Transcript Slide 1

Graphene bipolar heterojunctions
LG
VLG
VSD
LG
EL
EL
CLG
S
D
CBG
GLs
GLs
1 mm
VBG
Local Gate Region
-Density in GLs can be n or p type
G (e2/h)
7
VLG = -10 V
5
-Density in LGR can be n’ or p’ type
3
We expect two Dirac minima!
Oezyilmaz, Jarrilo-Herrero and Kim PRL (2007)
Related work by Huard et al. PRL (2007)
1
-50
-25
0
25
VBG (V)
50
Graphene heterojunction
Devices
p
n’ p
1 mm
G (e2/h)
potential
50
2 4 6 8 10 12
VBG (V)
25
0
n-p’-n
x
n
n’
n
n
p
n
n-n’-n
potential
-25
-50
p-p’-p
-5
0
VLG (V)
10
5
potential
-10
p-n’-p
5
x
p
p’
p
p
n
p
3
1
-50
-25
0
25
VBG (V)
50
potential
G (e2/h)
7
x
x
Ballistic Quantum Transport in Graphene Heterojunction
Graphene NPN junctions
Klein Tunneling
Novoselov et al, Nat. Phys (2006)
Transmission coefficient
Ttot
Collimation:
(resonance)
f
k2x = pn/L
potential
Perfect transmission
n
p
n
x
np=1x1012 cm2
np=3x1012 cm2
nn=0.5x1012 cm2
Realistic Graphene Heterojunction
Requirements for
Ballistic pn junctions
Mean free path < 100 nm
Smooth electrostatic
n ~ 1012 cm-2
lF ~ 30 nm
ddielectric ~ 20 nm
L ~ 100 nm
• Long Mean free path
-> Ballistic conduction
• Large electric field ->
Small d ->
promote resonance
transmission
T
SEM image of device
Tunneling through smooth pn junction
electrode
f
graphene
1 mm
Cheianov and Fal’ko (2006)
Zhang and Fogler (2008)
Mean free path
~ 50 nm
Tunneling through Classically Forbidden regime
T
20 nm
Transport Ballistic Graphene
Heterojunction
Young and Kim (2008)
electrode
nnn
VBG = 90 V
graphene
12
ppp
10
VBG = -90 V
PN junction resistance
Cheianov and Fal’ko (‘06)
8
npn
pnp
See also Shavchenko et al and Goldhaber-Gordon’s recent preprint
Conductance Oscillation: Fabry-Perot
n1,, k1,
n2,, k2
T
T
R
k1 /k2= sinq’ / sinq
T
q
Df= 2L /cosq’
4
18 V
L
R*
n1,, k1,
6
-18 V
-10
-8
-6
-4
-2
VTG (V)
0 0
2
4
6
8
10
Conductance (mS)
1 mm
Quantum Oscillations in Ballistic Graphene Heterojunction
Resistance Oscillations
5
n1,, k1,
1
0
-1
T
FB
R
L
R*
T
n1,, k1,
q
Magnetoresistance Oscillations (B=0)
0
FB=B L2 sinq ’/cosq ’
Aharonov-Bohm phase:
2
B (T)
nback (1012 cm2)
n2,, k2
dR/dntop ( h/e2 10-15 cm-2)
T
-5
-5
0
ntop
(1012
5
cm2)
dG/dntop (e2/h 10-15 cm-2)
-1
1
0
0
-2
0
2
4
6
VT (V)
)
8
10
(VB=-50 V)
Resonant Magneto-Oscillations in Graphene Heterojunctions
Exp
• Ballistic pn junction
• Collimation
See also Shytoy et al.,
arXiv:0808.0488
Theory
Two fitting parameters: lLGR = 27 nm; lGL= 50 nm
Graphene Electronics
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)
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
Acknowledgement
Meninder Purewal (nanotube)
Kirill Bolotin (suspended graphene)
Melinda Han (nanoribon)
Dmitri Efetov (graphene heterojuncton)
Andrea Young (graphene heterojunction)
Barbaros Oezyilmaz (now at NSU)
Pablo Jarrilo-Herrero (now at MIT)
Collaboration:
Horst Stormer
Funding:
Kim Group Picnic: 2008
Central Park, New York
Variable Range Hopping in Graphene Nanoribbons
E
EF
T
1


d
 T0  1 

Gmax  G0 exp   
 T  


d: dimensionality
Conductance (mS)
100
15 nm 22 nm
3
31 nm
37 nm
1
48 nm
0
70 nm
-2
0.0
0.2
0.4
T-1/3
0.6
31 nm
37 nm
0
48 nm
-1
-1
-1
60
15 nm 22 nm
1
ln(R)
ln(R)
ln(R)
48 nm
40
2
2
2
20
Arrhenius plot
1D VRH
31 nm
0
1
Vg (V)
3
37 nm
4K
15K
100K
200K
300K
0
2D VRH
15 nm 22 nm
1
10
0.1
x
3
W = 37 nm
70 nm
-2
0.0
0.2
0.4
T-1/2
70 nm
-2
0.0
0.1
0.2
T-1
Graphene Quantum Hall Edge State Conduction
LG
EL
GLs
GLs
EL
1 mm
Local Gate Region
simple model (following Haug et al)
Oezyilmaz, et al., PRL (2007) See also Related work by Williams et al. Science (2007)
Temperature Dependent Oscillations
12
nnn
VBG = 90 V
Conductance (mS)
10
8
npn
6
18 V
4
-10
-8
-6
-4
VTG (V)
-2
0