Coherent Phonon Spectroscopy of Liquid and Solid Materials and Study of Thermal Transport in Solids
Alex Maznev, Thomas Pezeril, Ievgeniia Chaban, and Ryan Duncan
1. Experimental Methods
(1) Picosecond Ultrasonics
In recent years, a novel approach for generation of frequency tunable shear acoustic waves in the GHz frequency range has been presented by the Nelson group using Time-Domain Coherent Brillouin Scattering (TDBS) technique. The group has demonstrated a sample and optical configuration that allows shear and longitudinal acoustic parameter measurements. The TDBS technique combines different picosecond laser ultrasonic techniques for acoustic wave generation and detection. Multiple-cycle longitudinal and shear acoustic waves can be optically generated using a crystallographically canted metal film transducer, which is obliquely deposited under ultrahigh vacuum by molecular beam epitaxy onto optical quality sapphire or glass substrates. When the transducer is hit by an optical pulse train, rapid thermal expansion launches acoustic wave packets of both longitudinal and shear polarizations, when the right configuration is met. After the wave packets propagate into and through the sample substrate, both shear and longitudinal acoustic waves are optically detected after transmission into a transparent substrate using TDBS. The signal intensity that shows time-dependent oscillations at the acoustic frequency can be acquired from the coherently scattered field, whose optical phase varies depending on the acoustic wave peak and null positions, when superposed with the reflected probe field.
Figure 1. (a) Schematic drawing of recirculating reflective pulse shaper, called Deathstar Compact, which generates a pulse train of seven pulses with a nearly Gaussian intensity envelope. The laser output gets injected in a system of retro-reflectors where the pulse makes several round trips. A variable reflector allows some amount of light to leave the system during each round trip and two sets of mirrors collect these individual beams in order to recombine them through a lens at one spot on a sample. The mirrors also compensate for the different time delays the pulses experience so that all seven pulses can be re-overlapped in time when the delay line is at its zero position. Movement of the delay line then allows adjusting the frequency of the pulse train between 2 to 2000 GHz. The output sequence was focused onto the sample (b) where it illuminated a metal transducer and generated an acoustic pulse train. The acoustic wave packet propagated into and through variable thickness transparent substrate layers before being detected interferometrically at the air interface of a second metal film. (c) Calculated example power spectrum of the photo-acoustic response in a polycrystalline Al transducer
(2) Transient Grating Spectroscopy
The Transient Grating (TG) technique has been used in the Nelson group for many years. We are currently using the TG technique for both thermal and acoustic measurements. The technique involves crossing two short pump pulses to create a sinusoidal interference pattern, which when absorbed by the sample induces a sinusoidal response. In most samples the light is absorbed and the sinusoidal response is manifest as a temperature profile, and upon thermal expansion an acoustic wave is generated. The temperature profile and the acoustic wave modulate the complex index of refraction of the material to create a sinusoidal time dependent grating that diffracts an incident continuous waveform (CW) probe beam. The diffracted signal is overlapped with a reference beam to allow for heterodyne detection. Detection of thermal grating decay and acoustic response are monitored in real time using a fast photo detector and oscilloscope.
Figure 2. Beam geometry for a typical transient grating experiment. PM denotes a binary phase mask from which the ± 1 diffraction orders are used. PS is a glass slide used to control the relative phase between signal and reference beams for heterodyne detection. ND is a neutral density filter used to attenuate the reference beam. After the sample the signal and reference beams are overlapped and are incident on detector D.
2. Current Projects: Coherent Phonon Spectroscopy of Liquids
The techniques above were used for optical generation and detection of gigahertz frequency longitudinal and shear acoustic waves in liquid samples, mainly DC 704 and glycerol. From MHz to lower GHz range, ultrasonics, impulsive stimulated thermal or Brillouin scattering, and spontaneous Brillouin scattering can be utilized to study dynamics. The THz longitudinal acoustic frequency ranges can be accessed using x-ray Brillouin scattering, but tens to hundreds of GHz range, where fast relaxation features occur, has only had limited access through deep-UV Brillouin scattering. TDBS study of liquid forming liquid was employed to fill the gaps that traditional techniques could not explore. Picosecond ultrasonics with access to much of the GHz-frequency longitudinal wave range has been adapted for both shear and longitudinal frequency-tunable, multipule-cycle acoustic wave generation and detection.
Figure 3. (a) Sketch of shear detection setup in a front-back pump-probe geometry and (b) close-up of sample assembly. (a) A balanced photo-detection approach was capable of recording the extremely weak depolarized shear Brillouin scattering signals with sufficient signal-to-noise levels. Differential detection (diode A - diode B) subtracted out common noise while adding the signal. The sample assembly was mounted on a computer controlled motorized stage whose translation (X position) allowed access to liquid thicknesses between ~0 nm and several microns. (b) A large diameter optical pump pulse, or pulse sequence, incident on a specialized shear transducer thin film launched both longitudinal and vertically polarized transverse acoustic wave packets into an adjacent liquid layer of thickness d. The acoustic waves were then detected in a transparent detection substrate by TDBS. Tightly focused, vertically polarized probe light interacted with the propagating, vertically polarized shear acoustic wave fronts which backscattered a small portion of the light with a 90° polarization rotation, or depolarized TDBS, as the signal beam (Sig). The portion of the probe light that was reflected by the sample structure served as the reference beam (Ref). In case of longitudinal acoustic waves, the vertically polarized probe light was backscattered without a change in polarization.
Figure 4. (a) Representative time derivative of the measured signal intensity for two distinct liquid layer thicknesses where the second sample has thicker layer. (b) Acoustic amplitude spectra of both acoustic signals and (c) the corresponding phases. The phase and amplitude differences yield the acoustic speed and attenuation length, respectively, in the liquid at the specified Brillouin frequency. Note that in (c), only the phase at frequencies around the Brillouin peak at 24.6 GHz contains relevant information. (d) Combined longitudinal and shear speeds of sound in glycerol at a wide range of frequencies as a function of temperature. Longitudinal speeds are taken with picosecond ultrasonic interferometry, time-domain Brillouin scattering, Brillouin light scattering, impulsive stimulated thermal scattering, and ultrasonics as a collaborative effort. Present results from TDBS shear measurements are shown together with results from conventional ultrasonics, and mechanical measurements.
The TG technique can generate low frequency acoustic waves from ~100MHz to ~1GHz. This technique has been used in the past to study a wide variety of glass forming liquids and through collaborations we have compiled acoustic data spanning 10 orders of magnitude in frequency. Other efforts involve generating surface acoustic waves (SAW’s) and measuring how the SAW interacts with materials deposited on the surface. A third project involves measuring the mechanical properties of polymers an example of which is shown below.
Figure 5. Representative traces taken from 3 different polymer samples. All three used have an acoustic wavelength of 6.6µm, clearly demonstrating a wide variety of mechanical properties between polymer samples.
 “Optical Generation of Gigahertz-Frequency Shear Acoustic Waves in Liquid Glycerol.” T. Pezeril, C. Klieber, et al. Phys. Rev. Lett. 102, 107402 (2009)
 “Optical generation and detection of gigahertz-frequency longitudinal and shear acoustic waves in liquids: Theory and experiment.” C. Klieber, T. Pezeril, et al. J. Appl. Phys. 112, 013502 (2012)
 “Mechanical spectra of glass-forming liquids. II. Gigahertz-frequency longitudinal and shear acoustic dynamics in glycerol and DC704 studied by time-domain Brillouin scattering.” C. Klieber, T. Hecksher, et al. J. Chem. Phys. 138, 12A544 (2013)
3. Current Projects: Coherent Phonon Spectroscopy of Solids
The recent efforts of coherent phonon spectroscopy of solids were focused photoacoustic determination of the speed of sound in crystals, property investigation of semiconductor super lattices, lifetime of coherent acoustic phonon, and acoustic attenuation measurements. Many energetic solid materials are molecular crystals with low crystal symmetry and anisotropic mechanical properties. Determining frequency-dependent elastic constants can be a significant step towards understanding extent of interactions between acoustic modes and other degrees of freedom. As a collaborative effort, Brillouin light scattering, impulsive stimulated light scattering, and picosecond acoustic interferometry were performed on single crystalline sample to investigate the speed of sound in the energetic crystal. Also, there is a project to measure high frequency phonon lifetimes. Phonons that contribute the most to thermal transport typically have frequencies above 1THz which is somewhat challenging to generate in materials of interest. One generation mechanism is to excite acoustic waves in a superlattice (SL) which can have very thin layers leading to high frequencies. One example of this is shown below. We are now working to generate and measure the lifetime of high frequency phonons in Si and GaAs. With high frequency phonon lifetimes we should be able to compare with and direct the development of theoretical models of thermal conductivity.
Figure 6. (a) Schematic diagram of the SL structure (not to scale), (b)experimental setup, (c) Measured signal waveform and acoustic oscillation trace, (d) Fourier spectrum of the acoustic oscillations.
Another ongoing investigation is narrow-band acoustic attenuation measurements in solids. Using the Deathstar Compact, evenly spaced Gaussian shaped pulse sequence can be generated. After thermoelastic propagation of longitudinal acoustic wave through sample layer into the detection film, the acoustic response can be probed by interferometric scheme by measuring surface displacement of the metal film.
Figure 7. Representative raw data for different sample thicknesses with pulse shaper frequencies set to (a) 165 GHz (b) 50 GHz (c) and 300 GHz. Smooth curves show interferometrically measured displacement while strongly modulated curves show corresponding strain, taken by time derivative. Data have been normalized and vertically shifted. Inset in (a) shows the Fourier spectrum of the transmitted acoustic signal.
 “Narrow-band acoustic attenuation measurements in vitreous silica at frequencies between 20 and 400 GHz.” C. Klieber, E. Peronne, et al. Appl. Phys. Lett. 98, 211908 (2011)
 “Broadband terahertz ultrasonic transducer based on a laser-driven piezoelectric semiconductor superlattice.” A. A. Maznev, K. J. Manke, et al. Ultrasonics 52, 1 – 4 (2012)
 “Lifetime of sub-THz coherent acoustic phonons in a GaAs-AlAs superlattice.” A. A. Maznev, F. Hofmann, et al. Appl. Phys. Lett. 102, 041901 (2013)
4. Current Projects: Thermal Transport in Solids
Thermal transport in semiconductors has a wide variety of applications particularly in the fields of thermal management of microelectronic devices and thermoelectric materials. Our group is interested in studying basic materials to further understanding of fundamental phonon physics. Using the TTG technique we can measure the decay time of the thermal grating and using the period of the sinusoidal pattern we can determine the thermal diffusivity. In addition changing the grating spacing provides information on how phonons with a given mean free path contribute to the transport because phonons with mean free path longer than the grating spacing have a reduced contribution. One example of these measurements is shown below.
Figure 8. (a) Two short laser pulses are crossed in a 400 nm-thick Si sample to create a spatially sinusoidal temperature profile. (b) Decay of the temperature grating via thermal diffusion measured via diffraction of a probe laser beam; the larger the grating period L the longer the decay time. (c) According to the diffusion theory the decay rate should scale as 1/L2 but the data show a deviation from the diffusive behavior. (d) Effective thermal conductivity at small distances is reduced in agreement with theory.
 “Onset of nondiffusive phonon transport in transient thermal grating decay.” A. A. Maznev, J. A. Johnson, K. A. Nelson. Phys. Rev. B, 84, 195206 (2011)
 “Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane.” J. A. Johnson, A. A. Maznev, et al. Phys. Rev. Lett. 110, 025901 (2013)
5. Current Projects: Guided Acoustic Waves
A collaborative study of a granular crystals, which consists of close-packed, ordered arrays of elastic particles, with various engineering application was conducted with Nanophotonics and 3D Nanomanufacturing Laboratory. We have studied the interaction of surface acoustic waves (SAWs) with the contact-based resonance of microspheres forming a two-dimensional granular crystal in the order of magnitude of 1 µm using TG technique by measuring phase velocity dispersion of SAWs. SAWs are acoustic modes that propagate while confined within a very shallow penetration depth, enabling a broad range of applications in nondestructive material characterization and signal processing. The experimental method can be used to study the adhesion and contact mechanics of microparticles and enables the study of granular crystals on the microscale. A rich array of dynamical phenomena observed in macroscale granular crystals, and their promise for practical applications, suggest interesting possibilities for microscale granular crystals. Finally, the nonlinearity of the Hertzian contact holds promise for an application of our approach to developing nonlinear SAW devices.
Figure 9. Surface acoustic waves experimental setup. (a) Microspheres interacting with a SAW via contact “springs”, with notations used in the theoretical model. (b) Photograph of the sample. (c) Representative image of the silica microsphere monolayer. (d) Schematic illustration of the TG setup. Switching phase mask patterns allows measurements at multiple acoustic wavelengths. The probe beam enters the sample through the silica substrate and is diffracted by surface ripples and refractive index variations in the substrate induced by SAWs.
Figure 10. Representative results for SAW studies on microspheres. (a) Normalized signal off-spheres, marked with black curve throughout the figure. (b) Normalized signal on-spheres, marked with red curve throughout the figure. For (a) and (b), the acquired signal S is normalized by the maximum signal amplitude S0. Fourier transform (FT) magnitudes, plotted in log scale (c) and linear scale (d). The longitudinal peak is unaffected by the presence of spheres whereas the SAW peak is split in two. (e) Dispersion relations. The solid red line is the dispersion calculated using our model. Also shown are lines corresponding to longitudinal, transverse, and Rayleigh waves in fused silica, and a horizontal line corresponding to the microsphere contact resonance frequency.
 “Generation and control of ultrashort-wavelength two-dimensional surface acoustic waves at nanoscale interfaces.” M. E. Siemens, E. H. Anderson, et al. Phys. Rev. B 85, 195431 (2012)
 “Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves.” N. Boechler, J. K. Eliason, et al. Phys. Rev. Lett. (2013)