APPLIED PHYSICS LETTERS 105, 161104 (2014)

Stark effect of excitons in individual air-suspended carbon nanotubes
M. Yoshida, Y. Kumamoto, A. Ishii, A. Yokoyama, and Y. K. Katoa)
Institute of Engineering Innovation, The University of Tokyo, Tokyo 113-8656, Japan(Received 30 June 2014; accepted 11 October 2014; published online 21 October 2014)
We investigate electric-field induced redshifts of photoluminescence from individual single-walledcarbon nanotubes. The shifts scale quadratically with field, while measurements with different excitation powers and energies show that effects from heating and relaxation pathways are small. We
attribute the shifts to the Stark effect and characterize nanotubes with different chiralities. By taking into account exciton binding energies for air-suspended tubes, we find that theoretical predicC 2014 AIP Publishing LLC.
tions are in quantitative agreement. V[http://dx.doi.org/10.1063/1.4899127]

Understanding of electric field effects on optical properties of single-walled carbon nanotubes (SWCNTs) is important for applications in nanoscale optoelectronic devices.1
One of the intriguing electro-optic effects is the Stark effect,
which causes redshifts on exciton resonances under an application of electric fields.2,3 The effect has been used to
explain spectral changes in electroabsorption,4–6 photoconductivity,7 and ultrafast measurements.8 Local variation of
excitonic energies9 and spectral diffusion at low temperatures10,11 have also been attributed to the Stark effect. Theseexperiments, however, have been performed on ensemblesof nanotubes,4–6 without well-defined electric fields,8–11 oron nanotubes with unknown chirality,4,7 making quantitative
analysis difficult.
Here, we investigate field-induced redshifts of E11 exciton emission in chirality-assigned individual SWCNTs.
Photoluminescence (PL) spectra of air-suspended nanotubes
within field-effect transistor structures are collected under anapplication of symmetric bias voltages on source and drain
contacts, revealing redshifts that scale quadratically withelectric field. We find that the shifts do not depend much on
excitation power or energy, ruling out effects from heatingor relaxation pathways. Attributing the redshifts to the Stark
effect, we have also performed measurements on different
chiralities, and a reasonable agreement with theoretical predictions2 is obtained by considering exciton binding energies
for air-suspended tubes. Analysis using the total field rather
than the longitudinal component shows more consistency,
suggesting that transverse fields induce shifts of similar
magnitude.
Our field-effect transistors with suspended nanotubes12
are fabricated from Si substrates with 1–lm-thick oxide[Fig. 1(a)]. Electron beam lithography is performed to pattern trenches with widths ranging from 1.0 to 1.7 lm, and an
inductively coupled plasma etcher using CHF3 gas is used toform 500-nm-deep trenches into the oxide layer. Anotherelectron-beam lithography step defines the electrode patterns, and we deposit Ti (3 nm) and Pt (45 nm) using an electron beam evaporator with a base pressure of 1  104 Pa.
Following a lift-off process for the contacts, catalysta)Author to whom correspondence should be addressed. Electronic mail:ykato@sogo.t.u-tokyo.ac.jp0003-6951/2014/105(16)/161104/4/$30.00

windows near the trenches are patterned with a third electron
beam lithography step. Catalyst solution for nanotube growthis prepared by ultrasonicating 5 mg of cobalt(II) acetate tetrahydrate and 25 mg of fumed silica in 10.0 g of ethanol, andthen we spin coat and lift off the catalyst. Finally, we perform chemical vapor deposition to synthesize single-walledcarbon nanotubes.13,14 The samples are placed in a quartz
tube furnace and heated in dry air while the temperature isramped up to 700  C over 12 min. After pumping out the dry
air, the quartz tube is filled by Ar with 3% H2, and the temperature in the furnace is elevated to 800  C. Ethanol is introduced as a carbon source by bubbling the carrier gas for
10 min.
The devices are characterized with a confocal micro-PL
system optimized for detection of nanotube emission.15–17
An output of a wavelength tunable Ti:sapphire laser isfocused onto the sample by an objective lens with a numerical aperture of 0.8 and a working distance of 3.4 mm. PL iscollected through a confocal pinhole corresponding to an
aperture with 5.4 lm diameter at the sample image plane. An
InGaAs photodiode array and a spectrometer with a spectral
resolution of 1 meV are used to detect PL from nanotubes.
We utilize an automated three-dimensional translation stage

FIG. 1. (a) A schematic of a device. (b) PL spectra taken with electric fieldsof 0 V/lm (black) and 15 V/lm (red). Open circles are data, and lines are
Lorentzian fits. (c) PL spectra as a function of electric field. Data in (b) and(c) are taken with excitation energy of 1.651 eV and excitation power of
10 lW, and a (10,6) tube with a suspended length of 1.3 lm characterized inRef. 12 is used. Laser polarization is parallel to the nanotube axis.

105, 161104-1

C 2014 AIP Publishing LLC
VThis article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
133.11.90.141 On: Tue, 21 Oct 2014 23:49:50

161104-2

Yoshida et al.

with a travel range of 610 mm and a resolution of 50 nm totake PL images and to find the nanotube positions. PL excitation spectroscopy is performed to determine the chiralities ofindividual SWCNTs using tabulated data for air-suspended
tubes.18 The nanotube length can be calculated from thewidth of the trench and the tube angle obtained from laser
polarization dependence of PL.15
Simultaneous PL and photocurrent (PC) measurements
are performed in the presence of electric field using two dc
source meters.12 We ground the Si substrate and apply symmetric bias voltages between the source and drain contacts inorder to avoid PL quenching caused by carrier-induced
Auger recombination.19,20 The longitudinal component ofelectric field F is obtained by dividing the applied voltage
with the tube length. We average the current with the excitation laser on the sample while a spectrum is taken, and thena background spectrum and a dark current are collected after
blocking the laser with a shutter. The PL spectrum isobtained by taking the difference of the two spectra. All
measurements are done in air at room temperature.
Figure 1(b) shows PL spectra taken with longitudinal
electric fields F ¼ 0 and 15 V/lm on a (10,6) nanotube under
excitation at the E22 resonance and a power P ¼ 10 lW. The
emission peak with F ¼ 15 V/lm shows a redshift as well asa reduction of intensity compared to F ¼ 0 V/lm. To investigate such a behavior in detail, we have measured the field dependence of PL spectra from 0 to 15 V/lm [Fig. 1(c)]. The
peak position, width, and area are extracted by fitting thespectra with a Lorentzian function, and we obtain good fits
as shown in Fig. 1(b). Such fits have been performed for allof the spectra in Fig. 1(c) in order to quantitatively characterize the field dependence.
In Fig. 2, we plot the electric field dependence of emission energy, linewidth, peak area, and current. The PL peakarea decreases with increasing field as photocarriers flow
into the contacts.12 We note that only those devices thatshow PC > 0.3 nA are investigated here, which is sufficiently
larger than the noise level. If PC is small, it is likely that the
nanotube has a bad contact to the electrodes, and the bias
voltage can act as an effective gate. It is important to avoid

FIG. 2. (a)–(c) Electric field dependence of emission energy, full width at
half maximum (FWHM), and peak area, respectively, obtained from fits ofdata in Fig. 1(c). (d) Current taken with P ¼ 10 lW (filled circles) and thedark current (open circles) as a function of electric field.

Appl. Phys. Lett. 105, 161104 (2014)

such devices as unintentional electrostatic doping can occur,
which is known to cause blueshifts.20
The emission energy [Fig. 2(a)] shows a quadratic redshift on the electric field, as expected from the Stark effect.2
The redshifts, however, could result from a rise in temperature21 caused by Joule heating, as there exists a current flowing in the tube [Fig. 2(d)]. Such a heating effect can bequantified from the linewidth broadening [Fig. 2(b)]. In thecase of F ¼ 15 V/lm, the tube temperature increase is estimated to be 32 K by using a coefficient of 0.023 meV/K.22
In order to identify the contribution of the heatinginduced redshifts, we have investigated the excitation power
dependence of the current, broadening, and redshift at different F [Figs. 3(a)–3(c)]. Because the current increases withthe excitation power [Fig. 3(a)], heating can be varied under
fixed fields to isolate the temperature-induced redshifts. At
F ¼ 15 V/lm, the broadening changes by a factor of 2.3
between P ¼ 5 lW and 25 lW [Fig. 3(b)], while the redshift
only increases by 25% [Fig. 3(c)], showing that the thermal
effects are limited. The data also indicate that 0.8-meV redshift occurs when heating causes 1-meV broadening, andusing this relation, we estimate the heating-induced shift tobe less than 22% of the redshift for the data taken at
P ¼ 10 lW and F ¼ 15 V/lm. This is consistent with a redshift expected from the temperature dependence of emission
energy21 when the heating estimated from the linewidth
broadening is used.
We further consider whether the temperature increase of
32 K is reasonable by solving a heat conduction equation in
one dimension with a fixed temperature at the ends. A rise in

FIG. 3. (a)–(c) Excitation power dependence of current, broadening, andredshift, respectively. Data from bottom to top correspond to F ¼ 3.8, 7.5,
11.3, and 15.0 V/lm. The excitation energy is fixed at 1.651 eV. The tube is
the same as in Figs. 1 and 2. The broadening and redshift are measured from
10.7 meV and 926.3 meV, respectively, taken at P ¼ 1 lW and F ¼ 0 V/lm.
(d) Field-induced redshift as a function of F taken at different excitationenergies. Data from bottom to top are taken at E22 (1.651 eV), E111
(1.351 eV), E12 (1.476 eV), and E211 (1.450 eV) resonances,25 where P ¼ 5,150, 1000, and 200 lW are used, respectively. The data are offset for clarity.
The laser polarization is parallel to the tube except for E12 excitation in (d)where it is perpendicular.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
133.11.90.141 On: Tue, 21 Oct 2014 23:49:50

161104-3

Yoshida et al.

Appl. Phys. Lett. 105, 161104 (2014)

the temperature by 2 K at the center of the tube is obtained
for uniform Joule heating of 58 nW/lm and assuming a thermal conductivity of 3600 W/(K m).23 A contact thermal resistance of 490 K m/W can explain the remainder of thetemperature increase for a contact length of 1 lm, and thisvalue is within the range observed for multi-walled nanotubes on Pt.24
Measurements at different excitation energies have also
been performed [Fig. 3(d)], and the electric-field dependenceshows similar quadratic behaviors for excitation at the E12,
E111 , and E211 states.25 These results show that relaxation pathways from the excited states to the E11 state do not influence
the shifts of the emission energy and that the redshifts are
the intrinsic response of the E11 excitons under electricfields.
We therefore attribute the redshift to the Stark effect,
and nanotubes with different chiralities have also been investigated (Fig. 4). The measurements are performed with thelaser polarization parallel to the tubes, and at low powers
such that the field-induced linewidth broadening is 0.6 meVor less. All of the tubes show redshifts that increase quadratically with electric fields, but the amounts of the shifts are different [Fig. 4(a)]. In order to characterize the strength of theeffect, the data are fit todE11 ¼ KF2 ;(1)

where dE11 is the redshift and K is a constant. The values ofK obtained for the eight tubes measured are plotted as a function of the tube diameter d [dots in Fig. 4(b)]. The diameter
dependence of the Stark effect is expected to be2
K ¼ jbðed Þ2;Eb(2)where jb is a unitless constant, e is the electronic charge,
and Eb ¼ 0:66=d eV is the exciton binding energy for airsuspended nanotubes.25 The thin line in Fig. 4(b) shows thefit to the data using Eq. (2). We obtain jb ¼ 5:2, which iscomparable to the theoretical values ranging from 3.0 to 4.2
in Ref. 2, although the data has a large scatter.
In particular, of the four (8,7) nanotubes we have measured, one shows a relatively large K. It turns out that thisnanotube is suspended at an angle of 37 with respect to thetrench. Since the electric field is established between thesource and drain contacts, this tube is at a large angle withthe field. If transverse fields can also induce Stark shifts,4,7 it
may explain the deviation as the analysis so far only considered the longitudinal component.
When we replot the data using the total field [crosses inFig. 4(b)] as opposed to the longitudinal field, we find that
K of the four (8,7) tubes falls within 69%. In addition,
jb ¼ 4:5 is obtained [thick line in Fig. 4(b)], which is closer
to the theoretical values. Although the data still show somedeviations from Eq. (2), our results are in reasonable agreement as the calculations also find chirality dependent jb thatcan differ by 617%.
With the reasonable agreement with theory, we can estimate the exciton dissociation time under the experimental
conditions. The dissociation rate can be written as2


F0
F0
;
(3)
C ¼ aEb exp FF
where a ¼ 4.1 is a constant and F0 is the dissociation field.
For a d ¼ 1.1 nm tube with Eb ¼ 288 meV, F0 has been calculated to be 198 V/lm in Ref. 2. Using the relation
3=2
F0 / Eb , we estimate F0 ¼ 595 V/lm for an air-suspended(10,6) tube by scaling for Eb ¼ 600 meV. The dissociation
time h=C, where h is the Planck constant, is longer than 1 s
for the highest applied field of 15 V/lm, and as the lifetimeof E11 excitons is much less than 1 ns,26 we do not expect
E11 exciton dissociation at these fields.12
In summary, we have investigated the redshifts of PL
emission from individual air-suspended SWCNTs caused byelectric fields. Since the shifts are quadratic in field and notdependent on excitation power or energy, they are attributed
to the Stark effect. By performing measurements on different
chiralities, we have shown that the shifts are in quantitative
agreement with theoretical calculations. The results on tubes
at large angles with the field suggest that transverse fields
may be causing Stark shifts of similar magnitude. As theestimated dissociation rates are negligible, it should be possible to achieve wider control of emission wavelength in stronger fields or larger diameter tubes.
We thank T. Kan and I. Shimoyama for the use of theevaporator, and S. Yamamoto for the plasma etcher. This
work was supported by KAKENHI (24340066, 24654084,
26610080), the Canon Foundation, Asahi Glass Foundation,
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. M.Y. is supported by ALPS, andA.I. is supported by MERIT and JSPS Research Fellowship.

1

P. Avouris, M. Freitag, and V. Perebeinos, Nat. Photonics 2, 341 (2008).
V. Perebeinos and P. Avouris, Nano Lett. 7, 609 (2007).
3
H. Zhao and S. Mazumdar, Phys. Rev. Lett. 98, 166805 (2007).
4
T. Takenobu, Y. Murayama, and Y. Iwasa, Appl. Phys. Lett. 89, 263510(2006).
5
H. Kishida, Y. Nagasawa, S. Imamura, and A. Nakamura, Phys. Rev. Lett.
100, 097401 (2008).
6
T. Ogawa, S. Watanabe, N. Minami, and R. Shimano, Appl. Phys. Lett.
97, 041111 (2010).
2

FIG. 4. (a) Stark effect for a 1.0-lm-long (8,7) tube (squares), a 1.3-lmlong (10,8) tube (triangles), and a 1.0-lm-long (9,7) tube (dots), measured
with E22 excitations. For the (8,7), (10,8), and (9,7) tubes, P ¼ 8, 10, and5 lW are used, and the redshifts are measured from 998.5, 862.7, and954.7 meV, respectively. (b) Diameter dependence of K. Dots and crosses
show data analyzed with longitudinal field and total field, respectively.
Lines are fits.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
133.11.90.141 On: Tue, 21 Oct 2014 23:49:50

161104-4
7

Yoshida et al.

A. D. Mohite, P. Gopinath, H. M. Shah, and B. W. Alphenaar, Nano Lett.
8, 142 (2008).
8
G. Soavi, F. Scotognella, D. Brida, T. Hefner, F. Sp€ath, M. R. Antognazza,
T. Hertel, G. Lanzani, and G. Cerullo, J. Phys. Chem. C 117, 10849(2013).
9
C. Georgi, A. A. Green, M. C. Hersam, and A. Hartschuh, ACS Nano 4,
5914 (2010).
10
K. Matsuda, T. Inoue, Y. Murakami, S. Maruyama, and Y. Kanemitsu,
Phys. Rev. B 77, 193405 (2008).
11
A. H€ogele, C. Galland, M. Winger, and A. Imamo
glu, Phys. Rev. Lett.
100, 217401 (2008).
12
Y. Kumamoto, M. Yoshida, A. Ishii, A. Yokoyama, T. Shimada, and Y. K.
Kato, Phys. Rev. Lett. 112, 117401 (2014).
13
S. Maruyama, R. Kojima, Y. Miyauchi, S. Chiashi, and M. Kohno, Chem.
Phys. Lett. 360, 229 (2002).
14
S. Imamura, R. Watahiki, R. Miura, T. Shimada, and Y. K. Kato, Appl.
Phys. Lett. 102, 161102 (2013).
15
S. Moritsubo, T. Murai, T. Shimada, Y. Murakami, S. Chiashi, S.
Maruyama, and Y. K. Kato, Phys. Rev. Lett. 104, 247402 (2010).

Appl. Phys. Lett. 105, 161104 (2014)
16

R. Watahiki, T. Shimada, P. Zhao, S. Chiashi, S. Iwamoto, Y. Arakawa, S.
Maruyama, and Y. K. Kato, Appl. Phys. Lett. 101, 141124 (2012).
A. Yokoyama, M. Yoshida, A. Ishii, and Y. K. Kato, Phys. Rev. X 4,011005 (2014).
18
Y. Ohno, S. Iwasaki, Y. Murakami, S. Kishimoto, S. Maruyama, and T.
Mizutani, Phys. Rev. B 73, 235427 (2006).
19
M. Freitag, M. Steiner, A. Naumov, J. P. Small, A. A. Bol, V. Perebeinos,
and P. Avouris, ACS Nano 3, 3744 (2009).
20
S. Yasukochi, T. Murai, S. Moritsubo, T. Shimada, S. Chiashi, S.
Maruyama, and Y. K. Kato, Phys. Rev. B 84, 121409(R) (2011).
21
J. Lefebvre, P. Finnie, and Y. Homma, Phys. Rev. B 70, 045419 (2004).
22
K. Yoshikawa, R. Matsunaga, K. Matsuda, and Y. Kanemitsu, Appl. Phys.
Lett. 94, 093109 (2009).
23
E. Pop, D. Mann, J. Cao, Q. Wang, K. Goodson, and H. Dai, Phys. Rev.
Lett. 95, 155505 (2005).
24
M. T. Pettes and L. Shi, Adv. Funct. Mater. 19, 3918 (2009).
25
J. Lefebvre and P. Finnie, Nano Lett. 8, 1890 (2008).
26
Y.-F. Xiao, T. Q. Nhan, M. W. B. Wilson, and J. M. Fraser, Phys. Rev.
Lett. 104, 017401 (2010).
17This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
133.11.90.141 On: Tue, 21 Oct 2014 23:49:50