PHONON ENGINERING & PHONON ENGINERING & CONFINED ACOUSTIC - - PowerPoint PPT Presentation

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

Clivia M Sotomayor Torres Clivia 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 Ahopelto A 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 i El-Houssain,(U Oujda), Y Pennec, B Djafari-Rouhani A Mlayah J Groenen A Zwick A Mlayah, J Groenen, A Zwick and F Poinsotte, U P Sabatier, Toulouse

OUTLINE

• Motivation

Motivation

• Methods

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

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

Perspectives 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 ZT Improve ZT Towards zero power ICT

LENGTH SCALES in Si

Phonon MPF in bulk Si = 41 nm @ RT Debye model @ y 260 nm considering dispersion 300 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 T velocity of sound 1.48 /kBT To confine phonons in the strong regime at RT need structures with ~ 1-10 nm lateral dimensions From A Balandin, UC Riverside lateral dimensions

MOTIVATION

Double-gate SOI transistors

top gate oxide, SiO2 Al n+ poly Si Top gate p g ,

n+ top gate

n poly Si BOX (back gate ox) bonded interface (111) n+ Si subst. Back gate n+ contact n- or p- Si

n+ back gate

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

M Prunnila, J Ahopelto, K Henttinen and F Gamiz APL 85, 5442 (2004)

MOTIVATION

• Effect on charge carrier mobility

7

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

MOTIVATION

Effect of phonon confinement

• n ZT of

quantum quantum wells

Rather controversial but crucial for Hicks & Dresselhaus 1993; 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 silicon matrix (B Djafari-Rouhani Y Pennec IEMN U Lille) matrix (B Djafari-Rouhani, Y Pennec, IEMN, U Lille)

Square He agonal Hone comb

y

1.0

triangular, f=0.6 y

1.0

square, f=0.3 y

1.0

honeycomb, f=0.3

Square Hexagonal Honeycomb

ed frequency

0.4 0.6 0.8

ed frequency

0.4 0.6 0.8

ed frequency

0.4 0.6 0.8

wavenumber reduce

0.0 0.2

 X J X

wavenumber reduce

0.0 0.2

 M X M

wavenumber reduce

0.0 0.2

 X J X

wavenumber ncy

0 8 1.0

triangular, f=0.85 wavenumber ncy

0 8 1.0

square, f=0.6 wavenumber ency

0.8 1.0

honeycomb, f=0.6 uced freque

0 2 0.4 0.6 0.8

uced freque

0 2 0.4 0.6 0.8

duced freque

0 2 0.4 0.6

wavenumber red

0.0 0.2

 X J X

wavenumber red

0.0 0.2

 M X M

wavenumber red

0.0 0.2

 X J X

MOTIVATION Coupled cavities: photon-photon photon 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 security

g 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 affecting frequencies and density of states affecting group velocities of modes, scattering mechanisms lifetimes and changes mechanisms, lifetimes and changes assumptions about boundary conditions and transport properties transport properties. Understanding of acoustic phonons confinement in nanostructures is crucial for phonon engineering and strategies for low power nanoelectronics.

OUTLINE

• Motivation

Motivation

• Methods

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

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

Perspectives and Conclusions

MEMBRANES

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

200nm 50nm 50nm with weak vacuum

MEMBRANES

HRTEM image of freestanding Si membrane, thickness 6 nm A Schcepetov M Prunnila J Ahopelto VTT

• A. Schcepetov, M. Prunnila, J. Ahopelto, VTT
• J. Hua, Aalto University

OUTLINE

• Motivation

Motivation

• Methods

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

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

Perspectives and Conclusions

Scattering Mechanisms

Photoelastic Scattering Corrugation (Ripple) Scattering 2 ) ( ) ( ) ' , ( ) (



        z z u z E z z G z p dz s I 

 

1 r

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

 

) , ( Im 1 z z G LDOS    qi

i

dEs

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



q

ks ki 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 unanalysed unanalysed

A Balandin 2000

Thin film SOI sample cross-section

Native oxide 3 nm

40 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

*

) ( ). ( . . . ) (



   z z z p E E dz I

S L qz

 

EL (ES) : laser (scattered) field p(z) : photoelastic constant Φ1(z) oxide p(z) : photoelastic constant Φ(z) : phonon displacement Φ2(z) silicon Φ3(z) oxide Silicon buffer F Poinsotte et al Proc Phonons 2004

• Vibrational part

Simulations Raman spectra SOI thin film

• phonons displacement and

stress boundary conditions

) ( ) ( ) ( ) (

2 1 / 2 / 1 Si Ox Si Ox

z C z C z z       

p

{

stress boundary conditions

) ( ) (

/ 2 2 / 1 1 Si Ox Si Ox

z z C z z C     

i i

• Assumptions

{

Phonons stationary waves Free surface

z iq z iq

e B e A z

1 1

1 1 1

) (



  

) (

1

 C 

Free surface Dispersion relation

) (

/ 1 1

 

Ox air

z z C 

v q 

sound velocity Vac(oxide) =5970 m s-1

Infinite silicon buffer

) (z P

ac z qz

v q .  

Vac(oxide) =5970 m.s-1 Vac(silicon) =8433 m.s-1

{

• Electronic part

1 ) ( ) (   z P z P

Si Ox

{

F Poinsotte et al Proc Phonons 2004

Free‐standing 30 nm silicon membranes

SOI membranes and configuration

Back-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 q Acoustic vibration periodic variation of strain  polarisation fi ld i f

t) (z, E ) , ( ) , (

i

z t z u p t z P

z S

  

field in presence of em wave

z 

ps photo-elastic coefficient of slab

P( ) OK f i S k

t z uz   ) , (

*

) , (         z t z uz

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

2 2 2 2

) ( 1 ) ( ) ( P E E   

Thus, scattered field: 2 2 2 2 2 2 2 2 2

) , ( 1 ) , ( ) , ( t t z P c t t z Es c n z t z Es          0

Where n = slab index of refraction. Forward scattering B k Back scattering Wavenumber cm-1 J Groenen et al, PRB 2008

OUTLINE

• Motivation

Motivation

• Methods

– Membranes – Inelastic light scattering e 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 Law Displacement‐Strain Relationship Elastic continuum approach Hooke’s Law Dispersion Relation Membrane (Lamb)

iz=0 z = +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

Dilatational Shear

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

• Motivation

Motivation

• Methods

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

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

Perspectives and Conclusions

S i l fi

Impact on thermal conductivity

6 8 Km/sec 6

/sec

Spatial confinement Modification of dispersion relation Modification of group velocity

2 4 6 velocity K 2 4



rad/

20 40 60 80 100 Group aq// 1 2 3

DW FW SW

aq//



Increase of relaxation rate Decrease of thermal conductivity

0,16 0,18

e / bulk

5 nm 4

0,12 0,14

membrane

4 nm 3 nm

300 400 500 600 700 800 0,10  m

Temperature K

3 nm



Impact on thermal conductivity

Change in dispersion relation and the emergence of more branches i i t ti b t increases interaction between phonons increase in relaxation increase in relaxation rates and a corresponding decrease in the thermal conductivity conductivity The thinner the membrane the lower the thermal membrane the lower the thermal conductivity 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) ( )

optac ~ 5 ps in Si

e-opt ph~ 100s fs Optical phonon i i hi h fi ld Acoustic phonons carry heat away emissionhigh-field Joule heating carry heat away from hot spots

Phonon anharmonic decay

Decay 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)

acac ~ fs-s in Si

But the smaller the acoustic 3-phonon decay rate But the smaller the acoustic phonons energy difference, the longer the lifetime & mfp. Caustics increasingly important

v v

Caustics increasingly important.

 = Gruneisen constant 

Must understand and control anharmonic decay into and propagation of acoustic phonons.

v

COMMUNITIES

• The Summer School Series Son et Lumiere participating groups
• CA ZEROPOWER partners

p

• The members of the European CNRS-sponsored Network for Thermal

Nanoscience and Nanoengineering Th 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 community

The 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 control NANOPACK thermal management in nanoelectronincs – NANOPACK – thermal management in nanoelectronincs – TAILPHOX, MINOS and QNEM – on fluctuations, qbuts and phonon engineering – CA NANOICT, NoE NANOFUNCTION,

OUTLINE

• Motivation

Motivation

• Methods

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

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

Perspectives and Conclusions

Perspectives & Conclusions

• Dispersion relations of confined acoustic phonons have

been measured and simulated in Silicon membranes.

• Phonon engineering is possible with membranes, phononic

crystals, 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 Installation IMB CNM IMB‐CNM, GICSERV 2010 grant

43

2010 grant