graphene field effect transistor
TRANSCRIPT
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GRAPHENE FIELD EFFECT TRANSISTORS
Prepared By:Ahmed Nader Al-AskalanySumit MohantyMohamed AtwaFaraz KhavariSupervisor:Jan Linnros
4/14/2015
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AGENDA
I. Introduction
II. Theory of Graphene
III. GFET
IV. Conclusion
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INTRODUCTION
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HISTORY OF GRAPHENE
Theoretically predicted 50 years ago
2004 making 2- D sheet
Andre Geim
www.observation-science.com
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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.
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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.
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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
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THEORY OF GRAPHENE
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SUB-AGENDA
2. Monolayer GrapheneA. Real Space StructureB. Reciprocal LatticeC. Electronic Structure
1. The Tight Binding Approximation
2. Results of Tight Binding
3. Bilayer GrapheneA. Real Space StructureB. Reciprocal LatticeC. Electronic Structure
1. The Tight Binding Approximation
2. Results of Tight Binding
Again For:
1. Synthesis of Graphene Reduction of Intercalated GO
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SYNTHESIS OF GRAPHENE
Deceptively Simple?
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RESULTING NUMBER OF LAYERSMonolayer 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 .
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HIGHLIGHTED METHOD: REDUCTION OF EXFOLIATED GRAPHENE OXIDE1. 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
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GRAPHENE: A FAMILIAR STRUCTURE
REVISITED
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MONOLAYER GRAPHENE Real Space Lattice Reciprocal Lattice:
1
2
3,
2 2
3,
2 2
a aa
a aa
2.46
1.423cc
a
aa
Å
Å
1
2
2 2,
3
2 2,
3
ba a
ba a
Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
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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 combineπ orbitals
Magazine, Paintings & Coatings Industry. Graphite: A Multifunctional Additive for Paint and Coatings. October 1, 2003. http://www.pcimag.com/articles/83004-graphite-a-multifunctional-additive-for-paint-and-coatings
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THE TIGHT BINDING APPROXIMATION
π orbitals One 2pz orbital per atom
is the orbital binding energy
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
10
2
2
( )
*( )p
p
fH
f
k
k
ò
ò
01
0
1 ( )
1*( )
s fS
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
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SOLVING THE SECULAR EQUATION FOR MONOLAYER GRAPHENE
Around the Brillouin zone edges K+ and
K-:
2 0
0
( )
1 ( )p f
Es f
k
kò
E p 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 𝜉 𝑝𝑥−𝑖𝑝 𝑦
𝜉 𝑝𝑥+𝑖𝑝𝑦 0 )
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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, Properties and Applications. Springer, 2012
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ANGULAR DEPENDENCY OF SCATTERINGRotating the Pseudospin Degree of Freedom Changing of the wavefunction on A or B
Rewriting the Hamiltonian:
Where:
Angular dependence of scattering:
No backscattering!
Klein tunneling, anisotropic scattering at potential barriers in monolayers
Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
Berry’s phase: Angular range of the scattering probability of the chiral wavefunction in monolayer
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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 Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
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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)21
41 1
2
pE
At low energies:
2 2 2( 1)
1
4
2
p pE
m
Quadratic, Chiral and Massive
Separation between each two bands is
Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
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CHIRALITY IN BILAYER GRAPHENE
Berry’s Phase: 2π
Forward and backward scattering!
2( ) cos ( )w
Raza, Hassan. Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications. Springer, 2012
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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
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)
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GFET
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AGENDA
I. Introduction
II. Theory of Graphene
III. GFETI. Bilayer Graphene Field Effect TransistorII. Graphene Nanoribbon Field Effect Transistor
IV. Conclusion
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BILAYER GRAPHENE FET
1.Breaking the Symmetry2.BLG Electrostatics3.Actual Device4.Charge Neutrality and
Bandgap Tunability5.Optical Absorption Spectra of
BLGFET6.I-V Characteristics
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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)
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BLGFET ELECTROSTATICS
Bottom Gate Top Gate
Interlayer Separation
top gateDielectric constant bottom gate
Dielectric constant
interlayer separation dielectric constant
top gate potential bottom gate potential
𝜎 1 h𝑐 𝑎𝑟𝑔𝑒 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 charge density𝜎 0𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑 h𝑐 𝑎𝑟𝑔𝑒
bottom gate distance top gate distance
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BLGFET ELECTROSTATICS
Asymmetry parameter Electric fields
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BLGFET ELECTROSTATICS
Both layers
Top layer
Electronic Density
Asymmetry parameter
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BLGFET ELECTROSTATICS
At low screening
CharacteristicDensity
(Screening)
DimensionlessScreeningParameter
Layers’ Densities in presence of Asymmetry
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BLGFET ELECTROSTATICS
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ACTUAL DEVICEDual-Gated BLGFET
Gate dielectrics
Channel: W=1.6m L=3m
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
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CHARGE NEUTRALITY AND BANDGAP TUNABILITY
ElectricalDisplacement
Fields
0 at CNP
Bandgap and CNPposition
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OPTICAL ABSORPTION SPECTRA FOR BLGFET
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BLGFET I-V CHARACTERISTICS
Output characteristics: (Vds – Ids)Vb = -100VVd = 0 – 50mVVt = -2 – 6V
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AGENDA
I. Introduction
II. Theory of Graphene
III. GFETI. Bilayer Graphene Field Effect TransistorII. Graphene Nanoribbon Field Effect Transistor
IV. Conclusion
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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.
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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
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GRAPHENE NANORIBBONS
1-D like singularities – CNTs!
Step width decreases with unit cells
Decreasing width of GNR pushes DiracPoints-Bandgap!
Density of states now! (Ennth sub-band)
[7] Lemme, Max C. Current status of graphene transistors, Solid State Phenomena. Vol. 156. 2010.
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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.
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CARRIER CONCENTRATIONCarrier 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.
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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.
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QUANTUM CONDUCTANCELandauer forumula for conductance:
From the experimental data, VBGEF 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..
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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).
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SO HOW DO THEY DO?GNR widthBandgapI-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.
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CONCLUSION
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ITRS AND FUTURE PERSPECTIVE• Silicon Technology Graphene Technology
Over 20 years
static power dissipation
leakage currentproduction costs and power density
Very low Ion/Ioff 270uA/um at VDD=2.5 100nA/um at 0.75v Very high static power dissipationBand 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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QUESTIONS?