Photoinduced spontaneous free-carrier generation in semiconducting single-walled carbon nanotubes.

Strong quantum confinement and low dielectric screening impart single-walled carbon nanotubes with exciton-binding energies substantially exceeding kBT at room temperature. Despite these large binding energies, reported photoluminescence quantum yields are typically low and some studies suggest that photoexcitation of carbon nanotube excitonic transitions can produce free charge carriers. Here we report the direct measurement of long-lived free-carrier generation in chirality-pure, single-walled carbon nanotubes in a low dielectric solvent. Time-resolved microwave conductivity enables contactless and quantitative measurement of the real and imaginary photoconductance of individually suspended nanotubes. The conditions of the microwave conductivity measurement allow us to avoid the complications of most previous measurements of nanotube free-carrier generation, including tube-tube/tube-electrode contact, dielectric screening by nearby excitons and many-body interactions. Even at low photon fluence (approximately 0.05 excitons per μm length of tubes), we directly observe free carriers on excitation of the first and second carbon nanotube exciton transitions.

Photoinduced free-carrier generation in semiconducting single-walled carbon nanotubes (SWCNTs) has been controversial because of the substantial binding energy (hundreds of meV) of photogenerated excitons, coulombically bound electron–hole pairs12. Although a low probability of exciton dissociation is expected in SWCNTs, photoinduced carrier generation has been observed in neat SWCNT samples in a number of studies3456789101112. Most of these examples of carrier generation have been observed in solid-state samples featuring either tube–tube contacts or tube–electrode contacts. As these interfaces can likely serve as carrier-generation sites, they obscure the intrinsic properties of the individual nanotubes. Examples of these potential solid-state artefacts include heterogeneous chiralities of SWCNTs that may form type-I or type-II energy-level alignments in SWCNT bundles, electrostatic screening effects in SWCNT aggregates that can enhance free-carrier generation, SWCNTs on substrates in air that often become p-doped or potential morphological defects or contacts with electrodes in which electric fields can dissociate excitons367111314. Therefore, the prevalence of intrinsic carrier generation processes in well-isolated SWCNTs remains unclear. Importantly, such unintentional carrier generation can be detrimental to applications requiring long exciton lifetimes and high luminescence quantum yields, such as biological imaging and photovoltaics151617.

Recent solution-phase photoluminescence and transient absorption studies have suggested that charges are generated at relatively high incident photon fluences in aqueous dispersions918. However, it is important to note that the exciton binding energy is predicted to decrease dramatically with increasing dielectric constant of the solvent (ɛr(H2O)=80.1, ref. 19), and high incident photon fluences can reduce the exciton binding energy via screening, facilitate exciton–exciton collisions that lead to Auger-like photoionization or even damage the CNT surface to generate defects.

In this study we demonstrate that free charge generation takes place in individual SWCNTs suspended in toluene (ɛr=2.38, ref. 19), even at ultra-low excitation fluences, which rules out both high dielectric and multi-exciton effects. We use flash-photolysis time-resolved microwave conductivity (fp-TRMC) on solution-phase samples, to study the complex photoconductance of individually suspended (7,5)-chirality-enriched SWCNTs ((7,5)-SWCNTs). The high sensitivity of this technique allows us to use excitation fluences that are much lower than has previously been possible (lower than 1011 photons per cm2); the lowest excitation fluences correspond to absorbed photon densities of approximately 0.04–0.06 photons per μm length of (7,5)-SWCNTs. We find that the low-fluence yield mobility product Φ∑μ, which is the product of charge-carrier generation efficiency Φ and the sum ∑μ of electron and hole mobilities μe+μh in isolated (7,5)-SWCNTs is approximately 0.17 and 0.4 cm2 V−1 s−1 following S11 and S22 photoexcitation, respectively.

Results

Dispersion of (7,5)-SWCNTs in toluene

The electronic absorption spectrum of (7,5)-SWCNTs suspended in toluene by poly[9,9-dioctylfluorenyl-2,7-diyl] (PFO) is shown in Figure 1a. Employing established methods with PFO as a dispersing agent2021, we obtain highly (7,5)-chirality enriched SWCNT solution and remove excess PFO until a polymer:SWCNT mass ratio of approximately 4 is obtained (see Methods for full details of sample preparation). The distinctive S11 and S22 excitonic transitions of (7,5)-SWCNTs, peaking at 1,044 and 653 nm, respectively, confirm the purity of the (7,5)-SWCNT solution sample. In addition, electronic absorption data preclude the possibility that PFO is excited in the range from 450 to 1,200 nm. The energy-level diagram shown in Figure 1b illustrates that the PFO polymers2223 and the (7,5)-SWCNTs24 form a type-I heterostructure and, therefore, it is evident that the (7,5)-SWCNT* state generated via S11 excitation should not exhibit electron/energy transfer from (7,5)-SWCNTs to PFO polymers, which is consistent with previous literature results25.

Figure 1

(7,5)-SWCNT dispersion wrapped with PFO polymer.

(a) Electronic absorption spectra of (7,5)-SWCNTs suspended in toluene via polymer wrapping in PFO (in red) and of PFO polymer dissolved in toluene (in blue), respectively (see Methods for sample preparation). (b) Energy-level diagram illustrating that the PFO polymer and (7,5)-SWCNTs form a type-I heterostructure. A dotted line depicts the S11 state of [(7,5)-SWCNT]*.

Probing photoinduced free-carrier generation of SWCNTs

We employ a cavity-based fp-TRMC technique to explore photoinduced free-carrier generation and recombination dynamics in the solution-phase (7,5)-SWCNTs. The use of the resonance cavity in fp-TRMC experiments allows us to operate at very low excitation photon fluences (approximately 1010–1012 photons per cm2) and to explicitly measure the complex conductivity, avoiding complications from many-body interactions such as exciton–exciton annihilation processes. In this regard, fp-TRMC has shown its versatility in determining the charge-carrier mobility, charge-carrier generation efficiency and subsequent carrier recombination dynamics for various conjugated polymer aggregates in solution, and thin-film layers, including organic layers or hybrid organic–inorganic layers726272829303132333435363738. Figure 2a displays representative time-resolved TRMC transients for (7,5)-SWCNTs suspended in toluene, as well as those for controls of PFO dissolved in toluene and neat toluene solvent in Supplementary Figure 1; the vertical axis is the change in microwave power reflected from the cavity at the resonance frequency. No reflected microwave transient signals are observed with either neat PFO dissolved in toluene (grey dashed line in Figure 2a, left y axis) or solvent alone (Supplementary Figure 1), showing that the change of microwave absorption is due solely to (7,5)-SWCNTs. fp-TRMC experiments for a variety of (7,5)-SWCNT concentrations (1.23–12.3 nM per μm length of (7,5)-SWCNTs) reveal that the transient decay dynamics are insensitive to concentration within this range (Supplementary Figure 2).

Figure 2

Phtoinduced free-carrier generation probed by microwave conductivity.

(a) Representative time-resolved reflected microwave transients for (red and blue) (7,5)-SWCNTs suspended in toluene and (grey, left y axis) PFO dissolved in toluene. The SWCNT transients result from photoexcitation at either the S22 transition (blue, left y axis) or S11 transition (red, right y axis). (b) Frequency-dependent reflected microwave power transients for (7,5)-SWCNTs suspended in toluene, following excitation at S22. In a, a biexponential fit is displayed as the solid black line. Experimental conditions: the excitation photon fluence was approximately 1.0–1.5 × 1012 photons per cm2 for the data presented in a and 4.4 × 1012 photons per cm2 for b; 5 ns pulse width; room temperature.

Frequency-resolved microwave conductivity measurements

The details of the solution-phase fp-TRMC experimental setup and discussion are described in Supplementary Figures 3–6 and Supplementary Methods, and the theoretical background of fp-TRMC can be found elsewhere28293940. In brief, in the most general terms, fp-TRMC experiments measure the time evolution of the complex dielectric constant ɛ of the sample after photoexcitation. The present experiments are conducted with the sample mounted in a microwave cavity and the complex dielectric constant of the sample is calculated from the cavity resonance characteristics. Changes in the real part of the dielectric constant lead to a shift in the resonance frequency, whereas the imaginary part determines microwave power loss in the cavity. Charges photogenerated in the sample (photoconductivity) can contribute to both the real and the imaginary parts of the dielectric constant depending on their mobility and degree of confinement40. Conductivity can be expressed in terms of dielectric constant as:

where σ, ω, ɛ0, ɛ′ and ɛ″ represent the complex conductivity, the radian frequency of the microwave electric field, the vacuum permittivity, and the real and imaginary parts of the dielectric constant at frequency ω, respectively. Thus, the real part of the conductivity is identified with the imaginary part of the dielectric constant—microwave absorption. An important caveat here is that real conductivity is only one of two possible components of the loss term. Dielectric loss can also contribute, as when molecular dipoles re-orient in the field. These two loss mechanisms are indistinguishable in the TRMC experiment and we rely on arguments later in the text, to show that a significant dielectric loss contribution to the signals we observe is unlikely.

fp-TRMC measurements made only at a single resonance frequency cannot distinguish between the real and imaginary parts of the conductivity, because a frequency shift simply modulates the reflected power, much as a change in power absorption would41. Frequency-dependent measurements are therefore necessary to identify the origin of the transient signals in (7,5)-SWCNTs. A set of reflected power transients were collected at 13 different microwave frequencies, spanning the cavity resonance curve, following S22 excitation of a (7,5)-SWCNT solution. Figure 2b and Supplementary Figure 7 show contour plots of frequency-dependent reflected microwave power transients generated from these data and exhibit a negligible frequency shift as a function of time, implying that the transient signals obtained on resonance are dominated by a change in the real conductivity of the sample. These results conclusively demonstrate that photoexcitation of (7,5)-SWCNTs generates some amount of mobile free carriers.

Transient photoconductance decay

Under both S11 and S22 excitation conditions, microwave transient decay dynamics normalized at the peak are indistinguishable as shown in Figure 2a. In a previous study of SWCNT thin films, the photoconductance ΔG signal, which is proportional to the reflected microwave power −ΔP/P, decayed by approximately 90% within the first 10 ns (ref. 7). In our current solution-phase fp-TRMC measurements, the transient signals persist much longer. Both transient decay profiles are fitted using a biexponential function with time constants τi and associated amplitudes ai of τ1=27 ns (a1=0.75) and τ2=212 ns (a2=0.25), and yield the average lifetime τavg of 161 ns, from τavg=Σifiτi, where fi is the fractional contribution of each time constant, which is (aiτi)/Σjajτj. The different transient decay behaviour between solution-phase individualized SWCNTs and thin-film SWCNTs suggest that inter-tube junctions in SWCNT thin films possibly facilitate carrier recombination by serving as recombination sites42. In contrast, the longer-lived solution-phase TRMC transient decay dynamics probably represent more intrinsic intra-tube carrier-recombination dynamics, as inter-tube contact is prohibited in the highly individualized SWCNTs.

Photoconductance action spectrum

Figure 3a displays the action spectrum of the peak reflected microwave power for (7,5)-SWCNTs suspended in toluene, which examines the correlation of carrier generation with excitation wavelength. Photoconductance values in the action spectrum are taken at low photon fluence (I0<5 × 1012 photons per cm2) and are normalized for excitation photon fluence. The shape of the action spectrum closely matches the absorptance spectrum of (7,5)-SWCNTs, demonstrating further that the origin of the photoconductance is indeed (7,5)-SWCNTs. Equations (2) and (3) show the relation between the reflected microwave power and the carrier-generation yield.

Figure 3

Photoconductance action spectrum and excitation wavelength dependence of photoconductance transients.

(a) Action spectrum for peak reflected microwave signal (ΔP/P, end of pulse) normalized by the excitation photon fluence (I0) for (7,5)-SWCNTs suspended in toluene (blue, left y axis). Electronic absorptance spectrum of (7,5)-SWCNTs suspended in toluene is overlaid for comparison (red, right y axis). (b) Normalized reflected microwave transients decay for a variety of excitation wavelengths noted in the figure. Experimental conditions: I0<5 × 1012 photons per cm2; room temperature.

In equations (2) and (3), I0 (photons per cm2 per pulse) is the excitation photon fluence, FA is the fraction of light absorbed at the excitation wavelength (absorptance), K (Ω) is a sensitivity factor, determined as 2,400 from the cavity resonance characteristics and the dielectric properties of the medium (see Supplementary Methods for evaluation of K factor), β is the ratio between the long and short axes of the sample cross-section that is perpendicular to the microwave propagation vector, qe (C) is the elementary charge and ∑μ is the sum of electron and hole mobilities. The reflected microwave power normalized by the incident photon fluence −ΔP/(PI0) is proportional to ΦFA, as the mobilities can be assumed constant. Therefore, by comparing −ΔP/(PI0) with the absorptance spectrum, we can extract the relative carrier-generation yield for S11 and S22 excitation. Interestingly, the action spectrum comparing ΦFA near S11 and S22 transitions (Figure 3a) shows that the carrier-generation quantum yield Φ under S22 excitation is about three times higher than that under S11 excitation.

Recently, Kumamoto et al.11 reported photocurrent with S22 excitation for an individual (10,6)-SWCNT grown on a Si substrate. Although the excitation wavelengths of their experiments reside within the S22 spectral domain, they clearly identified the presence of photocurrent with S22 excitation and non-zero conductivity even with zero applied bias, suggesting that the S22 exciton dissociation is a spontaneous process. In addition, Kazaoui et al.10 observed qualitatively higher photocurrent quantum yield with S22 excitation over that with S11 excitation for a (7,5)-SWCNT thin film. Likewise, as we probe photoinduced carrier generation in a low dielectric solvent, our results also suggest that exciton dissociation in (7,5)-SWCNTs is unlikely due to an electric field and more likely a spontaneous process in SWCNTs.

To rule out the possibility that the PFO wrapping the nanotube provides a locally higher dielectric constant, we have performed microwave cavity resonance measurements as a function of PFO:toluene mass ratio and compared them with analogous experiments where a higher dielectric constant solvent is added to the toluene. If the guest molecule added to neat toluene possesses a different dielectric constant from toluene, then the resonance frequency of the loaded microwave cavity will shift in response. The fact that the cavity resonance position does not shift detectably as PFO is added, in contrast to many of the more polar guest solvents, suggests that the PFO polymer has essentially the same dielectric constant as the toluene and does not provide a high local dielectric environment around the nanotubes (see Supplementary Figure 8 and Supplementary Methods for microwave cavity resonance measurements as a function of a guest molecule:toluene mass ratio).

As the action spectrum of the peak reflected microwave power (normalized for excitation photon fluence) near the S22 transition of (7,5)-SWCNTs appears to match its excitonic features, no other intermediate state seems to be involved between photoexcitation and S22 exciton formation. This correlation suggests that carriers are produced from S22 excitons and carrier generation seems to compete with the S22→S11 internal conversion process that is known to be very fast (faster than 50 fs)43. Given the exciton binding energy (approximately 0.4 eV) for (7,5)-SWCNTs12, the continuum states for the S11 exciton lie below the lowest unoccupied molecular orbital of the S22 state. Autoionization of S22 excitons via populating a vibronically hot S11 state or free-carrier continuum states has been proposed for the charge-generation mechanism previously544, and it should be noted that in our action spectrum the carrier-generation yield with excitation at the S11 phonon side band (approximately 900 nm) appears to be comparable to that of S22 excitation. Figure 3b demonstrates identical microwave-transient decay profiles for widely varying excitation wavelengths from S11 to energies higher than S22. The similarity of these transients suggests that the initial photoproducts from either S11 or S22 excitation do not have an impact on the carrier decay dynamics, implying that the mobile carriers generated from photoexcitation are the same species, regardless of excitation energy. It should be noted that, although these <1-nm diameter SWCNTs should have S11 exciton binding energies of approximately 0.4 eV12, carrier generation following S11 excitation even at lower excitation fluences (lower than 1011 photons per cm2; Figure 4a) is unambiguously observed, although the yield is one-third of that observed for S22 excitation.

Figure 4

Excitation fluence-dependent photoconductance.

(a,b) The dependence of the yield mobility product Φ∑μ transient decays on excitation photon fluence (I0) for excitation of the (a) S11 transition (black, red, green, blue, cyan, purple and grey: 3,470 × 1010, 1,030 × 1010, 584 × 1010, 197 × 1010, 70.0 × 1010, 22.3 × 1010 and 8.87 × 1010 photons per cm2, respectively) and (b) S22 transition (black, red, green, blue, cyan, purple and grey: 4,520 × 1010, 1,520 × 1010, 427 × 1010, 220 × 1010, 144 × 1010, 74.1 × 1010 and 7.41 × 1010 photons per cm2, respectively). (c,d) The peak of reflected microwave transients, ΔGmax (end of pulse), evincing the linearity of peak reflected transient signals below the absorbed photon density of approximately 0.8 photon per μm length of (7,5)-SWCNTs for both (c) S11 and (d) S22 transitions. The red solid lines represent a linear function. (e) Φ∑μ as a function of absorbed photon fluence for (7,5)-SWCNTs suspended in toluene with exciting at (blue) S22 or (red) S11 transitions, respectively. The top x axis corresponds to the absorbed photons per μm length of (7,5)-SWCNTs for given I0FA (bottom x axis).

Excitation fluence-dependent yield-mobility product

The figure of merit extracted from fp-TRMC using equations (2) is the product Φ∑μ of the free-carrier yield Φ and the sum of mobilities ∑μ, which is proportional to the photoconductance ΔG normalized by the absorbed photon fluence I0FA. Figure 4a,b (and further in Supplementary Figure 9) displays the time-resolved fp-TRMC results of toluene-suspended (7,5)-SWCNTs following S11 and S22 excitations, respectively, where the y axis has been converted to Φ∑μ. On photoexcitation at the S11 transition, Φ∑μ values can be as high as approximately 0.17 cm2 V−1 s−1 in a variety of excitation photon fluences I0 ranging from 5.6 × 1010 to approximately 3.5 × 1013 photons per cm2, corresponding to an absorbed photon density of approximately 0.056–35 photons per μm length of (7,5)-SWCNTs (Φ∑μ transient data from 5.6 × 1010 photons per cm2 is provided in Supplementary Figure 9, see Supplementary Methods for the calculation of absorbed photon density in (7,5)-SWCNTs). Assuming that one absorbed photon creates one exciton, the absorbed photon density per μm length of (7,5)-SWCNTs corresponds to the initial exciton population per μm length of (7,5)-SWCNTs (hereafter abbreviated as [Ex]μm). On the other hand, Φ∑μ values following excitation of the S22 transition are as high as approximately 0.4 cm2 V−1 s−1 with excitation fluences below 7.4 × 1011 photons per cm2, which is about 2.4 times higher than the maximum Φ∑μ observed for S11 excitation. As the carrier mobility can be assumed to be constant between S11 and S22 excitation, the 2.4 times higher Φ∑μ on photoexcitation of the S22 transition suggests the carrier-generation yield with S22 excitation is approximately 2.4 times higher than that with S11 excitation. This result is consistent with the fp-TRMC action spectrum results in Figure 3a.

Even with approximately three orders of magnitude fluence increase, the microwave transient decay dynamics appear to be insensitive to the exciton density, as shown in the normalized transient decay profiles in Supplementary Figure 9. This result infers that in this exciton density range (0.056–35 [Ex]μm of (7,5)-SWCNTs), carrier recombination effectively occurs through a first-order process and the interactions between a carrier and a neighbouring carrier created from another exciton are negligible for carrier recombination. The absence of fluence dependence within our excitation conditions (I0 between approximately 8 × 1010 and 4000 × 1010 photons per cm2) under our very low exciton density presumably infers a geminate carrier recombination process. Considering that our TRMC technique is detecting only free carriers, this carrier recombination is best described as a secondary geminate recombination process. Secondary geminate recombination requires dissociation and separation of the charges initially bound as an exciton, whereby subsequent recombination is diffusion mediated. The fairly long average transient decay lifetime (approximately 160 ns) suggests that one carrier might be trapped and only the other carrier is mobile.

Although we cannot attribute previously observed all long-lived (above the ns time domain) excited population in solution-phase studies to free carriers4546, using those yields (approximately 3–10%) we can estimate the lower limit of free-carrier mobilities. At a conservative estimate for free-carrier mobilities with 10% yield, assuming only one carrier species is mobile, 9 GHz free-carrier mobility of (7,5)-SWCNTs is calculated to be higher than 4 cm2 V−1 s−1 with S22 excitation. This estimated free-carrier mobility is comparable to the previous literature values of semiconducting SWCNT thin-film carrier mobilities that range from 1.3 to 2 cm2 V−1 s−1 (refs 7, 47). On the other hand, when using higher available literature values of SWCNT carrier mobility48, we can instead speculate the lower limit of the carrier-generation yield, which is 0.04% using approximately 1,000 cm2 V−1 s−1.

Figure 4c,d show that the maximum photoconductance ΔGmax extracted from the photoconductance peak intensity increases linearly with exciton density below approximately 0.8 [Ex]μm of (7,5)-SWCNTs. These results imply that carrier generation in this low fluence regime (lower than 0.8 [Ex]μm) is not a bimolecular process, although we cannot rule out the possibility that at a higher excitation intensity exciton–exciton interactions could mediate exciton dissociation79.

Figure 4e compares Φ∑μ as a function of I0FA with either S11 (red) or S22 (blue) excitation. At low I0FA, where many-body interactions such as exciton–exciton annihilation or exciton–carrier annihilation are negligible, and assuming carrier mobility is constant, then Φ∑μ should be independent of I0FA. As a result, Φ∑μ exhibits a plateau at sufficiently low I0FA range, which has been observed in many other neat thin films or donor–acceptor systems29303449. This plateau suggests that photoinduced carrier generation is a pseudo first-order reaction at low fluence. Likewise, Φ∑μ exhibits a plateau at exciton density below approximately 0.8–1 [Ex]μm and begins to decrease with I0FA increase, as a result of many-body interactions7. It is important to note that transient signals are present even at approximately 0.06 [Ex]μm of (7,5)-SWCNTs with the S11 excitation (much less than one exciton per SWCNT on average), suggesting that photoinduced carrier generation at these low fluences does not result from exciton–exciton interactions. Given the previous study showing electric-field dependence of photocurrent generation6, we conjecture that local electric fields present at tube ends or defects could induce exciton dissociation for the case of S11 excitation.

Discussion

In conclusion, we use a solution-phase fp-TRMC measurement and individualized highly (7,5)-chirality-enriched SWCNT samples dispersed in toluene by the PFO. We probe photoinduced mobile carrier generation in highly isolated SWCNTs in a low dielectric solvent (toluene, ɛr=2.38) at very low exciton densities (lower than 0.06 excitons per μm). Even under these mild conditions, we unambiguously observe photoconductance in well-isolated (7,5)-SWCNTs with a yield-mobility product of approximately 0.17 and 0.4 cm2 V−1 s−1 following S11 and S22 photoexcitation, respectively. The carrier-generation quantum yield with S22 excitation appears approximately 2.4 times higher than that with S11 excitation, suggesting that the autoionization of S22 excitons enhances the carrier-generation efficiency. In contrast, the transient decay dynamics are independent of excitation wavelength, suggesting that the mobile carriers generated from either S11 or S22 excitation undergo identical decay pathways, that is, trapping, recombination, etc. This study demonstrates that frequency-resolved solution-phase fp-TRMC is beneficial to interrogate carrier dynamics of SWCNTs, as selective monitoring of free carriers is achievable with relatively fast ns-time resolution, and photoinduced processes can be studied at extremely low excitation fluence conditions (lower than 1011 photons per cm2). In addition, in solution-phase fp-TRMC, morphology-mediated information can be avoided, to investigate intrinsic material properties and dynamics. With these advantages in mind, this frequency-resolved solution-phase fp-TRMC technique can be applied to a variety of other nanomaterial systems.

Methods

PFO-(7,5) SWCNTs purification and sample preparation

SWCNT powder was added to approximately 2 mg ml−1 PFO solution in toluene such that the final weight ratio between SWCNT powder and PFO in toluene becomes 1:2 and the solution was dispersed through tip sonication (1/2 in probe) for 30 min at 40% intensity (Cole-Palmer CPX 750) in a bath of cool (18 °C) flowing water. The dispersion was then centrifuged using an SW32Ti rotor (Beckman) at 13,200 r.p.m. and 20 °C for 10 min. The supernatant, containing highly (7,5)-enriched SWCNTs, was then collected. The (7,5)-SWCNT dispersion was then centrifuged at 24,100 r.p.m. and 0 °C for 20 h, to remove excess solution-phase (unbound) PFO and to concentrate the (7,5)-SWCNTs for the fp-TRMC experiments. In this case, the resulting supernatant (containing free solution-phase PFO polymer) was discarded and the pellet (containing the (7,5)-SWCNT material) was redispersed in toluene. After this process, the PFO:SWCNT mass ratio is approximately 4:1. To calculate PFO:SWCNT mass ratio, the PFO mass extinction coefficient was experimentally determined in toluene as 95.7 l g−1 cm−1 (ɛ387nm=37,000 M−1 cm−1 for fluorene repeating unit in toluene).

fp-TRMC experiments

The details of fp-TRMC experimental setup and its theoretical background have been reported elsewhere28293940 and the full accounts of solution-phase fp-TRMC are provided in Supplementary Methods. A schematic instrumental layout is described in Supplementary Figure 3. Although the details of fp-TRMC apparatus have been reported previously5051, several modifications to load a solution cell are necessary to carry out solution-phase fp-TRMC. The SWCNT solution sample is loaded in a custom-designed cuvette (5-mm beam path length), which is shown in Supplementary Figure 4. This cuvette is mounted in a pocket made of PTFE (poly tetra fluoro ethylene; Teflon) and the pocket is positioned at the brass base as shown in Supplementary Figure 4. For illuminating the cuvette, 13 holes are made in the waveguide with a diameter of 3.175 mm, to prevent leakage of microwaves. The details of the microwave resonance cavity characterization such as K-factor and resonance curve measurements are described in Supplementary Methods. The sample is optically excited through the pattern of 13 holes by an approximately 5-ns full width at half maximum laser pulse from an optical parametric oscillator (Continuum Panther), pumped by the 355 nm harmonic of an Nd:YAG laser (Continuum Powerlite) and sample photoconductance is measured by monitoring the transient change in microwave power absorption by the sample after the laser pulse. The excitation power is adjusted with a series of neutral density filters. To measure an incident excitation power through the 13-hole pattern, we manufacture a mask with a same pattern and mount on the laser power meter sensor.

Additional information

How to cite this article: Park, J. et al. Photoinduced spontaneous free-carrier generation in semiconducting single-walled carbon nanotubes. Nat. Commun. 6:8809 doi: 10.1038/ncomms9809 (2015).