Philip Kim

Department of PhysicsColumbia University

Toward Carbon Based Electronics

Outline: Carbon Based Electronics

Material Platform: Low dimensional graphitic systems

• 1-D: Carbon Nanotubes (since 1991)• 2-D: Graphene (since 2004)

Device Concepts

Conventional: (extended) CMOS, SET

Non-Conventional: Quantum Interference, Spintronics, valleytronics

SP2 Carbon: 0-Dimension to 3-Dimension

Fullerenes (C60) Carbon Nanotubes

Atomic orbital sp2

GraphiteGraphene

0D 1D 2D 3D

Graphene : Dirac Particles in 2-dimension

Band structure of graphene (Wallace 1947)

kx

ky

Ene

rgy

kx' ky'

E

kvE F

Zero effective mass particles moving with a constant speed vF

hole

electron

Single Wall Carbon Nanotube

ky

kxkx

ky

Allowed statesMetallic nanotube

E

k1D

E

k1D

Semiconducting nanotube

Eg ~ 0.8 ev / d (nm)

400

200

0

6040200

Length (m)

Res

ista

nce

(k

)

T = 250 K

= 8 k/m

Extremely Long Mean Free Path in Nanotubes

Multi-terminal Device with Pd contact

* Scaling behavior of resistance:R(L)

5

678

10

2

3

4

5

678

100

2

3

4

5

67

0.12 4 6 8

12 4 6 8

102 4 6 8

L (m)

R (

k)

T = 250 K400

200

0

6040200

R (

k)

L (m)

R ~ RQ

R ~ L

el

L

Ne

h

Ne

hLR

22)(

le ~ 1 m

M. Purewall, B. Hong, A. Ravi, B. Chnadra, J. Hone and P. Kim, PRL (2007)Room temperature mean free path > 0.5 m

Nanotube FET

Band gap: 0.5 – 1 eVOn-off ratio: ~ 106

Mobility: ~ 100,000 cm2/Vsec @RTBallistic @RT ~ 300-500 nmFermi velocity: 106 m/secMax current density > 109 A/cm2

Vsd (V)0-0.4-0.8-1.2

I sd (A

)

Ph. Avouris et al, Nature Nanotechnology 2, 605 (2007)

Schottky barrier switching

Advantages of CNTFET

• Novel architecture ->Band-to-band tunneling FET:

subthreshold slop ~ 40 meV/dB @RT

• No-dangling bond at surface -> high k-dielectric compatibleCg ~ CQ can be attainable; small RC, low energy

• Thin body (1-2 nm) -> suppressed short channel effectchannel length ~ 10 nm has been demonstrated

Javey et al. PRL (2004).

Appenzeller et al., PRL (2002)

Rodgers, UIUC

Aligned growth of Nanotubes

Nanotube Electronics: ChallengesPros:High mobility High on-off ratioHigh critical current densitySmall channel lengthSmall gate capacitanceLarge Fermi velocity

Con:Controlled growth

Artistic dream (DELFT)

IBM, Avouris group

Nanotube Ring Oscillators

graphene

Discovery of Graphene

Large scale growth efforts:CVD, MBE, chemical synthesis

Jun 0

7

Dec 0

6

Mar

07

Sep 0

6

Jun 0

6

Mar

06

Dec 0

5

Sep 0

5

Jun 0

5

Mar

05

Dec 0

4

Sep 0

4

Sep 0

7

Growth of Graphene Papers

Scotch tape method

Discovery of QHE in graphen

Jun 0

7

Dec 0

6

Mar

07

Sep 0

6

Jun 0

6

Mar

06

Dec 0

5

Sep 0

5

Jun 0

5

Mar

05

Dec 0

4

Sep 0

4

Sep 0

7

factor 4.5 / year

Graphene Mobility

103

104

105

-4 -2 0 2 4

n (1012 cm-2)

Mobility (cm

2/V sec)

TC17

TC12

TC145

TC130

Mechanically exfoliated graphene

Tan et al. PLR (2007)

Scattering Mechanism?

•Ripples•Substrate (charge trap)•Absorption•Structural defects

Modulate Doped GaAs: Pfeiffer et al.

GaAs HEMT

High mobility materials have been under intensive research as an alternative to Silicon for higher performance

mobility: Si (1,400 cm2/Vsec), InSb (77,000 cm2/Vsec)

Graphene mobility: > 100,000 cm2/Vsec @ room temperature

104

105

106

-0.2 0.0 0.2

unsuspended best

before annealing

after annealing

Density ( 1012 cm-2)

Mob

ilit

y (c

m2 /

V s

ec) 100

90

80

70

60250200150100500

holeselectrons

T (K)R

(

) |n|=2X1011 cm-2

Resistance at High Density

0.24 /K

0.13 /K

Strong density dependence!

Enhanced Room Temperature Mobility of Graphene

Low temperature direct atomic layer deposition (ALD) of HfO2 as high-κ gate dielectric

Top-gate electrode is defined with a final lithography step.

I-V measurements at two different back gate voltages show a distinct “kink” for different top-gate voltages

Transconductance can be as high as gm = 328μS (150μS/μm)

Poor on-off ratio: ~ 5-10due to zero gap in

bulk

Graphene FET characteristics

Meric, Han, Young, Kim, and Shepard (2008)

Graphene FET: High Saturation Velocity

GaAs: 0.7x107 cm/s

vFermi = 1x108 cm/sFor comparison:

Silicon: 1x107 cm/s

Operation current density > 1 mA/m

Vtop = 0 V

Vtop = -1.5 V

Vtop = -2 V

Vtop = -3 V

VtopDirac = 2 V @ Vg = -40 V

111 )( satdrift vEv

FFsat E

vv

0.8

0.6

0.4

0.2

0.00.50.40.30.20.10.0

EF (eV)

v sat (

108

cm/s

)

Saturation velocity

Meric, Han, Young, Kim, and Shepard (2008)

Graphene Device Fabrication

Developing Graphene Nanostructure Fabrication Process

Contacts:PMMAEBLEvaporation

Graphene patterning:HSQEBLDevelopment

Graphene etching:Oxygen plasma

Local gates:ALD HfO2

EBLEvaporation

graphene

Graphene device structure with local gate control

Oezyilmaz, Jarrilo-Herrero and Kim APL (2007)

Graphene Nanostructures

Geim (Manchester) Morpurgo (DELFT)Goldhaber-Gordon (Stanford)

Kim (Columbia)

Ensslin (ETH)Marcus (Harvard)

Quantum Dot AB Ring Graphene with local barrier

Graphene PN junctionsGraphene nanoribbons & nanoconstrictions Graphene Side Gates

1 m

Gold electrode Graphene

10 nm < W < 100 nm

W

Zigzag ribbons

Graphene nanoribbon theory partial list

Graphene Nanoribbons: Confined Dirac Particles

W

Dirac Particle Confinement

x

y

Egap~ hvF k ~ hvF/W

Wk y

2

Wk y

3

Wk y

1

Wk y

W

22 )/( WnkvE xF

Scaling of Energy Gaps in Graphene Nanoribbons

W (nm)

Eg (

meV

)

0 30 60 901

10

100

P1 P2 P3 P4 D1 D2

Eg = E0 /(W-W0)

Han, Oezyilmaz, Zhang and Kim PRL (2007)

-8 -4 0 4 8

75

50

25

0

-25

-50

-75

VLG (V)

VB

G (V

)

10-7 10-5 10-3 10-1

G (e2/h)

Top Gated Graphene Nano Constriction

source

Back gate

SiO2

drain graphene

-8 -4 0 4 810-6

10-5

10-4

10-3

10-2

10-1

VLG (V)

G (

e2/h

)

OFF

SEM image of device

sourcedrain top gate

graphene1 m

30 nm wide x 100 nm long

Hf-oxide

Top gate

Crystallographic Directional DependenceSon, et al, PRL. 97, 216803 (2006)

2m

0 30 60 900

20

40

Eg (

meV

)

(degree)

Graphene Nanoribbons Edge Effect

Rough Graphene Edge Structures

Localization of Edge Disordered Graphene Nanoribbons

See also:Gunlycke et al, Appl. Phys. Lett. 90 (14), 142104 (2007).Areshkin et al, Nano Lett. 7 (1), 204 (2007)Lherbier et al, PRL 100 036803 (2008)

Querlioz et al., Appl. Phys. Lett. 92, 042108 (2008)

Transport ‘gap’

T-1ln

(R)

3

2

1

0

-1

-2

0.20.10.0

Arrhenius plot

Variable Range Hopping in Graphene Nanoribbons

Con

duct

ance

(S

)

Vg (V)

W = 37 nm

0.1

1

10

100

6040200

4K 15K 100K 200K 300K

E

x

EF

1

1

00max exp

d

T

TGG

d: dimensionality

70 nm

48 nm

37 nm

22 nm15 nm

31 nm3

2

1

0

-1

-2

0.60.40.20.0

ln(R

)

T-1/3

70 nm

48 nm

37 nm

22 nm15 nm

31 nm

2D VRH3

2

1

0

-1

-2

0.40.20.0

ln(R

)

T-1/2

70 nm

48 nm

37 nm

22 nm15 nm

31 nm

1D VRH

T

Rodgers, UIUC

Aligned growth of Nanotubes

Graphene Electronics: ChallengesPros:High mobility High on-off ratioHigh critical current densitySmall channel lengthSmall gate capacitanceLarge Fermi velocity

Con:Controlled growth

Artistic dream (DELFT)

tunability of band gaps

Edge control

This can be turned into advantage:doping site, functionality, and etc…

Graphene Electronics: Conventional & Non-conventional

Conventional Devices

Cheianov et al. Science (07)

Graphene Veselago lense

FETBand gap engineered Graphene nanoribbons

Nonconventional Devices

Trauzettel et al. Nature Phys. (07)

Graphene psedospintronics

Son et al. Nature (07)

Graphene Spintronics

Graphene quantum dot

(Manchester group)

Pd (under HfO2)

Pd (under HfO2)

Pd (over HfO2)

SWCNT (under HfO2)

HfO2 on SiO2/Si+

Carbon Nanotube Superlattice

20 nm

60 nm

1 m

Purewal, Takekosh, Jarillo-Herrero, Kim (2008)

Kouwenhoven PRL (1992)

-54 -50 -45 -40

4

3

2

1

Back Gate (V)

Top Gate (V)

Co

nd

uc

tan

ce

(S

)0

1

1.0 1.5 2.00.0

0.2

dI/d

V (S

)

Top Gate (V)

Klein Tunneling

Transmission coef

Novoselov et al (2006)

Ballistic Quantum Transport in Graphene Heterojunction

n np xpote

ntia

l

Ballistic transport in the barrier

Graphene NPN junctions

Realistic smooth potential distribution

Total Internal Reflection

Cheianov and Fal’ko (2006)

Zhang and Fogler (2008)

Tunneling through smooth pn junction

Requirements forExperimental Observation:

• Long Mean free path -> Ballistic conduction

• Small d -> better collimination

Top gate width: 50 nm < Lm

graphene

electrode

1 m

SEM image of device

Transport Ballistic Graphene Heterojunction

VBG = 90 V

VBG = -90 V

ppp

pnpnpn

nnngraphene

electrode

1 m

Young and Kim (2008)

VTG (V)-10 0-2-4-6-8 0 108642

Conductance (m

S)

6

4

10

8

12

PN junction resistance

Zhang and Fogler (2008)

18 V

-18 V´

L

n1,, k1,

T

TT

RR*

n1,, k1,

n2,, k2

Conductance Oscillation: Fabry-Perot

k1 /k2= sin’ / sin = 2L /cos’

Mean free path~ 200 nm

Junction length< 100 nm

See also Shavchenko et al and Goldhaber-Gordon’s recent preprint

Quantum Oscillations in Ballistic Graphene Heterojunction

ntop (1012 cm2)

n back

(1012

cm

2 )

5-5 0

0

-5

5

0 1-1

dR/dntop ( h/e2 10-15 cm-2)

Resistance Oscillations

0 20 40 60

0

1

-10 -8 -6 -4

85

90

95

100

105

G (

e2 /h)

VTG

(V)

80K 60K 43K 30K 16K 4K

T (K)

Am

pli

tud

e

Oscillation persist high temperature!

ConclusionsConclusions

• Carbon nanotube FET is mature technology demonstrating substantial improvement over Si CMOS

• Controlled growth and scaling up of CNTFET remains as a challenge

• Graphene provides scaling up solution of carbon electronics with high mobility

• Controlled growth of graphene and edge contol remains as a challenge

• Novel quantum device concepts have been demonstrated on graphene and nanontubes