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(1)

Microwave Graphene Electronics

B. Plaçais

Laboratoire Pierre Aigrain – Ecole Normale Supérieure 24 rue Lhomond, 75231 Paris Cedex 05 France

www.lpa.ens.fr

drain gate

source

graphene

Al2O3

ER-Tremblay, 28/06/2012

(2)

(K. Novoselov et al., Science 2004)

« field effect in atomically thin carbon films »

ER-Tremblay, 28/06/2012

(3)

An exceptionnal 2D metal !

Semi-conducteur classique

Dirac point

ER-Tremblay, 28/06/2012

(4)

Large scale epitaxial graphene

(C. Berger and W. de Heer)

ER-Tremblay, 28/06/2012

(5)

Field-effect in suspended graphene

neutre

neutre

électrons trous

1. Importance of cleaning by current annealing 2. Efficient field effect in layered conductors

3. Tunable metal : broad range of electron and hole doping 4. Dirac fermion physics : conductivity at neutrality ~4 e

2

/h

(Bolotin et al. PRL2008)

(P. Kim, Le Tremblay 2009)

ER-Tremblay, 28/06/2012

(6)

(Columbia, 2010) (Manchester, 2011)

Layered Graphene on layered Boron Nitride

Black & White

ER-Tremblay, 28/06/2012

(7)

mobility/conductivity at room temperature

(encaps., Manchester, Nanolett.‘2011) (flake on BN, Columbia Nnano’2010)

(CVD on BN, Berkeley, APL’ 2011)

ER-Tremblay, 28/06/2012

  ;  ne E

v

d

 

  ;  ne E

v

d

(8)

List of key-numbers about graphene

 Gate tunable

e-concentration n

s

=10

11

-10

13

cm

-2

(symmetry) chemical potential E

F

= ±350 meV (from Cr to Pt)

e-color λ

F

= 10-100 nm (e-quantum optics) compressibility e

2

ϰ= 10-100 fF µm

-2

(Q-capacitance)

 high mobility 0.002 → 20 m

2

V

-1

s

-1

(!! Dirac Fermions)

 Finite residual conductivity : 4e

2

/h=(6,45 kOhms)

-1

(! quantum tunneling)

 Large Fermi velocity : v

F

=1, 10

6

m/s (Magic carbon-bond !)

 Large sound velocity : c = 2. 10

4

m/s (Magic carbon-bond !) V

g

<0 V

g

>0

ER-Tremblay, 28/06/2012

(9)

1) Introduction to magic graphene

2) Transit frequency of microwave transistors 3) Diffusion probed in a field‐effect capacitor 4) Acoustic phonons controls noise of resistors 5) New transistor architectures 

Outline

ER-Tremblay, 28/06/2012

(10)

Microwave Field Effect Transistor (FET)

drain gate

source

graphene

Al2O3

Drain-source resistance R

ds

Transconductance g

m

Gate-drain capacitance C

g

ER-Tremblay, 28/06/2012

2 2

2

2

2 2 2

L D E

eV L

D L

V C

f g

LW C L W V V

ne L

W V V

g I

F ds ds

g m T

ds g g

ds g

ds m

 

 

 

 

2 2

2

2

2 2 2

L D E

eV L

D L

V C

f g

LW C L W V V

ne L

W V V

g I

F ds ds

g m T

ds g g

ds g

ds m

 

 

 

 

(11)

Measuring microwave devices

80 GHz transistor (S‐parameters)

ER-Tremblay, 28/06/2012

Wave guide (CPW) S

D G

S

D

(BN) E. Pallecchi et al, APL 99, 113502 (2011)

16 GHz nano‐transistor (S‐paramters)

J. Chaste et al, Nanoletters 2008, APL 2011)

(12)

Transit frequency measurement

ER-Tremblay, 28/06/2012

Exfoliated GR on SiO2 : 16GHz

S

D G

(Pallecchi et al., APL 2011)

Exfoliated GR on Sapphire : 80GHz

f j f H  1 

T

:

gain

current

21

f j f H  1 

T

:

gain

current

21

(13)

Kings of microwave transistors (IBM)

ER-Tremblay, 28/06/2012

(CVD graphene on diamond, Wu et al., Nature 2011)

(P. Avouris)

Today 300GHz !

Tomorrow 500GHz ?

(14)

MOS‐FET transistors for digital applications 

ER-Tremblay, 28/06/2012

(Pentium 4, INTEL)

(taken from wikipedia.org)

(15)

Microwave transistors by IBM

ER-Tremblay, 28/06/2012

(CVD graphene on diamond, Wu et al., Nature 2011)

Today 300GHz !

Tomorrow 500GHz , ….  1THz ?

(16)

Applications of graphene transistors

ER-Tremblay, 28/06/2012

radars for aircrafts radar for (Google) Car THz imaging

(17)

1) Introduction to magic graphene

2) Transit frequency of microwave transistors 3) Diffusion probed in a field‐effect capacitor 4) Acoustic phonons controls noise of resistors 5) New transistor architectures 

Outline

ER-Tremblay, 28/06/2012

(18)

Tight-binding model → Dirac hamiltonian

(P.R. Wallace, PRB 1947)

(19)

Pseudo‐spin supresses back scattering

q

initial

q

final

Whence the large mobility at low temperature !

(20)

Pseudo-spin opens new scattering channels

Castro-Neto at el. RMP 2009, Peres et al. RMP 2010,

Das Sarma et al. RMP 2011,

etc……

(21)

A graphene capacitor

thin oxide

Thick metallic gate

V

dc

+V

rf

C

Q

C

geo

r I rf

Mono‐layer graphene

ER-Tremblay, 28/06/2012

G

D

quantum capacitance diffusion resistance

Low

resistance

contact

(22)

Electronic compressibility

comes as a quantum capacitance

ER-Tremblay, 28/06/2012

   

0) (T

2 cosh 4

2 2 2 ln

: graphene

0) (T

) ( 1 1

1

1 1

2 2 2

2

2 2

2

 

 

 

 

 

 

 

 

F F B

F F

B Q

F Q

géo géo

L L

v E e T

k E v

T k C e

E e

e C

e C

C

e q C q

e C

q e

n q V e

e V e

 

   

0) (T

2 cosh 4

2 2 2 ln

: graphene

0) (T

) ( 1 1

1

1 1

2 2 2

2

2 2

2

 

 

 

 

 

 

 

 

F F B

F F

B Q

F Q

géo géo

L L

v E e T

k E v

T k C e

E e

e C

e C

C

e q C q

e C

q e

n q V e

e V e

 

(23)

quantum capacitance geometrical capacitance

diffusion resistance

graphene flake

SiO

2

Pd

gate Au

drain

V

dc

+V

rf

C

Q

C

geo

r

Diffusion constant AlO

x

(4‐8nm)

Scattering time as function of energy

(24)

Our graphene RF devices

20GHz capacitor (admittance)

ER-Tremblay, 28/06/2012

Wave guide (CPW)

G

D

E. Pallecchi et al, PRB 83 (2011)

(25)

Evanescent waves to probe diffusion 

thin oxide

metal

V

dc

+V

rf

C

Q

C

geo

r I rf

graphene

ER-Tremblay, 28/06/2012

(26)

Cutt‐off frequency

(Transport scattering time probed through rf admittance of a graphene capacitor, Pallecchi et al., PRB 2011) ER-Tremblay, 28/06/2012

Thouless energy  protects

graphene device dynamics !

(27)

Gate voltage dependence

(Pallecchi et al., PRB 2011) ER-Tremblay, 28/06/2012

D(E F ) = Const (Dirac-mass disorder)

C

geo

(28)

Fermi energy dependence

(Pallecchi et al., PRB 2011) ER-Tremblay, 28/06/2012

(29)

1) Introduction to magic graphene

2) Transit frequency of microwave transistors 3) Diffusion probed in a field‐effect capacitor 4) Acoustic phonons controls noise of resistors 5) New transistor architectures 

Outline

ER-Tremblay, 28/06/2012

(30)

Electron‐phonon in graphene

ER-Tremblay, 28/06/2012

 Large O‐Phonon energy

 Weak A‐Phonon coupling

GR/BN

optical (strong)

acoustic (weak) Phonons spectrum

c = 20 000 m/s !

(31)

Raman spectroscopy

ICN Barcelone, 17/02/2012

(Berciaud, Han, Mak,Brus,Kim, Heinz, PRL2010)

OP interactions (Kohn anomalies)

OP/AP populations

(32)

Hot ‐electron experiment

V I

(metals)

(nanotubes)

P=V 2 /R

ER-Tremblay, 28/06/2012

(graphene ?)

S I =4k B T e /R

(33)

Hot ‐electron experiment

(Kubakaddi, PRB 2009, Viljas-Heikkila, PRB 2010) ER-Tremblay, 28/06/2012

heat sink (metals)

(1D nanotubes, Wu et al. APL 2011) cooling power

Theory : Viljas et al. PRB 2010

(34)

ER-Tremblay, 28/06/2012

What is electrical noise ? 

Fluctuations :  I ( t )I ( t )I ( t )

Statistical distribution +

- R

S

V

S

I

I 2 V

in

V S R S

S  

T

N

Noise spectrum : I

2

( t ) S

I

( )

Noise of an amplifier

I

2

(35)

ER-Tremblay, 28/06/2012

Physics of noise

e

I e 2 S I

Shot-noise and/or Thermal noise

+

- T

0

R T

k

S I  4 B 0 /

J.B. Johnson H. Nyquist W. Schottky

R S I

(36)

Noise thermometry

ER-Tremblay, 28/06/2012

)]

, (

[ )

, (

4 )

,

( g ds

e x N

B ds

g ds

g

I V V G V V k T T V V

S  

(37)

ER-Tremblay, 28/06/2012

True 2D acoustic phonon bath

T~P 1/4 ~V 1/2 !

(38)

Hot electrons but cold phonons 

ICN Barcelone, 17/02/2012

A. Betz et al., arXiv:1203.2753v1

Fabien Vialla, D. Brunel and C. Voisin 30K/V !

400K @ 1V

(39)

ER-Tremblay, 28/06/2012

The P=Σ T 4 dependence

(40)

ICN Barcelone, 17/02/2012

Electronic temperature profile

electron conduction

(41)

ER-Tremblay, 28/06/2012

Σ~ Σ LA /10 ! (lattice disorder)

The P=Σ T 4 dependence

(42)

Hot-electron bolometers

Yan et al., Nature nano 2012 Gabor et al., Science 2011

Vora et al., APL 2012 Fong-Schwab arXiv 2012

ER-Tremblay, 28/06/2012

(43)

electronic cosmology seen by noise

ICN Barcelone, 17/02/2012

Quantum noise defect

electron

LA-phonons LO-phonons ?

(44)

1) Introduction to magic graphene

2) Transit frequency of microwave transistors 3) Diffusion probed in a field‐effect capacitor 4) Acoustic phonons controls noise of resistors 5) New transistor architectures 

Outline

ER-Tremblay, 28/06/2012

(45)

Zoo of graphene transistors

Gr-FET MoS

2

-MOSFET

(B. Radisavljevic et al. Nature nano 2011)

Gr/hBN (2011) - Tunnel transistor Gr/Si (2012) Shottky-transistor

drain gate

source

graphene

Al2O3

hBN

ER-Tremblay, 28/06/2012

(46)

Vertical tunnel barrier

ER-Tremblay, 28/06/2012

( Britnell et al. Science 2012)

(47)

Barristor by Samsung

ER-Tremblay, 28/06/2012

( H. Yang, H.-J. Chung et al. Science 2012)

(48)

 Transistor:   large transit frequencies

 Capacitor :   anomalous diffusion

 Resistor :   weak electron‐phonon

 Devices :  High‐speed LNA’s, sensitive bolometers !

APS-Boston, 28/02/2012

Summary

(49)

graphene-team @ LPA

Gwendal Fève Bernard Plaçais Jean-Marc Berroir

Andreas Betz Emiliano Pallecchi Sung-Ho Jhang

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