Electron Transport in Molecules, Nanotubes and Graphene

Philip Kim

Department of PhysicsColumbia University

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

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

k1D

EF

Vg << 0

Metallic nanotube

Vg > 0~

E

k1DEF

E

k1D

EF

Vg << 0

Semiconducting nanotube

Vg > 0~

Atomic force microscope image of nanotube device

nanotubeelectrode

SiO 2

Si

OFFON

Electrical Transport in Nanotube Devices

E

k1DEF

E

k1D

EF

100

50

050-5

Vsd = 10 mV

Vg (V)

I(nA

)

E

k1DEF

Metallic nanotube

E

k1D

EF

Vg (V)

4

2

0-5 0 5

I(nA

)

Vsd = 10 mV

Semiconducting nanotubeIVsd

Vg

Controlled Growth of Ultralong Nanotubes

B. H. Hong, J. Y. Lee, T. Beetz, Y. Zhu, P. Kim and S. Kim (2005)

(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

Intershell and Intrashell Nanotube Devices

Hong, et al, PNAS (2005)

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

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

- +-

L

Ballistic Transport and Mean Free PathElectron Transport in 1D Channel

le : mean free path

R(L) = ρ LDiffusive transport: le << L

- +-

L

Ballistic transport: L < le

Resistance of N- 1D Channel:

For a nanotube, N = 4 ( 2 from spin and 2 from K and K’)

elL

Neh

NehLR 22)( +=

R(L) = h /N e2 = RQ

# of channel

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 !!

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

k1D

EF

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)

Electric Field Effect in Mesoscopic Graphite

Simple Yet Efficient Mechanical Extraction

Using Scotch Tape is Essential!!

1 µm

AFM Image

A Few Layer Graphene on SiO2/Si Substrate

0.8 nm

0.4 nm1.2 nm

Optical microscope images

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).

Graphene : Dirac Particles in 2D Box

Band structure of graphene

kx

ky

Ener

gy

kx' ky'

E

⊥′≈ kvE F

rh

Massless Dirac Particles with effective speed of light vF.

hole

electron

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

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

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

Quantum Hall Effect in Graphene

T = 1.7 KB = 9 T

Mobility ~ 60,000 cm2/V s

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

Nanotube device

Nanotube Nanogaps

Thin PMMA coating

Narrow (<10nm) trench via e-beam lithography

Oxygen Plasma etching creates gaps (0-10 nm) in tubes.

Cut ends likely to be carboxyl-terminated

Hone, Wind, Nuckolls, and Kim Collaboration

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

Molecular Bridges

Pyridine, EDCI

•Self-assembled•Covalently bonded•Conduction through π-back bone

Bis-oxazole

Guo et al., Science (2006)

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

* 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

Pyridine, EDCI

Oligoaniline: PH sensing

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

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

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

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

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,