1

Nanomaterial and NanotechnologyNanomaterial and Nanotechnology

Shigeo Maruyama丸山 茂夫

Department of Mechanical Engineering機械工学専攻

http://www.photon.t.u-tokyo.ac.jp

Molecular Dynamics and Nanotechnology 分子動力学とナノテクノロジーBasic Theory of Extended Nano Space 拡張ナノ空間理論 2016

Contents (1)

1. 9/27 Nanotechnology (Shigeo Maruyama, Nanomaterial and Nanotechnology)

2. 10/4 Nanotechnology (Yan Li, Chemical vapor deposition of carbon nanotubes)

3. 10/11 Nanotechnology (Yutaka Matsuo, Next generation solar cells using nanomaterials)

4. 10/18 Nanotechnology (Shigeo Maruyama, Application of graphene and carbon nanotubes)

5. 10/25 Nanotechnology (Shigeo Maruyama, Spectroscopy of nanomaterials)

6. 11/1 Nanotechnology (Kazu Suenaga, HR-TEM characterization of nanomaterials) (Bring your PC, Windows or Mac running Windows)

Contents (2)

http://www.phonon.t.u-tokyo.ac.jp/teaching/Molecular-dynamics-and-Nanotechnology.php

7 11/15 ShiomiMD Introduction to MD

8 11/22 Shiomi

MD MD Fundamentals 1: Potential function, Equation of motion, Initial & boundary conditions, ensembles.

9 11/29 ShigaMD

MD Practice 1: Simple equilibrium MD calculation, Realizing ensembles

10 12/6 Shiomi

MDMD Fundamentals 2: Calculation and control of static thermophysical properties (Energy, Temperature, Virial, Chemical potential etc)

11 12/13 ShigaMD

MD Practice 2：Transport properties（Diffusion，Thermal Conductivity，Shear）

12 12/20 KodamaNanotech

Nanoscale measurements techniques of structures and static and transport properties.

13 1/10 KodamaNanotech Thermal conductivity of nanoscale structures.

14 MD&Nanotech Final report

Professors (Maruyama-Chiashi Lab. and Shiomi Lab.)

from NNI Home Page: http://www.nano.gov

Nanometer Scale

2

Fullerene, Nanotubes, GrapheneFullerene, Nanotubes, Graphene

Fullerene

Carbon Nanotubes

Graphene

1996Nobel Prize for Chemistry

Kroto, Curl, Smalley

2010Nobel Prize for Physics

Geim, Novoselov

Sep. 4, 2010

FNTG Research SocietyFNTG Research Society

Fullerene

Single-Walled Carbon Nanotubes

(SWNTs)

Peapod

Multi-Walled Carbon Nanotubes Graphene

Nano-Diamond

Bundle of SWNTsDouble-Walled

Carbon Nanotubes

Metallofullerene

http://fullerene-jp.org/

Tips of AFM

Application of CNTs (1)

Electrode of Fuel Cell

FETBiosensorNanowires

Hydrogen Storage?

Field Emission

Li Ion Battery

Sumsong

NEC

Noritake

A.T.Woolley et al(2000)

C. Dekker, Delft

Endo, JJAP (2006)

Application of CNTs (2)

(5,5) SWNTs x 1.6 m 128000 atoms

Thermal Device

Super Capacitor

Electrode of Fuel Cell

TransparentConductive Film

Conductive Plastic

Mechanical Strength

Composite Material

T. Hatanaka et al. ECS Trans. (2006)

Yakobson et al. (1996)

Alnair Lab.Z. Wu et al., Science (2004)

Mode-locked Pulse laser

(Saturable absorbance)

Maruyama-Shiomi (2006)

(a) (a)(b)

Field Effect Transistor (FET)

DrainCNT Channel

SiO2

Highly Doped Si

Gate

Source

C. Dekker, Delft

Aikawa et al., 2011

Electrode of Fuel Cell

T. Hatanaka et al. ECS Trans. (2006)

VA-MWNTs+Pt

Better O2 access, Better Proton/ElectronTransfer, Higher Durability

TOYOTA FCHV BOOK

3

Transparent Conductive Film

Kaili Jiang

Rong Xiang

Shoushan FanYan Li

Fei Wei

Thin Film Network FET

From Esko Kauppinen Seminar at Aalto Univ.

D-M. Sun et al., Nature Nanotech. 6, 156 (2011)

IGZO (Indium, Gallium, Zinc, Oxide)discovered by Prof. Hideo Hosono

Japan Prize April 20, 2016

Solar Cell ApplicationsSolar Cell Applications

http://www.photon.t.u-tokyo.ac.jp

CNT-SiGraphene-Si

Organic Thin Film(Normal)

Perovskite(Inverted)

Perovskite(Normal)Organic Thin Film

(Inverted)

HoneycombCNTs

Space Elevator?

NHK NewsWeb2014/9/26

1-D: Carbon Nanotube

Allotropes of Carbon

3-D: Diamond2-D (3-D) Graphite

0-D: Fullerene

2-D: Graphene

Graphite Diamond (from CHAUMET Paris HP)

4

He gas

Power(+) Power(-)

Window

Graphite Electrodes

CCDCamera

Reflector

Stepping motor

Vacuum pump

Arc-Discharge Generator

TEM Images of Carbon Nanotubes

S.Iijima, Nature, 354, pp.56-58 (1991).

アルゴンガス

油回転ポンプ

電気炉

レーザービームNd:YAG 第2高調波 (532nm)

マノメータ

ピラニ真空計

ターゲットロッド

石英レンズ(f=1200mm) 石英管・セラミックス管

Laser Oven Fullerene/Nanotube Generator

H.Kataura (Tokyo Metropolitan Univ)

Individual tube diameter: 1.3 nmSpacing: 0.34 nmMisalignments and Terminations

TEM from Smalley et al. at Rice University

About 100 SWNTs

TEM Pictures of SWNT Ropes

5 nm

By ACCVD

Peapods

Suenaga et al., PRL 2003

Peapod with Sc2@C84Shinohara, 培風館

Horizontally Aligned SWNTs

200 nm

(ST-cut基板 13 h annealing)

SWNTs touching substrate

9 µm

(ST-cut基板 13h annealing)

Aligned SWNT

Zeolite

5

Single walled carbon nanotubes (swnt)from Hi pressure CO ( Pco)

R. E. SmalleyCNIRice University

1 step

Gas phase

$500/gram

The HiPco Process

TEM Bronikowski et al. (2001)

Disproportional ReactionWith Fe(CO)5

)(2 SolidCCOCOCO

Feb. 22, 2001 @ Univ. of Tokyo

Alcohol CCVD on Catalysts Supported with Zeolite

2.5/2.5 : Fe/Co (wt%) on USY Zeolite 30mg

AlcoholEthanolMethanol

vacuum

Electric FurnaceSimple, High-PurityLow-Temperature

(550-900C)

S. Maruyama et al., Chem. Phys. Lett. 360 (2002) 229.

As-Grown

500 1000 1500

Inte

nsi

ty (

arb

.un

its)

Raman shift (cm–1

)

(a) 600°C

(b) 700°C

(c) 800°C

(d) 900°C

(e) Laser–oven

RBM

G band

D band

BWF

7.4[Å]Shinohara& Nagy

Most Used Carbon Source in NT06 Nagano (2006)

& Ouro Preto NT07 (2007)

Vertically Aligned SWNTs on Quartz Substrate

Y. Murakami, S. Chiashi, Y. Miyauchi, M. Hu, M. Ogura, T. Okubo, S. Maruyama, Chem. Phys. Lett. 385 (2004) 298

0 500 1000 1500

100 200 300 400

2 1 0.9 0.8 0.7

Raman Shift (cm–1)

Inte

nsi

ty (

arb

. un

its)

Diameter (nm)

Dr. Yoichi Murakami

10 m25 nm

Challenge of SWNT Preparation

Orientation and Position Controlled Growth

High Purity and Efficient Growth

Specific Growth of Semiconducting or Metallic CNTs

Chirality Controlled Growth

HiPco, CoMoCAT, ACCVD, SuperGrowth, eDIPS, Kauppinen AerogelReduction, Oxygen, Growth Termination, Catalyst Deactivation, Carbon Over-coating,

Substrate Diffusion, Al2O3, Decomposition of Precursor

Vertically Aligned, Horizonally Aligned, Superlong SWNT, Patterned GrowthCatalyst Density, Crystal Quartz, Sapphire, Tip Growth, Laminar Flow

EtOH/MeOH, EtOH/Water, Water pretreatment, UV, CeO2Etching, Oxygenic Condition, Catalyst Facet

(6,5), Near Armchair, Cloning, Sulfur, Nitrogen, W6Co7Cap Structure, Thermodynamics, Kinetic Process, Catalyst,

PL quantum yield, Raman quantum yield

DGU separationGel chromatography

ATP

Electric BreakdownSDS-DGU, ATP

Purification

DEPCapillary

Laser-Oven, Arc Discharge

F. Yang,,, Yan Li, Nature 510 (2014) 522.

J. R. Sanchez-Valencia at al., Nature 512(2014) 61.

Defect free (14,1) by spiral growth

zigzagInterface

kink

• Co60，1550 K，n = 1• Equivalent to 21.4 kPa• Growth Speed 3090 μm/s

• (15, 2) is also grown

chain

Pentagon 7 memberedring

Growth of (14,1)

580 ns

579 ns

581 ns

582 ns

K. S. Novoselov, A. K. Geim, et al., Science, 2004, 306,

666

Scotch tape exfoliation

Bommel, A. V.; Crombeen, J.; Tooren, A. V. Surf. Sci. 1975, 48, 463

A. Charrier, J. Themlin, J. Appl. Phys. 2002, 92, 2479

G. Eda, G. Fanchini, M. Chhowalla, Nat. Nanotechnol. 2008, 3, 270–274. S. Stankovich, R. Ruoff, Carbon 2007, 45 (7), 1558

Epitaxial graphene on SiC

Reduction of grapheneoxide

C. Berger, W. A. de Heer, et al, J. Phys. Chem. B, 2004, 108,

19912

1000 ˚C in H2 to remove oxide layer

Desorption of Si in high vacuum at > 1250 ˚C

Dissolve powdered graphite in solution

Reduce exfoliated GO by hydrazine hydrate

Graphene synthesis methods

6

Growth of Graphene from Ethanol

5 mm

P. Zhao, S. Kim, X. Chen, E. Einarsson, M. Wang, S. Chiashi, R. Xiang, S. Maruyama, ACS Nano 8(2014)11631. X. Chen et al, (2014)

P Zhao et al, J. Phys. Chem. C 117(2013)10755.

(0,0)Ch = (10,0)

Wrapping (10,0) SWNT (zigzag)

a1a2

x

y

(0,0)Ch = (10,0)

Wrapping (10,0) SWNT (zigzag)

a1a2

x

y

(0,0)

Ch = (10,10)

Wrapping (10,10) SWNT (armchair)

a1a2

x

y

(0,0)

Ch = (10,10)

Wrapping (10,10) SWNT (armchair)

a1a2

x

y

(0,0)

Ch = (10,5)

Wrapping (10,5) SWNT (chiral)

a1a2

x

y

7

(0,0)

Ch = (10,5)

Wrapping (10,5) SWNT (chiral)

a1a2

x

y

Chirality and Radius of SWNT

(10,10)Armchair

(10,0) Zigzag

(10,5) Chiral

a1

a2

(10,10)(8,8)

(5,5)

Hexagonal Lattice (Definition of Vectors)

Chiral vector

21 aaC mnh a1

a2

O

(4,-5)

Ch

T

x

y

(6,3)

)2

3,

2

3(

)2

3,

2

3(

2

1

cccc

cccc

aa

aa

a

a

aacc 321 aa

a

a

)2

1,

2

3(

)2

1,

2

3(

2

1

a

a

Hexagonal Lattice (n,m) nanotubes

a1

a2

x

y

(0,0) (1,0) (2,0) (3,0)

(1,1) (2,1)

Zigzag

Armchair

(2,2)

(4,0) (5,0) (6,0)

(3,1) (4,1) (5,1)

(3,2) (4,2) (5,2)

(7,0) (8,0) (9,0)

(6,1) (7,1) (8,1)

(6,2) (7,2) (8,2)

(10,0) (11,0)

(9,1) (10,1)

(9,2) (10,2)

(3,3) (4,3) (5,3) (6,3) (7,3) (8,3) (9,3)

(4,4) (5,4) (6,4) (7,4) (8,4) (9,4)

(5,5) (6,5) (7,5) (8,5)

(6,6) (7,6) (8,6)

(7,7)

n - m = 3q (q: integer): metallicn - m 3q (q: integer): semiconductor

(n,m) Symmetry

Diameter of Tube 223mnmn

aCd cch

t

Chiral vector 21 aaC mnh

Chiral angle )2/(3tan 1 nmm

Lattice Vector Rdmnnm /)2()2( 21 aaT

Rh dCT /3

dofmultipleaismnifd

dofmultipleanotismnifddR 33

3

d: highest common divisor of (n,m)

Rd

nmnmN

)(2 22 Number of hexagons per unit cell:

cct an

d 3

Armchair

Electric Density of States of Graphene

幾何学構造と同様に，SWNTの電子構造はグラフェンの電子構造を基礎として理解できる．そこで，最初にグラフェンの電子構造について復習する．

炭素のπ電子の挙動が問題となる．電子の波動関数を波数(kx, ky)の平面波

で展開し，６角形のブリリアンゾーンにおける分散関係を求める．グラフェンは，ゼロバンドギャップ半導体であり，K点とM点でのみ，π電子とπ＊電子の分散関係が接する．

Reference P. R. Wallace, Phys. Rev, 71 622 (1947).

8

Reciprocal Lattice Vector逆格子ベクトル

2,2

/2,/2

2211

2211

baba

abab

aa

aa

3

4)

2

3,

2

1(

2)1,

3

1(

3

4)

2

3,

2

1(

2)1,

3

1(

2

1

b

b

aaPer

aaPer

ccy

ccx

3

33

a

a

)2

1,

2

3(

)2

1,

2

3(

2

1

a

a aacc 321 aa

Brillouin Zone

aaa 3

2)0,1(

3

2

3

2

2

2

1

1 k

b

bk

b

bk

y

a2

a1

x

kx

ky

M

K

b2

b1

475.1

3

22

3

1

ccaa

703.1

33

4

3

42

3

2

ccaaa

554.22

a

212

1bb

Reciprocal Lattice Vector

Brillouin Zone逆格子ベクトル

Brillouin Zone

y

a2

a1

x

kx

ky

M

K

b2

b1

475.1

3

22

3

1

ccaa

703.1

33

4

3

42

3

2

ccaaa

554.22

a

212

1bb

Reciprocal Lattice Vector

波長kx, kyで表現した位相空間を逆格子空間という．電子の平面波の高波数の上限は（π／格子定数）で表せる．このような上限波数範囲を逆格子空間で表したものをブリリアンゾーンとよぶ．６角格子の場合には，ブリリアンゾーンも６角形となる．方向が９０度ずれていることに注意！

Plane Wave Representation and Tight-Binding Wave Function

EHSchrödinger Equation

kriePlane Wave

rkk r )()( Gi

GGeC

G: reciprocal vector

Plane Wave Representation

Fourier Transform of wave function

),()( rkrk ii

iC Tight-binding wave function

R

kR Rrrk )(1

),( i

u

i eN Bloch orbital

Tight-Binding Method

EHInstead of Solving Schrödinger Equation

Find best which minimize

HE

With Tight-binding wave function

Functional Method

jiijji

jiijji

SCC

HCCH

E

,

*

,

*

jiij HH jiijS

Hamiltonian Matrix Overlap Integral

Here,

Tight-Binding Method 2

j

jj

ijjij CSECH )(k

0)(

*

iC

E k

0

,

*

,

*

ij

jj

jiijji

ijji

ji

ijj

j SC

SCC

HCC

HC

0)(

2

,

*

,

*

,

**

jiijji

ijj

jijji

ji

jiijji

ijj

j

i

SCC

SCHCC

SCC

HC

C

E k

2-D Electronic Energy Dispersions of Graphene

)(1

)()( 02

2 k

kk

sw

wE p

Dg

2cos4

2cos

2

3cos41)()( 22 akakak

fw yyx kk

1*)(

)(1

*)(

)(

20

02

ksf

ksfS

kf

kfH

p

p

H: (2x2) Hamiltonian

S: (2x2) Overlap integral matrix2p: Site Energy of 2p atomic orbital

2cos2)( 32/3/ ak

eekf yakak xx

0)det( ESHSecular equation (永年方程式)

where CCaa 3

where

9

2-D Energy dispersion relation for graphene

From: R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Trigonal warping effect of carbon nanotubes, Physical Review B, vol. 61, no. 4, 2981 (2000).[Color picture was from Professor R. Saito]

)(1

)()( 02

2 k

kk

sw

wE p

Dg

2cos4

2cos

2

3cos41)( 2

akakakw yyx k

Overlap integral: s=0.129C-C interaction energy: 0=2.9eV

2p = 0

Energy dispersion relation for and * bands

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

kx

ky

0.000

15.000

M

K

K’

M

M

K

MK’

M

M

K’

K

)(1

)()( 02

2 k

kk

sw

wE p

Dg

2cos4

2cos

2

3cos41)( 2 akakak

w yyx ks=0.129Gamma=2.9eV

CCaa 3

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

kx

ky

-10.000

0.000

2-D Energy dispersion relation for graphene

y

a2

a1

x

kx

ky

M

K

b2

b1

Reciprocal Lattice VectorFrom: R. Saito et al., Physical Review B (2000).

M

K

K’

MK’

Brillouin Zone

* (conduction)

(valence)

–10

–5

0

5

10

15

E (

eV

)

K M K

*

s = 0.129

s = 0 (symmetric)

Electric DOS of Nanotube

グラフェンを巻いたSWNTの場合には，円周方向に周

期境界条件を満たす電子の波動関数しか許されなくなる．このため，グラフェンの場合の６角形のブリリアンゾーン（平面）は，有限数の線となってしまう．この線が，K点かM点を通過すると金属，そうでないと半導体となる．

Reference最初の理論予測：R. Saito et al., Phys. Rev. B46, 1804 (1992).

詳細かつわかりやすい論文：R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Trigonal warping effect of carbon nanotubes, Physical Review B, vol. 61, no. 4, 2981 (2000).

M

K

K’

MK’

M

K

K’

MK’

Electric DOS of Carbon Nanotube

M

K

K’

MK’

0–4

–2

0

2

4

wave vector

en

erg

y(e

V)

0 1 2–4

–2

0

2

4

en

erg

y(e

V)

0–4

–2

0

2

4

wave vector

en

erg

y(e

V)

0 1 2–4

–2

0

2

4

en

erg

y(e

V)

1D Dispersion

Lattice Vector Rdmnnm /)2()2( 21 aaT

RNdmnnm /)2()2( 211 bbK

Nnm /)( 212 bbK

Discrete unit vector along the circumferential direction

Reciprocal lattice vector along the nanotube axis

1

2

22)( K

K

K kEkE Dg

Tk

T

N

,...,2,1

Rh dCT /322 mnmnaCh

h

R

C

mmnna

mmnnmmnna

Ndmmnna

2

12

)(2/22

/22

22

2222

221

K

Rd

nmnmN

)(2 22

Td

C

mmnn

d

a

mmnnmmnnda

Nmmnna

Rh

R

R

2

3

12

3

12

)(2/3

22

/3

22

22

2222

222

K

10

Summary

12

2 KK

Kk

Tk

T

N

,...,2,1

1

2

22)( K

K

K kEkE Dg

where

Slice

-2 -1 0 1 2-2

-1

0

1

2

kx

ky

0.000

3.000

-2 -1 0 1 2-2

-1

0

1

2

kx

ky

0.000

3.000

(10,0)K1=(0.221239,0.127732)K2=(-0.737463,1.277323)

-2 -1 0 1 2-2

-1

0

1

2

kx

ky

0.000

3.000

(10,10)K1=(0.147493,0.000000)K2=(0.000000,2.554647)

-2 -1 0 1 2-2

-1

0

1

2

kx

ky

0.000

3.000

(10,5)K1=(0.189633,0.036495)K2=(-0.105352,0.547424)

van Hove Singularity

ブリリアントゾーンを積分するといわゆる状態密度（Density of States, DOS)が求まることになる．

金属か半導体かという点以外にも，周期境界条件によって，ブリリアンゾーンが線となるために，一次元物質に特有のvan Hove特異点と呼ばれる発散するDOSとなる．

ReferenceDresselhaus, M. S. & Dresselhaus, G., Science of Fullerenes and Carbon Nanotubes, Academic Press (1996).Saito, R., ほか2名, Physical Properties of Carbon Nanotubes, Imperial College Press (1998).

点線はグラフェンのDOS

Comparison of DOS for Armchairs

Comparison of DOS for Zig-zagSchematic of Electronic Structure of SWNT

Valence band

Conduction band

Hexagonal Brillouin zone of graphite

(M)(M)

–1

0

1

Ene

rgy

(eV

)

11h

v1 v2

c1 c2

h

e

22h

–1

0

1

Ene

rgy

(eV

)

–1

0

1

Ene

rgy

(eV

)

11h 11h

v1 v2

c1 c2

h

e

22h 22h

The energy dispersion relations for 2D graphite

KK’

R. Saito et al.,

“Physical Properties of Carbon Nanotubes” Imperial College Press (1998)

Real space k space

n-m=3q : Cutting line goes K pointMetallic SWNT

11

Optical transition of SWNTs

M. J. O’Connell et al., Science 297 (2002) 593

S. M. Bachilo et al., Science 298 (2002) 2361

C. Fantini, et al., Phys. Rev. Lett., 93, 147406 (2004).

H. Kataura et al., Synth. Met. 103 (1999) 2555

Wang et al. Science 308, 838 (2005)

Optical absorption

Raman 2-photon absorption

Photoluminescence

Excitonic effect

Isolation of SWNTs

Photoluminescence (PL) excitation spectroscopy

(8,6) SWNT

E22

E11

E22E11

(8,6)

*** No fluorescence in metallic nanotube

Ground state

E22

E11