noise (L1) ballistic’s (L2)placais/publication/2015_Graphene-Study... · 2015. 5. 11. · Graphene-Study, Kaprun, March 27th 2015, noise / ballistics in graphene, B. Plaçais 1/80

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 placais@lpa.ens.fr

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 placais@lpa.ens.fr

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 !