C:/Documents and Settings/yohno/デスクトップ/岩崎論文/revtex4/manuscript070408.dvi
Environmental dielectric screening e�ect on exciton transition
energies in single�walled carbon nanotubes
Yutaka Ohno��� � Shinya Iwasaki�� Yoichi Murakami�� Shigeru
Kishimoto�� Shigeo Maruyama�� and Takashi Mizutani�� y
�Department of Quantum Engineering� Nagoya University�
Furo�cho� Chikusa�ku� Nagoya ��������� Japan
�Department of Mechanical Engineering�
The University of Tokyo� 	���
 Hongo�
Bunkyo�ku� Tokyo 
�������� Japan
�Dated� April �� �����
Abstract
Environmental dielectric screening e	ects on exciton transition energies in single
walled carbon
nanotubes �SWNTs� have been studied quantitatively in the range of dielectric constants from
��� to 
� by immersing SWNTs bridged over trenches in various organic solvents by means of
photoluminescence and the excitation spectroscopies� With increasing environmental dielectric
constant ��env�� both E�� and E�� exhibited a redshift by several tens meV and a tendency to
saturate at a �env � � without an indication of signi�cant �n�m� dependence� The redshifts can be
explained by dielectric screening of the repulsive electron
electron interaction� The �env dependence
of E�� and E�� can be expressed by a simple empirical equation with a power law in �env� Eii �
ii � A�
env� We also immersed a sample in sodium
dodecyl
sulfate �SDS� solution to investigate
the e	ects of wrapping SWNTs with surfactant� The resultant E�� and E��� which agree well with
Weisman�s data �Nano Lett� �� ��
� ����
��� are close to those of �env of �� However� in addition
to the shift due to dielectric screening� another shift was observed so that the ��n � m�
family
patterns spread more widely� similar to that of the uniaxial
stress
induced shift�
I� INTRODUCTION
Optical spectroscopy of single�walled carbon nanotubes �SWNTs� has received increasing
attention� not only for assigning the chiral vector� �n�m�� of the SWNTs��� but also to study
the physics of the one�dimensional excitons���� In paticular� photoluminescence �PL� and the
excitation spectroscopies are the most widely used for characterizing SWNTs with resonant
Raman scattering spectroscopy� Two�photon absorption spectroscopy� and Rayleigh scat�
tering spectroscopy combined with TEM or SEM observation	 are also powerful techniques
to investigate excitonic states of SWNTs and the bundle e�ect�
Recently� the environmental e�ect is one of the topics most investigated for its e�ect on
the optical properties of SWNTs�
��� It is known that the optical transition energies vary�
depending on the kind of surrounding surfactant used to individualize SWNTs�
��� Lefebvre
et al� have reported the optical transition energies of SWNTs bridging between two micro�
pillars fabricated on a Si wafer show a blueshift as compared to the SDS�wrapped SWNTs���
We have also compared air�suspended SWNTs grown on a quartz substrate with a grating
structure to SDS�wrapped SWNTs� and have shown that the energy di�erences between
air�suspended and SDS�wrapped SWNTs depend on �n�m�� especially on chiral angle and
on type of SWNTs� type�I �	n 
 m mod � � �� or type�II �	n 
 m mod � �	���� These
energy variations due to environmental conditions have been thought to be produced by
the di�erence in the dielectric constant of the surrounding materials� The energy of the
many�body Coulomb interactions between carriers depends on the environmental dielectric
constant ��env�� because the electric force lines contributing to the Coulomb interactions pass
through the matrix� as well as the inside of the SWNT�����	 Note that the environmental
e�ect is caused not only by the dielectric screening of Coulomb interactions� but also by
chemical����� and mechanical conditions��� Finnie et al� have reported that gas adsorption
a�ects the emission energy of SWNTs���
Investigations into the environmental e�ect have not been comprehensive� despite its
importance in understanding the optical properties of SWNTs� Quantitative and separate
investigations are necessary to understand the contributions of various environmental factors�
In this study� we have focused on the dielectric screening e�ect� which has been quantitatively
investigated by immersing the SWNTs grown over trenches into various liquids with di�erent
�env� from ��
 to ��� by means of photoluminescence and the excitation spectroscopies�
II� EXPERIMENTAL
For the study on environmental e�ects� the SWNTs grown between two micro�pillars����
or over a trench����� are suitable because the environmental conditions can be controlled
intentionally� The samples used in this work are SWNTs grown on a quartz substrate with
periodic trenches� as shown in Fig� �� Both the period and depth of the trenches are 	
�m� The trenches were formed by photolithography� Al�metal evaporation and lift�o�� and
subsequent reactive�ion etching of the quartz with the Al mask� The SWNTs were grown by
alcohol catalytic chemical vapor deposition�� at ����C for �� s� after spin coating of a water
solution of Co acetate� By optimizing the growth condition� isolated bridging SWNTs can
be formed over the trenches� The density of the SWNTs was ���	 �m�� along the direction
of the trench� Such low�density� isolated SWNTs were necessary to observe luminescence
when the sample was immersed in liquids� On the other hand� in case of a sample with a
relatively high�density of SWNTs as �	 �m���� PL intensity was degraded by immersing in
liquids� even though strong PL was obtained in air� This is probably because the SWNTs
form bundles with neighbors upon immersion in liquids� in the case of a sample with a
high�density of SWNTs�
The sample was mounted in a vessel with a quartz window� and immersed in various
organic solvents with �env from ��
 to �� �see Table I�� We also immersed a sample in
��wt� D�O solution of sodium�dodecyl�sulfate �SDS� to investigate the e�ect of wrapping
with surfactant molecules� PL and the excitation spectra were measured using a home�
made facility consisting of a tunable� continuous�wave Ti�Sapphire laser �������� nm�� a
monochromator with a focal length of 	� cm� and a liquid�N��cooled InGaAs photomultiplier
tube ���������� nm�� The excitation wavelength was monitored by a laser wavelength
meter� The diameter of the laser spot on the sample surface was �� mm� so that an
ensemble of many SWNTs was detected�
III� RESULTS AND DISCUSSION
Figure 	 shows PL maps of SWNTs �a���g� in various organic solvents with di�erent
�env and �h� in SDS solution� By immersing the sample in the organic solvents� the emission
and excitation peaks� which respectively correspond to E�� and E��� showed redshifts and
spectral broadening� In the PL map measured in SDS solution��� the peak positions agree
well with those of Weisman�s empirical Kataura plot for SDS�wrapped SWNTs represented
by crosses��
The E���E�� plots in air ��env � ����� hexane ���
�� chloroform ������ and SDS solution
are shown in Fig� � � Both of E�� and E�� showed redshifts with increasing �env� without
signi�cant �n�m� dependence� The amounts of the redshifts are ����
 meV for E�� and
	���� meV for E��� The redshift with increasing �env is consistent with the theoretical
work by Ando��� The optical transition energy in SWNTs is given by a summation of the
bandgap and the exciton binding energies� When the �env increases� the Coulomb interaction
is enhanced and the exciton binding energy decreases� This leads to a blueshift of the optical
transition energy in the SWNT� It should be noted that the bandgap is renormalized by the
electron�electron repulsion interaction� and consequently the change in the �env a�ects not
only the exciton binding energy� but also the bandgap� According to theoretical work������
the repulsive electron�electron energy is larger in magnitude than the exciton binding energy�
Therefore� if we consider that both energies show a similar dependence on �env� the decrease
in the electron�electron repulsion energy exceeds the decrease in the exciton binding energy
when �env increases� This results in a redshift in optical transition energies� The redshifts
observed in the present experiment are attributed to the decrease in the repulsion energy
of the electron�electron interaction with an increase in the �env� Note that even though
the redshift with increasing �env is consistent with the theoretical studies� the amount of
the redshift is much smaller than the calculations� This is probably because in the present
experiments� the �env only outside of the SWNTs was varied� whereas the theoretical studies
used a dielectric constant for the whole system�
E�� and E�� are plotted as a function of �env in Fig� �� The energy shifts show a tendency
to saturate at �env � �� The energy variations can be �tted to an empirical expression with
a power law in �
Eii � E
env ���
where E�ii corresponds to a transition energy when �env is in�nity� A corresponds to the
maximum value of the energy change by �
� and � is a �tting parameter� A and � are ��
meV and ��
 for E��� and 	
 meV and ��� for E��� respectively� on average� Perebeinos et al�
have reported power law scaling for excitonic binding energy by dielectric constant� where
the scaling factor � is estimated to be � ��� in the range of � � ���	 Although the power law
expression of Eq� � is quite similar to the Perebeinos�s scaling law for exciton binding energy�
the present empirical expression is attributed to the scaling of electron�electron repulsion
energy by �env� rather than exciton �electron�hole� binding energy as described above� Quite
recently� such a power�law�like�downshift in optical transition energy with �env has been
obtained by theoretical calculations based on a tight�binding model���
We have previously pointed out that the E�� and E�� varies depending on �n�m�� in
particular on chiral angle and on the type of SWNTs �type�I or type�II�� comparing those
of SDS�wrapped SWNTs to those of air�suspended SWNTs� The same behavior occurred
by immersing a sample in SDS solution� as shown in Fig� 	�h�� Most E�� and E�� of SDS�
wrapped SWNTs show a redshift� except for E�� of near�zigzag type�II SWNTs� which
show a blueshift as compared to those in air� This behavior is inconsistent with the results
of the �env dependence as described above� in which �n�m� dependence is not signi�cant�
Comparing the PL maps in SDS solution to those in organic solvents as shown in Fig� �� the
equivalent �env of SDS�wrapped SWNTs would be � 	� In addition to the shift due to the
dielectric screening� the peak positions of SDS�wrapped SWNTs shift so as the �	n 
family patterns spread more widely� This suggest that wrapping with SDS has another
e�ect in addition to the dielectric screening e�ect� The behavior of the additional shifts is
similar to the shift induced by uniaxial stress� reported by Arnold et al��� At present� it still
remains an issue whether such uniaxial strain is induced in the SWNTs by wrapping with
surfactants or not� A charging e�ect due to SDS� which is an anionic surfactant� should also
be considered� Further study is necessary to understand the e�ects of surfactants on optical
transition energies in SWNTs�
Finally� we note the broadening of the PL spectra in liquids� The representative spectra
are shown in Fig� �� The peaks show a broadening� in addition to the redshift with increasing
�env� The linewidth increased from 	� meV in air to �� meV in acetonitrile for �
��� SWNTs�
This linewidth broadening is probably attributed to inhomogeneous broadening due to local
�uctuations of �env on the nano�scale dimension� The dielectric constants we used in Table I
are macroscopic values� On such small dimensions as exciton diameters of a few nm��� the
size of molecules of the organic solvents would be considerable so that the local �env would
�uctuate depending on the number and orientation of the organic molecules� This would
result in inhomogeneous broadening of the PL spectrum�
IV� SUMMARY
In summary� dielectric screening e�ects due to the environment around SWNTs on exciton
transition energies in the SWNTs have been studied quantitatively by means of PL and the
excitation spectroscopies� We varied the �env from ��� to �� by immersing the samples
with SWNTs bridging over trenches in various organic solvents with di�erent �envs� With
increasing �env� both E�� and E�� showed a redshift by ����
 meV for E�� and 	���� meV
for E��� and a tendency to saturate at �env � �� without a signi�cant �n�m� dependence� The
redshift can be explained by dielectric screening of repulsive electron�electron energy� The
�env dependence of E�� and E�� were expressed by a simple empirical equation with a power
law in �env� The equivalent �env of SDS�wrapped SWNTs was estimated to be � 	� It was
suggested that the e�ect of wrapping SWNTs with SDS was not only a dielectric screening
e�ect� but also another e�ect which caused an energy shift like a uniaxial�stress�induced
shift�
� Also at PRESTO� Japan Science and Technology Agency� �
� Honcho� Kawaguchi� Saitama
����� Japan� Electronic address� yohno�nuee�nagoya�u�ac�jp
y Also at Institute for Advanced Research� Nagoya University� Furo
cho� Chikusa
ku� Nagoya�
����� Japan
� H� Kataura� Y� Kumazawa� Y� Maniwa� I� Umezu� S� Suzuki� Y� Ohtsuka� and Y� Achiba�
Synthetic Metals ���� ���� �������
� S� M� Bachilo� M� S� Strano� C� Kittrell� R� H� Hauge� R� E� Smalley� and R� B� Weisman�
Science ���� �
�� �������
� R� B� Weisman and S� M� Bachilo� Nano Lett� �� ��
� ����
��
� Y� Miyauchi� S� Chiashi� Y� Murakami� Y� Hayashida� S� Maruyama� Chem� Phys� Lett� ����
��� �������
� H� Htoon� M� J� O�Connell� P� J� Cox� S� K� Doorn� and V� I� Klimov� Phys� Rev� Lett� ���
������ �������
� F� Wang� G� Dukovic� L� E� Brus� T� F� Heinz� Science ���� �
� �������
	 F� Wang� M� Y� Sfeir� L� Huang� X� M� H� Huang� Y� Wu� J� Kim� J� Hone� S� O�Brien� L� E�
Brus� and T� F� Heinz� Phys� Rev� Lett �	� ������ �������
� P� T� Araujo� S� K� Doorn� S� Kilina� S� Tretiak� E� Einarsson� S� Maruyama� H� Chacham� M�
A� Pimenta� and A� Jorio� Phys� Rev� Lett� ��� ������ �������
 V� C� Moore� M� S� Strano� E� H� Haroz� R� H� Hauge� R� E� Smalley� J� Schmidt� and Y�
Talmon� Nano Lett� �� �
�� ����
��
�� S� G� Chou� H� B� Ribeiro� E� B� Barros� A� P� Santos� D� Nezich� Ge� G� Samsonidze� C�
Fantini� M� A� Pimenta� A� Jorio� F� Plentz Filho� M� S� Dresselhaus� G� Fresselhaus� R� Saito�
M� Zheng� G� B� Onoa� E� D� Semke� A� K� Swan� M� S� �Unl�u� and B� B� Goldberg� Chem�
Phys� Lett� ���� ��� �������
�� C� Fantini� A� Jorio� M� Souza� M� S� Strano� M� S� Dresselhaus� and M� A� Pimenta� Phys�
Rev� Lett� ��� ������ �������
�� J� Lefebvre� J� M� Fraser� Y� Homma� and P� Finnie� Appl� Phys� A ��� ���� �������
�� T� Hertel� A� Hagen� V� Talalaev� K� Arnold� F� Hennrich� M� Kappes� S� Rosenthal� J� McBride�
H� Ulbricht� and E� Flahaut� Nano Lett� 
� ��� �������
�� P� Finnie� Y� Homma� and J� Lefebvre� Phys� Rev� Lett� ��� ������ �������
�� Y� Ohno� S� Iwasaki� Y� Murakami� S� Kishimoto� S� Maruyama� and T� Mizutani� Phys� Rev�
B ��� �
���� �������
�� T� Ando J� Phys� Soc� Japan ��� ��� �������
�	 V� Perebeinos� J� Terso	� and Ph� Avouris� Phys� Rev� Lett� ��� ������ �������
�� K� Arnold� S� Lebedkin� O� Kiowski� F� Hennrich� and M� M� Kappes� Nano Lett� �� �
�� �������
 J� Lefebvre� Y� Homma� and P� Finnie� Phys� Rev� Lett� ��� ������ ����
��
�� Y� Ohno� S� Kishimoto� and T� Mizutani� Nanotechnology ��� ��� �������
�� Y� Murakami� Y� Miyauchi� S� Chiashi� and S� Maruyama� Chem� Phys� Lett� ���� �
 ����
��
�� In order to form micelle structure� the sample was kept in SDS solution for one night before the
PL measurement�
�� Y� Miyauchi� R� Saito� K� Saito� Y� Ohno� S� Iwasaki� T� Mizutani� J� Jiang� S� Maruyama �will
be published elsewhere�
�� C� D� Spataru� S� Ismail
Beigi� L� X� Benedict� and S� G� Louie� Phys� Rev� Lett� ��� ������
�������
TABLE I� �env of air and various liquids used in this study�
solvent �env
air ���
hexane ���
chloroform ���
ethyl acetate ���
dichloromethane ���
acetone ��
acetonitrile 
�
FIG� �� Plan
view and bird
view �inset� SEM images of SWNTs bridging over trenches on a quartz
substrate� Pt thin �lm was deposited on the sample in order to avoid charge up of the insulating
substrate and to observe individual SWNTs� By optimizing growth condition� individual SWNTs
can be obtained�
0.8 0.9 1.0 1.1
0.9 1.0 1.1
0.9 1.0 1.1
0.9 1.0 1.1
(a) air (b) hexane (c) chloroform (d) ethyl acetate
(e) dichloromethane (f) acetone (g) acetonitrile (h) SDS
FIG� �� PL contour maps for SWNTs� �a� in air ��env � ����� �b� hexane ��env � ����� �c� chloroform
��env � ����� �d� ethyl acetate ��env � ����� �e� dichloromethane ��env � ����� �f� acetone ��env �
������ and �g� acetonitrile ��env � 
����� and �h� SDS�D�O solution� The crosses and open circles
represent peak positions in air and in the liquid� In �h�� stars represent the peak positions of
wrapped SWNTs reported by Weisman et al�� The PL intensity color schemes are linear� but
di	erent scaling factors were used for each maps� The emission and excitation maxima correspond
to E�� and E��� respectively�
FIG� 
� E�� versus E�� plots in air ��env � ����� hexane ��env � ����� chloroform ��env � ����� The
stars represent the peak positions of SDS
wrapped SWNTs�� Both E�� and E�� show redshifts
with increasing �env with a small �n�m� dependence� The peak positions of SDS
wrapped SWNTs
deviate from the line of dielectric screening e	ect�
FIG� �� �env dependences of E�� and E�� of various �n�m� SWNTs� The solid lines are �tting
curves given by an empirical expression with power law in �
FIG� �� PL spectra in various liquids� With increasing �
� the emission spectra show linewidth
broadening in addition to redshift�

  Environmental dielectric screening effects on exciton transition energies in
single-walled carbon nanotubes (SWNTs) have been studied quantitatively in the
range of dielectric constants from 1.0 to 37 by immersing SWNTs bridged over
trenches in various organic solvents by means of photoluminescence and the
excitation spectroscopies. With increasing environmental dielectric constant
($\epsilon_{\rm env}$), both $E_{11}$ and $E_{22}$ exhibited a redshift by
several tens meV and a tendency to saturate at a $\epsilon_{\rm env} \sim 5$
without an indication of significant ($n$,$m$) dependence. The redshifts can be
explained by dielectric screening of the repulsive electron-electron
interaction. The $\epsilon_{\rm env}$ dependence of $E_{11}$ and $E_{22}$ can
be expressed by a simple empirical equation with a power law in $\epsilon_{\rm
env}$, $E_{\rm ii} = E_{\rm ii}^{\infty} + A\epsilon_{\rm env}^{-\alpha}$. We
also immersed a sample in sodium-dodecyl-sulfate (SDS) solution to investigate
the effects of wrapping SWNTs with surfactant. The resultant $E_{11}$ and
$E_{22}$, which agree well with Weisman's data [Nano Lett. {\bf 3}, 1235
(2003)], are close to those of $\epsilon_{\rm env}$ of 2. However, in addition
to the shift due to dielectric screening, another shift was observed so that
the ($2n+m$)-family patterns spread more widely, similar to that of the
uniaxial-stress-induced shift.

C:/Documents and Settings/yohno/デスクトップ/岩崎論文/revtex4/manuscript070408.dvi
Environmental dielectric screening e�ect on exciton transition
energies in single�walled carbon nanotubes
Yutaka Ohno��� � Shinya Iwasaki�� Yoichi Murakami�� Shigeru
Kishimoto�� Shigeo Maruyama�� and Takashi Mizutani�� y
�Department of Quantum Engineering� Nagoya University�
Furo�cho� Chikusa�ku� Nagoya ��������� Japan
�Department of Mechanical Engineering�
The University of Tokyo� 	���
 Hongo�
Bunkyo�ku� Tokyo 
�������� Japan
�Dated� April �� �����
Abstract
Environmental dielectric screening e	ects on exciton transition energies in single
walled carbon
nanotubes �SWNTs� have been studied quantitatively in the range of dielectric constants from
��� to 
� by immersing SWNTs bridged over trenches in various organic solvents by means of
photoluminescence and the excitation spectroscopies� With increasing environmental dielectric
constant ��env�� both E�� and E�� exhibited a redshift by several tens meV and a tendency to
saturate at a �env � � without an indication of signi�cant �n�m� dependence� The redshifts can be
explained by dielectric screening of the repulsive electron
electron interaction� The �env dependence
of E�� and E�� can be expressed by a simple empirical equation with a power law in �env� Eii �
ii � A�
env� We also immersed a sample in sodium
dodecyl
sulfate �SDS� solution to investigate
the e	ects of wrapping SWNTs with surfactant� The resultant E�� and E��� which agree well with
Weisman�s data �Nano Lett� �� ��
� ����
��� are close to those of �env of �� However� in addition
to the shift due to dielectric screening� another shift was observed so that the ��n � m�
family
patterns spread more widely� similar to that of the uniaxial
stress
induced shift�
I� INTRODUCTION
Optical spectroscopy of single�walled carbon nanotubes �SWNTs� has received increasing
attention� not only for assigning the chiral vector� �n�m�� of the SWNTs��� but also to study
the physics of the one�dimensional excitons���� In paticular� photoluminescence �PL� and the
excitation spectroscopies are the most widely used for characterizing SWNTs with resonant
Raman scattering spectroscopy� Two�photon absorption spectroscopy� and Rayleigh scat�
tering spectroscopy combined with TEM or SEM observation	 are also powerful techniques
to investigate excitonic states of SWNTs and the bundle e�ect�
Recently� the environmental e�ect is one of the topics most investigated for its e�ect on
the optical properties of SWNTs�
��� It is known that the optical transition energies vary�
depending on the kind of surrounding surfactant used to individualize SWNTs�
��� Lefebvre
et al� have reported the optical transition energies of SWNTs bridging between two micro�
pillars fabricated on a Si wafer show a blueshift as compared to the SDS�wrapped SWNTs���
We have also compared air�suspended SWNTs grown on a quartz substrate with a grating
structure to SDS�wrapped SWNTs� and have shown that the energy di�erences between
air�suspended and SDS�wrapped SWNTs depend on �n�m�� especially on chiral angle and
on type of SWNTs� type�I �	n 
 m mod � � �� or type�II �	n 
 m mod � �	���� These
energy variations due to environmental conditions have been thought to be produced by
the di�erence in the dielectric constant of the surrounding materials� The energy of the
many�body Coulomb interactions between carriers depends on the environmental dielectric
constant ��env�� because the electric force lines contributing to the Coulomb interactions pass
through the matrix� as well as the inside of the SWNT�����	 Note that the environmental
e�ect is caused not only by the dielectric screening of Coulomb interactions� but also by
chemical����� and mechanical conditions��� Finnie et al� have reported that gas adsorption
a�ects the emission energy of SWNTs���
Investigations into the environmental e�ect have not been comprehensive� despite its
importance in understanding the optical properties of SWNTs� Quantitative and separate
investigations are necessary to understand the contributions of various environmental factors�
In this study� we have focused on the dielectric screening e�ect� which has been quantitatively
investigated by immersing the SWNTs grown over trenches into various liquids with di�erent
�env� from ��
 to ��� by means of photoluminescence and the excitation spectroscopies�
II� EXPERIMENTAL
For the study on environmental e�ects� the SWNTs grown between two micro�pillars����
or over a trench����� are suitable because the environmental conditions can be controlled
intentionally� The samples used in this work are SWNTs grown on a quartz substrate with
periodic trenches� as shown in Fig� �� Both the period and depth of the trenches are 	
�m� The trenches were formed by photolithography� Al�metal evaporation and lift�o�� and
subsequent reactive�ion etching of the quartz with the Al mask� The SWNTs were grown by
alcohol catalytic chemical vapor deposition�� at ����C for �� s� after spin coating of a water
solution of Co acetate� By optimizing the growth condition� isolated bridging SWNTs can
be formed over the trenches� The density of the SWNTs was ���	 �m�� along the direction
of the trench� Such low�density� isolated SWNTs were necessary to observe luminescence
when the sample was immersed in liquids� On the other hand� in case of a sample with a
relatively high�density of SWNTs as �	 �m���� PL intensity was degraded by immersing in
liquids� even though strong PL was obtained in air� This is probably because the SWNTs
form bundles with neighbors upon immersion in liquids� in the case of a sample with a
high�density of SWNTs�
The sample was mounted in a vessel with a quartz window� and immersed in various
organic solvents with �env from ��
 to �� �see Table I�� We also immersed a sample in
��wt� D�O solution of sodium�dodecyl�sulfate �SDS� to investigate the e�ect of wrapping
with surfactant molecules� PL and the excitation spectra were measured using a home�
made facility consisting of a tunable� continuous�wave Ti�Sapphire laser �������� nm�� a
monochromator with a focal length of 	� cm� and a liquid�N��cooled InGaAs photomultiplier
tube ���������� nm�� The excitation wavelength was monitored by a laser wavelength
meter� The diameter of the laser spot on the sample surface was �� mm� so that an
ensemble of many SWNTs was detected�
III� RESULTS AND DISCUSSION
Figure 	 shows PL maps of SWNTs �a���g� in various organic solvents with di�erent
�env and �h� in SDS solution� By immersing the sample in the organic solvents� the emission
and excitation peaks� which respectively correspond to E�� and E��� showed redshifts and
spectral broadening� In the PL map measured in SDS solution��� the peak positions agree
well with those of Weisman�s empirical Kataura plot for SDS�wrapped SWNTs represented
by crosses��
The E���E�� plots in air ��env � ����� hexane ���
�� chloroform ������ and SDS solution
are shown in Fig� � � Both of E�� and E�� showed redshifts with increasing �env� without
signi�cant �n�m� dependence� The amounts of the redshifts are ����
 meV for E�� and
	���� meV for E��� The redshift with increasing �env is consistent with the theoretical
work by Ando��� The optical transition energy in SWNTs is given by a summation of the
bandgap and the exciton binding energies� When the �env increases� the Coulomb interaction
is enhanced and the exciton binding energy decreases� This leads to a blueshift of the optical
transition energy in the SWNT� It should be noted that the bandgap is renormalized by the
electron�electron repulsion interaction� and consequently the change in the �env a�ects not
only the exciton binding energy� but also the bandgap� According to theoretical work������
the repulsive electron�electron energy is larger in magnitude than the exciton binding energy�
Therefore� if we consider that both energies show a similar dependence on �env� the decrease
in the electron�electron repulsion energy exceeds the decrease in the exciton binding energy
when �env increases� This results in a redshift in optical transition energies� The redshifts
observed in the present experiment are attributed to the decrease in the repulsion energy
of the electron�electron interaction with an increase in the �env� Note that even though
the redshift with increasing �env is consistent with the theoretical studies� the amount of
the redshift is much smaller than the calculations� This is probably because in the present
experiments� the �env only outside of the SWNTs was varied� whereas the theoretical studies
used a dielectric constant for the whole system�
E�� and E�� are plotted as a function of �env in Fig� �� The energy shifts show a tendency
to saturate at �env � �� The energy variations can be �tted to an empirical expression with
a power law in �
Eii � E
env ���
where E�ii corresponds to a transition energy when �env is in�nity� A corresponds to the
maximum value of the energy change by �
� and � is a �tting parameter� A and � are ��
meV and ��
 for E��� and 	
 meV and ��� for E��� respectively� on average� Perebeinos et al�
have reported power law scaling for excitonic binding energy by dielectric constant� where
the scaling factor � is estimated to be � ��� in the range of � � ���	 Although the power law
expression of Eq� � is quite similar to the Perebeinos�s scaling law for exciton binding energy�
the present empirical expression is attributed to the scaling of electron�electron repulsion
energy by �env� rather than exciton �electron�hole� binding energy as described above� Quite
recently� such a power�law�like�downshift in optical transition energy with �env has been
obtained by theoretical calculations based on a tight�binding model���
We have previously pointed out that the E�� and E�� varies depending on �n�m�� in
particular on chiral angle and on the type of SWNTs �type�I or type�II�� comparing those
of SDS�wrapped SWNTs to those of air�suspended SWNTs� The same behavior occurred
by immersing a sample in SDS solution� as shown in Fig� 	�h�� Most E�� and E�� of SDS�
wrapped SWNTs show a redshift� except for E�� of near�zigzag type�II SWNTs� which
show a blueshift as compared to those in air� This behavior is inconsistent with the results
of the �env dependence as described above� in which �n�m� dependence is not signi�cant�
Comparing the PL maps in SDS solution to those in organic solvents as shown in Fig� �� the
equivalent �env of SDS�wrapped SWNTs would be � 	� In addition to the shift due to the
dielectric screening� the peak positions of SDS�wrapped SWNTs shift so as the �	n 
family patterns spread more widely� This suggest that wrapping with SDS has another
e�ect in addition to the dielectric screening e�ect� The behavior of the additional shifts is
similar to the shift induced by uniaxial stress� reported by Arnold et al��� At present� it still
remains an issue whether such uniaxial strain is induced in the SWNTs by wrapping with
surfactants or not� A charging e�ect due to SDS� which is an anionic surfactant� should also
be considered� Further study is necessary to understand the e�ects of surfactants on optical
transition energies in SWNTs�
Finally� we note the broadening of the PL spectra in liquids� The representative spectra
are shown in Fig� �� The peaks show a broadening� in addition to the redshift with increasing
�env� The linewidth increased from 	� meV in air to �� meV in acetonitrile for �
��� SWNTs�
This linewidth broadening is probably attributed to inhomogeneous broadening due to local
�uctuations of �env on the nano�scale dimension� The dielectric constants we used in Table I
are macroscopic values� On such small dimensions as exciton diameters of a few nm��� the
size of molecules of the organic solvents would be considerable so that the local �env would
�uctuate depending on the number and orientation of the organic molecules� This would
result in inhomogeneous broadening of the PL spectrum�
IV� SUMMARY
In summary� dielectric screening e�ects due to the environment around SWNTs on exciton
transition energies in the SWNTs have been studied quantitatively by means of PL and the
excitation spectroscopies� We varied the �env from ��� to �� by immersing the samples
with SWNTs bridging over trenches in various organic solvents with di�erent �envs� With
increasing �env� both E�� and E�� showed a redshift by ����
 meV for E�� and 	���� meV
for E��� and a tendency to saturate at �env � �� without a signi�cant �n�m� dependence� The
redshift can be explained by dielectric screening of repulsive electron�electron energy� The
�env dependence of E�� and E�� were expressed by a simple empirical equation with a power
law in �env� The equivalent �env of SDS�wrapped SWNTs was estimated to be � 	� It was
suggested that the e�ect of wrapping SWNTs with SDS was not only a dielectric screening
e�ect� but also another e�ect which caused an energy shift like a uniaxial�stress�induced
shift�
� Also at PRESTO� Japan Science and Technology Agency� �
� Honcho� Kawaguchi� Saitama
����� Japan� Electronic address� yohno�nuee�nagoya�u�ac�jp
y Also at Institute for Advanced Research� Nagoya University� Furo
cho� Chikusa
ku� Nagoya�
����� Japan
� H� Kataura� Y� Kumazawa� Y� Maniwa� I� Umezu� S� Suzuki� Y� Ohtsuka� and Y� Achiba�
Synthetic Metals ���� ���� �������
� S� M� Bachilo� M� S� Strano� C� Kittrell� R� H� Hauge� R� E� Smalley� and R� B� Weisman�
Science ���� �
�� �������
� R� B� Weisman and S� M� Bachilo� Nano Lett� �� ��
� ����
��
� Y� Miyauchi� S� Chiashi� Y� Murakami� Y� Hayashida� S� Maruyama� Chem� Phys� Lett� ����
��� �������
� H� Htoon� M� J� O�Connell� P� J� Cox� S� K� Doorn� and V� I� Klimov� Phys� Rev� Lett� ���
������ �������
� F� Wang� G� Dukovic� L� E� Brus� T� F� Heinz� Science ���� �
� �������
	 F� Wang� M� Y� Sfeir� L� Huang� X� M� H� Huang� Y� Wu� J� Kim� J� Hone� S� O�Brien� L� E�
Brus� and T� F� Heinz� Phys� Rev� Lett �	� ������ �������
� P� T� Araujo� S� K� Doorn� S� Kilina� S� Tretiak� E� Einarsson� S� Maruyama� H� Chacham� M�
A� Pimenta� and A� Jorio� Phys� Rev� Lett� ��� ������ �������
 V� C� Moore� M� S� Strano� E� H� Haroz� R� H� Hauge� R� E� Smalley� J� Schmidt� and Y�
Talmon� Nano Lett� �� �
�� ����
��
�� S� G� Chou� H� B� Ribeiro� E� B� Barros� A� P� Santos� D� Nezich� Ge� G� Samsonidze� C�
Fantini� M� A� Pimenta� A� Jorio� F� Plentz Filho� M� S� Dresselhaus� G� Fresselhaus� R� Saito�
M� Zheng� G� B� Onoa� E� D� Semke� A� K� Swan� M� S� �Unl�u� and B� B� Goldberg� Chem�
Phys� Lett� ���� ��� �������
�� C� Fantini� A� Jorio� M� Souza� M� S� Strano� M� S� Dresselhaus� and M� A� Pimenta� Phys�
Rev� Lett� ��� ������ �������
�� J� Lefebvre� J� M� Fraser� Y� Homma� and P� Finnie� Appl� Phys� A ��� ���� �������
�� T� Hertel� A� Hagen� V� Talalaev� K� Arnold� F� Hennrich� M� Kappes� S� Rosenthal� J� McBride�
H� Ulbricht� and E� Flahaut� Nano Lett� 
� ��� �������
�� P� Finnie� Y� Homma� and J� Lefebvre� Phys� Rev� Lett� ��� ������ �������
�� Y� Ohno� S� Iwasaki� Y� Murakami� S� Kishimoto� S� Maruyama� and T� Mizutani� Phys� Rev�
B ��� �
���� �������
�� T� Ando J� Phys� Soc� Japan ��� ��� �������
�	 V� Perebeinos� J� Terso	� and Ph� Avouris� Phys� Rev� Lett� ��� ������ �������
�� K� Arnold� S� Lebedkin� O� Kiowski� F� Hennrich� and M� M� Kappes� Nano Lett� �� �
�� �������
 J� Lefebvre� Y� Homma� and P� Finnie� Phys� Rev� Lett� ��� ������ ����
��
�� Y� Ohno� S� Kishimoto� and T� Mizutani� Nanotechnology ��� ��� �������
�� Y� Murakami� Y� Miyauchi� S� Chiashi� and S� Maruyama� Chem� Phys� Lett� ���� �
 ����
��
�� In order to form micelle structure� the sample was kept in SDS solution for one night before the
PL measurement�
�� Y� Miyauchi� R� Saito� K� Saito� Y� Ohno� S� Iwasaki� T� Mizutani� J� Jiang� S� Maruyama �will
be published elsewhere�
�� C� D� Spataru� S� Ismail
Beigi� L� X� Benedict� and S� G� Louie� Phys� Rev� Lett� ��� ������
�������
TABLE I� �env of air and various liquids used in this study�
solvent �env
air ���
hexane ���
chloroform ���
ethyl acetate ���
dichloromethane ���
acetone ��
acetonitrile 
�
FIG� �� Plan
view and bird
view �inset� SEM images of SWNTs bridging over trenches on a quartz
substrate� Pt thin �lm was deposited on the sample in order to avoid charge up of the insulating
substrate and to observe individual SWNTs� By optimizing growth condition� individual SWNTs
can be obtained�
0.8 0.9 1.0 1.1
0.9 1.0 1.1
0.9 1.0 1.1
0.9 1.0 1.1
(a) air (b) hexane (c) chloroform (d) ethyl acetate
(e) dichloromethane (f) acetone (g) acetonitrile (h) SDS
FIG� �� PL contour maps for SWNTs� �a� in air ��env � ����� �b� hexane ��env � ����� �c� chloroform
��env � ����� �d� ethyl acetate ��env � ����� �e� dichloromethane ��env � ����� �f� acetone ��env �
������ and �g� acetonitrile ��env � 
����� and �h� SDS�D�O solution� The crosses and open circles
represent peak positions in air and in the liquid� In �h�� stars represent the peak positions of
wrapped SWNTs reported by Weisman et al�� The PL intensity color schemes are linear� but
di	erent scaling factors were used for each maps� The emission and excitation maxima correspond
to E�� and E��� respectively�
FIG� 
� E�� versus E�� plots in air ��env � ����� hexane ��env � ����� chloroform ��env � ����� The
stars represent the peak positions of SDS
wrapped SWNTs�� Both E�� and E�� show redshifts
with increasing �env with a small �n�m� dependence� The peak positions of SDS
wrapped SWNTs
deviate from the line of dielectric screening e	ect�
FIG� �� �env dependences of E�� and E�� of various �n�m� SWNTs� The solid lines are �tting
curves given by an empirical expression with power law in �
FIG� �� PL spectra in various liquids� With increasing �
� the emission spectra show linewidth
broadening in addition to redshift�
