the graphene / sic interface and local imm transport...
TRANSCRIPT
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 0/22
IMMThe graphene / SiC interface and local
transport properties
V. Raineri, F. Giannazzo, S. Sonde, C. VecchioConsiglio Nazionale delle Ricerche
Istituto per la Microelettronica e MicrosistemiStrada VIII n.5 – Zona Industriale
95121 Catania, Sicily (Italy).
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 1/22
IMMOutline
Graphene on SiC as a material challenge for advanced electronics: the role of interfaces.
Electrical properties of graphene/4H-SiC(0001) interfaceDG/4H-SiC(0001) – EG/4H-SiC(0001)Scanning Current Spectroscopy
Local transport properties of graphene on 4H-SiC(0001)DG/4H-SiC(0001) – EG/4H-SiC(0001)Scanning Capacitance Spectroscopy
Summary
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 2/22
IMM 2D crystal of sp2 hybridized carbon atoms in a honeycomb lattice
Fullerene (0D)
Electric Field Effect in Atomically Thin Carbon Films, K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666-669 (2004).
Nanotube (1D)
xy plane: covalent bondsz direction: Van der Walls interactions
3.35 Å
Graphite (3D)
Graphene existence demonstrated in 2004:A single layer of graphene was separated from HOPG by mechanical exfoliation and was placed on an opportunely chosen substrate
Graphene:
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 3/22
IMM 2D crystal of sp2 hybridized carbon atoms in a honeycomb lattice
Fullerene (0D)
Electric Field Effect in Atomically Thin Carbon Films, K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666-669 (2004).
Nanotube (1D)
xy plane: covalent bondsz direction: Van der Walls interactions
3.35 Å
Graphite (3D)
Graphene existence demonstrated in 2004:A single layer of graphene was separated from HOPG by mechanical exfoliation and was placed on an opportunely chosen substrate
Graphene:
|Ε|<1eVπ
π∗
20
-20
0
Ener
gy (e
V)
(K)
σ
σ∗
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 4/22
IMM 2D crystal of sp2 hybridized carbon atoms in a honeycomb lattice
Fullerene (0D)
Electric Field Effect in Atomically Thin Carbon Films, K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666-669 (2004).
Nanotube (1D)
xy plane: covalent bondsz direction: Van der Walls interactions
3.35 Å
Graphite (3D)
Graphene existence demonstrated in 2004:A single layer of graphene was separated from HOPG by mechanical exfoliation and was placed on an opportunely chosen substrate
Graphene:
|Ε|<1eVπ
π∗
20
-20
0
Ener
gy (e
V)
(K)
σ
σ∗
Dispersion relation of electrons in graphene 2D lattice different than the common parabolic relation in semiconductors: ( )*m2
kk22hr
=ε
and formally analogous to that of photons and of Dirac fermions (i.e. relativistic particles with m~0) : ( ) kckr
hr
=ε
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 5/22
IMMMany excellent properties in one material
MEMS, NEMSYoung's modulus 0.5 Tpa.C. Lee, et al., Science 321, (5887) 385 (2008).
Mechanical
SpintronicsElectrical spin-current injection and detection up to 300 KN. Tombros, et al., Nature 448, 571 (2007).
Magnetic
Very high thermal conductivity (~50 Wcm−1K−1)A.A. Balandin, et al., Nano Letters 8, 902 (2008).
Thermal
High specific capacitance (~100 F/g)M. D. Stoller, et. al, Nano Letters, 8, 3498 (2008).
Large “intrinsic” electron mean free path (~1µm)X. Du, et al., Nature Nanotechnology 3, 491 (2008).
High frequency (GHz -THz) devicesHighly efficient passive components
(ultracapacitors).“Zero energy loss” devices
Giant “intrinsic” mobility of graphene 2DEG (~2×105 cm2V-1s-1)J.H. Chen, et. al, Nature Nanotechnology 3, 206 (2008).
Electronic
Possible applicationsPhysical Properties:
Electronic Properties
~ 03.43.43.31.430.671.1Energy band gap (eV) @ 300K
GrapheneAlGaN/GaN 2DEGGaN4H-SiCGaAsGeSi
1015
2
800
0.3
1019-1020
3
1500 - 2000
0.19
1019-10201015101510151015Carrier concentration (cm-3)
0.6
3900
0.55Electron effective mass (m*/me) 1.08 0.067 0.19 ~0
Electron mobility (cm2V-1 s-1) @300K 1350 4600 1300 2×105
Saturated electron drift velocity vs (107 cm/s) 1 2 3 >5
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IMMGraphene
Num
ber o
f pap
ers
Of course the literature is hugeand is impossible to cite all of the important paper and results aswell as groups that contributed tothe subject
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IMMApproaching ballistic transport in
suspended graphene
Approaching ballistic transport in suspended graphene, X. Du, I. Skachko, A. Barker, E. Y. Andrei, Nature Nanotechnology, 3, 491 (2008).
Suspendedgraphene
NotSuspendedgraphene
Ballistic limit
T=100 K
∑=n
nbal The
WL 24σ
enbal
balσµ =
The summation is over all availablelongitudinal transport channels
Ballistic conductivity (Landauer formula)
Tn transmission probability in the nth channel
L=0.5 µm lead separation
W=1.4 µm sample width
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 8/22
IMMElectron mobility in graphene
Sheet resistance (Ω)
12
34
IV
=ρµ
=ρqn
1
Hall resistance (Ω)
12
35H I
V=ρ
qnB
H =ρ
Carrier density n (cm-2)
Mobility µ (cm2V-1s-1)
Vg
1
2
345
6
B
A large range of mobility values (from 5×102 to 2 ×104 cm2V-1s-1) have been so far reported in literature for graphene
- Intrinsic mechanisms: scattering of carriers with phonons in graphene.- Extrinsic mechanisms: unintentional contaminations (impurities), scattering at interfaces…What are the scattering mechanisms limiting mobility?
Au
SiO2
graphene
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 9/22
IMMTemperature-dependent resistivity
of graphene on SiO2
( ) ( ) ( ) ( )T,VTVT,V gintLAg0g ρ+ρ+ρ=ρ
( )gV0ρ Residual resistivity at 0 K: dependent on n
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛= 2222
22
2 qh
vvhTkDT
Fs
BALA
sρ
πρ
Electron-longitudinal acoustic (LA) phononscattering: independent of n
ρs=7.6×10-7 kg/m2 2D mass-density of graphene
vF=106 m/s Fermi velocity in graphenevs=2.1×104 m/s velocity of sound in graphene
DA=18±1 eV acoustic deformation potential in graphene
( )
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
−⎟⎟⎠
⎞⎜⎜⎝
⎛+
−⎟⎟⎠
⎞⎜⎜⎝
⎛= −
1155exp
5.6
159exp
1,int
TkmeV
TkmeV
BVTV
BB
ggαρ Electron- interfacial phonon scattering by polar optical
phonons of the SiO2 substrate: dependent of n and T
The calculated two strongest surface optical phonon modes in SiO2 are ħω=59 meV and ħω=155 meV, with a ratio of coupling to the electrons of 1:6.5B=0.607(h/e2), α=1.04
0 100 200 3000.5
1.0
1.5
2.0
2.5
T (K)
ρ (1
0-2 h
/e2 O
hm)
Vg (V) n (1012 cm-2) 10 <--> 0.72 15 <--> 1 20 <--> 1.4 30 <--> 2.2 40 <--> 2.9 50 <--> 3.6 60 <--> 4.3
0 100 200 3000.5
1.0
1.5
2.0
2.5
T (K)
ρ (1
0-2 h
/e2 O
hm)
Vg (V) n (1012 cm-2) 10 <--> 0.72 15 <--> 1 20 <--> 1.4 30 <--> 2.2 40 <--> 2.9 50 <--> 3.6 60 <--> 4.3
0 100 200 3000.5
1.0
1.5
2.0
2.5
T (K)
ρ (1
0-2 h
/e2 O
hm)
Vg (V) n (1012 cm-2) 10 <--> 0.72 15 <--> 1 20 <--> 1.4 30 <--> 2.2 40 <--> 2.9 50 <--> 3.6 60 <--> 4.3
Intrinsic and extrinsic performance limits of graphene devices on SiO2, J.H. Chen, C. Jang, S. Xiao, M. Ishigami, M. S. Fuhrer, Nature Nanotechnology, 3, 206 (2008).
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 10/22
IMM
10 100
104
105
106Vg=15 V, n=1x1012 cm-2
µimpurities µinterface phonons µLA
µtot exp model
Mob
ility
(cm
2 V-1s-1
)
T (K)10 20 30 40 50 60
104
105
T=300 K
µimpurities µinterface phonons µLA
µtot model exp
Mob
ility
(cm
2 V-1s-1
)
Vg (V)
104
105
10 20 30 40
n (1011 cm-2)LA
LA ne1ρ
=µ
intphonons_erfaceint neρ
1=µ
intLAimpuritiestot
1111µ
+µ
+µ
=µ
0impurities neρ
1=µ
Intrinsic and extrinsic performance limits of graphene devices on SiO2, J.H. Chen, C. Jang, S. Xiao, M. Ishigami, M. S. Fuhrer, Nature Nanotechnology, 3, 206 (2008).
Giant “intrinsic” electron mobilityof graphene
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 11/22
IMMGraphene/Substrate related factors
limiting mobility in graphene
Charged‐impurity scattering
Surface Polar Phonon scattering
Due to polar nature of the substrates the carriers electrostatically couple to the long‐range polarization field created at the interface.
•Sizeable degradation at room‐temperature.•Dominant limiter of mobility above ~ 400K
•Charged‐impurities are considered to be located at the graphene/oxide interface or in the oxide layer.
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 12/22
IMMGraphene/Substrate related factors
limiting mobility in graphene
Charged‐impurity scattering
Surface Polar Phonon scattering
Due to polar nature of the substrates the carriers electrostatically couple to the long‐range polarization field created at the interface.
•Sizeable degradation at room‐temperature.•Dominant limiter of mobility above ~ 400K
•Charged‐impurities are considered to be located at the graphene/oxide interface or in the oxide layer.
However, no local measurements havebeen so far extensively proposed
Measurements should be implemented formore insight on defect influence on mobility
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 13/22
IMMGraphene on SiC methods
Mechanical exfoliation of highly oriented pyrolityc graphite (HOPG)
High material quality: Low defects density,High mobility
Small sheets;Low production yield
Epitaxial graphene on SiC by controlled graphitisation of the surface at high temperatures (1500 –2000 °C) in inert gas ambient
Large area (wafer scale) sheetson semiconductor substrate
DefectsInterface
Can be placed on different substrates:SiO2 , SiC, high-k dielectrics
• Growth in vacuum and in CVD reactors on 4H-SiC but also 3C-SiC• Growth at high pressure in inert ambient on 4H-SiC wafers … 3C-SiC • Growth in STD SiC oven up to 150 mm 4H-SiC
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IMMgrowth in commercial apparatus
Growth by Centrotherm Activator 150-5 in Ar
50
00.5µm
50
05µm
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 15/22
IMMgrowth in commercial apparatus
Growth by Centrotherm Activator 150-5 in Ar
50
00.5µm
50
05µm
Toward an ideal graphene material by defectcontrol and annihilationE. Cruz-Silva et. al. Physical Review Letters 105 (2010) 045501 by Joule heatingA.V. Krasheninnikov and F. Banhart, Nature Mater. 6 (2007) 723 by electron and ion beam irradiation
Growth can be achievedon low cost large area 4H-SiC wafers
n‐ 4H‐SiC, 1x1014/cm3
n++ 4H‐SiC, 1x1018/cm3
Starting material
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 16/22
IMM
•Interface layer: C layer with (6√3x6√3)R30ocovalently bonded to the Si face.•Layer 1: van der Waals interaction with the buffer layer.•Shift of the Fermi level in the conduction band.•Degradation of electronic transport properties.
2.9Å
Si
C
Graphene epitaxially grown on 4H‐SiC(0001) – EG
SiC bilayer
Phys. Stat. Sol. B 245, 1436–1446 (2008)
Epitaxial graphene on 4H‐SiC(0001)
•Van der Waals interaction between graphene and SiC bilayer
3.35Å
Graphene exfoliated onto 4H‐SiC(0001) – DG
Graphene/4H-SiC(0001) interface
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 17/22
IMM
n‐ 4H‐SiC, 1x1014/cm3
n++ 4H‐SiC, 1x1018/cm3
Starting material20
0
Height (nm
)
1µm0
100
n‐ 4H‐SiCn‐ 4H‐SiC
C‐AFM Electronic ModuleGraphene
n+ 4H‐SiCn+ 4H‐SiC
‐ Vg
3µm
0
20
S. Sonde F. Giannazzo, V. Raineri et al., Phy. Staut. Sol. B, 247, 912 (2009).
Experimental
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 18/22
IMMScanning Current Spectroscopy
S. Sonde, F. Giannazzo, V. Raineri, R. Yakimova, J.‐R. Huntzinger, A. Tiberj, and J. Camassel, Phy. Rev. B., 80, 241406 (R), 2009.
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 19/22
IMMSBH
S. Sonde, F. Giannazzo, V. Raineri, R. Yakimova, J.‐R. Huntzinger, A. Tiberj, and J. Camassel, Phy. Rev. B. (R), 80, 241406 (R), 2009.
k
E
x
E
ΦEG EC
EF
EG
EDirac
EF,gr
∆=0.49 eV
4H-SiC (0001)Buffer layer
++++
ΦEG EC
EF
EG
EDirac
EF,gr
∆=0.49 eV
4H-SiC (0001)Buffer layer
++++
(d)EF,EG
4H-SiC (0001)
EF
ΦDG EC
DG
r=EDirac
4H-SiC (0001)
EF
ΦDG EC
DG
r=EDirac
(c)
EF,DG
Graphene workfunction – 4H‐SiC electron affinity
Local density of interface states varying from ∼ 8 × 1012 to ∼ 1.8 × 1013
cm−2 within few µm lateral distance.
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 20/22
IMM3µm
Qdepl
Scanning Capacitance Spectroscopy
SCM Electronic Module
+ Vg
n+ SiCn+ SiC
n‐SiCAeffQscrGraphene
Under the influence of electric field, 2DEG manifests itself as a capacitor, Quantum capacitor.
+ Vg
Gnd
C’qC’depl
ΔVgr
ΔVdepl
• Pt coated n+ Si tip • Ultrahigh
sensitive capacitance sensor (10x10‐21 F/Hz)
• Modulating bias –ΔV = Vg/2 + Vg/2sin(ωt)
• ω = 100 kHz0.0 0.5 1.0 1.5 2.0
10-4
10-3
10-2
10-1
100
101
∆C
(a.u
.)
Vg (V)
Graphene
4H‐SiC(0001)
Qdepl
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 21/22
IMMGraphene nanoscale capacitive behavior
F. Giannazzo, S. Sonde, V. Raineri, E. Rimini, Nano Lett. 9, 23 (2009).S. Sonde, F. Giannazzo, V. Raineri, E. Rimini, J. Vac. Sci & Technl. B, 27, 868 (2009).
Ctot = AeffCtot
' = Aeff
Cdepl' Cq
'
Cdepl' + Cq
'
Cq >> Cdepl
Ctot ≈ AeffCdepl'
Cdepl
' =Cdepl
Atip
Ctot =
Aeff
Atip
Cdepl ⇒ Ctot
Cdepl
=Aeff
Atip• Charge distributed over Aeff• leff – Screening length
•Length scale over which the applied potential decays in graphene
SiO
SiC
leffAeff
SCM Electronic Module
+ Vg
FLG
n+ SiCn+ SiC
n‐SiCAeffQscr
Qdepl
Atip
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 22/22
IMMLocal electron mean free path
Electrons diffuse from the tip contact onto the graphene layer over leff at velocity νF.
Aeff = πleff2
D =νFleff
2Dµ
=n
q∂n∂EF
⎛ ⎝ ⎜ ⎞
⎠ ⎟
µ =qνFleff
EF leff ⇔ l
SiO
SiC
leffAeff
The diffusivity
Generalized Einstein relation
n =EF
2
πh2νF2( )
nqlπ
=µh
Far enough from the Dirac point
0.0 0.5 1.0 1.5 2.010-4
10-3
10-2
10-1
100
SiO2
Graphene
∆C
(a.u
.)
Vg (V)
4H-SiC
0.0 0.5 1.0 1.50
5
10
15
20
25
Aef
f (×1
04 nm
2 )
n (×1011 cm-2)
0 10 20 30 400
100
200
300
l eff (
nm)
n (× 106 m-1)
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 23/22
IMM
0
20
40
60
80
100
(iii) DG-SiO2
Fre
quen
cy (%
)
(i) DG-SiC306(+/-6.8)
0
20
40
60
80
100
36.87(+/-1)
114(+/-21)
(ii) EG-SiC
0 100 200 3000
20
40
60
80
100
l (nm)
Role of graphene/4H-SiC interface on l
1.5×1011 cm-2
0.5 1.0 1.50
100
200
300
(ii) EG-SiC
(iii) DG-SiO2
l gr (n
m)
nVg
-n0 (1011cm-2)
(i) DG-SiC
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 24/22
IMMRole of graphene/4H-SiC interface on µ
µSPP --> mobility limited by surface polar phonon scattering (simulated).
µci --> mobility limited by charged impurities at interface (simulated).
µequi --> equivalent mobility (simulated).
µexp --> mobility evaluated from average experimental mean free path.
Of course the case of epitaxial graphene should be further investigated to reallyunderstand the role of the interface
104
105
106DG-SiC
µSPP µci µequi µexp104
105
106EG-SiC
µ cm
2 /Vs
0.5 1.0 1.5104
105
106DG-SiO2
nVg-n0 (×1011 cm2/VS)
Nci_EG=2.5x1011cm-2
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 25/22
IMMSummary
Scanning Probe Microscopy based method to investigate
Interface electrical properties of graphene/4H-SiC(0001) andLocal electron mean free path in graphene on 4H-SiC(0001).
EpiGraphene/4H-SiC(0001)Due to Fermi level pinning towards conduction band, a reduced SBHhas been observed on EG as compared to DG. This effect shows that positively charged states localize at the interfacebetween the C rich (6√3 × 6√3)R30o reconstructed buffer layer and the Si face.
DepGraphene/4H-SiC(0001)Improvement in local electron mean free path was measured due to better dielectric screening of charged impurities and lower Surface Polar Phonon scattering at graphene/4H-SiC(0001) interface.
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 26/22
IMM1 µm1 µm 60 nm
µmnm
60 nm60 nm
µmnm
1 µm1 µm 60 nm
µmnm
60 nm60 nm
µmnm
Atomic force microscopy
Collegues at IMM:Fabrizio RoccaforteRaffaella Lo NigroPatrick FiorenzaSalvatore Di Franco Corrado Bongiorno
A. La MagnaI. Derentsis
This work has been partially supported by the European Science Foundation (ESF) under the Eurocore programme “Eurographene” by the co-ordinated project GRAPHIC-RF (V. Raineri coordinator -Italy, Thomas Seyller – Germany, R. Yakimova – Sweden, J. Camassel – France).
our partners:
Acknowledgements
10 µm
Optical Microscopy
Au
SiO2
graphene Au
SiO2
graphene
SIF – Bologna, Italy – September 20‐24, 2010 ‐ Slide 27/22
IMM1 µm1 µm 60 nm
µmnm
60 nm60 nm
µmnm
1 µm1 µm 60 nm
µmnm
60 nm60 nm
µmnm
Atomic force microscopy
Collegues at IMM:Fabrizio RoccaforteRaffaella Lo NigroPatrick FiorenzaSalvatore Di Franco Corrado Bongiorno
A. La MagnaI. Derentsis
This work has been partially supported by the European Science Foundation (ESF) under the Eurocore programme “Eurographene” by the co-ordinated project GRAPHIC-RF (V. Raineri coordinator -Italy, Thomas Seyller – Germany, R. Yakimova – Sweden, J. Camassel – France).
our partners:
Acknowledgements
10 µm
Optical Microscopy
Au
SiO2
graphene Au
SiO2
graphene
Thank you for your attention