ᣂቇⴚ㗔ၞ⎇ⓥ䇸䉮䊮䊏䊠䊷䊁䉞䉪䉴䈮䉋䉎‛⾰䊂䉱䉟䊮䋺ⶄว⋧㑐䈫㕖ᐔⴧ䉻䉟䊅䊚䉪䉴䇹ᐔᚑ22ᐕᐲ⎇ⓥળ䇮2011ᐕ3᦬4ᣣ䇮᧲੩ᄢቇᧄㇹ䉨䊞䊮䊌䉴⎇ⓥ㗄⋡A02ኒᐲ᳢㑐ᢙᴺℂ⺰䈮ၮ䈨䈒㕖ᐔⴧ䊅䊉䉴䉬䊷䊦㔚᳇વዉ䉻䉟䊅䊚䉪䉴᳇䉻⸘↹⎇ⓥઍ⴫⠪᧲ᄢᎿ ᷰㆺ⡡䊜䊮䊋䊷• ઍ⴫䋺ᷰㆺ⡡䋨᧲ᄢ䊶Ꮏ䋩ઍ⴫ ᷰㆺ⡡䋨᧲ᄢ Ꮏ䋩Ͳㅪ៤䋺ᄙ↰᦮ผ䋨ᯏ᪾♽GCOE․છ⻠Ꮷ䋩䇮ጊᧄ⾆ඳ• ಽᜂ䋺ᷰㄝ৻ਯ䋨᧲ℂᄢ䊶ℂ䋩ಽᜂ䋺ᷰㄝ ਯ䋨᧲ℂᄢ ℂ䋩Ͳㅪ៤䋺ዊ㍿ື䋨╳ᵄᄢ䊶ᢙℂ䋩䋨ї⢫ᤐᐔ䋩• ಽᜂ䋺⋧㚍⡡ᢥ䋨␹ᚭᄢ䊶Ꮏ䋩ಽᜂ ⋧㚍⡡ᢥ䋨␹ᚭᄢ Ꮏ䋩

⑳䈱⻠Ṷ

• ಽᜂ
ಽᜂ䋺ዊ㊁୶਽䋨㒋ᄢ䊶Ꮏ䋩
㊁୶ 䋨㒋ᄢ䋩䂾ㅪ៤䋺㈬੗᣿䋨੩ᄢ䊶Ꮏ䋩Јታ㛎ኅ䈎䉌䈱␜ໂ䉺䊷䉭䉾䊃䋺䊅䊉䉴䉬䊷䊦㔚᳇વዉ
Novel nanostructures(such as atomic chain)

Si device(further downsizing)

Nanoscale multi-terminal
resistance measurementCarbon nanotube transistor

Atomicswitch䊶㔚᳇વዉ⸘᷹䈱ㅴᱠ䊶ᣂⷙ䊅䊉᭴ㅧ䊶䊂䊋䉟䉴ᣂⷙ䊅䊉᭴ㅧ 䊂 䉟䉴
䊶㊂ሶലᨐ䈱㗼࿷ൻᧄ㗔ၞ䈱ਛ䈪䈱⎇ⓥ䈱䊘䉟䊮䊃• Interplay:l 㔚᳇વዉ䈫ઁ䈱᭽䇱䈭ⷐ⚛䈫䈱⛊䉂ว䈇㔚᳇વዉ䈫ઁ ᭽ 䈭ⷐ⚛䈫 ⛊ วͲ䊐䉤䊉䊮䊶ᾲ䇮䉟䉥䊮વዉ䇮䉴䊏䊮䇮㔚ሶബ⿠• Dynamics: ቯᏱї㕖ቯᏱͲㆊᷰᔕ╵䇮੤ᵹᔕ╵ㆊᷰᔕ╵ ੤ᵹᔕ╵• ᄖ႐䈻䈱ᔕ╵Ͳ䉭䊷䊃㔚࿶䇮శᾖ኿• Realisticmodeling:䉋䉍ᄙᢙ䈱ේሶͲ⸘▚䈱㜞ㅦൻ⸘▚䈱㜞ㅦൻᧄᣣ䈱⊒⴫ౝኈ䋨ᷰㆺಽ䋩䋱䋮䉦䊷䊗䊮䊅䊉䉼䊠䊷䊑䈱੤ᵹᔕ╵․ᕈ䋲䋮㌃/㉄ൻ䉺䊮䉺䊦ធว♽䈱વዉ․ᕈ䈫ශട㔚࿶䈻䈱ᔕ╵ 䈍䉋䈶㑐ㅪ䈚䈢ᣂⷙᣇᴺ⺰㐿⊒ᔕ╵䇮䈍䉋䈶㑐ㅪ䈚䈢ᣂⷙᣇᴺ⺰㐿⊒
䋨㊄ዻ/⛘✼૕/㊄ዻ♽䇮2䈧䈱䊐䉢䊦䊚Ḱ૏䋩䋳 4┵ሶ㔚᳇ᛶ᛫⸘▚䋳䋮4┵ሶ㔚᳇ᛶ᛫⸘▚䋴 䉦䊷䊗䊮䊅䊉䉼䊠䊷䊑䉴䊏䊮ਃ㊀㗄ബ⿠ሶ䈱⊒శᯏ᭴䋴䋮䉦䊷䊗䊮䊅䊉䉼䊠䊷䊑䉴䊏䊮ਃ㊀㗄ബ⿠ሶ䈱⊒శᯏ᭴
ℂ⑼ᄢ

䋵 䉫䊤䊐䉢䊮䊅䊉䊥䊗䊮䈎䉌䈱䊧䊷䉱䊷ೝỗ㔚⇇㔚ሶ᡼኿䋵䋮䉫䊤䊐䉢䊮䊅䊉䊥䊗䊮䈎䉌䈱䊧䊷䉱䊷ೝỗ㔚⇇㔚ሶ᡼኿䋶 䉫䊤䊐䉢䊮䊅䊉䊥䊗䊮䈱㔚᳇વዉ․ᕈ
䋶䋮䉫䊤䊐䉢䊮䊅䊉䊥䊗䊮䈱㔚᳇વዉ․ᕈ

␹ᚭᄢ੤ᵹᔕ╵䋺Motivation ᷰㆺ䇮ጊᧄ䇮ઁ䋨᧲ᄢᎿ䋩
In devices, switching is often important
Teraheltz technology is in progress ĺ time scale of electron dynamics
Gate-length dependence ofFET cutoff frequency

Exp.: THz electron dynamics

THz technology
Carbon Nanotubes

Zhong et al., Nature Nanotech. 3,201 (2008)(2008).
Burke, Solid-State Electronics 48, 1981
(2004)

SimulationMethod䋨䋱䋩
Hamiltonian:+ Nearest
Nearest-neighborneighbor ʌʌ-orbital
orbital tight-bindingtight binding model² No Coulomb interaction & electron-phonon interaction

AC response:+ Nonequilibrium Green’s function (NEGF) method² Wide-band limit approximation(= constant density of states for electrodes)

CONTACTEFFECTSONACTRANSPORT䋨Yamamotoetal.,PRB82,205404(2010).䋩ȖȖ

Contacteffectonsusceptancep%!: Inductive Susceptance%: Capacitive SusceptanceSusceptanceSusceptance(9 0) zigzag
(9,0)
iSWNT

(5 5) armchair(5,5)
h i SWNT

1.5

1.00.5
L=3m-2L3 2
L=3m-1
L=3m0
L=any positive integer-0.501.0Ȗ

2.0

3.0 01.0Ȗ

2.0

3.0䉮䊮䉻䉪䉺䊮䉴䉰䉶䊒䉺䊮䉴

g=2.0㬍G0
g=2.0㬍G0
g=1.0㬍G0
g=1 0㬍G0
g=1.0㬍G
g=0.25㬍G0
g=0.25㬍G0䋨Yamamotoetal.,PRB82,205404(2010).䋩

v s ConductanceSusceptance v.s.
(5,5) armchair SWNT(9,0) zigzag SWNT
0.3

Inductive

Capacitive

Inductive

Capacitive

02
0.2
0.1
001
-0.1

L=3m-2
L=3m-1
L=3m-0.2
-0.3
0.7

0.8

0.9

1.0

1.1

G [e2/h]

1.2

1.3

0.7

0.8

0.9

1.0

1.1

1.2

G [e2/h]TheinductiveͲcapacitivesusceptancetransitionoccursatG=e2/h.

1.3

SimulationMethod䋨䋲䋩ᐔ੗䋨D1䋩

Results
Metallic CNT without defects

conductance vsvs. frequency

susceptance vs.
vs frequencyᰳ㒱䉕฽䉃㊄ዻCNT䈱੤ᵹᔕ╵ૐ๟ᵄᢙ㗔ၞ䈪䈱䉝䊄䊚䉾䉺䊮䉴䋺ේሶⓨሹᰳ㒱䉕฽䉃႐ว

StoneͲWalesᰳ㒱䉕฽䉃႐วਛᔃ㗔ၞ䈱㐳䈘:ਛᔃ㗔ၞ䈱㐳䈘
2.214nm(9unitcells)ਛᔃ㗔ၞ䈱㐳䈘:ਛᔃ㗔ၞ䈱㐳䈘
2.214nm(9unitcells)᭴ㅧᦨㆡൻ䈭䈚

᭴ㅧᦨㆡൻ䈅䉍
10:ᰳ㒱䈅䉍
:ᰳ㒱䈭䈚

:ᰳ㒱䈅䉍
:ᰳ㒱䈭䈚

40

240

0

2

20

020

1
í0.5

0

0

0.5

0.1

í101
í0.5

00.5

0
í0.5

00.5

í0.5

00.5

Electrochemical resistive switch (atomic switch)
Cu/Ta2O5/Pt

T. Sakamoto et al
Tal., Appl
Appl. Phys.
Phys
Lett. 91, 092110 (2007)

Energy dispersive x-ray spectrometry

Cu/Ta2O5/Pt: Electronic Transport ofT 2O5 withTa
ith interstitial C
Cu or O defect1) P
Pure T
Ta2O52) O vacancies
3) Cu dopants

Cu1

Cu2

VCu

Cu3

VPt

2.5

Ta4O10

T 4O10Ta8TranssmissionTransmmissiont (PA) (PA)CurrenCurreent)

Cu4V10

Ta4O9
Ta4O10Cu(+)

64200.0(b ATK)
(by2.0

Ta4O9
Ta4O10Cu

1.5

1.00.50.0

0.1

0.20.30.40.5

0.6-2Voltage (V)(V)
Voltage-101E-E (eV)EEF (eV)F

Cu dopants- Apparently enhance the transport of Ta2O5 Gu et al., ANS NanoO vacancies - Hardly affects the transport of Ta2O5

4, 6477 (2010).

2Cu/Ta2O5 examined by ESM (& SIESTA)
Charge induced by
the applied electricfieldCu

Ta2O5x
Potential change dueto the applied fieldCu

Ta2O5Cu

Ta2O5

Small field near
the interface

VacuumVacuumComparison on the electric field
bet een ttwo
betweeno models

Electrric㔚႐(ev/Հfield Հ)((eV/Έ)Model A

Model B

0.045
0.040.035
0.03
0.025
0.02
0.015
0.01
0.005
0Ͳ0.005

0.045
0.040.035
0.03
0.025
0.02
0.015
0.01
0.005
0
Ͳ0.005

0.3

4.3

8.2

12.2

16.1

20.1

Cu⇇㕙䈮ᦨ䉅ㄭ䈇 Oේሶ䈎䉌䈱〒㔌(Έ)න૏⢩ 4䈧
ModelBන૏⢩ 3䈧
ModelAන૏⢩ 4䈧
න૏⢩ 3䈧

0.3

4.3

8.2

12.2

16.1

20.1

න૏⢩4䈧䈱䊝䊂䊦䉕ၮḰ䈮䈚䈢ᤨ䈱Cu⇇㕙䈎䉌䈱〒㔌(Έ)

Origin of the small field near the interface:
Interface states? Surface screening?
g Ј Interface ((mid-gap)g p) statesЈ Applied bias does not induce motions of Cu at the interface!!
Cu oxide formation at the interface may be essentialᣂ䈚䈇ᣇᴺ⺰䋺orbitalpartitionmethod═᧻䋨D1䋩䇮Prof.S.W.Han(SeoulNat’lU)• ConsideranMIMcapacitor
C id
MIMitinvacuum• NeartheFermilevel,theNear the Fermi level theorbitalsoftheleftandright
electrodesarecompletely
ddecoupledl d• Partitiontheorbitalsinto
left and right electrodes andleftandrightelectrodesand
occupythemdifferently• Applydipolecorrectionin
pp y pvacuumtosimulatean
isolatedslabinvacuum%$/
EFEF

8$/

Orbital partition approach
OrbitalpartitionapproachObtainasetoforbital
eigenvalues andfill
and fill
orbitalsfrombelowto
obtain the Fermi levelobtaintheFermilevel

'(7Orbital partition approach
Orbitalpartitionapproach
Takeorbitalswithinakb lh
presetwindow
aroundtheFermi
level'(

7Orbital partition approach
Orbitalpartitionapproach

Separatethemintogleftandright
electrodes'(7Orbital partition approach
OrbitalpartitionapproachSetdifferentfermi
levelsintheleftand
rightelectrodes'(.
'(47Orbital partition approach
OrbitalpartitionapproachCalculatechargedensity,'(.
'(4calculateVKSfromȡ,and continue SCF loop…
andcontinueSCFloop…

7

Electrostatic potential (Au/MgO/Au)
Electrostaticpotential(Au/MgO/Au)

Energy & capacitance vs voltage
Energy&capacitancevs.voltage

DielectricrelaxationÆDielectricrelaxation Æ furtherchargingofcapacitor
further charging of capacitor
Æ increaseinenergy4┵ሶᛶ᛫⸘▚䋺⢛᥊zኹỈ䋨D3䋩䇮㘧᧻䋨M2䋩ૐ᷷䈮䈍䈔䉎නጀ䉦 䊗䊮䊅䊉䉼ૐ᷷䈮䈍䈔䉎නጀ䉦䊷䊗䊮䊅䊉䉼䊠䊷䊑䈱4┵ሶᛶ᛫᷹ቯ
䊑䈱4┵ሶᛶ᛫᷹ቯ
[B. Gao et al., Phys. Rev. Lett. 95, 196802]
zz䉭䊷䊃㔚࿶䈮ᔕ䈛䈩4┵ሶᛶ᛫䈏ᄢ䈐䈒ᝄേ⽶䈱4┵ሶᛶ᛫䈱᷹ⷰ䋣

㊂ሶᐓᷤലᨐ䈏ᓇ㗀䋿ᄙ┵ሶ㔚᳇વዉ䉲䊚䊠䊧䊷䉺z⥄Ꮖή᠓⌕㔚⩄ኒᐲ᳢㑐ᢙᒝ᧤❈(SCC-DFTB)ᴺ[PRB 58, 7260 (1998), Phys. Stat. Sol. (b) 217, 41 (2000).]zz㕖ᐔⴧ䉫䊥䊷䊮㑐ᢙ(NEGF)ᴺ㕖ᐔⴧ䉫䊥䊮㑐ᢙ(NEGF)ᴺzz

ේሶਛᔃ䈱䊘䊁䊮䉲䊞䊦䉕ၮ␆䈮䈚䈢㔚ሶ䈱䊊䊚䊦䊃䊆䉝䊮䈱ේሶਛᔃ䈱䊘䊁䊮䉲䊦䉕ၮ␆䈮䈚䈢㔚ሶ䈱 䊚䊦䊃 䉝䊮䈱⥄Ꮖή᠓⌕䈭᳿ቯᴺ
㔚ᭂ䈮䉋䉍ᄖㇱ䈫ធ⸅䈚䈢♽䈱ኒᐲⴕ೉⸘▚䊝䊷䊄䊙䉾䉼䊮䉫ᴺ
䉾䉼䊮䉫ᴺ [[PRB,, 44,, 8017 ((1991).) PRB,, 72,, 035450 (2005).]()]z⥄Ꮖ䉣䊈䊦䉩䊷䈮䉋䉎㔚ᭂ䈱ᓇ㗀䈱ዉ౉ኒᐲⴕ೉䉫䊥䊷䊮㑐ᢙPේሶ䈱Mulliken㔚⩄㊀䈭䉍Ⓧಽ䊊䊚䊦䊃䊆䉝䊮PP⥄Ꮖ䉣䊈䊦䉩䊷ㅘㆊ㑐ᢙ᦭㒢䊋䉟䉝䉴䈱႐วㅘㆊ㑐ᢙ䈏䊋䉟䉝䉴㔚࿶䈮䉋䈦䈩ᄌൻ䈚䈭䈇䈖䈫䉕઒ቯ䈚䇮ൻቇ䊘䊁䊮䉲䊞䊦㑆䈱㑐ଥ䉕ㅘㆊ㑐ᢙ䈎䉌ዉ䈒z ൻቇ䊘䊁䊮䉲䊞䊦䈱ᓸዊᄌൻ dPp 䈫ㅘㆊ㑐ᢙ䈱㑐ଥzᄌᢙP eV䉕ቯ⟵䈚䇮䉕ቯ⟵䈚 P 䉕↪䈇䈩ฦ䊒䊨䊷䊑䉕↪
ฦ䊒䊑䈱ൻቇ䊘䊁䊮䉲䊞䊦ᄌൻ 'Pp 䈏ฝ䈱䉋䈉䈮ਈ䈋䉌䉏䉎䈫䈐䈮䇮㔚࿶䊒䊨䊷䊑䈮䈍䈔䉎㔚ᵹ䈏䉷䊨䈮䈭 䈩䈇䉎႐ว䉕⠨䈋䉎䈮䈭䈦䈩䈇䉎႐ว䉕⠨䈋䉎䇯ᓸዊᄌൻ dPp 䈮ኻ䈚
dI2=dI3=0 䉕⺖䈜䈫…

'P P P'P P P

I2=0

I3=0

I1=I

I4=I'P P = eV
eV14/2'P P = eV14/2

䈢䈣䈚ൻቇ䊘䊁䊮䉲䊞䊦'Pp 䈮ኻ䈜䉎㕖✢ᒻ䈭Ᏹᓸಽᣇ⒟ᑼ䋣ĺᢙ୯Ⓧಽ䈮䉋䈦䈩P eV䈮ኻ䈜䉎 PP 䈱㑐ᢙᒻ䈏ᓧ䉌䉏䉎὇⚛ේሶ㎮䈎䉌䈭䉎4┵ሶ♽䈮ኻ䈜䉎ㆡ↪
ൻቇ䊘䊁䊮䉲䊞䊦'Pp䈱䊋䉟䉝䉴㔚࿶V14ଐሽᕈz(b), (c)䈱႐ว䈮䈲'P'P䈏㕖✢ᒻ䈭ଐሽᕈ䉕␜䈜'Pp [eVV]

zd23ds-pds-p'P40.10'P30.00'P
P1-0.100.00'Pp [eV]'P20.00'P3'P1-0.10
0.00

0.05

0.10

0.20

0.25

V14 [V](b) d23 =2.10 nm, ds-p = 0.22 nm

0.30

0.10

0.15

0.20

0.25

V14 [V]( ) d23 =2.10(a)2 10 nm, ds-p = 0.18
0 18 nm

0.30'P30.00'P2'P1-0.10
0.15

0.05

'P40.10'Pp [eeV]'P40.10'P20.000.05

0.10

0.15

0.20

V14 [V](c) d23 =2.80 nm, ds-p = 0.18 nm

0.250.30

䊋䉟䉝䉴ශടᤨ䈱4┵ሶᛶ᛫᷹ቯ䉲䊚 䊧 䉲 䊮(1)4┵ሶᛶ᛫᷹ቯ䉲䊚䊠䊧䊷䉲䊢䊮(1)z㔚࿶䊒䊨䊷䊑䉕ᵹ䉏䉎㔚ᵹI2,I3 (a)zzz㔚ᵹ䊒䊨䊷䊑䉕ᵹ䉏䉎㔚ᵹI1,I4䈲
V14=0.3 V 䈮䈩0.3~0.5 [a.u]⒟ᐲ
ో䈩䈱႐ว䈪I1,II4䈮Ყ䈼I2,II3䈏䈝䈦䈫ዊ䈘䈇ĺ౏ᑼ䈲ㆡಾ䋣(c)䈮䈍䈇䈩䈲ઁ䈱႐ว䈫Ყ䈼I2,I3
䈏Ყセ⊛ᄢ䈐䈒䈭䈦䈩䈇䉎ĺㅘㆊ㑐ᢙ䈱䊋䉟䉝䉴ଐሽᕈ

(b)

I3
I2(c)
I2

I3

I2I3

䊐䉤䊉䊮㕖ᒢᕈᢔੂ䈱ᓇ㗀㕖ᒢᕈᢔੂ ᓇ㗀ᣇᴺ䋺⥄Ꮖή᠓⌕䊗䊦䊮ㄭૃᴺ䉕↪䈇䉎
T Frederiksen et al.,T.
al Phys.
Phys RevRev. B 75,75 205413 (2007)(2007).

䊝䊂䊦䋺⚿ᨐ䈱⸃ᨆ䉕◲න䈮䈜䉎䈢䉄䈮
9᳓⚛ේሶ㎮䊝䊂䊦䉕ណ↪
9ᮮゲᣇะ䈱ᝄേ䈣䈔䉕ᢔੂ䈮ነਈ䈜䉎䈫䈚䈩ណ↪

42mV䈱ᝄേ䉣䊈䊦䉩
42mV䈱ᝄേ䉣䊈䊦䉩䊷⸘▚⚿ᨐ㔚࿶ශട䈮䉋䉎㔚⩄ಽᏓᄌൻ䈲ήⷞ㔚᳇ᛶ᛫䈏ශട㔚࿶䈮ଐሽ䈜䉎䈱䈪䋬㔚᳇ᛶ᛫䈏ශട㔚࿶䈮ଐሽ䈜䉎䈱䈪ᓸಽᛶ᛫ dV/dI 䉕⸘▚: 2┵ሶᓸಽᛶ᛫䋨㕖ᒢᕈᢔੂ䈅䉍䋩: 2┵ሶᓸಽᛶ᛫䋨㕖ᒢᕈᢔੂ䈭䈚䋩: 4┵ሶᓸಽᛶ᛫䋨㕖ᒢᕈᢔੂ䈅䉍䋩┵ᛶ᛫ᕈᢔ 䈅: 4┵ሶᓸಽᛶ᛫䋨㕖ᒢᕈᢔੂ䈭䈚䋩

2┵ሶᓸಽᛶ᛫䋬4┵ሶᓸಽᛶ᛫䈫䉅䈮䋬
42 mV䈍䉋䈶75 mV䈪ห᭽䈭୯䈱ᕆፋ䈭ᄌൻ䈏⃻䉏䈢mV䈪ห᭽䈭୯䈱ᕆፋ䈭ᄌൻ䈏⃻䉏䈢䇯
¾ 42 mV ĺ ᝄേ䉣䊈䊦䉩䊷䈮ኻᔕ䇯
¾ 75 mV ĺ 2┵ሶવዉ䈪䈲⃻䉏䈭䈇䇯42䈱୚ᢙ䈪䉅䈭䈇䇯¾㔚ᵹ┵ሶ㑆䈱ශട㔚࿶ VA-D 䈏75 mV䈱䈫䈐
mV䈱䈫䈐䋬
¾㔚ᵹ䊶㔚࿶┵ሶ㑆䈱ශട㔚࿶ VA-C 䈍䉋䈶 VB-D 䈏¾ᝄേ䉣䊈䊦䉩 䈱42 mV䈮ኻᔕ䈚䈩䈇䈢䇯¾ᝄേ䉣䊈䊦䉩䊷䈱42V䈮ኻᔕ䈚䈩䈇䈢
¾VA-B 䈍䉋䈶 VC-D 䈏42 mV䈫䈭䉎䈫䈐䈱ශട㔚࿶100mV䈪䈲¾ᓸಽᛶ᛫䈲ᕆፋ䈮ᄌൻ䈚䈭䈎䈦䈢䇯㗔ၞౝㅪ៤䋺A01ᒛవ↢䋨ฬᄢ䋩G䈫䈱⼏⺰
¾Generalized shifted COCG method (ฬᄢ䊶ᒛG)
᭽䇱䈭 E 䈮ኻ䈚䈩 G(0) 䉕㜞ㅦ䈮᳞䉄䉎䈖䈫䈏䈪䈐䉎䇯¾㐿᡼♽䈱㔚ሶ⁁ᘒ䋯ャㅍ⸘▚ᢙ⊖䈎䉌ᢙජ䈱 E 䈮ኻ䈚䈩 G 䉕㜞ㅦ䈮᳞䉄䉎ᔅⷐ䈏䈅䉎䇯䉕㜞ㅦ䈮᳞䉄䉎ᔅⷐ䈏䈅䉎
Ȉ(E) 䈱 E ଐሽᕈ䈱䈢䉄਄⸥ᚻᴺ䉕䈠䈱䉁䉁ㆡ↪䈪䈐䈭䈇䇯Ȉ(E) 䈱 E ଐሽᕈ䉕䈫䉍䈖䉃䉝䉟䊂䉝~1. Ȉ 䉕✢ᒻ䊐䉞䉾䊁䉞䊮䉫䈜䉎䈖䈫䈮䉋䉍ᓧ䈢G(0)䉕

Generalized shifted COCG method 䈎䉌᳞䉄䉎䇯

2 G(0) 䉕Neumannዷ㐿䋨Dysonᣇ⒟ᑼ䋩䈎䉌᳞䉄䉎䇯
2.
䉕Neumannዷ㐿䋨Dysonᣇ⒟ᑼ䋩䈎䉌᳞䉄䉎m: Iteration䉴䊏䊮ਃ㊀㗄ബ⿠ሶ⊒శ䈫䊧䊷䉱䊷ೝỗ㔚⇇㔚ሶ᡼኿᧲ℂᄢℂ ᷰㄝ৻ਯ䋱䋮䉦䊷䊗䊮䊅䊉䉼䊠䊷䊑䉴䊏䊮ਃ㊀㗄ബ⿠ሶ䈱⊒శ䊜䉦䊆䉵䊛䉦䊷䊗䊮䊅䊉䉼䊠䊷䊑(CNT)䈱శᔕ╵䈱․ᓽ

᳓⚛ේሶๆ⌕

9 ബ⿠ሶലᨐ䈏ᡰ㈩⊛䋺ᄙ૕⋧੕૞↪䈱㊀ⷐᕈ
9 ᥧബ⿠ሶ(శቇ⑌೙)䈱ሽ࿷䋺⊒శ㊂ሶല₸䈱ૐਅ䉴䊏䊮ਃ㊀㗄ᥧബ⿠ሶ䈮䉋䉎⊒శ䊜䉦䊆䉵䊛䈲ᧂ⸃᣿䋮⊒శ䉦䈲ᧂ⸃᣿䈭䈟䈭䉌䋬὇⚛䈱䉋䈉䈭䉴䊏䊮゠㆏⋧੕૞↪䈏ᒙ䈇‛⾰䈪䈲䋬䉴䊏䊮ਃ㊀㗄ബ⿠ሶ䈮䉋䉎⊒శ䈲⿠䈖䉍䈋䈭䈇(ബ⿠ሶ䈱䉴䊏䊮෻ォ䈲⿠䈖䉌䈭䈇)⿠䈖䉍䈋䈭䈇(ബ⿠ሶ䈱䉴䊏䊮෻ォ䈲⿠䈖䉌䈭䈇)䋮

䈪䈲䋬ബ⿠ሶ䉴䊏䊮⁁ᘒ䉕ᄌ䈋䉎䊜䉦䊆䉵䊛䈲૗䈎???

Nagatsuetal:PRL105,157403(2010).

ๆ⌕᳓⚛ේሶ䈫᦭ല䉴䊏䊮⋧੕૞↪
ታ㛎੐ታ ᳓⚛ේሶ᥸㔺ਅ䈮䈍䈇䈩ਃ㊀㗄ബ⿠ሶ䈮䉋䉎⊒శታ㛎੐ታ䋺᳓⚛ේሶ᥸㔺ਅ䈮䈍䈇䈩ਃ㊀㗄ബ⿠ሶ䈮䉋䉎⊒శ᳓⚛ේሶๆ⌕ലᨐ゠㆏䈏ዪᚲ⊛䈮 䈎䉌゠㆏䈏ዪᚲ⊛䈮sp2䈎䉌sp3䈻䉴䊏䊮゠㆏⋧੕૞↪䈫゠㆏ᷙᚑ䈮䉋䉎᦭ല䊊䊚䊦䊃䊆䉝䊮᦭ല䉴䊏䊮゠㆏⋧੕૞↪
A䋺sp3䈻䈱ᷙᚑౕวA䋺sp3䈱ᷙᚑౕว᳓⚛ේሶๆ⌕䈪䈲A=0.2
䉅䈫䉅䈫䈱䉴䊏䊮゠㆏⋧੕૞↪䋺0.01(meV)400୚ !
᳓⚛ๆ⌕᦭ല䉴䊏䊮゠㆏⋧੕૞↪䋺4.0(meV)᳓⚛ේሶๆ⌕䈮䉋䉎䉴䊏䊮Ͳ゠㆏⋧੕૞↪䈱ᄢ᏷䈭Ⴧടๆ᦭ല䉴䊏䊮゠㆏⋧੕૞↪䈫ബ⿠ሶ䈱ᷙᚑ᳓⚛ේሶๆ⌕ਅ䈮䈍䈔䉎ബ⿠ሶ⁁ᘒ[䉴䊏䊮Ͳ゠㆏⋧੕૞↪&゠㆏ᷙᚑ]+BetheͲSalpeterᣇ⒟ᑼ
䉴䊏䊮৻㊀㗄ബ⿠ሶ䈫ਃ㊀㗄ബ⿠ሶ䈱ᷙᚑ᳓⚛ේሶๆ⌕ኒᐲ䈱Ⴧട䈫䈫䉅䈮৻㊀㗄ബ⿠ሶ䈫ਃ㊀㗄ബ⿠ሶ䈱㑆䈮ᷙᚑ䈏⿠䈐䉎䋮
䉴䊏䊮ਃ㊀㗄ബ⿠ሶ䋺᦭㒢䈱ᝄേሶᒝᐲ
৻㊀㗄ബ⿠ሶ䈫ਃ㊀㗄ബ⿠ሶ䈱ᷙᚑ䈱⚿ᨐ䋬ਃ㊀㗄ബ⿠ሶ䈏శቇ⸵ኈ䈫䈭䉎䋮

Konabe&Watanabe:
PRB 83,045407(2011).

᳓⚛ේሶๆ⌕ 䉋䉍 ㊀㗄ബ⿠ሶ శቇᵴᕈ 䈭䉎᳓⚛ේሶๆ⌕䈮䉋䉍ਃ㊀㗄ബ⿠ሶ䈏శቇᵴᕈ䈫䈭䉎䈖䈫䉕䉕᣿䉌䈎䈮䈚䈢䋮ታ㛎⚿ᨐ䉕ℂ⺰⊛䈮⺑᣿䋮䋲䋮䉫䊤䊐䉢䊮䊅䊉䊥䊗䊮䈎䉌䈱䊧䊷䉱䊷ೝỗ㔚⇇㔚ሶ᡼኿䋨㪣㪘㪝㪜䋩㪣㪘㪝㪜䈫䈲䈬䈱䉋䈉䈭⃻⽎䈎䊧䊷䉱䊷ബ⿠㔚⇇㔚ሶ᡼኿㗼ᓸ㏜䋨㪮䋩⇇᡼ 㗼ᓸ㏜㔚⇇㔚ሶ㌂଀䋨㪪㫀䋩

H.Yanagisawaetal,PRL103,257603(2009)

Field emission

Photo field emission!Z
EFe-metalvacuume-

Optical field emission!Ze-weak laser fieldstrong laser fieldEffect of width modulation in semiconducging armchair GNR
N( 7)
N(=7)

Armchair-edged GNR (A-GNR)
Metallic when N=3m-1 (m:integer)

Energyy [eV]32
10-1-2-3-44-50.0

A-GNRA GNR
N NN=5N=555 AGNR

0.2

0.4

kza/S

0.6

0.8

5432
10-1-2-3-44-50.0

Energyy [eV]⋧㚍䋨␹ᚭᄢ䋩 54

1.0

N=6NAA-GNR
GNR
N=6N
66AGNR

0.2

0.4kza/S

0.6

0.8

1.0

Our question: How does the presence of narrow ribbon region influences thetransport characteristics in “originally semiconducting” armchair GNR?

N vac
Wide (N=6)

7(N b off edge
(Numberd llatticetti vacancies)i )Narrow (N=5)

Wide (N=6)

Switching behavior in the absence of width modulation(N=6 Armchair GNR)
31

10

PS

-2

PD

VGS=0[V]-1
Vdope=1[V]

-3
-1

0ka/S

VDS

0.1[V ]

0ka/S

T(E)

ElectrodeGate

10 150.150.10

Mch=150 05
0.05-20.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0-3

VGS [V]ElectrodeGate

Topp Gate

Insurator N

16 tins

2[nm]

GNR

Electrode
Gate

Bottom Gate

Drain

1[V ]

-1

VGS=1[V]1 0 1 2 3 -1

VDoping

0

N=6 A-GNR
P f t Edge
PerfectEd

ID/I020.20

Enerrgy [eV]

2Source

Enerrgy [eV]Drain

Source

3I0eE0h1>eV@38.74>PA @ÅSide view

ElectrodeGate

Top view
N=6Lch15 u 3a06.4nm

Local density of states in the absence of width modulation

3䎖22䎕

11䎔0PS
PD-11-2

Vdope=1[V]-3-10ka/S-11䎐䎔-2䎐䎕

1 0 1 2-1

T(E)
1[V ]

VGS

0[V ]

VDS

0.1[V ]

0ka/S

-3䎐䎖
1 䎓䎕

䎗䎙

Electrode
Gate

Insurator

N

16

Bottom Gate

䎔䎓ElectrodeGate

T GateTopG tGNR
ElectrodeGate䎛z [nm]t ins

2[ nm ]Drain
nVDoping

Lch=6.4 nm0䎓S
SourceEnnergy [[eV]

3Local Density
y of States

Drain

SourceElectrode43Gate

Effect of width modulation(appearance of resonant peak in transmission)
322110PS

Nvac=1-1-20PD-1

Vdope=1[V]-3-10ka/S

1 00.20

Energyy [eV]
ID/I0

Energyy [eV]

DrainSource

30.15T(E)

2 -10ka/S

1

Nvac=10.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0-315 u 3a0(Perfect Edge)

0.05

VGS [V]N vac 1
Lch

Nvac=00

0 10
0.10-21N 6A
N=6A-GNR
GNR
Mch=15I0eE0h1>eV@

38.74>PA @6.4nm

Appearance of resonant peak in the transmission Æ influences the current

Effect of Edge Lattice Vacancy
D iDrain

22211110PSPD-11-20

Vdope=1[V]-3-110ka/S

N-1
1Nvac=2

1 0

612T(E)-110ka/S

N

1

Ennergy [eVV]

2Ennergy [eV]]30PS

Vdope=1[V]-2-2-3-3-1

2N vac

750PD-1N vac

30ka/S

1 0-1

Nvac=77-2
1T(E)

2 -10ka/S

1-3

Ennergy [eVV]

Source33Ennergy [eV]]DrainSourceLocal density of states in the presence of width modulation
3䎖22䎕

11䎔0䎓

3Ennergy [eV]

Local Density of States

DrainSource0PSPD-1-2

Vdope=1[V]-3-1VDoping

0ka/SNarrowregion-1 䎐䎔

Nvac=7N=6

N=5

N=6N 6N=6

N=6-2 䎐䎕10 1 2-1T(E)

1[V ]㧘VGS

0ka/S

0[V ]㧘VDS

1-3 䎐䎖䎓

䎕䎗z [nm]

䎙䎛

0.1[V ]

Discrete levels in narrow region Å continuum energy levels in narrow region)
Our conclusion: In contrast to ordinary semiconductor nanostructure, transport
in armchair GNR can be influenced significantly even by a small widthmodulation (or edge vacancies)!

䎔䎓