CONFINED ACOUSTIC PHONONS IN SILICON

Transcription

1 PHONON ENGINERING & CONFINED ACOUSTIC PHONONS IN SILICON MEMBRANES Clivia M Sotomayor Torres

2 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 MIT J Johnson, A A. Maznev J Eliason, A Minnich, K Collins, G Chen, K A Nelson, A Bruchhausen, M Hettich, O Ristow and T Dekorsy. El-Houssain,(U Oujda), Y Pennec, B Djafari-Rouhani i A Mlayah, J Groenen, A Zwick and F Poinsotte, U P Sabatier, Toulouse

3 OUTLINE Motivation Methods Membranes Inelastic light scattering Dispersion relations Impact on heat transfer Perspectives and Conclusions

4 MOTIVATION Modification of dispersion relation (phonon engineering) i Modification of group velocity Modification of relaxation rate Thermal conductivity Improve ZT Improve ZT Towards zero power ICT

5 LENGTH SCALES in Si Phonon MPF in bulk Si = 41 RT Debye model 260 nm considering dispersion 300 nm (Ju & Goodson, APL 1999) Dominant phonon wavelength d = v s / f d (cf Electron MFP = 7.6 nm) in Si d = 1.4 RT = 4000 K velocity of 148/k 1.48 B T sound From A Balandin, UC Riverside To confine phonons in the strong regime at RT need structures with ~ 1-10 nm lateral dimensions

6 MOTIVATION Double-gate SOI transistors top pg gate oxide, SiO2 Top gate n+ poly Si BOX (back gate ox) Al bonded interface n+ top gate (111) n+ Si subst. n+ contact Back gate n- or p- Si n+ back gate M Prunnila, J Ahopelto, K Henttinen and F Gamiz APL 85, 5442 (2004) Cross-sectional bright field TEM image of a DG-SOI FET with a 18 nm-thick channel

7 MOTIVATION Effect on charge carrier mobility L. Donetti et al J. Appl. Phys. 100(2006),

8 MOTIVATION Effect of phonon confinement on ZT of quantum wells Hicks & Dresselhaus 1993; A Balandin and K L Wang 1998 See also, M.S. Dresselhaus et al, Adv Mat 19, 1043 (2007). Rather controversial but crucial for thermoelectric energy conversion in the nm scale. Suitable charge conduction in phonon glasses needed.

9 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, (1999), Liu et al PRB 62, 2446 (2000) Psaroba et al PRB 62, 278 (2000). And for a database : ml cell phones have phononic crystal-like BAW filters

10 2D infinite phononic crystal: air holes in silicon matrix (B Djafari-Rouhani, Y Pennec, IEMN, U Lille) Square Hexagonal Honeycomb reduce ed frequency 1.0 square, f= M X M wavenumber reduce ed frequency X triangular, f=0.6 J X wavenumber reduce ed frequency X honeycomb, f=0.3 J X wavenumber ncy uced freque red 1.0 square, f= M X M wavenumber ncy uced freque red X triangular, f=0.85 J X wavenumber red duced freque ency X honeycomb, f=0.6 J X wavenumber

11 MOTIVATION Coupled cavities: photon-photon cavities. Trigo et al PRL 2002

12 MOTIVATION Physics of weak to strong coupling regimes Trigo et al PRL 2002

13 MOTIVATION Optical forces control mechanical modes prospects for cooling, heating, M Eichenfield et al. Optomechanical Crystals, Nature 462, (2009)

14 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 Elastic material parameters down to the nm-scale

15 Previous work: 30 nm SOI membrane

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

17 OUTLINE Motivation Methods Membranes Inelastic light scattering Dispersion relations Impact on heat transfer Perspectives and Conclusions

18 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

19 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

20 OUTLINE Motivation Methods Membranes Inelastic light scattering Dispersion relations Impact on heat transfer Perspectives and Conclusions

21 Scattering Mechanisms Photoelastic Scattering Corrugation (Ripple) Scattering I s 2 u( z) dzp( z) G( z, z') E( z) z q i i r des 1 LDOS Im G ( z EHElB El Boudouti et al, Surf fsci ireports 64, 471 (2009) q, z ) k i k s Related to power spectrum of normal displacement Benedek, G B & Fritsch, K Phys Rev, 149, 647 (1966) Rowell, N. L. & Stegeman, G. I. PRB (1978,)

22 Raman scattering of Silicon 300 K, 514 nm unanalysed A Balandin 2000

23 Thin film SOI sample cross-section 40 nm SOI Native oxide 3 nm 28 nm Buried (thermal) oxide (SiO 2 ) 400 nm Base Si wafer CZ p-type <100> 525 micrometer SOI is a key European technology

24 Simulations Raman spectra SOI thin film Photoelastic model 2 * ( z ) for scattering by LA phonos I( qz) dz. EL. ES. p( z). z Φ 1 (z) oxide Φ2(z) silicon E L (E S ) : laser (scattered) field p(z) : photoelastic constant Φ(z) : phonon displacement Φ3(z) oxide Silicon buffer F Poinsotte et al Proc Phonons 2004

25 Simulations Vibrational Raman part spectra SOI thin film { 1( zox / Si ) 2( zox / Si ) - phonons displacement and stress boundary conditions 1 2 C ( ) ( ) 1 zox / Si C2 zox / Si - Assumptions Phonons stationary waves Free surface Dispersion relation Infinite silicon buffer z z iq1 z iq1 z 1 ( z) Ae 1 B1 e 1 C 1 ( z air / Ox ) z sound velocity q qz q z. v Vac(oxide) =5970 m.s ac -1 Vac(silicon) =8433 m.s-1 0 Electronic part F Poinsotte et al Proc Phonons 2004 { P P Ox Si (z) z 0 ( z) 1

26 Free standing 30 nm silicon membranes SOI membranes and configuration 500 m Back-scattering Laser spot Forward scattering Sotomayor Torres et al phys stat sol c 2004

27 Simulations of RS spectra of SOI membranes Treat SOI layer as a cavity for acoustic phonons, ie, confined since longitudinal v s in Si = 8433 m/s (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 Acoustic vibration periodic variation of strain polarisation field in presence of em wave cos( n z) ) t u z ( z, t) P( z, t) ps E i (z,t) z p s photo-elastic coefficient of slab P(z,t) )OKf for anti-stokes is part. Obtain Stoke part by changing u z ( z, t) z by u z ( z, t) zz *

28 RS spectra of 31.5 nm thick SOI membrane ) ( 1 ) ( ) ( P E E Thus, scattered field: ), ( 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

29 OUTLINE Motivation Methods Membranes Inelastic light scattering Dispersion relations (mainly by J Cuffe, E Chavez, both PhD students at ICN, work unpublished) Impact on heat transfer Perspectives and Conclusions

30 From bulk to membranes Elastic continuum approach Displacement Strain Relationship Hooke s Law Newton s Second Law Membrane (Lamb) z = +a/2 iz =0 Dispersion Relation z = a/2 iz =0 Flexural (Anti symmetric) Dilatational (Symmetric) 30

31 430 nm Si Membrane Spectra at 3mm Mirror Spacing Dispersion Relation LA 35GHz (Reference Peak) Spectra observed with Brillouin Light Scattering spectroscopy Multiple l modes observed d(deviation from bulk lkbehaviour) Good agreement with theoretical calculations (Lamb waves)

32 10 nm Si Membrane Spectra at 3 mm Mirror Spacing Shear Dilatational Spectra at 10 mm Mirror Spacing Flexural Dilatational Shear (SH) 32

33 Phase Velocity vs q.a Phase(Group) velocity decreases dramatically for thinner membranes

34 OUTLINE Motivation Methods Membranes Inelastic light scattering Dispersion relations Impact on heat transfer Perspectives and Conclusions

35 Impact on thermal conductivity Spatial confinement Modification of dispersion relation Modification of group velocity rad/ /sec DW FW SW aq // velocity Km/sec Group aq // Increase of relaxation rate Decrease of thermal conductivity membrane e / bulk 0,18 0,16 0,14 5 nm 4 nm 0,12 3nm 0, Temperature K

36 Impact on thermal conductivity Change in dispersion relation and the emergence of more branches increases interaction ti between phonons increase in relaxation rates and a corresponding decrease in the thermal conductivity The thinner the membrane the lower the thermal conductivity K. Including all the confined modes and calculating Umklapp processes

37

38 Phonon anharmonic decay Optical phonons Acoustic phonons (10 s ofmev) (few mev) optac ~ 5 ps in Si e-opt ph ~ 100s fs Optical phonon emissionhigh-field i h Joule heating Acoustic phonons carry heat away from hot spots

39 Phonon anharmonic decay Decay can involve only acoustic phonons. Cubic case and frequency < Debye frequency Higher energy Lower energy acoustic acoustic phonons phonons (few mev) (few mev) 3-phonon decay rate v v acac ~ fs-s in Si But the smaller the acoustic phonons energy difference, the longer the lifetime & mfp. Caustics increasingly important. v = Gruneisen constant Must understand and control anharmonic decay into and propagation of acoustic phonons.

40 COMMUNITIES The Summer School Series Son et Lumiere participating groups CA ZEROPOWER partners The members of the European CNRS-sponsored Network for Thermal Nanoscience and Nanoengineering The Fluctuations ti and Statistical ti ti Physics community The Phonons & Fluctuation informal 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 TAILPHOX, MINOS and QNEM on fluctuations, qbuts and phonon engineering CA NANOICT, NoE NANOFUNCTION,

41 OUTLINE Motivation Methods Membranes Inelastic light scattering Dispersion relations Impact on heat transfer Perspectives and Conclusions

42 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 are needed. Heterogeneous coupled cavities need better description with, e.g., quantum physics and elasticity theory. Phonon coherence ence studies in confined structures unavoidable Need contribution ti from statistical ti ti and quantum physics. Only then we can seriously address low power electronics.

43 Support Large Installation IMB CNM, GICSERV 2010 grant 43