Prsentation PowerPoint

1
Heat Transfer in Nanostructures From Particles
to Waves
Sebastian Volz Laboratoire dEnergétique
Moléculaire et Macroscopique, Combustion, CNRS -
Ecole Centrale Paris - France
TIENCS08 - Singapour June 4th
2
From Scattering to Wave Mechanisms
3
QUASI-BALLISTIC HEAT TRANSFER
Joseph Fourier 1824
Ludwig Boltzman
Martin Knudsen
4
ELECTRON-PHONON COUPLING in NANOPARTICLES
 we have performed the first investigation of
the internal electron thermalization dynamics in
metal clusters. 
PRL, 85, 2200, (2000)
Pump-Probe Femtolaser
Electron absorbing Relaxing on Phonons in
Nanoparticles
5
CORE-SHELL
Majid Rashidi
BALLISTIC-DIFFUSIVE EQUATIONS
G. Chen, PRL, 86, 2297
6
QUASI-BALLISTIC EFFECT
Journal of Heat Transfer, in press
7
PHONON PARTICLE ?
?k.?xgt2?
?x
?k
?klt ?/a gt ?x gt 10a 5nm
8
PHONON WAVE
p(?, ?, pol, ?)
Hokudai U.
9
CONFINEMENT
e ikLe ika0 k n . 2?/L L/a1
BVK e ik(Lx)e ikx k n . 2?/L L/agtgtgtn
un expi(kna-wt) expi(-kna-wt) cos(kna)e-iwt
STATIONNARY WAVE, zero group velocity
10
Phononic Cristals
THERMOELECTRIC FACTOR OF MERIT
Jean-Numa Gillet

• In a superlattice
• l can be several orders of magnitude smaller than
  bulk material
• But ZT gt alloy limit because
• 2 major drawbacks
• Lattice mismatch can occur between layers of a
  superlattice as in Si/Ge superlattices formation
  of defects and dislocations reduces s and avoids
  increase of ZT compared to alloy limit.
• 2) Superlattices only decrease heat conduction in
  the perpendicular direction to the thin-film
  surfaces

11
Insulating Materials
Recent work on a stack layered WSe2 SL
?0.04W/mK at ambiant!! Einstein model (Mean
FPWaveL/2) ?0.2W/mK The lowest theoretical
limit for a crystal.
ELECTRICAL CONDUCTIVITY STRONGLY
DECREASED PRESERVE CRYSTAL STRUCTURE?
Chiritescu et al., Science 315, 351, 2007.
12
Macroscopic phononic crystals

• Phononic crystals inspired by remarkable
  properties of photonic crystals
• Show band gaps -destructive interferences- of
  acoustic wave.
• Macroscopic phononic crystals periodic
  structure of elastic rods
• for 2D crystals or beads for 3D crystals within a
  solid matrix or a fluid.
• Lattice constant usually of ? 1 to ? 10 mm
• Problem band gap cannot occur
• at frequencies that are higher than ? 1 MHz

13
Atomic-scale 3D phononic crystal
Supercell with N 5 and M 3
Equilibrium positions of the Si (blue) and Ge
(red) atoms obtained by conjugated gradient
method
Ma 1.629 nm
d Na 2.715 nm

• Band Gaps?
• And low thermal conductivity?

14
3 x 8 x N3 3000 dispersion curves
Lattice dynamics to compute the dispersion
curves - Use of the Stillinger-Weber potential -
3000 dispersion curves (3 1000 3000 d.o.f. in
supercell) Use of General Utility Lattice
Program (GULP) Quasi ab initio only potential
shape is set
Curves are very flat Phonon confinement
results in very low group velocities instead of
band gaps
Phonon Trap
Half of first BZ in 1 0 0
15
Thermal conductivity model
Boltzmann and from Fourier law
Mode MFP
Mode heat capacity
DOS / V
Mode group velocity
Angular frequencies wk,m and group velocities
obtained by lattice dynamics!
Much easier to compute than preceding eqs. based
on integration over ?, because Debye
approximation cannot be used for the 3000 - 3
2997 optical dispersion curves!
16
Relaxation-time model
Use of Matthiessen rule
Bulk Si and Ge
High-purity Silicon at T gt 100 K boundary (?B)
and isotopic-and-defects (?l) scattering can be
neglected compared to umklapp (?u) scattering
Phononic nanomaterial
tScat due to phonon scattering by the Ge QDs Low
T tScat ltlt tB and tI
17
Incoherent scattering cross section
M 3
M 2
M 1
HBZ
For the smallest Ge QD (M 1), scattering in HBZ
is not efficient For the largest Ge QD (M 3),
scattering in HBZ becomes very efficient with
sinc that can be higher than d2/2
18
Thermal conductivity results
lmax gt lreal is an upper bound because sinc lt
sinccoh
19
?max decrease at T 300 K
lt Cv gt / lt Cv gtSi
lt l gtmax / lt l gtSi
lmax / lSi
For small Ge atomic densities x ? 0.2 lt Cv gt
decrease effect are predominant over lt l gtmax
decrease at T 300 K
To be published in Journal o f Heat Transfer.
20
Conclusion / Phononic Cristal
At T 300 K, the thermal conductivity can be
reduced by at least a 400 factor in an
atomic-scale 3D phononic crIstal to reach a
value lower than 0.4 W/Km.This reduction is due
to the shrunk MFPs of phonons but also to their
very low GROUP VELOCITIES.No Gap effect is
noticed.We expect a further decrease when
coherent scattering will be introduced.This
material may break the Einstein limit and be an
interesting candidate for thermoelectric
applications.
21
Nanowires and Thermal Contact Resistances
22
Macro-FOURIER
Thermal Bath T0
23
NanoContact ? gt ? D
Thermal Bath T1
Thermal Bath T0
24
Multireflections
IF D lt PHONON WAVELENGTH?
S. Volz et al., J.App. Phys. 103, 34306
25
Wire Thermal Conductance
-Conductance of 1 phonon BRANCH /NOT/ 1
Quantum -Temperature Dependent -Predominant
CONDUCTANCE?
26
CONTACT CONDUCTANCE
Diffuse Transmission Phonons loose memory at
interface
27
DISPERSION CURVES
Lattice dynamics
Solution Stillinger Weber potential
28
Group Velocities
29
WIRE vs CONTACT
CONTACT RESISTANCE PREDOMINANT 2 ODM SUBSTRATE
HEAT CAPACITY
Phys. Rev B in press
30
THERMAL RESERVOIRS
31
CONCLUSION Nanowire and Contact
At low temperatures, Heat flux in of SUB-10nm
Nanowires is dominated by CONTACT RESISTANCE
. Quantum thermal conductance can not be
measured in those wires. At low temperatures,
Specific Heat of the substrate following a T3 law
is smaller than the nanowire specific heat, which
is proportional to T. We also infer that at low
temperatures The conductance of a membrane
suspended between two 3D substrate follows a T3
law (Cv of a 3D substrate). The conductance of
a wire suspended between two membranes follows a
T2 law (Cv of a 2D subtrate)
32
Collaborators
Academic J.-J. Greffet, EM2C-ECP M. Laroche,
EM2C-ECP M. Massot, EM2C-ECP J. Bai,
LMSSMAT-ECP B. Palpant, INSP-Paris J.-Y.
Duquesne, INSP-Paris L. Jullien, ENS Ulm
Paris Charlie Goss, LPN - Paris M. Mortier,
ENSCP-Paris G. Tessier, ESPCI-Paris S. Ravaine,
ICMCB-Bordeaux S. Dilhaire, CPMOH Bordeaux S.
Gomès, CETHIL-Lyon S. Lefèvre, CETHIL-Lyon G.
Domingues, LT-Nantes B. Charlot, TIMA-Grenoble C.
Bergaud, LAAS-Toulouse Industries/Institutes D.
Rochais, CEA_Le Ripault N. Mingo, CEA-LITEN M.
Plissonnier, CEA-LITEN
J.-J. Greffet
M. Laroche
Post-Doc Students
J.-N. Gillet
E. Rousseau
P.-O. Chapuis
Ph.D. Students
Y. Chalopin
C. Bera
33
THANK YOU !
34
THERMAL DIODES
Arunava Majumdar
With the availability of nonlinear
thermal control, phonons should no longer be
considered the unwanted by-products of
electronics. Phonons, like electrons and photons,
are information carriers and should be processed
accordingly.
35
The Mysterious Story of Nanowires Thermal
Conductivity
Nature, Roukes 27/04/00
M.R. says not obtained for long wires