#### Transcript Talk - Iramis

Heat and Nanotechnologies: Focus on Thermoelectricity Sebastian Volz Yann Chalopin, Ali Rajabpour, Yuxiang Ni Gang Chen, Natalio Mingo, Laurent Jalabert, Michel Kazan, Ravi Prasher, Pawel Keblinski, Deepak Srivastava Laboratoire EM2C UPR CNRS 288, Ecole Centrale Paris Thermal Nanosciences Group - [email protected] Nanoelectronics: Concept, theory and Modeling , – Cargèse, France – October 24th 2012 Heat carries in non-metals are SOUND PARTICLES or PHONONs, the quanta of lattice vibrational energy Fij = K.(uj- ui) a i-1 i i+1 ka K sin am 2 ka w aK cos 2 k m w &n K 2un un1 un1 mu& w 2 un=u.expi(kna-wt) k Periodic Boundary Conditions: k = n . 2/L Density of states Eks 1 t hw ks . nks t 2 Phonons form a GAS of particles to propagate heat Acoustics: Coherent Phonons w Continuous limit k=>0 2u u&& K ' 2 x w aK k m k Heat Flux: the Phonon Gas w max Cw vw .w dw 0 Knudsen Transport Applies Phonon Wien’s Wavelength: 3nm (300K) Mean free path: 1-1000nm Kn>1: Boundary scattering predominates over diffusive scattering L =1/3 C v p(, w, pol, ) Confinement: Cavity modes appear if L< Wavelength Periodicity: e ik(L+x)=e ikx e ikL=e ika=0 un ~ expi(kna-wt)+ expi(-kna-wt) ~ cos(kna)e-iwt =1/3 C v a STEADY WAVE has ZERO group velocity The number of phonon modes depends on Dimensionnality k-space Dimension: Number of States /dk: 1D (wire) 2D (film/SR) D(k) dk ~ 1 dk D(k ) dk ~ k dk 3D (bulk) D(k) dk~ k2 dk =1/3 C v Nanostructures have exceptional thermal conductivities Carbon Nanotubes 2400-3000 W/mK@RT Silicon Nanowires 1-3 W/mK@RT WASTED HEAT RECOVERY US: 30% of the world energy consumption The Non-Dimensioned Figure of Merit ZT Qualifies TE Materials TE Applications are mostly ‘Niche’ Applications -Laser, PCR Large scale applications are still expected CAR INDUSTRY What are the Physical Mechanisms underlying TE Properties Nanostructured TE Material Concept was launched by Dresselhaus …but electron design did not yield significant ZT improvement. However, phonon thermal conductivity reduction is possible. High ZT Superlattices Ge Si Ge Boltzmann Equation Predictions Match Experimental Data G. Chen 1998 In the thin layer limit, phonon transport within each layer is ballistic, and the TBR dominates the effective thermal conductivity of superlattices.’ Gang Chen PRB, 57, 23, 1998 Confinement should also contribute to the thermal conductivity decay in films Alexander Balandin 1998 ‘We show that strong modification of phonon group velocities due to spatial confinement leads to a significant increase in the phonon relaxation rates. Modification of the lattice thermal conductivity by confined phonon modes opens up a novel tuning capability of thermoelectric properties of heterostructures, and may lead to a strong increase of ZT in specially designed semiconductor nanostructures.’ Strain Effects strongly affect thermal conductivity showing importance of interface scattering Experimental results - T. Borca-Tasciuc, G. Chen BOLTZMANN - G. CHEN Experiences Si/Ge superlattices SV, Saulnier, Chen, Beauchamp, Microelectronics Journal, 31, 815, 2000. According to Molecular Dynamics technique, interfacial roughness explains the experimental trend EXPERIMENTAL DATA Daly, Maris, Imamura, Tamura, PRB, 66, 24301, 2002. MD DATA Superlattices have provided a Breakthrough in TE history ZT=S2T/ Thermal Conductivity of Thermoelectric Material Superlattices is lower than Bulk ones p.597 High ZT Nanoparticles? Alloying scatter high frequency phonons. How to break middle frequency phonons? DESIGNING Impurity Size Phonon Scatterers Phonon ‘Particle’ OPENING Band Gaps Thermal Phononic Crystals Phonon ‘Wave’ Si/Ge Thermal Phononic Crystal Thermal Conductivity as Low as 0.2W/mK J.N. Gillet, Y. Chalopin, SV, Journal of Heat Transfer, 131, 043206 (2009) Can Middle Frequency Phonons be Scattered by 10nm Nanoparticles Thermal Conductivity below the Alloy Limit was Obtained with Nanoparticles NPs however deteriorate TE properties Impact of Nanoparticles on ZT was proven but in conventional TE compounds Can Nanowires also Improve ZT? • D,L >> regime κbulk is the bulk thermal conductivity D : diameter L : length Λ : mean free path (100nm in Si) Cv: heat capacity Vp : phonon velocity (6000 m/s) • D ~< Λ and L>> Effective MFP • D < Λ and L< Fourier law 1 1 1 e D G bulk D2 L D D2 G Bulk L Ballistic regime 3D: Sharvin Law G Cvvp D2 1D: Quantum of Conductance SMOOTH SURFACES, NANOJUNCTIONS Is the 1D behaviour at low temperatures impacted by reflections at nw/substrate interface? 1D in k-space K. Schwab, E. A. Henriksen, J. M. Worlock and M. L. Roukes, Nature 404, 974 (2000) Quantum of Conductance L. G. C. Rego and G. Kirczenow, Phys Rev. Lett. 81, 232 (1998) The contact conductance includes nw and substrate contributions Qw Qb Diffuse Mismatch Model for Transmission: The contact resistance is predominant compared to the nw one The density of modes is lower in the substrate at low temperatures (k) ? TL ? TR 1D DOS Excited Modes 1D WIRE 3D SUBSTRATE T Experiments tend to confirm this trend T2 T3 T3 Metal nanowires also have predominant contact resistances at higher electron density R. Venkatesh, Y. Chalopin, J. Amrit, SV, PRB 83, 115425 (2011) Is a Nanojunction a good TE system? MEMS Actuation allows forming and characterizing Nanojunctions G GS TS TH TS T H TA GS1/2 TS G GS1/2 TA The constriction diameter reduces with elongation Experiments agree with a Ballistic Thermal Conductance Model Jalabert, Sato, Ishida, Fujita, Chalopin, SV, Nanoletters, 12, 5213–5217, 2012 Experiments GJex GS Theory TS TH TS GJth Cp vSJ D=7nm 5 D=19nm 3 1 D=38nm 1 before after 3 5 30nm Rough Si Nanowires are relevant candidates for improved ZT Diameter=48nm ZT=S2T/ CONCLUSION on NANOWIRES and NANOJUNCTIONS Quantum of Conductance: At low temperatures, Heat flux in 1D Si Nanowires is dominated by CONTACT RESISTANCE . A similar but less drastic behaviour is observed in metal nws. Nanojunctions: Ballistic Heat Conduction was shown in the 400-500K range in short nanojunctions. Conclusions on ZT -Superlattices, Nanoparticles and Rough NWs present High ZT values because of enhanced Phonon Scattering. -Nanostructuraction has yielded unequalled ZT values (ZT=2-3). -Bulk TE materials can not be obtained by atomic scale fabrication techniques (MBE) and alternative routes are being explored. -Large scale applications remain quite out of reach. Restrictions on TE materials make these expectations even more difficult. -Cost effective Thermoelectric materials remains an option: ZT also depends on $ -But how to Improve electronic properties? Collaborators: 2007 European CNRS Network Thermal Nanosciences and NanoEngineering 2010 Team: Y. Chalopin (CNRS) T. Antoni (Ass. Prof.) T. Dumitrica (Inv. Prof.) Pdocs: J. Ordonez O. Pokropivny PhDs: Y. Ni, S. Xiong, L. Tranchant W. Kassem, J. Jaramillo A.Ramière, H. Han B. Latour, J. Soussi France: N. Mingo (CEA-LITEN) E. Ollier (CEA-LITEN) A. Ziaei (Thales R&T) L. Divay (Thales R&T) P. Cortona (SPMS, Ecole Centrale Paris) H. Dammak (SPMS, Ecole Centrale Paris) J. Bai (SPMS, Ecole Centrale Paris) L. Aigouy (LPM, ESPCI) B. Palpant (LPQM, ENS Cachan) S. Merabia (LPMNC, U Lyon) P. Chantrenne (MATTEIS, U Lyon) D. Lacroix (LEMTA, U Nancy) J. Amrit (LIMSI, U Orsay) B. LePioufle (SATIE, ENS Cachan) D. Fourmy (Centre de Génétique Mol., Gif) K. Termentzidis (LEMTA, Nancy France) Abroad G. Chen (MIT) H. Ban (Utah U.) C.W. Chang (National Taiwan Uniiversity) B. Kim (U Tokyo) H. Fujita (U Tokyo) H. Kawakatsu (U. Tokyo) Y. Kosevich (Semenov Inst. Moscow) M. Kazan (U Américaine de Beyrouth) A.Rajabpour (U Teheran) Y. Ciumakov (Moldova) THANK YOU FOR YOUR ATTENTION Round Table: Thermoelectric energy conversion, insights, prospects for real applications? -2D Electron: Graphene, SrTiO2… -Magnetic Tunnel Junctions -3 or 4 terminals devices, Chaos, Fluctuations