supercollision cooling of electrons in graphenejonckhee/vietnampresentations/quy...phd andreas betz...
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Supercollision cooling of electrons in graphene
Meso‐group : A.C. Betz, E. Pallecchi, S‐H. Jhang, G. Fève, J‐M. Berroir, B. Plaçais Optic‐group : D. Drunel, F. Vialla, C. Voisin, R. Ferreira
Laboratoire Pierre Aigrain – Ecole Normale Supérieure24 rue Lhomond, 75231 Paris Cedex 05 France
www.lpa.ens.fr
h-BN
Drain
Si++ Gate SiO2
Source
1
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Why studying cooling processes ?
2EDISON-18, Matsue, 25/7/2013
1. Hot carriers affect resolution detectors
2. Can be useful as bolometers
3. Graphene lab for electron‐phonon physics
4. Acoustic phonon bottleneck
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Acoustic phonon bottleneck
F. Wu et al. , APL 97, 262115 (2010) (nanotube)A. Fay et al., PRB 84, 245427 (2011) (Bilayer)K.C. Fong, K. C. Schwab, PRX, 031006 (2012)A.C. Betz et al., PRL 109, 056805 (2012)A.C. Betz, et al. nphys 19, 109 (2013)
Optical absorption (2.3%)
N.M. Gabor et al., Science 334 , 648 (2011)S. Winnerl et al. PRL 107, 237401 (2011)J. Yan et al., nnano 7, 472 (2012)M. Freitag et al., nphoto 453 (2013)M.W. Graham et al., nphys 19, 103 (2013)
optical-phonons(200 meV)
Joule heating
photons
photo‐current or pump‐probe noise thermometry (this work)
acoustic-phonons
Electric field + scattering
3Nanophysics, Quy-Nhon, 7/8/2013
acoustic-phonons only
C = 3x108 m/sVF = 1x106 m/sS = 2x104 m/s
+ fast electron-electron
-
4
SI=4kB/R
VI
P=V2/R
W
L
Nanophysics, Quy-Nhon, 7/8/2013
noise thermometry
Steady state Heat conduction Joule heating phonon P=Tα
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5
SI=4kB/R
VI
P=V2/R
W
L
Nanophysics, Quy-Nhon, 7/8/2013
noise thermometry
electron-electron
electron-impurity
Electron-p
Fano factor
α=5 in 3D metals (Wellstood, Urbina, Clarke, PRB 1994)α=3 in 1D CNTs (Wu, …, Hakonen, APL 2010)
α=d+2 => α=4 in 2D graphene ???
Steady state Heat conduction Joule heating phonon P=Tα
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Outline
6Nanophysics, Quy-Nhon, 7/8/2013
1. Introduction : the Bloch‐Grüneisen phonon resistivity
2. Relaxation by acoustic phonons Betz et al., PRL 109, 056805 (2012).
3. Disorder assisted relaxation : supercollisionsBetz et al., Nature Physics 9, 109 (2013)
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Phonon resistivity
GR/BN
Chen-Fuhrer., Nat. Nano 2008 Efetov-Kim PRL 2010
OP‐phononsirrelevant
large AC‐phononsvelocity
(s = 2x104 m/s)
weakAC‐phonons
effect
7Nanophysics, Quy-Nhon, 7/8/2013
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Phonon resistivity in (2D) graphene
GR/BN
Chen-Fuhrer., Nat. Nano 2008 Efetov-Kim PRL 2010
OP‐phononsirrelevant
large AC‐phononsvelocity
(s = 2x104 m/s)
AC‐phononsweak effect
8
0.1Ω/K
Nanophysics, Quy-Nhon, 7/8/2013
Bloch-Gruneisencrossover
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The Bloch‐Grüneisen crossover
Fermi surface Available phonon space
kFq
qmax α T2 kF >
T < TBG (cold)
qmax2 kF =
T = TBG=(2s/VF)TF
q=kT/s
(Efetov-Kim PRL2010)
2 kF qmax<
T > TBG(hot)
(Hwang-Das-Sarma PRB2008)
4%
9
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Outline
10Nanophysics, Quy-Nhon, 7/8/2013
1. Introduction : the Bloch‐Grüneisen phonon resistivity
2. Relaxation by acoustic phonons Betz et al., PRL 109, 056805 (2012).
3. Disorder assisted relaxation : supercollisionsBetz et al., Nature Physics 9, 109 (2013)
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acoustic‐phonon cooling (theory)
(Viljas-Heikkila PRB 2010) 11Nanophysics, Quy-Nhon, 7/8/2013
kF
q
T < TBG (cold phonons)
T > TBG (hot phonons)
(non-degenerate electrons)
Electron-Phonon conductance
Bloch-Gruneisencrossover
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AC‐phonon cooling (principles)
phonon thermal conductance
12
phonon cooling power
Nanophysics, Quy-Nhon, 7/8/2013
Σph ~10 mW/m2/K4
KapitzaΣK ~ 10 W/m2/K4
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phonon thermal conductance
13
T0 = 4 K
phonon cooling power
Tph ~ 40 K
Te ~ 400 K
AC‐phonon cooling (practicals)
P ~100 µW/µm2
Nanophysics, Quy-Nhon, 7/8/2013
Σph ~10 mW/m2/K4
KapitzaΣK ~ 10 W/m2/K4
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Device fabrication
Gr/BN (diffusive) CVD (doped and diffusive)
Schneider et al., Nano Letters 2010 10 (5)
Wedging transfer: polymer CAB & water
CVD grown on Cu (A. Madouri, LPN)
Length (μm)
R (k
Ω)
14
Mitutoyo
Nanophysics, Quy-Nhon, 7/8/2013
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Noise thermometry
SI=4kBTe(P)/R
15
P=V2/R
linear sub-linear linear
Te(x)
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Relaxation by « cold AC phonons »
WF-dip
Agreement with T4 dependence for 2D acoustic phonons
Σ* =0.5-2 mW/m2K4 is disorder dependent and Σ* < Σ = 10mW/m2K4
ΣT4 plateaus
16Nanophysics, Quy-Nhon, 7/8/2013
Sample GR/BN1kF
q
Tph < TBG (cold phonons)
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Outline
17Nanophysics, Quy-Nhon, 7/8/2013
1. Introduction : the Bloch‐Grüneisen phonon resistivity
2. Relaxation by acoustic phonons Betz et al., PRL 109, 056805 (2012).
3. Disorder assisted relaxation : supercollisionsBetz et al., Nature Physics 9, 109 (2013)
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Crossing the Bloch‐Gruneisen temperature
Fermi surface Available phonon space
kFq
qmax2 kF >
T > TBG
qmax2 kF =
T = TBG=(2s/VF)TF
q=kT/c
2 kF qmax<
T > TBG
4%
18
electrons Te
phonons Tph
substrate To
I I=V/R
P=ΣK Tph4P
decrease µ
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Relaxation at the Charge Neutrality Point
0,0 -0,5 -1,0 -1,50,0
0,5
1,0
1,5
2,0
0 V
-20 V
-10 V
-32 V
+12 V (CNP)
T4 /
P (K
4 /mW
)Vds (V)
Sample GR/BN2
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
ReplotSample GR/BN2
19Nanophysics, Quy-Nhon, 7/8/2013
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We measure PαT3 instead of PαT
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
)
Replot
0,0 -0,5 -1,0 -1,50,0
0,5
1,0
1,5
2,0
0 V
-20 V
-10 V
-32 V
+12 V (CNP)
T4 /
P (K
4 /mW
)
Vds (V)
T2T4
T3
20Nanophysics, Quy-Nhon, 7/8/2013
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Supercollisions
2 kF qmax<
Tph > TBG
electron‐impurity
Theory : Song-Reizer-Levitov, PRL 109, 106602 (2012)
21Nanophysics, Quy-Nhon, 7/8/2013
Ordinary collision
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supercollisions
Theory : Song-Reizer-Levitov, PRL 109, 106602 (2012)
22Nanophysics, Quy-Nhon, 7/8/2013
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
)
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supercollisions
23Nanophysics, Quy-Nhon, 7/8/2013
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
)
Experiment
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Effect of disorder on relaxation
24Nanophysics, Quy-Nhon, 7/8/2013
Te3
Te4
Theory clean ‐‐‐‐‐‐‐‐Exp. disorder _____
Electron-Phonon conductance
?
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Conclusion
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 e
3 / P
(K3 m
2 /W)
Te4
Te3
“ordinary collisions” rule momentum “Supercollisions” rule energy
25
Te2
Nanophysics, Quy-Nhon, 7/8/2013
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Supercollision in the photocurrent(Graham et al. Nat Phys. 2013)
26Nanophysics, Quy-Nhon, 7/8/2013
~µ2~µ ~100 ps
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Conclusions and perspectives
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• Ordinary phonon collisions observed at low temp (T4 law)
• Phonon bottelneck (T law) is overcomed by supercollisions (T3 law)
• Need for a theoretical approach for disorder
• Hot electrons useful for photodetection (from UV to THz)C. McKitterick et al., JAP 2013 and arXiv:1307.5012v1
Nanophysics, Quy-Nhon, 7/8/2013
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Graphene teams at LPA‐ENS
Gwendal Fève Bernard PlaçaisJean-Marc BerroirPhD Andreas Betz(Hitachi Cambridge)
Emiliano Pallecchi(Assist-Prof, IEMN)
post‐doc positions at ENS‐LPA !!!!
Dr.Sung-Ho Jhang(Assist-Prof. Seoul)
PhD Fabien Viala Christophe VoisinDr David Brunel
Coherent and Non Linear Optics team
Mesoscopic physics team
28Nanophysics, Quy-Nhon, 7/8/2013
Robson Ferreira
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