072008 ERG WG Carbon Kim

Report
Toward Carbon Based Electronics
Philip Kim
Department of Physics
Columbia University
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
SP2 Carbon: 0-Dimension to 3-Dimension
p
Atomic orbital sp2
0D
Fullerenes (C60)
1D
Carbon Nanotubes
2D
Graphene
3D
Graphite
s
Graphene : Dirac Particles in 2-dimension
Band structure of graphene (Wallace 1947)
E
Energy
hole
kx'
ky'
electron
ky
kx

E   v F k 
Zero effective mass particles moving with a constant speed vF
Single Wall Carbon Nanotube
Allowed states
Semiconducting nanotube
E
Metallic nanotube
E
ky
ky
k1D
kx
k1D
kx
Eg ~ 0.8 ev / d (nm)
Extremely Long Mean Free Path in Nanotubes
Multi-terminal Device with Pd contact
7
6
R (kW)
5
4
3
Resistance (kW)
400
2
T = 250 K
400
200
T0= 250 K
0
20
40
60
L (mm)
R (kW)
100
200
8
r = 8 kW/mm
7
6
5
le ~ 1 mm
4
30
0
2
20
R ~ RQ
60
h
R(L) 
8
7
6
M. Purewall, B. Hong, A. Ravi, B. Chnadra, J. Hone and P. Kim, PRL (2007)
40
Length (mm)
10
* Scaling behavior of resistance:
R(L)
R~L
Ne
2
h

Ne
L
2
le
5
2
0.1
4
6 8
2
4
6 8
1
2
4
6 8
10
L (mm)
Room temperature mean free path > 0.5 mm
Isd (mA)
Nanotube FET
-1.2
-0.8
-0.4
0
Vsd (V)
Schottky barrier switching
Band gap:
0.5 – 1 eV
On-off ratio:
~ 106
Mobility:
~ 100,000 cm2/Vsec @RT
Ballistic @RT ~ 300-500 nm
Fermi velocity: 106 m/sec
Max current density
> 109 A/cm2
Ph. Avouris et al, Nature Nanotechnology 2, 605 (2007)
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 meV/dB @RT
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
Aligned growth of Nanotubes
IBM, Avouris group
Rodgers, UIUC
Nanotube Ring Oscillators
Artistic dream (DELFT)
Discovery of Graphene
Large scale growth efforts:
CVD, MBE, chemical synthesis
Growth of Graphene Papers
factor 4.5 / year
Discovery of QHE in graphen
Scotch tape method
Graphene Mobility
Mechanically exfoliated graphene
GaAs HEMT
Modulate Doped GaAs:
Pfeiffer et al.
10
•Ripples
•Substrate (charge trap)
•Absorption
•Structural defects
TC17
TC12
10
Mobility (cm2/V sec)
Scattering Mechanism?
5
4
TC145
TC130
-4
-2
0
2
n (1012 cm-2)
Tan et al. PLR (2007)
4
10
3
Enhanced Room Temperature Mobility of Graphene
Graphene mobility: > 100,000 cm2/Vsec @ room temperature
6
after annealing
Resistance at High Density
100
Strong density dependence!
holes
electrons
|n|=2X1011 cm-2
90
10
5
before annealing
R (W)
Mobility (cm2/V sec)
10
0.24 W/K
80
0.13 W/K
70
60
unsuspended best
10
0
50
100
150
200
250
T (K)
4
-0.2
0.0
0.2
Density ( 1012 cm-2)
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)
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)
Graphene FET: High Saturation Velocity
Meric, Han, Young, Kim, and Shepard (2008)
Saturation velocity
Vtop = -3 V
Vtop = -2 V
Vtop = -1.5 V
Vtop = 0 V
VtopDirac
= 2 V @ Vg = -40 V
vsat (108 cm/s)
0.8
v sat  v F
0.6
W
0.4
EF
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
EF (eV)
For comparison:
vFermi = 1x108 cm/s
Silicon: 1x107 cm/s
GaAs: 0.7x107 cm/s
v drift
1
 ( mE )
1
 v sat
1
Operation current density > 1 mA/mm
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)
Graphene Nanostructures
Quantum Dot
Geim (Manchester)
Graphene nanoribbons
& nanoconstrictions
AB Ring
Morpurgo (DELFT)
Goldhaber-Gordon (Stanford)
Graphene PN junctions
Graphene Side Gates
Ensslin (ETH)
Kim (Columbia)
Graphene with local barrier
Marcus (Harvard)
Graphene Nanoribbons: Confined Dirac Particles
Gold electrode
Graphene
Dirac Particle Confinement
ky 
W
3 p
W
W
ky 
1 mm
10 nm < W < 100 nm
2 p
W
x
ky 
y
1p
W
Graphene nanoribbon theory partial list
W
Zigzag ribbons
E   vF
Dk y 
k x  (p n / W )
2
p
W
2
Egap~ hvF Dk ~ hvF/W
Scaling of Energy Gaps in Graphene Nanoribbons
Eg (meV)
100
10
Eg = E0 /(W-W0)
P1
P2
P3
P4
D1
D2
1
0
30
60
W (nm)
90
Han, Oezyilmaz, Zhang and Kim PRL (2007)
Top Gated Graphene Nano Constriction
SEM image of device
Top gate
drain
Hf-oxide
drain
source
top gate
source
graphene
graphene
1 mm
30 nm wide x 100 nm long
SiO2
Back gate
75
VBG (V)
G (e2/h)
50
OFF
10-1
10-2
10-3
25
0
10-4
-25
10-5
-50
10-6
-75
G (e2/h)
-8
-4
0
VLG (V)
4
8
10-7 10-5 10-3 10-1
-8
-4
0
VLG (V)
4
8
Graphene Nanoribbons Edge Effect
Crystallographic Directional Dependence
Son, et al, PRL. 97, 216803 (2006)
Eg (meV)
40
20
2mm
0
Rough Graphene Edge Structures
0
30
60
q (degree)
90
Localization of Edge Disordered Graphene Nanoribbons
Querlioz et al., Appl. Phys. Lett. 92, 042108 (2008)
See also:
Gunlycke et al, Appl. Phys. Lett. 90 (14), 142104 (2007).
Areshkin et al, Nano Lett. 7 (1), 204 (2007)
Lherbier et al, PRL 100 036803 (2008)
Transport ‘gap’
Variable Range Hopping in Graphene Nanoribbons
E
G max
EF
T
1


d
 T 0  1 

 G 0 exp  

 T 



d: dimensionality
Conductance (mS)
100
W = 37 nm
10
4K
15K
100K
200K
300K
1
0.1
0
x
3
1D VRH
15 nm 22 nm
3
3
31 nm
31 nm
48 nm
0
37 nm
1
48 nm
0
70 nm
-2
0.0
0.2
0.4
T-1/3
0.6
60
Arrhenius plot
15 nm 22 nm
31 nm
37 nm
1
0
48 nm
-1
-1
-1
ln(R)
37 nm
1
ln(R)
ln(R)
2
2
2
40
Vg (V)
2D VRH
15 nm 22 nm
20
70 nm
-2
0.0
0.2
0.4
T-1/2
70 nm
-2
0.0
0.1
0.2
T-1
Graphene Electronics: Challenges
Pros:
High mobility
tunability of band gaps
High on-off ratio
High critical current density
Small channel length
Small gate capacitance
Large Fermi velocity
This can be turned into advantage:
doping site, functionality, and etc…
Con:
Controlled growth
Edge control
Aligned growth of Nanotubes
Rodgers, UIUC
Artistic dream (DELFT)
Graphene Electronics: Conventional & Non-conventional
Conventional Devices
FET
Band gap engineered
Graphene nanoribbons
Graphene quantum dot
(Manchester group)
Nonconventional Devices
Graphene Veselago lense
Cheianov et al. Science (07)
Graphene Spintronics
Graphene psedospintronics
Son et al. Nature (07)
Trauzettel et al. Nature Phys. (07)
Carbon Nanotube Superlattice
Purewal, Takekosh, Jarillo-Herrero, Kim (2008)
dI/dV (mS)
Pd (under HfO2)
0.2
SWCNT
(under HfO2)
3
0.0
1.0
1.5
Pd (over HfO2)
1
2
1
2.0
Top Gate (V)
HfO2 on SiO2/Si+
1 mm
Pd (under HfO2)
0
Conductance (mS)
Top Gate (V)
4
20 nm
60 nm
-54
-50
-45
-40
Back Gate (V)
Kouwenhoven PRL (1992)
Ballistic Quantum Transport in Graphene Heterojunction
Realistic smooth potential distribution
Requirements for
Experimental
Observation:
• Small d ->
better collimination
Graphene NPN junctions
potential
Tunneling through smooth pn junction
n
p
n
SEM image of device
x
electrode
Cheianov and Fal’ko (2006)
Ballistic transport in the barrier
Klein Tunneling
• Long Mean free path
-> Ballistic conduction
graphene
Zhang and Fogler (2008)
Total Internal Reflection
1 mm
Novoselov et al (2006)
Top gate width: 50 nm < Lm
Transmission coef
Transport Ballistic Graphene Heterojunction
Young and Kim (2008)
Mean free path
~ 200 nm
electrode
graphene
12
nnn
VBG = 90 V
ppp
VBG = -90 V
10
PN junction resistance
Zhang and Fogler (2008)
8
npn
pnp
See also Shavchenko et al and Goldhaber-Gordon’s recent preprint
Conductance Oscillation: Fabry-Perot
n1,, k1,
n2,, k2
T
6
T
R
n1,, k1,
k1 /k2= sinq’ / sinq
T
q
Df= 2L /cosq’
4
18 V
L
R*
-18 V
-10 -8
-6
-4
-2
0 0
VTG (V)
2
4
6
8
10
Conductance (mS)
Junction length
< 100 nm
1 mm
Quantum Oscillations in Ballistic Graphene Heterojunction
Oscillation persist high temperature!
1
0
-1
100
G (e /h)
0
2
nback (1012 cm2)
105
dR/dntop ( h/e2 10-15 cm-2)
5
1
Amplitude
Resistance Oscillations
0
0
20
40
60
T (K)
95
80K
60K
43K
30K
16K
4K
90
-5
-5
0
ntop (1012 cm2)
5
85
-10
-8
-6
VTG (V)
-4
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

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