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(1)

HF-Graphene Electronics

noise (L1) ballistic’s (L2) ( electron-phonon) (Dirac Fermion Optics)

Bernard Plaçais 

placais@lpa.ens.fr

(2)

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 »

(3)

L1: Noise outline

o Introduction noise physics

o Quantum shot noise in graphene

o Hot-electron noise in graphene

o Phonon cooling in graphene

o Perspectives

(4)

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  

Noise spectrum : I

2

( t ) S

I

( )

Noise of an amplifier

I

2

(5)

Basic noises in macro-systems

e

I e 2 S I

Shot-noise Equilibrium noise

+

- T

0

R T

k

S I  4 B 0 /

J.B. Johnson W. Schottky

R S I Vacuum

tube

Tunnel

junction

(6)

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 photons

50 Ω

(7)

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

(8)

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

(9)

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 (Vrms^2) Bruit

Transmission

= 2

QPC

soon GaAs

QPC in Graphene

(CNRS-Grenoble)

(10)

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

(11)

~ ~

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

(12)

Current noise spectrum

Low bias

active device

(13)

Current noise spectrum

≡ 50Ω 4

10 Ω 4

!

(14)

Cryogenic RF-noise measurement

Aalto set-up (650-750 MHz) ENS-setup (0.1-2GHz, 1-12GHz)

See : Antti Laitinen poster !!

(15)

Example of noise spectra and Fano factor plot

FFT

A. Betz, PhD-thesis, https://tel.archives-ouvertes.fr/tel-00784346

Examples of Fano(V)

(16)

L1: Noise in graphene devices

o Introduction noise physics

o Quantum shot noise in graphene

o Hot-electron noise in graphene

o Phonon cooling in graphene

o Perspectives

(17)

~ ~

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

(18)

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

(19)

Shot noise in graphene junctions

R. Danneau et al./ Phys. Rev. Lett. 100 (2008) 196802 J. Tworzillo et al. / Phys. Rev. Lett. 96 (2006) 246802

F=1/3 at DP

Noise suppression in ballistic graphene (W=5L)

(20)

R. Danneau et al. / Phys. Rev. Lett. 100 (2008) 196802 J. Tworzillo et al. / Phys. Rev. Lett. 96 (2006) 246802

Shot noise in graphene ribbons

theory experiment

(21)

~ ~

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

(22)

2 ⁄ 3 25 Ω

4 2eI 3

4

Heat equation : .

Hot electron shot noise

« Wiedemann-Franz regime »

, 1 exp

e-e interactions at finite bias

=> µ(x) and electron temperature profile T e (x)

(23)

~ ~

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

(24)

Phonon resistivity

GR/BN

OP-phonons irrelevant

large AC-phonons velocity

(s = 2x10 4 m/s)

weak AC-phonons

effect

Chen-Fuhrer / Nat. Nano (2008)

Efetov-Kim / Phys. Rev. Lett. (2010)

(25)

Fermi surface Available phonon space

k

F

q

q

max

α T 2 k

F

>

T < T

BG

(cold)

q

max

2 k

F

=

T = T

BG

=(2s/v

F

)T

F

q=kT /s

2 k

F

< q

max

T > T

BG

(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 ⁄ 7 μ /

L. Wang et al. / Science 342 (2013) 614

(26)

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 only

Graphene : V

F

=10 /

s/V

F

=0.02

P=∑

P=∑

=∑

(27)

Fermi surface Available phonon space

k

F

q

q

max

α T 2 k

F

>

T < T

BG

(cold)

q

max

2 k

F

=

T = T

BG

=(2s/v

F

)T

F

q=kT /s

2 k

F

< q

max

T > T

BG

(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 ⁄ 7 μ /

L. Wang et al. / Science 342 (2013) 614

(28)

2

≪ 15

≫ 1 9.62

8 Heat equation

Cold phonon cooling

Supercollisison regime

Phonon relaxation (hot phonons)

Impurity

T T

3

Ordinary electron-phonon 3-body electron-phonon-impurity

(29)

Shot-noise (A2/Hz) Ids (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 powder

by St Gobain

(30)

0 200 400 600 800

T

ph

-55 V

-43 V -32 V

-20 V -10 V Vg = +12 V (CNP) 0 V

T

e

(K )

P (mW [  m]

-2

)

-30 0 30 1

2 3

R (k  )

V

g

(V) 0.00 0.05 0.10 0.15 0.20

Electronic temperature measurement

A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805

(31)

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=∑

(32)

0 200 400 600 800

T

ph

-55 V

-43 V -32 V

-20 V -10 V Vg = +12 V (CNP) 0 V

T

e

(K )

P (mW [  m]

-2

)

-30 0 30 1

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

k

F

q

q

max

α T 2 k

F

>

T < T

BG

(cold)

q

max

2 k

F

=

T = T

BG

=(2s/v

F

)T

F

q=k

T/s

2 k

F

q

ma

x

<

T > T

BG

(hot )4%

T

BG

(33)

Impurity

T T 3

Ordinary electron-phonon collision 3-body electron-phonon impurity

1

4 47 56 62 67

T

BG

0.20 0.15

0.10 0.05

0 0.5

4 3 2

40

T

ph

(K)

-55 V

-43 V -32 V

-20 V -10 V

0 V Vg = +12 V (CNP)

P (mW [  m]

-2

) T

e3

/ P (K

3

m

2

/W )

T

2

T

4

T

3

0 200 400 600 800

T

ph

-55 V

-43 V -32 V

-20 V -10 V Vg = +12 V (CNP) 0 V

T

e

(K )

P (mW [  m]

-2

)

-30 0 30 1

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

(34)

Impurity

T 4 T 3

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 9.62

8

(35)

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) 109

A. Laitinen et al. / Nano Lett..14 (2012) 3009.

The full AC-Phonon scenario

Suspended G : Antti Laitinen poster !!

(36)

Supercollisions are also seen in optics

Pump-probe experiment at Cornell (Graham et al., Nat. Phys 2013)

(37)

Phonon cooling optoelectronics

RF Thermal noise Black-body (tail)

Collaboration with Ch. Voisin’s Optics group at LPA

(38)

Phonon cooling optoelectronics

RF Thermal noise Black-body (tail)

Collaboration with Ch. Voisin’s Optics group at LPA

« Janus » setup

(39)

Black-body spectrum (tail) RF Thermal noise

Comparing RF and Optical C-power

Collab. Ch. Voisin’s Optics group at LPA

(40)

Suspended bi-layer graphene : Low carrier density

Suppressing AC-phonon cooling

A. Laitinen et al. / Phys. Rev. B, Rapid Comm. (2015) in press

Optical phonon cooling (bilayer)

WF++

OPs

(41)

L2 : Ballistic graphene devices

Applications of hot electron effect ?

(42)

applications

Applications of the hot electron effects ?

• THz-UV bolometers

• Noise standard (for scientists only ?)

LNA’s

(43)

~ ~

4 ∑

20

impurity

e-e

phonons

less-impurities

universal !

2 3

4

Short diffusive graphene

T 2 - hot-electrons as a noise standard

(44)

C B McKitterick et al. / special issue “hot carriers in graphene”, J. Phys.: Condens. Matter 27 (2015)

T 4 - Bloch-Gruneisen for THz detectors

THz photo-detectors at Yale, etc…

(45)

300

T 4 – supercollisions for LNA’s, Optics …

(46)

Conclusions on noise (L1)

o Electron-phonon in graphene is weak for ACs and strong for OPs

o Hot electron effects are prominent

o Next : investigate OP-cooling, SPP-cooling etc….

(47)

HF-Graphene Electronics

noise (L1) ballistic’s (L2) ( electron-phonon) (Dirac Fermion Optics)

Bernard Plaçais 

placais@lpa.ens.fr

(48)

L2 : Ballistic graphene devices

Ballistic electronics is possible thanks to weak e-ph

scattering ( )

Question : How can we exploit it ?

(49)

L2 : Ballistic graphene devices

o Motivation : Dirac Fermion Optics

o Ballistic graphene and junctions

o Ballistic graphene FETs

o Conclusions

(50)

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

(51)

M.I. Katsnelson, K. Novoselov, A. Geim / Nat. Phys. 2 (2006) 620

Single-layer Bi-layer

Refraction at p-n junctions

(52)

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

(53)

Klein tunneling reflector (easier)

Q. Wilmart et al. / 2D Materials 1 (2014) 011006

Relies on large and tunable refraction index contrast sin sin

(54)

Klein tunneling transistor (modelling)

Q. Wilmart et al. / 2D Materials 1 (2014) 011006

Diffraction limited nano KT-FETs device Klein Tunneling conductance

Refraction effect

Scattering model and NGEF simulations

(55)

Wave packet approach

Q. Wilmart et al. / 2D Materials 1 (2014) 011006

1-T

Courtesy of D. Jimenez (UAB)

(poster Enrique Colomes)

(56)

o Widely tunable index n=-k n/ k p

o Incoherent DFO at room temperature

o Ballistic transport L << l B , l e-e

o Geometrical optics L >> F

o Sharp junctions d/ F ≤ 1

o Homogeneous medium δk F <<k F L

d

Requirements for DFO

(57)

Getting ballistic graphene

4 56

6450

A.S. Mayorov et al. / Nano Lett. 11 (2011) 2396

Landauer-Büttiker GBN heterostructure

o =n/10

12

cm

-2

(58)

Bend resistance criterion (GaAs)

; 2 2

S. Tarucha et al. / Phys. Rev. B 45 (1992) 13465

bend resistance ballistic length

(59)

Bend resistance criterion (Graphene)

(van der Pauw mobility)

o R

B

smaller than diffusive limit

o Negative R

B

at high doping

o Temperature dependence (phonons)

A.S. Mayorov et al. / Nano Lett. 11 (2011) 2396

μ μ

o L

mfp

=1µm @ µ=10

5

cm

2

/V/s, n=10

12

cm

-2

o Ballistics requires high mobility and density!

(60)

“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 !

(61)

“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

⁄ 1

1 sinh sinh

sinh sinh

1 cos 1 cos

Fermi-function-like potential step Anomalous Snell-Descartes refraction

Fresnel-like relations

sin ⁄ sin

(62)

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

p

o

-p

p

o

-n

(63)

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

(64)

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 !!

(65)

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

(66)

Can we use contact junctions for Dirac Fermion optics ?

Yes, provided that one can tune contact doping

L

d

(67)

Field-effect control of metallic doping

G. Giovanetti et al. / Phys. Rev. Lett. 1001 (2008) 026803

1 1 4 ⁄

with

∆ ; ⁄

Back-gate

V

g

C

dl

C

g

contact : is gate-tunable (2DM only !!)

(68)

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

(69)

In graphene, contact is also tunable

Q. Wilmart thesis

p-contacts neutral n-contacts

Ballistic limit

(70)

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

(71)

Fitted parameters

Q. Wilmart thesis

Measured Simulated

Fixed parameters : junction length (30nm) , hBN -thickness (16 nm)

Fitted parameters : μ = 6000 cm

2

/V/s, Pd doping : 50meV, double layer thickness (2nm), metal-graphene resistance (~100 Ohm.µm)

V

g

-contact V

g

-contact

V

g

-channel V

g

-channel

(72)

Gated-contacts can be useful

o Use contact junctions for DFO

o Contact gated transistor (below)

o p-n junctions for photo-detection/mixing

o Nano-plasmonics, etc…

(73)

L2 : Ballistic graphene devices

Benefits of ballistics in conventionnal FETs ?

• High-mobility G-FETs

• Contact-gated transistor

(74)

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.

(75)

Glossary of RF transistors

Transconductance : ⁄

Differential conductance : ⁄ 1⁄

Voltage gain : ⁄

Current gain : 1 1 ⁄

Transit frequency : ⁄ 2

Power gain : U ⁄

Max oscillation frequency : ~ ⁄ 2

(76)

Power cutoff frequency ?

Y. Wu et al. / Nano Letters 12 (2012) 3062

In conventional G-FETs : . ≪ ∝

(77)

power cutoff frequency ?

Y. Wu et al. / Nano Letters 12 (2012) 3062

~ ⁄ 2

~ 1

Problem is the lack of current saturation

(78)

Phonon saturation in high-mobility graphene

I. Meric et al. / IEEE (2011)

Solution : graphene on BN (one more time !)

~ ‼

L=0.6 µm

(79)

No Phonon saturation in ballistic graphene

I. Meric et al. / IEEE (2011)

GoBN G-FET

Ballistics enhances (differential) resistance !!

~ ‼

L=0.6 µm

(80)

Differential resistance Pulsed contact gating RF-gain switching

G2

Drain G1

Source

100µm

contact gate

Channel gate SEM

Drain

Source

V

cont

V

ch

V

ds

The contact gated RF transistor

(81)

Differential resistance Pulsed contact gating RF-gain switching

G2

Drain G1

Source

100µm

SEM Drain

Source

V

cont

V

ch

V

ds

The contact gated RF transistor

S D

Q. Wilmart thesis

(82)

Conclusions

o Tunable p-n junctions are building blocks for Dirac Fermion Optics

o Dirac Fermion Optics proposal are still challenging but feasible

o Graphene on BN offers new perspectives for HF electronics

(83)

Thank you for your attention !

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