Fabrication and characterization of graphene nanodevices

FABRICATION AND CHARACTERIZATION OF GRAPHENE

NANODEVICES

Cayetano Sánchez-‐Fabrés Cobaleda

Outline

•  IntroducFon •  FabricaFon of graphene devices •  QHE in graphene •  WL-‐WAL in graphene •  PPT in h-‐BN/graphene/h-‐BN •  SuperconducFvity in 3D porous graphene

18/06/14 FabricaFon and characterizaFon of

graphene nanodevices Cayetano Sánchez-‐Fabrés Cobaleda

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QHE in graphene: number of layer maXers



3

Integer Quantum Hall effect

•  QuanFzaFon in Landau levels: Rxy=h/νe2

•  Standard 2DEGs: ν = ng •  Graphene: ν = g(n+1/2)



4

Quantum phase transiFons

•  LocalizaFon-‐delocalizaFon transiFons •  CriFcality of the transiFon

•  Ec: criFcal energy and ξ localizaFon length •  γ: criFcal exponent of the transiFon



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ξ ∝ E −Ec−γ

Experiment<-‐>Theory

•  p: coherence length dependence on T

•  γ yields informaFon on the kind of disorder •  Need of extremely high quality samples – Low n, high µ and high homogeneity



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∂ρxy

∂B"

#$

%

&'max

∝T −κ

κ = p / 2γ

lφ ∝T− p/2

FABRICATION OF GRAPHENE NANODEVICES



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Graphene producFon

•  Mechanical exfolia-on: scotch-‐tape technique

•  CVD grown graphene

•  Epitaxial graphene

•  Reduced graphene oxide

Mechanical cleavage •  Ingredientes: Natural graphite and scotch tape •  Layer by layer exfoliaFon •  DeposiFon onto the wafer



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Mechanical cleavage •  IdenFficaFon using the opFcal microscope



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50 um 25 um

Processing: e-‐beam lithography



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15 um

Processing: e-‐beam lithography



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50 um 15 um

EvaporaFon of contacts



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50 um 15 um

Processing: ReacFve ion etching



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25 um 15 um



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Sample monFng and bonding

Our LAB 3He Heliox cryostat

(2008) 0.285 K < T < 300 K

3He/4He dilu-on cryostat (2011)

0.01 K < T < 30 K RuO2 therm. closer to the sample CalibraFon: nuclear thermometer



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SC magnet (2008)

B = 12 T Bore diameter 55 mm

Sample rod

•  Thermally linked to the cryostat •  Sample cooled down via the wires •  Home made and designed holders



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Quantum Hall effect in graphene



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QHE in bilayer graphene



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1 2 3 4 5

2800

3000

3200

3400

3600

3800

µ (

cm2/V

s)

n (1012 cm-2)

QHE in trilayer graphene

•  ObservaFon of the ν=6 plateau

•  Study of the QHE as a funcFon of T



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C. Cobaleda et al. Physica E 44 530-‐533 (2011) C. Cobaleda et al. Phys. Status Solidi C 9 1411-‐1414 (2012)

Weak localizaFon weak anFlocalizaFon

•  Electrons counter propagaFng in closed paths –  Phase conserved –  Time reversal symmetry conserved •  Broken if B is applied

•  Back scaXering enhanced –  WL: Maximum of ρ at B=0



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Weak localizaFon weak anFlocalizaFon

•  Electrons counter propagaFng in closed paths –  Phase conserved –  Time reversal symmetry conserved •  Broken if B is applied

•  Back scaXering enhanced –  WL: Maximum of ρ at B=0

•  Carriers in graphene are chiral –  Back scaXering forbidden!

•  WAL: Minimum of ρ at B=0 –  Chirality at low energies



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WAL-‐WL transiFon



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-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.100.0

0.2

0.4

0.6

0.8

T=0.3K T=1.6K T=3K T=6K T=10K T=15K

σ(B

) - σ

(0) (

e2 /h)

B(T)

0.3 K

15 K

-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.080.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

σ(B

) - σ

(0) (

e2 /h)

B (T)

T=0.3 K T=1.6 K T=2.6 K T=6 K T=10 K T=15 K0.3 K

15 K

Vg = 0 V Vg = -‐10 V

S. Pezzini, C. Cobaleda et al. Physical Review B 85 165451 (2012)

h-‐BN/bilayer graphene/h-‐BN heterostructure



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Dirac peak vs Temperature



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Dirac peak vs Temperature



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nc nc

Transport regimes

•  n < nc – T < 10 K

•  ∂ ρxx/ ∂ T<0



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Transport regimes

•  n < nc – T < 10 K

•  ∂ ρxx/ ∂ T<0

– 10 K < T < 50 K •  ∂ ρxx/ ∂ T<0



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Transport regimes

•  n < nc – T < 10 K

•  ∂ ρxx/ ∂ T<0

– 10 K < T < 50 K •  ∂ ρxx/ ∂ T<0

•  n > nc – T < 10 K

•  ∂ ρxx/ ∂ T<0



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Transport regimes

•  n < nc –  T < 10 K

•  ∂ ρxx/ ∂ T<0 –  10 K < T < 50 K

•  ∂ ρxx/ ∂ T<0

•  n > nc –  T < 10 K

•  ∂ ρxx/ ∂ T<0 –  10 K < T < 50 K

•  ∂ ρxx/ ∂ T>0



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All together...



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C. Cobaleda et al. Phys. Rev B 89 121404R (2014)

Magnetotransport characterizaFon •  Vd~0.5 V •  n~1011 cm-‐2

•  µ~40000 cm2/Vs



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Quantum phase transiFons



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Measurements

•  n=10.2·∙1011cm-‐2



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ν=12

ν=16

ν=8

Measurements

•  n=10.2·∙1011cm-‐2 •  12-‐>8 •  16-‐>12



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ν=12

ν=16

ν=8

Measurements

•  n=10.2·∙1011cm-‐2 •  12-‐>8 •  16-‐>12



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ν=12

ν=16

ν=8

∂ρxy

∂B"

#$

%

&'max

∝T −κ

Measurements

•  n=10.2·∙1011cm-‐2 •  12-‐>8 •  16-‐>12



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ν=12

ν=16

ν=8

∂ρxy

∂B"

#$

%

&'max

∝T −κ

κ ≈ 0.3

Measurements



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κ ≈ 0.3

Universality of the transiFon



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n = 14.6×1011 cm-‐2 n = 10.2×1011 cm-‐2 n = 6.07×1011 cm-‐2

Universality of the transiFon



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n = 14.6×1011 cm-‐2 n = 10.2×1011 cm-‐2 n = 6.07×1011 cm-‐2

n = (-‐)4.74×1011 cm-‐2 n = (-‐)6.84×1011 cm-‐2 n = (-‐)9.03×1011 cm-‐2

n-‐independent κ

•  SaturaFon for T<5 K



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κ = 0.30± 0.02

Effect of disorder

•  γ = p/2κ



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Short range disorder (Anderson model)

Long range disorder (Classic percolaFon)

Our data

κ=0.42 κ=0.75 κ=0.3

If p=2; γ=2.38 If p=2; γ=4/3 If p=2; γ=3.3

Effect of disorder

•  γ = p/2κ •  What if p≠2? •  Next goal: measure p and γ independently

18/06/14

FabricaFon and characterizaFon of graphene nanodevices

Cayetano Sánchez-‐Fabrés Cobaleda 43



Our data

κ=0.42 κ=0.75 κ=0.3

If p=2; γ=2.38 If p=2; γ=4/3 If p=2; γ=3.3

LocalizaFon length: γ

•  Tails of the LL: VRH •  CriFcal transiFon:



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σ xx ∝ exp − T0 /T( )

T0 ∝ξ−1

γνν

ξ−

⎟⎟⎠

⎞⎜⎜⎝

⎛ −∝

4c

Coherence length: p

•  Phase coherence preservaFon depends on T •  WL as funcFon of T •  Measurement of lϕ as funcFon of T



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lϕ ∝T− p/2

WL in bilayer graphene



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-10 0 10

0.0

0.1

0.2

0.3

15 K

∆σ

xx (e

2 /h)

B (mT)

0.3 K

0.1 1 100.1

1

10

Lφ

bestFIT

L φ (µ

m)

T (K)

p = 0.9

Classical percolaFon

•  Measurements of κ, γ and p are compaFble

•  Both methods are compaFble with a PPT driven by classical percolaFon*



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* C. Cobaleda et al. SubmiXed to Phys. Rev. LeX



Our data

κ=0.42 κ=0.75 κ=0.3

If p=2; γ=2.38 If p=2; γ=4/3 p =0.9; γ=1.4±0.1

γ=1.3±0.3

Classical percolaFon

•  Measurements of κ, γ and p are compaFble

•  Both methods are compaFble with a PPT driven by classical percolaFon*

•  CompaFble with STM observaFons



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* C. Cobaleda et al. SubmiXed to Phys. Rev. LeX



Our data

κ=0.42 κ=0.75 κ=0.3

If p=2; γ=2.38 If p=2; γ=4/3 p =0.9; γ=1.4±0.1

γ=1.3±0.3

SuperconducFvity in 3D porous graphene



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The samples



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3D porous carbon

3D porous carbon+Ta 3D porous graphene+Ta

3D porous graphene

3D graphene vs 3D carbon



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H2c =φ0

2πξ (0)21− T

T0

"

#$

%

&'

SuperconducFng properFes of Ta

3D graphene •  Bc = 2 T •  Tc = 1.2 K •  ξ(0) = 14 nm •  vF = 1.2·∙104 m/s

3D carbon •  Bc = 2.3 T •  Tc = 0.96 K •  ξ(0) = 11 nm •  vF = 0.8·∙104 m/s



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C. Cobaleda et al. SubmiXed to App. Phys. LeX

SuperconducFng properFes of Ta

3D graphene (sp2 bonds) •  Bc = 2 T •  Tc = 1.2 K •  ξ(0) = 14 nm •  vF = 1.2·∙104 m/s

3D carbon (sp3 bonds) •  Bc = 2.3 T •  Tc = 0.96 K •  ξ(0) = 11 nm •  vF = 0.8·∙104 m/s



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Stronger hybridizaFon between e-‐ in Ta and 3DG than between Ta and 3DC

C. Cobaleda et al. SubmiXed to App. Phys. LeX

Conclusions



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Conclusions

•  FabricaFon of graphene devices



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Conclusions

•  FabricaFon of graphene devices •  QHE in inhomogeneous graphene



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Conclusions

•  FabricaFon of graphene devices •  QHE in inhomogeneous graphene •  WL-‐WAL transiFon in monolayer graphene



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Conclusions

•  FabricaFon of graphene devices •  QHE in inhomogeneous graphene •  WL-‐WAL transiFon in monolayer graphene •  Transport regimes in hBN/graphene/hBN



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Conclusions

•  FabricaFon of graphene devices •  QHE in inhomogeneous graphene •  WL-‐WAL transiFon in monolayer graphene •  Transport regimes in hBN/graphene/hBN •  First observaFon of a QPT fully driven by a classical percolaFon regime in graphene



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Conclusions

•  FabricaFon of graphene devices •  QHE in inhomogeneous graphene •  WL-‐WAL transiFon in monolayer graphene •  Transport regimes in hBN/graphene/hBN •  First observaFon of a QPT fully driven by a classical percolaFon regime in graphene

•  Study of charge transfer effects between tantalum and 3D graphene and carbon



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Agradecimientos



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Dr. Enrique Diez Dr. Yahya Meziani

Dr. ViXorio Bellani Dr. Francesco Rossella Sergio Pezzini

David López-‐Romero Maika Sabido Alicia Fraile

Dr. Wei Pan Dr. Duncan Maude Dr. Walter Escoffier Dr. Benjamin Piot Fabrice Iacovella

Electronic instrumentaFon



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V~1V f~15 Hz

100 MΩ ~10 nA

SR Lock-‐in amplifier 830 and Keithley Sourcemeter 2601 A

Vg

Future perspecFves

•  Novel routes towards effecFve ambipolar FETs – Non perpendicular top gates – MoS2, InSb, etc – van der Waals structures

•  QHE in 4 layered graphene •  Study the QPT in suspended graphene •  CharacterisaFon of QPT in TLG and 4LG



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Fabrication and characterization of graphene nanodevices

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