Environmental dielectric screening effect on exciton transition energies
  in single-walled carbon nanotubes
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� �� �
�� ����
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�� 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�
