Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 1/80 WP4 - HF Electronics
HF-Graphene Electronics
noise (L1) ballistic’s (L2)(electron-phonon) (Dirac Fermion Optics)
Bernard Plaçais [email protected]
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 2/80 WP4 - HF Electronics
Why studying noise ?
Because noise limits the performance of graphene electronics
Because it tells us something about graphene physics
It may be usefull to something
Finally, because it is there ….. « noise is the signal »
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 3/80 WP4 - HF Electronics
L1: Noise outline
o Introduction noise physicso Quantum shot noise in grapheneo Hot-electron noise in grapheneo Phonon cooling in grapheneo Perspectives
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 4/80 WP4 - HF Electronics
electrical noise
Fluctuations : )t(I)t(I)t(I Statistical distribution
+
-
R
SV
SI
I2
VinV SRSS
Noise spectrum : )()(2IStI
Noise of an amplifier
2I
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 5/80 WP4 - HF Electronics
Basic noises in macro-systems
e
Ie2SI
Shot-noise Equilibrium noise
+
-T0
RTkS BI / 4 0
J.B. JohnsonW. Schottky
R SI
Vacuum tube
Tunnel junction
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 6/80 WP4 - HF Electronics
Noise in macro-systems
RF-black-body Optical black-body
J. Hooge
/4
H. Nyquist M. Planck
h
2 1⁄ 1
⁄
Resistance noise
~10
1D-TEM mode 3D photons50 Ω
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 7/80 WP4 - HF Electronics
coherent scattering shot noise
Conductance is transmission Quantum scattering is noisy
Fano factor F<1 : a measure of noise intensity
4 2 ∑ 1
∑ 2 " "
Ya.M. Blanter, M. Büttiker / Physics Reports 336 (2000) 1-166
R. Landauer and M . Büttiker
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 8/80 WP4 - HF Electronics
Combining population + scattering noise
Thermal noise Tunnel junction Diffusive metal Q-point contact
2 2
= 4
2
= 2
2 1
= 2 1
2 2 coth 2 1
= 2
tunnel junctions are used as a primary noise standard
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 9/80 WP4 - HF Electronics
Combining population + scattering noise
Thermal noise Tunnel junction Diffusive metal Q-point contact
2 2
= 4
2
= 2
2 1
= 2 1
2 2 coth 2 1
PIB
(V
rms^
2)
Bru
it
Transmission
= 2
QPC
GaAssoonQPC in Graphene(CNRS-Grenoble)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 10/80 WP4 - HF Electronics
A.H. Steinbach et al. / Phys. Rev. Lett. 76(1996) 3806
ballistic → diffusive → hot-electrons → phonons → macroscopic world
Metallic sample : from meso to macro
… on increasing the sample length
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 11/80 WP4 - HF Electronics
~ ~4 ∑
difffusive
e-e
phonons
Semi-ballistic
universal !
Metallic sample : from meso to macro
... on increasing the bias voltage
Shot noise Hot electrons Phonon cooling
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 12/80 WP4 - HF Electronics
Current noise spectrum
Low bias
active device
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 13/80 WP4 - HF Electronics
Current noise spectrum
≡50Ω4
10 Ω4
!
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 14/80 WP4 - HF Electronics
Cryogenic RF-noise measurement
Aalto set-up (650-750 MHz) ENS-setup (0.1-2GHz, 1-12GHz)
See : Antti Laitinen poster !!
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 15/80 WP4 - HF Electronics
Example of noise spectra and Fano factor plot
FFT
A. Betz, PhD-thesis, https://tel.archives-ouvertes.fr/tel-00784346
Examples of Fano(V)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 16/80 WP4 - HF Electronics
L1: Noise in graphene devices
o Introduction noise physicso Quantum shot noise in grapheneo Hot-electron noise in grapheneo Phonon cooling in grapheneo Perspectives
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 17/80 WP4 - HF Electronics
~ ~4 ∑
difffusive
e-e
phonons
Semi-ballistic
universal !
Metallic sample : from meso to macro
... on increasing the bias voltage
Shot noise Hot electrons Phonon cooling
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 18/80 WP4 - HF Electronics
Shot noise in graphene junctions (@ DP)
J. Tworzillo et al. / Phys. Rev. Lett. 96 (2006) 246802
Evanescent wave transmission
Conductance
Fano
Short junction with W>>L
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 19/80 WP4 - HF Electronics
Shot noise in graphene junctions
R. Danneau et al./ Phys. Rev. Lett. 100 (2008) 196802J. Tworzillo et al. / Phys. Rev. Lett. 96 (2006) 246802
F=1/3 at DPNoise suppression in ballistic graphene (W=5L)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 20/80 WP4 - HF Electronics
R. Danneau et al. / Phys. Rev. Lett. 100 (2008) 196802J. Tworzillo et al. / Phys. Rev. Lett. 96 (2006) 246802
Shot noise in graphene ribbonstheory experiment
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 21/80 WP4 - HF Electronics
~ ~4 ∑
difffusive
e-e
phonons
Semi-ballistic
universal !
Metallic sample : from meso to macro
... on increasing the bias voltage
Shot noise Hot electrons Phonon cooling
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 22/80 WP4 - HF Electronics
2
3⁄ 25 Ω
4 2eI34
Heat equation : .
Hot electron shot noise
« Wiedemann-Franz regime »
, 1 exp
e-e interactions at finite bias=> µ(x) and electron temperature profile Te(x)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 23/80 WP4 - HF Electronics
~ ~4 ∑
difffusive
e-e
phonons
Semi-ballistic
universal !
Metallic sample : from meso to macro
... on increasing the bias voltage
Shot noise Hot electrons Phonon cooling
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 24/80 WP4 - HF Electronics
Phonon resistivity
GR/BN
OP-phononsirrelevant
large AC-phononsvelocity
(s = 2x104 m/s)
weakAC-phonons
effect
Chen-Fuhrer / Nat. Nano (2008)Efetov-Kim / Phys. Rev. Lett. (2010)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 25/80 WP4 - HF Electronics
Fermi surface Available phonon space
kF
q
qmax α T2 kF >
T < TBG (cold)
qmax2 kF =
T = TBG=(2s/vF)TF
q=kT/s
2 kF qmax<
T > TBG(hot )
4%
1000 ↔ 40
Phonon scattering : Bloch-Gruneisen temp.
Chen-Fuhrer / Nat. Nano (2008)Efetov-Kim / Phys. Rev. Lett. (2010)
∆ ≪8
~
∆ ≪ ~ . !!! ; . 0.1Ω⁄ !!!
300 1 ∆⁄ 2 10 /
300 μ ⁄ 7μ /
L. Wang et al. / Science 342 (2013) 614
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 26/80 WP4 - HF Electronics
Phonon relaxation / cooling
10 / ≪ 10 / ≪ 500 /
Joule heating and phonon cooling at 4K (cold phonons)
Very weak AC-phonon coupling
Electric field + scattering
acoustic-phonons onlyGraphene : VF=10 /s/VF=0.02
P=∑
P=∑
∝
=∑
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 27/80 WP4 - HF Electronics
Fermi surface Available phonon space
kF
q
qmax α T2 kF >
T < TBG (cold)
qmax2 kF =
T = TBG=(2s/vF)TF
q=kT/s
2 kF qmax<
T > TBG(hot )
4%
1000 ↔ 40
Phonon scattering : Bloch-Gruneisen temp.
Chen-Fuhrer / Nat. Nano (2008)Efetov-Kim / Phys. Rev. Lett. (2010)
∆ ≪8
~
∆ ≪ ~ . !!! ; . 0.1Ω⁄ !!!
300 1 ∆⁄ 2 10 /
300 μ ⁄ 7μ /
L. Wang et al. / Science 342 (2013) 614
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 28/80 WP4 - HF Electronics
2
≪ 15
≫1 9.62
8
Heat equation
Cold phonon cooling
Supercollisison regime
Phonon relaxation (hot phonons)
ImpurityT T3
Ordinary electron-phonon 3-body electron-phonon-impurity
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 29/80 WP4 - HF Electronics
Shot
-noi
se (
A2/H
z)
I ds
(mA
)
linear I-V’s (diffusive) noise: from linear to sublinear
RF noise measurement
A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805
Thermal + 1/f noise diffusive G/hBN sample
very-BN™hBN powderby St Gobain
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 30/80 WP4 - HF Electronics
0
200
400
600
800
Tph
-55 V
-43 V-32 V
-20 V-10 V
0 VVg = +12 V (CNP)T e (
K)
P (mW [m]-2)
-30 0 301
2
3
R (k
)
Vg (V)
0.00 0.05 0.10 0.15 0.20
Electronic temperature measurement
A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 31/80 WP4 - HF Electronics
Checking the phonon temperature
A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805 B. Collab. C. Voisin group
Temperature dependent Raman shift of 2D Peak
≪ ~
P=∑
P=∑
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 32/80 WP4 - HF Electronics
0
200
400
600
800
Tph
-55 V
-43 V-32 V
-20 V-10 V
0 VVg = +12 V (CNP)
T e (K)
P (mW [m]-2)
-30 0 301
2
3
R (k
)
Vg (V)
0.00 0.05 0.10 0.15 0.20
Data analysis : Bloch-Gruneisen regime
A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805
kF
q
qmax α T2 kF >
T < TBG (cold)
qmax2 kF=
T = TBG=(2s/vF)TF
q=kT/s
2 kF qmax
<
T > TBG(hot )
4% ∑
TBG
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 33/80 WP4 - HF Electronics
ImpurityT T3
Ordinary electron-phonon collision 3-body electron-phonon impurity
1
4 47 56 62 67
TBG
0.200.150.100.050
0.5
43
2
40Tph (K)
-55 V-43 V-32 V
-20 V
-10 V0 V
Vg = +12 V (CNP)
P (mW [m]-2)T e3 /
P (K
3 m2 /W
)
T2T4
T3
0
200
400
600
800
Tph
-55 V
-43 V-32 V
-20 V-10 V
0 VVg = +12 V (CNP)
T e (K)
P (mW [m]-2)
-30 0 301
2
3
R (k
)
Vg (V)
0.00 0.05 0.10 0.15 0.20
Hot phonons : supercollisions
A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805 A. Betz et al. / Nat. Phys. 9 (2012) 109
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 34/80 WP4 - HF Electronics
ImpurityT4 T3
Ordinary electron-phonon collision 3-body electron-phonon-impurity
Supercollisons regime
A. Betz et al. / Nat. Phys. 9 (2012) 109 Song-Levitov / PRL (2013)
1 9.628
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 35/80 WP4 - HF Electronics
C. Voisin and B. Plaçais / special issue “hot carriers in graphene”, J. Phys.: Condens. Matter 27 (April 2015)A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805 A. Betz et al. / Nat. Phys. 9 (2012) 109A. Laitinen et al. / Nano Lett..14 (2012) 3009.
The full AC-Phonon scenarioSuspended G : Antti Laitinen poster !!
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 36/80 WP4 - HF Electronics
Supercollisions are also seen in optics
Pump-probe experiment at Cornell (Graham et al., Nat. Phys 2013)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 37/80 WP4 - HF Electronics
Phonon cooling optoelectronics
RF Thermal noise Black-body (tail)
Collaboration with Ch. Voisin’s Optics group at LPA
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 38/80 WP4 - HF Electronics
Phonon cooling optoelectronics
RF Thermal noise Black-body (tail)
Collaboration with Ch. Voisin’s Optics group at LPA
« Janus » setup
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 39/80 WP4 - HF Electronics
Black-body spectrum (tail) RF Thermal noise
Comparing RF and Optical C-power
Collab. Ch. Voisin’s Optics group at LPA
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 40/80 WP4 - HF Electronics
Suspended bi-layer graphene :Low carrier densitySuppressing AC-phonon cooling
A. Laitinen et al. / Phys. Rev. B, Rapid Comm. (2015) in press
Optical phonon cooling (bilayer)
WF++
OPs
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 41/80 WP4 - HF Electronics
L2 : Ballistic graphene devices
Applications of hot electron effect ?
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 42/80 WP4 - HF Electronics
applications
Applications of the hot electron effects ?
• THz-UV bolometers• Noise standard (for scientists only ?) • LNA’s
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 43/80 WP4 - HF Electronics
~ ~4 ∑
20
impurity
e-e
phonons
less-impurities
universal !
234
Short diffusive graphene
T2 - hot-electrons as a noise standard
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 44/80 WP4 - HF Electronics
C B McKitterick et al. / special issue “hot carriers in graphene”, J. Phys.: Condens. Matter 27 (2015)
T4 - Bloch-Gruneisen for THz detectors
THz photo-detectors at Yale, etc…
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 45/80 WP4 - HF Electronics
300
T4 – supercollisions for LNA’s, Optics …
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 46/80 WP4 - HF Electronics
Conclusions on noise (L1)
o Electron-phonon in graphene is weak for ACs and strong for OPso Hot electron effects are prominento Next : investigate OP-cooling, SPP-cooling etc….
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 47/80 WP4 - HF Electronics
HF-Graphene Electronics
noise (L1) ballistic’s (L2)(electron-phonon) (Dirac Fermion Optics)
Bernard Plaçais [email protected]
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 48/80 WP4 - HF Electronics
L2 : Ballistic graphene devices
Ballistic electronics is possible thanks to weak e-ph scattering ( )
Question : How can we exploit it ?
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 49/80 WP4 - HF Electronics
L2 : Ballistic graphene devices
o Motivation : Dirac Fermion Opticso Ballistic graphene and junctionso Ballistic graphene FETso Conclusions
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 50/80 WP4 - HF Electronics
Vasalego lens and splitters (proposal)
V.V. Cheianov, V. Falko, B.L. Altshuler / Science 315 (2007) 1252
Relies negative refraction index (and a point source) : sin ⁄ sin
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 51/80 WP4 - HF Electronics
M.I. Katsnelson, K. Novoselov, A. Geim / Nat. Phys. 2 (2006) 620
Single-layer Bi-layer
Refraction at p-n junctions
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 52/80 WP4 - HF Electronics
Klein tunneling reflector (easier)
Transmission T
1-T
Here : total internal reflection
Q. Wilmar et al. / 2D Materials 1 (2014) 011006
Relies on large refraction index contrast sin ⁄ sin
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 53/80 WP4 - HF Electronics
Klein tunneling reflector (easier)
Q. Wilmart et al. / 2D Materials 1 (2014) 011006
Relies on large and tunable refraction index contrast sin ⁄ sin
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 54/80 WP4 - HF Electronics
Klein tunneling transistor (modelling)
Q. Wilmart et al. / 2D Materials 1 (2014) 011006
Diffraction limitednano KT-FETs device
Klein Tunneling conductance
Refraction effect
Scattering model and NGEF simulations
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 55/80 WP4 - HF Electronics
Wave packet approach
Q. Wilmart et al. / 2D Materials 1 (2014) 011006
1-T
Courtesy of D. Jimenez (UAB)
(poster Enrique Colomes)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 56/80 WP4 - HF Electronics
o Widely tunable index n=-kn/kp
o Incoherent DFO at room temperatureo Ballistic transport L << lB, le-e
o Geometrical optics L >> F
o Sharp junctions d/ F ≤ 1o Homogeneous medium δkF<<kF
L
d
Requirements for DFO
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 57/80 WP4 - HF Electronics
Getting ballistic graphene
4 566450
A.S. Mayorov et al. / Nano Lett. 11 (2011) 2396
Landauer-Büttiker GBN heterostructure
o =n/1012 cm-2
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 58/80 WP4 - HF Electronics
Bend resistance criterion (GaAs)
; 2 2
S. Tarucha et al. / Phys. Rev. B 45 (1992) 13465
bend resistance ballistic length
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 59/80 WP4 - HF Electronics
Bend resistance criterion (Graphene)
(van der Pauw mobility)
o RB smaller than diffusive limito Negative RB at high dopingo Temperature dependence (phonons)
A.S. Mayorov et al. / Nano Lett. 11 (2011) 2396
μ μ ⁄
o Lmfp=1µm @ µ=105 cm2/V/s, n=1012 cm-2
o Ballistics requires high mobility and density!
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 60/80 WP4 - HF Electronics
“smooth” p-n junctions
V.V. Cheianov and V.I. Falko / Phys. Rev. B. 74 (2006) 041403 (R)
4
transparency is too low for DFO !
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 61/80 WP4 - HF Electronics
“sharp” p-n junctions
J. Cayssol, B. Huard et al. / Phys. Rev. B. 74 (2006) 041403 (R)Q. Wilmart et al. / 2D Materials 1 (2014) 011006
⁄ 11
sinh sinh
sinh sinh
1 cos 1 cos
Fermi-function-like potential step Anomalous Snell-Descartes refraction
Fresnel-like relations
sin ⁄ sin
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 62/80 WP4 - HF Electronics
as function of channel doping as function of junction length (p-n)
Transmission of a “sharp” p-n junction
J. Cayssol et al. / Phys. Rev. B. 74 (2006) 041403 (R)Q. Wilmart et al. / 2D Materials 1 (2014) 011006
po-p
po-n
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 63/80 WP4 - HF Electronics
Experiments with top + bottom gates
Huard-Stander et al. / Phys. Rev. Lett. 98 (2007) 236803; Phys. Rev. Lett. 102 (2009) 026807;A. Young and P. Kim al. / Nat. Phys. XX (2009) YYYYYYY
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 64/80 WP4 - HF Electronics
Suspended graphene with (remote) back gates
A.L. Grushina et al. / Appl. Phys. Lett. 102 (2013) 223102; Maurand et al./ Carbon 79 (2014) 486
Fabry-Pérot oscillations, Guiding effects, Quantum Hall effect, Snakes states, ...
Suspended G : Simon Zihlmann and Bàlint Fülöp posters !!
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 65/80 WP4 - HF Electronics
Sharp contact junctions
Y. Wu et al. / Nano Letters 12(2012) 1417
L=500 nm
L=170 nm
L=50 nm
weak Fabry-Pérot oscillations
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 66/80 WP4 - HF Electronics
Can we use contact junctions for Dirac Fermion optics ?
Yes, provided that one can tune contact doping
L
d
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 67/80 WP4 - HF Electronics
Field-effect control of metallic doping
G. Giovanetti et al. / Phys. Rev. Lett. 1001 (2008) 026803
1 1 4 ⁄
with∆ ; ⁄
Bac
k-ga
te
Vg
Cdl Cg
contact : ⇒ is gate-tunable (2DM only !!)
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 68/80 WP4 - HF Electronics
contact junctions with gated contacts
Q. Wilmart thesis
Cont. gate
channel gate
Drain
Source
Numerical simulation of 2D potential Calculated potential step at the contact
OV
+2V-1V
Artist view Sample : local back gates with 30 nm gaps
contact gate
30 nm
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 69/80 WP4 - HF Electronics
In graphene, contact is also tunable
Q. Wilmart thesis
p-contacts neutral n-contactsBallistic limit
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 70/80 WP4 - HF Electronics
Modelling tunable contact junctions
Ballistic junction model(Cayssol et al, PRB 2009)(Wilmart et al., 2DM 2014)
Electrostatic model of the metallic contact
(Giovanni et al, PRL 2008)(Xia et al, nature 2011)
Q. Wilmart thesis
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 71/80 WP4 - HF Electronics
Fitted parameters
Q. Wilmart thesis
Measured Simulated
Fixed parameters : junction length (30nm) , hBN -thickness (16 nm)
Fitted parameters : μ = 6000 cm2/V/s, Pd doping : 50meV, double layer thickness (2nm), metal-graphene resistance (~100 Ohm.µm)
Vg-contact Vg-contact
V g-c
hann
el
V g-c
hann
el
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 72/80 WP4 - HF Electronics
Gated-contacts can be useful
o Use contact junctions for DFOo Contact gated transistor (below)o p-n junctions for photo-detection/mixingo Nano-plasmonics, etc…
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 73/80 WP4 - HF Electronics
L2 : Ballistic graphene devices
Benefits of ballistics in conventionnal FETs ?
• High-mobility G-FETs• Contact-gated transistor
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 74/80 WP4 - HF Electronics
High-frequency field effect transistors
600 GHz 70GHz 50-500 GHz
e.g. >90 GHz
Radars for aircrafts for vehicules THz imaging
LNAs for telecom.
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 75/80 WP4 - HF Electronics
Glossary of RF transistors
Transconductance : ⁄
Differential conductance : ⁄ 1⁄
Voltage gain : ⁄
Current gain : 1 1 ⁄
Transit frequency : 2⁄
Power gain : U ⁄
Max oscillation frequency : ~ 2⁄
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 76/80 WP4 - HF Electronics
Power cutoff frequency ?
Y. Wu et al. / Nano Letters 12 (2012) 3062
In conventional G-FETs : . ≪ ∝
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 77/80 WP4 - HF Electronics
power cutoff frequency ?
Y. Wu et al. / Nano Letters 12 (2012) 3062
~ 2⁄
~ 1
Problem is the lack of current saturation
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 78/80 WP4 - HF Electronics
Phonon saturation in high-mobility graphene
I. Meric et al. / IEEE (2011)
Solution : graphene on BN (one more time !)
~ ‼L=0.6 µm
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 79/80 WP4 - HF Electronics
No
Phonon saturation in ballistic graphene
I. Meric et al. / IEEE (2011)
GoBN
G-FET
Ballistics enhances (differential) resistance !!
~ ‼L=0.6 µm
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 80/80 WP4 - HF Electronics
Differential resistance Pulsed contact gating RF-gain switching
G2
G1Drain
Source100µm
contact gate
Channelgate
SEM
Drain
Source
Vcont
VchVds
The contact gated RF transistor
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 81/80 WP4 - HF Electronics
Differential resistance Pulsed contact gating RF-gain switching
G2
G1Drain
Source100µm
SEM
Drain
Source
Vcont
VchVds
The contact gated RF transistor
DS
Q. Wilmart thesis
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 82/80 WP4 - HF Electronics
Conclusions
o Tunable p-n junctions are building blocks for Dirac Fermion Opticso Dirac Fermion Optics proposal are still challenging but feasibleo Graphene on BN offers new perspectives for HF electronics
Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 83/80 WP4 - HF Electronics
Thank you for your attention !