Chapter 4 Epoch Making Simulation

Large Scale Simulations for Carbon Nanotubes
Project Representative

Kazuo Minami

Research Organization for Information Science &TechnologyAuthors

Syogo Tejima 1, Kazuo Minami 1, Yoshiyuki Miyamoto 2, Mari Ohfuti 3Mamoru Sakaue 3, Tsuyoshi Miyazaki 4 and Hisashi Nakamura 1
1 Research Organization for Information Science &Technology (RIST)
2 Fundamental and Environmental Research Laboratories, NEC Corporation
3 Nanotechnology Research Center, Fujitsu Laboratories Ltd.
4 National Institute for Materials Science (NIMS)CARBON NANOTUBE RESARCH GROUPE

Morinobu Endo, Eiji Osawa, Atsushi Oshiyama, Yasumasa Kanada, Susumu Saito,
Riichiro Saito, Hisanori Shinohara, David Tomanek, Tsuneo Hirano,
Shigeo Maruyama, Kazuyuki Watanabe, Ohno Takahisa, Yoshiyuki Miyamotoand Hisashi Nakamura

Carbon nanotubes (CNTs) and fullerenes have a lot of potential applications in nanotechnology. In the stream of efforts toexploit these nanoscale materials, the computational simulations have turned out to be powerful and efficient tools. Especially, as
the recent trend in technology made it possible to manipulate further miniaturized structures, required simulations for emerging
material become bigger and bigger. Aiming at realistic simulations for nanomaterials, we have developed a large-scale computation technique utilizing tight-binding molecular dynamic method, ab initio density functional theory (DFT), and time-dependent
DFT method. By an efficient optimization on ES, we achieved the performance of 7.04 Tera flops using 435 processors.
We have studied various physical properties of nano-carbon material e.g., hot carrier dynamics, atomic and electronic structure of CNT-Metal contacts, structure of bundle CNTs, and creation of novel nanocarbon structures. During these works, wehave realized that the Earth Simulator is a very powerful tool for large-scale material simulations.
Keywords: Large-scale simulation, TB theory, ab initio theory, DFT, Carbon Nanotube, Fullerens

1. INTRODUCTION

subjects in this work, which are described in the next section.
There are three primary objectives: design of innovative
nanomaterials with certain desired properties; obtaining fundamental properties in nano-scale matter, and nano-applications. Our purpose is to give the clear explanation of properties and phenomena of nano-scale events and deduce guiding
principle to design new materials from nano-structures using
super-computers.

Carbon materials have been expected to make a breakthrough in material science and nanotechnology. A lot of
potential applications of nanotubes and fullerenes e.g., electronic field emitter and electronic devices have attracted ascientific community. In the investigation and utilization of
their material properties, numerical simulation using
a supercomputer has turned to be a very efficient tool. A
recent development in nanotechnology has required more
efficient supercomputing capable of large-scale simulationof up to 104 atoms.
Aiming at large-scale simulation utilizing the EarthSimulator, we have developed computational software packages based on ab initio DFT theory and parameterized tightbinding (TB) method. The TB code we have developed isshown to be suitable for very large systems in spite of thelack of symmetrical arrangement. We have carried out some

2. PHYSICAL STUDIES ON NANOMATERIALS
2.1. Hot carrier dynamics in carbon nanotube
In 2003, we started the simulation on hot-carrier decay incarbon nanotubes which enables us to extract time-constantof carrier decay and this parameter will be crucial for
designing optimum running frequency of carbon nanotube
devices, such as transistor, and optical switch. We obtained
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Energy (eV)3.0

remarkably change, compared with CNT-titanium contacts.
Although CNTs have shown potential properties forelectronic devices, the contacts with the metal, which
would play important roles in the applications, have notbeen understood enough. The atomic and electronic structures of CNT-metal contacts have been studied by using
ab-initio molecular dynamics. We have examined titanium(Ti) and molybdenum (Mo) as possible contact materials,
because they are usually used in the layers under catalysts
for CNT growth. The initial atomic structure is formedby simply connecting metallic (5,5) CNTs with metalslabs. The unit cell has 90 carbon atoms and 96 metalatoms. Both Ti and Mo in the simple contacts give goodelectronic structures, where the electronic states of themetal distribute around the Fermi level of CNT. Whenthe system is stabilized, the atomic structure of the CNTMo contact remarkably changes, compared with the CNTTi contact. The remarkable change in the atomic structure
also brings a change in the electronic structure. The densityof states around the Fermi level is obviously increased,
which seems to suggest that Mo is better as a contact
material. We also will investigate semiconductor andmulti-walled CNTs.

Ekininit =300K

2.0
Ekininit =150K
1.00.00

Ekininit =77K
100200300400

Time (fs)Fig. 1 Time-evolution of the potential energy of ionic system in electronically excited carbon nanotubes. Lower initial temperature
gives slower drift of the potential.

which can be interpreted as early electron-electron decay
and later electron-phonon coupling.
In this year, we have confirmed temperature-dependenceof the electron-phonon coupling appeared in the later timedomain. The temperature dependence is mimicked by giving
a certain scale of the randomized velocities on all ions in thebeginning of the simulation in accordance with the MaxwellBoltzmann distribution function. Then we compare the timeevolutions of the potential energy of ionic system with different scales of the initial velocities on ions. Figure 1 shows
temperature dependence of the potential lowering. One cannote that lower temperature case shows slower drift of thepotential which means slower rate of energy transfer fromthe electronic system to ionic system. The dotted lines aretime-average of the fluctuating potentials which highlightthe trend of the potential drift. Corresponding paper is now
under preparation.

120Simple
Stable

100
80
60
40
202.2. Atomic and Electronic Structures of CNT-Metal Contacts
We have studied the atomic and electronic structures ofCNT-metal contacts by using ab-initio molecular dynamics.
While the systems are stabilized from the simple contacts, both the structures of CNT-molybdenum contacts

0–4–3–2–1

0

1

2

3

Energy (eV)Fig. 3 Density of states of CNT-Ti contacts.

Fig. 2 Simple and stable atomic structures of CNT-Ti contacts.

Fig. 4 Simple and stable atomic structures of CNT-Mo contacts.

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Chapter 4 Epoch Making Simulation120

SimpleStable

100
80
60
40
20
0–4–3–2–10

1234Energy (eV)Fig. 5 Density of states of CNT-Mo contacts.

2.3. Advantaged order-N first-principle method for large
complex systems.
Conventional first-principles calculations based on thedensity functional theory (DFT) are very inefficient forlarge complex systems because the memory and CPU
requirements increase rapidly as the number of atoms in thetarget systems increases. In order to overcome this problem,
we are developing a linear-scaling DFT code, whichenables us to perform DFT calculations on very large systems. Within this fiscal year, we have optimized the codefor the Earth Simulator and have demonstrated its high performance especially in parallelization. We have succeededin performing DFT calculations on the system of threedimensional Ge overlayers on Si (001), which includes
about ten thousands of atoms. The present parallelization
ratio is 99.91% and we can expect even higher values when
we treat larger systems.

Fig. 6 Creation process of bundle by twelve nanotubes

2.4. Structure of bundle CNTs for composite materials
In 2003, we reported mechanical properties as pull andpush of single- and double-CNT using the large scale tigthbinding simulation. In that works, we presented the structure
dependence on collapse and fracture in CNTs.
When we used the strong nanotube as a real material, it
was necessary to bundle these CNTs. As a first stage, theeffect of Van der Waals attractive interaction between thedifferent number of CNTs to bundle together was simulated
under no applied forces. Two types of bundle CNTs areplaced at triangle lattices at an appropriate distance between
CNTs (Fig. 6, 7). When each CNTs tried to approach together by the attractive force, then faces of contact become flat
(Fig. 6 (1, 2, 3) and Fig. 7 (1, 2, 3) ).
In spite of same simulation time steps, the bundle consisting of a small number of nanotubes shown in Fig. 6 looks
like structure separation as a reaction. We predicted thatbinding of CNTs could be stronger with increasing CNTs.

Fig. 7 Creation process of bundle by twenty-seven nanotubes.

2.5. Creation of novel nanocarbon structures using GSW
rearrangement
This work is on quantum combinational chemistry simulation. Its objective is to find new nanocarbon structure by isomerization using generalized Stone-Wales (GSW) rearrangement and C2 loss. Isomerization is extremely compute intensive, so the simulation clearly needs very large-scale computers. There is a parallel code using a master-slave algolism. One processor as master is gather and classify all reaction paths generated on other processors as slave. The fig.8
shows the generation of a capped long CNT from a short
CNT and a fullerene. The Fig. 9 exhibits the nanotube generation from three fullerenes applying the boundary periodic
condition. The zigzag and one chilral nanotube appear in thesimulations. The long-term goal is to find a path to makenew nanodevices from the many generated nano structuresby self-organization.
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Initial structure

GSW: 20 times

GSW: 6 times

GSW: 30 times

Energy level

zigzagchiralFig. 8 Generation of capped CNT from two fullerenes.

05101520

Initial structure
Fig.10 Energy v.s number of GSW sequence

GSW: 10 times

GSW: 21 times (chiral)

GSW: 25 times (zigzag)

Fig. 9 Generation of CNTs.

3. SUMMARY
The large-scale simulations on nanomaterials have been
carried by ab initio density functional method and the parameterized out tight-binding calculations. The optimized
codes showed that the computation on the Earth Simulator
could give an exceptional performance and enable morelarge-scale realistic simulations. Our large scale simulations
for nano applications will contribute to valuable on novel
nano material properties and on nano electrical designs.

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3

3

41

12 NECCNT

34

1.
CNT

2.
H14

H15123
C60

GWS169