some things you might be interested in knowing about graphene
DESCRIPTION
some things you might be interested in knowing about Graphene. FEW EXAMPLES OF MOST RECENT WORK @ MANCHESTER. Serge Morozov unpublished. Physics at the Dirac Point (Lifshitz transition in bilayer). suspended devices. 2 m. 2 K. resistivity (k). 20. 5 K. 10. Temperature. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/1.jpg)
some things you might be interested in knowing
about Graphene
FEW EXAMPLES OF MOST RECENT WORK
MANCHESTER
Physics at the Dirac Point
(Lifshitz transition in bilayer)
Serge Morozovunpublished
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m2 K
level degeneracy lifted lt 01T
SdH oscillations start lt 100Gquantum mobilities gt 1000000 cm2Vs
transport mobilities gt 1000000 cm2Vs remnant doping lt 109 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
R (
k)
200
800
600
400
B=05T
zero B
T = 2K
GAP IS OPEN BY MAGNETIC FIELDfor some devices lt1T
(VALLEY GAP)
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m
fractional QHE
Manchester unpublished
first reported by Andreirsquos group Nature rsquo09Kimrsquos group Nature rsquo09 Laursquos group arxiv 2010
million mobilities but the quality of quantization
remains really bad
need 4-p
robe d
evices
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
(k
)
4
16
8
zero BT = 2K
12
can smoothly pass from one electron to one hole
Fermi energy scale lt 1 meV
14
10
(k
)
-5
n (108cm-2)0
~T
remnant doping lt 109 cm-2
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
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- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 2: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/2.jpg)
FEW EXAMPLES OF MOST RECENT WORK
MANCHESTER
Physics at the Dirac Point
(Lifshitz transition in bilayer)
Serge Morozovunpublished
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m2 K
level degeneracy lifted lt 01T
SdH oscillations start lt 100Gquantum mobilities gt 1000000 cm2Vs
transport mobilities gt 1000000 cm2Vs remnant doping lt 109 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
R (
k)
200
800
600
400
B=05T
zero B
T = 2K
GAP IS OPEN BY MAGNETIC FIELDfor some devices lt1T
(VALLEY GAP)
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m
fractional QHE
Manchester unpublished
first reported by Andreirsquos group Nature rsquo09Kimrsquos group Nature rsquo09 Laursquos group arxiv 2010
million mobilities but the quality of quantization
remains really bad
need 4-p
robe d
evices
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
(k
)
4
16
8
zero BT = 2K
12
can smoothly pass from one electron to one hole
Fermi energy scale lt 1 meV
14
10
(k
)
-5
n (108cm-2)0
~T
remnant doping lt 109 cm-2
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 3: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/3.jpg)
Physics at the Dirac Point
(Lifshitz transition in bilayer)
Serge Morozovunpublished
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m2 K
level degeneracy lifted lt 01T
SdH oscillations start lt 100Gquantum mobilities gt 1000000 cm2Vs
transport mobilities gt 1000000 cm2Vs remnant doping lt 109 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
R (
k)
200
800
600
400
B=05T
zero B
T = 2K
GAP IS OPEN BY MAGNETIC FIELDfor some devices lt1T
(VALLEY GAP)
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m
fractional QHE
Manchester unpublished
first reported by Andreirsquos group Nature rsquo09Kimrsquos group Nature rsquo09 Laursquos group arxiv 2010
million mobilities but the quality of quantization
remains really bad
need 4-p
robe d
evices
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
(k
)
4
16
8
zero BT = 2K
12
can smoothly pass from one electron to one hole
Fermi energy scale lt 1 meV
14
10
(k
)
-5
n (108cm-2)0
~T
remnant doping lt 109 cm-2
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 4: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/4.jpg)
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m2 K
level degeneracy lifted lt 01T
SdH oscillations start lt 100Gquantum mobilities gt 1000000 cm2Vs
transport mobilities gt 1000000 cm2Vs remnant doping lt 109 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
R (
k)
200
800
600
400
B=05T
zero B
T = 2K
GAP IS OPEN BY MAGNETIC FIELDfor some devices lt1T
(VALLEY GAP)
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m
fractional QHE
Manchester unpublished
first reported by Andreirsquos group Nature rsquo09Kimrsquos group Nature rsquo09 Laursquos group arxiv 2010
million mobilities but the quality of quantization
remains really bad
need 4-p
robe d
evices
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
(k
)
4
16
8
zero BT = 2K
12
can smoothly pass from one electron to one hole
Fermi energy scale lt 1 meV
14
10
(k
)
-5
n (108cm-2)0
~T
remnant doping lt 109 cm-2
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 5: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/5.jpg)
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
R (
k)
200
800
600
400
B=05T
zero B
T = 2K
GAP IS OPEN BY MAGNETIC FIELDfor some devices lt1T
(VALLEY GAP)
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
suspended devices
2 m
fractional QHE
Manchester unpublished
first reported by Andreirsquos group Nature rsquo09Kimrsquos group Nature rsquo09 Laursquos group arxiv 2010
million mobilities but the quality of quantization
remains really bad
need 4-p
robe d
evices
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
(k
)
4
16
8
zero BT = 2K
12
can smoothly pass from one electron to one hole
Fermi energy scale lt 1 meV
14
10
(k
)
-5
n (108cm-2)0
~T
remnant doping lt 109 cm-2
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 6: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/6.jpg)
suspended devices
2 m
fractional QHE
Manchester unpublished
first reported by Andreirsquos group Nature rsquo09Kimrsquos group Nature rsquo09 Laursquos group arxiv 2010
million mobilities but the quality of quantization
remains really bad
need 4-p
robe d
evices
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
(k
)
4
16
8
zero BT = 2K
12
can smoothly pass from one electron to one hole
Fermi energy scale lt 1 meV
14
10
(k
)
-5
n (108cm-2)0
~T
remnant doping lt 109 cm-2
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 7: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/7.jpg)
continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2
suspended devices
2 m
-1 1
n (1011cm-2)
-2 0 20
(k
)
4
16
8
zero BT = 2K
12
can smoothly pass from one electron to one hole
Fermi energy scale lt 1 meV
14
10
(k
)
-5
n (108cm-2)0
~T
remnant doping lt 109 cm-2
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 8: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/8.jpg)
-5 5
concentration (1010 cm-2)-10 0 10
10
resistivity (k)
0
20
5 K
200 K
Tem
pera
ture
resistivity Dirac point
PROBING DIRAC POINTbull NO ENERGY GAP
bull NO METAL-INSULATORTRANSITION
even with one electron per device
monolayer min moves closer to 4e2h
bilayer min remains gt 4e2h
50 150T (K)
0 100 200
max
imum
res
istiv
ity (
h4e
2 )
0
1
2
2 monolayers
2 bilayers
T approaches T=0 approx linearly
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 9: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/9.jpg)
PROBING DIRAC POINT
MONOLAYERgradual gap opening
BILAYERmore complex behavior
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 10: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/10.jpg)
PROBING DIRAC POINT
BILAYERmore complex behavior
magnetoresistance at Dirac point
(k
)
5
15
(k)12 8
B =025 T
~3x
109 c
m-2 energy gap
induced by gateis less than T
=4
=-4
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 11: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/11.jpg)
-10 10
gate-induced concentration (109 cm-2)
00
- m
in
e (
109 cm
-2)
5
10
5 K
50 K
100 K
150 K
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
near Dirac point curves collapse on
a universal dependence
totalconcentration
measure concentration ofthermally excited carriers
first let us analyze
monolayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 12: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/12.jpg)
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
(k)
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
0
ther
mal
car
riers
(10
10 c
m-2)
5
1
50 150T (K)
0 100 200
T 2
monolayer
first let us analyze
monolayer
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 13: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/13.jpg)
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
Tbilayer
0
ther
mal
car
riers
(10
10 c
m-2)
10
20
50 150T (K)
0 100 200
T 2
monolayer
thermalbroadening
(k)
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 14: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/14.jpg)
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
thermalbroadening
(k)
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 15: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/15.jpg)
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
~3x109 cm-2
DENSITYDIMINISHES
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 16: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/16.jpg)
PROBING DIRAC POINT
-5 5
n (1010 cm-2)-10 0 10
10
0
20
5 K
200 K
Tem
pera
ture
(k)
thermalbroadening
like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS
within the gap
number of carriers at energy ~kT
~3x109 cm-2
~1 meV
0
ther
mal
car
riers
(10
10 c
m-2)
1
2
10 20T (K)
0 30
3
bilayer
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 17: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/17.jpg)
PROBING DIRAC POINT
one of many possibilitiessymmetry-breaking e-e phase transition
Falkorsquos group arxiv 2010
OPEN FOR INTERPRETATION
cyclotron gaps between different Landau levels
0026m0
gap between zero and first LLdoes not want to close
with decreasing B down to 500G
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 18: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/18.jpg)
MESSAGE TO TAKE AWAY
LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()
DIRAC POINT PHYSICSIS ACCESSIBLE
TO STUDIES IN ALL DETAILS
million mobilities in 4-probe geometry should bring a lot more of new physics
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 19: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/19.jpg)
Leaving the Carbon Flatland
Peter Blakeunpublished
vertical transport through one-atom-thick crystals
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 20: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/20.jpg)
Many Other 2D Materials Possible
1m
0Aring 9Aring 16Aring 23Aring
05m
2D boron nitride in AFM
2D MoS2 in optics
1 m
1m
0Aring 8Aring 23Aring
2D NbSe2 in AFM
1 m
2D Bi2Sr2CaCu2Ox in SEM
SOME AREINSULATORS
Manchester PNAS 2005
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 21: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/21.jpg)
spin tunneling devicesresonant tunneling devices
tunneling devices
SS
superconducting junctions
one-atom-thick barriersatomically smooth and continuous
(impossible by MBE)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 22: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/22.jpg)
2D CRYSTALS AS TUNNEL BARRIER
1 layer BN
can now find BN monolayersin an optical microscope
top Au contact
Au contact
boron nitrideAuAu
2m
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 23: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/23.jpg)
7-layer BN
breakdown 2 Vnm
-04
tunn
el c
urre
nt (
A)
0
02
04
-02
voltage (V)-5 0 5
I (A)
4535voltage
40
01
001
1
exponentialdependence
monolayer
resistivity ~1 Mm2
-1
tunn
el c
urre
nt (
A)
0
05
1
-05
-025 025
voltage (V)-05 0 05
voltage-04 0400
(1
M)
2
resistivity ~1 km2
-80
tunn
el c
urre
nt (
A)
0
40
80
-40
-01 01voltage (V)
-02 0 02
-01 01voltage
0
04
02
(1k)
trilayer
NO temperature dependenceexcept for Zero Bias Anomaly
MONOLAYER BARRIERheight gap ~5eV
effective thickness ~5-6Aring
NO pin holes
AuAu
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 24: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/24.jpg)
MESSAGE TO TAKE AWAY
LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES
amp QUANTUM WELLS
NEW VENUEATOMICALLY SMOOTH CONTINUOUS
ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS
(beyond MBE any surface)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 25: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/25.jpg)
Pseudo-Magnetic Fields by Strain
Paco Guinea M Katsnelson amp AKG Nature Phys 2010
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 26: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/26.jpg)
Electronic Properties under Strain
elastically stretched by gt 15
Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009
band structure changes littleno gap expected even at 25 stretch
Castro Neto PRB 2009
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 27: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/27.jpg)
practically always rippled
non-uniform strain causes pseudo-magnetic field
Manchester PRL 2006
B+
B-
Non-Uniform Strain
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 28: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/28.jpg)
[100]
[010][001]
Creating Uniform Pseudo-Magnetic Field
graphenedisk
graphenerectangular
UNIFORM FIELD
KKrsquoinsulating bulk
counter propagating edge currents
STRAIN ONLY
Nature Phys 2010 PRB 2010
field of 10T10 strain in m samples
spacing lattice size sample
straineff
e
hB
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 29: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/29.jpg)
equivalent to magnetic fields of ~400T
Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles
on Pt surface
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 30: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/30.jpg)
MESSAGE TO TAKE AWAY
Strain Engineering Can Open Really Large Gaps
Pseudo-Magnetic fieldcan be UNIFORM
Landau quantization and QHE in zero magnetic field
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 31: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/31.jpg)
Magneto Oscillationsin Quantum Capacitance
Leonid Ponomarenko arxiv amp PRL 2010
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 32: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/32.jpg)
Capacitance Measurements
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
T = 10 K
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
~10000 cm2Vs
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 33: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/33.jpg)
Capacitance Measurements
saturates to classical value Coxide
sharpness of the dip is determined by vF
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-2 0 2030
035
040
045
C (F
cm
2 )
Vtop gate
(V)
Coxide
T = 10 K
22π
2
Fv
E
dE
dn
~10000 cm2Vs
QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008
Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 34: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/34.jpg)
Capacitance Varies with Concentration
vF 11(plusmn01)middot106 ms
100 m SiO2insulating Si
AuTi Al (top gate)
10 nm aluminium oxide
graphene
-04 -02 00 02 040
2
4
6
Cq (F
cm
2 )
EF (eV)
best fit 16 to 23 Fcm2
for several devices
smearingn 5middot1011 cm-2
saturates to classical value Coxide
sharpness of the dip is determined by vF
QUANTITATIVE AGREEMENT
~10000 cm2Vs
22π
2
Fv
E
dE
dn
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 35: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/35.jpg)
Magneto Capacitance Oscillations
250K
150K
100K
200K
-1 0 1
04
06B =16 T
C (F
cm
2)
Vtop gate
(V)
30K
12T
8T
4T
B =0T
T =10 K
-1 0 1
035
040
C (F
cm
2)
Vtop gate
(V)
pronouncedmagneto-oscillations
easily survive toroom T
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 36: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/36.jpg)
MESSAGE TO TAKE AWAY
Quantum Capacitanceis a Huge Effect in Graphene
Landau QuantizationSurvives at Room T in Modest Fields
(unlike transport this does not require gt30T)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 37: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/37.jpg)
CONCLUSION
GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS
does NOT feel at all like a mature research area
MUCH MORE TO COME
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 38: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/38.jpg)
Misha Katsnelson(Nijmegen)
Rahul NairSergey Morozov(Chernogolovka)
F Schedin P Blake
Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko
graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09
Kostya Novoselov
D Elias A Ferrari(Cambridge)
LPonomarenko A Castro Neto(Boston)
Irina Grigorieva
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 39: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/39.jpg)
ldquographene dreamsrdquosubstitute for Si
Manchester Science 2004de Heer et al JPhysChem 2004
see also Dresselhaus 1996
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 40: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/40.jpg)
GRAPHENE ELECTRONICS
ballistic transport on submicron scale
high velocitygreat electrostaticsscales to nm sizes
BUTno pinch off
-100 -50 0 10050
Vg (V)
(k
)
0
2
4
6
SiO2
Si graphene
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 41: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/41.jpg)
GRAPHENE NANO-CIRCUITS
)(
1
nm
eV
DE
E = vF h2D
not 1D2 as for electrons
but much larger 1Das for slow photons
10 nm
e-b lithography
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 42: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/42.jpg)
E = vF h2D
gate (V)
(S
)0 0402
2
0
6
4
few nm300 K
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
GRAPHENE NANO-CIRCUITS
Manchester Science lsquo08also Dai et al Science lsquo08
e-b lithography
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-
![Page 43: some things you might be interested in knowing about Graphene](https://reader038.vdocument.in/reader038/viewer/2022110403/56812b26550346895d8f2cdc/html5/thumbnails/43.jpg)
10 nm
10 nm
stable and robust down to a few nm in sizesustains large (~1 A per atom) currents
gate (V)
(S
)0 0402
2
0
6
4
1-10 nm300 K
PROBLEM no tools to sculpture at true nm scale
(same for any other nanoelectronics approach)
GRAPHENE NANO-CIRCUITS
top-down molecular electronics
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
-