NANO LETTERS
Long-Lived Charged States in Single-Walled Carbon Nanotubes
2006 Vol. 6, No. 2 301-305
Christoph Gadermaier,*,† Enzo Menna,‡ Moreno Meneghetti,‡ W. Joshua Kennedy,§ Z. Valy Vardeny,§ and Guglielmo Lanzani† ULTRAS-INFM, Dipartimento di Fisica, Politecnico di Milano, P.za L. da Vinci 32, 20133 Milan, Italy, Department of Chemical Sciences, UniVersity of PadoVa, Via Marzolo 1, 35131 PadoVa, Italy, and Physics Department, UniVersity of Utah, 115 S 1400 E, Salt Lake City, Utah 84112 Received October 4, 2005; Revised Manuscript Received November 14, 2005
ABSTRACT We present continuous wave photoinduced absorption spectroscopy of single-walled carbon nanotubes dispersed in a polymer matrix. The spectrum is dominated by a modulation of the absorption line shape, predominantly of large diameter tubes, that we assigned to electroabsorption caused by local electric fields arising from trapped photoinduced charges. The lack of selectivity in the excitation points to an efficient migration of the photoexcited states, either the singlet excitons or the charges resulting from their dissociation
Single-walled carbon nanotubes are elongated members of the fullerene family1 that are currently the focus of intense multidisciplinary study because of their unique physical and chemical properties and their prospects for practical applications.2 Because of the nanometer scale diameter and extended dimension along the tube, single-walled carbon nanotubes (SWNTs) are considered to be quasi-one-dimensional (quasi1D) solids.2 Depending on tube diameter and chiral wrapping angle describing its construction from a graphene sheet, SWNTs can be either semiconducting or metallic.3,4 Within a simple tight binding approach, assuming delocalized states, transitions between Van-Hove singularities have been assumed as the dominant features of the absorption spectrum5 of semiconducting nanotubes. In recent years however, the importance of Coulomb interaction in quasi-1D electronic systems6 has been largely reckoned. Consequently a new picture for describing the elementary excitations in nanotubes is emerging, which considers bound electron-hole pairs in one dimension. Theory predicts that low dimensional Wannier excitons show large binding energy7 and very large oscillator strength almost exclusively toward the excitonic levels, suppressing the transitions toward the band (continuum) states. Recent improvements in sample preparation led to the discovery of fluorescence in isolated semiconducting SWNTs8,9 and to solid evidence on the role of electronelectron correlation and the existence of excitons.10-15 In particular, it is clear that they are responsible for the measured fluorescence, and that the tight binding approxima* Corresponding author. E-mail:
[email protected]. † ULTRAS-INFM, Dipartimento di Fisica, Politecnico di Milano. ‡ Department of Chemical Sciences, University of Padova. § Physics Department, University of Utah. 10.1021/nl051970t CCC: $33.50 Published on Web 12/30/2005
© 2006 American Chemical Society
tion to calculate the electronic band structure is insufficient for describing the features seen in the optical absorption spectrum of SWNTs. Long-lived photoexcitations, which play a crucial role in many device applications and reveal information on the presence of traps of both energy and charge in the material, have so far not been investigated. In this report we present the first study of photoexcitation dynamics on the millisecond time scale, suggesting the presence of long-lived excited states, which are tentatively assigned to charge carriers that modulate the absorption spectrum. Trapping of charges is typical of disordered materials, such as amorphous semiconductors and conjugated polymers, and is consistent with the observed preference to affect large diameter, smaller gap tubes. We studied samples of SWNTs grown by the high-pressure carbon monoxide procedure (HiPco). Purified HiPco tubes from Carbon Nanotechnologies, Inc., were functionalized with poly(ethylene glycol) (PEG) chains to improve dispersion in a polymer matrix. The derivatization was achieved through amidation of nanotube-bound carboxylic acids with PEG-amine16 The functionalized SWNTs were embedded in poly(methyl methacrylate) (PMMA) films that were cast on glass cover slips. Resonance Raman spectra showed that the oxidation reaction used for the functionalization destroyed the nanotubes with diameter below ≈0.85 nm.17 In this work we apply the continuous wave (cw) photoinduced absorption (PA) technique, which probes long-lived photoexcited states via their absorption. It consists of a cw excitation, most commonly a laser, which is periodically modulated. This causes a periodic variation in the population
of the photoexcited states and consequently also of the ground state. A broad-band light source probes the transmission of the sample, which undergoes a periodic variation, ∆T, as a consequence of the variation in the absorbing states population. The PA signal is commonly expressed as the normalized change in transmission, ∆T/T, which gives a direct measure of the change in the population of excited states. For slow modulation compared to the excited-state lifetime, the population modulation is almost in phase with the excitation, while for fast modulation it lags behind by almost 90°. Therefore, one usually measures both the inphase and quadrature (i.e., at 90° with respect to the excitation) components of the signal and relates to the respective components Nin and Nqu of the population modulation (see also below for details). The pump beam for the cw photoinduced absorption experiments was provided by either the fundamental (1.17 eV) or the second harmonic (2.33 eV) of a neodynium-YAG laser. The beam was modulated via mechanical chopping. The transmitted light from a halogen lamp was picked up by an amplified InGaAs photodiode, whose signal output was measured by a lock-in amplifier, with the reference signal provided by the chopper control unit. During the measurement the samples were kept under vacuum at liquid nitrogen temperature. Electroabsorption measures the change in the transmission of the sample in response to an electric field. This depends in a very specific way on characteristics of the electronic structure such as polarizability, dark states, and delocalization, providing useful information about them. The EA substrate consisted of two interdigitated sets of a few hundred gold electrodes 30 µm wide patterned on a sapphire disk. An applied potential V ) 600 V resulted in field strength F ) 2 × 105 V/cm. We varied V on the electrodes using a sinusoidal signal generator at f ) 1 kHz and a simple transformer to achieve high voltages. ∆T was measured using a diode detector and a lock-in amplifier set to twice the frequency (2f) of the applied field. Figure 1 shows the absorbance of an SWNT/PMMA sample in the spectral range where we performed PA measurements. For different samples and different spots on the sample the optical density varies without any significant changes in the shape of the spectrum. A series of peaks from different semiconducting SWNTs is found. The dashed line shows a fit of the absorption in the region 0.78-1.15 eV with five Lorentzian peaks plus a flat background, which perfectly reproduces the spectrum in this region. The parameters of these peaks are reported in Table 1. To give an idea of the possible chiralities involved, Table 2 shows the assignment of SWNTs as found in the literature.9,18,19 Figure 2 shows the PA spectrum for excitation at 2.33 eV at a modulation frequency of 12 Hz and a photon flux of 4 × 1018 cm-2 s-1. The spectrum shows a series of positive and negative peaks in the region of 0.7-1.2 eV, with the highest peak at 0.96 eV reaching a value of ∆T/T ) -0.004. In the range from 0.7 to 1.25 eV the quadrature and the inphase components of the signal have essentially the same shape and an almost constant ratio of 4:1, which hints to a dominant state of origin in this region, whose lifetime 302
Figure 1. Absorption spectrum of a SWNT/PMMA film (solid). The dashed lines are fits of the region 0.78-1.15 eV using five Lorentzian peaks. The bold line is the sum of these peaks plus a flat background, which is congruent with the measured spectrum. The inset shows the relative change in transmission for room and liquid nitrogen temperature. Table 1. Parameters of the Lorentzian Peaks Fitted to the Absorption Spectrum in Figure 1 and Their First and Second Derivatives Fitted to the PA Signal in Figure 4 peak no.
central position (eV)
width (eV)
height coeff
first derivative rel wt (%)
second derivative rel wt (%)
1 2 3 4 5
0.8301 0.9222 1.0037 1.0605 1.1234
0.0813 0.1035 0.0881 0.1098 0.1234
0.0085 0.0206 0.0081 0.0057 0.0069
62 38 0 0 0
10 38 52 0 0
determines this ratio. The inset in Figure 2 depicts the inphase and quadrature components of the 0.96 eV peak as a function of modulation frequency. The frequency dependence of the signal has been fitted with the following relations for the in-phase and quadrature components Nin and Nqu20 Nin ) g
β ω + β2
(1a)
Nqu ) g
ω ω + β2
(1b)
2
2
where ω is the angular modulation frequency, g is a generation term, and β ) 1/τ. For unimolecular decay (i.e., each photoexcitation decays independently) these are the exact analytic expressions and yield the lifetime τ. For bimolecular decay (i.e., due to mutual annihilation of photoexcitations), these are approximations21 that yield an effective lifetime depending on the excitation density. This simple model reproduces the frequency dependence very well with τ ) 43 ms. To check for contributions to the signal from sample heating during illumination, we measured the sample transmission for room temperature and liquid nitrogen temperature. In fact, we found a difference in the transmission, which is expressed in terms of ∆T/T relative to the low-temperature transmission in the inset of Figure 1. The negative sign means Nano Lett., Vol. 6, No. 2, 2006
Figure 2. Photoinduced absorption of SWCNTs for excitation at 2.33 eV for a modulation frequency of 12 Hz, in quadrature (solid) and in phase (dash) with the excitation. The inset shows the frequency dependence in phase (triangles) and quadrature (squares) components of the 0.96 eV peak. Solid lines are fits to a unimolecular decay. Table 2. First Optical Transition Energies and Tube Diameters of Selected SWNTs as a Function of Chiral Vector peak no. and energy interval
identification NT
E11/eV
d/nm
1: 0.770-0.879 eV
(10,9) (11,7) (14,1) (12,5) (13,3) (13,5) (10,8) (15,1) (11,6) (9,8) (13,0) (10,6) (12,2) (11,4) (12,4) (9,7) (13,2) (11,1) (8,7) (10,3) (10,5) (9,5) (11,3) (8,6) (12,1) (7,6) (9,4)
0.797 0.818 0.826 0.827 0.828 0.834 0.844 0.869 0.877 0.879 0.896 0.900 0.900 0.904 0.924 0.938 0.949 0.980 0.981 0.993 0.993 0.999 1.036 1.057 1.060 1.107 1.126
1.307 1.248 1.153 1.201 1.170 1.278 1.240 1.232 1.186 1.170 1.032 1.111 1.041 1.068 1.145 1.103 1.120 0.916 1.032 0.936 1.050 0.976 1.014 0.966 0.955 0.895 0.916
2: 0.880-0.979 eV
3: 0.980-1.039 eV
4: 1.040-1.099 eV 5: 1.100-1.170 eV
a higher transmission at higher temperature. The shape of this spectrum is almost identical to the absorbance spectrum, which means that higher temperature leads to a homogeneous decrease of the optical density and no changes in shape such as broadening. This reduction of the optical density is probably most simply due to thermal expansion, which reduces the number of absorbers in the illuminated area. Since it is completely different from the PA signal (see following figures) and bears the same sign over the whole spectral range, the PA signal is not due to sample heating, Nano Lett., Vol. 6, No. 2, 2006
Figure 3. Quadrature components of photoinduced absorption signal at a modulation frequency of 12 Hz for excitation at 1.17 eV (solid) and 2.33 eV (dash). The inset shows the excitation intensity dependence of the 0.96 eV peak (squares) and a fit to a power law (solid line).
although a small contribution from such an effect cannot be excluded. Figure 3 displays the PA spectrum under the same conditions as above, for excitation energies 1.17 and 2.33 eV. The shape and signal magnitude are almost the same. Photons at 1.17 eV pump the transition to the first excited state in smaller diameter, higher transition energy tubes and the second excited state of the larger diameter, lower transition energy ones. The 2.33 eV light populates the respective second and third electronic excited states. The higher electronic states relax to the first excited state with a time constant of 40 fs.22 For isolated tubes, achieved via dispersion in surfactant micelles,8,9 a fluorescence spectrum with sharp peaks has been found, whose position shows a clear dependence on the excitation energy. This has been explained with the selective excitation of a certain type (diameter and chiral vector) of nanotubes depending on the excitation energy. Such a selectivity is not found in our PA spectra. Since the nanotubes in our samples are intertwined into small bundles, they can exchange excitation energy. The excitation energy is therefore not confined to the tubes which absorb the photons, and it is also not confined to the type of tube which absorbs photons at the particular pump energy. We conclude that (i) the exchange of excitation energy is rather efficient and covers the whole variety of tubes that can be identified in the absorption spectrum and (ii) the excitation of metallic tubes, if occurring at all, does not affect the long time phenomena. Probably photoexcited electrons in metallic tubes thermalize back to the ground state before any scattering other than electron-phonon events can be effective. We note that this is one of the first experimental reports involving energy transfer and the specific mechanism in carbon nanotubes still has to be clarified. In the inset of Figure 3 the dependence of the 0.96 eV peak on the pump intensity is depicted. The intensity dependence of the signal can be fitted with a power-law dependence ∆T/T ) Iβ, with an exponent β ) 1.5. The intensity dependence is generally used to gain information about the nature of the generation and decay processes of the underlying photoexcited species and will be discussed in detail in the next section. 303
Figure 4. Quadrature PA signal at 12 Hz (solid) normalized to peak at 0.9 eV compared to a linear combination of first and second derivatives of the Lorentzians shown in Figure 1 with respect to energy (dash). The inset shows the electroabsorption signal.
The interpretation of the line shape is less straightforward. A tight succession of positive and negative peaks, on the other hand, is typical of a modulation, i.e., the result of small changes in line shape and position of the spectral features. Those could be due to a number of causes, as for example photoinduced strain on the nanotubes. On the basis of the comparison with previously studied conjugated polymers23 however, we suggest that electroabsorption (EA) is responsible for our spectra.24 In an electric field one-photon-allowed exciton states exhibit a Stark shift, while previously forbidden two-photon excitonic states become weakly allowed due to admixing with one-photon states and appear as peaks in the EA spectrum. The inset of Figure 4 shows an EA signal on a sample of the same type, which is consistent with other electroabsorption studies on SWNT samples.25 The peak positions of the PA and EA spectra are in good agreement, but their relative intensity is different, pointing toward different contribution by the individual nanotube chiralities. Moreover, the EA signal extends toward higher energies, i.e., beyond 1.2 eV, where PA is essentially zero. The occurrence of an electroabsorption signal upon photoexcitation can be rationalized if one assumes that after excitation charge states are formedsvia dissociation of excitons, as indicated by photoconductivity studies26sthat diffuse and get trapped in the sample, generating strong local electric fields, which modulate the absorption. Such a phenomenon, which has also been observed in conjugated polymers,23 is a photorefractive effect by nature.27 Standard photorefractivity involves changes in the real refractive index due to the electrooptic effect in χ(2) materials. By measuring PA, we observe changes in the imaginary part of the refractive index, i.e., a χ(3) process due to the Kerr effect. The photorefractive effect is usually realized in diffraction geometry, exploiting the periodicity in space caused by the interference of two exciting light beams. In our case illumination is homogeneous in space and modulated in time. In inorganic semiconductors, whose optical absorption spectra are governed by band-to-band transitions, the EA signal originates from the Frantz-Keldysh effect, which is due to field-induced changes in the transition probabilities 304
toward continuum states and shows a characteristic line shape with a F2/3 dependence on the electric field. This effect diminishes fast with increasing temperature. Since our spectra show neither the characteristic oscillations nor any pronounced temperature dependence, we conclude that this effect does not play an essential role in our measurements. Electronic transitions that involve excitons, on the other hand, show a first and second derivative line shape in EA due to quadratic and linear Stark shifts.28 In a first attempt (not displayed), overall first and second derivatives with respect to energy of the absorption spectrum have been applied to fit the PA. The sole use of either first or second derivative leads to incorrect peak positions while a combination of both correctly reproduces the peak positions and widths but not the relative peak intensities. Therefore we separately calculated the first and second derivatives of each of the five peaks and performed a weighted superposition to obtain the fit curve shown in Figure 4. The presented curve, which fits much better also the peak heights, is obtained with the coefficients for the higher energy peaks equal zero. (See Table 1 for the relative weights of the derivatives of the individual peaks.) Since the peaks represent different nanotube types with different transition energies, this means that the higher transition energy tubes of the ensemble do not contribute to the signal. As discussed above, the spectra hint toward an efficient migration of singlet excitons and/or the charges created toward lower energy tubes. On the other hand, the regular EA signal shows a much larger contribution by the higher transition energy tubes, since there the field is applied externally and not biased by migration and trapping of charges at low energy tubes. Both first and second derivative contributions to the EA signal are quadratic in the electric field. We have no means of estimating the electric field amplitude, but we can give a qualitative relation to the number of charges nc, which we assume to be located at defect-related trap sites.30 Inferring an average distance 2r ) nc-1/3 and a Coulombic field F ∼ r-2 ∼ nc2/3. Hence the signal should show a dependence nc4/3 on the number of trapped charges present. Assuming a linear dependence of nc with pump light intensity, this predicts a signal magnitude which is superlinear in the light intensity, in agreement with our findings in the inset of Figure 3, which is best fitted with an I1.5 power law. A comparison with the results obtained for conjugated polymers is meaningful due to the existing similarities. Longlived charged excitations are identified in quasi-steady-state PA spectra in many conjugated polymers.29 They have characteristic absorption spectra, comprising one or two bands in the visible-near-IR range, ascribed to molecularlike transitions within the ion. Here we observe their presence indirectly via the electric field effect on the absorption spectrum. Apparently they do not have strong absorption features in the explored range.
Conclusion The PA spectrum of a SWNT/PMMA blend where the nanotubes are entangled into small bundles shows a series Nano Lett., Vol. 6, No. 2, 2006
of narrow positive and negative peaks, which we interpret as electroabsorption (transient photorefractive effect) induced by local electric fields arising from photoinduced charge separation. Excitation at two different photon energies, likely reaching different sets of nanotubes, leads to the same spectra. The lack of selectivity in the excitation points to an efficient migration of the photoexcited states, either the singlet excitons or the charges resulting from their dissociation. The modeling of the PA spectra is consistent with this idea, describing EA as due to modulation of only the lower gap tubes which act as excitation traps. The frequency dependence of the signal suggests an effective lifetime of τ ) 43 ms of the trapped charges. Acknowledgment. We greatly appreciate the stimulating discussions with C. Manzoni, A. Gambetta, G. Cerullo, and E. Ehrenfreund. C.G. acknowledges the Erwin-Schro¨dinger Grant J2418-N02 from the Austrian Fonds zur Fo¨rderung der Wissenschaftlichen Forschung. Funding from MIUR (GR/No. 2004035502, RBAU017S8R, RBNE01P4JF) and from ITM-CNR is gratefully acknowledged. The work at the University of Utah was supported in part by the DOE Grant FG-04-ER46109. References (1) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerenes and Nanotubes; Academic Press: San Diego, CA, 1996. (2) Carbon Nanotubes: Synthesis, Structure, Properties, and Applications; Dresselhaus, M. S., Dresselhaus, G., Avouris, P., Eds.; Springer: Berlin, 2001; Vol. 80. (3) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998. (4) Bockrath, M.; Cobden, D. H.; Lu, J.; Rinzler, A. G.; Smalley, R. E.; Balents, L.; McEuen, P. L. Nature 1999, 397, 598. (5) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Phys. ReV. B 2000, 61, 2981. (6) Pope, M.; Swenberg, C. Electronic Processes in Organic Crystals and Polymers, 2nd ed.; Oxford University Press: Oxford, 1999.
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