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