Terahertz acoustics with multilayers and superlattices Bernard Perrin Institut des NanoSciences de Paris

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1 Terahertz acoustics with multilayers and superlattices Bernard Perrin Institut des NanoSciences de Paris

2 Daniel Lanzillotti-Kimura CNEA Bariloche & INSP Paris Florencia Pascual-Winter CNEA Bariloche & INSP Paris Shuo Zhang INSP Paris Laurent Belliard INSP Paris Agnès Huynh INSP Paris Bernard Jusserand INSP Paris Emmanuel Péronne INSP Paris Bernard Perrin INSP Paris Alejandro Fainstein Aristide Lemaître Annie Michel Grégory Abadias Christaine Jaouen CNEA Bariloche LPN Marcoussis LMP Poitiers LMP Poitiers LMP Poitiers

3 Ultrasonic acoustics with piezoelectric transducers Piezoelectric transducers detected acoustic pulses sample Electrical pulse 1 cm Time delay (μs) Piezoelectric films 1 - a few GHz

4 What could be done with terahertz acoustics? Sound wave velocity in solids : 5 1 nm/ps THz range Phonons : nm scale The role of phonons confinement and phonons scattering by the interfaces on the thermal transport in nanostructures and heterostructures : Sound absorption in glasses Figure of merit for the thermoelectric effect Cooling of electronic devices σ Z e κ ph Mean freepath in bulk systems κ ij = C λ sλ, isλ, j λ Lifetime of confined phonons Selective excitation of nano-objects τ λ

5 How to do it? The first step :Picosecond acoustics with an optical pump-probe technique Im(Δr/r) (arb. units.) 2.e-5 1.5e-5 1.e-5 5.e-6.e+ Impulsion sonde Impulsion 5e-5 sonde Impulsion Impulsion sonde sonde Ni film (2nm) Impulsion sonde Impulsion sonde Impulsion sonde Impulsion sonde Impulsion sonde Impulsion sonde Frequency Impulsion Delay sonde Im(Δr/r) (arb. units.) e+ Impulsion sonde Impulsion -5e-5 sonde Impulsion sonde Delay Impulsion Impulsion sonde sonde Film absorbant Substrate Impulsion Impulsion laser Impulsion laser Impulsion laser Impulsion laser Impulsion pompe Impulsion pompe Impulsion pompe Impulsion pompe pompe Impulsion Impulsion sonde sonde Mesure

6 SONAR experiments in [Cu 5.56nm /Co 1.29nm ] 3 [Cu 3nm ][Si] multilayers (C. Rossignol, B. Perrin, 1997) pump probe 235nm Silicon substrate Lock-in signal Time (ps) rst echo Time (ps) f =.79 THz

7 Terahertz acoustic vibrations in Copper (.8-5.5nm) /Cobalt (1.3nm) multilayers CuCo - d = 2.1nm CoCu - d = 6.3 nm nm 3.7 nm.71 THz.97 THz q (nm -1 ) q (nm -1 ) 2.1 nm 1.42 THz 1.3 nm.8 nm 1.8 THz 2.25 THz Time (ps) Period (nm)

8 The second step : transduction with a superlattice Δr r η( q) p = q = Phonon generation with ligth dzσ dzσ gen. gen. iqz ( q) e E( z) iqz ( q) e I( z) p δ ( q) k : effective electromagnetic wave vector in the superlattice p j q = 2k Phonon detection with light dq dze «Forward scattering q =» 2ikz e 2iqz η 2 ( j, q) p η( j,2k) j «Backscattering modes q = 2k» forward scattering q= backscattering q=2k ; detected in (semi)-transparent media Resonant modes : surface localized modes, Cavity modes, q=2k Brillouin Z t < Z b π/d Acoustic wave vector

9 Al (3nm) AlAs GaAs Al (3nm) PUMP GaAs substrate Probe ~ 35 μm Propagation time ~ 73ns Bragg mirror superlattice ~ 1 μm

10 Acoustic mirror without capping Acoustic mirror transmission Surface displacement (Arb. units) Experiment Frequency (GHz) Acoustic mirror with a 3nm aluminum cap layer Simulation Surface displacement (Arb. units) Frequency (GHz)

11 Large acoustic mismatch : Mo/Si Z Z Mo Si = 1 Z Mo Z Si = Z Si Z Mo q vector (nm -1 )

12 Real(Δr/r) (Arb. Units) Experiment Fitering Generation with a transducer made of forty 25 nm periods pump GaAs probe Time delay (ps) 356 µm Forward scattering mode at q = im(δr/r) (Arb. Units) Fourier transform (arb. units) im(δr/r) 2 real(δr/r) Time delay (ps)

13 Terahertz detection with a superlattice probe GaAs pump µm Acoustic mirror Δr/r Wave vector q (nm -1 ) Time delay (ps)

14 Detection with a transducer made of eighty 12.5 nm periods.1.8 r q r = 2k q(ω) Δr/r(ω) detection by a 3nm Al film λ = 12.5 nm λ = 6.25 nm λ = 4.1 nm

15 .15 lattice dispersion q (nm -1 ).1.5 Stationary mode V g = Filtered signal 8e-4 4e-4 filter.3-.5 THz filter.7-.9 THz x 1 Amplitude 3 2-4e Time delay (ps)

16 Acoustic transduction on both sides of a substrate «wedged» superlattice GaAs/AlAs period 12 nm PUMP probe flat superlattice GaAs/AlAs period 12 nm k (electromagnetic wavevector) Wave vector (nm -1 )

17 PUMP 2D Graph 2 probe Subterahertz acoustics (.4 THz) 4e-4 high pass filter (.35 THz) 15 x = + 4 mm Δr/r 2e-4-2e-4 signal Im(Δr/r) (normalized) 1 5 x = + 3 mm x = + 2 mm x = mm x = - 2 mm Time delay BS in GaAs BS in SL 1 ps probe Time delay (ps) ( ps) Oscillations period 2.5ps (4GHz) Delay (ps) ( ps)

18 364.5µm Terahertz acoustics (1 THz) PUMP probe Superlattices 1.5e-4 1.e-4 6 ps (Filtered signal 1 THz x1) 5.e-5 Δr/r. -5.e-5-1.e-4-1.5e-4-2.e Time (ps)

19 Detection with a transducer made of eighty 12.5 nm periods.1.8 r q r = 2k q(ω) Δr/r(ω) detection by a 3nm Al film λ = 12.5 nm λ = 6.25 nm λ = 4.1 nm

20 .15 lattice dispersion q (nm -1 ).1.5 Stationary mode V g = Filtered signal 8e-4 4e-4 filter.3-.5 THz filter.7-.9 THz x 1 Amplitude 3 2-4e Time delay (ps)

21 Acoustic transduction on both sides of a substrate «wedged» superlattice GaAs/AlAs period 12 nm PUMP probe flat superlattice GaAs/AlAs period 12 nm k (electromagnetic wavevector) Wave vector (nm -1 )

22 PUMP 2D Graph 2 probe Subterahertz acoustics (.4 THz) 4e-4 high pass filter (.35 THz) 15 x = + 4 mm Δr/r 2e-4-2e-4 signal Im(Δr/r) (normalized) 1 5 x = + 3 mm x = + 2 mm x = mm x = - 2 mm Time delay BS in GaAs BS in SL 1 ps probe Time delay (ps) ( ps) Oscillations period 2.5ps (4GHz) Delay (ps) ( ps)

23 364.5µm Terahertz acoustics (1 THz) PUMP probe Superlattices 1.5e-4 1.e-4 6 ps (Filtered signal 1 THz x1) 5.e-5 Δr/r. -5.e-5-1.e-4-1.5e-4-2.e Time (ps)

24 Phonon dispersion in bulk GaAs f =.3925THz f = 1.8THz 2 3 l δt = γω = 97 ps 4 s 2 3 l δt = γω = 6 ps 4 s

25 Phonon mean freepath in bulk GaAs Attenuation α=1.2*1-8 ω 1.13 T Attenuation (μm -1 ) attenuation at 1.8 THz attenuation at.3925 THz *1-8 *T *1-8 *T Temperature (K)

26 Propagation through a thick substrate 2. Δr/r (*1-4 ) ps Thick susbtrate (983 μm) high pass filter (.35 THz) attenuation (μm-1).12 Thin substrate (36mm) Thick substrate (1mm) Fit Time *1 5 (ps) Temperature (K)

27 Sound absorption in bulk systems ω λ τ μ ω, q r λ λ ω λ q r λ : : Acoustic frequency : Acoustic wave vector q r μ : ω, q r μ μ ω, q r λ λ ω μ α λ Thermal phonon frequency Thermal phonon wave vector μ, ν ( n n ) δ ( ω ω ω ) 36π = 2 Λ λμν ν μ λ μ + h s ν > 1 ω λ τ μ r ω, q r + q λ + ω μ λ μ r + G Elastic continuum approximation Λ λμν q λ q μ q ν Thermal phonons have to be dressed << 1 ω λ τ μ Isotropic and dispersive medium = a λ Anisotropic medium Herring processes An infinite series of ladder diagrams has to be taken into account Boltzmann equation approach α ω λ a = a 5 T a λ αλ = AωλT

28 Conclusions Terahertz acoustics is no more a fiction but things have still to be improved