Hot Exciton Relaxation and Exciton Trapping in Single-Walled Carbon

Oct 10, 2016 - generation of multiple excitons per absorbed photon is not observed for an ..... t = 500 fs, the hot exciton is relaxed and no signific...
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Hot Exciton Relaxation and Exciton Trapping in Single-Walled Carbon Nanotube Thin Films Tika R. Kafle, Ti Wang, Bhupal Kattel, Qingfeng Liu, Youpin Gong, Judy Wu, and Wai-Lun Chan* Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, United States ABSTRACT: Time-resolved two-photon photoemission spectroscopy (TRTPPE) was employed to investigate the hot exciton relaxation and exciton trapping dynamics in semiconductive, single-walled carbon nanotube thin films. Compared to other conventional optical ultrafast spectroscopy techniques, the TR-TPPE can temporally resolve both the energy and the population of optically excited excitons, which enables unambiguous identification of hot and relaxed band-edge exciton states. It is found that hot excitons populated by photons with energies above the band gap lose most of their excess energy within the first 100 fs after photoexcitation. Unlike isolated nanotubes, the generation of multiple excitons per absorbed photon is not observed for an excitation energy as high as five times the optical band gap. This difference is attributed to the different dielectric environment and the presence of intertube interaction in nanotube thin films. The subsequent population decay and energy relaxation dynamics of the band-edge excitons are measured. The excitons are either annihilated or trapped within a few picoseconds after photoexcitation. The rapid exciton annihilation and trapping implies that a device structure that can facilitate ultrafast exciton dissociation is critically needed for high performance nanotube optoelectronic devices.

1. INTRODUCTION Single-walled carbon nanotubes (SWCNTs) have optical and electronic properties such as tunable bandgap and fast electron transport that are desirable for next generation optoelectronic applications. They have been used in many devices including photodetectors,1,2 photovoltaics,3 and light emitting diodes.4,5 The low dielectric constant and the one-dimensional (1-D) quantum confinement possessed by nanotubes give rise to many-body phenomena such as exciton6−8 and trion9−12 formation, enhanced Augers recombination,13 and exciton and carrier multiplication.14−18 In semiconductive, single-walled carbon nanotube (s-SWCNT), Coulombic-bound electron− hole pairs known as excitons are produced upon photon absorption.6−8 If the photon energy is larger than the bandgap, hot excitons can be produced. The excess energy possessed by these so-called hot excitons may initiate electronic processes such as multiple exciton generation (MEG)14,15,18 and instantaneous free carrier generation,19−21 which could potentially increase the photocurrent in photovoltaics and photodetectors. The excess energy carried by these hot carriers can also be used to boost the efficiency of solar cells beyond the Shockley−Queisser limit through hot carrier extraction.22 However, the 1-D confinement found in nanotubes results in undesirable properties such as exciton−exciton annihilation via enhanced Auger recombination.13,18,23 Because the interplay between these competing electronics processes plays a critical role in determining the quantum efficiency of nanotube optoelectronic devices, a systematic study of these processes is important and necessary for a thorough understanding of the underlying physics. The hot electronic processes discussed above are associated with different competing relaxation pathways when a hot © XXXX American Chemical Society

exciton converts into a band-edge exciton. A spectroscopic tool that can distinguish different excited states and quantify the rate of energy dissipation is critical to understand these processes. Transient absorption spectroscopy and time-resolved photoluminescence spectroscopy have been widely used to study the excited state dynamics in s-SWCNTs.13,14,17,23−28 However, distinguishing different excited states using these methods can be challenging. Important quantities such as the amount of excess energy carried by hot excitons cannot be obtained directly using these techniques. Recently, more advanced tools such as two-dimensional white light spectroscopy29−31 have been used to separate the spectral signatures of excitons residing in different nanotubes in aggregates and thereby to resolve the exciton transport channels in s-SWCNT thin films. In this work, time-resolved two-photon photoemission spectroscopy (TR-TPPE) is employed. The photoemission probe measures the electronic energy directly, which allows the cooling dynamics of hot excitons to be mapped out in both the time and energy domains. The same technique has been used recently to study the hot electron dynamics in other nanomaterials such as semiconducting quantum dots32 and quantum wells.33 The ability to measure the electronic energy and transient population simultaneously also allows us to study the exciton trapping dynamics in the s-SWCNT thin film. Most of the previous works on the ultrafast exciton dynamics in s-SWCNTs focus on isolated and highly purified s-SWCNTs. In this work, we focus on the exciton dynamics in s-SWCNT thin films that have been used in high performance Received: August 31, 2016 Revised: October 7, 2016

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DOI: 10.1021/acs.jpcc.6b08805 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C optoelectronic devices.34,35 In these thin films, nanotubes are bundled and interlinked together, and intertube transport is feasible.29,30,36 The s-SWCNTs are a mixture of tubes with different chirality and bandgaps, which can further facilitate ultrafast downhill intertube exciton transfer.29,30,36 To study the hot exciton dynamics, the s-SWCNT thin films are excited by photons with energies in the range of 2−5 times the optical bandgap. The average energy of these hot excitons is resolved temporally. It is found that the cooling process is rather rapid. Depending on the amount of excess energy, the relaxation times lie in the range of 10−200 fs. After the hot exciton cooling is completed, the time-evolution of the population and the average energy of the relaxed excitons are measured. The population decay and energy relaxation rates decrease with the increase of the pump−probe delayed time. The observation is attributed to the downhill migration of excitons to lower energy sites where the excitons are eventually trapped. The trapped excitons have a slower energy relaxation rate. Moreover, they are less likely to encounter recombination sites and thus have longer lifetimes. Finally, we will discuss whether MEG is observed in our sSWCNT thin films. MEG and carrier multiplication has been observed in isolated s-SWCNTs for excitation energies as low as two times the optical bandgap.14−16 On the contrary, in sSWCNT thin films, we have found that the number of excitons generated per absorbed photon does not depend on the pump photon energy after the optically generated hot exciton is relaxed. As we will discuss, the better dielectric screening found in the nanotube thin film would reduce the MEG rate. Furthermore, the nanotube thin film used in our study is polydisperse, which is different from the near single-chirality nanotubes used in other studies. This would result in other exciton relaxation channels that compete with the MEG process. We conclude that MEG is either not effective in our nanotube thin films or the multiple excitons formed under MEG recombine rapidly to yield one exciton per photon as soon as the hot exciton is cooled.

Figure 1. (a) Absorption spectrum of the s-SWCNT aqueous solution. (b) The SEM image of the s-SWCNT thin film on an ITO substrate. The tubes are bundled together, and these bundles form an intertwining network. The length of the scale bar is 400 nm.

nanotube thin films. The as-prepared thin film was loaded into an ultrahigh vacuum (UHV) chamber with a base pressure ∼1 × 10−10 Torr. The sample was annealed for ∼30 h at a temperature of 300 °C. Using ultraviolet photoemission spectroscopy (UPS), it was confirmed that further annealing of the sample did not shift the surface work function nor change the sharpness of the valence band features. UPS was used to determine the valence band structure of the s-SWCNT thin films. The He−I and the He−II emission lines generated from a standard gas discharge lamp were used to photoionize the electrons. The kinetic energy of the electrons was measured by a hemispherical electron analyzer (Phoibos 100, SPECS) to obtain the photoemission spectrum. TR-TPPE was used to study the exciton dynamics in s-SWCNTs. In the TR-TPPE experiment, the sample was excited by femtosecond pump laser pulses. The excited electrons were ionized by time-delayed probe laser pulses. In optically excited SWCNTs, an electron is bound by the nearby hole to form an exciton. Therefore, a portion of the probe photon energy is consumed to overcome the exciton binding, which lowers the kinetic energy of the ionized electrons. In a typical photoemission experiment, the kinetic energy of ionized electrons is measured. Hence, a photoemission peak originated from the ionization of an exciton should appear at a lower energy in the spectrum as compared to the peak originated from the ionization of a free electron. This energy difference is approximately equal to the exciton binding energy. The transient photoemission spectra were measured by the same electron analyzer mentioned above. Pump photon energies in the range of 1.55−3.76 eV were used. The probe photon energy was fixed at 4.59 eV. Either the direct output (1.55−1.87 eV) from a noncollinear optical parametric amplifier NOPA (Orpheus-N-2H, Light Conversion) or the second harmonics of this output (3.1−3.76 eV) were used as the pump pulses. The second harmonic of the output from another NOPA (Orpheus-N-3H Light Conversion) was used as the photoemission probe pulses. The cross-correlation of the pump and probe pulses was ∼65 fs. Both NOPAs were pumped by a Yb:KGW regenerative amplifier running at 125 kHz (Pharos 10W, Light Conversion). The laser beam was defocused to

2. EXPERIMENTAL METHODS Semiconducting SWCNTs of 98% purity (Nanointegris IsoNanotubes-S) were used in our experiments. These nanotubes have diameters and lengths in the range of 1.2− 1.7 nm and 0.3−5 μm, respectively. The semiconducting tubes are a mixture of tubes with different chiral indexes. Based on the tube diameters, the first three optical transitions are expected to be in the following ranges: E11 ≈ 0.6−0.8 eV, E22 ≈ 1.1−1.4 eV, and E33 ≈ 2−2.7 eV.37,38 Figure 1a shows the optical absorption spectrum of the s-SWCNTs in the nearinfrared and the visible range. The E22 and E33 transitions at the expected photon energies can be seen. The E11 exciton energy, which is centered at 0.7 eV, can be resolved from the TR-TPPE spectrum. The very small band gap (∼0.7 eV) of our nanotubes is ideal for studying processes such as MEG. The s-SWCNT films were fabricated by vacuum filtrating 150 mL of s-SWCNT aqueous solution (∼5 μg/mL) through 0.2 μm mixed cellulose ester filter membrane, and then transferred onto an indium tin oxide (ITO) substrate.34 In order to obtain a uniform sSWCNT film, the ITO substrate was cleaned by acetone, isopropyl alcohol, and deionized water subsequently in an ultrasonic bath, followed with nitrogen gas blow dry and baking in an oven at 200 °C for 10 min to remove any adsorbed moisture prior to transferring the s-SWCNT film. Figure 1b shows a scanning electron microscopy (SEM) image of the B

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Figure 2. UPS spectrum for the s-SWCNT thin film at energies (a) near the SECO region and (b) below Ef. The spectra were recorded either with the He−I or the He−II emission line. The emission line used is indicated in the figure. (c) The valence band structure near Ef. The intensity is plotted in a log-scale.

Figure 3. TR-TPPE spectra collected with pump photon energies equal to (a) 1.77 eV and (b) 3.76 eV. (c) The transient photoemission spectra at two delays times. The two 3.76 eV spectra are rescaled with a constant factor for the comparison with the 1.77 eV spectra. The expected spectral positions for the optically excited hot excitons before any relaxation are indicated by the red (1.77 eV) and the blue (3.76 eV) arrows. At t = 500 fs, we assign the peak of the spectra to the band edge exciton (labeled as E11).

ensure a low laser fluence. The full width at half-maximum (fwhm) of the beam diameter at the sample was 0.8 mm. The sample was kept at room temperature during the experiment.

are symmetric and E11 ≈ 0.7 eV, we can estimate the transition energies E22 and E33 from the relative positions of V1, V2, and V3. The estimated E22 and E33 are 1.5 and 2.9 eV, respectively. This is in reasonable agreement with the measured E22 and E33 (1.1−1.4 eV and 2−2.7 eV), considering that the peaks in the UPS spectrum are rather broad and their actual positions are difficult to be identified. The third feature V3 at E − Ef = −1.7 eV is rather broad in energy, which agrees with the widespread of the E33 transition energies observed in the absorption spectrum (Figure 1a). Moreover, we note that the UPS spectrum has a tail that extends up to Ef. Although the nanotubes are mostly semiconductive, several factors such as metallic impurities,41 defects on tubes and tube bending42 may result in the presence of electron states within the bandgap. 3.2. Hot Exciton Cooling Dynamics. To study the hot exciton dynamics in these s-SWCNT thin films, TR-TPPE was employed. A photon energy that is larger than the average optical bandgap (Eg ≈ 0.7 eV) of the s-SWCNT films was used to excite the sample. Figure 3a,b shows the TR-TPPE spectrum for a pump photon energy of 1.77 and 3.76 eV, respectively. The energy scale in the TR-TPPE spectrum is referenced with respect to the position of the first discrete valence band (V1) in the UPS spectrum. The brightness represents the intensity of photoemitted electrons at various energies and pump−probe delay times (t). Nearer t = 0, the ionized electrons have a higher

3. RESULTS AND DISCUSSION 3.1. Valence Band Structure. UPS is used to characterize the band structure of the s-SWCNT thin film. Figure 2 shows the photoemission spectrum for spectral regions (a) near the secondary electron cutoff (SECO) and (b) below the Fermi level (Ef). Figure 2c is a magnified view near Ef. Either the He− I (21.2 eV) or the He−II (40.8 eV) line was used to ionize the electrons. The surface work function of the sample obtained from the SECO is 4.24 ± 0.10 eV, which is slightly lower than the work function (4.5−4.6 eV) of pristine graphene and graphite.39,40 Figure 2b shows the valence band structure of the nanotubes. Two main peaks at ∼3 eV (π- band) and ∼8 eV (σband) below Ef can be identified, which are the typical features found in the s-SWCNT spectrum.41 Near the Ef (Figure 2c), photoemission intensity rises gradually with increasing binding energies. Three features at −0.6, −1.0, and −1.7 eV can be identified. We assign them to the first three van Hove singularities in the density of state of the s-SWCNTs. These singularities represent the onset of the quantized bands of s-SWCNTs. They are labeled as V1, V2, and V3 in Figure 2c. Assuming the valence and conduction bands C

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than exciton−exciton annihilation23,25 have rarely been reported at this short time scale in s-SWCNT. The rate for exciton−exciton annihilation often depends on the pump laser fluence. However, it will be shown in the next section that the hot exciton dynamics is independent of pump fluence, which indicates that the exciton−exciton annihilation is not a dominant channel under the current experimental condition. In order to quantify the hot exciton relaxation dynamics, the intensity is plotted as a function of time at various electron energies (Figure 4a) for the spectrum collected at pump

average energy as shown by a rather broad high energy tail in the spectrum. Interestingly, the excitons with energies close to the band-edge are populated almost instantaneously after photoexcitation, which implies an extremely fast hot exciton relaxation. This result agrees with previous studies in which interband exciton relaxation is found to occur in 40 fs after photoexcitation.27 Figure 3c shows the spectra at two selected times (20 and 500 fs). At t = 20 fs, electrons with much higher energies above V1 can be found. In the case for pump photon energy equal to 1.77 eV (red lines), if we assume that the ionization of the hot exciton produces a hot hole, which carries the same amount of excess energy as the hot electron before ionization, the spectral weight of for the optically excited exciton before it loses any excess energy should be centered at E − EV1 ≈ 1.2 eV. This energy is indicated by the red arrow. At t = 500 fs, the hot exciton is relaxed and no significant change in the spectral shape is found at larger delay times. The spectral shape of the relaxed exciton is rather symmetric and is centered at ∼0.7−0.8 eV above V1, which is in good agreement with the expected first optical transition energy (E11 ≈ 0.7 eV) based on the tube diameter.37 This peak is assigned as E11 and it will be referenced to as the band-edge exciton. Note that the E11 state is an exciton state and it is not equivalent to the first conduction band (C1). The E11 state is located at energy lower than that of the C1 state and the energy difference is approximately equal to the exciton binding energy. The energy position of the photoemission peak indicates that the relaxed excitations are in form of excitons instead of free electrons. In order to access even higher energy excitonic states, a pump photon energy of 3.76 eV was also used, which is equivalent to 5.4 Eg. The TR-TPPE spectrum for the 3.76 eV pump photon energy is shown in Figure 3b. At t ≈ 0 fs, photoemission intensities are observed at even higher energies as compared to Figure 3a. The spectra at 20 and 500 fs are shown in Figure 3c (blue lines). For a comparison, the 3.76 eV spectra are multiplied by a constant factor so that the spectra obtained at the two different photon energies have a similar maximum intensity at t = 20 fs. As expected, the spectrum obtained with the 3.76 eV pump shows a broader high energy tail near time zero. The expected position of the optically excited exciton before it loses any excess energy is indicated by the blue arrow. Most of the spectral weight is located below this energy, which indicates that a considerable amount of relaxation has already occurred within the laser pulse duration (the cross-correlation of our pump and probe pulse is 65 fs). At t = 500 fs, the exciton is already relaxed, and the spectral shape becomes similar to that of the 1.77 eV case. The 3.76 eV spectrum appears to have a small blue-shift (∼0.04 eV) compared to that of the 1.77 eV spectrum. However, this shift is within our experimental uncertainty ( 300 fs, the energy relaxation is essentially independent of the pump photon energy, which is assigned to the dynamics of the relaxed band-edge excitons (see section 3.4). The generation of the band-edge excitons on the order of ∼100 fs is in a general agreement with previous studies.23,27,28 However, our measurement gives a much detailed view on how the excess energy of the hot exciton dissipates as a function of time. 3.3. Fluence Dependence. In previous ultrafast experiments, the ultrafast intensity decay observed in optical pump− probe experiments of s-SWCNTs is often attributed to higher order processes such as exciton−exciton annihilation via Auger recombination. At a high excitation density, the presence of more than one exciton per nanotube allows the excitons to

Figure 6. (a) Time-evolution of the intensity of the E11 peak for various pump fluences. (b) The photoemission intensity at the E11 peak near the time-zero. The solid line is a linear fit. (c) The hot exciton dynamics for various pump fluences. Three electronic energies: E − E11 = 0, 0.4, and 0.8 eV are chosen for comparison. At the lowest fluence, the photoemission intensity at long delay times and high electron energies is below the noise-level of our measurement. Therefore, some of these curves are truncated.

the intensity decay at the band-edge energy E11 for different incident laser fluences. The dynamics is essentially independent of the fluence. The amplitude of the photoemission signal near time zero also scales up linearly with the fluence (Figure 6b), which precludes higher order processes. Figure 6c shows the intensity decay at two higher energies together with the intensity at E11 for various fluences. The results show that the hot exciton cooling dynamics is also independent of the laser fluence. For the higher pump photon energy (3.76 eV), an even lower incident fluence, 3.19 μJ/cm2, was used. Therefore, the dynamics is not expected to be fluence dependent. Based on these results, it is concluded that the experiment was done in a regime in which the interaction between excitons created by different photons does not have observable effects on the dynamics. Thus, the observed dynamics correspond to the internal conversion and relaxation of the exciton. E

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The Journal of Physical Chemistry C 3.4. Exciton Trapping and the Dynamics of Relaxed Band-Edge Excitons. For t > 300 fs, the exciton cooling process is mostly completed and the dynamics is independent of the pump photon energy. We will focus on the result obtained using the 1.77 eV pump photon energy to investigate the relaxation dynamics of these band-edge excitons. The temporal evolution of the intensity at the E11 peak is shown in Figure 7a. The intensity is fitted with a simple biexponential

The funneling of excitons into these low energy sites can be seen in the TR-TPPE spectrum in which the spectral weight of the E11 peak shifts gradually to lower energies. Figure 7b shows the centroid of the E11 peak as a function of time. After the initial fast hot exciton cooling as discussed in Figure 5, an average energy relaxation rate of 30 ± 10 meV/ps is found in the first 3 ps (inset in Figure 7b). This relaxation rate becomes progressively slower as longer delay times. For t = 3−40 ps, the average relaxation rate decreases by an order of magnitude to 2.6 ± 0.3 meV/ps. The switching between the two energy relaxation rates correlates well with the switching between the two population decay rates. This observation is consistent with a typical exciton migration and trapping scenario. The exciton migrates to lower energy sites where it is trapped. Once it is trapped, the volume that can be sampled by these excitons decreases significantly. Therefore, they will have a much smaller probability to encounter exciton recombination sites, which leads to a longer exciton lifetime. Using this interpretation, we hypothesis that after the rapid population decrease in the first 3 ps after photoexcitation, the remaining excitons (∼18%) are trapped within the s-SWCNT thin film. The fast population decay and exciton trapping rates can have important implications for optoelectronic device applications based on carbon nanotubes. For example, in nanotube photodetectors, recent works have found that the quantum efficiency is improved by orders of magnitude when nanotubes can form interface heterojunctions with another semiconductor in the so-called nanohybrid structure.34,35 The band edge offset across the heterojunctions facilitates exciton dissociation and charge transfer at heterojunctions located right next to the nanotube where excitons are optically generated. This enables ultrafast charge transfer and separation which is critical to overcome the short exciton lifetime and trapping. Moreover, in SWCNT/polymer bulk heterojunction solar cells, the short circuit current decreases significantly with the increase of SWCNT concentration and the presence of SWCNT bundling.49 In light of this work, SWCNT bundling increases the time for the exciton to reach the SWCNT/polymer interface. As a result, a significant amount of excitons may be trapped or annihilated before exciton dissociation can occur, which results in poor photocurrent. 3.5. Multiple Exciton Generation and Pump Photon Energy Dependence. Finally, we investigate how the exciton dynamics depends on the pump photon energy. For isolated and highly purified s-SWCNTs, it is observed that MEG14 or carrier multiplication16 can occur at photon energies as low as two times the optical bandgap. This onset of MEG in sSWCNTs is low compared to other materials such as quantum dots,50 which makes nanotubes a promising materials for MEG. In previous spectroscopy works, the decays of the exciton population measured at different pump photon energies are compared to determine the MEG yield.14,17 To understand how the MEG yield is determined in these works, we note that the rate of MEG is often assumed to be very rapid. For instance, in graphene, impact ionization (one of the carrier multiplication mechanisms) occurs within 25 fs after photoexcitation.51 Theories for MEG in s-SWCNTs predict that MEG can occur coherently almost instantaneously upon photoexcitation.15 At high pump photon energies, if MEG occurs, more than one excitons can be generated within a single carbon nanotube. These excitons can interact with each other within a short period of time because of the fast intratube transport. Then, rapid Auger recombination occurs, which

Figure 7. (a) Normalized intensity of the E11 peak. The red line is a biexponential fit. The pump photon energy is 1.77 eV. (b) The centroid (or center of mass) of the E11 peak. The inset shows a magnified view at small delay times. Red-lines are linear fits.

function (red line) with two time-constants: 0.9 ± 0.1 and 38 ± 7 ps. The faster component dominates the first 3 ps after photoexcitation. Because our sample only has a 98% purity, it would contain a small portion of metallic nanotubes. The faster population decay in the first few picoseconds can be caused by exciton quenching at these metallic sites. Even though 3 ps is a short period of time, the diffusion constant of excitons in sSWCNTs can be rather large: 1−10 cm2 s−1.47,48 Therefore, the exciton can travel a distance ∼10−30 nm within this period of time. This transport range is consistent with the 24 nm range determined by the spectral diffusion in time-resolved hole burning spectroscopy.31 We note that intertube transport can also occur within this time scale,29,30,36 which allows the excitons to diffuse to nanotubes with different band gaps. The excitons that survive these early annihilations have longer lifetimes. We can estimate the portion of the long-lived excitons from the relative amplitude of the two terms in the biexponential fit. From the fit shown in Figure 7a, we determine that 18% of the excitons survive the early annihilations. These long-lived excitons can be those that are trapped within nanotubes with smaller band gaps. Finally, we like to comment that the fluctuations observed at larger delay times are measurement noises. These fluctuations are more pronounced because of the rather weak pump-induced photoemission signal in this time regime. F

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Figure 8. (a) Time-evolution of the intensity of the E11 peak for various pump photon energies. (b) The photoemission at t = 500 fs for various photon energies. The photoemission intensity is scaled by the factor hυ/Fα. The scaled intensity is proportional to the intensity per absorbed photon.

multiple band-edge excitons are produced after the cooling process is completed. Finally, we like to comment on why our result differs from other spectroscopy works on isolated nanotubes in which MEG is observed for photon energies larger than 2Eg.14,17 MEG is a many-body electronic process with its rate depending on the electron−electron interaction strength. In the s-SWCNT thin films studied in this work, many nanotubes are bundled together. As a result, they can have a larger electronic screening compared to the isolated nanotubes, and nanotubes embedded in a polymer matrix or in solution. This would in turn reduce the electron−electron interaction strength and the MEG rate. For example, a recent work shows that the increase in electron screening can lead to a larger exciton size in s-SWCNTs,52 which is a sign of reduced electron−electron interaction. The larger spatial size of excitons can also increases the rate of the Auger recombination, which can make the multiple excitons recombine once they are generated. Furthermore, our sSWCNTs are polydisperse with a mixture of chiral indexes. Therefore, tubes with different bandgaps can be bundled together or intersect each other in which downhill energy transfer can occur. Recent studies have reported that the intertube transport can occur in a time scale as short as tens of femtoseconds.29,36 These fast relaxation channels can compete with the MEG process, resulting in a low MEG yield. These factors would explain the absence of the formation of multiple excitons in our s-SWCNT thin films for pump photon energy as high as 5Eg.

produces an additional sub-picoseconds to few picoseconds decay component in the exciton population. The amplitude of this additional decay component, which increases with the pump photon energy, is often used to determine the MEG yield.14,17 Following the same idea, we conducted our experiment at various pump photon energies. The transient photoemission intensity at the E11 peak is shown in Figure 8. The highest photon energy used is 3.76 eV, which is equivalent to 5.4Eg. It is found that the decay dynamics is almost the same for various pump photon energies (2.2Eg − 5.4Eg), and no additional population decay component is observed even for the highest energy pump. Therefore, in our s-SWCNT thin films, we do not observe the generation of multiple excitons per absorbed photon for the pump photon energy as high as five times the bandgap. To further support our finding, we compared the raw intensity of the transient photoemission spectra at t = 500 fs for various pump photon energies. At t = 500 fs, the hot exciton is already relaxed and the photoemission intensity is proportional to the number of the band-edge excitons. To compare the spectra for different excitation conditions, we rescale the intensity with the pump laser fluence (F), pump photon energy (hν), and the optical absorption coefficient (α) of the nanotubes. The raw intensity is multiplied by hυ/Fα. The rescaled intensity is proportional to the intensity per absorbed photon. These spectra are shown in Figure 8b. The rescaled intensity of each of the curves is within ±15% of the averaged value, which is within experiment uncertainties due to factors such as sample-to-sample variations. Therefore, we conclude that the number of band-edge excitons generated per absorbed photons is approximately the same for all photon energies at t = 500 fs. In another words, no formation of multiple excitons per absorbed photon was observed in s-SWCNT thin films. It is mentioned earlier that the photoemission peak becomes narrower in the first few hundred femtoseconds after photoexcitation due to hot exciton cooling. As a result, there is a drop in the total integrated photoemission intensity as a function of time. We cannot exclude the possibility that multiple excitons may have formed right after photoexcitation and these excitons annihilate each other via the reverse process, Auger recombination, while these excitons are cooled. Because the relative photoionization cross-section for hot and relaxed excitons is not known, we cannot quantify the number of excitons in the first few hundred femtoseconds after photoexcitation. Nevertheless, we can conclude that even if MEG is present, the Auger recombination is rapid enough such that no

4. CONCLUSION In this work, TR-TPPE was used to resolve the hot exciton cooling dynamics in s-SWCNT thin films. This technique enables us to quantify the rate of energy relaxation of hot excitons and the hot electron decay rate as a function of excess energy in s-SWCNT, which have not been measured directly so far using conventional ultrafast optical spectroscopy techniques. Extremely fast exciton cooling in the time scale of 10−100 fs was observed. The observed fast cooling rate of the hot excitons can make the harvest of the excess energy of these hot carriers difficult. This is because processes such as hot carrier injection and MEG need to outcompete the exciton cooling to be effective. This imposes a practical limitation on using these mechanisms to boost the efficiency of s-SWCNT-based optoelectronic devices. In contrast to the reported MEG on isolated nanotubes, negligible MEG was observed on the polydisperse s-SWCNT films even at a pump photon energy as high as five times of the band gap. The absence of the G

DOI: 10.1021/acs.jpcc.6b08805 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

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generation of multiple excitons may be due to the enhanced electronic screening in nanotube aggregates, which reduces the electron−electron interaction strength and the MEG rate. Moreover, the ultrafast intertube exciton transport enabled by the polydispersity of the s-SWCNTs would outcompete the MEG process, resulting in a low MEG yield. The lifetime and energy relaxation rate of the band-edge excitons were also measured. In the first few picoseconds after photoexcitation, a relatively faster population decay rate (1.1 ps−1) accompanied by a relative fast energy relaxation rate (30 meV ps−1) was observed. This observation is attributed to the fast diffusion of excitons, which allows excitons to sample a large space within the relative inhomogeneous environment in the s-SWCNT thin films. The rapid sampling allows the exciton to search for lower energy sites effectively. At the same time, it increases the probability of the exciton to encounter recombination sites. As a result, rapid population decay and energy relaxation are observed. At longer delay times (t > 3 ps), both the population decay and energy relaxation rates decrease significantly by an order of magnitude. We attribute this to the trapping of the excitons presumably at nanotubes with smaller bandgaps. The trapping impedes further exciton diffusion. As a result, the trapped excitons have longer lifetimes. For optoelectronic applications, it is desired that excitons can be dissociated into free carriers before they are trapped. The observed rapid exciton trapping in nanotube thin films points to the need of nanohybrid structures in high performance optoelectronic devices.34,35,49 In these nanohybrid structures, the nanotubes form interface heterojunctions with another semiconductor, facilitating ultrafast charge transfer and separation at the interface that can outcompete the rapid population decay and exciton trapping in s-SWCNT thin films. Therefore, the exciton annihilation and trapping time scale measured in this work provide a benchmark for the design of the nanotube-based optoelectronic devices.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 785-8646413. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work is primarily supported by US National Science Foundation, grant DMR-1351716. J.W. acknowledges support from ARO contract W911NF-16-1-0029 and NSF contracts DMR-1337737 and DMR-1508494.

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DOI: 10.1021/acs.jpcc.6b08805 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.6b08805 J. Phys. Chem. C XXXX, XXX, XXX−XXX