Graphene bipolar heterojunctions

S DLG

VBG

CBG

CLG

VLGVSD

-Density in GLs can be n or p type

-Density in LGR can be n’ or p’ type

We expect two Dirac minima! -50 -25 0 25 501

3

5

7

VBG (V)

G (e

2 /h)

VLG = -10 V

Related work by Huard et al. PRL (2007)

EL EL

LG

GLs GLs

Local Gate Region

1 m

Oezyilmaz, Jarrilo-Herrero and Kim PRL (2007)

Graphene heterojunction Devices

n npxpo

tent

ial

n nn’

xpote

ntia

l

p pp’

x

pote

ntia

l

p pnxpo

tent

ial

-10 -5 0 5

50

25

0

-25

-50

VLG (V)

V BG (V

)

2 4 6 8 10 12

G (e2/h)

10

n-n’-n

p-n’-pp-p’-p

n-p’-n

p pn’

-50 -25 0 25 501

3

5

7

VBG (V)

G (e

2 /h)

1 m

Ballistic Quantum Transport in Graphene Heterojunction

n npxpo

tent

ial

Graphene NPN junctionsNovoselov et al, Nat. Phys (2006)

Klein Tunneling

Transmission coefficientTtot

np=1x1012 cm2

np=3x1012 cm2

nn=0.5x1012 cm2

Collimation: (resonance) k2x = n/L

Perfect transmission

Realistic Graphene Heterojunction

Requirements forBallistic pn junctions

• Long Mean free path -> Ballistic conduction

• Large electric field -> Small d -> promote resonance

Smooth electrostatic n ~ 1012 cm-2

F ~ 30 nmddielectric ~ 20 nmL ~ 100 nm

transmission

T

Tunneling through Classically Forbidden regime

T

Cheianov and Fal’ko (2006)

Zhang and Fogler (2008)

Tunneling through smooth pn junctionStrong forward

Collimation!

graphene

electrode

1 m

SEM image of device

20 nm

Mean free path~ 50 nm

Mean free path < 100 nm

Transport Ballistic Graphene Heterojunction

VBG = 90 V

VBG = -90 V

ppp

pnp

npn

nnngraphene

electrode

1 m

Young and Kim (2008)

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

Conductance (mS)6

4

10

8

12

PN junction resistance

Cheianov and Fal’ko (‘06)

18 V

-18 V´

L

n1,, k1,

T

TT

RR*

n1,, k1,

n2,, k2

Conductance Oscillation: Fabry-Perot

k1 /k2= sin’ / sin = 2L /cos’

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

´

L

n1,, k1,

T

TT

RR*

n1,, k1,

n2,, k2

Magnetoresistance Oscillations (B=0)

Aharonov-Bohm phase: B=B L2 sin’/cos ’

0 2 4 6 8 10

2

0

-2

VT (V)

B (

T)

0 1-1dG/dntop (e2/h 10-15 cm-2)

(VB=-50 V)

)

Resonant Magneto-Oscillations in Graphene Heterojunctions

Exp

Theory

Two fitting parameters: lLGR = 27 nm; lGL= 50 nm

• Ballistic pn junction

• Collimation

See also Shytoy et al.,arXiv:0808.0488

Graphene Electronics

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)

Many body & correlated effect to come!

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

Acknowledgement

Meninder Purewal (nanotube)

Kirill Bolotin (suspended graphene)

Melinda Han (nanoribon)

Dmitri Efetov (graphene heterojuncton)

Andrea Young (graphene heterojunction)

Barbaros Oezyilmaz (now at NSU)

Pablo Jarrilo-Herrero (now at MIT)

Funding:

Collaboration: Horst Stormer

Kim Group Picnic: 2008 Central Park, New York

T-1

ln(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

Graphene Quantum Hall Edge State Conduction

EL EL

LG

GLs GLs

Local Gate Region

1 m

simple model (following Haug et al)

Oezyilmaz, et al., PRL (2007) See also Related work by Williams et al. Science (2007)

Temperature Dependent OscillationsTemperature Dependent OscillationsCo

nduc

tanc

e (m

S)

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

VBG = 90 V

npn

nnn

6

4

10

8

12

18 V