PHONON ENGINERING &PHONON ENGINERING & CONFINED ACOUSTIC PHONONS IN SILICON MEMBRANESMEMBRANES

Clivia M Sotomayor TorresClivia M Sotomayor Torres

COLLABORATORS

J Cuffe (UCC-IRCSET, IE), E Chavez (CONICYT, Chile), P-O. Chapuis, F Alzina, N Kehagias, L Schneider, T Kehoe, C Ribéreau-Gayon, (ECP, FR) … the ICN team

A Shchepetov M Prunnila S Laakso J AhopeltoA Shchepetov, M Prunnila, S Laakso, J Ahopelto

J Johnson, A A. Maznev J Eliason, A Minnich, K Collins, MIT, , , ,

G Chen, K A Nelson,

A Bruchhausen, M Hettich, O Ristow and T Dekorsy.

El H i (U O jd ) Y P B Dj f i R h iEl-Houssain,(U Oujda), Y Pennec, B Djafari-Rouhani

A Mlayah J Groenen A ZwickA Mlayah, J Groenen, A Zwickand F Poinsotte, U P Sabatier, Toulouse

OUTLINE

• MotivationMotivation• Methods

– Membranes– Inelastic light scatteringe as c g sca e g

• Dispersion relations• Impact on heat transfer• Perspectives and ConclusionsPerspectives and Conclusions

MOTIVATION

Modification of dispersion l ti ( h i i )relation (phonon engineering)

Modification of group velocity Modification of relaxation rate

Thermal conductivity

Improve ZTImprove ZTTowards zero power ICT

LENGTH SCALES in Si

Phonon MPFin bulk Si = 41 nm @ RT Debye model @ y

260 nm considering dispersion300 nm (Ju & Goodson, APL 1999)

(cf Electron MFP = 7.6 nm)Dominant phonon wavelength

d = vs / fd in Si d = 1.4 nm @ RT= 4000 nm @0.1 K @

velocity of 1 48 /k Tvelocity ofsound

1.48 /kBTTo confine phonons in the strong regime at RT need structures with ~ 1-10 nm lateral dimensions

From A Balandin, UC Riversidelateral dimensions

MOTIVATION

Double-gate SOI transistors

top gate oxide, SiO2

Aln+ poly Si

Top gatep g ,

n+ top gate

n poly Si

BOX (back gate ox)

bondedinterface

(111) n+ Si subst.Back gate

n+ contact

n- or p- Sin+ back gate

Cross-sectional bright field TEM image of a DG-SOI FET with a 18image of a DG SOI FET with a 18

nm-thick channelM Prunnila, J Ahopelto, K Henttinen and F GamizAPL 85, 5442 (2004)

MOTIVATION

• Effect on charge carrier mobility

7L. Donetti et al J. Appl. Phys.  100(2006),   013701

MOTIVATION

Effect of phonon confinement on ZT of quantumquantum wells

Rather controversial but crucial forHicks & Dresselhaus1993;

Rather controversial but crucial for thermoelectric energy conversion in the nm scale.Suitable charge conduction in

A Balandin and K L Wang 1998

Suitable charge conduction in phonon glasses needed.

See also, M.S. Dresselhaus et al, Adv Mat 19,al, Adv Mat 19, 1043 (2007).

MOTIVATION

Phononic crystals– Acoustic and elastic analogues of photonic crystals– ‘stop bands’ in phonon spectrum (phonon mirrors); – ‘negative refraction’ of phonons (phonon caustics)– Good theory available: Multiple scattering theory for

elastic and acoustic waves. See, for example:Kafesaki & Economou PRB 60, 11993 (1999), Liu et al PRB 62 2446 (2000)Liu et al PRB 62, 2446 (2000)Psaroba et al PRB 62, 278 (2000).

And for a database 2006-2008:http://www.phys.uoa.gr/phononics/PhononicDatabase.ht

ml… cell phones have phononic crystal-like BAW filters

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)

Square He agonal Hone comb

y 1.0triangular, f=0.6

y 1.0square, f=0.3

y 1.0honeycomb, f=0.3

Square Hexagonal Honeycomb

ed fr

eque

ncy

0.4

0.6

0.8

ed fr

eque

ncy

0.4

0.6

0.8

ed fr

eque

ncy

0.4

0.6

0.8

wavenumber

redu

ce0.0

0.2

X J Xwavenumber

redu

ce

0.0

0.2

M X Mwavenumber

redu

ce

0.0

0.2

X J Xwavenumber

ncy

0 8

1.0triangular, f=0.85

wavenumber

ncy

0 8

1.0square, f=0.6

wavenumber

ency

0.8

1.0honeycomb, f=0.6

uced

freq

ue

0 2

0.4

0.6

0.8

uced

freq

ue

0 2

0.4

0.6

0.8

duce

d fre

que

0 2

0.4

0.6

wavenumber

red

0.0

0.2

X J Xwavenumber

red

0.0

0.2

M X Mwavenumber

red

0.0

0.2

X J X

MOTIVATION

Coupled cavities: photon-photonphoton photon cavities.

Trigo et al PRL 2002

MOTIVATION

Physics of weak to strong coupling regimes

Trigo et al PRL 2002

MOTIVATION

M Eichenfield et al. Optomechanical Crystals, Nature 462, 78-82 (2009)

Optical forces control mechanical modes prospects for cooling, heating, …

MOTIVATION

Acoustic phonons have also an impact in:

Noise and thermal limits in NEMS and nanoelectronics Coherence control in quantum information processing Phonon engineering: sources, detectors and other

components Photon-phonon coupling: Phoxonic Crystals and Opto

mechanical oscillators Energy harvesting and storage THz technologies for medical diagnostic and securityg g y Elastic material parameters down to the nm-scale

Previous work: 30 nm SOI membrane

HYPOTHESIS and STATEMENT

The confinement of phonons modifies their frequencies and density of states affectingfrequencies and density of states affecting group velocities of modes, scattering mechanisms lifetimes and changesmechanisms, lifetimes and changes assumptions about boundary conditions and transport propertiestransport properties.

Understanding of acoustic phonons confinement in nanostructures is crucial for phonon engineering and strategies for low power nanoelectronics.

OUTLINE

• MotivationMotivation• Methods

– Membranes– Inelastic light scatteringe as c g sca e g

• Dispersion relations• Impact on heat transfer• Perspectives and ConclusionsPerspectives and Conclusions

MEMBRANES

Free-standing Si membranes Corrugation due to residual compressive strain in SOI films Methods to avoid corrugation are being developed.

200nm 50nm50nm with weak vacuum

MEMBRANES

HRTEM image of freestanding Si membrane, thickness 6 nm

A Schcepetov M Prunnila J Ahopelto VTTA. Schcepetov, M. Prunnila, J. Ahopelto, VTTJ. Hua, Aalto University

OUTLINE

• MotivationMotivation• Methods

– Membranes– Inelastic light scatteringe as c g sca e g

• Dispersion relations• Impact on heat transfer• Perspectives and ConclusionsPerspectives and Conclusions

Scattering Mechanisms

Photoelastic Scattering Corrugation (Ripple) Scattering

2)(

)( )',( )(

zzu

zEzzGzpdzs

I

1

rEH El B d ti t l S f S i R t 64 471 (2009)

),(Im 1

zzGLDOS

qii dEs

EH El Boudouti et al, Surf Sci Reports 64, 471 (2009)

q

kski

Related to power spectrum of normal

Benedek, G B & Fritsch, K  Phys Rev, 149, 647 (1966) Rowell, N. L. & Stegeman, G. I. PRB   18 2598 (1978,)

Related to power spectrum of normal displacement

Raman scattering of Silicon

300 K, 514 nm unanalysedunanalysed

A Balandin 2000

Thin film SOI sample cross-section

Native oxide 3 nm40

Buried (thermal) oxide (SiO2) 400 nm

SOI 40 nm

28 nm

Buried (thermal) oxide (SiO2) 400 nm

Base Si wafer CZ p-type <100> 525 micrometer

SOI is a key European technology

Simulations Raman spectra SOI thin film

Photoelastic model 2)(Photoelastic model for scattering by LA phonos

* )().(...)(

zzzpEEdzI SLqz

EL (ES) : laser (scattered) fieldp(z) : photoelastic constant

Φ1(z) oxide

p(z) : photoelastic constantΦ(z) : phonon displacementΦ2(z) silicon

Φ3(z) oxide

Silicon buffer

F Poinsotte et al Proc Phonons 2004

• Vibrational partSimulations Raman spectra SOI thin film

- phonons displacement and stress boundary conditions )()(

)()(

21

/2/1 SiOxSiOx

zCzC

zz

p

{stress boundary conditions )()( /2

2/1

1 SiOxSiOx zz

Czz

C

ii- Assumptions

{Phonons stationary waves

Free surface

ziqziq eBeAz 11111 )(

0)(1C Free surface

Dispersion relation

0)( /1

1 Oxairzz

C

vqsound velocity

Vac(oxide) =5970 m s-1

Infinite silicon buffer

0)(zP

aczqz vq . Vac(oxide) =5970 m.s-1

Vac(silicon) =8433 m.s-1

{• Electronic part1)(0)(

zPzP

Si

Ox{F Poinsotte et al Proc Phonons 2004

Free‐standing  30 nm silicon membranes

SOI membranes and configurationBack-scattering

500 m

Laser spot

Forward scattering

Sotomayor Torres et al phys stat sol c 2004

Simulations of RS spectra of SOI membranes

)(n Treat SOI layer as a cavity for acoustic phonons, ie, confined since longitudinal vs in Si = 8433 m/s ( f 332 / i i t 0 C) )cos( z

t(cf. 332 m/s in air at 0 C).

Displacement field of acoustic vibrations in a slab of thickness t is proportional to:

n is the order of the confined frequencies can be derived from LA dispersion branch, considering discrete wave vectors q = n /t

thickness t is proportional to:

p , g qAcoustic vibration periodicvariation of strain polarisationfi ld i f

t)(z,E),(

),( iztzu

ptzP zS

field in presence of em wave z

ps photo-elastic coefficient of slab

P( ) OK f i S ktzuz

),( *),(

ztzuz

P(z,t) OK for anti-Stokes part.Obtain Stoke part by changing by

z z

RS spectra of 31.5 nm thick SOI membrane

2222 )(1)()( PEE

Thus, scattered field:

2

2

20

2

2

2

2

2

2 ),(1),(),(t

tzPct

tzEscn

ztzEs

0Where n = slab index of refraction.

Forward scattering

B kBack scattering

Wavenumber cm-1 J Groenen et al, PRB 2008

OUTLINE

• MotivationMotivation• Methods

– Membranes– Inelastic light scatteringe as c g sca e g

• Dispersion relations (mainly by J Cuffe, E Chavez, both PhD students at ICN work unpublished)both PhD students at ICN, work unpublished)

• Impact on heat transfer• Perspectives and Conclusions

From bulk to membranes

Newton’s Second LawDisplacement‐Strain RelationshipElastic continuum approach

Hooke’s Law

Dispersion RelationMembrane (Lamb)

iz=0z = +a/2

Dispersion Relation

z = a/2 =0

Flexural (Anti‐symmetric)

z = ‐a/2 iz=0

Dilatational (Symmetric)

30

430 nm Si Membrane

Spectra at 3mm Mirror Spacing Dispersion Relation

LA Lens @ 35GHz(Reference Peak)

• Spectra observed with Brillouin Light Scattering spectroscopy

M lti l d b d (d i ti f b lk b h i )• Multiple modes observed (deviation from bulk behaviour)

• Good agreement with theoretical calculations (Lamb waves) 

10 nm Si Membrane

Spectra at 3 mm Mirror Spacing

DilatationalShear

Spectra at 10 mm Mirror Spacing

Flexural Dilatational Shear (SH)

32

Phase Velocity vs q.a

Phase(Group) velocity decreases dramatically for thinner membranes

OUTLINE

• MotivationMotivation• Methods

– Membranes– Inelastic light scatteringe as c g sca e g

• Dispersion relations• Impact on heat transfer• Perspectives and ConclusionsPerspectives and Conclusions

S i l fiImpact on thermal conductivity

6

8

Km

/sec6

/sec

Spatial confinement Modification of dispersion relation Modification of group velocity

2

4

6

velo

city

K

2

4

rad/

0 20 40 60 80 100

0

Gro

up

aq//0 1 2 3

0

DW FW SW

aq//

Increase of relaxation rate Decrease of thermal conductivity

0,16

0,18

e /

bul

k 5 nm

4

0,12

0,14

mem

bran

e 4 nm

3 nm

300 400 500 600 700 8000,10

m

Temperature K

3 nm

Impact on thermal conductivity

Change in dispersion relation andthe emergence of more branchesi i t ti b tincreases interaction betweenphonons

increase in relaxationincrease in relaxationrates and a correspondingdecrease in the thermalconductivityconductivity

The thinner themembrane the lower the thermalmembrane the lower the thermalconductivity K.

Including all the confined modes and calculating Umklapp processes

Phonon anharmonic decay

Optical phonons(10’s of meV)

Acoustic phonons(few meV)(10 s of meV) ( )

optac ~ 5 ps in Si

e-opt ph~ 100s fsOptical phonon

i i hi h fi ld

Acoustic phonons carry heat awayemissionhigh-field

Joule heating

carry heat away from hot spots

Phonon anharmonic decayDecay can involve only acoustic phonons. Cubic case and frequency < Debye frequency

Lower energy acoustic phonons(few meV)

Higher energy acoustic phonons(f V) (few meV)

~ fs s in Si

(few meV)

acac ~ fs-s in Si

But the smaller the acoustic3-phonon decay rate

But the smaller the acoustic phonons energy difference, the longer the lifetime & mfp.Caustics increasingly importantv

v

Caustics increasingly important.

= Gruneisen constantMust understand and control anharmonic decay into and propagation of acoustic phonons.

v

COMMUNITIES

• The Summer School Series Son et Lumiere participating groups• CA ZEROPOWER partnersp• The members of the European CNRS-sponsored Network for Thermal

Nanoscience and NanoengineeringTh Fl t ti d St ti ti l Ph i it• The Fluctuations and Statistical Physics community

• The Phonons & Fluctuation informal community• The solid state quantum physics communityThe solid state quantum physics community• The mechanical engineering heat transfer community• The multi-scale physics modelling community • Partners of the EU projects, eg:

– NANOPOWER –three future scenarios of future heta transport controlNANOPACK thermal management in nanoelectronincs– NANOPACK – thermal management in nanoelectronincs

– TAILPHOX, MINOS and QNEM – on fluctuations, qbuts and phonon engineering

– CA NANOICT, NoE NANOFUNCTION,

OUTLINE

• MotivationMotivation• Methods

– Membranes– Inelastic light scatteringe as c g sca e g

• Dispersion relations• Impact on heat transfer• Perspectives and ConclusionsPerspectives and Conclusions

Perspectives & Conclusions

• Dispersion relations of confined acoustic phonons havebeen measured and simulated in Silicon membranes.

•Phonon engineering is possible with membranes, phononiccrystals, cavities and coupled cavities.

• Phonon sources are needed for progress in the field

• Nanofabrication (3D) and nanometrology developments• Nanofabrication (3D) and nanometrology developments are needed.

• “Heterogeneous” coupled cavities need better description• Heterogeneous coupled cavities need better description with, e.g., quantum physics and elasticity theory.

Phonon cohe ence st dies in confined st ct es• Phonon coherence studies in confined structures unavoidable

N d t ib ti f t ti ti l d t h i• Need contribution from statistical and quantum physics.

• Only then we can seriously address low power electronics.

Support

Large InstallationIMB CNMIMB‐CNM, GICSERV 2010 grant

43

2010 grant