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 El-Houssain,(U Oujda), Y Pennec, B Djafari-Rouhani i (U O jd ) Y P B Dj f i R h i 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 relation (phonon engineering) l ti ( h i i ) 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 = v s / f d in Si  d = 1.4 nm @ RT = 4000 nm @0.1 K @ velocity of velocity of 1 48  /k T 1.48  /k B T sound To confine phonons in the strong regime at RT need structures with ~ 1-10 nm lateral dimensions lateral dimensions From A Balandin, UC Riverside

MOTIVATION Double-gate SOI transistors top gate oxide, SiO2 p g , Top gate n+ top gate Al n+ poly Si n poly Si bonded interface BOX (back gate ox) (111) n+ Si subst. n+ contact Back gate n+ back gate n- or p- Si 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 on ZT of quantum quantum wells Rather controversial but crucial for Rather controversial but crucial for Hicks & thermoelectric energy conversion in Dresselhaus the nm scale. 1993; Suitable charge conduction in Suitable charge conduction in A Balandin phonon glasses needed. and K L Wang 1998 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 Square He agonal Hexagonal Hone comb Honeycomb honeycomb, f=0.3 square, f=0.3 triangular, f=0.6 1.0 1.0 1.0 y ed frequency y ed frequency ed frequency y 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 reduce reduce reduce 0.2 0.2 0.2 0.0 0.0 0.0    X J X M X M X J X wavenumber wavenumber wavenumber wavenumber wavenumber wavenumber honeycomb, f=0.6 square, f=0.6 triangular, f=0.85 1.0 1.0 1.0 ency ncy ncy 0.8 0 8 0.8 0 8 0.8 duced freque uced freque uced freque 0.6 0.6 0.6 0.4 0.4 0.4 0 2 0.2 0.2 0 2 0.2 0 2 red red red 0.0 0.0 0.0    X J X M X M X J X wavenumber wavenumber wavenumber

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 Optical forces control mechanical modes  prospects for cooling, heating, … M Eichenfield et al. Optomechanical Crystals, Nature 462, 78-82 (2009)

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. 50nm with weak 50nm 200nm 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 Corrugation (Ripple) Scattering Photoelastic Scattering 2    u ( z )     ( ) ( , ' ) ( ) I dz p z G z z E z  s z       1 1   LDOS Im G ( z , z )  r EH El Boudouti et al, Surf Sci Reports 64 , 471 (2009) EH El B d ti t l S f S i R t 64 471 (2009) i dE s q i q  k i k s Related to power spectrum of normal Related to power spectrum of normal displacement Benedek, G B & Fritsch, K Phys Rev, 149, 647 (1966) Rowell, N. L. & Stegeman, G. I. PRB 18 2598 (1978 ,)

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

Thin film SOI sample cross-section Native oxide 3 nm 40 40 nm SOI 28 nm Buried (thermal) oxide (SiO 2 ) 400 nm Buried (thermal) oxide (SiO 2 ) 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 Photoelastic model     2 ( ( z ) )    * ( ) . . . ( ). I dz E E p z for scattering by LA phonos qz  L S z Φ 1 (z) oxide E L (E S ) : laser (scattered) field p(z) p(z) : photoelastic constant : photoelastic constant Φ 2(z) silicon Φ (z) : phonon displacement Φ 3(z) oxide Silicon buffer F Poinsotte et al Proc Phonons 2004

Simulations Raman spectra SOI thin film • Vibrational part p    ( z ) ( z ) { { 1 / 2 / Ox Si Ox Si - phonons displacement and        stress boundary conditions stress boundary conditions 1 1 2 2 C C ( ( z z ) ) C C ( ( z z ) )   1 Ox / Si 2 Ox / Si z z - Assumptions     i iq z i iq z ( z ) A e B e 1 1 Phonons stationary waves 1 1 1     Free surface Free surface 1 1 ( ( ) ) 0 0 C C z  1 air / Ox z Dispersion relation sound velocity    q q . v v Vac(oxide) =5970 m s -1 Vac(oxide) =5970 m.s -1 qz z ac Infinite silicon buffer Vac(silicon) =8433 m.s-1 { {  P P ( ( z z ) ) 0 0 • Electronic part Ox  P ( z ) 1 Si 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