Phonon Engineering: Phonon Engineering: an introduction – part 1 an introduction part 1 C M Sotomayor Torres, P.-O. Chapuis, F Alzina, D Dudek, J Cuffe and L Schneider Catalan Institute of Nanotechnology (CIN2-ICN-CSIC) NISP Summer School on “Energy Harvesting at the micro- and nano-scale” 1 NISP Summer School on Energy Harvesting at the micro- and nano-scale Avigliano Umbro TR, Italy, 1 st -8 th August 2010
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Phonon Engineering:Phonon Engineering: an introduction – part 1an introduction part 1
C M Sotomayor Torres, P.-O. Chapuis, F Alzina, D Dudek, J Cuffe and L Schneider
Catalan Institute of Nanotechnology (CIN2-ICN-CSIC)
NISP Summer School on “Energy Harvesting at the micro- and nano-scale”
1
NISP Summer School on Energy Harvesting at the micro- and nano-scaleAvigliano Umbro TR, Italy, 1st-8th August 2010
Collaborators• N Kehagias, V Reboud - ICNg ,
• J Ahopelto, M Prunnila – VTTp ,
• E H El Boudouti – U Oujda & IEMN, U Lillej ,
• B Djafari-Rouhani - IEMN, U Lillej ,
•A Zwick, J Groenen, F Poinsotte, A Mlayah – U Paul , , , ySabatier (LPST now part of CNRS-CEMES)
2
SupportSupport
www.nanopack.org
3www.tailphox.org
The Phononic and Photonic N t t G (P2N)Nanostructures Group (P2N)
- Confined acoustic phonons• Thermal transport (part 2-O Chapuis)p (p p )
– the 3-omega methodConclusions
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Conclusions
Phonons in solidsKey excitation in energy and momentum relaxation in, e.g, semiconductor quantum wells wires and dots (1 THz ~ 4 meV)
(meV)
semiconductor quantum wells, wires and dots (1 THz 4 meV)
Typical dispersion relations
TOLO
65-30of optical phonons and
TALA
TO
acoustic phonons TA
up to~30
p
/2a k in bulk material
6
Focus on acoustic phononsFocus on acoustic phononsReasons to study THz acoustic phonon engineering:
- Imaging with nm resolution acoustic wavelength ~ 5nm at 1 THz5nm at 1 THz
- Thermal dissipation- Thermoelectricityy- Optoelectronic devices modulation at high speed- Phonon caustics
C t l f d h- Control of decoherence- Detrimental role in nanoelectronic devices (mobility)- NanometrologyNanometrology- Design of density of phonon states- A candidate for a non-charge state variable
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Phonon anharmonic decayPhonon anharmonic decay
Optical phonons Acoustic phonons(f V)(10’s of meV) (few meV)
optac ~ 5 ps in Si
e-opt ph~ 100s fsOptical phonon
Acoustic hOptical phonon
emissionhigh-field Joule heating
phonons carry heat away from hot spots
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hot spots
“Phonon bottleneck” in deep etched quantum dots
- Intrinsic model of luminescence yield in decoupled 1- and 0-D semiconductors.
wires and dots- wires and dots decoupled from surrounding (unlikesurrounding (unlike self-organised ones)
9 H Benisty, C M Sotomayor Torres & C Weisbuch, Phys Rev B 44 (19) 10945 (1991)
Effect of phonon confinement on ZT of quantum wells
A Balandin and K L Wang 1998
See also, M.S. Dresselhaus et al, Adv Mat 19, 1043
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(2007).
Electronic, Photonic and Phononic crystals
Common key parameters: periodicity contrast filling factor geometry
11 Adapted from Sigalas et al Z. Kristallogr, vol. 220, pp. 765–809, 2005
Common key parameters: periodicity, contrast, filling factor, geometry
Phonons in Low Dimensional Systems– Interface phonons – Zone-folded acoustic phononso e o ded cous c p o o s– Geometrically confined surface modes– Localised and or confined phononsLocalised and or confined phonons– Surface acoustic waves– Acoustic cavity modesAcoustic cavity modes
– …
Treat as standing waves (eg, confined) or propagating waves (eg., zone-folding in superlattices)
“Phonon Raman scattering in semiconductors, quantum wells and superlattices: Basic results and applications “ Tobias Ruf, Springer (Berlin, New York) 1998.
“Ph i S i d t N t t ” Ed J P L b t J P l d C M
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“Phonons in Semiconductor Nanostructures”, Eds J-P Leburton, J Pascual and C M Sotomayor Torres, Kluwer Publishing, The Netherlands, 1993
Folded acoustic phonons in superlattices
F iFor a review on vibrations in superlattices, see B. Jusserand and M. Cardona, in Light Scattering in Solids, edited by M Cardonaby M. Cardona and G. Güntherodt(Springer-Verlag,
14 From Lecture notes of B Jusserand, Son et Lumiere 2006
( p g gHeidelberg, 1989), p. 49.
Surface Phonons in semiconductor cylinders 1Surface Phonons in semiconductor cylinders 1(nh)2/()2=( m nh)/( m nh),
El t t ti ti d l f R i d
with nh in terms of modified Bessel functions and derivatives.
Electrostatic continuum model of Ruppin and Engelman (1970) with geometry determined by boundary conditions, neglecting retardation effects.
GaAs pillar 100 nm diameter 700 nm high
15 M Watt et al Semicond Sci Technol 5, 285-290 (1990)
700 nm high.
Surface Phonons in semiconductor cylinders 2GaAs cylinders of 80 nm diameter and 250 nm high.
Contribution of surface phonons to the RamanContribution of surface phonons to the Raman signal appear between the TO and LO phonons as expected.
Pillars coated with SiN: surface phonon frequencies
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surface phonon frequencies decrease.
M Watt et al Semicond Sci Technol 5, 285-290 (1990)
Phononic crystals– Acoustic and elastic analogues of photonic crystals
y
– ‘stop bands’ in phonon spectrum (phonon mirrors); – ‘negative refraction’ of phonons (phonon caustics)g p (p )– Good theory available: Multiple scattering theory
for elastic and acoustic waves See for example:for elastic and acoustic waves. See, for example:Kafesaki & Economou PRB 60, 11993 (1999), Li t l PRB 62 2446 (2000)Liu et al PRB 62, 2446 (2000)Psaroba et al PRB 62, 278 (2000).
A d f d t b 2006 2008And for a database 2006-2008:http://www.phys.uoa.gr/phononics/PhononicDatabase.html
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2D infinite phononic crystal: air holes in siliconmatrix (B Djafari-Rouhani Y Pennec IEMN U Lille)matrix (B Djafari Rouhani, Y Pennec, IEMN, U Lille)
44Sotomayor Torres et al phys stat sol c , 1, 2609 (2004)
Si membrane
30 nm SOI + 400 nm BOX
45
30 SO 00 O
Examples of raw datap
Wavenumber (cm-1)
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Wavenumber (cm )
Sotomayor Torres et al, unpublished
Simulations of Raman spectra of SOI membranes
T t SOI l it f ti h i
Simulations of Raman spectra of SOI membranes
Treat SOI layer as a cavity for acoustic phonons, ie, confined since longitudinal vs in Si = 8433 m/s (cf. 332 m/s in air at 0 C)m/s in air at 0 C).
Displacement field of acoustic vibrations in a slab of thi k t i ti l t
)(n thickness t is proportional to:
)cos( zt
n order of the confined frequencies can be derived fromn order of the confined frequencies can be derived from LA dispersion branch, considering discrete wave vectors q = n /t
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q n /t
Simulations of Raman spectra of SOI membranes- cont.
t)(zE),(
)(tzu
ptzP zAcoustic vibration periodici i f i l i i
Simulations of Raman spectra of SOI membranes cont.
t)(z,E),( izptzP z
S variation of strain polarisation
field in presence of em wavep photo-elastic coefficient of slab
tzu ),( *),(
tzuz
ps photo elastic coefficient of slab
P(z,t) OK for anti-Stokes part.Obtain Stoke part by changing by
ztzuz
),( ),(
zzObtain Stoke part by changing by
Thus, scattered field:
2
2
22
2
2
2
2
2 ),(1),(),( tzPtzEsntzEs
22
0222 tctcz
Where n = slab index of refraction.
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Raman spectra of 31.5 nm thick SOI membrane
Forward scatteringscattering
BackBack scattering
Wavenumber cm-1
49
J Groenen et al PRB 77, 045420 (2008)
Data from five SOI membranes
50Sotomayor Torres et al phys stat sol c , 1, 2609 (2004)
15 nm Si QW, expect shear, dilatation & flexural modes
2nd dilatation2 dilatation mode
3rd dilatation mode
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A Balandin 2000 in-plane V-group 0 at cusps
Raman & Brillouin scattering Inelastic Light Scattering (I vs. )
vs k [~ Phononic Dispersion Relation vs. k [~ Phononic Dispersion Relation
Frequency Range
0.2 – 500 GHz> 90 GHz0.0067 – 16.6 cm-1> 3 cm-1
5282.7 ev – 2.07 meV> 0.37 meV
Conclusions and trends• Phonon engineering possible with phononic crystals, cavities, coupled cavities., p
• Phonon sources are needed for progress in the field
• A wealth of device-relevant physics expected• A wealth of device-relevant physics expected
• Nanofabrication (in 3D) and nanometrology developments neededneeded.
• “Heterogeneous” coupled cavities need better description with e g quantum mechanics and elasticity theorywith, e.g., quantum mechanics and elasticity theory.
• Phonon coherence studies in confined structures are expected to become important soon (Impulsive Ramanexpected to become important soon (Impulsive Raman scattering, see work by R Merlin, U Michigan)
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References (see, for example, in addition to refs in slides)
An early work:D F Sheahan and R A Johnson, Crystal and mechanical oscillators, IEEE Trans Circuits and Systems, Vol CAS-22, pp 69-89, February 1975
On 2D Phononic Crystals:M.S. Kushwaha et al, Phys. Rev. Lett. 71, 2022 (1993)J. Vasseur et al, J. Phys.: Cond. Matter, 7, 8759 (1994)J Vasseur et al J Phys : Cond Matter 9 7327 (1997)J. Vasseur et al J. Phys.: Cond Matter, 9, 7327 (1997)Y. Pennec et al, Optics Express (2010)
On Light scattering:Book series «Topics in Applied Physics” volumes on “Light Scattering in Solids” Ed MBook series «Topics in Applied Physics , volumes on Light Scattering in Solids , Ed M. Cardona, Springer.
On modeling of light scattering and acoustic structures:E H El Boudouti et al Surface Science Reports 64 (2009) 471594E.H. El Boudouti et al., Surface Science Reports 64 (2009) 471594.
On phonon-photon interaction:Lecture Notes of Summer Schools Son et Lumiere 2006, 2008 and 2010, http://prn1.univ-lemans fr/prn1/siteheberge/Son et lumiere/index php?page=1lemans.fr/prn1/siteheberge/Son_et_lumiere/index.php?page=1M Maldovan and EL. Thomas. Appl Phys Lett, 88(25):251907, 2006.
On thermal rectifiers: C Dames J Heat Transfer vol 131 061301-1 to 061301-7 (2009)
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C Dames, J Heat Transfer, vol 131, 061301-1 to 061301-7 (2009)