice Quantum Institute,and Center for Nanoscale Science and Tech-nology,Rice University,Houston,Texas 77005

Department of Chemistry,Rice Quantum Institute,and Center for Nanoscale Science and Technology,Rice University,Houston,Texas 77005

Received:date /Revised version:date

Abstract We present results of wavelength-dependent ultrafast pump-probe experiments on micelle-suspended single-walled carbon nanotubes.The linear absorption and photoluminescence spectra of the samples show a number of chirality-dependent peaks,and consequently,the pump-probe results sensitively depend on the wave-length.In the wavelength range corresponding to the second van Hove singularities (VHSs),we observe sub-picosecond decays,as has been seen in previous pump-probe studies.We ascribe these ultrafast decays to intra-band carrier relaxation.On the other hand,in the wave-length range corresponding to the ?rst VHSs,we observe two distinct regimes in ultrafast carrier relaxation:fast (0.3-1.2ps)and slow (5-20ps).The slow component,which has not been observed previously,is resonantly enhanced whenever the pump photon energy resonates with an interband absorption peak,and we attribute it to radiative carrier recombination.Finally,the slow com-ponent is dependent on the pH of the solution,which suggests an important role played by H +ions surround-ing the nanotubes.

Corresponding author;kono@https://www.wendangku.net/doc/1d18267821.html,.

Present address:Department of Chemical and Biomolec-ular Engineering,University of Illinois,Urbana,IL.

for excitons in 1-D systems [1,2,3],SWNTs are expected to show a new class of optical phenomena that arise from their unique tubular structure with varying diam-eters and chiral angles.Linear and nonlinear optical co-e?cients are expected to be diameter-and chirality-dependent,and an external magnetic ?eld is expected to induce drastic modi?cations on their band structure via the Aharonov-Bohm phase [4,5,6,7].Furthermore,nonlinear harmonic generation is expected to be highly selective for creating certain orders of high harmonics [8].

However,these predicted optical phenomena and prop-erties have not been probed experimentally.This is be-cause in standard production methods SWNTs appear in the form of bundles (or ‘ropes’)due to their strong van der Waals forces.This ‘roping’results in signi?-cant broadening of electronic states,smearing out any chirality-dependent features in optical spectra [9,10,11,12,13,14,15].Very recently,a new technique for produc-ing individually suspended SWNTs has been reported [16].These samples revealed,for the ?rst time,a num-ber of clearly observable peaks in linear absorption and photoluminescence (PL)spectra,corresponding to inter-band transitions in di?erent types of tubes.A subse-quent PL excitation (PLE)spectroscopy study success-fully provided detailed peak assignments [17,18].These seminal studies have provided opportunities to system-atically study other predicted,unique optical properties of SWNTs.

Ultrafast laser spectroscopy is one of the best meth-ods for measuring carrier distribution functions and re-laxation https://www.wendangku.net/doc/1d18267821.html,ing a wide variety of techniques employing femtosecond pulses,one can directly exam-ine dynamical processes after creation of electron-hole pairs across the band gap,i.e.,carrier dephasing pro-cesses,carrier-carrier scattering,carrier-phonon scatter-ing,exciton formation,and radiative and non-radiative recombination dynamics.There have been several ultra-

2J.Kono et al.

fast

optical studies of SWNTs[19,20,21,22].Hertel and

Moos[19]used ultrafast photoemission spectroscopy to determine thermalization times in metallic SWNTs to be～200fs.Three groups[20,21,22]independently ob-served subpicosecond to a ps lifetimes for semiconduct-ing SWNTs in pump-probe spectroscopy.Although such ultrashort lifetimes can be expected for intraband re-laxation towards the band edge,the microscopic origin of the fast interband decay(which is likely to be non-radiative)is still unclear.One important issue is that these studies were performed on bundled SWNTs,which did not show any PL.It is thus desired to carry out ultra-fast spectroscopy on SWNT samples that show chirality-assigned absorption and PL peaks.

In this article,we report results of a femtosecond pump-probe study of chirality-assigned SWNTs.The lin-ear absorption and PL spectra of such micelle-suspended SWNT samples show a number of chirality-dependent peaks,and as a result,the pump-probe data sensitively

depends on the wavelength used.In the wavelength range corresponding to the second van Hove singularities(VHSs), we observe ultrafast(sub-picosecond)decays,as has been reported previously[20,21,22].We ascribe these ultra-fast decays to intraband carrier relaxation.On the other hand,in the wavelength range corresponding to the?rst VHSs,we observe two distinct regimes in ultrafast carrier relaxation:fast(0.3-1.2ps)and slow(5-20ps).The slow component has not been observed previously,is reso-nantly enhanced when the pump photon energy matches an absorption peak,and is attributed to radiative car-rier recombination.The slow component is also strongly dependent on the pH of the solution,especially in large diameter tubes.

2Samples Studied

The SWNTs studied in the present work were dispersed in aqueous sodium dodecyl sulfate(SDS)surfactant,son-icated,and centrifuged,which left micelle-suspended nan-otube solutions.Details of the sample preparation method were described previously[16].

Typical linear absorption and photoluminescence(PL) spectra for such micelle-suspended SWNTs are shown in Fig.1(b),together with a schematic density of states ver-sus energy of semiconducting SWCNTs in Fig.1(a).The PL peaks occur in the near-infrared(～0.9-1.4eV)and are due to transitions involving the?rst conduction(E1) and valence(H1)subbands.The absorption spectrum shows peaks from the near-infrared to the visible range, consisting of three overlapping bands:E1H1transitions in semiconducting tubes(0.78-1.55eV),E2H2transi-tions in semiconducting tubes(1.38-2.26eV),and transi-tions in metallic tubes(2.07-3.11eV).Detailed analyses and interpretations of these linear absorption/emission features are described in[17,18].

(

)

Fig.

ter

was

cal parametric ampli?er(OPA)pumped by a chirped pulse ampli?er(Clark-MXR CPA2010).We used a low pulse-repetition rate(1kHz)for minimizing the average power and reducing any thermal e?ects while keeping the?uence high.To detect small photoinduced changes in probe transmission,we synchronously chopped the pump beam at500Hz and measured the transmission with(T)and without(T0)the pump using two di?erent gates of a box-car integrator.The smallest detectable di?erential transmission[(T?T0)/T0≡?T/T0]was ～10?4.We used a noncollinear geometry with a pump beam diameter of～220μm in the overlap area.We tuned the OPA throughout the range of?rst subband tran-sitions(i.e.,E1H1transitions;see Fig.1)with photon energies hν=0.8eV to1.13eV(wavelengthsλ=1.1μm to1.55μm).In addition,by directly using the CPA beam(hν=1.60eV,λ=775nm),we probed a region of second subband transitions(E2H2).

Ultrafast Optical Spectroscopy of Micelle-Suspended Single-Walled Carbon Nanotubes

?T /T 0

Time Delay (ps)

Fig.2Ultrafast pump-probe data at two wavelengths,cor-responding to ?rst and second subband transitions.A very fast single decay is seen in the second subband case while two decay components (τ1and τ2)are clearly seen in the ?rst sub-band case.Solid lines show Gaussian and exponential ?ts in the appropriate delay regimes.

4Experimental Results

4.1First vs.Second Subband Excitations

Figure 2shows typical di?erential transmission (?T/T 0)data as a function of time delay.Two traces are shown,taken at 0.89eV (1393nm)and 1.60eV (775nm),cor-responding to E 1H 1and E 2H 2ranges,respectively (refer to Fig.1).Both show a positive change (or an increase)in transmission,i.e.,photoinduced bleaching,which is consistent with band ?lling.An exponential ?t reveals a fast,single decay time of 770fs for the E 2H 2transi-tion,which is consistent with earlier reports and can be explained by the very fast intraband carrier relaxation towards the band edge [22].On the contrary,data in the range of E 1H 1transitions exhibit multiple exponen-tial decays .The major decay of the photoinduced signal happens in the ?rst picosecond (with decay time τ1),which is followed by a much slower relaxation process.For the particular data shown in Fig.2,we obtained an exponential decay time of τ2≈10ps.This long decay time has not been reported previously for either metallic [19]or semiconducting SWNTs [20,21,22].4.2Pump Fluence Dependence

For both ?rst and second subband transitions,the pump ?uence dependence of the maximum value of ?T/T 0re-veals clear saturation at high ?uences,as shown in Fig.3.This implies that,in the saturation regime,most of the

M a x i m u m ?T /T 0

Pump Fluence (mJ/cm

)

Fig.3The pump ?uence dependence of the maximum pho-toinduced transmission change at the two wavelengths cor-responding to the two traces in Fig.2.In both cases clear saturation is seen.

?T /T 0

Time Delay (ps)

Fig.4Power-dependent pump-probe spectroscopy data taken at a wavelength of 1402nm (or a photon energy of 0.884eV).The decay dynamics do not show any power dependence,excluding any nonlinear recombination mechanisms.

carrier states are ?lled up and thus the sample absorp-tion is nearly completely quenched.A careful analysis of the di?erential transmission decays for the hν=0.89eV case showed that relaxation dynamics are not de-pendent on the pump ?uence,including the saturation regime.As an example,in Fig.4we show pump-probe data at a wavelength of 1402nm for four di?erent pump ?uences.This precludes the possibility of any nonlinear recombination process such as the Auger recombination.

4J.Kono et al.

α (c m -1

)

M a x i m u m ?T /T 0

Energy (eV)

0.20

0.15

0.100.05

0.00

Slow/Fast

Fig.5(a)Linear absorption in the E 1H 1range.The num-bers (1-16)correspond to the 16photon energies at which pump-probe measurements were made.(b)The peak value of ?T /T 0(left axis)and the ratio of slow to fast components (right axis)vs.photon energy.

4.3Resonant vs.Non-resonant Excitations

To study any di?erences between resonant and non-resonant excitations in carrier relaxation as well as any diameter-and/or chirality-dependent phenomena,we scanned the photon energy from 0.8eV to 1.1eV,corresponding to the E 1H 1transitions of 0.82-1.29nm diameter tubes

[17].For all the photon energies,the pump ?uence was kept constant at 1mJ/cm 2,which is below the saturation regime [see Fig.3].Figure 5(a)shows the linear absorp-tion spectrum in the E 1H 1transition range.The photon energies at which we performed pump-probe measure-ments are labeled 1?16,covering both peaks and val-leys in absorption.Figure 5(b)shows the maximum value of ?T/T 0as a function of photon energy;it loosely fol-lows the absorption curve in (a).Also shown in Fig.5(b)(right vertical axis)is the ratio of the slow component (de?ned as ?T/T 0at 5ps)to the fast component (de-?ned as ?T/T 0at 0ps)as a function of photon energy;it also follows the absorption curve in (a),indicating that the slow component is resonantly enhanced at absorp-tion peaks.

Time Delay (ps)

?T /T 0

Fig.6Wavelength-dependent (one-color)pump-probe spec-troscopy data,corresponding to the photon energies labeled #2,#3,#4,#6,#7,#8,#11,and #13in Fig.5(a),cov-ering both absorption peaks and valleys.For the energies corresponding to absorption peaks [(a),(c),(e),and (g)],the chirality indices (n ,m )of the SWNTs probed at those en-ergies are (a):(10,2),(c):(12,1)and (8,6),(e):(10,3)and (10,5),and (g):(11,4).

Ultrafast Optical Spectroscopy of Micelle-Suspended Single-Walled Carbon Nanotubes 5

?T /T 0

?T /T 0?T /T 0

Time Delay (ps)

Fig.7pH-dependent pump-probe data for di?erent wave-lengths.The pH dependence becomes stronger for smaller photon energies,corresponding to larger-diameter SWNTs.

To demonstrate this more directly,eight traces of dif-ferential transmission dynamics taken at di?erent pho-ton energies are shown in Figs.6(a)-6(h).The chosen photon energies correspond to the peaks and valleys in the linear absorbtion data in Fig.5(a),marked as 2,3,4,6,7,8,11,and 13.For the photon energies correspond-ing to peaks in linear absorption [(a),(c),(e),and (g)],the chirality indices (n ,m ),assigned through PL excita-tion spectroscopy [17,18],are (a):(10,2),(c):(12,1)and (8,6),(e):(10,3)and (10,5),and (g):(11,4).The slow component is clearly observable for the photon energies corresponding to absorption peaks [(a),(c),(e)and (g)]while the traces corresponding to valleys [(b),(d),(f)and (h)]show only the initial,fast decay.4.4pH Dependence

By adjusting the pH of the solution via adding NaOH or HCl,we found that pump-probe dynamics are strongly dependent on the pH and the dependence is stronger at longer wavelengths (or larger tube diameters).Speci?-cally,we observed that the slow component drastically

diminishes as the pH is reduced.Examples are shown in Fig.7.As previously reported [23],adding hydrogen ions,H +,to the solution (or,equivalently,decreasing the pH value)diminishes,and ?nally collapses,linear absorption and PL peaks.This e?ect starts from the longer wavelength side,i.e.,from larger diameter tubes.The corresponding reduction and disappearance of the slow component shows exactly the same trend,as shown in Fig.7.For example,at hν=1.118eV (or 1.11μm),there is almost no change in pump-probe dynamics from pH =5.5to pH =4.5[see Fig.7(a)].However,as the pho-ton energy is decreased to 0.906eV [(b)],0.879eV [(c)],and 0.853eV [(d)],the disappearance of the slow com-ponent becomes increasingly more drastic.Figures 8(a),8(b),and 8(c)show,respectively,the pH-dependence of (a)near-infrared absorbance spectra in the E 1H 1energy range,(b)the maximum value of the di?erential trans-mission,and (c)the ratio of the slow component (?T/T 0at 3ps)to the fast component (?T/T 0at 0ps)as func-tions of photon energy.It is clearly seen that all the three quantities decrease with decreasing pH,and the decrease is more signi?cant at longer wavelengths (or wider-diameter tubes).

5Discussion

As we presented in the last section,our wavelength-dependent single-color pump-probe spectroscopy data on micelle-suspended SWNTs revealed two di?erent de-cay components,suggesting two di?erent carrier relax-ation processes.One component is fast (0.3-1.2ps)and the other is slow (5-20ps).In the following we discuss possible origins of these two dynamical processes as well as the intriguing pH dependence of the pump-probe data we obtained.

Both the positive sign of the di?erential transmission and the initial ultrafast (?1ps)relaxation agree with the recent reports for semiconducting SWNTs [20,21,22].The positive sign can be interpreted as state ?lling as the cause of the photo-bleaching signal and is consistent with the saturation at high ?uences (Fig.3).Namely,the pump-induced carriers ?ll states and reduce the probe absorption.We believe that the ultrafast decay mech-anism is non-radiative (i.e.,phonon and/or impurity-mediated)and intraband .It is likely to be non-radiative because this signal exists even for samples that do not luminesce [20,21,22].It is likely to be intraband relax-ation (as opposed to interband relaxation)since it exists both in resonant and non-resonant cases.Note that even when the photon energy is resonant with the E 1H 1ab-sorption peak of a particular tube type,it creates non-resonant carriers in other types of tubes whose band gaps are smaller than that of the resonant tube.Note also that we are not seeing any pump-power-dependent decay times,as shown in Fig.4,which precludes carrier-density-dependent non-radiative processes such as Auger

6J.Kono et al.

Energy (eV)

Fig.8pH-dependence of(a)near-infrared absorbance in the E1H1energy range,(b)maximum value of the di?er-ential transmission,and(c)the ratio of the slow component (?T/T0at3ps)to the fast component(?T/T0at0ps)as a function of photon energy.

recombination as the origin of the fast decay component. In addition,it is likely that there is some coherent contri-bution to the pump-probe signal in this ultrashort time scale.However,since we have not observed any four-wave mixing signal,we do not have an estimate on the dephasing time and thus will not discuss how large this contribution is.

On the other hand,the slow decay signal,which was resonantly enhanced when the photon energy coincided with an interband absorption peak,has not been re-ported previously.We interpret this slow component as interband carrier recombination.Note that in bundled samples band edges are not well de?ned for individual tubes due to electronic coupling,and thus photo-created carriers cannot show clear interband dynamics in pump-probe measurements.In other words,there is no clear distinction between inter-tube dynamics and intraband dynamics in bundled tubes because van Hove singular-ities of di?erent tube types form a van Hove absorp-tion band.We further argue that the slow component we observed is probably related to radiative recombi-nation.An important fact for supporting this claim is that in the previous work no PL was observed whereas

our sample exhibits PL peaks at the same energies as E1H1absorption peaks(see Fig.1).In addition,reduc-ing the pH of the solution destroys PL and absorption peaks while at the same time the slow decay also van-ishes(see Fig.7),indicating an intimate relationship be-tween PL and the slow decay signal.The actual value of the radiative recombination lifetimeτr depends on the value of the radiative e?ciency(or quantum yield)η=τ?1

/(τ?1

+τ?1

),whereτnr is the nonradiative lifetime, since what we measure experimentally is the total de-

cay rate,τ?1=τ?1

+τ?1

.Direct measurements ofτr through time-resolved PL are in progress.

Finally,we propose possible scenarios for the drastic pH dependence we observed.Decreasing the pH leads to an increase in the density of H+.First,adsorbed H+ions on the nanotube surface could add a relax-ation channel by the creation of ultrafast carrier trap-ping centers(defects).This should make the fast non-radiative recombination dominant over the slower radia-tive recombination if the density of such trapping cen-ters is high.In addition,as previously noted,H+ions e?ectively act as acceptors in SWNTs,and thus the Fermi energy(E F)depends on the H+density.When the density is so high that E F lies inside the valence band,interband absorption peaks disappear,irrespec-tive of whether the peaks are due to excitons or van Hove singularities.This can be viewed as a1-D manifestation of the well-known Burstein-Moss e?ect[24,25].Larger-diameter tubes are expected to have smaller acceptor binding energies due to their smaller e?ective masses, and thus should be more susceptible to pH changes.In a heavy doping regime,there is a degenerate hole gas in the valence band,which can completely quench excitonic processes.

6Summary

In summary,we have carried out an ultrafast optical study of micelle-suspended single-walled carbon nanotubes. We have observed two relaxation regimes in the dynam-ics of micelle-suspended single-walled carbon nanotubes under resonant excitations.We interpret the previously observed shorter decay timeτ1as nonradiative intra-band relaxation and the previously unobserved larger decay timeτ2as related to radiative interband recom-bination.The relaxation of photoexcited carriers can be made faster by increasing the density of H+ions in the solution while simply increasing the number of photoex-cited carriers does not change the dynamics.The sensi-tive pH dependence provides a novel means to chemically control carrier states and dynamics in nanotubes.

Ultrafast Optical Spectroscopy of Micelle-Suspended Single-Walled Carbon Nanotubes7

7Acknowledgements

This work was supported by the Robert A.Welch Foun-dation(Grant No.C-1509),the Texas Advanced Tech-nology Program(Project No.003604-0001-2001),and the National Science Foundation CAREER Award(Grant No.DMR-0134058).

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