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Wei Yang
Hyperbolic cooling of graphene Zener-Klein transistors
Drain
Source
Gate
W. Yang, S. Berthou, X. Lu2, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi3, K. Watanabe3, G. Fève, J.M. Berroir, G. Zhang2, C. Voisin, E. Baudin, Bernard Placais
1) LPA β ENS, Meso-Group + Optics-group + Engineers, Paris, France, 2) Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, China, 3) Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Japan
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G/BN Zener-Klein Transistor (GoBN-ZKT)
OUTLINE
What is a G/hBN Zener-Klein transistor?
Scattering: Current saturation in high mobility bilayer Graphene on BN
Relaxation and Cooling : Emission of Hyperbolic Phonon Polaritons
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G/BN Zener-Klein Transistor (GoBN-ZKT)
3
OUTLINE
What is a G/hBN Zener-Klein transistor?
Scattering: Current saturation in high mobility bilayer Graphene on BN
Relaxation and Cooling : Emission of Hyperbolic Phonon Polaritons
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Zener Tunneling at a high electrical field
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large electrical field
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Sharp Klein p-n junction
Klein tunneling
πππ =4π2
βΓ
ππΉπππ
4π
π πββππ
=π ππΉπ2 β
πΈππ
SLG BLG
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Katsnelson, Novoselov, Geim, Nat. Phys.2, 620 (2006)
Smooth Klein p-n junction
πππ = πΌ4π2
βΓ
ππΉπππ
4π ; (πΌ~0.2)
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Zener-Klein tunneling
Zener-Klein Tunneling, Pauli blocking:
πππΎ = πΌ4π2
β
ππΉπππΎ
4π= πΆπππ π‘. ; π πββ
ππΎ =π ππΉ
π2 β (πΈ β πΈππΎ)
π¬ππ =ππ¬π
ππππ (dashed line)
S D
lZK
2EF
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GoBN ZKT is a graphene/hBN transistor operating at a high electrical field
where interband Zener-Klein tunneling dominating the transport
high electrical field
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G/BN Zener-Klein Transistor (GoBN-ZKT)
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OUTLINE
What is a G/hBN Zener-Klein transistor?
Scattering: Current saturation in high mobility bilayer Graphene on BN
Relaxation and Cooling : Emission of Hyperbolic Phonon Polaritons
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Characteristic of the GoBN ZKT device
-6 -4 -2 0 2 4 6
0
5
10
R (
k
)
Vg (V)
T = 4.2K
Drain
Source
Gate
Bias is gating
BL-Graphene
Gate
8
CQ
Cgeo
30 000 cm2V-1s-1
m* ~ 0.03me
E
DOS
e
h
2 2
2
kE
m
CQ ~ 40 mF/m2
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Comparison with GaN or Si transistors
GoBN Zener-Klein transistor Panasonic : X-GaN Power transistor
GoBN Lg=4Β΅m
ππ = 250Β΅π/ππ πΊπππ = 10
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I-V characteristics
Constant gate
Constant carrier density
Impurity scattering
Optical phonon scattering
Zener-Klein tunneling
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Focus on current saturation at low field
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π =ππΒ΅
1 + πΈ/πΈπ ππ‘2
Saturation energy Ιsat
EF at a low doping
100meV at a high doping
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G/BN Zener-Klein Transistor (GoBN-ZKT)
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OUTLINE
What is a G/hBN Zener-Klein transistor?
Scattering: Current saturation in high mobility bilayer Graphene on BN
Relaxation and Cooling : Emission of Hyperbolic Phonon Polaritons
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Relaxation in Graphene
1. e-e interactions β electron multiplication and thermalisation
(π~20 ππ ) + heat conduction : div βΞΊπ»π = βπΈ. π½ , ΞΊ =π2ππ΅
3
3π2π π
2. e-AC-imp supercollisions β prominent in diffusive G but suppressed in G/BN
3. e-OP interaction β deformation potential coupling (π β₯ 2 ππ )
4. e-HPP interaction β fast (π β 200 ππ )!!
Impurity T T3
Ordinary electron-phonon collision 3-body electron-phonon-impurity supercollisions
A. Betz et al. / Phys. Rev. Lett. 109 (2012) 056805; A. Betz et al. / Nat. Phys. 9 (2013) 109
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Noise in graphene transistor
Alexander A. Balandin, Nat. Nano. 8, 549 (2013).
thermal noise
Stotal = Ξ±H V2/ N f + SV
A. Betz et al. PRL.109,056805 (2012).
The bandwidth of Noise spectra in GHz range 14
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Bath temperature π0 = 4.2 πΎ Noise temperature ππ΅ππ β‘ ππΌ 4πΊππππ
Hot electrons, heat equation, Wiedemann-Frantz
ππ΅ππ β‘ ππ΅ππ =3
8 Γ πΏππππ‘π Γ π
π
Hot Fermi sea + holes
ππ΅ππ = π 1 β π ππΈβ
βββ ππ΅ππ +
ππ
π·ππ
RF noise thermometry principles
E
f
ππ΅ππ
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What do we learn from noise ?
Discontinuity in ππ΅ππ πΈ at πΈ β πΈπ§π
Superlinear ππ΅ππ πΈ for πΈ β€ πΈπ§π
Quasi-plateaus ππ΅ππ πΈ for πΈ β₯ πΈπ§π
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Hot electron analysis of noise
Β« hot Β» electron dashed line : ππ΅ππ πΈ β€ πΈπ§π βπ
ππΏ π/π
Β« cold Β» electron dashed line : ππ΅ππ πΈ β₯ πΈπ§π β ππ΅ππ πΈπ§π +π
ππ πΏ π/π
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Hyperbolic Phonon Polaritons of h-BN ?
(Courtesy of F. Koppens, Kaprun School 2015) 18
Reststrahlen band
Type-II Β« in-plane Β»
~170-200meV
Type-I Β« out-of-plane Β»
~90-100meV
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Graphene/HPP impedance matching
HPPs are propagative modes
Superplanck HPP cooling of Graphene
π =π
4π2Ρπβπ
eπ₯π Ρπ ππ΅π β 1Γ π
π =π βππ π, π βπ π, π
ππ + π π
Semi-infinite h-BN : ππ~ππΒ΅πΊ (M~0.01)
Confined HPPs :ππ π, π ~ πΈ Γ ππΒ΅πΊ ( π ~0.1)
β
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HPP relaxation time
e-h pumping : π πββππΎ =
π ππΉ
π2 β(πΈ β πΈππΎ) =
ππββ
ππ»ππ β ππ»ππ =
π2 β
π ππΉ πππββ
ππΈ
Noise temperature Β« Cold electron regime Β» ππββ β€ π·ππ Γ ππ΅βππ/2
ππ»ππ β€π2 β
π ππΉ π·ππ
πππ΅ππππΈ
= 0.46 ππ (π = 1. 1012)
ππββ β€ π·ππ Γ ππ΅βππ/2
E
f 1 0
ZK+HPP at charge neutrality
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HPP cooling in the ZK regime
ZK current : π½π§π = πΌ4π2
β
ππΉππ§π
4ππΈ β πΈπ§π ZK pumping : π πββ
ππΎ =π ππΉ
π2 β(πΈ β πΈππΎ)
HPP cooling : ππ»ππ = βΞ© π πββπ»ππ = βΞ© π πββ
ππΎ = βΞ©π ππΉ
π2 βπΈ β πΈπ§π
Joule Heating : βππ½ππ’ππ = π½π ππ‘ πΈ β πΈπ§π = ππΊππππ ππΉ
π2 βπΈ β πΈπ§π
in GoBN,where βπΊπΌπΌ β 2βπΊπΌ β 200 πππ β π·π―π·π· β π·π±ππππ
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E
f
2EF
HPP cooling doped regime
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HPP cooling of hot electrons
E
f 1 0
HPP thermal emission
Super-Planck HPP thermal emission (πβππ‘(π, π) by Polini at al. )
ππ½ = 0.5πΊπ
π2 , ππ = 0,4ππ, ππ= 4 1012
ππ»πππ‘β = 2.4 Γ π
πΊπ
π2 = 0,24 πΊπ
π2 = ππ½ 2 = πππΉ ππ¦ π‘πππππ ππ‘β β 0.1
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Conclusions
G/BN ZKT-Transistors are performant
HPP-I is responsible for current saturation
HPP-II s give rise to hyper-Plank cooling in the ZKT regime
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Thanks very much for your attention