1. Toward Carbon Based Electronics
Philip Kim
Department of Physics
Columbia University

2. Outline: Carbon Based Electronics
Material Platform: Low dimensional graphitic systems
1-D: Carbon Nanotubes (since 1991)
2-D: Graphene (since 2004)
Device Concepts
Conventional:
(extended) CMOS, SET
Non-Conventional:
Quantum Interference, Spintronics, valleytronics

3. SP2 Carbon: 0-Dimension to 3-Dimension
Atomic orbital sp2 s p 0D 1D 2D 3D
Fullerenes (C60)
Carbon Nanotubes
Graphene
Graphite

4. Graphene : Dirac Particles in 2-dimension
Band structure of graphene (Wallace 1947)
kx'
ky' E kx ky
Energy
hole
electron
Zero effective mass particles moving with a constant speed vF

5. Single Wall Carbon Nanotubeky kx
Allowed states
Metallic nanotube E
k1D
Semiconducting nanotube
Eg ~ 0.8 ev / d (nm)

6. Extremely Long Mean Free Path in Nanotubes
Multi-terminal Device with Pd contact
L (mm)
R (kW)
T = 250 K
R (kW)
L (mm)
Length (mm)
Resistance (kW)
T = 250 K
r = 8 kW/mm
R ~ L
le ~ 1 mm
R ~ RQ
* Scaling behavior of resistance:
R(L)
Room temperature mean free path > 0.5 mm
M. Purewall, B. Hong, A. Ravi, B. Chnadra, J. Hone and P. Kim, PRL (2007)

7. Nanotube FET Band gap: 0.5 – 1 eV On-off ratio: ~ 106
Vsd (V)
-0.4
-0.8
-1.2
Isd (mA)
Ph. Avouris et al, Nature Nanotechnology 2, 605 (2007)
Schottky barrier switching
Band gap: 0.5 – 1 eV
On-off ratio: ~ 106
Mobility: ~ 100,000
~ nm
Fermi velocity: 106 m/sec
Max current density > 109 A/cm2

8. Advantages of CNTFET
Thin body (1-2 nm) -> suppressed short channel effect
channel length ~ 10 nm has been demonstrated
Javey et al. PRL (2004).
No-dangling bond at surface -> high k-dielectric compatible
Cg ~ CQ can be attainable; small RC, low energy
Appenzeller et al., PRL (2002)
Novel architecture ->
Band-to-band tunneling FET:
subthreshold slop ~ 40

9. Nanotube Electronics: Challenges
Pros:
High mobility
High on-off ratio
High critical current density
Small channel length
Small gate capacitance
Large Fermi velocity
Con:
Controlled growth
graphene
Rodgers, UIUC
Aligned growth of Nanotubes
Artistic dream (DELFT)
IBM, Avouris group
Nanotube Ring Oscillators

10. Discovery of Graphene Large scale growth efforts:
CVD, MBE, chemical synthesis

11. Growth of Graphene Papers
Jun 07
Dec 06
Mar 07
Sep 06
Jun 06
Mar 06
Dec 05
Sep 05
Jun 05
Mar 05
Dec 04
Sep 04
Sep 07
Jun 07
Dec 06
Mar 07
Sep 06
Jun 06
Mar 06
Dec 05
Sep 05
Jun 05
Mar 05
Dec 04
Sep 04
Sep 07
factor 4.5 / year
Discovery of QHE in graphen
Scotch tape method

12. Graphene Mobility GaAs HEMT Scattering Mechanism? Ripples
Modulate Doped GaAs:
Pfeiffer et al.
GaAs HEMT
n (1012 cm-2)
Mobility (cm2/V sec)
TC17
TC12
TC145
TC130
Mechanically exfoliated graphene
Scattering Mechanism?
Ripples
Substrate (charge trap)
Absorption
Structural defects
Tan et al. PLR (2007)

13. Enhanced Room Temperature Mobility of Graphene
Graphene mobility: > 100,000 room temperature
unsuspended best
before annealing
after annealing
Density ( 1012 cm-2)
Mobility (cm2/V sec)
T (K)
R (W)
|n|=2X1011 cm-2
Resistance at High Density
0.24 W/K
0.13 W/K
Strong density dependence!
High mobility materials have been under intensive research as an alternative to Silicon for higher performance
mobility: Si (1,400 cm2/Vsec), InSb (77,000 cm2/Vsec)

14. Graphene FET characteristics
Low temperature direct atomic layer deposition (ALD) of HfO2 as high-κ gate dielectric
Top-gate electrode is defined with a final lithography step.
I-V measurements at two different back gate voltages show a distinct “kink” for different top-gate voltages
Transconductance can be as high as gm = 328μS (150μS/μm)
Poor on-off ratio: ~ 5-10
due to zero gap in bulk
Meric, Han, Young, Kim, and Shepard (2008)

15. Graphene FET: High Saturation Velocity
Meric, Han, Young, Kim, and Shepard (2008)
Vtop = 0 V
Vtop = -1.5 V
Vtop = -2 V
Vtop = -3 V
VtopDirac = 2 Vg = -40 V
EF (eV)
vsat (108 cm/s)
Saturation velocity
GaAs: 0.7x107 cm/s
vFermi = 1x108 cm/s
For comparison:
Silicon: 1x107 cm/s
Operation current density > 1 mA/mm

16. Graphene Device Fabrication
Developing Graphene Nanostructure Fabrication Process
graphene
Contacts:
PMMA
EBL
Evaporation
Graphene patterning:
HSQ
EBL
Development
Graphene etching:
Oxygen plasma
Local gates:
ALD HfO2
EBL
Evaporation
Graphene device structure with local gate control
Oezyilmaz, Jarrilo-Herrero and Kim APL (2007)

17. Graphene Nanostructures
Quantum Dot
AB Ring
Graphene with local barrier
Goldhaber-Gordon (Stanford)
Geim (Manchester)
Morpurgo (DELFT)
Graphene nanoribbons
& nanoconstrictions
Graphene PN junctions
Graphene Side Gates
Ensslin (ETH)
Marcus (Harvard)
Kim (Columbia)

18. Graphene Nanoribbons: Confined Dirac Particles
1 mm
Gold electrode
Graphene
10 nm < W < 100 nm W W
Dirac Particle Confinement x y
Egap~ hvF Dk ~ hvF/W W
Zigzag ribbons
Graphene nanoribbon theory partial list

19. Scaling of Energy Gaps in Graphene Nanoribbons
W (nm)
Eg (meV) 30 60 90 1 10
100 P1 P2 P3 P4 D1 D2
Eg = E0 /(W-W0)
Han, Oezyilmaz, Zhang and Kim PRL (2007)

20. Top Gated Graphene Nano Constriction
SEM image of device
source
drain
top gate
graphene
1 mm
Hf-oxide
30 nm wide x 100 nm long
drain
source
graphene
SiO2
Back gate -8 -4 4 8 75 50 25
-25
-50
-75
VLG (V)
VBG (V)
10-7
10-5
10-3
10-1
G (e2/h) -8 -4 4 8
10-6
10-5
10-4
10-3
10-2
10-1
VLG (V)
G (e2/h)
OFF

21. Graphene Nanoribbons Edge Effect
Crystallographic Directional Dependence 30 60 90 20 40
Eg (meV)
q (degree)
Son, et al, PRL. 97, (2006)
2mm
Rough Graphene Edge Structures

22. Localization of Edge Disordered Graphene Nanoribbons
Querlioz et al., Appl. Phys. Lett. 92, (2008)
See also:
Gunlycke et al, Appl. Phys. Lett. 90 (14), (2007).
Areshkin et al, Nano Lett. 7 (1), 204 (2007)
Lherbier et al, PRL (2008)
Transport ‘gap’

23. Variable Range Hopping in Graphene Nanoribbons
Conductance (mS)
Vg (V)
W = 37 nm
0.1 1 10
100 60 40 20 4K
15K
100K
200K
300K E
d: dimensionality T EF x
ln(R)
T-1/3
70 nm
48 nm
37 nm
22 nm
15 nm
31 nm
2D VRH
ln(R)
T-1/2
70 nm
48 nm
37 nm
22 nm
15 nm
31 nm
1D VRH
T-1
ln(R) 3 2 1 -1 -2
0.2
0.1
0.0
Arrhenius plot
70 nm
48 nm
37 nm
22 nm
15 nm
31 nm

24. Graphene Electronics: Challenges
Pros:
High mobility
High on-off ratio
High critical current density
Small channel length
Small gate capacitance
Large Fermi velocity
Con:
Controlled growth
tunability of band gaps
Edge control
Rodgers, UIUC
Aligned growth of Nanotubes
This can be turned into advantage:
doping site, functionality, and etc…
Artistic dream (DELFT)

25. Graphene Electronics: Conventional & Non-conventional
Conventional Devices
Band gap engineered
Graphene nanoribbons
Graphene quantum dot
(Manchester group)
FET
Nonconventional Devices
Son et al. Nature (07)
Graphene Spintronics
Trauzettel et al. Nature Phys. (07)
Graphene psedospintronics
Cheianov et al. Science (07)
Graphene Veselago lense

26. Carbon Nanotube Superlattice
Purewal, Takekosh, Jarillo-Herrero, Kim (2008)
Conductance (mS) 1
Pd (under HfO2)
Pd (over HfO2)
SWCNT
(under HfO2)
HfO2 on SiO2/Si+
20 nm
60 nm
1 mm
Kouwenhoven PRL (1992)

27. Realistic smooth potential distribution Graphene NPN junctions
Ballistic Quantum Transport in Graphene Heterojunction
Realistic smooth potential distribution
Requirements for
Experimental
Observation:
Small d ->
better collimination
Graphene NPN junctions
Long Mean free path
-> Ballistic conduction n p x
potential
Cheianov and Fal’ko (2006)
Zhang and Fogler (2008)
Tunneling through smooth pn junction
Top gate width: 50 nm < Lm
graphene
electrode
1 mm
SEM image of device
Klein Tunneling
Transmission coef
Novoselov et al (2006)
Ballistic transport in the barrier
Total Internal Reflection

28. Transport Ballistic Graphene Heterojunction
Young and Kim (2008)
VTG (V)
-10 -2 -4 -6 -8 10 8 6 4 2
Conductance (mS) 12
graphene
electrode
1 mm
Mean free path
~ 200 nm
ppp
pnp
npn
nnn
18 V
-18 V
VBG = 90 V
Junction length
< 100 nm
VBG = -90 V
PN junction resistance
Zhang and Fogler (2008)
See also Shavchenko et al and Goldhaber-Gordon’s recent preprint q´ q L
n1,, k1, T R R*
n2,, k2
Conductance Oscillation: Fabry-Perot
k1 /k2= sinq’ / sinq
Df= 2L /cosq’

29. Quantum Oscillations in Ballistic Graphene Heterojunction
Oscillation persist high temperature!
Resistance Oscillations
ntop (1012 cm2)
nback (1012 cm2) 5 -5 1 -1
dR/dntop ( h/e cm-2)

30. Conclusions
Carbon nanotube FET is mature technology demonstrating substantial improvement over Si CMOS
Controlled growth and scaling up of CNTFET remains as a challenge
Graphene provides scaling up solution of carbon electronics with high mobility
Controlled growth of graphene and edge contol remains as a challenge
Novel quantum device concepts have been demonstrated on graphene and nanontubes