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Length-Dependent Photoluminescence Lifetimes in Single-Walled Carbon Nanotubes Yuhei Miyauchi,*,†,‡ Kazunari Matsuda,† Yuki Yamamoto,§ Naotoshi Nakashima,§,| and Yoshihiko Kanemitsu†,⊥ Institute for Chemical Research, Kyoto UniVersity, Uji, Kyoto 611-0011, Japan, Center for Integrated Science and Engineering, Columbia UniVersity, New York, New York 10027, Department of Applied Chemistry, Graduate School of Engineering, Kyushu UniVersity, Fukuoka 819-0395, Japan, Japan Science and Technology Agency, CREST, 5 Sanbancho, Chiyoda-ku, Tokyo 102-0075, Japan, and Photonics and Electronics Science and Engineering Center, Kyoto UniVersity, Kyoto 615-8510, Japan ReceiVed: March 26, 2010; ReVised Manuscript ReceiVed: June 17, 2010
We describe the length-dependent exciton dynamics in DNA-wrapped single-walled carbon nanotubes (SWNTs) using time-resolved photoluminescence (PL) excitation correlation spectroscopy. We demonstrate that the effective PL lifetimes have substantial upper limits in longer SWNTs. Our results suggest that the exciton diffusion to the ends of the nanotube has only a limited contribution to the net nonradiative relaxation rate, and the nonradiative processes that occur before the excitons reach the ends of SWNT are the dominant contribution to the nonradiative lifetime. From the length-dependent PL lifetimes and relative intensities in DNA-wrapped SWNTs, the exciton diffusion length was found to be ∼50 nm, and the diffusion coefficient was ∼1 cm2/s. Introduction Single-walled carbon nanotubes (SWNTs) are a quasi-onedimensional material and have attracted considerable attention as promising candidates for use in future nano-optoelectronic devices.1 One of the most important material parameters for applications as light-emitting materials is the photoluminescence (PL) quantum yield. Although recent improvements in sample quality have improved the yields to ∼10-2-10-1,2-4 further dramatic improvement of the quantum yield is obviously still needed for the realization of efficient light-emitting devices. The PL quantum yields are determined from the radiative and nonradiative recombination rates. Because PL lifetimes (on the order of 10-100 ps5-9) are considerably shorter than the radiative lifetimes (on the order of 1-10 ns8), PL lifetimes are dominated by nonradiative recombination processes of excitons.10-13 It has been suggested that nonradiative exciton recombination occurs due to defects, processes mediated by doped carriers,14-16 and/or multiphonon emission.14 However, it has recently been proposed that recombination at the ends of the nanotube may be the dominant contributor to the nonradiative exciton relaxation rate in SWNTs.17 The length-dependent optical properties of SWNTs have recently been studied in some depth,18-21 and a length dependence of PL quantum yields was observed,18,19 which was attributed to exciton diffusion and subsequent nonradiative relaxation at the nanotube ends.17 A recent nearfield spectroscopy study also revealed that the PL intensity decreased toward the ends of the nanotube.22 However, the lack of information on the length-dependent PL lifetimes and intensities of the same sample resulted in considerable uncer* To whom correspondence should be addressed. E-mail: y.miyauchi@ at7.ecs.kyoto-u.ac.jp. † Institute for Chemical Research, Kyoto University. ‡ Columbia University. § Kyushu University. | Japan Science and Technology Agency. ⊥ Photonics and Electronics Science and Engineering Center, Kyoto University.
tainty as to the contribution of the ends of the nanotubes to the net nonradiative exciton relaxation rate in SWNTs. In this study, we measured the PL lifetimes and the relative PL intensities of different lengths of DNA-wrapped SWNTs simultaneously and revealed that these increased with increasing length of the nanotubes; however, there were asymptotic upper limits. We determined that the exciton diffusion length was ∼50 nm, which was extracted self-consistently with the length dependences of both the PL lifetimes and intensities. The exciton diffusion coefficient was found to be ∼1 cm2/s, which was determined from the estimated maximum PL lifetimes of ∼17 ps for the infinite length limit. We found that the PL lifetime was significantly shorter than the radiative lifetime, even for the infinite length limit. From this, it follows that the dominant nonradiative recombination process does not occur at the ends of the nanotube. Experimental Section The PL lifetimes were measured using a femtosecond excitation correlation (FEC) method to obtain the recombination lifetimes of excitons.8,23,24 In the FEC experiments, SWNTs were excited with optical pulses from a Ti:sapphire laser of central wavelength 730 nm, repetition rate 80 MHz, pulse duration ∼150 fs, and spectral width 8 nm. The two beams separated by the delay time τ were chopped at 800 and 670 Hz, respectively, and collinearly focused onto the same spot (∼10 µm). Only the PL signal components modulated at the sum frequency (1470 Hz) were detected as FEC signals with a photomultiplier and a lock-in amplifier after dispersion of PL by a monochromator. The measurements were carried out under the excitation condition of ∼100 µJ/cm2. We prepared length-separated oligoDNA [d(A)20-d(T)20]-SWNTs (DNA-wrapped SWNTs) in aqueous solutions using size-exclusion chromatography. The singlestranded oligo DNAs, (dA)20 and (dT)20, were purchased from Hokkaido System Science. Their purities estimated by HPLC are greater than 99%. The as-produced SWNTs, so-called HiPco, were obtained from Carbon Nanotechnologies, Inc., and used
10.1021/jp1027492 2010 American Chemical Society Published on Web 07/14/2010
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Miyauchi et al. TABLE 1: Average Nanotube Lengths and Standard Deviations, σ, in Each Fraction
Figure 1. (a) Obtained chromatogram for solutions with oligo-DNA [d(A)20-d(T)20]-SWNTs (dA_dT_SWNT, solid curve) and without SWNTs (dA_dT, dashed curve). Typical AFM images of SWNTs in fractions (b) 24-26 and (c) 32-34. Insets show histograms of nanotube lengths.
as received. The hybridization of the (dA)20 and (dT)20 were carried out by mixing their equimolar solutions (each 3 mL, 50 µM), followed by heating to 90 °C and then gradually allowed to cool to 5 °C. Solubilization of the SWNTs using the oligoDNAs was conducted following the procedures described in ref 25. Typically, ∼0.5 mg of the SWNTs was added to an aqueous solution of the oligo-DNA (5 mL, 25 µM tris-EDTA buffer, pH 8.0) and sonicated using a bath-type ultrasonic cleaner (Branson 5510) at temperatures below 5 °C for 1 h, followed by centrifugation (Sigma, 3K30C) at 60 000g at temperature below 5 °C for 1 h. The top 80% of the solutions were separated and used for this study. Tris-EDTA buffer (pH 8.0) was eluted at a flow rate of 1.0 mL/min. We collected fractions corresponding to the retention times from 24 to 36 min (fractions 24-26, 26-28, 28-30, 30-32, and 32-34), in which the obtained chromatograms with and without SWNTs (shown in Figure 1a) indicated that length-separated SWNTs were included. Atomic force microscopy (AFM) measurements were performed to investigate the length distribution of SWNTs in each fraction. Aqueous solutions of DNA-wrapped SWNTs were deposited onto mica substrates, spread using a spin coater for 1 min, and dried in vacuo for 2 h. We carefully investigated lengths of more than 50 SWNTs for each fraction from the AFM images.
fraction
average (nm)
σ (nm)
24-26 26-28 28-30 30-32 32-34
520 280 160 110 90
200 110 50 30 40
Figure 2a shows the optical absorption spectra of the lengthcontrolled SWNTs. The inset shows the absorption spectra around the E22 peaks after subtraction of the background. A recent report on the high-quality dispersion of SWNTs suggested that the large background in the absorption spectra was primarily due to bundled SWNTs, residual impurities, and/or other amorphous and graphitic carbon.4 Because of this, we subtracted the background signal to evaluate the net absorption of isolated SWNTs in the sample. We approximated the background signal to a linear function of energy and determined the coefficients of the linear function using regression. Figure 2b shows the PL spectra of each fraction excited at 1.69 eV (732 nm), which corresponds to the excitation energy of the E22 resonance of the (9, 4) SWNTs.26 We assigned the chirality (n, m) of the nanotube to each peak according to the data reported in ref 26. A slight increase in the relative PL peak intensities from the larger diameter SWNTs was observed when the nanotube length decreased. However, throughout all the fractions, no dramatic change in the relative peak intensities or positions corresponding to each (n, m) nanotube was observed, and the (9, 4) SWNTs remained the dominant contribution to the PL spectra (excited at 1.69 eV).
Results and Discussion Parts b and c of Figure 1 show typical AFM images of the SWNTs for fractions 24-26 and 32-34 on mica substrates, respectively. The fractions with shorter retention times tended to include longer SWNTs. The insets of Figure 1b,c show histograms of the measured SWNT lengths. The mean and standard deviation of the lengths for each fraction were obtained and are summarized in Table 1. The SWNTs have average lengths of ∼90-520 nm, depending on the retention time in each fraction. Hereafter, we will use the average lengths to refer to each fraction.
Figure 2. (a) Optical absorption and (b) PL spectra of each fraction. Fractions are referred by the average lengths of SWNTs given in Table 1. The inset in part a shows the absorption spectra after background subtraction, around the excitation energy of 1.69 eV for PL spectroscopy. The inset in part b shows the relative PL intensities for SWNTs with different average lengths. The dashed line shows a fit to eq 2 with τ2/τ1 ) 0.4 and LD = 65 nm. Error bars for the horizontal axis indicate (σ (where σ is given in Table 1).
Photoluminescence Lifetimes in SWNTs
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IC(τ) ∝ -(LNT - 2LD)τ1 exp(-τ/τ1) - 2LDτ2 exp(-τ/τ2) (1)
Figure 3. FEC signals for (9, 4) SWNTs with different average lengths under 1.69 eV excitation at ∼100 µJ/cm2. The upward direction on the vertical axis indicates that the FEC signals have a negative sign. The solid curves are fits to eq 1 with the global parameters τ1 ) 17 ( 4 ps, τ2 ) 7 ( 3 ps, and LD ) 40 ( 20 nm for all the decay curves corresponding to SWNTs with different lengths. The inset plots the calculated effective PL lifetime, τEFF, as a function of nanotube length using τ1 ) 17 ps, τ2 ) 7 ps, and LD ) 40 nm.
where τ1 and τ2 are the effective exciton lifetimes around the center and the end regions along SWNTs, respectively. We confirmed the validity of the approximation described above from the fact that the exciton decay population around the end regions obtained by solving the diffusion equation17 can be closely approximated by a single exponential function, when the τ1 is comparable to 2τ2. In this model, we assume that the effective lifetime in the central part τ1 is constant for the samples with different lengths and take the contribution of the ends into account as an effective exciton lifetime change in the region that is less than LD from the ends. From the above effective lifetime model, we can also roughly approximate the relationship between the nanotube length, LNT, and the relative PL intensities. Considering the change of effective PL lifetime within LD from the ends, the lengthdependent relative PL intensity IPL(LNT) is expressed as
IPL(LNT) ∝ (LNT - 2LD)
The inset in Figure 2b shows the length-dependence of the relative PL intensities of the SWNTs under 1.69 eV excitation. The relative PL intensity is proportional to the PL quantum yield and can be defined as the integrated PL intensity in the whole detection range (0.89-1.38 eV), normalized by the absorptance, for which the dominant contribution was from the (9, 4) SWNTs. The relative PL intensity was found to increase with increasing nanotube length; it was evident that longer SWNTs have higher PL quantum yields. To gain further insight into the length-dependent PL properties, we performed time-resolved PL measurements using the FEC method.8,23,24 Figure 3 shows the FEC decay curves of the (9, 4) SWNTs under 1.69 eV excitation at ∼100 µJ/cm2 plotted after subtracting the background signal for each fraction. A strong exciton-exciton annihilation effect in SWNTs enables us to observe single exciton decay under this excitation condition.24 Because the decay times of the FEC signals corresponding to PL lifetimes are considerably shorter than the radiative lifetimes, the PL lifetimes are dominated by the nonradiative recombination of excitons. We found that FEC decay became faster with decreasing nanotube length, LNT. The exciton dynamics depend on the length of the nanotube, and thus we conclude that, when an exciton is able to interact with the ends of the nanotube, an additional nonradiative recombination pathway becomes available. To analyze the length-dependent change in the FEC decay curve, we consider a nonradiative recombination process when the excitons reach the ends of the nanotube, in addition to other nonradiative processes unrelated to nanotube length. The FEC signal as a function of delay time, τ, in SWNTs can be expressed as IC(τ) ∝ -∫∞τ N(t) dt,24 where N(t) is the average exciton population as a function of time. For simplicity, we approximated the exciton population decay for SWNTs with ends as exponential functions. The FEC signals can be described as a combination of the contributions from the region around the end of the nanotube specified by the exciton diffusion length defined as LD and from the remaining central part of the SWNT, with length LNT - 2LD, as
∫0∞ exp(-t/τ1) dt + 2LD ∫0∞ exp(-t/τ2) dt ∞ LNT ∫0 exp(-t/τ1) dt (2)
Equation 2 can be rewritten as IPL(LNT) ∝ 1 -(2LD/LNT)(1 τ2/τ1). We estimated LD, τ1, and τ2 from a regression to the experimental results shown in Figure 3 and in the inset of Figure 2 using eqs 1 and 2, respectively. Equation 1 provides a good fit to the five experimentally obtained FEC decay curves for different values of LNT shown in Figure 3 with the global fitting parameters τ1 ) 17 ( 4 ps, τ2 ) 7 ( 3 ps (corresponding to τ2/τ1∼ 0.4), and LD ) 40 ( 20 nm for all the decay curves, where the average nanotube length for each fraction obtained from the AFM measurements was used. In addition to the FEC signals, eq 2 provides a good fit to the length dependence of the relative PL intensities in the inset of Figure 2b with LD ) 65 ( 10 nm and τ2/τ1 ) 0.4 (fixed in the fitting procedure), indicating that the length-dependence of the PL lifetimes and intensities are consistent with each other. The value of τ1 directly corresponds to the exciton lifetime without the effects of the ends of the nanotubes, i.e., the lifetime of an infinitely long SWNT, τ∞ (τ∞ ) τ1 = 17 ps). The inset in Figure 3 shows the calculated effective PL lifetime τEFF of SWNTs as a function of LNT, defined as τEFF ) [(LNT - 2LD)τ1 + 2LDτ2]/LNT, when τ1 ) 17 ps, τ2 ) 7 ps, and LD ) 40 nm. τEFF is proportional to IPL(LNT). The effective lifetime increases with an increase in LNT and asymptotically approaches a limiting value in the infinite length limit (i.e., τ∞). From LD = 40 nm and τ∞ = 17 ps, we can evaluate the exciton diffusion coefficient D ∼ 1 cm2/s in the DNA-wrapped SWNTs using the relationship, D ) LD2/τ∞. The obtained exciton diffusion coefficient D ∼ 1 cm2/s is consistent with previously reported values of D ∼ 0.1-2 cm2/s.27-29 Although the nonradiative exciton relaxation at the ends of the nanotube has a significant contribution to the PL intensity and dynamics of short SWNTs, as discussed above, our results indicate that nonradiative relaxation of excitons in the DNAwrapped SWNTs still occurs at a relatively fast rate without the effects of the ends. Rajan et al.17 have recently proposed an
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exciton diffusion model, in which the nonradiative relaxation of excitons at the nanotube ends dominates the PL lifetimes. In their model, only exciton quenching at the ends contributed to the nonradiative recombination, and the calculated PL lifetimes became longer as a function of the squared nanotube length. However, our results indicate that there are substantial upper limits of PL lifetimes for long SWNTs and that the estimated lifetime for an infinite-length SWNT is still much shorter than the radiative lifetime of excitons. This suggests that the PL lifetimes on the order of 10 ps in the DNA-wrapped SWNTs are dominated by nonradiative pathways such as scattering by unintentionally doped carriers and/or quenching at defect sites rather than quenching at the nanotube ends. Further studies to clarify which are the dominant nonradiative pathways are required to gain an understanding of the exciton dynamics in SWNTs, which is also required for significant improvement in PL quantum yields. In summary, we demonstrated the length dependence of exciton dynamics in length-controlled DNA-wrapped SWNTs (LNT ∼ 90-520 nm). We found that both the relative PL intensities and lifetimes increased with increasing nanotube length; however, the length dependence shows saturation behavior for long nanotubes. Our results indicate that excitons in SWNTs with PL lifetimes on the order of 10 ps have dominant nonradiative relaxation paths other than quenching at the ends of the nanotubes. We evaluated the exciton diffusion length and found LD∼50 nm and a diffusion coefficient of D ∼ 1 cm2/s in DNA-wrapped SWNTs. Acknowledgment. Part of this work at Kyoto University was supported by JSPS KAKENHI (No. 20340075) and MEXT KAKENHI (Nos. 20048004 and 20104006) and by JSPS KAKENHI (No. 21350110) for N.N. One of the authors (Y.M.) was supported by a JSPS Research Fellowships (No. 20-3712). References and Notes (1) Avouris, P.; Freitag, M.; Perebeinos, V. Nature Photon. 2008, 2, 341. (2) Crochet, J.; Clemens, M.; Hertel, T. J. Am. Chem. Soc. 2007, 129, 8058.
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