PRL 112, 117401 (2014)

week ending
21 MARCH 2014

PHYSICAL REVIEW LETTERS

Spontaneous Exciton Dissociation in Carbon Nanotubes
Y. Kumamoto, M. Yoshida, A. Ishii, A. Yokoyama, T. Shimada, and Y. K. Kato*
Institute of Engineering Innovation, The University of Tokyo, Tokyo 113-8656, Japan(Received 8 July 2013; published 17 March 2014)
Simultaneous photoluminescence and photocurrent measurements on individual single-walled carbon
nanotubes reveal spontaneous dissociation of excitons into free electron-hole pairs. The correlation of
luminescence intensity and photocurrent shows that a significant fraction of excitons are dissociating
before recombination. Furthermore, the combination of optical and electrical signals also allows for
extraction of the absorption cross section and the oscillator strength. Our observations explain the reasons
why photoconductivity measurements in single-walled carbon nanotubes are straightforward despite thelarge exciton binding energies.
DOI: 10.1103/PhysRevLett.112.117401

PACS numbers: 78.67.Ch, 71.35.-y, 78.55.Kz, 78.56.-a

An enhancement of the Coulomb interaction occurs in
one-dimensional systems because of limited screening [1],and single-walled carbon nanotubes (SWCNTs) are an
ideal model system where such an effect manifests itself[2]. Electron-hole pairs form tightly bound excitons with abinding energy of a few hundred meV, which amounts toa significant fraction of the band-gap energy [3,4]. Such alarge binding energy warrants the stability of excitons evenat room temperature, and with exciton size being a few nm[5,6], strong fields on the order of 100 V=μm would be
required for exciton dissociation [7].
In contrast to the expectation that the generation of free
carriers from charge-neutral excitons would be difficult,photocurrent and photovoltaic measurements have proved
to be simple and convenient tools for studying the properties
of SWCNTs. Not only have they been used to measurepotential landscapes [8–11], optical absorption properties[12–14], and ultrafast carrier dynamics [15], they have been
instrumental in investigating unique effects that occur in
SWCNTs, such as band-gap renormalization [16] andmultiple electron-hole pair generation [17]. It has been a
perplexing situation where exciton dissociation has not beenbrought up as an obstacle for performing these experiments.
In interpreting the results, quantitative discussion on the
dissociation process has been scarce, and in some cases theexcitonic effects have not been considered at all.
Here we resolve such an inconsistency by performing
simultaneous photoluminescence (PL) and photocurrent(PC) measurements on individual SWCNTs. Nonzero
photoconductivity is observed even at small fields, indicating that excitons are spontaneously dissociating. A simple
model is constructed to consistently describe the excitation
power and voltage dependencies of the PL and PC. Using
this model, we find that a good fraction, if not a majority, of
excitons are dissociating into free carriers. Within the same
analysis framework, we are also able to extract theabsorption cross section and the oscillator strength at theE22 resonance.
0031-9007=14=112(11)=117401(5)Our devices are field-effect transistors with individual
air-suspended SWCNTs [18] as shown in Fig. 1(a). We startwith a Si substrate with 1 μm-thick oxide, and etch
∼ 500 nm-deep trenches into the oxide layer. An electron
beam evaporator is used to deposit 3 nm Ti and 45 nm Pt forelectrodes. Finally, catalyst particles are placed on thecontacts and alcohol chemical vapor deposition is performed to grow SWCNTs [19,20]. A scanning electron
micrograph of a typical device is shown in Fig. 1(b).
We look for devices that show nanotube PL at the trenchin between the electrodes using a confocal microscope[21,22]. A continuous-wave Ti:sapphire laser is used for
excitation and PL is detected by an InGaAs photodiodearray attached to a spectrometer. The PC measurements are
performed by monitoring the current through the device inthe presence of a bias voltage V. We apply −V=2 and þV=2
to the two contacts, respectively, and ground the Si
substrate. Although we do not expect much electrostatic
doping because of the relatively thick oxide, this configuration ensures that the effective gate voltage at the centerof the trench is zero. The current is averaged while a PL
spectrum is collected, and the PC is obtained by subtracting
the dark current measured in a similar manner with the laser
blocked by a shutter. All measurements are done in air atroom temperature.
Figure 1(c) is an optical microscope image of the device,
and in the area indicated by the black box, we performreflectivity, PL, and PC imaging simultaneously at an
excitation laser power P ¼ 15 μW. The reflectivity image[Fig. 1(d)] shows the position of the trench, and aluminescent nanotube suspended over the trench can beseen in the PL image [Fig. 1(e)]. The PC image shows thatthe signal is maximized at the same spot as PL [Fig. 1(f)]. In
contrast to the case of Schottky barrier imaging [8–11], we
do not observe PC when the laser spot is near or on thecontacts. This confirms that band bending and electrostatic
doping near the contacts are negligible in our voltage
configuration.

117401-1© 2014 American Physical Society

(d)

3

(e)

8
6
4
2

PL (arb. units)1

1.7

PL (arb. units)
2 4 6 8(a)

1.6
P = 5 µW
1.5 V = 0 V
0.8 0.9 1.0
Em
mission energy (eV)

2.0

8
6

(b) P = 8 µW
V = 20 V

1.5

4

1.0

2

0.5

0

1.5
1.6
1.7
Excitation energy (eV)0.0

FIG. 2 (color). (a) A PL excitation map for the same nanotube
as shown in Figs. 1(d)–(f) for P ¼ 5 μW and V ¼ 0 V. (b) PL(red curve) and PC (open circles) spectra taken with P ¼ 8 μW
and V ¼ 20 V. Laser polarization is parallel to the nanotube axis.
PL intensity is obtained by fitting the emission spectra withLorentzian functions and taking the peak area.

(b)
0
(f)
2

1

PC (nA)(c)0

PL intensity (arb. units)

lyst

Excitation energy (eV)

5

cata

Reflectivity (arb. units)(a)week ending
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PHYSICAL REVIEW LETTERS

Photocurrent (nA)

PRL 112, 117401 (2014)

0

FIG. 1 (color). (a) A schematic of a device. (b) A scanningelectron micrograph of a typical device. (c) A top-view optical
microscope image of a device with a trench width of 1.3 μm. The
black box shows the scan area for imaging measurements shownin (d)–(f). The scale bars in (b) and (c) are 0.5 μm and 4 μm,
respectively. (d), (e), and (f) are reflectivity, PL, and PC images,
respectively. The scale bars are 1 μm. Excitation energy and bias
voltage are 1.651 eV and 20 V, respectively, and laser polarization
angle is adjusted to maximize the PL signal. For (e), the PL image
is extracted at an emission energy of 922 meV with a spectral
integration window of 7 meV.

PL excitation spectroscopy performed on this nanotube
at zero bias voltage shows a clear single peak [Fig. 2(a)],and we identify the nanotube chirality to be (10, 6). By
performing such an excitation spectroscopy under anapplication of bias, we obtain PL and PC excitation spectra
simultaneously [Fig. 2(b)]. Both PL and PC have a peak at
the same excitation energy corresponding to the E22
resonance. The spatial and spectral coincidence of the
PL and PC signals show that both are indeed coming fromthe same nanotube.
On this device, the excitation power and bias voltage
dependencies are investigated in Figs. 3(a)–3(d). We first
discuss the excitation power dependence. For all of thevoltages, the PC signal shows a linear increase withexcitation power [Fig. 3(a)], whereas PL shows a sublinear
increase [Fig. 3(b)]. The latter behavior is known to becaused by exciton-exciton annihilation [21,23–25]. If theobserved PC is caused by dissociation of the E11 excitons,
then we expect PC to scale with PL, as both of the signals
should be proportional to the number of E11 excitons.
Rather, the linear behavior suggests that the PC is
proportional to the number of excitons injected at theE22 energy, and that dissociation of E11 excitons is
negligible. There are at least two different processes thatcan result in the dissociation of E22 excitons. It is
possible that the applied electric field induces thedissociation, and in this case one would expect somethreshold voltage at which the dissociation occurs [7].
Another conceivable scenario is the dissociation that
happens spontaneously in the course of relaxation down
to E11 exciton states.
The two pictures can be distinguished by examining thevoltage dependence of the PC [Fig. 3(c)]. We observethat the PC has a slightly superlinear dependence on theapplied voltage, but there exists some slope near V ¼ 0.
This implies that the conductivity is nonzero even at zero
applied bias, supporting the interpretation that the injected
excitons are spontaneously dissociating. Those carriers thatare swept into the contacts before binding into E11 excitons
would generate the PC.
We note that the lack of field-induced dissociation forE22 excitons is consistent with the interpretation of theintensity dependencies that E11 exciton dissociation is
negligible. The binding energy for E22 excitons is larger
than E11 excitons [26], and therefore we do not expect
field-induced dissociation of E22 excitons if E11 excitons
are still intact. Measurements with an excitation at the E12resonance do not show much change in PL intensity with
voltage [27], also suggesting that field-induced dissociation
is not important at these fields.
As the continuum for E11 excitons lies below E22, it may
seem reasonable to attribute the spontaneous dissociation
to direct electronic transition to free electron-hole pairs. It
has been suggested, however, that such a process is much
weaker than phonon-mediated relaxation to E11 and E12
exciton states [28]. Since relaxation to excitonic states does
not result in free carriers, we speculate that dissociation
involving a free electron-hole pair with an emission of aphonon may be responsible for the observed photocurrent.
Another possible mechanism is the free-carrier generation from E11 exciton-exciton annihilation [29]. As the117401-2

PRL 112, 117401 (2014)4

V = 20 V
15 V
10 V
5V

Photocurrent (nA)

(a)

2
0
20

(e)

15 µW
1
1 µW
10
5 µW

2

η21

10
5
0

10
20
Excitation power (µW)

30

E22

ηPC

Γ2

E11

ηr

1

Ground
state

15

0.6

10

0.4

(f)

ηPC

(b)
(

15

0

(c) P = 20
2 µW

3

0
PL intensity (arb. unitss)

PL intensity (arb. unitss)

Photocurrent (nA)6week ending
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PHYSICAL REVIEW LETTERS

0.2

5

(d)
0

0

5

10
15
Bias voltage (V)

20

0.0
0

5
10
15
Bias voltage (V)20

FIG. 3 (color online). (a) Excitation power dependence of PC. Data from bottom to top correspond to V ¼ 5, 10, 15, and 20 V.
(b) Power dependence of PL, with data from top to bottom corresponding to V ¼ 5, 10, 15, and 20 V. (c) and (d) Bias voltage
dependence of PC and PL, respectively. Data from bottom to top correspond to P ¼ 5, 10, 15, and 20 μW. For (a)–(d), the same tube
as shown in Figs. 1(d)–(f) was measured with the laser spot at the center of the nanotube. The excitation energy is fixed at 1.651 eV andthe laser polarization is parallel to the nanotube axis. Symbols are data and lines are simulation results as explained in the text. (e) A
schematic of the model used to produce the curves shown in (a)–(d). (f) ηPC as a function of V. Open circles are data obtained from(b) and the line is a fit as explained in the text.

annihilation process is extremely efficient for air-suspended
nanotubes [21,25], it may explain the existence of free
carriers. It is not clear why we do not observe trion emission
as in the case of micelle-encapsulated nanotubes [29].
The voltage dependence of the PL [Fig. 3(d)] shows adecrease of PL with increasing voltage. Different from thecase where no PC flows [30], we expect that less excitons
relax into E11 at higher voltages as photocarriers are
extracted into the contacts. As the current gives the absolute
rate of electron-hole pairs extracted from the nanotube, we
can deduce the number of excitons removed from thesystem. By modeling such a fractioning in the exciton
population, we are able to determine the number of injected
excitons, and in turn the absorption cross section.
Figure 3(e) shows a schematic of our model. E22
excitons are generated at a rate
Z
Γ2 ¼

rﬃﬃﬃ


2P
x2
2 n
σP;
nσ 2 exp −2 2 dx ¼
π rE
πr E
r

(1)

where n ¼ 130 nm−1 is the number of atoms per length,
σ is the absorption cross section per carbon atom, r ¼
492 nm is the 1=e2 radius of the laser spot, and E is thelaser photon energy. The fraction of the excitons that are
extracted by PC is denoted by ηPC, while η21 ¼ 1 − ηPCrepresents the fraction that relax down to the E11 sublevel.
The fraction of the E11 excitons that recombine radiatively
and contribute to PL is represented by a nonlinear function
ηr ðΓ1 Þ which includes the effects of exciton-exciton

annihilation. Here, Γ1 ¼ Γ2 η21 is the rate at which theE11 excitons are populated.
The absolute values of η21 can be obtained from theexcitation-power dependence of PL [Fig. 3(b)]. At V ¼ 0,
there are no PC and therefore ηPC ¼ 0 and η21 ¼ 1. Whenvoltages are applied, Γ1 decreases by a factor η21. By
scaling the excitation power to match the dependence at
V ¼ 0, the values of η21 are obtained for the four voltages.
We plot ηPC ¼ 1 − η21 in Fig. 3(f).
Having obtained the explicit values of ηPC , we can now
determine σ. Within our model, the PC is given byrﬃﬃﬃ
2 eηPC n
I ¼ eηPC Γ2 ¼
σP;
π rE

(2)

where e is the electron charge, and the only unknown
parameter is σ. We find that a value of σ ¼ 2.4 × 10−17 cm2
best matches the PC data in Fig. 3(a). This value iscomparable to recent measurements of σ at the E22
resonance in micelle-encapsulated tubes [31] andon-substrate tubes [32].
In addition to σ, the oscillator strength f is obtainedusing its relation to the integrated absorption cross section [33]. We fit the E22 resonance with a Lorentzian profileand obtain a linewidth of ℏγ ¼ 44.5 meV, where ℏ is the
Planck constant, and we use f ¼ ϵ0 mcσγ=e2 , where ϵ0 isthe vacuum permittivity, m is the electron mass, and c is the
speed of light. We find f ¼ 0.015, which is somewhat
larger compared to (6,5) nanotubes [6].

117401-3

PRL 112, 117401 (2014)

PHYSICAL REVIEW LETTERSTABLE I. Absorption cross section and oscillator strength forthe eight nanotubes measured. Lorentzian fits to PL excitation
spectra at V ¼ 0 V are used to obtain the E22 energy and full
width at half-maximum ℏγ.
Chirality

E22 (eV)ℏγ (meV)σ (×10−17 cm2 )

f

(8,7)
(8,7)
(8,7)
(8,7)
(9,7)
(9,8)
(10,6)(10,8)

1.724
1.712
1.717
1.725
1.593
1.555
1.652
1.452

66.6
58.4
71.3
69.1
44.2
50.5
44.5
51.5

2.1
2.6
1.7
2.5
9.5
7.1
2.4
1.3

0.020
0.022
0.017
0.025
0.060
0.052
0.015
0.009

To verify the validity of our model, we simulate theintensity and voltage dependencies of PC and PL using theparameters obtained above. For the voltage dependence ofηPC , we fit the data in Fig. 3(f) with a linear term and aquadratic term. We use an analytic expression derived inRef. [24] for the form of ηr ðΓ1 Þ, with the parameters adjusted
to fit our data. As shown as solid lines in Figs. 3(a)–(d), themodel consistently explains all the data simultaneously.
The behavior of ηPC shows that a large fraction of theinjected excitons are dissociating, reaching a value ashigh as ηPC ¼ 0.53 at V ¼ 20 V. We expect PC to saturate
above a certain voltage when all free carriers are extracted,
but we do not see any signs of such saturation. Thissuggests that there are much more free carriers available
even at the highest bias voltage we used, implying that the
majority of the injected excitons are dissociating.
In order to check the reproducibility and to obtain σ forother chiralities, we have performed similar measurements
on other devices and the results are summarized in Table I.
For four tubes with a chirality of (8,7), we find that f falls
within 20% and that the values are close to the theoreticalestimate of ð0.014 eV−1 ÞE22 ¼ 0.024 [26]. We haveobserved that σ can differ by a factor of 3 or so for otherchiralities, but additional measurements should be performed as these are based on single devices for each chirality.
We note that our model does not consider any direct
recombination of E22 excitons, which occurs prior torelaxation to the E11 state—for example, exciton-exciton
annihilation at the E22 level [34]. Such a process would leadto an underestimate of the number of injected excitons, andσ would be larger than what we have deduced from ourmodel. We also do not take into account any field-inducedchanges to ηr , but further measurements at different
excitation energies are expected to clarify the contributionof such effects.
In summary, we have performed simultaneous PL andPC spectroscopy on individual SWCNTs and constructed amodel that consistently explains the excitation power andvoltage dependencies. Within the voltage range explored,
we did not find evidences of field-induced excitonweek ending
21 MARCH 2014

dissociation, for either of the E11 and E22 excitons.
Instead, a considerable fraction of the injected excitons
are found to spontaneously dissociate into free electronhole pairs. We have also obtained the absorption crosssection and the oscillator strength from these air-suspended
SWCNTs. Our findings explain why the large exciton
binding energies do not impede photoconductivity measurements in SWCNTs.
We thank R. Saito, Y. Miyauchi, and S. Maruyama for
helpful discussions, T. Kan and I. Shimoyama for the use of
the evaporator, S. Chiashi and S. Maruyama for the electron
microscope, and S. Yamamoto for the plasma etcher. This
work is supported by KAKENHI (21684016, 23104704,
24340066, 24654084), SCOPE, and KDDI Foundation, as
well as the Photon Frontier Network Program of MEXT,
Japan. The devices were fabricated at the Center for Nano
Lithography & Analysis at The University of Tokyo.

*

Corresponding author.
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