Probing Probing GrapheneGraphene Field Effect TransistorsField Effect Transistors

MSMMSM--09,S N Bose Inst, 09,S N Bose Inst, KolkataKolkata ,Nov 11, 2009,Nov 11, 2009

A . K . SoodPhysics Department

Indian Institute Of ScienceBangalore,India

Different forms of Carbon

Diamond

Graphite C60

C70

Fullerenes

SWNT

DWNT

MWNT

3D

0 D

Centuries oldCenturies old

19851985

1991 & 19931991 & 1993

1 D

2D :

Graphene

Single sheets of graphene can be formed by rubbing graphite flakes on a substrate.

K. S. Novoselov et al., Nature 438, 197 (2005)Y. Zhang, Y.-W. Tan, H. L. Stormer, P. Kim, Nature 438, 201 (2005)

Making Graphene……..

Source: A.K Geim, Science 324, 1530 (2009)

Ultrasound cleavage of graphiteUltrasound cleavage of graphite

CVD growth on Ni and transferredCVD growth on Ni and transferred

Heating of Heating of SiCSiC

Large area ultrathin films of reduced Graphitic oxide

Ø Eda et. al. Nature Nanotech. Vol 3, 270 (May 2008)

Ø Li et. al. Nature Nanotech. Vol 3, 101 (Feb 2008)

Ref. Eda et. al Nature Nanotech.

Vacuum heating of 6 H or 4H Vacuum heating of 6 H or 4H -- SiCSiC : Georgia Inst of Technology,: Georgia Inst of Technology,Walt A deWalt A de HeerHeer group group

# # Prof C N R Rao’s group: New method Arc discharge (2009), Nano-diamond

# IISC: Prof # IISC: Prof SampathSampath, Joint student , Joint student MrMr K .K .VasuVasu with my groupwith my group

• σ - bonds in the xy-plane: sp2 hybridization of the 2s, 2px and 2pyorbitals

• π - bonds the fourth valence electron (2pz orbitals) is in a π-orbital with its lobes perpendicular to the plane

• A single graphene layer : honeycomb lattice with two atoms ( A & B ) per unit cell

A B

What you already know…..

Linearize the Hamiltonian near the K point for small k.

θ

θ

−

+

− = = = +

hh

, where Fermi velocity k

k

ix ycc cc

F Fix y

k ik eta tav k v

k ik eH

0 03 302 20

Eigen values:

ε = ± h( ) ,Fk v k

Eigen states:θ

θ

−

+

Ψ = Ψ ±

/.

/,

k

k

iik rA

iB

ee

e

2

22

Tight binding calculation: Energy dispersionTight binding calculation: Energy dispersionε ′∑ †

kk

= k kC CH For Bloch wave function (extended)

′∑ †

R

= R Rt C CH For Wannier wave function (localized), t is the hopping integral

Effective mass Hamiltonian

( )σσ σ σ

==

= − ∇h

ˆ.Pauli matrix ,

ˆand

F

x y

v P

P i

H

Linear dispersion.DOS linear with E.Electron hole symmetry

Pseuodospin.No back scattering.Ballistic transport.

Effective mass=0, Dirac FermionKlein tunneling.

Other interesting physics: Berry phase Anomalous QHE

εΨ Ψ

= Ψ Ψ ( )A A

BB B B

kAA AB

BA

H H

H Hε ′−

′

′−∑ .( )k

R-R

= ( )ik R Re t R R

Wallace et al.

Electronic Structure of Electronic Structure of GrapheneGraphene

Graphene lattice is made of two equivalent carbon sublatticesA and B.

Electronic state near zero E are composed of states belonging to different sub-lattices and their relative contribution in the make up of quasi particle is taken into account using twocomponent wave functions (spinors)

Electronic Structure of Electronic Structure of GrapheneGraphene

PseudoPseudo--spin:Canspin:Can it be manipulated using strain ??it be manipulated using strain ??

Quasi-particle Zoo

Source: A.K. Geim 324, 1530 (2009)

What is so exciting about What is so exciting about GrapheneGraphene ??

Future Possibility of large scale Nano-Devices

Highly directional bonds ,leading to Highly directional bonds ,leading to Perfect crystalline order Perfect crystalline order

Exotic phenomena Exotic phenomena described by relativistic QM described by relativistic QM

+ Fractional QHE seen very recently !! (+ Fractional QHE seen very recently !! (DuDu et al et al Nature(OctNature(Oct 14,2009))14,2009))

Anomalous integer QHE seen even at room temperature.(Science 315, 1379, (2007))

(Signatures of 2 D nature and (Signatures of 2 D nature and masslessmassless DiracDirac Fermions)Fermions)

(signatures of interactions and correlations in (signatures of interactions and correlations in graphenegraphene——beyond nonbeyond non--interacting interacting DiracDirac Fermions in 2D)Fermions in 2D)

2

xye 1G = ν ; ν = 4(n+ )h 2

GrapheneGraphene

2D EG2D EG

A.K. A.K. GeimGeim and and NovoselovNovoselov

Graphene – A rising star

Graphene~ 1300 paper published in 2008 !

Ref: A Barth & W. Marx ,http://arxiv.org/abs/0808.3320(2008)

An indication of the intense interest in graphene. Statistics of searches on all nature.com websites in January and February 2009.

Popularity of “graphene”

Solid State Comm. 149,1039(June 2009)

Electrochemically Top Gated Graphene:Monitoring Dopants by Raman Scattering

Anindya Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha,U. V. Waghmare, R.Yang, H.R.Krishnamurhthy,

A. K. Geim, A. C. Ferrari, A.K. Sood

Nature Nanotechnology 3,210 (2008)

Raman spectroscopy of graphene on different substrates and influence of defects

Anindya Das, Biswanath Chakraborty and A.K. Sood

Bulletin of Material Science,31,579 ( 2008)

Phonon renormalization in doped bilayer grapheneAnindya Das, B. Chakraborty, S.Piscanec,S. Pisana,A K Sood and A. C. Ferrari

Phys Rev B 79,155417 (2009)

REFERENCES and ACKNOWLEDGEMENTSREFERENCES and ACKNOWLEDGEMENTS

Funding from Dept of Science and Technology, IndiaFunding from Dept of Science and Technology, India

--------------------------------------------------------------------------------------------------------------Simultaneous Simultaneous pp--nn junction formation in gated junction formation in gated bilayerbilayer graphenegraphene..

B.ChakrabortyB.Chakraborty, A , A DasDas and A K and A K SoodSood, Nanotechnology, Nanotechnology (2009)(2009)------------------------------------------------------------------------------------ ----------------------------------------

K K VasuVasu ,,B.Chakraborty,SB.Chakraborty,S SampathSampath and A K and A K SoodSood (2009)(2009)--------------------------------------------------------------------------------------------------------------------

Raman Finger prints of Raman Finger prints of GrapheneGraphene

SLGAFM Image

Optical Image

1300 1400 1500 1600 2600 2650 2700 2750 28

0.0

0.2

0.4

0.6

0.8

1.0

1.2

No D mode

(a)

G/2D ~ 0.17

Inte

nsity

(a.u

)

Raman Shift (cm-1)

2D mode ~ 2682.3 cm-1

G mode ~ 1582.5 cm-1

Anindya Das, Biswanath Chakraborty and A.K. Sood, Bulletin of Material Science, 2008

Method of Preparation and characterization of SLG using RamanGraphene samples are prepared by micromechanical cleavage of

bulk graphite and de-posited on 300 nm thick SiO2 substrate.

SLG BLG

1300 1400 1500 1600 2600 2700 2800

0.0

0.2

0.4

0.6

0.8

1.0

1.2

No D mode

(b) ω2D

1

~ 2654 cm-1

ω2D2

~ 2687 cm-1

ω2D3

~ 2607 cm-1

ω2D3

~ 2722 cm-1

G mode ~ 1582.3 cm-1

Raman Shift (cm-1)

Inte

nsity

(a.u

)

1300 1400 1500 1600 2600 2650 2700 2750 2800

0.0

0.2

0.4

0.6

0.8

1.0

1.2

No D mode

(a)

G/2D ~ 0.17

Inte

nsity

(a.u

)

Raman Shift (cm-1)

2D mode ~ 2682.3 cm-1

G mode ~ 1582.5 cm-1

I2D/IG = 5.8

Raman spectrum of graphene

1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 4 5 0 0

Int.

(a.u

)

Raman shift (cm-1)

D (1350)G (1583)

G’ (1620)

2D (2699)

D+G (2947)2G’ (3245) 2D+G (4290)

Raman ModesSymmetry allowed

Disorder activated

G mode: 1583 cm-1 (Γ point)

D mode: 1350 cm-1 (near K point - TO)2D mode: 2700 cm-1 (near K point - TO)G’ mode: 1620 cm-1 (near Γ point)

2G’ mode: 3240 cm-1 (near Γ point)

Yan PRB, 77, 125401 (2008)

εk

First order Raman mode at Γ: G mode

1

2

3

( )( )γ ω γ∝

− − − − −∑h,

R ep R

a b L a ph b

b b a aR

E E i E E iE EH H H

1

0 0

Bosko: PR B 78, 125418 (2008)

Numerator vanishes due to high symmetry of low energy electronic Dirac Hamiltonian.

Raman process responsible for G – mode is off-resonance.

D and G’ modes

K K/

defect

K

D G’

Inter-valley Intra-valley'1(TO - A mode near K) Γ(LO - mode near )

ωh ph

phonon phonon

defect

( )( )( )∑a b

eR e-def ep er

e q e q ea,b,c 1 1 p 1 p c

M M M MR =

E -E -iγ E -hω -E -iγ E -hω -E -iγ

Why there is a single peak in SLG and four peaks in BLG

( )( )( )γ ω γ ω ω γ∝

− − − − − − − − −∑h h h h h h,

R L L

a b L ai L ph bi L ph ph ci

f c c b b a a iIntensity

E E i E E i E E iE E E ERH H H H

2Double resonance Raman scattering:

DR if two denominators become zero. The peak position of 2D depends on laserexcitation and phonon dispersion around K point.

Ferrari et al.Graf et al..

Field Effect TransistorField Effect Transistor

VdsVgs

Graphene/CNT

1. Scattering of carriers by phonons limits the mobility of carriers and device characteristics

Electron-phonon coupling2. Maximum limit of the current: determined by Hot phonons

Raman spectroscopy an IDEAL probe forCharacterisation and el-ph coupling study.

Graphene

McEuen et al. Novoselov et al.

VBG VTG

S

Si

SiO2

Platinum

Electrochemical Gating

PEO + LiClO4

S

Si

SiO2

SLGBack Gating

How to tune the Fermi energy??How to tune the Fermi energy??

d

Advantages of electrochemical gating:

Nanometer thick Debye layer act as a capacitor compared 300 nm thick SiO2. As a result higher doping level is possible for a small gate voltage.

Doping amount does not depend on the shape of the platinum as well as its position.

The Debye layer thickness depends on the concentration of ions and as a result doping will be homogenous in SLG.

D

D

Top gated graphene transistor

-0.5 0.0 0.5 1.0 1.5 2.03

6

9

12

15

18

21

-4 -2 0 2 4 6102

103

104

105

-40 -20 0 20 40468

10121416

n (1012 cm-2)

Mob

ility

(cm

2 /V s

ec)

VTG (Volt)

Res

istiv

ity (k

Ohm

)

b

a

ρ (k

Ohm

)

b

VBG (Volt)

Das et al. Nature Nanotechnology 3,210(2008)

For ideal graphene the transport should be ballistic.

There should be a minimal value of conductivity as n ~ 0

σ π=min

/e h24

Diffusive transport explains the experimental results.

The charge impurities (trapped charges) induce electron and hole puddles in graphene.

( ) −

c2 2

TG D

L/WR = R +

eµ δn + n V V

( )

2 2TG Dσ = eµ δn + n V -V

+-

++ +- --- + +- - - + ++

++ +

+

- -- ----

Position (X)

Cha

rge

Chem. Pot. Vg=0

(I) (II) (III) (IV) (V) (VI)

Continuum (E = 0)

Work function (Φ)

Charge puddles in Charge puddles in graphenegraphene

δEFVg>0

Vg<0

-1.2 -0.8 -0.4 0.0 0.4 0.8 1.22

4

6

8

10

12

14 Rc = 1.56 Kohmµ = 247 cm2/V.sδn = 1.3X1012/cm2

Res

ista

nce

(Koh

m)

VTG - VD (V)

δEF ~ 100 meV

Raman scattering in electrochemically top-gated

monolayer graphenetransistor

Nature Nanotechnology 3,210(2008)

Anindya Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha,U. V. Waghmare, R.Yang, H.R.Krishnamurhthy, A. K. Geim, A. C. Ferrari,

A.K. Sood

Yan et al.

Simone et al.

Recent Experiments on doped monolayerRecent Experiments on doped monolayer

VTG

Platinum

SiSiO2

SourceDrain

To spectrometer

From Arlaser (514 nm)

× 50 objective

VDS Polymer Electrolyte

Top gated graphene transistor

Device fabricated byDevice fabricated byProf Prof GeimGeim’’ss group group

1550 1575 1600 2600 2650 2700 2750

1.2

Inte

nsity

(a.u

)

Raman Shift (cm-1)

-2.2

-1.6

4.0

3.5

-1.2

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2 -0.1

0 V

0.5

1.0

1.62.0

2.4

2.6

2.8

3.0

Evolution of G and 2D Evolution of G and 2D band of band of graphenegraphene with with

gate voltage gate voltage

G mode 2D mode

The G peak monitors the doping level and

2D discriminates between electron and hole doping

-2 -1 0 1 2 3 4

12

15

18

Gate Volt (V)

FWH

M (c

m-1)

Ram

an S

hift

(cm

-1)

1580

1590

1600

1610

-2 -1 0 1 2 3 4

25

30

35

40

45

FWH

M (c

m-1)

Ram

an S

hift

(cm

-1)

Gate Volt (V)

2660

2680

2700

Two contributions:1. Adiabatic correction with relaxed lattice

Phonon renormalization due to doping

2. Beyond adiabatic approximation: Dynamic corrections.

PRL, 2006: Michele Lazzeri and Francesco Mauri

Inverse of phonon pulsation ~ 3 fs. Electron momentum relaxation time ~ few hundred fs.Therefore, phonon is dynamic perturbation to electron.

Gωh Gωh Gωh

Physically what happen with Fermi energy shift:Physically what happen with Fermi energy shift:

Static perturbation (adiabatic) is not enough and we have to consider the time dependent perturbation (non-adiabatic effect or “dynamic” effect)

Breakdown of BornBreakdown of Born--Oppenheimer approximationOppenheimer approximation

Inverse of phonon pulsation ~ 3 fs. Electron momentum relaxation time ~ few hundred fs.Therefore, phonon is dynamic perturbation to electron.

Gωh Gωh

FE

2 k k qphkq

k k q

f fE W

δ δε ε ω

+

+

−∆ =

− +∑ hk

21( ln( ))4 2

F GFG

G F G

ε ωεω λω ε ω

−∆ = +

+hh

h h

At room temp ( ) 22 2

00

[ ( ) ( )]4Re [ ]...........(1)(2 ) ( )

FDynamic E F FG

f E f Ekdki

ε ε εω α γε ω δ

∞ − − − −=

− +∫hh

What happens with Fermi energy shift

T=0

T. Ando(2006)

F.Mauri(2006)

2

o2 2 -2

12 -2

~ EPC( ) , we have taken

EPC( ) 45.6eV A (DFT)and =0.1eV ( n~10 cm ) is determined from the FWHM.

α

δ δ

Γ

Γ =

-3 -2 -1 0 1 2 3 4

5

10

15

Electron Concentration (1013/cm2)

FWH

M (c

m-1)

-1 < 1cm

EPC anharmonic

anharmonic

γ γ γ

γ

= +

1580

1585

1590

1595

1600

1605

1610

Ram

an S

hift

(cm

-1)

-3 -2 -1 0 1 2 3 4Electron Concentration (1013/cm2)

Re + G G

lattice laxation dynamicGω ω ω∆ =∆ ∆

( ) 2Im(1)FEGFWHM =

2

o2 2 -2

12 -2

~ EPC( ) , we have taken

EPC( ) 45.6eV A (DFT)and =0.1eV ( n~10 cm ) is determined from the FWHM.

α

δ δ

Γ

Γ =

Life time of phonon

2( )( )ph

kq k k q k k qW f fγ π δ ε ε ω+ += − + −∑ h

Phonons are no longer eigenstates because of perturbation. Phonon will decay intoElectron-hole pair. Only the real transitions will contribute to the life time.

From Fermi golden rule:

Otherwise:

-3 -2 -1 0 1 2 3 4

5

10

15

Electron Concentration (1013/cm2)

FWH

M (c

m-1)

-1 < 1cm

EPC anharmonic

anharmonic

γ γ γ

γ

= +

Das et al. Nature Nanotechnology 3,210(2008)

-3 -2 -1 0 1 2 3 4

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.5

1.0

1.5

2.0

(b)

Electron Concentration (1013/cm2)

Int.

ratio

2D

/GIn

t. (a

.u)

(a)

Intensity of 2D and G modes

G

2D

Intensity ratio also monitors the doping.

Note that ratio cannot be used to infer number of layers.

Das et al. Nature Nanotechnology 3,210(2008)

-3 -2 -1 0 1 2 3 4

20

25

30

35

40

45

50

2660

2670

2680

2690

2700

(b)

(a)

Electron Concentration (1013/cm2)

FWH

M (c

m-1)

Ram

an S

hift

(cm

-1)

NonNon--adiabatic effect will be small for 2D as the momentum of phononadiabatic effect will be small for 2D as the momentum of phonon (q) (q) is far away from the KA at K Point. Therefore, static part is mis far away from the KA at K Point. Therefore, static part is main ain contributor in the phonon renormalization of 2D mode.contributor in the phonon renormalization of 2D mode.

2D discriminates between electron and hole doping.

DFT calculation (only static part)

Saha,Waghmare,KrishnamurthySaha,Waghmare,KrishnamurthyAnd And SoodSood, Phys , Phys RevBRevB 78,165421(2008)78,165421(2008)

Bilayer Graphene

Anindya Das, B. Chakraborty, S.Piscanec,S. Pisana,A K Sood and A. C. Ferrari

Phys Rev B 79, 155417 (2009)

A1

A1

A1B1

B1B1

A2

B2 B2

B2

A2

A2

Bilayer grapheneTop view

1γ

0γ

Side view

1 1 2 2 0

/0

2 1 1

2 1 3

2 1 2 1 4

A B or A B ( 3 eV)

Next nearest neighbour ( 0.1eV)A B ( 0.4 eV from graphite)B A ( 0.12 eV)A A or B B ( 0.12 eV)

γ

γγγ

γ

− − →

→− →− →− − →

03.4 A

AB stacking

01.4 A

Hopping energies

In plane

Inter-layer

Most relevant hopping terms

Tight binding Hamiltonian near K point

γγ γ

γ γγ

=

k

k

k

k

H

0

0 1

1 0

0

0 0 00 0

0 00 0 0

1j =

2j =

1j =

2j =

1s =

1s = −

sjkε

k1γ

1γ( )

221 1

0( ) + 12 2

jsjk s kγ γε γ

= + −

kx

Reciprocal spaceEnergy dispersion of BLG

No No bandgapbandgap in pristine in pristine bilayerbilayer..BandgapBandgap can be opened by perpendicular can be opened by perpendicular electric Field.electric Field.

γ1

γ1

k

j=2

j=1

j=1

j=2

s=1

s= -1

g∆

sjkε

∆V

( ) ( )( )2 22 2g 1 1 = γ V / γ V∆ ∆ + ∆

( )blg blgV = e E d∆ ×Potential energy difference between two layers

Properties of Properties of bilayerbilayer graphenegraphene• Energy dispersion is parabolic near zero energy.

• Massive Dirac Fermion.

• Finite density of states (DOS) near zero energy .

• Tunable band gap with a perpendicular electric field.

• Ballistic transport, high mobility.

• Large on/off ratio for field effect transistor (FET) devices.

Experimental setup

VTG

Green Laser (2.41 eV)

Spectrometer

50 X Objective

SLG

BLG

SiSi

SiOSiO22

PtAuAu

2D peakSEM image

5 µm

2565 2610 2655 2700 2745 2790

SLG

BLG

Raman Shift (cm-1)

Das et al. PR. B 2009

-1 0 1 2 31580

1585

1590

1595

1600

1605ElectronHole

Pos

(G) (

cm-1)

VG (V)

1550 1575 1600 2600 2650 2700 2750

3.6

3.2

2.8

2.4

2.0

1.6

1.2

0.8

0.4

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0 V

2D22D1

Raman Shift (cm-1)

Evolution of G and 2D mode Evolution of G and 2D mode of a BLG with Vof a BLG with VTGTG

2DG

Change of slope

SLG

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.44

8

12

16

1584

1588

1592

1596

1600

FWHM

(G) (

cm-1)

Fermi Energy (eV)

Pos(

G) (

cm-1)

Pos (G) and FWHM of BLG as a function of EF

Signature of 2nd

sub-band population

( ) ( )' ' ' '2' 2 2

, ' , ' ' ' 00

[ ( ) ( )][ ]Re ( ) ........ 1

( ) ( )sjk s j k sjk s j kDynamic

G F jjs s j j sjk s j k

f fE kdk k

iε ε ε ε

ω α γε ε ω δ

∞ − − = Φ − − + ∑∑∫h

h

( ) 2Im(1)FEGFWHM = T. Ando JPSJ 76, 104711 (2007)

2

11 22 2 21

( )0.5( / 2) ( )

kk

γγ γ

Φ = Φ =+

21

12 21 2 21

( / 2)0.5( / 2) ( )k

γγ γ

Φ = Φ =+

T5

T6

T2T1 T3T4Gωh

Gωh EF

EF

EF

0.0 0.1 0.2 0.3 0.4 0.5 0.6-5

0

5

10

15

20

EF(eV)

Temp = 4Kδ=0.001eV

Intraband transition

Interband transition

BLG

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4468

10121416

1584

1588

1592

1596

1600

(d)FWHM

(G) (

cm-1)

Fermi Energy (eV)

Pos(

G) (

cm-1)

2

o2 2 -2

12 -2

1

~ EPC( ) , we have taken

EPC( ) 45.6eV A (DFT)and =0.03eV ( n~10 cm ) is determined from the FWHM.

γ ~ 0.38 eV

α

δ δ

Γ

Γ =

Comparison of experiment with theory at T=300KComparison of experiment with theory at T=300K

Re + G G

lattice laxation dynamicGω ω ω∆ = ∆ ∆

( ) 2Im(1)FEGFWHM =

Summary of bilayer Raman resultsSeparation between two sub bands γ1 estimated

(~ 0.38eV) from the phonon renormalization using Raman spectroscopy.

From life time of G mode, we corroborate the DFT value

Of electron-phonon coupling for low doping.At higher doping there can be renormalisation of EPC (el-el interactions).

The amount of unintentional doping in bilayer grapheneestimated from linewidths is ~ δEF = 0.03eV .

o2 2 -2EPC( ) 45.6eV AΓ =

12 -2n~10 cmδ

Position of G peak gives amount of doping level in a bilayer graphene device using non-invasive Raman spectroscopy.

S

BG

TG

TGV

BGV

BLG

Debye layer

SiO2

Top Gate Top Gate ––Back Gate combinationBack Gate combination

B. Chakraborty, Anindya Das and A.K Sood (2009)

S

Si

SiO2

Platinum

TGV

BGV

# # We determine CWe determine CTGTG..

** Current saturation .** Current saturation .

D

Rchannelis the resistance of the bilayer graphene

µ, δn and 2RC are the fitting parameters.

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1450

500

550

600

650

700

750

Experimental data Fitted curve

VDS = 10 mV

2Rc = 110 ohmµ = 770 cm2/V.secδn = 1.55 X 1012 cm-2

Res

istan

ce (o

hm)

VTG (volts)

( ) ( )22 indTG

L 12 2W n

C channel CR R R Rnδ

= + = ++

VT

G(v

olts

)

VBG(volts)

Resistance (ohm

s)

-40 -30 -20 -10 0 10 20 30 40 50

400

500

600

700 - 0.7 V

- 0.6 V

- 0.5 V

- 0.4 V

- 0.3 V

- 0.2 V - 0.1 VVTG= 0 V

Res

istan

ce (o

hms)

VBG

(volts)

VDS=10mV

Observation of energy gap in Bilayer graphene

γ1

γ1

k

j=2

j=1

j=1

j=2

s=1

s= -1

g∆

sjkε

∆V

( ) ( )( )2 22 2g 1 1 = γ V / γ V∆ ∆ + ∆

( )blg blgV = e E d∆ ×Potential energy difference between two layers

1 1TG BGn , n

2 2TG BGn , n

dblg

2 2TG BG

blgblg blg

n nEε ε

= −

VTG

VBG

( ) ( )blg blg

TG TG BG BGblg d / λ d / λ

blg blg

C V C VEε 1 ε 1e e

= −+ +

λ = infinity implies unscreened situation

Top gate

Back gate

blg

ind 1 2TG TG TG

-d / λ2 1TG TG

n n n

n n e

= +

=

ind TG TGTG

C Vne

=

1 2top TG TG TGblg

blg blg blg

n n nE2ε 2ε 2ε

e e e= − +

In presence of both top and back gate the electric field between two carbon layers

Electric field due to top gate alone

λ=5 Aoo

We have used

λ=5 Aoo

Screening length

-40 -30 -20 -10 0 10 20 30 40 50

400

500

600

700 - 0.7 V

- 0.6 V

- 0.5 V

- 0.4 V

- 0.3 V

- 0.2 V- 0.1 VVTG= 0 V

R

esist

ance

(ohm

s)

VBG (volts)

Observation of energy gap in Bilayer graphene

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.10

20406080

100120140160

With screening No screening

∆ g(meV

)

VTG (volts)

I DS

(mA

)

VTG – VDirac (volts)TG VDS (volts)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0

0.5

1.0

1.5

2.0

2.5 TG VTG - VDirac = 1 V 0.8 V 0.7 V 0.5 V 0.4 V 0.2 V 0.0 V - 0.2 V

I DS (m

A)

VDS (volts)

Current Saturation in Current Saturation in bilayerbilayer????

B. Chakraborty, Anindya Das and A.K Sood (2009)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

3

2

1

electrons and holes

electrons only

VTG- VDirac= 0.5 volts

I DS(m

A)

VDS

(volts)

TG

Formation of Formation of pp--nn junction :Simultaneous junction :Simultaneous ee--hh injunctioninjunction

Drain current (Id) as a function of source-to-drain voltage (Vsd)for Vgs-top = - 0.3 V, -0.8 V, -1.3V,-1.8V, -2.3V and -2.8V(from bottom to top)

Nature Nanotech. 3, 654(2008)

dVv µE=µd

dx=

L

DS d0

WI e n( )v ( )L

x x dx= ∫

DS C DS

C DS

V R I

DSR I

WI = eµ n(V)L

dx−

∫

TG

RC = 55 Ωµ= 770 cm2/V.s

indTGF

TGTG

nEVC

ee

= +

( ) ( )22 indTGn= n nδ +

( )ind 2TG 1 F Fn γ E Eα= +

( )2F

1α=vπ

h

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0

0.5

1.0

1.5

2.0 VBG= 0 V

Model

Experimental

0.5 V

0 VV TG

- V Dirac= 0.7 V

I DS(m

A)

VDS(volts)

( )indTG TG TGn C , Vf=

Modeling nonModeling non--linear Ilinear I--V curvesV curves

B. Chakraborty, Anindya Das and A.K Sood (2009)

Electrically induced Optical Emission from Nanotube FET

Misewich et.al Science 300, 783 (2003)

IR emission maximum when

2d

gVV =

Partial conclusions….1.Combination of TG and BG determines 1.Combination of TG and BG determines top gate top gate capacitance.Thiscapacitance.This value of 1.5 value of 1.5 µµF/cmF/cm22,,which is the highest value so far.which is the highest value so far.

2.Control of Current using top gate and 2.Control of Current using top gate and draindrain--source voltage source voltage –– characteristic of characteristic of MOSFET device.MOSFET device.

3.Can we get THz emission from 3.Can we get THz emission from bilayerbilayerpp--nn junction ,similar to IR emission in CNT?junction ,similar to IR emission in CNT?

Tuning of Fermi level by gating is an ideal probe of e-ph coupling.

Static Born-Oppenheimer fails to account for G band, dynamic corrections large.

Results for G and K point phonon are very different.

Bilayer graphene G band dependence on doping is different from single layer.Determination of subband separation .

Simultaneous injection of electrons and holes in bilayer FET.

Spatially resolved Raman confirms n(x) model.

Devices made of RGO .

ConclusionsConclusions

Thank You