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

2

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



5

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



6

∂ρxy

∂B"

#$

%

&'max

∝T −κ

κ = p / 2γ

lφ ∝T− p/2

FABRICATION OF GRAPHENE NANODEVICES



7



8

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



9

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



12

50 um 15 um

EvaporaFon of contacts



13

50 um 15 um

Processing: ReacFve ion etching



14

25 um 15 um



15

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



16

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



17

Quantum Hall effect in graphene



18

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



20

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...



31

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



35

ν=12

ν=16

ν=8

Measurements

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



36

ν=12

ν=16

ν=8

∂ρxy

∂B"

#$

%

&'max

∝T −κ

Measurements

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



37

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*



47

* 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



48

* 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



51

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



52

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



54

Conclusions

•  FabricaFon of graphene devices



55

Conclusions

•  FabricaFon of graphene devices •  QHE in inhomogeneous graphene



56

Conclusions

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



57

Conclusions

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



58

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



59

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



60

Agradecimientos



61

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



62

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



63

fabrication and characterization of graphene nanodevices

Science

experimenttheory p

landau levels

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