PROBING PHONONS WITH INELASTIC LIGHT SCATTERING: phonons in silicon nanostructures

Transcription

1 PROBING PHONONS WITH INELASTIC LIGHT SCATTERING: phonons in silicon nanostructures Clivia M. Sotomayor Torres and Bartlomiej Graczykowski, Francesc Alzina, Marianna Sledzinska, Emigdio Chavez-Angel, Alexandros El Sachat, J S Reparaz, M R Wagner, Juliana Jaramillo-Fernandez Phonon School, Oléron, France, 3-8 th September 2017

2 P2N group research landscape Hypersonic phonons Optomechanics phonon-photon interactions Nanoscale thermal transport 1 GHz 1 THz Frequency (Hz) novel nanofabrication nanometrology instrumentation novel nanostructures methods 2

3 Concepts OUTLINE Instrumentation & methods Examples o Bulk Si and Si membranes o Optical phonon plasmon coupling, Atomic-like excitons in quantum dots and Surface phonons Laser Raman thermometry in 2D materials Conclusions 3

4 Frequency Animation courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State 4 Phonons in solids WHAT IS DISPERSION RELATION? Dispersion relation: relationship between phonon frequency and its wavevector. Optical Longitudinal waves No motion of the centre of mass Direction of propagation Acoustic Wavevector Transverse waves

5 Phonons in solids Key excitation in energy and momentum relaxation. (mev) up to ~30 LO TO LA TA Typical dispersion relations of acoustic phonons in bulk material /2a k Acoustic phonons are heat carriers in non-metallic materials, whereas electrons are the heat carriers in metals.

6 Considerations Momentum conservation: Typical laser line incident = 4880Å Thus 2n k ; n(gaas) cm 4.33 maximum momentum transfer is twice this, i.e., 1.1 x 10 6 cm -1 Extent of the Brillouin Zone /a with a = lattice parameter = 5.65Å for GaAs B.Z. boundary ~ 6 x10 7 cm -1 Maximum wavevector transfer << B.Z. extent First order approximation: Raman scattering probes excitations with q0.

7 Phonons in Low Dimensional Systems Several types of phonons not found in bulk materials: Interface Zone-folded Geometrically confined surface modes Localised and or confined Treat as standing waves (eg., confined) or propagating waves (eg., zone-folding in superlattices) Phonons in Semiconductor Nanotructures, Eds J-P Leburton, J Pascual and C M Sotomayor Torres, Kluwer Publishing, The Netherlands, 1993

8 PHONON DETECTION: INELASTIC LIGHT SCATTERING Light-matter interactions Processes studied by Optical spectroscopy. Inelastic light scattering detects the transfer of energy and momentum between photons and phonons and directly measures the phonon energy. Rayleigh scattering sub mev Brillouin scattering - mev Raman scattering 10s mev Other techniques to study phonons include: Far infrared Fourier Spectroscopy Neutron scattering X-ray synchrtron based-methods 8

9 f (THz) CONFINED PHONONS Displacement-Strain Relationship Hooke s Law Newton s Second Law Standing Waves d 0 q z Dispersion Relation Longitudinal [100] Transverse [100] Rayleigh SAW q // (nm -1 ) a Longitudinal and transverse standing waves at q // = 0 Analogous to acoustic modes in an organ pipe 9

10 ELASTIC CONTINUUM MODEL AND BULK WAVES Continuum Elasticity : Displacement-strain relationship Hooke s Law : Stress-strain relationship Newton s 2 nd Law : Force-displacement relation ship S Strain Continuum elasticity kl ( S kl U x j i S lk ) U x Displacement i j Hooke s law Stress T C ij ijkl S kl Elastic Tensor T x ij j Newton s 2 nd law density 2 U t i 2 U i u i e i( q x t) J. Cuffe, PhD Thesis, UCC, Cork, Ireland,

11 Raman scattering in semiconductors Raman scattering is one type of inelastic light scattering. S cb E g vb S l light incident Optical phonon scattering can be seen as a result of light interacting with dipoles in the solid. Dielectric function e as a measure of dipole activity D = e 0 E + P = ee 0 P Assumes P is constant over several interatomic distances. e is complex, includes terms for optical phonons, plasmons, magnons, etc. Formalism for allowed frequencies, polarisations and intensities needs crystal symmetry and its group representation.

12 Inelastic Light Scattering Light scattering Direction E i E s q Wavevector (q) of phonons Spectrum Frequency () of phonons

13 Sound waves 13 ACOUSTIC MODE DETECTION: SCATTERING MECHANISMS Ripple mechanism (surface) SAWs acts as dynamical diffraction grating Photoelastic effect (Bulk) Bulk waves modulates the dielectric constants producing a quasi-static grating. Incident light k I a I a S k s Scattered light Surface waves

14 PHONON DETECTION: BRILLOUIN LIGHT SCATTERING SPECTROSCOPY k I k s a y Energy and momentum conservation k S s k I I q Traveling Grating v saw a q 4 q// q sin( a) sin( a) Parallel component of the wavevector x q 2 q q Scattering wavevector ki ks 2 2 ki ks 2 ki ks cos( q ) 2 k (back scattering) I with k S k I 2 14

15 Inelastic Light Scattering Light scattering from Fluctionations Wavevector and Frequency r i q i des k s q k i q i Benedek, G. B. & Fritsch, K. Brillouin Scattering in Cubic Crystals Phys. Rev., American Physical Society, 1966, 149,

16 Concepts OUTLINE Instrumentation & methods Examples o Bulk Si and Si membranes o Optical phonon plasmon coupling, Atomic-like excitons in quantum dots and Surface phonons Laser Raman thermometry in 2D materials Conclusions 16

17 Overview of two set ups Vibrational+Optical THz cm -1 < 0.4 ev < 4 x J Rotational 100 GHz 1 THz 3.83 cm -1 <4 mev < 4 x J Translational cm GHz < 0.4 mev < 4 x J Raman Triple Grating Spectrometer Tandem Fabry-Perot Interferometer Range > 90 GHz Res. = 3 GHz Range > 3 cm -1 Res. = 0.1 cm-1 Range = GHz Res. = 0.2 GHz Mainly for Optical modes Range = cm -1 Res. = cm -1 Mainly for Acoustic modes 17

18 Schematics of a triple Raman spectrometer

19 Schematics of a Brillouin spectrometer

20 TANDEM FABRY-PEROT KIT FOR BRILLOUIN SCATTERING Single Fabry-Perot Tandem Fabry-Prot Input Detector q FP2 FP1 20 Multi-Pass q

21 Concepts OUTLINE Instrumentation & methods Examples o Bulk Si and Si thin films o Optical phonon plasmon coupling, Atomic-like excitons in quantum dots and Surface phonons o 2D materials 2LRT Conclusions and perspectives 21

22 Raman scattering spectrum of Si 300 K, 514 nm unanalysed Supported BESOI, ca 30 nm thick A Balandin 2000

23 Confined Acoustic Phonons: Phonon cavity approach Acoustic mismatch air Si 2 V 2 / 1 V 1 i density V i =sound velocity q // in-plane (small) q z v sound transverse longitudinal + q z Large wave vector LA phonon scattering allowed due to lack of translational invariance SOI

24 Sample for Si thin film studies 40 nm SOI Buried (thermal) oxide (SiO 2 ) 400 nm Native oxide 3 nm 28 nm air SOI BOX 2 V 2 / 1 V 1 i density V i =sound velocity Base Si wafer CZ p-type <100> 525 micrometer Phonons in SOI/BOX Longitudinal acoustic mismatch = 0.69 (significant) Transverse acoustic mismatch = 0.99 (almost negligible)

25 Confined acoustic phonons in 30 nm SOI membranes Confined phonons observed in supported thin films. Laser spot 500 mm - Validation of photo-elastic model in thin membranes for q=0. - Mode assignment incomplete. Need dispersion relations of confined phonons C M Sotomayor Torres et al Physica Status Solidi (C), 1, 2609 (2004). J Groenen et al, PRB, (2008) 2 5

26 EFFECT OF BOUNDARY: RAYLEIGH WAVES Boundary effect Dispersion Relation 0 z x y T zj z0 0 U i u e i e q z i( q// x t) SAW J. Cuffe, PhD Thesis, UCC, Cork, Ireland,

27 EFFECT OF BOUNDARY: LAMB WAVES Membrane T jz za / 2 0 Isotropic approximation Sagittal solutions 2 4Q// QlQ ( Q Q 2 t t 2 2 // ) tan( Qt tan( Ql / 2) / 2) 1 T jz za / n Q v i 2 L aq i ; a Q Q v Q Q // l, n T // t, n 2 n Shear solutions 2 v T q 2 // ( n / a) 2 Dilatational (Symmetric) Flexural (Anti-symmetric) Decomposition of wavevectors 27

28 f (THz) CONFINED PHONONS Longitudinal and transverse standing waves at q // = 0 Analogous to acoustic modes in an organ pipe Standing Waves q // = 0 d 6 Dispersion Relation: 520 nm nm 0 q z 4 2 Bulk q // (nm -1 ) 28

29 CONFINED PHONONS Dispersion Relation Membrane (Lamb) modes 6 Dilatational (Symmetric) f (THz) Flexural (Anti-symmetric) q// (nm ) Coupling of L and SV polarizations 29

30 . INELASTIC SCATTERING MECHANISMS Experimental Set-Up Surface ripple scattering: Momentum conservation Conservation of in-plane wavevector, q // 4 q// 2ki sinq sinq 30

31 INELASTIC SCATTERING MECHANISMS Surface ripple scattering mechanism Surface Displacement U ( x,0, t ) U e i z ( q // xt ) Intensity proportional to RMS displacement I(, q 2 //) U z (, q// ) z0 Calculated with Green s functions U k T G zz, q// z 0 2 B z (, q// ) Im z0 Conservation of in-plane wavevector, q // Projected LDOS at the surface El Boudouti, E. H., Djafari-Rouhani, B., Akjouj, A., & Dobrzynski, L. (2009). Surface Science Reports, 64(11),

32 IN-PLANE DISPERSION: ULTRA-THIN MEMBRANES 31 nm membrane - Fundamental Flexural Mode (F0) Flexural Mode (Exp.) F0 D0 Calculations with Green s functions U z 2 (, q // ) kbt Im z0 G zz, q // z 0 Scattering intensity well described by z-component of surface displacement

33 10 NM MEMBRANES Spectra at 3 mm Mirror Spacing Shear Dilatational Spectra at 10 mm Mirror Spacing Flexural Dilatational 33

34 IN-PLANE DISPERSION: ULTRA-THIN MEMBRANES Fundamental flexural mode (F0) Dispersion relation for ultra-thin membranes also described by calculations Experimental values slightly lower than predicted 34

35 Slow phonons Dimensionless Dispersion relation Membranes from nm v ph q // Fundamental flexural mode (A0) Membranes from 8 30 nm 2 Aq // Aq// v ph v g 2Aq// All membranes of different thickness values plotted on same dimensionless dispersion relation Phase (Group) velocity decreases dramatically for thinner membranes J Cuffe et al., Nano Letters (2012)

36 Phonons dispersion relations in Si membranes Band structure from atomistic models WITH Tersoff potentials Flexural modes data points from Brillouin Scattering in free-standing membranes from 5 to 27 nm thick S Neogi et. Al, ACS Nano, 9, 3820(2015)

37 Phonon lifetimes Pump-and-probe ASOP Track D1 mode Boundary scattering tanh 1 L 2 B 2 2 L v 2 L J Cuffe et al., Phys. Rev. Lett., (2013)

38 Phonon engineering with membranes Membrane thickness modifications: Dispersion relations from continuum-like to discrete acoustic phonon frequencies Velocities and lifetimes of phonon modes Membrane patterning modifications: Thermal conductivity tuning Heat directionality (Nomura s group) Membranes with additional nano/microstructures Hybrid modes energy storage and transfer Possible path towards 3D integration Coupling to photons optomechanics, RF techniques

39 Concepts OUTLINE Instrumentation & methods Examples o Bulk Si and Si thin films o Optical phonon plasmon coupling, Atomic-like excitons in quantum dots and Surface phonons o 2D materials 2LRT Conclusions 39

40 LO phonon-plasma coupling splits LO phonons into L1 and L2. Optical phonon-plasmon coupling 2 2 LO 2 p e = e00 ( ) 2 2 TO 2 - depletion layer - confirm carrier concentration - Monitor surface damage in reactive ion etching Assumption: abrupt change in carrier density between depleted and doped regions. P D Wang, et al, JAP 71, 3714 (19

41 Atomic-like excitons in doped quantum dots Measured and calculated Raman spectra of quantum dots (8x10 11 cm -2 ) 75 nm radius. Hartree energy levels and DOS of a dot in B=0 and 5T. Arrows denote strong Raman transitions. D Lockwood et al, PRL 77, 354 (1996)

42 M Watt et al, Semicond Sci Technol (1990) Surface Phonons in semiconductor cylinders ( nh ) 2 /( TO ) 2 =(e o e m nh )/(e o e m nh ), with nh in terms of modified Bessel functions and derivatives. Electrostatic continuum model of Ruppin and Engelman (1970) with geometry determined by boundary conditions, neglecting retardation effects. M Watt et al 1989 GaAs pillar 100 nm diameter 700 nm high.

43 Surface Phonons in semiconductor cylinders M Watt et al, Semicond Sci Technol (1990) GaAs cylinders of 80 nm diameter and 250 nm high. The contribution of surface phonons to the Raman signal appear between the TO and LO phonons as expected. Pillars coated with SiN: surface phonon frequencies decrease.

44 Concepts OUTLINE Instrumentation & methods Examples o Bulk Si and Si thin films o Optical phonon plasmon coupling, Atomic-like excitons in quantum dots and Surface phonons o 2D materials 2LRT Conclusions 44

45 From dispersion relations to thermal conduction Modified phonon dispersion relation in Si membranes measured. Good agreement v ph / q// between experiment / Q// theory Group velocity (dω/dq) depends on wavevector. Decrease of the phase velocity (/q) of fundamental flexural waves. From Boltzmann transport equation: 2 v g ( qs) CV ( qs) ( q, s Dispersion relation Group velocity Relaxation time Specific heat qs ) 45

46 Contactless thermal conductivity experiment Experiment Schematic Model Microscope Objective = nm Steady-State Heat Equation 2 T P 0 ( r, z) b r Gaussian Power Source 2Pabs 2 P0 ( r, z) exp[ 2r / b 2 ab 2 ] T=300K a Laser Gaussian heat source Room temperature condition at the boundary Steady-State Heat Equation kñ r 2 T = - 2P abs pab 2 exp[-2r 2 / b 2 ] E Chavez-Angel et al, APL Materials 2 (1) (2014) & JS Reparaz et al Rev Sci Inst (2014). 25

47 One- and Two-Laser Raman Thermometry Assumptions for analysis on one-laser Raman thermometry exposed setting conditions for - Light penetration depth vs laser spot - Laser spot and sample thickness (J Jaramillo-Fernandez, submitted for publication)

48 Thermal conductivity of MoS 2 polycrystalline nanomembranes 488 nm probing laser 405 nm heating laser Room temperature 10-3 mbar pressure M Sledzinska et al, 2D Materials, 3, (2016)

49 Raman spectroscopy of MoS 2 nanosheets On Si/SiO 2 substrate Raman active modes E 2g mode ~ 383 cm -1 A 1g mode ~ 408 cm -1 Free-standing nanosheets M. Placidi, M. Sledzinska et al. MRS conference 2014

50 Temperature dependence of the Raman shift w 0 (cm -1 ) w/ 10-2 T= 294K (cm -1 /K) Ref. Bulk MoS Adv. Phys. 18, (1969) Bulk MoS Adv. Phys. 18, (1969) Nanosheets MoS J.of Phys.Chem. C, 117, 9042 (2013) Nanosheets MoS J.of Phys.Chem. C, 117, 9042 (2013) Nanosheets MoS This work Nanosheets MoS This work 488nm line

51 2LRT of MoS 2 P abs = mW Thermal conductivity: k=0.75 +/ W/mK Lower than previously reported for single and few-layer crystalline MoS 2 M Sledzinska et al., 2D Mater. 3 (2016)

52 Finite element method (FEM) simulations Reconstruction of the nanocrystalline 2D films (3000 grains), <d> = 5 nm (Laguerre tessellation, Neper package) Heat flux Temperature Phonon blocking on grain boundaries Grain size below 10nm comparable with the THz phonon wavelength Possible application in thermoelectricity 100 W/mK (full points) 34 W/mK (open squares) M Sledzinska et al., 2D Mater. 3 (2016)

53 Stop press: K of 2D membrane-based PnCs B Graczykowski et al, Nature Comms 8, art nr 415 (2017) PnCs diameter: 100 um Heating island: 5 um PnCs period: 200, 250, 300nm Hole diameter: around 135 nm Square lattice Thickness: 250 nm

54 Convection: 2D membrane-based Phononic Crystals (PnCs) PnC, lattice parameter a = 200 nm, hole diameter d = 130 nm Profile Slope Thermal conductivity k 350 K = 3 W/(m*K) k 350 K = 76 W/(m*K) k 350 K = 140 W/(m*K) 50-fold reduction of k at 350 K 300pitch/135diametre and 250/140 nm also examined- trend confirmed B Graczykowski et al, Nature Comms 8, art nr 415 (2017) 54

55 2D membrane-based PnCs Temperature fields B Graczykowski et al, Nature Comms 8, art nr 415 (2017) 55

56 2D membrane-based PnCs Thermal conductivity d = lattice parameter a = hole diameter B Graczykowski et al, Nature Comms 8, art nr 415 (2017) 56

57 2D membrane-based PnCs Thermal conductivity K of a-si 1.5 Wm -1 K -1 Take home messages: - Strong suppression of temperature dependence of κ. - No signature of coherent effects from 2-phonon Raman spectra. - Air-mediated losses are significant and size tunable. B Graczykowski et al, Nature Comms 8, art nr 415 (2017) 57

58 Conclusions 58 Inelastic light scattering is a powerful research set of techniques to study phonons. Augmented power with magnetic and electric fields, also with high pressure

59 Related topics Confocal Raman scattering- kind of tomography good for 2D materials (but resolution and flexibility re lateral sizes. New experimental tools: micro and scanning probe Raman scattering, time-resolved RS. Single and many-particle excitations (single particle excitations, charge density waves, in 2D materials Time-resolved methods (Perrin s lectures) Link between low frequency phonons and the fluctuation regime. 59

60 References - 1 C M Sotomayor Torres et al, Phys Stat Sol (c) 1, 2609 (2004) J Groenen et al, PRB 77, (2008) J Cuffe et al., NanoLetters 12, 3569 (2012) E Chavez et al JPCS 395, (2012) J Cuffe et al., PRL 110, (2013) E Chavez et al, IoP Journal of Physics: Conference Series, 395 (1) (2013) A Shchepetov et al., Appl Phys Lett 102, (2013) E Chavez et al., IEEE 14th Intl Conf on Ultimate Integration on Silicon (ULIS), 186 (2013) J A Johnson et al., Phys Rev Letts 110 (2) (2013) E Chavez Angel et al., Appl Phys Lett Materials 2 (1) (2014) J S Reparaz et al., Review of Scientific Instruments (2014). S D Rhead et al, Applied Physics Letters 107 (17) (2014). B Graczykowski et al., Applied Physics Letters 104 (12) (2014). E Chávez-Ángel et al., Semiconductor Science and Technology 29 (12) (2014). B Graczykowski et al., NJP 16, (2014)

61 References - 2 B Graczykowski et al., PRB 91, (2015) S Neogi et al., ACS Nano 9, 4, 3820 (2015) J Cuffe et al., Physical Reviews B. 91 (24) (2015). J Jaramillo-Fernandez et al., ECS Transactions, 69 (9) 53 (2015). M Sledzinska et al., Microelectronic Engineering 149, 41 (2016) B Graczykowski et al, Journal of Applied Physics 119, (2016) J Ordonez-Miranda et al., International Journal of Thermal Sciences 108, 185 (2016) D Yudistira et al., Physical Review B 94, (2016). M Sledzinska et al., 2D Materials, 3, (2016). M R Wagner et al., Nano Letters 16, 5661 (2016) A Vega-Flick et al., AIP Advances 6 (12) (2016) J Jaramillo-Fernandez et al., Crystal Engineering Communications, 19, (14) 1843 (2017) B Graczykowski et al., accepted Nature Comms, ms ID NCOMMS T

62 References - 3 BOOK CHAPTERS: D Leadley et al, Chapter 12 Thermal Isolation via Nanostructuring, in: Beyond-CMOS Nanodevices 1, Ed F Ballestra, Wiley (2014) M Mouis et al., Chapter 7 Thermal Energy Harvesting, in: Beyond-CMOS Nanodevices 1, Ed F Ballestra, Wiley (2014) C M Sotomayor Torres et al., Acoustic phonons in ultrathin free-standing silicon membranes: Fundamental science and applications, chapter 12 in: Silicon Nanomembranes, J Roger and J Ahn (Eds.), Wiley, Berlin, (2016)

63 COLLABORATORS & SUPPORT VTT: Jouni Ahopelto Andrey Shchepetov Mika Prunnila Univ Lille - IEMN Bahram Djafari-Rouhani Yan Pennec Univ Mohamed I, Oujda El Houssain El Boudouti Univ Konstanz: Thomas Dekorsy Oliver Ristow Mike Hettich, Alex Bruchhausen MPI-Polymer Mainz Davide Donadio Shangamitra Neogi Luiz F. C. Pereira CNRS Centrale Supelec Sebastian Volz MIT: Alex Maznev A Minnich Jeremy Johnson Jeremy Eliason Kimberly Collins Keith A Nelson Gang Chen PHENTOM