Chapter 4 Epoch Making Simulation

Large Scale Simulations for Carbon Nanotubes
Group Representative

Kazuo Minami

Research Organization for Information Science & TechnologyAuthors

Syogo Tejima 1 Yoshiyuki Miyamoto 2
Hisashi Nakamura 1

Kazuo Minami 1

Mikio Iizuka 1

1 Research Organization for Information Science & Technology
2 R&D Unit Central Res. Labs. Fundamental and Environmental Research Laboratories, Nanotube Technology Center NEC
CorporationCarbon Nanotube Research Group

Morinobu Endo
Eiji Osawa Atsushi Oshiyama
Yasumasa Kanada Susumu Saito
Riichiro Saito Hisanori Shinohara
David Tomanek Tsuneo Hirano
ShigeoMaruyama Kazuyuki Watanabe Yoshiyuki Miyamoto
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 a further miniaturized structures, required simulations for
emerging material become lager and lager. Aiming at realistic simulations for nanomaterials, we have developed a large-scalecomputation technique utilizing tight-binding molecular dynamic method, ab initio density functional theory (DFT), and timedependent DFT method.
We have studied various physical properties of nano-carbon material e.g., Mechanical properties of CNT, transformation ofstructure of fullerens inside CNT and carrier Lifetime in CNT.
During these works, we have realized that the Earth Simulator is very powerful tool for large-scale material simulations.
Keywords: Large scale simulation, TB theory, ab initio theory, DFT, Carbon Nanotube, Nano Diamond, MechanicalProperties

1. INTRODUCTION

section. 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-structuresusing super-computers.

Carbon materials have been expected to make a breakthrough in material science and nanotechnology. A lotof potential applications of nanotubes and fullerenes e.g.,
electronic field emitter and electronic devices have attracted
scientific community. In the investigation and utilizing theirmaterial properties, numerical simulation using supercomputer has turned out to be a very efficient tool. A recent
development in nanotechnology has required more efficient
supercomputing capable of a large-scale simulation of up to104 atoms.
Aiming at large-scale simulations utilizing EarthSimulator, we have developed computational software
package based on ab initio DFT theory and parameterizedtight-binding (TB) method. The TB code we have developed
is shown to be suitable for the very large systems despite of
the lack of symmetrical arrangement. We have carried out
three subjects in this work, which are described in the next

2. PHYSICAL STUDIES ON NANOMATERIALS
2.1. Mechanical Properties of CNT
It has been suggested that the tensile strength of carbon
nanotubes might exceed that of other known fibers becauseof the inherent strength of the carbon-carbon bond. So nanotubes have beneficial consequences for their application incomposite bulk materials and as individual elements ofnanometer-scale devices and chip of sensors.
The mechanical properties of nanotubes are predicted to
be sensitive to details of their structure and to the presenceof defects, which means that understanding on individual
nanotubes are essential to examine these properties.
A lot of simulations on compression and stretch of isolat125

Annual Report of the Earth Simulator Center April 2003 - March 2004

ed nanotubes have been carried out. As peculiar phenomena,
Young's modulus, bending, collapse, twisting and bucklingare investigated on. Almost all the simulations adopt theYoung's modulus based on the first principle calculation
with a small number of atoms in unit cell, or deformations
like an undulation based on the tight binding method under
external filed for a short length nanotube. But for an undulation process of nanotube, one can speculate easily that itdepends on a length of nanotube.
We investigated the undulation process of long nanotubes
under axial pressures by help of a large scale tight binding
simulation. For example, the number of atoms for the(10,10) nanotube is 2200. This size is ten times as large as
conventional calculations. Undulation structure obtained
from our simulations are very different from the previous
one [1].
Our first principle calculations of the elastic properties ofnanotubes also confirm that they are extremely rigid in theaxial direction. The Young's modulus of (10,10) nanotube isequal to 1.06 Tera Pa. We will continue simulations on elastic properties for a variety of materials as double wall nanotube and peapod with different chiral vectors.

2.2. Structure of fullerenes inside CNT
Carbon fullerenes, such as C60, are molecules with alarge range of interesting properties. Our previous simulations on thermal stability in carbon materials indicatethat C60 melts at about 3500 k, while some nanotubes arestill stable at the temperature. Our question raised here isabout "peapod", which has a structure of one-dimensionalarray of C60 inside a nanotube. How fullerenes of "peapod"
are changed here to a new phase? Experimental observations tell us that at high temperature fullerenes inside ananotube connect each other forming an inner nanotube.
Thus peapod turns out to be double-wall nanotube. The
result indicates a potential of creating new materials bypacking more complicated carbon materials, yet, thedetailed mechanisms on the phenomenon is not clarified
yet. This phenomenon will be deeply affected by the condition of the system temperature and pressures of interfullerenes. The structure simulation of fullerenes inside ananotube is performed up to 4ps with 80,000 time steps.
Figure 2 depicts initial condition and Figure 3 after 4ps.
Growth to spread carbon net can be seen in the figure.

Fig. 1 Structure of nanotube by 92% compression.

Fig. 2 Initial condition of fullerens inside a nanotube.

Fig. 3 Structure of fullerens inside a nanotube after 4ps at 3500k.

126Chapter 4 Epoch Making Simulation

Optical Excitation

42

Energy (eV)2.3. The Carrier Lifetime in CNT
As for device application of carbon nanotubes, the lifetimeof excited carriers in nanotubes is very important information
since the lifetime is a key factor for switching speed andquantum efficiency of the devices. We have investigated thecarrier lifetime in carbon nanotube by performing the timedependent density functional theory (TDDFT) being coupledwith the molecular dynamics (MD). This kind of simulation
can include both electron-electron and electron-phonon interaction without any adjustable parameters. Figure 4 shows theenergy gap reduction of hot-hole and electron in (3,3) carbon
nanotube. The decay time-constant is extremely fast, the initiation of the decay is observed at 70 fs while significant gap
reduction is observed around 200 fs. We will search temperature dependence of this decay process to highlight the electron-phonon coupling in this decay process.

0–2ElectronHole–4
050

100

150

200

Time (fs)

References

Fig. 4 The energy gap reduction of hot-hole and electron in (3,3)
carbon nanotube.

[1] D.Srivastava et.all Phys. Rev. Lett. 83, 2973,1999

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