Graphene Field Effect Transistor

GRAPHENE FIELD EFFECT
TRANSISTORS
Prepared By:
Ahmed Nader Al-Askalany
Sumit Mohanty
Mohamed Atwa
Faraz Khavari
Supervisor:
Jan Linnros
4/14/2015

AGENDA
I. Introduction
II. Theory of Graphene
III. GFET
IV. Conclusion

HISTORY OF GRAPHENE
Theoretically predicted 50 years ago
2004 making 2- D sheet
Andre Geim
www.observation-science.com

MONOLAYER AND BILAYER
GRAPHENE
Monolayer
single layer of Graphite
zero band gap semiconductor
or a semimetal
Linear dispersion relation
Hassan Raza, Hassan, Graphene nanoelectronics:
Metrology, synthesis, properties and applications, Springer
Science & Business Media, 2012.
E. L. Wolf, “Applications of Graphene”, SPRINGER BRIEFS IN MATERIALS, Springer, ISBN 978-3-319-
03945-9, 2014.

MONOLAYER AND BILAYER
GRAPHENE
Bilayer Graphene
same methods to grow bilayer Graphene
Semimetal, high carrier mobility, parabolic
Hassan Raza, Hassan, Graphene nanoelectronics: Metrology, synthesis, properties and applications, Springer Science &
Business Media, 2012.

POTENTIAL APPLICATION
tolerating tension, bending
heat and electricity conductors
Tunable Fermi
Single velocity of 106m/s
high electron mobility, chemically inert
very large area of 2600m2/g
1. organic and CdTe based solar cells
2. transparent electrodes in Touch Screens
3. FET switches& Tunneling FET Devices
4. High Frequency FET
5. Flash memories

SUB-AGENDA
2. Monolayer Graphene
A. Real Space Structure
B. Reciprocal Lattice
C. Electronic Structure
1. The Tight Binding Approximation
2. Results of Tight Binding
3. Bilayer Graphene
A. Real Space Structure
B. Reciprocal Lattice
C. Electronic Structure
1. The Tight Binding Approximation
2. Results of Tight Binding
Again For:
1. Synthesis of Graphene Reduction of Intercalated
GO

SYNTHESIS OF GRAPHENE Deceptively Simple?

RESULTING NUMBER OF LAYERS
Monolayer Graphene
•Micromechanical cleavage of
High-Purity Graphite
•CVD on metal surfaces
•Epitaxial growth on an insulator
(SiC)
•Intercalation of graphite
•Dispersion of graphite in water,
NMP
•Reduction of single-layer
graphene oxide
Bi/Multi-Layer Graphene
•Chemical reduction of exfoliated
graphene oxide (2–6 layers)
•Thermal exfoliation of graphite
oxide (2–7 layers)
•Aerosol pyrolysis (2–40 layers)
•Arc discharge in presence of H2 (2–4
layers)
C. N. R. Rao, Ajay K. Sood. Graphene: Synthesis, Properties, and Phenomena.
John Wiley & Sons, 2013 .

HIGHLIGHTED METHOD:
REDUCTION OF
EXFOLIATED
GRAPHENE OXIDE
1. Oxidation of graphite with strong
oxidizing agents such as KMnO4 and
NaNO3 in H2SO4 /H3PO4
2. Oxygen atoms interleave between the
layers increasing the atomic spacing
from 3.7 to 9.5 Å
3. Ultrasonication and reduction in
dimethyl fluoride or water yields
bilayer
Boya Dai, Lei Fu, Lei Liao, Nan Liu, Kai Yan, Yongsheng Chen, Zhongfan Liu. "High-quality single-
layer graphene via reparative reduction of graphene oxide." Nano Research, 2011: 434-439

GRAPHENE: A FAMILIAR
STRUCTURE REVISITED

MONOLAYER GRAPHENE
Real Space Lattice Reciprocal Lattice:
1
2
3
,
2 2
3
,
2 2
a a
a
a a
a
 
   
 
 
   
 
2.46
1.42
3cc
a
aa

 
Å
Å
1
2
2 2
,
3
2 2
,
3
b
a a
b
a a
 
 
 
  
 
 
  
 
Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012

ELECTRONIC STRUCTURE
OF MONOLAYER
GRAPHENE
sp2 Hybridization:
2s +2px+2py  sp2 hybridization
three sp2 orbitalsCarbon atoms each possess six
electrons:
• Two 1s core electrons
• Four valance electrons:
• 1 2s
• 1 2px
• 12py
• 1 2pz
• 3 sp2 Orbitals
• Adjacent pz orbitals combineπ
orbitals
Magazine, Paintings &
Coatings Industry.
Graphite: A
Multifunctional Additive
for Paint and Coatings.
October 1, 2003.
http://www.pcimag.com/a
rticles/83004-graphite-a-
multifunctional-additive-
for-paint-and-coatings

THE TIGHT BINDING
APPROXIMATION
π orbitals  One 2pz orbital per atom
is the π orbital binding energy
𝛾0 is the nearest-neighbor hopping energy
s0 is a factor accounting for the non-
orthogonality of orbitals on adjacent atomic
sites
and are the structure factor
and its complex conjugate describing
nearest neighbor hopping
0
1
0
2
2
( )
*( )
p
p
f
H
f


 
  
 
k
k
ò
ò
0
1
0
1 ( )
1*( )
s f
S
s f
 
  
 
k
k
Transfer integral matrix
Overlap integral matrix
2 pò
0 ( )s f k 0 *( )s f k
Relation between H and S:
j j jH E S 
Solving the secular equation Ej
 det 0jH E S 

SOLVING THE SECULAR
EQUATION FOR
MONOLAYER GRAPHENE
Around the Brillouin zone edges K+ and K-
:
2 0
0
( )
1 ( )
p f
E
s f

 
 k
k
ò
E p  
𝜐 is the mean electron velocity:
 
03
2
a
 
p is the canonical momentum:
p  k K
Effective Hamiltonian:
Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis,
Properties and Applications. Springer, 2012
𝐻1𝜉 =
0 𝜉𝑝 𝑥 − 𝑖𝑝 𝑦
𝜉𝑝 𝑥 + 𝑖𝑝 𝑦 0

CHIRALITY: NOT ALL FIELD IS
EQUAL
Pseudospin:
H and Eigenstates near each K point  Two
values
Called “Psudospins”
Deg. of freedom for the relative amplitude of the
wavefunction on each sublattice:
All electrons on sublattice A:
Pseudospin “Up”
All electrons on sublattice B:
Pseudospin “Down” Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis,

ANGULAR
DEPENDENCY OF
SCATTERING
Rotating the Pseudospin Degree of
Freedom 𝜑  Changing of the
wavefunction on A or B
Rewriting the Hamiltonian:
𝐻1𝜉 = 𝜐(𝜉𝜎𝑥 𝑝 𝑥 + 𝜉𝜎 𝑦 𝑝 𝑦 = 𝜐𝑝𝛔𝐧
∧
𝟏
Where: 𝐧
∧
𝟏 = 𝜉cos𝜑, sin𝜑, 0
Angular dependence of scattering:
𝑤(𝜑 = cos2
( 𝜑 2
No backscattering!
Klein tunneling, anisotropic scattering at
potential barriers in monolayers
Berry’s phase: Angular range of the scattering probability
of the chiral wavefunction 𝜋 in monolayer

BILAYER GRAPHENE
Real Space Lattice B1 and A2, are directly below or
above each other (dimer sites)
A1 and B2, do not have a
counterpart in the other layer
(Bernal Stacking, AB-Stacking)
0 3.033 eV 
1 0.39 eV 

ELECTRONIC STRUCTURE
OF BILAYER GRAPHENE
• Four atoms per unit cell
• One pz orbital in tight binding model
per atomic site
• We expect 4 bands near zero energy
Solving the Secular Equation:
2 2
( 1)
2
1
4
1 1
2
p
E
 

 

 
    
 
 
At low energies:
2 2 2
( 1)
1
4
2
p p
E
m



   
Quadratic, Chiral and Massive
Separation between each two bands is 𝛾1

CHIRALITY IN
BILAYER
GRAPHENE
Berry’s Phase: 2π
Forward and backward scattering!
2
( ) cos ( )w  

KEY TAKE-AWAYS
Comparison Monolayer Graphene Bilayer Graphene
E-k relation Around the K
points
Linear Dispersion
Number of Bands One Conduction, One
Valance
Two Conduction, Two
Valance, Split by 𝛾1
Bandgap at zero bias No-(opened via additional
confinement)
No-(opened via doping,
sandwiching or application
of field)
Scattering Anisotropic forward
scattering (Berry’s Phase π)
Anisotropic forward and
backward scattering
(Berry’s Phase 2π)

AGENDA
I. Introduction
II. Theory of Graphene
III. GFET
I. Bilayer Graphene Field Effect Transistor
II. Graphene Nanoribbon Field Effect Transistor
IV. Conclusion

BILAYER GRAPHENE FET
1.Breaking the Symmetry
2.BLG Electrostatics
3.Actual Device
4.Charge Neutrality and
Bandgap Tunability
5.Optical Absorption Spectra of
BLGFET
6.I-V Characteristics

BREAKING THE SYMMETRY?
A1 and B2 symmetry
Zero bandgap at K point
Perpendicular E breaks symmetry
A1 and B2 at different energies
Bandgap opened
Fermi level position (effective
doping)

BLGFET ELECTROSTATICS
Bottom Gate Top Gate
𝐶0 Interlayer Separation
𝜀𝑡 top gate
Dielectric constant𝜀 𝑏 bottom gate
Dielectric constant
𝜀 𝑟 interlayer separation dielectric constant
𝑉𝑡 top gate potential𝑉𝑏 bottom gate potential
𝜎1 𝑐ℎ𝑎𝑟𝑔𝑒 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝜎2 charge density𝜎0 𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑 𝑐ℎ𝑎𝑟𝑔𝑒
𝐿 𝑏 bottom gate distance 𝐿 𝑡 top gate distance

Asymmetry parameter Electric fields

Both layers
Top layer
Electronic Density
Asymmetry parameter

At low screening
Characteristic
Density
(Screening)
Dimensionless
Screening
Parameter
Layers’ Densities in presence of Asymmetr

ACTUAL DEVICE
Dual-Gated BLGFET
Gate dielectrics
Channel: W=1.6𝜇m L=3𝜇m
Organic seed layer: 9 nm (HfO2
growth, enhanced mobility)
HfO2: 10 nm
SiO2: 300nm
Max. bandgap: 250 mV
Ion/Ioff=100 at RT and 2000 at
LT

CHARGE NEUTRALITY AND
BANDGAP TUNABILITY
Electrical
Displacement
Fields
0 at CNP
Bandgap and CNP
position

OPTICAL ABSORPTION SPECTRA
FOR BLGFET

BLGFET I-V CHARACTERISTICS
Output characteristics: (Vds –
Ids)
Vb = -100V
Vd = 0 – 50mV
Vt = -2 – 6V

GRAPHENE CONFIGURATIONS
Electronic Confinement
Zigzag – Metallic – Edge State formation
Armchair – Metallic or Semiconductor (bandgap)
Fraternal to Carbon Nanotubes
[6] Reddy, Dharmendar, et al., Graphene field-effect transistors, Journal of Physics D: Applied Physics 44.31 (2011): 313001, 2011.
[7] Chung, H. C., et al., Exploration of edge-dependent optical selection rules for graphene nanoribbons, Optics express 19.23: 23350-23363, 2011.

TIGHT BINDING APPROXIMATION
DOS (low energy) near these Dirac points:
Remember?
Hamiltonian Dirac-like-Hamiltonian
[7] Raza, Hassan, Graphene nanoelectronics: Metrology, synthesis, properties and applications, Springer Science & Business Media, 2012.
[8] Davies, John H., The physics of low-dimensional semiconductors: an introduction, Cambridge university press, 1997

GRAPHENE NANORIBBONS
1-D like singularities – CNTs!
Step width decreases with unit cells
Decreasing width of GNR pushes Dirac
Points-Bandgap!
Density of states now!
(Ennth sub-band)
[7] Lemme, Max C. Current status of graphene transistors, Solid State Phenomena. Vol. 156. 2010.

BANDGAP VS WIDTH
Bandgap increases with width of GNR
Device characteristics enhanced:
ON/OFF current(low temp)
Switching speed
Upto 100meV with 10nm width!
Comparison with CNTs
[7] Lemme, Max C. Current status of graphene transistors, Solid State Phenomena. Vol. 156. 2010.

CARRIER CONCENTRATION
Carrier concentration adding up all the sub-bands:
Remember old brother Davies?
3-D density looked like-
[8] Davies, John H., The physics of low-dimensional semiconductors: an
introduction, Cambridge university press, 1997
[9] Tahy, Kristf., 2D Graphene and Graphene Nanoribbon Field Effect
Transistors, Diss. University of Notre Dame, 2012.

HOW DOES THE DEVICE LOOK
LIKE?
[9] Tahy, Kristf., 2D Graphene and Graphene Nanoribbon Field Effect Transistors, Diss. University of Notre Dame, 2012.
[10] Wang, Xinran, et al. "Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors." Physical review letters 100.20 (2008): 206803.

QUANTUM CONDUCTANCE
Landauer forumula for conductance:
From the experimental data,
VBGEF to know transmission
Equating charge densities in channel:
Transmission (t) was found to be around 0.02
But why is this important?
F
[9] Tahy, Kristf., 2D Graphene and Graphene Nanoribbon Field Effect Transistors, Diss. University of Notre Dame, 2012..

EDGE ROUGHNESS
Roughness (r)Scattering
Parameterizes transmission and hence conductance
Proportional
to width of GNR
Depreciates the ON/OFF current
Hence, the dilemma,
Bandgap or performance?
[10] Basu, D., et al., Effect of edge roughness on electronic transport in graphene nanoribbon channel metal-oxide-semiconductor field-effect transistors, Applied Physics Letters 92.4, (2008).

SO HOW DO THEY DO?
GNR widthBandgapI-V
Device benchmarked at room
temperatures
Compatible with planar IC manufacturing
Pragmatic solution to traditional CMOS
Limitations:
Lithography and patterning
Edge termination/roughness
Non classical switching
Integration with Si MOSFET
[10] Wang, Xinran, et al. "Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors." Physical review letters 100.20 (2008): 206803.

ITRS AND FUTURE PERSPECTIVE
• Silicon Technology Graphene TechnologyOver 20 years
static power dissipation
leakage current
production costs and power density
Very low Ion/Ioff
270uA/um at VDD=2.5
100nA/um at 0.75v
Very high static power dissipation
Band gap engineering
GFETs for CMOS logic
mobility
Vt
controlling contact resistance
ITRS “Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems”, Royal Society of
Chemistry, Nanoscale, 2015

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