the graphene / sic interface and local imm transport...

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).


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


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:



Fullerene (0D)


Nanotube (1D)


3.35 Å

Graphite (3D)


Graphene:

|Ε|<1eVπ

π∗

20

-20

0

Ener

gy (e

V)

(K)

σ

σ∗



Fullerene (0D)


Nanotube (1D)


3.35 Å

Graphite (3D)


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


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


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


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


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


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).


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


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.


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


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


IMMgrowth in commercial apparatus

Growth by Centrotherm Activator 150-5 in Ar

50

00.5µm

50

05µm


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


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


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


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.


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.


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


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


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)


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


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


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.


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


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

the graphene / sic interface and local imm transport...

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