Electron Transport in Molecules, Nanotubes and GrapheneMicrosoft PowerPoint - NT2006.ppt Author:...
Transcript of Electron Transport in Molecules, Nanotubes and GrapheneMicrosoft PowerPoint - NT2006.ppt Author:...
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Electron Transport in Molecules, Nanotubes and Graphene
Philip Kim
Department of PhysicsColumbia University
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ky
kx
Rolling Up Graphene: Periodic Boundary Condition
(n, 0)
(n, n)
Ch(n, m)
a1
a2
Ch Periodic Boundary Condition
qkCh π2=⋅ ⊥r
kx
ky
Allowed statesMetallic nanotube
E
k1D
E
k1D
Semiconducting nanotube
x
E(k2D)
kx
ky+ band
- band
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Tuning Carrier Density by Electric Field Effect
Vg
Vsd IDoped Si
SiO2
metalmetal
nanotube
+ + + + + + + + + + + + + + + +
- - - - - - -
Induced charge: Cg Vg = e n = e (D.O.S) ∆EF
E
k1DEF
E
k1DEF
Vg 0~
E
k1DEF
E
k1DEF
Vg 0~
Atomic force microscope image of nanotube device
nanotubeelectrode
SiO 2
Si
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OFFON
Electrical Transport in Nanotube Devices
E
k1DEF
E
k1DEF
100
50
050-5
Vsd = 10 mV
Vg (V)
I(nA
)
E
k1DEF
Metallic nanotube
E
k1DEF
Vg (V)
4
2
0-5 0 5
I(nA
)
Vsd = 10 mV
Semiconducting nanotubeIVsd
Vg
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Controlled Growth of Ultralong Nanotubes
B. H. Hong, J. Y. Lee, T. Beetz, Y. Zhu, P. Kim and S. Kim (2005)
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(Avouris, IBM)
Extraction of Inner Shells from MWNTs
Hong, et al, PNAS (2005)
AFM manipulation of long MWNTs
2 µm
5 µm
2 µm 2 µm
5 µm
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Intershell and Intrashell Nanotube Devices
Hong, et al, PNAS (2005)
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15 mm
Extremely Long SWNT Field Effect Transistor
gatesource drain
100 µm
100 µm
FET characteristics
-9 -6 -3 0 3 6 90
10
20
30
40
Vg (V)
I sd(n
A)
Vsd = 20 V
ρ ~ 10-7 Ω m
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400
200
0
6040200
Length (µm)
Res
ista
nce
(kΩ
)
T = 250 K
ρ = 8 kΩ/µm
Electron Transport in Long Single Walled Nanotubes
Multi-terminal Device with Pd contact
M. Purewall, A. Ravi, and P. Kim (2006)
* Scaling behavior of resistance:R(L)
5678
10
2
3
4
5678
100
2
3
4
567
0.12 4 6 8
12 4 6 8
102 4 6 8
L (µm)
R(kΩ
)
T = 250 K400
200
0
6040200
R(kΩ
)
L (µm)
R ~ RQ
R ~ L
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- +-
L
Ballistic Transport and Mean Free PathElectron Transport in 1D Channel
le : mean free path
R(L) = ρ LDiffusive transport: le
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5
6789
10
2
3
4
5
6789
100
2
3
4
5
67
2 3 4 5 61
2 3 4 5 610
2 3 4 5 6100
Electron Mean Free Path of Nanotube
L (µm)
R(kΩ
)
T = 250 K
175 K
110 K
60 K
30 K
400
200
040200
L (µm)
R(kΩ
)
T = 250 K
175 K
110 K
60 K
30 K
ec l
Leh
ehRLR 22 44
)( ++=
Lines are fit to
45.64 2
=eh
kΩ
Non-ideal contact resistance Rc < 2 kΩ
Temperature (K)
mea
n fr
ee p
ath
(µm
)
0.1
2
46
1
2
46
10
2
12 4 6 8
102 4 6 8
1002 4
le ~ 0.5 µm @ RT !!
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Extremely Long Mean Free Path: Hidden Symmetry ?
le ~ 0.5 µm @ 300 K
le ~ 10 µm @ 1.6 K
Carbon nanotube: Ga[Al]As HEMT:le ~ 100 µm @ 1.6 K
le ~ 0.06 µm @ 300 K
E
k1DEF
right moving left moving
•Small momentum transfer backward scattering must be inefficient.
Selection rules by hidden symmetry in graphene?
T. Ando, JPSJ (1998);McEuen at al, PRL (1999)
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Electric Field Effect in Mesoscopic Graphite
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Simple Yet Efficient Mechanical Extraction
Using Scotch Tape is Essential!!
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1 µm
AFM Image
A Few Layer Graphene on SiO2/Si Substrate
0.8 nm
0.4 nm1.2 nm
Optical microscope images
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Transport Single Layer Graphene
Cleaved graphite crystallite
20 µm
Single layer graphene device 5000
4000
3000
2000
1000
0
-80 -60 -40 -20 0 20 40 60 80
Vg (V)
Rxx
(Ω)
< 1 nm
10 nm
Field Effect Resistance~h/4e2
Zhang, Tan, Stormer & Kim (2005), see also Novoselov et al (2005).
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Graphene : Dirac Particles in 2D Box
Band structure of graphene
kx
ky
Ener
gy
kx' ky'
E
⊥′≈ kvE Fr
hMassless Dirac Particles with effective speed of light vF.
hole
electron
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Graphene v.s. Conventional 2D Electron System
Conventional 2D Electron System
Graphene
E
N2D(E)
*
22
2 emkE h=
*
22
2 hmkE h−=
N2D(E)
E 2*
hπem
2
*
hπhm
Band structures Density of States
• Zero band mass• Strict electron hole symmetry• Electron hole degeneracy
~ h/4e2
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DOS
E
2D Gas in Quantum Limit : Conventional Case
DOS
E2
*
hπem
2
*
hπhm
Density of States
*/ meBc hh =ω
Landau Levels in Magnetic FieldQuantum Hall Effect in GaAs 2DEG
s
s
EF
Graphene• Vanishing carrier mass near Dirac point• Strict electron hole symmetry• Electron hole degeneracy *m
eBc =ω
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15
10
5
086420
6
4
2
0
Hal
l Res
ista
nce
(kΩ
)
Magnetoresistance (kΩ
)B (T)
Quantum Hall Effect in Graphene
____ he2
12
____ he2
16
____ he2
110
T=50 mK
____ he2
12
-15
-10
-5
0
5
10
15
-50 0 50Vg (V)
Hal
l Res
ista
nce
(kΩ
)
T= 1.5K, B= 9T
____ he2
16
____ he2
110
____ he2
114
h1 ____e2-14
e2____ h1
-10
____ he2
1-6
____ he2
1-2
Quantization:
4 (n + )Rxy =-1 ___ e
h2
21
Vg=-2 V
-
EF
σxy
Ene
rgy
gse2/h
Relativistic Landau Level and Half Integer QHE
Landau Level +_Landau Level Degeneracygs = 4
2 for spin and 2 for sublattice
Quantized Condition
Haldane, PRL (1988)
T. Ando et al (2002)
n = 1
n = 2
n = 3
n = -3
n = 0
n = -1
n = -2
DOS
Ene
rgy
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Quantum Hall Effect in Graphene
T = 1.7 KB = 9 T
Mobility ~ 60,000 cm2/V s
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Nanotube Electrodes for Molecular Electronics
• Nanotubes are inherently small, yet compatible to microfabrication processes
• Covalent chemistry between electrode and molecules
• Potentially good conduction via π-bonding network
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Nanotube device
Nanotube Nanogaps
Thin PMMA coating
Narrow (
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Process are optimized to Yield of cut tubes: 25% of ~2600 devices
AFM micrographSEM micrograph
Nanotube Nanogaps
~ 5 nmSEM micrograph
Columbia NSEC (Hone, Wind, Nuckolls, and Kim) Collaboration
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Molecular Bridges
Pyridine, EDCI
•Self-assembled•Covalently bonded•Conduction through π-back bone
Bis-oxazole
Guo et al., Science (2006)
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Does It Work?
50
40
30
20
10
0
-5 0 5
Vg (v)
Cur
rent
(nA
)
before cut
after cut
after reconnection
Metallic Nanotube + Molecular Bridge
Vsd
~ 10-15% of reconnectionout of ~ 100 fully cut tubes
after reconnection
Semiconducting Nanotube + Molecular Bridge
after cut
Vg (v)
Cur
rent
(nA
)
before cut
Vsd = 50 mV
14
12
10
8
6
4
2
0
-5 0 5
Vg
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* Pyridine +EDCI without molecules No connection
* Bis-oxazole without amines No connection
* Bis-oxazole with Monoamine No connection
* 1,12 dodecane diamine (insulator) No connection
Connection with diamine bisoxazole
Control Experiments
Pyridine, EDCI
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Pyridine, EDCI
Oligoaniline: PH sensing
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Transport Measurement
-100
-50
0
50
-800 -400 0 400 800
250 K
180 K
120 K50 K
10 K
1.6 K
Vsd (mV)
I (nA
)
Bis-oxazole + metallic SWNT
I (nA
)
40
20
0
-20
-40-800 -400 0 400 800
Vsd (mV)
1.6 K
-8
-6
-4
-2
0
-450 -400 -350 -300
1.0
0.5
0.0
350300250200150
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Temperature Dependence Transport Spectroscopy
20
10
0
-600 -400 -200 0 200 400 60020
10
0
-600 -400 -200 0 200 400 60020
10
0
-600 -400 -200 0 200 400 60020
10
0
-600 -400 -200 0 200 400 600
1.6 K
10 K
50 K
180 K
Vsd (mV)
dI/d
V(10−
8 S)
4
3
2
1
0
300250200150
1.6K10K20K50K
Vsd (mV)
dI/d
V(10−
8 S)
10
8
6
4
2
0
-250 -200 -150Vsd (mV)
dI/d
V(10−
8 S)
30 K
50 K80 K
120 K
180 K220 K250 K
20 K
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Gate Voltage Dependence
Vg (V)
Vsd
(mV
)
150
175
200
225
125-9.3 -9.25 -9.2
0
0.2
0.4
dI/dV(µS)
0.3
0.2
0.1
0180170160150
Vg=-9.25 V-9.23 V-9.21 V-9.19 V-9.17 V
Vsd (mV)
dI/d
V(µ
S)
200
-5.0-6.0 -4.0
-500
-250
250
500
0
Vg (V)
Vsd
(mV
)
dI/dVsd (µS)0 0.1
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Summary
•Nanotube electrode for single molecular electronics
•Transport in graphene:Unusual quantum Hall effectGraphene nano ribbon devicesGate dependent Raman spectroscopy
•Transport in long nanotubes:Subshell extraction in MWNTsExtremely long mean-free path in SWNTs
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AcknowledgementSpecial Thanks to: Yuanbo ZhangMeninder PurewalByung Hee HongJosh SmallMelinda HanBarbaros Oezyilmaz
Kim Group 2004 Summer Central Park
Funding:
Collaboration: Stormer, Pinczuk, Heinz, Nuckolls, Brus, Flynne, Hone,