Hyperbolic cooling of graphene Zener-Klein transistors Transport...

Hyperbolic cooling of graphene Zener-Klein transistors

Transport PLUS Noise thermometry

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K.

Watanabe, G. Fève, J.M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais

Drain

Source

Gateh-BN

Hyperbolic cooling

Noise thermometry brings new information

on scattering and relaxation of graphene carriers.

Current saturation regime is investigated here

Graphene 2017, opto-electronics

Introduction


Hyberbolic Phonon Polaritons of uniaxial hBN

𝜖𝑚 = 𝜖∞,𝑚 + 𝜖∞,𝑚 ×𝜔𝐿𝑂,𝑚

2− 𝜔𝑇𝑂,𝑚

2

𝜔𝑇𝑂,𝑚2−𝜔2 − 𝑖𝜔Γ𝑚

𝑘𝑥2

𝜖⫠+𝑘𝑧2

𝜖||=𝜔2

𝑐2

𝜖⊥ < 0, 𝜖∥ > 0

𝑒𝑖(𝑘𝑥𝑥−Ω𝑡) × 𝑒𝑖(𝑘𝑧𝑧)

Dai et al. Nat. Nano. 2015 Kumar et al., Nano Letters 2015Caldwell et al. Nat Comm. 2014 ; Brar et al., Nano Letters 2014 ; …..


Propagating HPPs

HPPs and hot graphene ?

SLG, BLG, TLGLxW=4x3 µmSource Drain

Gate

2D h-BN HPPs

Near field coupling of graphene hot electrons with substrate phonons

Graphene on 3D oxide Graphene on 2D h-BN

heat diffusion to the gate heat propagation to the gate

SLG, BLG, TLGLxW=4x3 µmSource Drain

Gate

SiO2, Al2O3, HfO2, … SPPs


Graphene current fluctuations

emit HPP radiations deep into

hBN bulk

Klein Tunneling across n-p-n barriers Electric field induced Zener tunneling

zero bandgap semiconducitor

Angular-dependent transmission

Klien and Zener Tunneling


SLG BLG

Katsnelson, Novoselov, Geim, Nat. Phys.2, 620 (2006) Kane et al., J. Phys. : Condens. Matter 27 (2015)

Source

Drain

lZK

E𝑙 𝑧𝑘

BLG junction conductivity :

𝜎𝑍𝐾 =4𝑒2

ℎ

𝑘𝐹𝑙𝑍𝐾4𝜋

Zener-Klein Tunneling (ZKT)

lZK

lZK

lZK

lZK

lZK

Source

Drain

ZKT conductivity (BLG) :

𝜎𝑍𝐾 = 𝛼4𝑒2

ℎ


≈ 𝐶𝑡𝑒

𝛼~0.3 ; 𝑙𝑍𝐾 = 0.7 − 4𝜇𝑚Graphene 2017, opto-lectronics

Threshold field for ZKT

Pauli blocking of ZKT E > 𝐸𝑧𝑘 = 2𝐸𝐹𝑒𝑙𝑧𝑘

~ 𝑘𝐹3

e-h creation by ZKT 𝑛𝑒−ℎ𝑍𝐾 =

𝑒 𝑘𝐹

𝜋2 ℏ(𝐸 − 𝐸𝑍𝐾)

𝐸𝑧𝑘𝑙 𝑧𝑘=2𝐸𝐹


𝑛𝑒−ℎ𝑍𝐾

𝜎𝑍𝐾 = 0.34𝑒2

ℎ


𝑬𝒛𝒌

High frequency to overcome 1/f noise

Thermal current noise 𝑆𝐼 = 4 𝐺 𝑘𝐵𝑇𝑁

Fast e-e thermalisation (20 fs)

𝑘𝐵𝑇𝑁 = −∞

∞

𝑓 1 − 𝑓 𝑑𝐸 = 𝑘𝐵𝑇𝑒

Noise thermometry at high bias

Betz et al. / Phys. Rev. Lett. 109 (2012) 056805 Betz et al. / Nat. Phys. 9 (2013) 109Brunel et al. / J. Phys. : Condens. Matter 27 (2015) 164208 Laitinen et al. / Phys. Rev. B. 91 (2015) 121414(R)

E

f10


Noise thermometry in the ZKT regime

Out-of-equilibrium e-h population

𝑘𝐵𝑇𝑁 = −∞

∞

𝑓 1 − 𝑓 𝑑𝐸 ≈𝑛𝑒 + 𝑛ℎ𝐷𝑂𝑆

𝑛𝑒 = 0∞𝐷𝑂𝑆 × 𝑓𝑑𝐸 ;

𝑛ℎ = 0∞𝐷𝑂𝑆 × 1 − 𝑓 𝑑𝐸

Hot electrons + holes

−∞

∞

𝑓 1 − 𝑓 𝑑𝐸

𝑘𝐵𝑇𝑁 ≈ 𝑘𝐵𝑇𝑒 +𝑛ℎ𝐷𝑂𝑆

E

f10

2EF

E

f


𝑛𝑒−ℎ𝑍𝐾

Experiment


High mobility BLG sample

m* ~ 0.03me

E

DOS

e

h

2 2

2

kE

m

CQ ~ 40 mF/m2

Drain

Source

Gate

h-BN

h-BN23 nm

SLG, BLG, TLGLxW=4x3 µm

Gate

CQ

Cgeo

CQ

Cgeo

CQ

Cgeo

Source Drain


µ = 30 000 𝑐𝑚2𝑉−1𝑠−1

Intraband current saturation


See e.g. N. Meric et al., Nat. Nanotech. 3, 654 (2008)

𝜀𝑠𝑎𝑡 ≈ 100 𝑚𝑒𝑉

𝜀𝐻𝑃𝑃 ≈ 100 𝑚𝑒𝑉

𝜎 =𝑛𝑒µ

1 + 𝐸/𝐸𝑠𝑎𝑡2 ; 𝑣𝑠𝑎𝑡 = µ𝐸𝑠𝑎𝑡 ≤ 3 105𝑚/𝑠

Importantly : 𝑬𝒔𝒂𝒕 ≪ 𝑬𝒁𝑲

𝐽𝑠𝑎𝑡 = 𝑛𝑒𝑣𝑠𝑎𝑡 ; 𝜀𝑠𝑎𝑡 =𝜋

2ℏ𝑘𝐹𝑣𝑠𝑎𝑡

Velocity saturation by type-I hBN phonons

Zener-Klein Transport Noise thermometry

Drain

Source

Gateh-BN

Noise temperature features

𝜀𝐻𝑃𝑃2 ≈ 200 𝑚𝑒𝑉

𝜀𝑂𝑁 ≈ 200 𝑚𝑒𝑉

Transport is featureless. Main noise features are :

1) Superlinear TN(E) ⟺ current saturation

2) Temperature plateaus in ZKT regime

3) Thershold at ZKT onset (arrows)

4) Linear TN(E) at neutrality (ZKT e-h creation )

5) Voltage threshold ⟺ activation energy 200 meV


Same features in SLG/TLG


SLG

TLG

Conventional cooling mechanism ?


electron conduction to the leads

Raw noise thermometry Wiedemann-Frantz analysis

e-e interactions (thermalisation) → 𝜏𝑒𝑒~20 𝑓𝑠

Wiedemann-Frantz heat conduction 𝑘𝐵𝑇𝑁 ≡ 𝑘𝐵𝑇𝑒 =3

8× 𝐿𝑒𝑛𝑔𝑡ℎ × 𝑃 𝜎

electron conduction Graphene 2017, opto-electronics

0

200

400

600

800

Tph

-55 V

-43 V

-32 V

-20 V

-10 V

0 VVg = +12 V (CNP)

Te (

K)

P (mW [m]-2)

-30 0 301

2

3

R (

k

)

Vg (V)

0.00 0.05 0.10 0.15 0.20

AC phonon cooling ?

this work AC phonon cooling

Yang et al. / arXiv:1702.02829v1 (2017) Betz et al. / Phys. Rev. Lett. 109 (2012) 056805; Betz et al. / Nat. Phys. 9 (2013) 109

arXiv:1702.02829v1 (2017

Neutral graphene cools better than doped graphene at high bias !

AC phonons


OP phonon cooling ?arXiv:1702.02829v1 (2017


e-OP interaction = deformation potential ⇒ Γ𝑂𝑃 ≪ Γ𝐻𝑃𝑃,𝑆𝑃𝑃

OP-phonon Raman thermometry ⇒ OP cooling negligible

HPP cooling !


Impedance matching HPPs are propagative modes

Superplanck HPP cooling of Graphene

h-BN23 nm

Gate

Graphene

HPPs

near-field

Gate

Graphene near-field

h-BNSemi-infinite

HPPs

IWEPNM2017 – Kircheberg 6/3/201721

HPP II

k//

E (m

eV)

170

200

𝑃 =𝑛

4𝜋2ђ𝜔∆𝜔

e𝑥𝑝 ђ𝜔 𝑘𝐵𝑇 − 1×𝑀

M=𝟒𝑹𝒆(𝒀𝟎)𝟒𝑹𝒆(𝝈)

𝒀𝟎+𝝈𝟐 (non-local emissivity)

𝜎(𝑞, 𝜔) (non-local graphene conductivity)

The thermal radiative cooling picture

IWEPNM2017 – Kircheberg 6/3/201722

EXPERIMENT

THEORY

From thin to thick h-BN


23nm

200nm

23nm

200nm

23nm

200nm

• HPP cooling ≫ Joule Power in ZKT regime• Emissivity ≈ 1 in ZKT regime

• Same 𝐽𝑠𝑎𝑡• Smaller 𝜎𝑍𝐾

M =1

Noise measurement of 𝜏𝐻𝑃𝑃

e-h pumping rate (th.) 𝑛𝑒−ℎ𝑍𝐾 =

𝑒 𝑘𝐹

𝜋2 ℏ(𝐸 − 𝐸𝑍𝐾) =

𝑛𝑒−ℎ

𝜏𝐻𝑃𝑃

e-h density (exp.): 𝑛𝑒−ℎ = 𝐷𝑂𝑆 × 𝑘𝐵∆𝑇𝑁/2

HPP cooling rate : 𝜏𝐻𝑃𝑃 ≤ 0.46 𝑝𝑠4𝜋2

∆Ω𝐻𝑃𝑃2≈ 0.8 𝑝𝑠

E

f10

Stationary e-h pair density


HPP cooling balances max Joule Power

ZK current : 𝐽𝑧𝑘 = 𝛼4𝑒2

ℎ

𝑘𝐹𝑙𝑧𝑘

4𝜋𝐸 − 𝐸𝑧𝑘 ZK pumping : 𝑛𝑒−ℎ

𝑍𝐾 =𝑒 𝑘𝐹

𝜋2 ℏ(𝐸 − 𝐸𝑍𝐾)

HPP cooling : 𝑃𝐻𝑃𝑃 = ℏΩ 𝑛𝑒−ℎ𝐻𝑃𝑃 = ℏΩ 𝑛𝑒−ℎ

𝑍𝐾 = ℏΩ𝑒 𝑘𝐹

𝜋2 ℏ𝐸 − 𝐸𝑧𝑘

Joule Heating : ∆𝑃𝐽𝑜𝑢𝑙𝑒 = 𝐽𝑠𝑎𝑡 𝐸 − 𝐸𝑠𝑎𝑡 = 𝟐𝜺𝒔𝒂𝒕𝑒 𝑘𝐹

𝜋2 ℏ𝐸 − 𝐸𝑠𝑎𝑡

in GoBN,where ℏ𝛺𝐼𝐼 ≈ 2ℏ𝛺𝐼 ≈ 200 𝑚𝑒𝑉 ⇒ 𝑷𝑯𝑷𝑷 ≈ 𝑷𝑱𝒐𝒖𝒍𝒆

E

f2EF

HPP cooling doped regime


ZKT-FETs as power amplifiers

with efficient HPP cooling


Bottom gated G-FETs

Constant carrier density

Constant gate voltage

h-BN20 nm

Bi-Layer-GrapheneLxW=4x3 µm

Gate

CQ

Cgeo

CQ

Cgeo

CQ

Cgeo

Source Drain

Transconductance


Zener-Klein-Tunneling transistor

𝑔𝑚 = 250µ𝑆/𝑚𝑚 𝐺𝑎𝑖𝑛 = 10

GoBN

• High mobility (30 000 cm2/V/s)

• Low contact resistance

• Current saturation ++

• High-power ++

• Zener-Klein regime operation ++

• Negligible self heating effects

Bottom gating

• Drain gating (bottom gate effect)

• Transconductance (250 µS/mm)

• Large voltage gain (G~10)


ZKT-FETs as power amplifers

GoBN Zener-Klein transistor Panasonic : X-GaN Power transistor

GoBN Lg=4µm

5 merits of h-BN

1. High mobility

2. Large saturation currents (power amplification ?)

3. Pinchoff replaced by Zener-Klein tunneling

4. Compensation of ZK tunneling by a bias induced doping depletion

5. No thermal degradation => cooling by hyperbolic hBN phonons !!!


Conclusions

1. HPP cooling promotes h-BN is the ideal heat sink

2. Zener-Klein Tunneling optimizes HPP emission

3. ZKT-FETs are promising high power transistors


Contributors

W. Yang (post-doc), S. Berthou (PhD student), Q. Wilmart (PhD student)

A. Denis, M. Rosticher (LPA, RF electronics and clean room engineers)

X. Lu, G. Zhang (Beijing, sample fabrication)

T. Taniguchi, K. Watanabe (NIMS, hBN crystals)

G. Fève, J.M. Berroir, BP, C. Voisin, E. Baudin (LPA meso / optics groups)


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Hyperbolic cooling of graphene Zener-Klein transistors Transport...

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