Graphene Field Effect Transistor

GRAPHENE FIELD EFFECT TRANSISTORS

Prepared By:Ahmed Nader Al-AskalanySumit MohantyMohamed AtwaFaraz KhavariSupervisor:Jan Linnros

4/14/2015

AGENDA

I. Introduction

II. Theory of Graphene

III. GFET

IV. Conclusion

INTRODUCTION

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

THEORY OF GRAPHENE

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

SYNTHESIS OF GRAPHENE

Deceptively Simple?

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 .

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

GRAPHENE: A FAMILIAR STRUCTURE

REVISITED

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

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

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

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 )

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

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

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

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

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

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)

GFET

AGENDA

I. Introduction

II. Theory of Graphene

III. GFETI. Bilayer Graphene Field Effect TransistorII. Graphene Nanoribbon Field Effect Transistor

IV. Conclusion

BILAYER GRAPHENE FET

1.Breaking the Symmetry2.BLG Electrostatics3.Actual Device4.Charge Neutrality and

Bandgap Tunability5.Optical Absorption Spectra of

BLGFET6.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

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

BLGFET ELECTROSTATICS

Asymmetry parameter Electric fields

BLGFET ELECTROSTATICS

Both layers

Top layer

Electronic Density

Asymmetry parameter

BLGFET ELECTROSTATICS

At low screening

CharacteristicDensity

(Screening)

DimensionlessScreeningParameter

Layers’ Densities in presence of Asymmetry

BLGFET ELECTROSTATICS

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

CHARGE NEUTRALITY AND BANDGAP TUNABILITY

ElectricalDisplacement

Fields

0 at CNP

Bandgap and CNPposition

OPTICAL ABSORPTION SPECTRA FOR BLGFET

BLGFET I-V CHARACTERISTICS

Output characteristics: (Vds – Ids)Vb = -100VVd = 0 – 50mVVt = -2 – 6V

AGENDA

I. Introduction

II. Theory of Graphene

III. GFETI. Bilayer Graphene Field Effect TransistorII. Graphene Nanoribbon Field Effect Transistor

IV. Conclusion

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 DiracPoints-Bandgap!

Density of states now! (Ennth 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 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.

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 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..

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 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.

CONCLUSION

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

QUESTIONS?