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
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(K. Novoselov et al., Science 2004)
« field effect in atomically thin carbon films »
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An exceptionnal 2D metal !
Semi-conducteur classique
Dirac point
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Large scale epitaxial graphene
(C. Berger and W. de Heer)
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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)
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(Columbia, 2010) (Manchester, 2011)
Layered Graphene on layered Boron Nitride
Black & White
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mobility/conductivity at room temperature
(encaps., Manchester, Nanolett.‘2011) (flake on BN, Columbia Nnano’2010)
(CVD on BN, Berkeley, APL’ 2011)
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; ne E
v
d
; ne E
v
dList of key-numbers about graphene
Gate tunable
e-concentration n
s=10
11-10
13cm
-2(symmetry) chemical potential E
F= ±350 meV (from Cr to Pt)
e-color λ
F= 10-100 nm (e-quantum optics) compressibility e
2ϰ= 10-100 fF µm
-2(Q-capacitance)
high mobility 0.002 → 20 m
2V
-1s
-1(!! Dirac Fermions)
Finite residual conductivity : 4e
2/h=(6,45 kOhms)
-1(! quantum tunneling)
Large Fermi velocity : v
F=1, 10
6m/s (Magic carbon-bond !)
Large sound velocity : c = 2. 10
4m/s (Magic carbon-bond !) V
g<0 V
g>0
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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
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Microwave Field Effect Transistor (FET)
drain gate
source
graphene
Al2O3
Drain-source resistance R
dsTransconductance g
mGate-drain capacitance C
gER-Tremblay, 28/06/2012
2 2
2
2
2 2 2L 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 2L 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
Measuring microwave devices
80 GHz transistor (S‐parameters)
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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)
Transit frequency measurement
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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
21f j f H 1
T:
gain
current
21Kings of microwave transistors (IBM)
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(CVD graphene on diamond, Wu et al., Nature 2011)
(P. Avouris)
Today 300GHz !
Tomorrow 500GHz ?
MOS‐FET transistors for digital applications
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(Pentium 4, INTEL)
(taken from wikipedia.org)
Microwave transistors by IBM
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(CVD graphene on diamond, Wu et al., Nature 2011)
Today 300GHz !
Tomorrow 500GHz , …. 1THz ?
Applications of graphene transistors
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radars for aircrafts radar for (Google) Car THz imaging
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
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Tight-binding model → Dirac hamiltonian
(P.R. Wallace, PRB 1947)
Pseudo‐spin supresses back scattering
q
initial
q
finalWhence the large mobility at low temperature !
Pseudo-spin opens new scattering channels
Castro-Neto at el. RMP 2009, Peres et al. RMP 2010,
Das Sarma et al. RMP 2011,
etc……
A graphene capacitor
thin oxide
Thick metallic gate
V
dc+V
rfC
QC
geor I rf
Mono‐layer graphene
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G
D
quantum capacitance diffusion resistance
Low
resistance
contact
Electronic compressibility
comes as a quantum capacitance
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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
quantum capacitance geometrical capacitance
diffusion resistance
graphene flake
SiO
2Pd
gate Au
drain
V
dc+V
rfC
QC
geor
Diffusion constant AlO
x(4‐8nm)
Scattering time as function of energy
Our graphene RF devices
20GHz capacitor (admittance)
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Wave guide (CPW)
G
D
E. Pallecchi et al, PRB 83 (2011)
Evanescent waves to probe diffusion
thin oxide
metal
V
dc+V
rfC
QC
geor I rf
graphene
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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 !
Gate voltage dependence
(Pallecchi et al., PRB 2011) ER-Tremblay, 28/06/2012
D(E F ) = Const (Dirac-mass disorder)
C
geoFermi energy dependence
(Pallecchi et al., PRB 2011) ER-Tremblay, 28/06/2012
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
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Electron‐phonon in graphene
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Large O‐Phonon energy
Weak A‐Phonon coupling
GR/BN
optical (strong)
acoustic (weak) Phonons spectrum
c = 20 000 m/s !
Raman spectroscopy
ICN Barcelone, 17/02/2012
(Berciaud, Han, Mak,Brus,Kim, Heinz, PRL2010)
OP interactions (Kohn anomalies)
OP/AP populations
Hot ‐electron experiment
V I
(metals)
(nanotubes)
P=V 2 /R
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(graphene ?)
S I =4k B T e /R
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
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What is electrical noise ?
Fluctuations : I ( t ) I ( t ) I ( t )
Statistical distribution +
- R
S
VS
II 2 V
in
V S R S
S
T
NNoise spectrum : I
2( t ) S
I( )
Noise of an amplifier
I
2
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Physics of noise
e
I e 2 S I
Shot-noise and/or Thermal noise
+
- T
0R T
k
S I 4 B 0 /
J.B. Johnson H. Nyquist W. Schottky
R S I
Noise thermometry
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)]
, (
[ )
, (
4 )
,
( g ds
e x N
B ds
g ds
g
I V V G V V k T T V V
S
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True 2D acoustic phonon bath
T~P 1/4 ~V 1/2 !
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
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The P=Σ T 4 dependence
ICN Barcelone, 17/02/2012
Electronic temperature profile
electron conduction
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Σ~ Σ LA /10 ! (lattice disorder)
The P=Σ T 4 dependence
Hot-electron bolometers
Yan et al., Nature nano 2012 Gabor et al., Science 2011
Vora et al., APL 2012 Fong-Schwab arXiv 2012
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electronic cosmology seen by noise
ICN Barcelone, 17/02/2012
Quantum noise defect
electron
LA-phonons LO-phonons ?
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
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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
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Vertical tunnel barrier
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( Britnell et al. Science 2012)
Barristor by Samsung
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( H. Yang, H.-J. Chung et al. Science 2012)
Transistor: large transit frequencies
Capacitor : anomalous diffusion
Resistor : weak electron‐phonon
Devices : High‐speed LNA’s, sensitive bolometers !
APS-Boston, 28/02/2012
Summary
graphene-team @ LPA
Gwendal Fève Bernard Plaçais Jean-Marc Berroir
Andreas Betz Emiliano Pallecchi Sung-Ho Jhang