Nanoacoustics II Lecture #2 More on generation and pick-up of phonons Dr. Ari Salmi www.helsinki.fi/yliopisto 26.3.2018 1
Last lecture key points Coherent acoustic phonons = sound at nanoscale Incoherent phonons = heat Four mechanisms of phonon generation by ultrafast lasers One can detect phonons by changes in the reflectivity of the sample Optical delay line
Heat to strain Increase in temperature causes thermal expansion Localized expansion of material strain Causes stresses in the material Temperature Linear rise expansion in 3D Elastic modulus, not energy! V Strain Coefficient of linear expansion 26.3.2018 3
Light reflectivity vs strain The resulting reflectivity has two terms Oscillating term and a transient term Both wavelengths, excitation and pick-up, matter!
Light reflectivity vs strain Assumptions for the equation(s) Matsuda et al., Ultrasonics 2015
Optical phase change detection for RX If we write the reflectivity as And re-write r as We get 26.3.2018 6
Optical phase change detection for RX Two contributions Real part = last lecture s topic (change of reflectance) Imaginary part = phase change The phase change has two components One from the surface displacement One from the CAP 26.3.2018 7
Parameters of laser ultrasound (In macroscale) Matemaattis-luonnontieteellinen tiedekunta / Henkilön nimi / Esityksen nimi www.helsinki.fi/yliopisto 26.3.2018 8
Four parameters of laser ultrasonics Beam shape Beam color = wavelength Energy (+ energy density) Pulse length E E t 26.3.2018 9
Beam shape Changes the shape of the transducer Circle Point Line (reduces the situation to a 2D-problem) Circular line Alters the energy density (= E/A) 26.3.2018 10
Beam color = wavelength Alters the heated volume and amount of absorbed energy Also affects laser safety! Higher absorption coefficients mean smaller transducer volumes Double tap: First pulse changes material Second pulse excites ultrasound 26.3.2018 11
Energy(density) Affects the regime (thermoelastic/ablation) As high energy as possible without surface damage Ablation threshold depends on power density For metals, approx. 1-10 MW/cm 2 for infrared laser at room temperature Thermoelastic Ablation Scruby & Drain 1990 26.3.2018 12
Pulse length Affects two things Generation mechanism (P = E/t) Leitz et al., 2011: nanosecond pulses differ from pico- and femtosecond pulses in ablation Frequency content 26.3.2018 13
Effect of pulse length Matemaattis-luonnontieteellinen tiedekunta / Henkilön nimi / Esityksen nimi www.helsinki.fi/yliopisto 26.3.2018 14
Photoacoustic excitation Modes of energy transfer Ablation Removal of matter Wave amplitude ~100 nm - µm Thermal expansion Elastic expansion of the material Wave amplitude ~ nm Radiation pressure Very small effect (momentum transfer) Wave amplitude ~ pm Pozar et al., Optics Express 23(6), 2015 26.3.2018 15
Photoacoustic excitation - ablation Metal for simplicity What happens when a laser pulse hits metal? Electron heating via inverse Brehmsstrahlung (~ 1 fs) Heat transfer to the lattice (~1 ps) Three important time scales Duration of the laser pulse t L Electron cooling time t E Lattice heating time t I 26.3.2018 16
Ablation nanosecond laser In nanosecond scale, t L >> t I Sample surface: melting -> vaporization Heat conduction into the solid material Thermal wave creates a large layer of molten material If large enough fluence, particle ejection La Haye et al., J. Anal. At. Spectrom., 28, 2013 http://www.ilm-ulm.de/en/competence-groups/process-development/kurzzeitbelichtung.html 26.3.2018 17
Ablation picosecond laser In nanosecond scale, t E << t L << t I Lattice temperature << electron temperature On the surface, solid vapor transition Thermal confinement Still, a liquid phase inside the target ns ps Shorter time S. Dimitriy et al., Phys. Rev. B 68, 2003 26.3.2018 18
Ablation femtosecond laser In femtosecond scale, t L << t E No time for heat transfer to the bulk energy from electrons to lattice ions direct solid vapor transition + stress confinement Also, no time for heat transfer inside the lattice ns ps fs http://inside.hlrs.de/_old/htm/edition_01_12/article_15.html Shorter time 26.3.2018 19
Stress confinement Very high localized pressures Heating faster than the mechanical wave stress confinement http://inside.hlrs.de/_old/htm/edition_01_12/article_15.html 26.3.2018 20
Ablation generated wave amplitudes (longitudinal) Hebert et al., JAP 98, 2005 Through transmission 26.3.2018 21
Photoacoustic excitation - thermoelastic Thermal expansion Fourier s law Works well in macroscopic scales Two problems in nanoscale: q = kδt No time dependence infinite propagation velocity Temperature gradient and heat flux simultaneous causality? 26.3.2018 22
Photoacoustic excitation - thermoelastic Non-Fourier model of heat propagation Heat waves Second sound Example: Steel First sound (longitudinal) ~ 5000 m/s Second sound (heat) ~ 2000 m/s Bargmann and Favata ZAMM 94(6), 2014 26.3.2018 23
Thermoelastic waves nanosecond scale Displacement of the surface in sync with the temperature increase Propagating compressional wave (low tensile component) Low attenuation 26.3.2018 24
Thermoelastic waves picosecond scale Displacement of the surface still in sync with the temperature increase Propagating compressional and tensional wave Second sound visible! Thermal wave, disappears in under <200 ps 26.3.2018 25
Thermoelastic waves femtosecond scale Displacement of the surface not in sync with the temperature increase Thermal wave from heating from inside the sample Propagating strong compressional and tensional wave Second sound visible! Thermal wave, disappears in under <2 ps 26.3.2018 26
Pulse length On the last lecture, we learned that short = short But, how short is short? Dehoux et al., JAP 2006 Adjust the pulse duration by a special setup
Pulse length Echo shape as a function of pulse length
Pulse length Spectrum as a function of pulse duration Levels off at some point, why?
Pulse length Amplitude of the acoustic echo as a function of pulse duration Levels off at a certain point, why?
Pulse length How short pulses can we do? What is the period of a single wave for IR light? Krausz and Ivanov, Rev. Mod. Phys. 2009
Pulse length Development of measurement capability
Pulse length Example: <100 as probe (13 nm), <5 fs pump (750 nm) Schultze et al., Science 2014 Detect both the highest possible optical phonons in silicon (~15.6 THz) and electron response to the excitation
Effect of color Matemaattis-luonnontieteellinen tiedekunta / Henkilön nimi / Esityksen nimi www.helsinki.fi/yliopisto 26.3.2018 34
Effect of color Devos and Lerouge, PRL, 2001 Changed the pump and probe wavelengths W film deposited on a silicon substrate
What does this look like in practice? Integrate the equation for the reflection coefficient Two piezo-electric coupling coefficients! 1 3 20
What does this look like in practice? Different color pump and probe Blue probe, NIR adjustable pump Blue pump, NIR adjustable probe
Light reflectivity vs strain If there is a localized area of strain in the material localized change in the permittivity
What does this look like in practice? Absorption has an effect on the pulse shape Change of absorbance Length of oscillations 3. 6. 1. 2. 4. 5. 7.
What does this look like in practice? Large absorbance = large bandwidth = short Brillouin oscillations
Examples of pump absorption Silicon (a semiconductor) Absorption depth varies between ~80 nm @ 400 nm to 10 µm+ @ 800 nm
Practical example: usage of pump absorption Indium phosphide (InP) doped with quantum dots (QD s) Devos et al., PRL 2007
Practical example: usage of pump absorption By changing the wavelength (and the absorption) one can selectively generate phonons inside the sample
Practical example: usage of probe color Glass-silicon structure Devos and Cote, Phys Rev B, 2004
Practical example: usage of probe color Change the probe color and keep pump color constant Glass is transparent at both 804 nm and 402 nm Silicon is transparent at 804 nm but not at 402 nm
Practical example: usage of probe color Measure attenuation (in glass!) by changing the width of the glass layer and repeating the measurement
Shear CAPs Matemaattis-luonnontieteellinen tiedekunta / Henkilön nimi / Esityksen nimi www.helsinki.fi/yliopisto 26.3.2018 47
Exciting shear CAPs Why are we interested in shear? 26.3.2018 48
Exciting shear CAPs How to generate shear CAPs? Counterquestion why cannot we with normal laser ultrasonic means? Rossignol et al., PRL 2005 Spot size dependence 26.3.2018 49
Exciting shear CAPs by TE/DP/PE In isotropic crystals, either Small spot size Shear generation by mode conversion in reflections from surface Only works up to a few GHz Break axial symmetry of the elastic tensor 26.3.2018 50
Glimpse to the future: Exciting shear CAPs Transient grating method Gusev, APL 2009 and Koyate et al., JAP 2011 Mathematically sound, but extremely difficult in practice 26.3.2018 51
Glimpse to the future: Exciting shear CAPs Ultrafast release of magnetostriction (ultrafast localized demagnetization) Pezeril, Optics & Laser Technology 2016 Generated shear in Terfenol (TbFe2) films 26.3.2018 52
Detecting shear CAPs Polarized light Two equations for the change in reflection (depends on the polarization direction) 26.3.2018 53
Detecting shear CAPs Photoelastic tensor Links the change in the dielectric constants to strain Wave equation for light at an oblique angle (from Maxwell s equations) 26.3.2018 54
Detecting shear CAPs Since the photoelastic tensor for isotropic materials is of the form Change in shear strain only couples to the z component of the E-field p-polarized light in probe has to be used (either incident or reflected) 26.3.2018 55
Detecting shear CAPs For s-polarized light, field when strain is present 26.3.2018 56
Detecting shear CAPs For p-polarized light, field when strain is present 26.3.2018 57
Detecting shear CAPs This means that the polarization is scattered from p to s (or the other way around) 26.3.2018 58
Detecting shear CAPs 26.3.2018 59
Example Matsuda et al., PRL 2004 Glass-zinc layered system 26.3.2018 60
Generating surface CAPs: Absorption grating Generate a periodic grating with an absorption coefficient different from that of the surrounding material Hurley and Telshow, Phys. Rev. B, 2002 26.3.2018 61
Absorption grating Example of a generated Lamb wave Grossmann et al., APL 2015 26.3.2018 62
Take-home Matemaattis-luonnontieteellinen tiedekunta / Henkilön nimi / Esityksen nimi www.helsinki.fi/yliopisto 26.3.2018 63
Take-home Four parameters that can be changed to generate different kinds of excitation transducers The detected signal strongly depends on the color Shear phonons can be excited and picked up
References / further reading Krausz, Rev. Mod. Phys. 81, 2009 Gamaly and Rode, Prog. Quant. El. 37, 2013 Pezeril, Optics & Laser Technology 83, 2016