Large Scale Simulations for Carbon Nanotubes - jamstec

Chapter 2 Epoch-Making Simulation
Large Scale Simulations for Carbon Nanotubes
Project Representative
Syogo Tejima
Research Organization for Information Science & Technology
Syogo Tejima* , Satoshi Nakamura* , Yoshiyuki Miyamoto* , Yoshikazu Fujisawa* and
Hisashi Nakamura*
*1 Research Organization for Information Science & Technology (RIST)
*2 R&D Unit Central Res. Labs. Green Innovation Research Laboratories, NEC Corporation
*3 Honda R&D Co., Ltd
Morinobu Endo, Eiji Osawa, Atushi Oshiyama, Yasumasa Kanada, Susumu Saito,
Riichiro Saito, Hisanori Shinohara, David Tomanek, Tsuneo Hirano, Shigeo Maruyama,
Kazuyuki Watanabe, Takahisa Ohno, Yutaka Maniwa, Yoshikazu Fujisawa,
Yoshiyuki Miyamoto, Hisashi Nakamura
Nano carbon materials as nanotube and fullerene have a potential for applications to the advanced industries. For nano carbon
materials, it has been recognized that large-scale simulation is a powerful and efficient tool to find and create new functional nano
carbon materials.
Aiming at conducting the productive simulation for nano-materials, we have developed the large-scale simulation models such as
tight-binding molecular dynamic model, ab-initio density functional theory (DFT), and time-dependent DFT model.
In this term, by utilizing these models effectively, we have studied various physical properties of nano-carbon and applications
such as (1) Novel Functions of Mackay Crystal, (2) Structural relaxation of Nano Diamond, (3) Large-scale Simulation on Electron
Conduction in Carbon Nanotubes at Finite Temperature, (4) Application of time-dependent density functional theory for irradiation
of strong optical field on nano-carbons. Along these works, we have realized that the Earth Simulator is a very powerful tool for
large-scale nano-material simulations.
Keywords: Large scale simulation, TB theory, ab initio theory, Time-dependent DFT, Carbon Nanotube, Fullerenes, Green energy,
solar cell, photoelectric material
1. Introduction
In this term, we have carried out simulation studies, in
Nano-carbon materials have been expected to bring
which there are three primary objectives as (1) design of
breakthrough to material science and nanotechnology. A lot of
innovative nonmaterial with the required properties; (2) obtain
potential applications of nanotube and fullerene to electronic
fundamental properties in nano-scale matter, and (3) develop
devices have been attracted to scientists and engineers.
new applications.
In the present days, large-scale numerical simulation by
2. Physical studies on nano materials
2.1 Novel Functions of Mackay Crystal [1]
using supercomputer's computational performance has turned to
be a very efficient tool and leverage for investigating their novel
The comprehensive simulation has been conducted so far on
material properties. It now allows us to simulate complex nano-
properties of the Mackay crystal, focusing on synthesis process
structures with more than ten thousand atom of carbon.
Aiming at using large-scale simulations on the Earth
through atomic arrangement of GSW and mechanical properties
Simulator, we have developed an application package of
as stiffness, etc.. As Mackay crystals, it is well known that there
ab initio DFT theory and parameterized tight-binding (TB)
are three different sizes and types. The crystal is classified as P,
models. Especially, the TB model shows that it is very suitable
D, G-types, by the atomistic bonding configuration of hexagon
for the very large systems even if it has a lack of symmetrical
or octagon on the surface curvature of the unit cell.
In this term, focusing P type crystal, the dependency of
Annual Report of the Earth Simulator Center April 2009 - March 2010
energy band gap on the crystal size has been investigated though
in Figs. 1-3. These show that the band gaps are ranged from
simulating the electronic band structure by DFT model.
0.05eV to 0.94 eV and the electron density depends on the
This result indicates that Mackay crystal has a potential for
size of atomic unit cell. The peak of electron density appears
highly efficient photoelectric material for solar cell. The energy
at octagon bonding and the lowest at hexagon in the direction
band structures and electron density distribution are shown
to (111). It is the reason why the intrinsic electron density
Fig. 1 Energetically optimized structure of P48 zigzag Mackay crystal and energy band structure.
Fig. 2 Energetically optimized structure of P144 zigzag Mackay crystal and energy band structure. The color
represents number of electrons, which decreases in the order of yellow and red.
Fig. 3 Energetically optimized structure of P192 armchair Mackay crystal and energy band structure. The
color represents number of electrons, which decreases in the order of yellow, red and aqua.
Chapter 2 Epoch-Making Simulation
distribution and band gap are due to the existence of octagon
and pressure dependence. The relaxation simulation has made
forming the negative curvature of Mackey crystal.
on two sizes of nano-diamond by using DFT model. The initial
Absorbable wavelengths of sun light depend on the energy
structure is set in truncated octahedron and the number of atoms
band gap of the photo-electric material. By stacking Mackey
is 147 and 413 .
crystal films with the different size, a tandem-type solar cell has
The structure of before- and after- relaxation are shown in
been designed conceptually, which would be able to absorb the
Figs. 4 and 5 for C147 and C413 , respectively. It shows that the
sun light with near infrared light. As the next step, the feasibility
surface layer of the (111) is graphitized with sp2 bond. The
study of Mackey crystals for solar cell will be made by large-
area of graphite layer increases as the size of the nano-diamond
scale simulations.
increases. The direction (100) consists of the diamond structure
with sp3 bond. The mixing state of sp2 and sp3 bonds is expected
2.2 Structural relaxation of Nano Diamond
to generate the polarized electric fields with functional elements.
Recently the fragment-diamond transformed into carbon-
The polarized nano-diamond might be one of the functional
onions, so called as nano-diamond, was synthesized
elements for the drug delivery system or some fields. As a next
experimentally. Some researches & developments have been
step, large-scale simulation will be carried out on nano-diamond
made by modifying the nano-diamond chemically to disperse
with thousand atoms.
or gel in solution for a drug delivery system. Presently there
2.3 Large-scale Simulation on Electron Conduction in
Carbon Nanotubes at Finite Temperature [2]
is no information on the characteristics of the surface of nanodiamond that leads us to select the adequate molecules to
According to Moore's law, which states that the number
chemical modification.
For reliable and accurate simulations, DFT simulations have
of transistors in integrated circuit (IC) will double every 18
been carried out to describe the properties on size, temperature
months, the rapid development of ICs has to a large extent
Fig. 4 C147 octahedral nanodiamond structure before (left) and after (right) the relaxation simulation.
Fig. 5 C413 octahedral nanodiamond structure before (left) and after (right) the relaxation simulation.
Annual Report of the Earth Simulator Center April 2009 - March 2010
Fig. 6 (a) shows a schematic view of the system under consideration. Figures 1 (b), (c), and (d) show our simulation results under three different
conditions: (b) The line connecting two electrode-junctions is not parallel to the axis of CNT. (c) Under the identical condition as Fig. (a)
except for the existence of a defect in the CNT. (d) Many electrodes are attached on the CNT.
been enabled due to the improvement of a transistor design
Carbon nanotubes (CNTs) are considered attractive candidates
based on Silicon. By scaling down dimensions, the silicon-
for new technologies that could take the place of the silicon-
based technologies have been pushed close to its physical
based electronic.
limits as soon as the end of this decade. Therefore it becomes
It is still difficult, however, to manipulate CNTs
crucial to develop technologies that will enable continued
experimentally; and besides the macroscopic Ohm's law breaks
implementation of increasingly higher performance devices.
down due to the various effects caused by the microscopic
size effect. In this context, it is necessary to study the transport
behavior of CNTs using a quantum mechanical simulation. We
have developed a simulation code by which electron transport
simulations of nano- and meso-scale CNTs can be performed.
We focused on the system under consisting of two semi-infinite
electrodes and a scattering region sandwiched between these
electrodes (see Fig. 6 (a)).
Using non-equilibrium Green's function (NEGF) technique,
we obtain the following expression for electron current from j1
site to j2 site.
∑ t j ξ j ξ ({R})∫{ f (ω – μ R) – f (ω – μ L)}
a (ω) ]
∑ Re [G rCC (ω){–iГ (ω)}G CC
( j ,ξ ,σ)( j ,ξ ,σ ) dω,
Jj → j = e
Fig. 7 CPU time versus the number of carbon atoms
2 2
1 1
ξ 1ξ 2
Chapter 2 Epoch-Making Simulation
– i Г L (ω) = Σ r (ω) – Σ a (ω),
a defect in the CNT, circular current decreases. When many
electrodes are attached on the CNT, current flows along the axis
GCC ( z) =
z I CC – H CC – Σ L (z) –Σ R (z)
Σ L ( z) = H CL
H ,
z – H LL LC
Σ R ( z) = H CR
z–HRR RC .
of the CNT and circular current does not occur.
Finally, CPU time versus the number of carbon atoms is
shown in Fig. 7. One can see that our simulation code achieves
the order (N) algorithm with respect to the size of the system.
The sustained performance of 13 Tera flops was achieved, and
the computing efficiency was seventeen percent of the peak
Here Hcc is the matrix describing the scattering region
sandwiched between electrodes. ΣL is the self-energy of the lefthand side electrode, and ΣR the self-energy of the right-hand
becomes the most heavy part of the model computationally. An
2.4 Application of time-dependent density functional
theory for irradiation of strong optical field on nanocarbons [3]
embedding potential algorithm is implemented to obtain the
In this term, we discovered field enhancement inside
side. In this scheme, the large-dimensional matrix inversion
to calculate the Green's function in the scattering region
nanotube and pulse-laser induced exfoliation of graphene from
equilibrium and non-equilibrium Green's functions.
Since the NEGF technique is also applicable to calculate
graphite surfaces. These phenomena suggested the possibility
the density of electrons, we determined NEGF self-consistently
of efficient photo-fabrication of nano-carbons with controlled
together with Poisson equation. The substitute charge method
manners. This term, we further investigated these two subjects.
is considered to be a simple and effective method to solve the
As for the exfoliation of graphene from graphite surface,
Poisson equation. The positions of substitute charges, however,
we searched more efficient process, i.e., faster exfoliation with
are empirically determined. Therefore, in our solution method,
lower energy cost of laser-shot, by tuning the shape of pulse
both the positions and the values of charges are determined
laser in the time-axis. Last year, the assumed wavelength of the
so that the differences of the potentials on boundary are
laser was 800 nm, and pulse width was 45 fs. In this year, we
least in a sense of the least square method. In this case, the
just shorten the pulse width as 10 fs and compared the dynamics
implementation of least square method is made with Davidon-
shown in Fig. 1.
When we further shorten the pulse width, nothing happened
Fletcher-Powell algorithm.
on the surface. Therefore, we believe that the pulse width as 10
These figures 6 (b), (c), and (d) show our simulation results
fs is optimized for graphene exfoliation which should be tested
at 300 (K). The arrows represent the electron current in CNTs
by experiments in future.
From figures 6 (b), (c), and (d), one can find the following
results: When the line connecting two electrode-junctions is not
As for the photochemistry of molecule inside carbon
parallel to the axis of the CNT, circular current occurs. On the
nanotube, we rely on experience of last year which was the
other hand, under the same condition except for the existence
enhancement of the electric field (E-field) inside semiconducting
Fig. 8 Time evolution of heights of graphene layers (10-layer slab model having two surfaces on top and bottom) after irradiation
of laser shot (a) with wavelength 800 nm, pulse width = 45 fs, and power per shot is about 87.9 mJ/cm2, (b)with the same
wavelength, pulse width 15 fs, and power 20 mJ/cm2.
Annual Report of the Earth Simulator Center April 2009 - March 2010
Fig. 9 Disintegration of an HCl molecule inside an (8,0) nanotube induced by very short pulse.
nanotube. We thus expect that trapping molecule inside
semiconducting nanotube can make light illumination to
[1] S. Tejima, et al, Journal of the Surface Science Society of
molecule more efficient. We tested photo-induced disintegration
Japan, HYOMEN KAGAKU, vol.30, no.12, pp.673-679,
of an HCl molecule inside an (8,0) nanotube.
[2] S. Nakamura, SC09, HCPNano09 Workshop, Oregon,
Figure 9 shows the geometrical time-evolution of an HCl
November 15.
molecule inside an (8,0) nanotube after giving very short
[3] S. Miyamoto, et al, Phys. Rev. lett., Vol.104, pp.208302-1-
pulse shot with wavelength 800 nm, pulse width is 1 fs and
208302-4 (2010).
maximum intensity of E-field is 12 V//Å. (Such an extremely
high E-field is available only at such very short pulse.) One can
note spontaneous disintegration of HCl molecule and an ejected
H atom is sticking nanotube wall, so the H atom is expected
to reflect from the wall. According to our preliminary test, the
nanotube itself is sustainable under such short pulse with the
same field-intensity, but show significant shaking motion. We
therefore think further simulation is needed to check whether
the nanotube can remain and to check trajectory of reflected H
atom. We believe this simulation will design efficient photochemical processes using encapsulation of molecules inside
carbon nanotubes.
Large-scale simulations have been carried out on
nonmaterial by using ab initio density functional theory and the
parameterized tight-binding models. These optimized models
allowed us to simulate the properties with excellent performance
on the Earth Simulator. It enables us to come across discoveries
of novel phenomena in nano scale and find out some useful
materials for clean energies.
Chapter 2 Epoch-Making Simulation
手島 正吾 高度情報科学技術研究機構
手島 正吾 * ,中村 賢 * ,宮本 良之 * ,藤沢 義和 * ,中村 壽 *
NEC R&D ユニット 中央研究所 グリーンイノベーション研究所
1. 研究目的
2. 成果
せた。サイズが異なる単位セルにそれぞれ 48、144、192 個の炭素をもつ P 型マッカイ結晶のエネルギーバンド構造
を第一原理計算で調べたところ、0.05eV から 0.94eV のエネルギーギャップを持つこと、原子が中性電荷からずれ
6 員環構造に 8 員環が混じり、特殊な電荷ポテンシャルが生じたためである。異なるバンドギャップをもつ積層半
最適化により得られるが、分子化学修飾が可能な表面の性質は未だ詳細に得られていない。DFT 計算手法により、
147、413 原子について調べた。その結果、
(111)方向は sp2 結合による黒鉛化し、
(100)方向は sp3 結合によるダイヤモンド構造であることが明らかとなった。サイズが大きくなると黒鉛層が大き
くなる。sp2 と sp3 の混在により、ナノダイヤモンドの電荷偏極が発生していると予測される。電荷偏極したナノダ
子数に比例するオーダー N であり、大規模計算が可能である事を確認した。
表面からの原子一 層分のグラフェンをはがせることが、第一原理計算より判明した。
キーワード : 大規模シミュレーション , タイトバインディング理論 , 時間依存密度汎関数法 , オーダー N 法 ,
カーボンナノチューブ , マッカイ構造 , ナノダイヤモンド , 量子伝導 , グラファイト加工技術