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https://doi.org/10.1038/s41467-022-30508-z

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Formation of organic color centers in air-suspended
carbon nanotubes using vapor-phase reaction

1234567890():,;

Daichi Kozawa 1 ✉, Xiaojian Wu 2, Akihiro Ishii1,3, Jacob Fortner2, Keigo Otsuka 3, Rong Xiang
Taiki Inoue 5,6, Shigeo Maruyama 5, YuHuang Wang 2,7 & Yuichiro K. Kato 1,3 ✉4,5,Organic color centers in single-walled carbon nanotubes have demonstrated exceptional
ability to generate single photons at room temperature in the telecom range. Combining thecolor centers with pristine air-suspended nanotubes would be desirable for improved performance, but all current synthetic methods occur in solution which makes them incompatible. Here we demonstrate the formation of color centers in air-suspended nanotubes using avapor-phase reaction. Functionalization is directly veriﬁed by photoluminescence spectroscopy, with unambiguous statistics from more than a few thousand individual nanotubes. The
color centers show strong diameter-dependent emission, which can be explained with amodel for chemical reactivity considering strain along the tube curvature. We also estimate
the defect density by comparing the experiments with simulations based on a onedimensional exciton diffusion equation. Our results highlight the inﬂuence of the nanotube
structure on vapor-phase reactivity and emission properties, providing guidelines for thedevelopment of high-performance near-infrared quantum light sources.

1 Quantum Optoelectronics Research Team, RIKEN Center for Advanced Photonics, Saitama 351-0198, Japan. 2 Department of Chemistry and Biochemistry,
University of Maryland, College Park, MD 20742, USA. 3 Nanoscale Quantum Photonics Laboratory, RIKEN Cluster for Pioneering Research, Saitama 3510198, Japan. 4 State Key Laboratory of Fluid Power and Mechatronic Systems, School of Mechanical Engineering, Zhejiang University, Hangzhou 310027,
China. 5 Department of Mechanical Engineering, The University of Tokyo, Tokyo 113-8656, Japan. 6 Department of Applied Physics, Osaka University, Osaka
565-0871, Japan. 7 Maryland NanoCenter, University of Maryland, College Park, MD 20742, USA. ✉email: daichi.kozawa@riken.jp; yuichiro.kato@riken.jp

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Quantum technologies offer various advantages beyond theclassical limits in secure communications1, parallel
computing2, and sensing3. Solid-state single-photon
sources4 are a fundamental component in these technologies, andconsiderable progress has been made in various systems including
quantum dots5, diamond6, SiC7, and two-dimensional materials8.
Of practical interest are single-walled carbon nanotubes(SWCNTs), since operation at room temperature and in thetelecom range is possible. In particular, organic color centersformed on nanotubes9 offer additional advantages with their
optical properties being chemically tunable using a variety ofmolecular precursors, including aryl-halides10–13, diazoniumsalt14–22, ozone23–25, and hypochlorite26 that can covalently bondto the carbon lattice. By introducing dopant states with different
emission energies and achieving potential traps deeper than thethermal energy, single-photon sources with desired properties canbe produced27.
Further development of quantum emitters with improved
performance is expected if color centers can be introduced to asgrown air-suspended SWCNTs known for their pristinenature28,29. In comparison to solution-processed tubes that havenaturally formed quenching sites30, the air-suspended nanotubes
can be considered defect free except for the tube ends28,29. Such asystem should provide an ideal platform for investigating photophysics of color centers14,24, opening up new opportunities innanoscale photonics using one- and zero-dimensional hybrid
structures. Existing methods, however, require liquid-phasereactions where solvents and surfactants are inevitably in contact with the nanotubes, making the reactions incompatible with
air-suspended nanotubes. To combine the excellent opticalproperties of the air-suspended SWCNTs with these organic color
centers, an intelligent design of chemical reactions is needed.
In this work, we propose and demonstrate a vapor-phasereaction to create organic color centers in air-suspended
SWCNTs. Tubes are functionalized with a photochemical reaction where adsorbing precursor vapor allows for preserving thesuspended structures because of a weak mechanical perturbation.
Individual tubes are characterized by confocal microspectroscopy
to verify the formation of color centers, and we conduct a statistical survey of more than 2000 photoluminescence (PL) spectra
to investigate diameter-dependent emission intensities andenergies. PL intensity changes are interpreted using a theoreticalmodel for reactivity that considers strain along the curvature of a
SWCNT. We are also able to estimate the defect density bycomparing experimentally obtained quenching with simulations
based on numerical solutions of a diffusion equation. Characteristic trapping potential depths of color centers are studied byanalyzing emission energies to elucidate the nature of the dopant
states. Furthermore, we perform time-resolved PL measurements
to investigate the dynamics of color center emission.
Results and discussion
PL spectroscopy for individual SWCNTs before and after thefunctionalization. Air-suspended SWCNTs are grown acrosstrenches on Si substrates by chemical vapor deposition31, andvapor-phase reaction using iodobenzene under ultraviolet (UV)
irradiation is then conducted to create color centers. Figure 1ashows a schematic of a functionalized nanotube. Scanning electron microscopy conﬁrms that the tubes stay suspended after thefunctionalization (Fig. 1b). We emphasize that the vapor-phasereaction here differs from typical functionalization techniques
established for dispersed SWCNTs in liquid10–13. The solution
process results in contaminating the tube surface and quenches
PL due to interactions between SWCNTs and surrounding
environment32. It is noteworthy that directly immersing tubes
2

into water inevitably destroys the air-suspended structures due tothe high surface tension of the solvent (Supplementary Fig. 1).
We begin by examining PL spectra before and after thefunctionalization of a (10,5) SWCNT (Fig. 1c) by using thecoordinates of the tube on the chip31 to ensure that we arecomparing the same individual tube. The pristine tube only shows
exciton emission at a higher energy, whereas the functionalized
tube shows two additional peaks at lower energies. We label the
exciton emission at 1.02 eV as E11 and the additional peaks at 0.94

and 0.88 eV as E
11 and E11 , respectively. The lower energies ofE11 and E11 indicate that sp3 defects of phenyl group are formed
on SWCNTs which introduce dopant states33. No remarkable
spectral shift of E11 emission peak is detected, suggestingnegligible changes in dielectric environment due to the vapor
residue. The overall PL intensity reduces to less than a quarter
which implies introduction of quenching sites in addition to color
centers. Hereafter, we refer to defects that decrease the E11
intensity as quenching sites and defects that give rise to the E
11and the E
11 peaks as color centers.
Imaging measurements are performed to characterize thespatial distributions of E11, E
11 , and E11 emission. We scan overa (9,7) SWCNT to collect PL spectra and construct intensity maps
for the three peaks by spectrally integrating intensities of eachpeak (Fig. 1d–f). The edges of the trench can be identiﬁed using areﬂection image in the same area (Fig. 1g). Bright PL is emitted
from the suspended region, as typically observed for air-suspended
nanotubes31. The spatial proﬁle of the E11 emission indicates thelocation of the nanotube and the additional peaks are observed
along this tube, consistent with emission originating from colorcenters formed on the same tube. It is noted that E
11 and E11
emission show some spatial inhomogeneity in the intensity.
Statistical investigation of emission intensities. Emission fromvarious chiralities are now studied by collecting PL spectra ofmore than 2000 individual SWCNTs before and after the functionalization. All PL data are obtained from a single substrate
which assures that the reaction condition is the same, allowing for
direct comparison among the chiralities. To acquire the data
efﬁciently, we perform two sets of measurements with excitationenergies of 1.46 and 1.59 eV which are near-resonant to manychiralities. Assuming that excitation is close to the E22 energy,
chiralities of SWCNTs are assigned based on the E11 emission
energy. For statistical analysis, 12 chiralities with sufﬁcientnumbers of tubes are used.
We ﬁrst consider the intensity of E11 emission before thereaction. PL spectra are ﬁtted by a Lorentzian function to obtainthe spectrally integrated intensity I0. Large dispersion is observed(Supplementary Figs. 12, 13, and 14), which can be attributed tovarious suspended lengths (Supplementary Note 1). Many
SWCNTs are not fully suspended as observed in PL images(Supplementary Fig. 15), and their suspended lengths are likely
shorter than the trench widths. Indeed, the intensity dispersion iswell reproduced by simulations of length dependent PL
intensity28,29 assuming a log-normal length distribution34
centered at 0.78 μm (Supplementary Fig. 16), indicating thatmost nanotubes have lengths ranging from 0.5 to 1.0 μm. We notethat the simulations cannot be directly compared to experiments
for nanotubes with no detectable PL, but the fraction of tubes isnegligible at low intensities for the distribution reproducing theexperimental data.
After the functionalization, color center emission appears inthe PL spectra (Fig. 2a, b). All chiralities exhibit E
11 and E11
emission except for (10, 8), (11, 7), and (12, 5) SWCNTs whoseE
11 is beyond the low energy detection limit. We ﬁnd that mostE
11 peaks are taller than E11 peaks.

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NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-30508-zabcCatalyst

Nanotube

d

e

f

g
Reflectivity (arb. units)

1

PL intensity (arb.units)

1

0

0

Fig. 1 Introducing organic color centers to air-suspended nanotubes using vapor-phase reaction. a A schematic of a functionalized SWCNT suspended
across a trench on a Si substrate. b A scanning electron micrograph of a tube after the functionalization and the series of PL measurements. Particles on the
top are patterned catalysts for growing SWCNTs and the nanotube is indicated by an arrow. c Representative PL spectra of an identical air-suspend (10,5)
SWCNT before and after the functionalization taken with a laser power of 10 μW and an excitation energy of 1.59 eV. PL intensity maps of (d) E11, (e) E
11 ,and (f) E
11 emission from a (9,7) tube where the intensity is integrated within a window of 37.4, 32.5, and 28.5 meV centered at each emission peak,
respectively. The color scales are normalized to the maximum intensities in the respective maps. The dim features on the right of the tube are caused by
reﬂection of the excitation laser from the bottom of the trench. The white broken lines indicate the edges of the trench. g A reﬂection image in the same
area, where brighter and darker regions correspond to the surface of the substrate and the bottom of the trench, respectively. The scale bars in panels(b, d–g) are 1.0 μm. Source data for panels (b–g) are provided as a Source Data ﬁle.
abFig. 2 Dopant state emission from various chiralities. PL spectra offunctionalized SWCNTs collected with excitation laser energies of (a) 1.46
and (b) 1.59 eV and with an excitation power of 100 μW, where the spectra
are displaced vertically for clarity. Black and gray arrows indicate E
11 andE
11 , respectively. Chirality (n, m) is labeled next to the E11 peaks. Source
data are provided as a Source Data ﬁle. Logscale PL spectra for eachchirality are presented in Supplementary Fig. 2.

The intensity of E
11 emission can be used to quantify color
center density, but care must be taken because of the large
variation in the emission intensity. We use the subpeak ratio
I
11 =I 11 as a measure of the color center density, where I 11 and I11
are the spectrally integrated intensities of E
andE
11 emission,11
respectively. By taking the ratio, the variations of E11 emission
intensity can be canceled out to some degree. The subpeak ratioI
11 =I 11 is plotted as a function of E11 emission energy in Fig. 3and for each chirality in Supplementary Fig. 3. We observe a

monotonically increasing trend with emission energy, indicatingthat smaller diameter tubes have more color centers (Supplementary Fig. 4). It should be noted that the chirality dependent
E22 energy (Supplementary Fig. 5) results in emission intensity
differences, since we ﬁx the excitation energy either at 1.46 or
1.59 eV. Taking the ratio cancels out the chirality dependent E11emission intensity, allowing for direct comparison between
different chiralities. The intensity dispersion can also be causedby resonance shifts due to initial strain generated during growthand inhomogeneity of dielectric environment, but PL intensity
variations should be insigniﬁcant since energy shifts are typicallywithin ±10 meV29. Although small, the effects of these variations
are likewise reduced by taking the ratio.
It is also possible to study the effects of the defects from thereduction of E11 emission due to the functionalization. In amanner similar to the subpeak ratio, we take the quenchingdegree (I0 − I11)/I0 as a more physically relevant quantity forcomparison between different nanotubes with various suspended
lengths and chiralities. The quenching degree exhibits anincreasing trend with emission energy as in the case of I 
11 =I 11
except for (9, 8) and (12, 5) nanotubes, which do not have astatistically sufﬁcient number of data points (Fig. 3c, d). The large
variation of the ratios (Supplementary Fig. 6) are likely caused bymultiple factors including inhomogeneity among SWCNTs,
temporal ﬂuctuations in intensity (Supplementary Fig. 7), andpositions of the defects35. We note that (I0 − I11)/I0 reﬂects theeffects of color centers in addition to quenching sites, as bothresults in reduced E11 emission through trapping excitons.
A model for the chemical reactivity. To quantitatively interpretthe trend of the subpeak ratio and the quenching degree, a theoretical model is developed. Chemical reactivity of SWCNTs
depends on both π-orbital pyramidalization angle36 and π-orbital
misalignment angle between adjacent pairs of conjugated C
atoms18,37. The former is subject to strain arising from the

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a

b

b

a

θp
V1

c

d

e

f

d

c

Fig. 3 Statistical analysis of PL intensities. Subpeak ratio I
11 =I11 as afunction of emission energy for experiments conducted with excitationenergies of (a) 1.46 and (b) 1.59 eV and an excitation power of 100 μW.
Quenching degree (I0 − I11)/I0 measured with excitation energies of (c)1.46 and (d) 1.59 eV and an excitation power of 10 μW. Source data areprovided as a Source Data ﬁle.

curvature of the tubular structure and is diameter dependent,
whereas the latter originates from a bond angle with respect to thetube axis and is chiral angle dependent. As we observe a clear
diameter dependence, our model considers the π-orbital pyramidalization angle θp depicted in Fig. 4a. The C-C bonds are
more bent for larger θp, corresponding to larger strain. Figure 4b
shows calculated pyramidalization angles as a function of thenanotube diameter d along with a ﬁt by a scaling law θp = δ/dwhere δ = 4.01∘ nm−1 is the coefﬁcient. Because the strain fromthe curvature increases the chemical reactivity36, we assume thatthe reduction in the activation energy is proportional to thepyramidalization angle. The activation energy of the reaction isthen Ea(d) = Ea(∞) − ηθp(d) where Ea(∞) is the activation energy
for graphene, and η is the coefﬁcient. According to the Arrhenius
equation, it follows that the chemical reaction rates are proportional to


E ð1Þ
1 ηδ
ð1Þ
þ

exp  akB T
kB T dwhere kB is the Boltzmann constant and T = 298 K is the temperature. The ratios I 11 =I 11 and (I0 − I11)/I0 should therefore
scale as exp k 1T  ηδd .
BSince data dispersion is large, we use the average values of theseratios for each tube diameter (Fig. 4c, d). We only include thetubes on the widest trenches with 3.0 μm width to reduce end
quenching effects. It is conﬁrmed that SWCNTs with smaller
diameters show higher ratios, indicating that these tubes are morereactive despite the smaller surface areas. We ﬁt the model to theexperimental data, and both ratios show good agreement. The ﬁt
to I 
11 =I 11 yields η = 41.3 ± 9.4 meV/deg, whereas the ﬁt to(I0 − I11)/I0 results in η = 13.4 ± 1.9 meV/deg. The higher η forI
11 =I 11 by a factor of 3.08 indicates that the formation of color
centers is more responsive to strain compared to quenching sites,
although the higher excitation power used to obtain the subpeak
4

Fig. 4 Diameter-dependent reactivity. a A schematic deﬁning the
pyramidalization angle θp where Vπ is a π-orbital axis vector, V1 is a unit
vector pointing from the target atom to an adjacent atom55. The
pyramidalization angle can be analytically estimated using a relationshipcosðθp þ 90 Þ ¼ V1  Vπ . b Diameter dependence of computed
pyramidalization angle, where the angles of armchair, zigzag, and chiraltubes are separately plotted. Diameter dependence of (c) subpeak ratioI
11 =I11 and (d) quenching degree (I0 − I11)/I0, where error bars are thestandard error of the mean. The solid line in panel (b) is a ﬁt as explained in
the main text, and the solid lines in panels (c, d) are ﬁts by Eq. (1).
e Simulations of E11 steady-state exciton density proﬁle for no defects(blue), ρ = 1.0 (orange), and ρ = 2.0 μm−1 (green). The origin of thecoordinate system is taken to be the center of the tube. f Diameter
dependence of estimated defect density, where error bars are the standard
error of the mean. The error bars in (c, d, f) are calculated from 5 to 53
measurements for each data point. Source data for panels (b–f) areprovided as a Source Data ﬁle.

ratio could lead to underestimation of the reactivity for the color
centers (Supplementary Fig. 18 and Note 2). It should be possible
to use this difference for preferential creation of color centers bychoosing tubes with smaller diameters. We note that an opposite
diameter dependence on chemical reactivity has been reported fora reaction with 4-hydroxybenzene diazonium38, where electrontransfer limits the reaction rate.
Defect density estimation. The ratio (I0 − I11)/I0 also allows us toquantify the defect density by modeling the effects of functionalization on PL intensity. We use the fact that pristine airsuspended nanotubes are defect free except for end
quenching28,29. Although the nanotubes used in this study havevarying suspended lengths (Supplementary Note 1), the experimentally obtained distribution of I0 (Supplementary Fig. 12) is
consistent with a simulation assuming defect free nanotubes(Supplementary Fig. 16). In comparison, the experimental results

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cannot be reproduced if initial defects are included in the simulations (Supplementary Fig. 17), and we therefore estimate thedefect density in pristine SWCNTs to be much less than 0.25 μm−1.
Our model is based on a steady-state one-dimensional
diffusion equation
d2 nðzÞ nðzÞ
Γ0
z2
ð2Þ
p
ﬃﬃﬃﬃﬃﬃﬃﬃﬃ
D
þ
¼0
exp


dz 2
τ
2r 2
2πr 2
where D is the diffusion coefﬁcient, n(z) is the E11 exciton density,z is the position on the tube, τ = 70 ps is the intrinsic lifetime of
excitons31, Γ0 is the exciton generation rate, and r = 530 nm is the
1/e2 radius of the laser spot. The ﬁrst term accounts for theexciton diffusion, the second term represents the intrinsic
recombination, and the third term describes exciton generation
which is proportional to the Gaussian laser proﬁle. We consider
SWCNTs with inﬁnite length and set the boundary conditions tobe n(±∞) = 0. Additional boundary conditions n(zd) = 0 are
imposed for the functionalized tube where zd is the position of
defects, assuming that the sites are uniformly distributed withdensity ρ. For the diffusion coefﬁcient, we use the expression
D ¼ D0 ðd=d 0 Þα where D0 = 15.36 cm2/s is the diffusion coefﬁcient atpdiameterd0 = 1.00 nm corresponding to a diffusion
ﬃﬃﬃﬃﬃﬃ
length Dτ ¼ 328 nm, and α = 2.56 is the exponent31. The
diffusion equation is numerically solved to obtain n(z) and theresults are plotted for various site densities in Fig. 4e (Supplementary Fig. 8a). When the defect separation is much shorter
than the laser spot diameter, the quenching process becomesdominant over the intrinsic decay and results in a signiﬁcantdecrease in the exciton density.
The defect density is estimated by comparing (I0 − I11)/I0
obtained from the experiments with the simulations. We use theexperimental data of tubes on the widest trenches with 3.0 μm
widths, and the PL intensity in the simulation is computed byintegrating n(z) (Supplementary Fig. 8b). The only unknown
parameter ρ is extracted by matching the simulated quenchingdegree with the experimental values. The results are plotted as afunction of the diameter in Fig. 4f. The defect density ranges from0.95 to 2.2 μm−1 and shows a diameter dependence which isconsistent with the trend of the reactivity (Fig. 4c, d). The
estimated defect density represents a lower bound because of theassumption in the simulations that defects are uniformly
distributed in nanotubes (Supplementary Note 3). We also
compare the distribution of (I0 − I11)/I0 between experiments andsimulations (Supplementary Note 4). The experiments are well
reproduced by a simulation assuming the log-normal length
distribution and ρ = 1.5 μm−1 (Supplementary Figs. 19 and 20a).
In comparison, a simulation with a high defect density ofρ = 10 μm−1 cannot reproduce the experimental results (Supplementary Fig. 20b). It is worth mentioning that the estimateddefect density includes contributions from color centers andquenching sites as they both reduce the number of E11 excitons.
Emission energy analyses for various chiralities. We now pro
ceed to analyze E
11 and E11 peak positions. Energy separations



ΔE
¼
E

E
and
ΔE
11
11
11 ¼ E 11  E 11 can be interpreted as11trapping potential depths for E11 and E
11 excitons, respectively,and we plot ΔE
11 and ΔE11 as a function of E11 in Fig. 5a, b. Theenergy separations show correlated increase with E11, conﬁrmingthat E
11 and E11 originate from dopant states of E11 exciton, andnot of other states such as E22 and E33 excitons. It is noted that we
observe smaller clusters for ΔE
11 as marked by circles in Fig. 5a,whose trapping potentials are smaller than the main clusters. The
differences in E
11 could be assigned to different binding conﬁgurations of the phenyl functional group, where ortho- and paraconﬁgurations exhibit different emission energies11,18,39. We

a

c

b

d

Fig. 5 Statistical analysis of emission energies. Energy separation ΔE
11
and ΔE
11 of functionalized SWCNTs as a function of emission energy, where
the data are collected with excitation energies of (a) 1.46 and (b) 1.59 eV
and a power of 100 μW. The color of the dots represents the nanotube
chirality and isolated clusters are indicated by circles. Diameterdependence of average (c) ΔE
11 and (d) ΔE 11 , where error bars are thestandard error of the mean and calculated from 25 to 373 measurements
for each data point. The solid and broken lines are ﬁts by the power laws 1/
 2
d2 and 1/d, respectively. The data are better described by ΔE
11 ¼ A =d and 2− = 84.0 ± 2.64 meV ⋅ nm2 and A−* = 154 ± 1.43
ΔE 
¼
A
=d
,
where
A
11

meV ⋅ nm2 are the coefﬁcients for ΔE
11 and ΔE 11 , respectively. Source data
are provided as a Source Data ﬁle.

similarly interpret the E
11 emission to be arising from otherbinding conﬁgurations.
The diameter dependence of the trapping potentials provides
additional insight to the nature of the dopant states. The averagevalues of ΔE
11 and ΔE11 for each chirality are plotted as afunction of the diameter in Fig. 5c, d. The dependence shows amonotonic decrease and differs from the constant energy
separation of 130 meV for the K-momentum excitons, and we
thus exclude them from the origin of E
11 and E11 . To describe thedependence, we consider the 1/d scaling observed for the exciton
binding energies and the 1/d2 scaling for singlet-triplet
splitting40–44 (Supplementary Note 5). The 1/d2 scaling yields

better ﬁts to both ΔE
11 and ΔE 11 than the 1/d scaling.

The values of the energy separations ΔE
11 and ΔE11 observed
42,43
in this work show more similarity to triplet
and trion states45.
,ΔE
Examining the higher energy peak E
11 = 84.0 meV at
11
d = 1 nm is as high as the energy splitting reported for triplet
excitons; Matsunaga et al. found 1/d2 dependence of energy
separation for laser-induced defects in air-suspended SWCNTs43,
with a value of 70 meV at d = 1 nm. Nagatsu et al. showed the 1/
d2-dependent energy separation in air-suspended SWCNTs forH2-adsorption-induced peaks where ΔE
11 = 68 meV at d = 1 nm
is attributed to triplet excitons42. The comparable values of theenergies and the 1/d2 scaling for E
11 suggest that the triplet
exciton state is brightened at the color centers. Further study with
optically detected magnetic resonance46 and magneto-PL
spectroscopy47 would be required to clarify the triplet origin ofE
11 excitons. Considering the lower energy peak E11 , ΔE 11 = 154
meV at d = 1 nm is close to 175 meV-separation between excitonand trion energies for air-suspended SWCNTs45 with a diameterof 1 nm. Using chemical47 or electric-ﬁeld48 doping to investigate

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trions trapped at color centers in air-suspended nanotubes mayhelp elucidate the origin of the state. We note that the tubes
studied here have larger diameters than typical SWCNTs

dispersed in liquid11,18, but the observed ΔE
11 and ΔE11 areconsistent with the extrapolation of the d dependence for smaller
diameters.
The diameter dependence of the trapping potential is partially
responsible for the difference of subpeak ratio between airsuspended and solution-processed nanotubes33. The larger
diameters for air-suspended SWCNTs lead to shallower trapping
potentials15,22, resulting in lower quantum yields for E
11emission. In addition, pristine air-suspended nanotubes can beconsidered defect free28,29, whereas solution-processed tubes havenaturally formed defects with a typical density of 8.3 μm−1 30. I0in air-suspended nanotubes is therefore stronger than solutionprocessed tubes, further reducing the subpeak ratio.
The dynamics of excitons in a functionalized SWCNT. The
dynamics of the color center emission is also investigated by timeresolved PL measurements to compare to the decay lifetimes ofE11. We use a pulsed laser for excitation, and the E11 emission is
spectrally differentiated from the E
11 and E11 emission with aband-pass ﬁlter and a long-pass ﬁlter (Supplementary Fig. 9).
Figure 6 shows PL decay curves for these emission peaks from an(11, 3) functionalized tube. Decaylifetimes
byﬁtting are extracteda biexponential function a1 exp t=τ 1 þ a2 exp t=τ 2 convoluted with the instrument response function, where τ is the
decay lifetime and a is the amplitude with the subscripts 1 and 2
denoting fast and slow components, respectively. We ﬁnd that τ1
for color center emission is 1.6 times longer than τ1 for E11
exciton emission. This difference is moderate compared to 3.3
times observed for solution-processed SWCNTs15 likely becauseof the lower defect density in air-suspended nanotubes resulting
in longer E11 exciton lifetime.
The biexponential behavior for E11 and E
11 emission isconsistent with previous reports for solution-processed
samples15,22,49, where the decay for E11 can be understood by athree-level model including bright, dark, and ground states50,51.
Both bright and dark excitons are populated by E22 resonant
excitation and inter-state transitions take place between the brightand dark states, resulting in the fast component from bright

exciton recombination and the slow component reﬂecting the
dynamics of dark excitons. The bixponential decay for color
center emission can be similarly understood by considering anE
11 manifold having three levels associated with the color center
which is independent from the E11 states15,23.
The lifetimes τ1 = 69.1 and τ2 = 172.0 ps for the color centersof the air-suspended nanotube are comparable to τ1 = 86 andτ2 = 171 ps for solution-processed tubes15. This result is reasonable because color centers are isolated and other defects should
not affect the excitons trapped at the color centers. The
comparable lifetimes also indicate that the vapor-phase reaction
can form as high-quality color centers as the solution-processed
methods. Although the diameter dependence of the potential
depth for E
11 exciton suggests its triplet nature, the observed
lifetime is several orders of magnitude shorter than 30–200 μs
reported for the triplet states46,52. Lifetime shortening may becaused by hybridization of the singlet and triplet excitons53.
Finally, we discuss how improvements can be made to take fulladvantage of the vapor-phase reaction. The formation of color
center density can be adjusted by optimizing the duration ofreaction time (Supplementary Fig. 10), ideally creating a single
color-center per nanotube. We are aware of quenching sites
introduced by UV irradiation itself, as observed in control
experiments in the absence of iodobenzene (Supplementary
Fig. 11). Suppression of this process could be possible by
optimizing the power and the energy of UV light. By introducing
deeper traps by different precursor molecules, quantum yield for
22,33. It is desirable to develop vapor-phaseE
11 may be improved
chemistry with these molecules for air-suspended nanotubes as
the quantum yield in solution-processed nanotubes has improvedby ~50% with a trapping potential deeper by 16 meV22. Because
the potential depth depends on the diameter (Fig. 5c, d),
SWCNTs with smaller diameters would be suited for higher
quantum yield.
In summary, we have demonstrated functionalization of airsuspended SWCNTs using iodobenzene as a precursor. The
comparison of PL spectra before and after the vapor-phasereaction shows additional peaks E
11 and E11 from color centers
and PL intensity reduction of the E11 peaks. Twelve representativechiralities are characterized using spectra from more than 2000
individual tubes, where the diameter dependent subpeak ratio andquenching degree are observed. We have modeled the diameter
dependent reactivity which is found to be proportional toexpð1=dÞ, explaining the experimental results. By further
performing the exciton diffusion simulations, we have estimatedthe defect density and found that these values are also diameter
dependent. The analysis of peak energies reveals that both E
11and E
11 states originate from dopant states of E11 excitons andhave trapping potentials scaling as 1/d2. We observe a longer PL
lifetime for dopant states, similar to the reports on solutionprocessed tubes. By elucidating the exciton physics as well asfunctionalization chemistry, color centers in air-suspended
SWCNTs should provide new opportunities in photonics andoptoelectronics for quantum technologies.
Methods

Fig. 6 Time-resolved PL properties. PL decay curves of E11 emission (blue)and E
11 and E11 emission (orange) from a functionalized (11, 3) SWCNT
suspended across a trench with a width of 1.0 μm measured by an
excitation energy of 1.59 eV and a power of 10 nW using the pulsed laser.
The broken lines are the ﬁts by a biexponential decay function convoluted
with the instrument response function (gray), showing τ1 = 42.2 andτ2 = 122.0 ps for E11 and τ1 = 69.1 and τ2 = 172.0 ps for E
11 and E11 . Source
data are provided as a Source Data ﬁle.
6

Air-suspended carbon nanotubes. Electron-beam lithography and dry etching
are used to fabricate trenches on Si substrates54 with a depth of ~1 μm and a widthof up to 3.0 μm. Another electron-beam lithography is conducted to deﬁne catalyst
areas near trenches, and Fe-silica catalyst dispersed in ethanol are spin-coated andlifted off. SWCNTs are synthesized over trenches using alcohol chemical vapor
deposition31,54 under a ﬂow of ethanol with a carrier gas of Ar/H2 at 800 °C
for 1 min.
Formation of organic color centers. Vapor-phase reaction is used to functionalize
air-suspended nanotubes with iodobenzene as a precursor. As-grown SWCNTs on
the Si substrates are placed facing up inside a glass chamber having a diameter of

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NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-30508-z

15 mm and a height of 5 mm. Iodobenzene (5 μL) is introduced to the bottom of
the chamber by a micropipette. The chamber is then covered with a quartz slideand sealed using high vacuum grease. We leave the chamber for 10 min to ﬁll itwith iodobenzene vapor, after which the reaction is triggered by irradiating thesample with 4.88-eV UV light through the quartz slide. The samples are collectedfrom the chamber and stored in dark for characterization by subsequent
spectroscopy.
Micro-PL measurements. PL spectra are obtained with a home-built scanningconfocal microscope31, where we use a continuous-wave Ti:sapphire laser for
excitation and a liquid-N2-cooled InGaAs photodiode array attached to a 30-cm
spectrometer for detection. Laser polarization is kept perpendicular to trenches,
and the beam is focused using an objective lens with a numerical aperture of 0.85
and a focal length of 1.8 mm. The 1/e2 diameters of the focused beams are 1.31 and1.06 μm for excitation energies of 1.46 and 1.59 eV, respectively, where the diameters are characterized by performing PL line scans perpendicular to a suspended
tube. PL excitation spectroscopy is conducted by scanning excitation wavelength ata constant power29. The reﬂected laser light is collected with a biased Si photodiodefor reﬂection images. All PL spectra and decay curves are taken at the center of thenanotubes except for the hyperspectral PL imaging.
Spectral analysis. Peak parameters are extracted by ﬁtting a Lorentzian function
to PL spectra for pristine SWCNTs and a triple-Lorentzian function for functionalized SWCNTs. Pristine nanotubes with an E11 peak height of less than 500
counts/s are excluded in the statistics and not used for further measurements. We
also exclude functionalized nanotubes with an E11 peak height of less than 400
counts/s.
Decay lifetime measurements. For time-resolved PL measurements, the Ti:sapphire laser is switched from continuous wave to ~100-fs pulses with a repetition
rate of 76 MHz. A ﬁber-coupled superconducting single-photon detector is used tomeasure PL decay. Emission from E11 excitons and dopant states are separately
obtained with a band pass ﬁlter and a long pass ﬁlter.

Data availability
All the data generated in this study have been deposited in the R2DMS-GakuNinRDM
database at https://dmsgrdm.riken.jp/nxuar/. Source data are provided with this paper.

Received: 26 February 2021; Accepted: 28 April 2022;

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Acknowledgements
This work is supported in part by MIC (SCOPE 191503001 to Y.K.K.), JSPS
(JP18H05329, JP20H00220 to S.M., JP19H02543, JP20KK0114 to R.X., JP20H02558 to
Y.K.K., JP20K15112 to D.K., JP20K15137 to K.O.), MEXT (Nanotechnology Platform
JPMXP09F19UT0077), NSF (RAISE-TAQS PHY-1839165 to Y.H.W.), and JST (CREST
JPMJCR20B5 to S.M.). D.K. acknowledges support from RIKEN Special Postdoctoral
Researcher Program. K.O. is supported by JSPS Research Fellowship. We thank the
Advanced Manufacturing Support Team at RIKEN for technical assistance.

Author contributions
Y.K.K., Y.H.W., and S.M. conceptualized the idea, and formulated the overarchingresearch goals. A.I., T.I., and R.X. synthesized SWCNTs. X.W. and J.F. conducted the8functionalization. D.K., A.I., and K.O. performed the optical measurements. D.K., A.I.,
and Y.K.K. interpreted the results. D.K. and Y.K.K. wrote the original draft with input
from all the authors.

Competing interests
The authors declare no competing interests.

Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41467-022-30508-z.
Correspondence and requests for materials should be addressed to Daichi Kozawa or
Yuichiro K. Kato.
Peer review information Nature Communications thanks the anonymous reviewers fortheir contribution to the peer review of this work. Peer reviewer reports are available.
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