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Direct proof of a defect-modulated gap transition in semiconducting nanotubes Ryosuke Senga, Thomas Pichler, Yohei Yomogida, Takeshi Tanaka, Hiromichi Kataura, and Kazutomo Suenaga Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01284 • Publication Date (Web): 22 May 2018 Downloaded from http://pubs.acs.org on May 22, 2018

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TOC figure 171x76mm (150 x 150 DPI)

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Figure 1 439x618mm (150 x 150 DPI)


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Figure 2 498x346mm (150 x 150 DPI)


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Figure 3 413x685mm (150 x 150 DPI)


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Direct proof of a defect-modulated gap transition in semiconducting nanotubes

AUTHOR NAMES Ryosuke Senga1, Thomas Pichler2, Yohei Yomogida1, Takeshi Tanaka1, Hiromichi Kataura1 and Kazu Suenaga1* AUTHOR ADDRESSES 1

Nano-Materials Research Institute, National Institute of Advanced Industrial Science

and Technology (AIST), Tsukuba 305-8565, Japan. 2

Faculty of Physics, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria

*Correspondence to: [email protected] [email protected]

KEYWORDS carbon nanotube, optical property, defect analysis, electron energy-loss spectroscopy, transmission electron microscopy

ABSTRACT Measurements of optical properties at a nanometer level are of central importance for the characterization of optoelectronic devices. It is, however, difficult for conventional lightprobe measurements to determine the local optical properties from a single quantum object with nanometrical inhomogeneity. Here, we successfully measured the optical gap transitions of an individual semiconducting carbon nanotube with defects by using a monochromated electron source as a probe. The optical conductivity extracted from an


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electron energy-loss spectrum for a certain type of defect presents a characteristic modification near the lowest excitation peak (E11) where excitons and nonradiative transitions, as well as phonon-coupled excitations, are strongly involved. Detailed lineshape analysis of the E11 peak clearly shows different degrees of exciton lifetime shortening and electronic state modification according to the defect type.

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MAIN TEXT The optical properties of semiconducting carbon nanotubes are strongly governed by exciton behavior in which bound electron–hole pairs are confined in the limited dimensionality. Excitons generated in a carbon nanotube, which is an ideal onedimensional system, exhibit extremely strong binding energies1,2 and, therefore, show unique behaviors such as an extended exciton Bohr radius (a few nanometers3), unusual stability at room temperature, and a long diffusion distance (more than 500 nm4,5). In general, such stable and free mobile exciton behaviors, as well as other fascinating physical properties of carbon nanotubes, should be advantageous for light-emitting devices or photovoltaic batteries. In such a confined system, the gap transition is believed to be drastically modified at nonperfect structures such as defects or impurities, that may affect overall optical properties such as the luminescence quantum yield6–13. Therefore, the direct correlation between local exciton behavior and atomically identified defects must be investigated for further understanding. Especially if one can extract the absolute optical absorption properties which directly reflect the joint density of states (JDOS) of the material with a nanometer-scale resolution, the local excitonic transition process at defects can be quantitatively pictured. However, it is difficult for conventional light-probe measurements to extract an absolute absorption spectrum from a single carbon nanotube because of the low transmission contrast. Only a few experimental approaches have estimated the optical absorption cross-section of individual carbon nanotubes in absolute values14,15. Even in such experiments dedicated to a single molecular system, the local measurement at defects is hardly possible because of their inferior spatial resolution, which is limited by the optical wavelength. Although near-field scanning optical microscopy can overcome the diffraction limit of the optical source, its spatial resolution is only a few tens of nanometers16, and thus it is still unable to probe single defects. Nevertheless, an electron probe in a transmission electron microscope (TEM), which has a much smaller wavelength (= 0.05 Å at 60 kV), can picture the atomic structures of materials with atomic resolution and induce optical excitation in single quantum objects. The recent development of a monochromator for TEM electron sources has further pushed up the electron energy-loss spectroscopy (EELS) energy resolution to better than a few tens of millielectron volts, allowing us to identify the absorption peaks for optical excitation involving the quantum effects17–22. In this study, we measured the EEL spectra including the gap transitions from single isolated carbon nanotubes by using the monochromated TEM with different polarization conditions. Since the different polarizability reflects different selection rules,


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the absence/presence of transition peaks will help us to understand their origins. Then, we further processed the EELS spectra by the Kramers–Kronig (KK) transformation to extract the optical absorption properties in absolute values. In this process, we have successfully obtained the practical optical absorption coefficient and optical conductivity of a single carbon nanotube by correlating the EELS and optical absorption spectroscopy (OAS) data collected from carbon nanotubes of the same chirality prepared by the highyield chirality separation method23,24. Consequently, the local modifications of the exciton behaviors were detected, and their lifetime-shortening and extra states of excitons were unambiguously discriminated at specific defective sites on a carbon nanotube. Figure 1 shows EEL spectra for a single isolated (9, 2) carbon nanotube (freestanding in vacuum) with two different polarization conditions. The experimental setup is shown in the Supplementary text and Fig. S1. In the near-field condition (the left pathway in Fig. 1a), an electron beam directly targets a carbon nanotube with a large convergence semiangle of 40 mrad, while an electron beam passes by (aloof position) more than 10 nm away from the nanotube (the right pathway in Fig. 1a) in the far-field condition. The former polarization condition can excite the multipolar-induced transitions. Therefore, the EEL spectrum (the upper line in Fig. 1b) shows E12 (and/or E21) and E23 (and/or E32) transitions, which are basically forbidden in typical OAS. In order to observe such Eij (i ≠ j) transitions by a light source, polarized light perpendicular to the tube axis should be applied to the carbon nanotube25. Moreover, direct band-to-band transitions were also seen in the near-field condition. Such detailed information related to the JDOS is beneficial for understanding the optical properties of single carbon nanotubes. On the other hand, the far-field EELS follows a comparable selection rule to the typical OAS in which only the dipolar-induced transitions are dominant and therefore the Eij (i ≠ j) become silent (the bottom line in Fig. 1b) and no band-to-band transition is observed. Compared to the near-field condition mentioned above, the E11 peak in the farfield condition is considerably sharper, probably due to the absence of dark exciton states which can only be activated by multipoles. The simplest way to extract the optical constants from EEL spectra is the Kramers–Kronig (KK) transformation, which was successfully adapted to investigate EELS data for isotropic bulk solids. However, analysis for the diluted and anisotropic systems is more complex. Indeed, previous studies on boron nitride and carbon nanotubes with lower resolution reported that the KK transformation is hardly applicable for the plasmon features at high energy as they are strongly affected by the polarizability26,27. However, this does not account for the low energy gap transitions in semiconducting carbon nanotubes which have a vanishingly small momentum dependence28. In addition,


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the high-energy plasmon of the individual tubes has a strong forward scattering component and does not affect the gap transitions beyond an effective screening. Therefore, we can still directly compare EELS and OAS by simply discussing the energy (frequency)  dependence of the classical complex dielectric function by using the KK transformation. The details of the KK transformation employed here are discussed in the Supplementary text and Figs. S2–S6. We recorded two spectra with different dispersions at each point for the KK analysis. One is the detailed spectrum with a dispersion of 5 meV/channel for the fine structure analysis, and the other covers the wider range of energy with a dispersion of 50 meV for the extrapolation fitting. Figure 2 shows the obtained KK transformed EEL spectra (the absorption coefficient) calculated from far- and near-field conditions. The systematic red shift of OAS in comparison with raw EEL spectra definitely becomes smaller or vanishes between OAS and the absorption coefficient. The far-field EELS condition provides the result consistent with the OA spectrum including the peak positions for exciton−phonon couplings. In this analysis, the experimental broadening in the EEL spectra must be taken into account in comparison to optics systems, which do not need to consider experimental broadening. Indeed, a 30-meV Gaussian broadening in the full width at half-maximum (FWHM) to the OA spectrum (the blue broken line in Fig. 2), which is reasonable for the energy resolution of the monochromated electron source (dE = 30–50 meV in FWHM), fitted well to the left side of the first peak in the optical absorption coefficient. The scale of absorption coefficient obtained here is reasonably consistent with the previously reported values14,15. As another independent confirmation of accuracy of our analysis, we checked that the total area under the loss function was comparable to that of C60 crystals, which should reflect the effective electron density in the system by following the sum rule and is therefore supposed to be close for all the nanocarbon family. Figure 3 presents local modifications in the optical conductivity, Re σ , where 0 denotes the permittivity of the vacuum, corresponding to atomic structure variations for a 230-nm-long (9, 2) carbon nanotube placed on a TEM grid with three different defects (defects B, C, and D in Fig. 3e). Figures 3a–d show the optical conductivity at the defect-free region (A) and at the different defect structures (B, C, and D). It was already reported that the excitons in carbon nanotubes are well-localized and that their spatial extension is limited to 3–5 nm at most21. The three defects in the (9, 2) carbon nanotube shown in Fig. 3 are separated from each other by more than 50 nm, and, therefore, the defects did not interfere with each other. In this study, we resolved the E11 feature into three components: I) an exciton that is asymmetrically modified by the joint DOS of the carbon nanotubes, II) an exciton–


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phonon coupling, and III) a nonradiative band-to-band transition (namely, E11', see Fig. S7 for details). The first exciton peak (component I, indicated by the red lines in Figs. 3a– d) was fitted by a model function consisting of a reciprocal square root singularity multiplied by a Gaussian cumulative and a Lorentzian. The function simulated the experimentally broadened joint DOS by the Gaussian cumulative component. The relative intensities and the damping factors (lifetime) were extracted from each Lorentzian component (Table 1). Component II (purple lines in Figs. 3a–d) was nicely fitted by equidistantly separated multiple damping peaks. The gap between each peak (32–37 meV) is consistent with the radial breathing mode (RBM) phonon. Such damping peaks can be interpreted as damped Franck–Condon satellites (FCSs) reflecting the coupling between the exciton and the phonon corresponding to the RBM29,30. Based on the Franck-Condon principle of spectroscopy, the variety of strength for each satellite corresponds to the exciton-phonon coupling in excited states in which adiabatic potentials are slightly shifted from ground states (so-called the Franck-Condon shift). These FCSs are basically observed in molecules and are usually strongly damped in solids31. In our results, the Franck-Condon satellites induced by the RBM are observed at the defect-free region (the inset of Fig. S7). This is quite reasonable because the nanotube consists of only ten or a few more carbon atoms in the circumference direction and behaves as a molecule in that direction. Consequently, the FCSs at the defects where the strength of higher order satellites is more enhanced while the first exciton peak is suppressed can be also qualitatively interpreted as the locally shifted or distorted wave function in excited states. From this view point, one can expect that the exciton-phonon coupling at the defects is more enhanced than the perfect periodic region and possibly leads to the jam of electron/exciton transportation by Franck-Condon blockade32. However the current energy resolution is not good enough to fully resolve each satellite peak for further investigations. Therefore, more precise measurements with a higher energy resolution as well as associated theoretical investigations must be needed. Note that the exciton–phonon coupling related to the Gband bound state approximately 200 meV above the main peak in the OA spectra (Fig. S1), which was also reported in previous studies29,30,33, was not visible in the EEL spectra. This is probably because the exciton–RBM phonon coupling was more prominent in our near-field condition, and thus it suppressed the components of exciton–phonon coupling related to the G-band. The energy gap between the peak in component III (indicated by E11′ in Figs. 3a–d) and the exciton peak (E11) was approximately 330 meV, which is comparable to the exciton binding energy for similar-size nanotubes2,34. In addition, the gap between E11


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and E11′ was almost inversely proportional to the tube diameter (Fig. S7). Such direct band-to-band transitions are excited only at higher momentum transfers35 and cannot be seen in typical OA spectra or under far-field condition EELS (Fig. 1). Components II and III were fitted by Voigt functions in which a Gaussian line width was fixed at 30 meV to include the experimental broadening effect. The relative intensities compared to the defect-free region for component III are shown in Table 1. Defect B, which was a small bump on the nanotube wall, showed only a small reduction in the exciton lifetime as compared to the defect-free region. The integrated intensity for the exciton decreased to 86%, whereas the area under the nonradiative bandto-band transition (component III) increased by 35%. In addition, the nonradiative peak shifted slightly, probably due to the band-structure modification. Defect B also has a small prepeak approximately 50 meV below the E11 main peak (indicated by the black arrow). The energy position of the prepeak was close to that of the dark-exciton states, which can become “active” or “bright” when the symmetry is broken by an external field or by the existence of nonperiodic structures12,36. Such bump type defects found in different nanotubes also show a similar trend in which the lifetime does not change while the strength of E11 main exciton peak slightly decays (Fig. S10). Defect C consisted of multiple defects with a complex structure, which may have involved a fullerene-type defect37. Defect C showed minimal lifetime changes in the radiative component. The integrated intensity of component I largely decreased to 61% for this defect type. In addition, components II and III were also reduced here. The shift of the nonradiative component by ~0.07 eV was also prominent, which suggests a defect state generated between the intact bandgap or a decreased exciton binding energy. The lifetime of excitons at defect D, where a few nanometer-sized carbon impurities were attached, was significantly reduced to almost one-seventh of the original lifetime. This means that only the wave function at defect D had a strong enough distortion to significantly influence the exciton lifetime. The integrated intensity of component I was also reduced by 40%. However, defect D had an extra peak below the E11 main peak (indicated by the black arrow in Fig. 3d). The extra prepeak can be assigned as a brightened inactive exciton state induced by the symmetry breaking, as was the case with defect B. Another interpretation for the prepeak is a contribution from charged excitons (trions). Because holes seemed to be induced effectively at defect D, as seen from the reduction of the main E11 peak, it is reasonable that trions may have been generated13. These distinctive modifications corresponding to the defects were only seen in the E11 features. The other higher-order peaks (E22) did not show obvious changes (Fig.


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S8). This is explainable by the hole-doping effect, which was previously reported for functionalized carbon nanotubes13,38. If a charge transfers to the defects or to attached impurities, it is reasonable that only E11, which is quite sensitive to the Fermi level, would be affected. In addition, our results can provide possible scenarios for absorption/emission properties at defects from several key factors (see the Supplemental text), though further studies such as a combination between EELS and cathode luminescence39 will be needed to directly know the exact emission properties. In this study, EELS spectra were transformed by KK analysis to directly compare with the OAS. We should note that, since our KK analysis does not fully consider the multipolarizability or the anisotropic dielectric function of the graphene layer, the extracted optical constants are not completely accurate, especially in plasmon regions higher than 4 eV. One can therefore focus on only the E11 bandgap region for systematic analysis with/without defects, which are the most important features for nanotube optoelectronics. Further confirmation of our experimental findings by theory would help us deepen our understandings of defect-related physics. In order to corroborate the observed variation of excitons at defects, a full theoretical study will be needed in which excitonic effects (GW and Bethe–Salpeter approach40) and different selection rules are considered for a complex asymmetric atomic model. A cathodoluminescence (CL) study in a microscope41 will also be an important partner for such a high-resolution EELS study. One could quantify the emitting photon from a single molecule by combing the CL study with the quantitative absorption by high-resolution EELS, the luminescence/absorption properties including the quantum yield related to defects will be fully identified. The method described here will find wide application in assigning defect-related excitonic behaviors for other semiconducting materials comprising opto-electronic devices, such as light-emitting diodes (LEDs), if the sample can be successfully prepared thin enough.


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Figure 1. (a) The schematic of near- (left) and far- (right) field EELS experimental condition. (b) The EEL spectra for near- (upper line) and far- (bottom line) field condition. Multipolar-induced transitions are allowed in the near-field condition, while only dipolarinduced transitions are allowed in the far-field condition, in which the band-to-band and Eij (i≠j) transitions are silent. Note that the S/N ratio is quite low at the far-field condition due to the significantly smaller cross section.


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Figure 2. Comparison between OAS and KK-transformed EELS. Absorption coefficients calculated from far- and near-field EEL spectra are shown in the black solid and broken lines, respectively. The OA spectra (and one broadened at 30 meV Gaussian) are also shown in the blue solid (and broken) lines. Note that the same experimental broadening is not applicable for the higher-order peaks (~E22) because of the following reason. Since the dual EELS system can focus two different peaks, we focused on the E11 transition and the zero-loss peak to align the peak position. Thus, although the higher-order peaks (~E22) can be detected in the same E11 focused spectra, they are slightly defocused and cannot be broadened by the same experimental broadening factor.


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Figure. 3 (a)–(d) The optical conductivities (black dots in bottom panels) for the defectfree region (A) and three types of defects (B: a bump type topological defect probably consisting of a few sets of topological defects, C: a fullerene-like carbon cage attached to the nanotube side-wall37, D: a few-nanometer-sized amorphous carbon cluster (contamination) wrapping the carbon nanotube) in a 230-nm long (9, 2) carbon nanotube suspended between TEM grid, as shown in (e). The initial EEL spectra were collected when the electron beam scanned the defects in scanning TEM (STEM) mode and then transferred to the optical conductivities. The line-shape analysis on the optical conductivity for each defect was performed in the same manner as shown in Fig. S7. The line width of the exciton peak was extracted from the Lorentzian component in the simulated scaled DOS (listed in Table 1). All the cases are summarized as stacked lines in Fig. S8 (E22–E44 are shown in the inset).


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E11 intensity ratio (%)

Linewidth of exciton (lifetime)

E11′ intensity ratio (%)

Defect-free

100

47±5 meV (340±40 fs)

100

Defect B

86

50 ± 5 meV (320±38 fs)

135

Defect C

61

48 ± 5 meV (332±35 fs)

69

Defect D

62

283 ± 5 meV (57±1 fs)

75

Table 1. Extracted line width of exciton peak and integrated intensity ratio for E11 and E11′ corresponding to the defect types. The line widths (FWHM) were extracted from Lorentzian components in the fitting lines for the exciton peaks, as shown in Fig. 3. The corresponding exciton lifetimes estimated from the simple oscillator model (Fig. S9) are shown in brackets. Integrated intensities for components I (E11) and III (E11′) expressed as relative values, with the defect-free region being 100%. The estimated error of 5 meV is involved in the measured line width which is the channel width of the detector in our experimental condition.


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ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: Materials and Methods. KK transformation (Figure S1–S6). Fine structure of the lowest excited state (Figure S7). Modulation of the excitonic behaviors corresponding to the defect types (Figure S8). Line-shape analysis by a standard oscillator model (Figure S9). E11 line width and relative intensity for other nanotubes (Figure S10). Further discussion of the optical properties corresponding to defect types.

AUTHOR INFORMATION Corresponding Author E-mail: [email protected] [email protected] Author contributions RS and KS designed the experiments. YY, TT, and HK prepared the materials and contributed OAS. RS performed EELS and microscopy. RS and TP analyzed the data. RS, TP, HK, and KS cowrote the paper. All commented on the manuscript.

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS


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We would like to thank S. Maruyama, Y. Miyauchi, M. Kociak, and O. Stéphan for fruitful discussions. This work was supported by KAKENHI (17H04797, 16H06333 and 25220602). T.P. would like to thank FWF P27769-N20 for funding.

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