Well-defined sub-nanometer graphene ribbons synthesized inside carbon nanotubes

Graphene nanoribbons with sub-nanometer widths are extremely interesting for nanoscale electronics and devices as they combine the unusual transport properties of graphene with the opening of a band gap due to quantum confinement in the lateral dimension. Strong research efforts are presently paid to grow such nanoribbons. Here we show the synthesis of 6- and 7-armchair graphene nanoribbons, with widths of 0.61 and 0.74 nm, and excitonic gaps of 1.83 and 2.18 eV, by high-temperature vacuum annealing of ferrocene molecules inside single-walled carbon nanotubes. The encapsulation of the so-obtained graphene nanoribbons is proved by atomic resolution electron microscopy, while their assignment is provided by a combination of an extensive wavelength-dependent Raman scattering characterization and quantum-chemical calculations. These findings enable a facile and scalable approach leading to the controlled growth and detailed analysis of well-defined sub-nanometer graphene nanoribbons.


Introduction
Sub-nanometer graphene ribbons (graphene nanoribbons, GNRs) are promising structures for future electronic devices 1,2 as they are considered of unifying the unique electronic properties of graphene 3 with a reasonably sized gap in their electronic structure. The gap results from quantum confinement in the lateral direction and consequently scales with the inverse width of the ribbons. 4,5 The ribbons are strips of carbon atoms cut out from a graphene lattice. At present most common strips are of the armchair type, i.e., the edge of the ribbons consists of coaxial carbon pairs oriented parallel to the direction of the ribbon axis (arm-chair graphene nanoribbons (AGNR)). They are characterized by the number n of such pairs across their width. The electronic structures of AGNR can be classified into n= 3p, 3p+1 and 3p+2 species, where p is an integer. 4 One of the most commonly investigated structures is the n=7 AGNR (7-AGNR) 6,7 with band gaps between 2.1 and 2.3 eV as reported from scanning tunneling spectroscopy (STS) and optical studies. 8 More recently ribbons with more complex topologies were grown which have coved zigzag, chevron or chiral type structures. 7,9,10 The ribbons are usually grown on Au substrates from preselected and properly designed flat poly-aromatic hydrocarbon molecules (PAHs). 11 In general, the carbons at the edge of the ribbons are saturated by hydrogen but by selecting special PAHs, bandgap engineering, [12][13][14] construction of ribbon heterojunctions 15,16 and ribbons with unusual electronic properties 17 have been demonstrated where topological properties of the ribbons under investigation play an important role. Most recently ribbons became relevant for applications in photocatalytic hydrogen generation. 18 Besides STS and electron microscopy, Raman scattering has repeatedly been used to characterize GNR. Several Raman active vibrational modes were identified to characterize the ribbons. Such modes are among others the radial breathing like mode (RBLM), the CH in plane bending mode (CH-ipb), the D line, and the graphene G line. 12,19 The RBLM frequency scales with the square root of the inverse ribbon width and is the pendant to the radial breathing mode of the carbon nanotubes. 20 Filling and consecutive chemical reactions inside single-walled carbon nanotubes (SWC-NTs) is a promising technique to grow new nanoscale materials in general. 21,23,24 In addition, the one-dimensional geometry of the CNTs is an excellent template for the controlled growth of conventional or exotic low-dimensional compounds. [25][26][27] The growth of GNRs inside SWCNTs has been demonstrated by first filling the SWCNTs with flat precursor molecules, such as coronene 28,29 or other PAHs, 30 and subsequently transforming them at elevated temperature. Although these initial results were very promising, growth of high-quality specific types of GNRs with well-defined widths and edge-state still remained a challenge and the analysis of electronic structures of the objects inside the tubes remained difficult. 31 In this work, we demonstrate the synthesis of two specific GNRs, i.e., 6-and 7-AGNRs, with well-defined width and edges, from the bulky molecule ferrocene (FeCp2). Evidence for the growth of the AGNRs inside the tubes comes from aberration-corrected high-resolution transmission electron microscopy (AC-HRTEM) and from Raman scattering. We also show that wavelength-dependent Raman spectroscopy gives direct access to the electronic and optical properties of the encapsulated objects by the evaluation of resonance Raman excitation profiles. This allows determining experimentally the excitonic gap and even more the electronic structure beyond the gap. High level first principle calculations provide for the first-time relative intensities of the Raman lines of the GNRs by using the Placzek formulation with energy dependent polarizabilities. 22 The latter procedure is a fundamental progress in the evaluation of Raman intensities.

Results and discussion
Aberration-Corrected Transmission Electron Microscopy The standard feature for the observation of encapsulated ribbons in TEM is an alternating pattern of narrow and wide signals from the material inside. 30,34 It originates from an electron beam induced twisting of parts of the ribbons.  The modulation of the response with time is evidence for a flat ribbon. f,g, Two typical AC-HRTEM images in atomic resolution showing a flat 7-AGNR dominated structure confined in a SWNT. Scale bar is 1 nm. In f an interfacing between extended 7-AGNR and 6-AGNR is observed. The inserted models in red present the corresponding atomic structure of the ribbon. h, TEM image simulation for confirming the structure of 7-AGNR@SWCNT in g. It depicts the tube (18,0), the ribbon, the combination of the two and the simulation. The most part of 7-AGNR and the wall of SWNT are AA stacked showing clear graphene structure for the former, while a small mismatch part as indicated by yellow arrows results in blurred contrast in the simulated TEM and in the raw TEM image in g. i,j, Intensity profiles along the yellow line of the recorded pattern i and of the simulated pattern j. The round (outer) tubes exhibit a strong reduction of contrast at the edge whereas the contrast is weaker at the edge of the flat ribbons. Indicated distances correlate with the diameter of a (18,0) tube and evidence a net ribbon width between 0.64 and 0.69 nm.
Raman Scattering Previously, we reported the observation of a set of Raman lines after thermal conversion of FeCp2 filled SWCNT 24,35 but the origin of these lines remained unclear as they did not fit to proper model calculations and high resolution TEM was not available. Here we identified the origin of the Raman lines which turned out to be very sensitive to transformation temperature. Figure 2a-d depicts this behavior in a plot where Raman intensities are characterized by a color code as a function of Raman frequency and transformation temperature. Raman spectra were normalized to the 2D band which is least influenced by the changes induced by the GNR encapsulation. Figure 2a The lower panels of Fig. 2 depict the Raman spectra explicitly. Panels e and f are spectra recorded at 568 nm (transformation temperature 600 • C) and g and h are spectra recorded at 633 nm (transformation temperature 700 • C), for two different Raman frequency regions.
When comparing the Raman spectra of the ferrocene-filled and temperature-transformed samples (red) with the spectra of filled SWCNTs without transformation (black), the new Raman features appear very well separated from the response of the SWCNTs in general. In the high-frequency region, the spectra of the SWCNTs can be subtracted straight forwardly, yielding the Raman response of the newly synthesized objects (blue dotted spectra in panels e and g). For the low-frequency region, a subtraction is more difficult, since during the transformation also inner tubes are formed thereby changing the response of the SWCNTs as well (red arrows). Even though, due to their higher frequency, the lines from the RBLMs of the GNRs can be well separated from the response of the CNTs. The figures demonstrate • Figure 2: Raman scattering for temperature dependent transformation. a-d, Color-code maps for Raman line intensities observed after transformation of FeCp2@SWCNTs as a function of Raman frequency and transformation temperature. The latter was increased in 50 • C steps. Vertical white arrows highlight the positions of the main new Raman lines. Horizontal white arrows are located at temperatures of maximum Raman response. Raman spectra in a and b and in c and d were excited with a yellow laser (568 nm) and red laser (633 nm), respectively. e-h, Raman spectra for FeCp2@SWCNT tuned by transformation temperature to optimized response for the two groups of lines. e, Spectra as observed for yellow laser excitation at 568 nm in the high frequency region, from bottom to top: tubes filled with FeCp2 (black) and subsequent transformation at 600 C (red), AGNR contribution by subtracting the Raman signals from the nanotubes (blue, dotted), and calculation (green) for 7-AGNR. The Raman line marked by a down-arrow was also subtracted since it originates form 6-AGNR as discussed below. f, Raman signals from low frequency region, from bottom to top: filled tubes, transformed at 600 • C, and calculated for 7-AGNR. The arrow marks the response from DWCNTs obtained during the transformation process. g,h, Similar spectra as in e,f but for transformation temperatures of 700 • C, recorded with 633 nm laser, and as calculated for 6-AGNR.
very narrow line widths of the order of 10 cm −1 for the response of the nanoribbons, indicating their high quality. Figure 2 also presents the calculated Raman spectra for 7-AGNR species (panels e and f, in green) and for 6-AGNR (panels g and h, in green) which were obtained from first principle calculations using the dynamical Placzek formalism. 22 Table 1 presents the experimental Raman frequencies and line widths for both the 6-AGNR and 7-AGNR and compares it to our theoretical values as well as to values for the same modes measured on Au-substrates for 7-AGNR. 6 For the 6-AGNR a comparison is made with the only reported data originating from the fusion of linear chains of poly-paraphyenlye at 800 K. 36 The agreement between calculated and experimentally determined Raman frequencies in the high-frequency region is better than 2% and also the agreement between calculated and experimental relative line intensities is excellent, except for the CH-ipb of the 6-AGNR which appears too weak in the calculation. The table highlights the unusually narrow width of the Raman lines from the encapsulated species. In three very recent reports, Raman spectra for 7-AGNR grown on Au substrates and subsequently transferred to transparent substrates are shown to exhibit similar narrow line widths as observed here. 2,19,37 Table 1: Raman lines of 7-AGNR and 6-AGNR; Frequencies (ωph), intensities (weak (w), medium (m), strong (s), very strong (vs)), and linewidths W (FWHM, in parentheses) for the observed Raman lines (column Exp.) as compared to calculation (column Calc.) and to reference (column Ref.). For 7-AGNR and 6-AGNR the latter are from reference 6 and reference, 36 respectively. The column with the calculated frequencies depicts also the difference to the experiment in %. The last two columns depict the excited state frequencies (ω p * h ) and the Huang-Rhys factor (HR) for the first excited state, both obtained from a fit of the resonances to the Albrecht A-term. All frequencies are given in cm −1 and rounded to integer values.   Table 2 lists the observed transition energies as compared to our calculations and to reported values from optical reflection measurements. 8 The comparison depicted in the table further evidences the successful growth of 7-AGNR and 6-AGNR inside SWCNT.
µ The two peaks in the resonance for the 6-AGNR represent the transitions to the first and to the second vibronic level in the excited state, or equivalently, the ingoing and outgoing resonance. Higher vibronic levels are neither observed for the 6-AGNR nor for the 7-AGNR. For the analysis of AGNR@SWCNT the RBLMs are particularly important since they exhibit a strong and characteristic response in a frequency region which is free from other Raman lines. In the case of the 7-AGNR@SWCNT the response is unusual since it exhibits several components. Figure 4a shows a zoomed-in Raman map of region R2. Several peaks can be observed in this region, which become also evident when plotting the Raman spectra for two distinct laser excitations (Fig. 4b). The main peak (highest intensity) appears at a vibrational frequency of 414 cm −1 for 569.5 nm excitation with an exceptionally small line width of only 7 cm −1 . In addition, a shoulder can be observed around 400 cm −1 , which is considerably broader (13 cm −1 ) and exhibits dispersion, i.e. line position shifts with changing excitation energy. Such behavior is well known for the D-line in CNTs but also for conjugated polymers like poly-acetylene. 43 It is an indication for defective structures where vibrational frequencies and electronic transitions exhibit some correlation which eventually leads to photo-selective resonance scattering. In our case such structures may be represented by interfaces between extended or short ribbons of different structure and different topology. In such cases new electronic state inside the gap can be created. 16   As for the growth model we suggest a high degree of breakup of the ferrocene molecule during the heat treatment and a condensation into the energetically more stable form of the ribbon. Such condensation processes of organic molecules into nanoribbons has been observed previously for tetrathiofulvalene (TTF) molecules inside CNTs. 30 The results presented above demonstrate that Raman scattering combined with first principle calculations and resonance excitation analysis is an excellent tool to identify the structure of GNR even if the ribbons are buried inside SWCNTs. Due to its frequency selective character it is superior to any other optical method such as optical absorption or luminescence spectroscopy. In addition, the method allows determining the electronic structures of the ribbons, even beyond the HOMO-LUMO gap. This holds in particular for the analysis of the RBLM.
The results provide a challenge that ribbons with larger or smaller width than those reported here, can be grown in larger or smaller SWCNTs, respectively, and can be detected with Raman scattering. They thus open a new field in subnanometer graphene ribbon research.

Synthesis of GNRs@SWCNT SWCNTs as grown by the eDIPS technique 47 with mean
diameter around 1.3 nm were used as a starting material. All tubes were purified by first etching in air and subsequent treating with HCl as described previously 48 to remove amorphous carbon and catalytic particles from tube growth. SWCNT buckypaper was obtained by washing and filtering the tubes with distilled water and ethanol.
For the filling process the tubes were first opened by etching in air at 420 • C and then exposed to ferrocene at 400 • C for two days in previously evacuated quartz tubes.

Analysis by Transmission Electron Microscopy
To obtain information on the grown objects TEM investigations were performed with a Thermo Fisher (formerly FEI) TITAN G2 80-300 (Fig. 1a-e) at 80 kV. Figure 1f, g and i are acquired by the specific Thermo Fisher Raman scattering Raman spectra were excited at room temperature and at ambient conditions with various lasers in the visible spectral range. Spectra were recorded with a Dilor xy 800 and with a LabRAM HR800 microscope. Spectra in Figure 2 were normalized to the 2D line of the carbon nanotubes. This line is known to be highly independent from defects. In the case of resonance analysis normalization was performed to the fundamental Raman line of Si.

Evaluation of Excitation Profile
Resonance Raman spectra were evaluated for wavelength dependent excitation in the range between 400 and 800 nm with 5 nm step-size. To cover the requested energy range for excitation the following three laser systems were used.

Competing Financial Interests
The authors declare that they have no competing financial interests associated to the publication of this manuscript.

Graphical TOC Entry (a) Transmission Electron Microscopy
In AC-HRTEM one can discriminate between flat objects and tubular objects inside the tubes. In addition, electron diffraction allows determining stacking and tube chirality.
Examples are depicted in Fig. 1. Significant intensity difference can be observed between the edge of 7AGNR ( Figure S1a) and the edge of the inner SWNT in DWNT ( Figure S1e).
Whereas for the nanoribbons@SWCNT the intensity profile for the inner objects is flat (Fig.   S1f, top) it exhibits strong dips for the inner objects in SWCNT@SWCNT (Fig. S1f, center and bottom).

(c) Control of Filling Process
Evidence for the location of the ribbons inside the tubes comes from a comparison between the response from ribbons for tubes which were opened before the filling process to tubes which were closed before the filling process. This is demonstrated in Figure 3. The small line representing response from 6AGNR (1245 cm −1 ) in the spectrum of the closed tubes originates from tubes which were not completely closed. This line is at least 16 times smaller than the corresponding response after the tubes were opened. Figure 3: Raman spectra from SWCNTs after transformation procedure for tubes which were opened before filling (red) and for tubes which were explicitly closed before filling (black). Figure 4 shows a blown-up presentation of the calculated and observed spectra 6AGNR and 7AGNR. Response from the tubes and background was subtracted. The very strong response of the mode at 1245 cm −1 in the case of the 6AGNR is surprising considering the results of the calculations. However, recent experiments for 5AGNR and 9AGNR exhibit indeed a very strong Raman response for this mode. 4 The less strong response in the case of the 7AGNR seems to be the exception rather than the rule. Also, it must be kept in mind that the

(e) Wavelength-Dependent Raman Experiments and Their Analysis
Wavelengthdependent resonant Raman experiments were performed in the excitation wave-length range 400-800 nm with 5 nm step size. In order to cover the entire excitation wave-length range, three lasers were used: • 400-526 nm: A single-frequency Ti:sapphire laser with external cavity frequency doubler (SolsTiS and ECD-X platform from M-Squared) which is pumped by an 18W Sprout-G diode-pumped solid state laser (532 nm) from Lighthouse Photonics. • 690-800 nm: A tunable Ti:sapphire laser (Spectra Physics model 3900S) A high resolution triple-grating Dilor XY800 Raman spectrometer was used, equipped with a liquid nitrogen cooled CCD detector and 1800gr/mm gratings. Raman intensities were calibrated by measuring the Raman intensity of the 520.7 cm −1 Raman mode of silicon before and after each experiment.
For the high-frequency regions (regions R4 and R5 in Figure 3 in the main text) a simultaneous least squares fitting was performed using a sum of Lorentzians for the vibrational modes, with shared peak positions and line widths for all excitation wavelengths, but different amplitudes for each excitation wavelength. The amplitudes of the Raman modes for each spectrum (i.e. for each excitation wavelength) are calculated analytically by linear regression. This approach results first of all in a much better determination of the Raman frequencies of the different GNR modes, and in addition also allows for fitting those modes in spectra with very low intensities. In addition to the Lorentzians for the Raman lines, a linear background was included, as well as two broad Lorentzians that accounted for the background and in addition also the D-band from the CNTs was incorporated in the fit.
The latter shows a strong dispersion with laser wavelength, and at different excitation wave- lengths is hidden behind the much stronger GNR signals, therefore its peak position and line width were obtained from measuring and fitting a reference sample of the same CNTs, without the GNRs being present (see Figure 5).  Fig. 6) and the CH-ipb (cyan data points), which are also presented in Figure 4 in the main text, two very weak Raman modes are observed, i.e. with a vibrational frequency of 1312.4 cm −1 (orange data points) and 1221.1 cm −1 (magenta data points), which follow a similar energy profile as compared to the other 7AGNR Raman modes, but also seem to exhibit smaller peaks at lower excitation energies. These peaks at excitation energies lower than 2.2 eV however originate from cross-contamination from the peaks of the 6AGNR in that same region, a consequence of the simultaneous fit procedure with a simple sum of Lorenzians, and are therefore not intrinsic to the 7AGNRs (note that e.g. the intensity of the 1221.1cm −1 line (magenta in Fig. 6) is about 15-20 times weaker than that of the 1243.3 cm −1 line of the 6AGNR). Figure 6 also includes a comparison of the experimental and fitted wavelength-dependent Raman colormaps. To exemplify the goodness of the fit even further, 1D spectra at a few selected excitation wavelengths are shown together with their fit in Figure 7.
In region R1 we observe two different components which follow the exact same resonance profile, corresponding to the 6AGNR RBLMs ( Figure 8). In region R2, multiple components are found. In order to disentangle the different features that overlap in vibrational frequency, we performed a simultaneous fit using a sum of Lorentzian peaks, with common positions and line widths for all wavelengths. To obtain a satisfactory fit, 5 different Lorentzian peaks were needed, as is also clear from the individual Raman spectra obtained at different excitation wavelengths shown in Fig. S8. Figure 7: Selected Raman spectra of the high-frequency Raman modes of 6-and 7AGNRs. Experimental data are represented by black circles, the fit is superimposed with a red line and the laser excitation wavelengths are given on the right side. Each of the spectra is shifted vertically for clarity.
The amplitudes of this simultaneous fit yield the Raman excitation profiles for these 5 Raman features, as presented in Figure S9 together with their vibrational frequencies and line widths. This shows that the 414 cm −1 (cyan) and 401 cm −1 (green) features follow the same excitation profile with two prominent peaks, while the 417 cm −1 (red) feature has a different excitation behavior peaking at 2.65 eV. At first sight, the 414cm −1 profile (also shown in Fig. 4c in the main text) also presents a very minor resonance at 2.65 eV, however, careful error analysis demonstrates that this feature is not statistically significant but rather due to cross-contamination with the overlapping 417 cm −1 peak (leading to highly correlated errors for the amplitudes of both peaks). Similarly, the amplitude of the 397 cm −1 feature is highly correlated with that of the 401 cm −1 feature, explaining the large error bars on the fitted amplitudes. The 375 cm −1 feature is tentatively ascribed to 8AGNR, based on the excellent match with its calculated Raman frequency (see Fig. 4d) and previously determined band gap. 5  : Raman spectra for the RBLM of the 7AGNR as in Figure 4b, but with an additional spectrum with an excitation energy of 2.66 eV, showing that this feature has a different Raman frequency than the main peak at an excitation energy of 2.18 eV (and 2.45 eV), leading to a total of 5 different Raman features.