Olivier Bourgeois Institut Néel. Séminaire Collège de France Mardi 19 Novembre 2013

Transcription

1 Olivier Bourgeois Institut Néel Séminaire Collège de France Mardi 19 Novembre 2013

2 ! Introduction: motivations, nanophononics! Part 1: History of phonons and thermal measurements " Phonons " Thermal conductance, transport of phonon at the nanoscale, mean free path " Micro-nano and low temperature! Part 2: Measurement of thermal transport in Si nanowire " Si Nanowire: Casimir Ziman model " Transmission coefficient " Ballistic transport! Part 3Manipulation of heat and thermoelectricity " Phonon blocking " Corrugated nanowire: strong reduction of mean free path " Application to nanothermoeletricity! Perspectives and Conclusive remarks

3 Heat storage (Specific heat) Heat transport (Thermal conductivity)

4 ! Debye and Einstein theory of specific heat of solids! Mandelshtam and Raman 1928! Igor Tamm sound quanta or heat quanta 1930! Yakov Frenkel proposes the name phonon from ancient greek!"#$ (voice) 1932! Quantification of vibrational modes! Photon interaction with solids (Brillouin scattering, Raman scattering) Igor Tamm! vib! 0 +! vib! 0 E=!#%

5 ! Linear monoatomic chain! Periodic conditions: Born-von Karman! Quantization of the vibrational modes! Dispersion relation! Group velocity! v = "! k! Elementary excitation: phonon E = n q +1/ 2! ( )! d u m dt ' = 2 n 2 u n-1 u n u n+1 = n K( 2( un+ 1! un) + ( un! u! 1)) u n = exp( i( kna "! t)) K am & sin$ ka % 2 #! "

6 ! Diatomic chain! Acoustic and optical modes! Spatial extension of a phonon?! Phonon=Wave packet! Propagating modes TA and LA (related to!) Raman Brillouin v =! "! k

7 ! Boson (Bose-Einstein distribution)! Number of phonons not conserved! Quasi-particle! At low temperature : only large wave length phonon are excited (low energy)! No optical phonon (only acoustic modes)! Planck black body radiation (for infinitely rough surfaces) n q 1 = '!( $ exp % "! 1 & kbt # High temperature n q " kbt!! Low temperature! n q Dom &!) # ( exp $ '! % kbt " = hvs 4.25k B T

8 Two kind of heat carriers (radiation neglected) Electrons & e- ~nm ' F ~0.1nm L!~10µm T diffusive fermions Mean free path Relevant wave length Coherence length Temperature dependence (K, C) Transport statistic Phonons & ph ~mm ' ph ~100nm Not coherent T 3 ballistic bosons

9 ! Landauer model for heat transfer! Universal quantum of thermal conductance! Thermal rectification (Chris Dames review Proceedings of HT2009, page 1, (2009))! Thermal insulation (phonon trapping, phonon blocking etc )

10 Implications: thermalization, nanothermoelectricity! Ballistic phonon->no local temperature! Thermal conductivity ->thermal conductance (driven by the size of the systems)! Play with the phonons: phonon focusing, phonon blocking etc..! Application to thermoelectricity: phonon scattering at the nanoscale with clusters, nanoparticles, superlattice etc ZT = S 2 T! ( k k ) elec + ph " max = " c ZT ZT ! 1 + 1

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12 ! Early days : Guillaume Amontons ( ): heat flow along the temperature gradient! Heat, matter and temperature: Latent heat, Joseph Black ( )! First measurements: Jean-Henri Lambert ( ) published in 1779 : convection, geometry Joseph Black T+dT T

13 Les Physiciens sont partagés sur la nature de la chaleur Nouveaux concepts : chaleur libre, capacité de chaleur, chaleur spécifique Plusieurs d entre eux la regarde comme un fluide répandu dans la nature! D autres physiciens pensent que la chaleur n est que le résultat des mouvements insensibles des molécules de la matière. Lavoisier et Laplace (Mémoire sur la chaleur 1780).

14 ! Treatise on calorimetry published in 1782! First experiment of heat capacity! Ice calorimeter (temperature reference ) L (latent heat ice/ water at T = 0 C) Pierre Simon de Laplace = 334 J/g ( 80 cal/g L (latent heat water/ water vapour at T = 100 C) = 2260 J/g ( 539 cal/g Antoine Laurent Lavoisier

15 ! Benjamin Franklin ( ) compared thermal conductivity of different metals! Jan Ingen-Housz ( )! Count Rumford ( ) insulating materials! Joseph Fourier ( ) 2 experiments: steady state (K,h), transient (C,h>>K) Temperature! = C K )T T 0 Time Time dependent experiments: Joseph Fourier )t Physics Today 63, 36 (2010)

16 Copper 6x10 7 S/m Electrical Thermal Germanium 3 S/m Diamond, graphen 10 3 W/mK 10-1 W/mK Polysteren, glass Glass S/m Teflon S/m At 300K

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18 AsGa nanowires (LPN, Marcoussis) Si nanowires with phonon cavities (Institut Néel, Grenoble) Loss of the bulk behavior, competition between surface and volume. Relevant characteristic lengths (dominant phonon wave length, mean free path, thermal length, etc!) Specific thermal behavior at small length scale (universal thermal conductance, definition of temperature!) Systems under study need to be thermally isolated : membrane, suspended structure (nanowire, graphene sheet, sensitive sensors) Development of new experimental tools using nanotechnology adapted to very small thermal signals and adapted to very small mass samples of the order of zepto (10-21 J) or yoctojoule (10-23 J).

19 ! Focus on electrical based measurement! Problems related to measurement using continuous signal! Preamplification of the signal before measurement! AC thermal measurements: proposed since 1910/1911 by O. Corbino! Measure by lock-in amplifier! Differential geometry Orso Mario Corbino ( )

20 ! Proposed par Lu et coll.! Adapted for suspended nanowires! Limit at low frequency X=0 X=L V thermometer (transducer) Joule Heating nanowire (suspended) substrate I ac

21 2 2 2 " " I0 sin ( wt) dr $ CP T( x, t) # k T( x, t) = [ R + ( ) ( T( x, t))] 2 T! 0 " t " x LS dt T ac max Temperature profile T 0 T 0 Low frequency )T )T )T High frequency 1.2 Vac=V 0 /(1+(4"f#) 2 ), avec #=C/(" 2 K)=0.011s -L/2 0 K sensitive L/2 K and C sensitive C sensitive V 3! (µv) V 3! = 4 # K( 4I 3 0 R 2 $ 1+ (2!" ) 2 K = 3 2 4I0 R # 4 " V 3! 0.2 à 2K f élec (Hz) O. B, Th. Fournier and J. Chaussy, J. Appl. Phys, 101, (2007)

22 ! Measurement between 0.3K and 10K! Power law in temperature (T 2 and T 3 )! Different geometries! 4 channels for heat transfer

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24 k k k k!! Phonon elastic scattering (impurity) k = k' k! Inelastic scattering k' and! "!'

25 ! Scattering on dislocation (static imperfection)! Anharmonic scattering (three phonons, Umklapp processes)! Electron-phonon interaction (doped semiconductor)! Boundary scattering (finite size effect) Mathiessen rule: " n 1! " 1 # = # " = v! i ph ph scatt i= 1

26 ! Mean free path & ph! & Cas =D (Diameter of the nanowire)! Boundary scattering: black body radiation for phonons! Expression for K(T)! Still diffusive! Comment on the specific heat (kinetic equation) T 1 T 1 >> T 2 r B T 2 V n Breakdown of the concept of thermal conductivity

27 ! At low temperature, the dominant phonon wave length is increasing:! Probability of specular reflection p(' dom ) depending on ' dom (phenomenological parameter)! Dom = hvs 4.25k r B B T! p(' dom )=0 (perfectly rough surface) ' dom <<$ 0 Casimir model! p(' dom )=1 (perfectly smooth surface) ' dom >>$ 0% V n V n "n $ 0 is the root mean square of the asperity

28 ! Ziman-Casimir model! ph = 1+ 1" p! p Cas where p probability of specular reflection If p=0 transport is diffusive (Casimir), if p=1 ballistic transport p( $ ) $ dom = P( #) e d#! 3 " 16% # 2 2 Probability distribution of asperity

29 ! Ziman model of phonon transport: ballistic contribution Dom = hvs 4.25k B T K = 2/ k S! ) ' * $ B eff 3 3.2( 10 % T v "! s L! eff & + p =! 1" p # 1 "! 1 = "! 1 + L! 1 Cas ph eff p ! ph (!m) T(K) T (K) J.-S. Heron, T. Fournier, N. Mingo and O. Bourgeois, Nano Letters 9, 1861 (2009).

30 Evidence of contribution from ballistic phonons K/4K 0 Dominated by the thermal resistance of the wire/ reservoir junction Competition between ballistic and diffusive regime: roughness effect Diffusive transport: classical Casimir model Fitting parameter: Roughness h=4nm Speed of sound 9000m/s Contribution of the contact (Chang, C.; Geller, M. Phys. Rev. B 2005, 71, ) 1 10 T(K) J.-S. Heron, T. Fournier, N. Mingo and O. B, Nano Letters 9, 1861 (2009).

31 Four different nanowires, different section and different length K = 2/ " k S# + ) & B eff * 10 ' T =! T 3 3 Zim 5 v $! s L ( %

32 Four different nanowires, different section and different length K = 2/ " k S# + ) & B eff * 10 ' T =! T 3 3 Zim 5 v $! s L ( %

33 ! Profiled contact! Identical normalization! Optimal acoustic adaptation: catenoidal shape! Above 1K, transmission coefficient T~1

34 ! Profiled contact! Identical normalization! Optimal acoustic adaptation: catenoidal shape! Above 1K, transmission coefficient T~1

35 0K 0.1K 1K 10K 100K 300K! dom (T) < " ph (T) < L Diffusive regime Silicon nanowire of diameter: 100nm Maxwell Boltzmann : k C s = " 3! ph! dom (T) < L ~ " Cas < " ph-bulk (T) Casimir regime Casimir model K T Cas = "! Cas 3! dom (T) ~ L < " Ziman (T) L <! dom (T) < " ph (T) Ziman regime Ballistic regime Ziman model Landauer :! Ziman 1 T = 1+! 1+ p =! 1" p eff / L Cas

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37 ! Introducing of a serpentine nanostructure in the suspended nanowire (5#m long)! Length scale 200nm! Blocking only the ballistic phonons! Reduce the thermal conductance

38 ! Reduction of up to 40% of the thermal conductance! Model this system by transmission function analysis! Very good agreement between the model and the data! Concerning ballistic phonons the reduction is of the order of 80% J-S. Heron, C. Bera, T. Fournier, N. Mingo, and O. Bourgeois, Blocking phonons via nanoscale geometrical design, Phys Rev B 82, (2010)

39 ! Intoducing periodic modulations! Phononic crystal geometry! Major effect when the periodicity of the phononic crystal corresponds to the dominant phonon wave length! For Si: ' dom =60nm at 1K Cleland et al., P. R. B, 64, (2001)

40 ! Multiple scattering! Backscattering in sawtooth nanowire! Reduction of the mean free path

41 ! Samples made by ebeam lithography! ' dom =60nm at 1K in silicon very close to the periodicity of the modulation of roughness! Comparison to smooth nanowire '=200nm 10 #m 320 nm d=200 nm *=55 nm 200 nm

42 ! " T L S v k T K s B # $ $ % & ' ' ( ) * = ) (! Cas p p! " + =! ) ( T L S v k T K Cas s B! " " # $ % % & ' ( =! )

43 ! Smooth nanowire have large mean free path! Comparable temperature power law (+=2.6)! Mean free path strongly reduced by regular corrugated surfaces! Comparison to smooth nanowire

44 ! Presence of backscattering! Phonon trapped in the Si tooth

45 10 #m Ali Rajabpour, S. Volz 200 nm

46 Strong backscattering effect of the corrugation (negative parameter p) The corrugation acts like a trap for the phonons Factor of 9 in the mean free path between smooth and corrugated wires C. Blanc, A. Rajabpour, S. Volz, T. Fournier, and O. Bourgeois, Phonon Heat Conduction in Corrugated Silicon Nanowires Below the Casimir Limit, Appl. Phys. Lett. 103, (2013).

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48 Implications: thermalization, nanothermoelectricity! Ballistic phonon->no local temperature! Thermal conductivity ->thermal conductance (driven by the size of the systems)! Play with the phonons: phonon focusing, phonon blocking etc..! Application to thermoelectricity: phonon scattering at the nanoscale with clusters, nanoparticles, superlattice etc ZT = S 2 T! ( k k ) elec + ph " max = " c ZT ZT ! 1 + 1

49 (! GeMn inclusions in Ge matrix (single crystal)! Broad distribution of scatterers! Much higher ZT as compared to regular semiconductor! Collaboration ARC Energy with CETHIL (Séverine Gomes)! EU collaboration MERGING CEA INAC (André Barski), ICN (Barcelone), VTT (Helsinki), Max Planck I. (Mainz)) 10" e-! ph )**+,-.*-( (!& %' %& ' &! " # $ %& %! /0.12.* (,052+4(6.78 Thermal conductivity (W.cm -1.K -1 ) Ge Bulk Ge Mn film e = 100 nm Temperature (K) Thesis Yanqing Liu (ARC Energy project)

50 ! Heater=thermometer=Platinum (no NbN)! Thermal conductance measurement at low frequency (Cahill RSI 1990)! Application to multilayers Platinum GeMn Germanium/GaAs ALD (Al 2 O 3 ) Copper or Glass Yanqing Liu (Thesis) and Dimitri Tainoff (Post-doc) D. G. Cahill, Rev. Sci. Instrum. 61, 802 (1990) J.-Y. Duquesne, Phys. Rev. B. 79, (2009)

51 * k 2 3 % " R " I dv 3# inph. =! 2 2 " $ " l ( ) d ln#! 1 D = "! f # th K Ge =44 W/mK * V 3! (µv) V 3! = ax I (ma)!"#$%&'()*+, -./'!0 1 %2 ) +34,5 ) ( ' & *+),-./01)23 *+),-./01"23 *+),-./014 23! " # $ % 5.!

52 ! &>>d! ' dom >>d! 4 acoustic phonon modes K 0 2 4! k = 3h! Conduction channel (Similar to the Landauer model of electrical conductance)! Not dependant on the materials! Valid whatever the heat carrier statistic! Pendry, Maynard: flow of entropy or information 2 B T K/4K D 3D T(K)

53 ! Heat nano-engineering at small length scale! K: 3" method, hot wire, thermal gradient! Single crystals: serpentine and corrugation! Amorphous materials! Breakdown of the concept of thermal conductivity (MFP larger than the size of the system)! Quantum regime: universal behavior of K (dom. phonon wavelength is bigger than the size of the system)

54 ! Phononics conference every two years! 2015 Phononics in Paris! 2017 Phononics in China (Changsha)! Creation of The Phononics Society (2013)

55 !!!!!! Nanofab(rication), Electronic, mechanical facilities, Pole Capteur Christophe Blanc, Hossein Ftouni, Yanqing Liu, (Jean-Savin Heron) Kunal Lulla, Dimitri Tainoff Séverine Gomes, Sebastian Volz, Natalio Mingo TPS, UBT etc! Financial supports from Région Rhones Alpes (ARC Energy), Agence Nationale de la Recherche, European Union (FP7) MERGING