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科研費新学術領域研究「コンピュティクスによる物質デザイン：複合相関と非平衡ダイナミクス」
計画研究「密度汎関数理論に基づく非平衡ナノスケール電気伝導ダイナミクス」代表 渡邉聡（東大工）2012.3.16-17@東大工学部

時間依存密度汎関数法によるグラフェンリボンからのレーザー刺激電界電子放射シミュレーション
Time-Dependent Density Functional Theory Calculationsof Laser-Assisted Electron Field Emission
from Graphene Nanoribbons

D. Utsugi, J. Haruyama, C. Hu, K. Watanabe
Department of Physics
Tokyo University of Science

14OUTLINE
1. Background: FE & LAFE
2. Objectives : Mechanism
3. Method: TDDFT
4. Models: GNR
5. Results: Excitation & tunneling are correlated.
6. Summary: Controlled emission path.

131. BACKGROUND
Field Emission from Carbon Nanostructures

Review: Carbon Nanotubes and Related Field Emitters, ed. Y. Saito FE from metals

 FE fromgraphene nanoribbon (GNR)

EFEF

TheoryK.Tada,KW:PRL88,127601(2000),
M.Araidai,Y.Nakamura,KW:
PRB70,245410(2004).

 FE from reducedgraphene oxide edges

Experiment
H.Yamaguchi et al.,ACSNano 5,4945(2011)

12

Laser-Assited FE from Tungsten Tip
 Experimental setup

Yanagisawa et al.,PRL103, 257603(2009),
ibid. 107, 087601(2011)

 Laser-assisted photo-field emission

 MechanismsP. Hommelhoff et al.,PRL96, 077401(2006),
ibid. 97, 247402(2011)

1.Photo-field emission

2. Optical field emission

3. Photoemission(Over-barrier emission)

11

Former Theories for LAFE
Modified Fowler-Nordheim equation
 B 
, F (t )  Fdc  Flaser (t )J (t )  AF (t ) 2 exp  F(t)

P. Hommelhoff et al.,PRL96, 077401(2006),
ibid. 97, 247402(2011)

2. optical field emission

Boltzmann equation

L. Wu and L.K. Ang, PRB78, 224112(2008)
B. Rethfeld, et al., PRB65, 214303(2002)
H. Yanagisawa et al., PRL107, 087601(2011)

f (k ) f (k )f (k )f (k ),tt eet e pht elaser
J (t )emission em
D(W ) f ( E, t )dEdW , D(W )  Tunneling probability
2 3 W2 with WKB.

1.photo-field emission

10Needs for Ab-initio Dynamics Simulation

Because, semi-classical theories assumeFree electrons in a jellium, instead of atomic structures.
One-dimensional system (2D perfectly flat surface ).
Electron tunneling is not fully quantum (WKB).
Electronic excitation is “adiabatic”.

So,Time-dependent density functional theory (TDDFT)
Fully quantum electron dynamics excitedin real materials.

92. OBJECTIVES Explore excited electron dynamics
under fs laser and dc field by ab-initio
calculations.
 Reveal emission mechanism dependingon laser and materials parameters, andpredict & control the emission path.

83. THEORYTDDFT studies on FE & LAFE

FE fron CNT: S.Han & J.Ihm, PRB66,241402(R)(2002).
FE from GNR: K.Tada & KW, PRL88, 127601(2000).
FE from Diamond: M.Araidai, KW, JJAP42,L666(2003).
LAFE from CNT: J.A.Driscoll et al., PRB83,233405(2011).

What is TDDFT ?
E. Runge, E.K.U Gross, PRL52,997 (1984)

Electrons:i  i (r , t )  H KS (r , t ) i (r , t )
t





v(r,t)
eE(t)
r
H KS (r , t )  H 0 (r , t )  vlaser (r , t ), laser i (r , t  t )  exp  it /   H KS (r , t ) i (r , t )7Field Emission from (5,5)CNT@H2
1000 steps = 1.2fs

96Field Emission “Microscopy” of (5,5)CNT
1.2fs

K. Nishida et al., APEX 4, 115102(2011)

10

5

4. EMITTER & LASERGraphene nanoribbon (GNR)

FS laser pulse
Edc  0 ~ 0.2 V/A, Elaser  0 ~ 0.1 V/A,
I laser  11011 W/cm2

  1 ~ 7 eV

Clasere-dc

Electric field[V/Å]

H

0.0
−0.0
−0.1
−0.1
−0.204812 16Time[fs]20245. RESULTS:Emission current

H-terminated GNR

Edc= - 0.1 V/AElaser= 0.1 V/AEmission starts undera laser of energy
corresponding todipole transition.

Energy band

42E-E F [eV]4~6eV0−2−4−6ΓX3

Which electronic levels cause emission ?

Γ point

σ state
15→20

17→18
Top view

Side view

π stateTransition is large for 17->18,
but, emission is large from 20,
because of the orbital symmetry.

J   D( )E ( )T ( )d2

Excitationin the band6

3. over-barrier emission

214

16 →21=5.46 eV

418 π*

2

1.photo-field emission
15 →18=6.29 eV

217016 DB−2π1516 →17=0.35 eV

0Edc=0.075 V/A−2
10−4−6Emission
through the potentialΓ

ky20

30
40Position[Å]50Dangling-bond assisted
X over-barrier emission dominatesphoto-field emission.

16. SUMMARY
Laser-Assisted FE

 is highly non-stationary; J   D( )E ( )T ( )d , reflects the electronic structures of the tip, changes critically depending on
laser parameters, static field & work function.
Emission PathPFEOBEOFE can be selected by tuning laser parameters.