Transient Thermal Grating Research Articles

Ultrafast electron diffuse scattering as a tool for studying phonon transport: Phonon hydrodynamics and second sound oscillations.

Hydrodynamic phonon transport phenomena, like second sound, have been observed in liquid helium more than 50 years ago. More recently second sound has been observed in graphite at over 200 K using transient thermal grating (TG) techniques. In this work, we explore signatures of phonon hydrodynamic transport and second sound oscillations in ultrafast electron diffuse scattering patterns, which can provide time, momentum, and branch resolved information on the state-of-excitation of the phonon system beyond that available through TG experiments. We use the density functional theory and solve the Boltzmann transport equation to determine time-resolved non-equilibrium phonon populations and model phonon transport in graphite. This model also provides the information necessary to calculate the time evolution of one-phonon structure factors and diffuse scattering patterns during thermal transport covering ballistic, diffusive, and hydrodynamic regimes where the effect of a second sound oscillation on the phonon distribution is observed. Direct measurements of how the phonon distribution varies in time and space in various thermal transport regimes should yield new insights into the fundamental physics of the underlying processes.

Using deep learning to identify the depth of metal surface defects with narrowband SAW signals

An effective nondestructive testing technique that enables the detection and quantification of surface and subsurface defects is highly demanded for assuring the safety and reliability of materials. In this paper, we classified and regressed defects with different depths. A transient thermal grating (TTG) method induced by a pulsed laser is used to characterize the properties of surface defects. Based on thermo-elasticity theory, a theoretical model with different types of surface defects is established with the finite element method (FEM). Surface acoustic waves (SAWs) excited by the TTG method propagate at the surface of a sample with defects at different penetration depths and are measured by a vibrometer.By combining the simulation and experimental results, the time–frequency scalograms of 8200 images were obtained by wavelet transform analysis. 70 % of the images are randomly selected to train the residual network (Resnet) model, and the remaining data (2460 images), as well as 10 scalograms in an independent experiment, are used as previously unknown experimental signals to test the robustness of the Resnet model. The results indicate that the Resnet with scalograms via wavelet transform achieves a 96.21 % classification accuracy on the validation set, with a prediction accuracy of 90.00 % for the 10 scalograms. Moreover, compared with three widely used machine learning algorithms, VGG16, back propagation (BP), and support vector machine (SVM), this method achieves the highest classification accuracy. Finally, 500 data selected randomly from the previously trained experimental database and 10 data in an independent experiment are used for regression prediction. The result shows that the data are well located along or close to a straight line with a slope of 1. The statistical results suggest that 80.6 % (66.0 %) of the residuals of the experimental data fell within the size range ±10 μm (±5 μm). This work proves the feasibility and reliability of the combination of the Resnet model with wavelet transform and numerical simulation to identify the depth of surface defects using laser ultrasonics.

Thermal decay in the one-dimensional transient thermal grating experiment using modified Debye-Callaway model

We calculate the thermal decay in the one-dimensional transient thermal grating (TTG) experiment by solving the transient Boltzmann-Peierls transport equation (BPTE) within the framework of the single-mode relaxation time approximation and using modified Debye-Callaway model in which both longitudinal and transverse phonon modes are included explicitly. We consider surface heating of an opaque thick semiconductor (SC) crystal film that we assume to have a cubic symmetry and is treated as a continuum, elastic, isotropic, and dispersionless medium. We obtain a nonuniversal spectral suppression function (SSF) in the integrand of the effective apparent thermal conductivity that is similar to the one obtained by Chiloyan et al. [Phys. Rev. B 93, 155201 (2016)] using the standard single-mode relaxation time approximation (RTA) model. Therefore, the nonuniversal character of the SSF in the TTG experiment does not depend on the form of the collision operator approximation in the BPTE: Callaway's or standard. Moreover, the analysis of the behavior of the thermal decay rate shows how the peculiar crystal momentum shuffling effect of phonon-phonon scattering Normal processes (N processes) that is captured by Callaway's model influences the onset of the nondiffusive (quasiballistic) regime in the phonon transport process in SC crystals. This effect tends independently from the other phonon scattering processes to favor the maintenance of the phonon diffusive regime over a large length-scale range, a remarkable feature that cannot be put into light with the standard RTA model used in previous works. Hence, the implicit effect of N processes has certainly an important impact on the extraction of the phonon mean-free path spectrum distribution, especially in the high-temperature regime.

Remote in-line evaluation of acousto-elastic effects during elastic–plastic transition in an aluminum plate under uniaxial tensile and dynamic fatigue loading by laser generated, optically detected surface acoustic waves

Early detection and monitoring of heavy load induced plastic deformation in the structure is crucial for timely intervention before cracking occurs and the material completely fails. Ultrasound can be used for detecting plastic deformation provided the mechanical modulus, which can be probed via changes in velocities. This work presents a measurement scheme that makes use of optically detected, laser-induced surface acoustic waves (SAWs) for remote, real-time, online monitoring of the wave velocity during the elastic–plastic transition occurring in an aluminum plate undergoing a uniaxial tensile test and a dynamic fatigue test. Monochromatic SAWs were photoacoustically generated in a wavelength-controlled way through a transient thermal grating based laser ultrasonics excitation scheme. The SAWs were detected by a home-built photorefractive interferometer. The results reveal both regions of acceleration and slowing down, indicating that the material first stiffens and then starts to form microcracks that make it behave effectively softer for propagating SAWs.

Using a Convolutional Neural Network to Identify the Penetration Depth of Surface Defects with Saw Signals Excited by the Transient Thermal Grating Method

Using a Convolutional Neural Network to Identify the Penetration Depth of Surface Defects with Saw Signals Excited by the Transient Thermal Grating Method

Thermal transport in nanoporous holey silicon membranes investigated with optically induced transient thermal gratings

In this study, we use transient thermal gratings—a non-contact, laser-based thermal metrology technique with intrinsically high accuracy—to investigate room-temperature phonon-mediated thermal transport in two nanoporous holey silicon membranes with limiting dimensions of 120 nm and 250 nm, respectively. We compare the experimental results with ab initio calculations of phonon-mediated thermal transport according to the phonon Boltzmann transport equation (BTE) using two different computational techniques. We find that the calculations conducted within the Casimir framework, i.e., based on the BTE with the bulk phonon dispersion and diffuse scattering from surfaces, are in quantitative agreement with the experimental data and thus conclude that this framework is adequate for describing phonon-mediated thermal transport in silicon nanostructures with feature sizes of the order of 100 nm.

Characterization of Texture Evolution during Recrystallization by Laser-Induced Transient Thermal Grating Method

The analyses of texture evolution of cold rolled interstitial free (IF) steel sheets during annealing and recrystallization are presented, in which the dispersion curves of surface acoustic waves (SAW) excited by laser-induced transient thermal grating method are measured. The results show that the angular anisotropy of the SAW velocity changes due to the texture changes at different stages of recrystallization. The theoretically simulated angular dispersion of SAW velocity within individual crystal revealed that the change of SAW velocity is closely related to recrystallization texture evolution. A model for the angular dependence of the SAW velocity in textured polycrystalline IF steel with different oriented crystals is presented and the simulations are yielded, which show that the results agree with those of experiments.

Phonon relaxation time reconstruction from transient thermal grating experiments and comparison with density functional theory predictions

Phonon relaxation time and free path distributions are reconstructed from experimental measurements on a two-dimensional transient thermal grating and compared with density functional theory (DFT) results for silicon. The reconstruction is performed using the inverse problem formulation of Forghani et al. [Phys. Rev. B 94, 155439 (2016)]. The discrepancies observed between reconstructed and DFT results are analyzed in terms of the ability of each set of data to reproduce the experimental temperature relaxation profiles; the reconstructed data are found to predict temperature profiles in closer agreement with the experimental data than the DFT results, possibly due to discrepancies between the actual material and the idealized model studied in the DFT calculations. The reconstructed phonon properties accurately predict temperature relaxation profiles at grating length scales smaller than those spanned by the experimental data. This is a very important feature since in a variety of experimental setups, including the one providing the data in the present study, measurements are not available at all scales spanned by the material free paths.

Unifying first-principles theoretical predictions and experimental measurements of size effects in thermal transport in SiGe alloys

In this work, we demonstrate the correspondence between first principle calculations and experimental measurements of size effects on thermal transport in SiGe alloys. Transient thermal grating (TTG) is used to measure the effective thermal conductivity. The virtual crystal approximation under the density functional theory (DFT) framework combined with impurity scattering is used to determine the phonon properties for the exact alloy composition of the measured samples. With these properties, classical size effects are calculated for the experimental geometry of reflection mode TTG using the recently-developed variational solution to the phonon Boltzmann transport equation (BTE), which is verified against established Monte Carlo simulations. We find agreement between theoretical predictions and experimental measurements in the reduction of thermal conductivity (as much as $\sim$ 25\% of the bulk value) across grating periods spanning one order of magnitude. This work provides a framework for the tabletop study of size effects on thermal transport.

Modeling quasi-ballistic transient thermal transport with spatially sinusoidal heating: A McKelvey-Shockley flux approach

Ballistic phonon effects, arising on length scales comparable to the mean-free-path, result in non-diffusive heat flow and alter the thermal properties of materials. Simple theoretical models that accurately capture non-diffusive transport physics are valuable for experimental analysis, technology design, and providing physical insight. In this work, we utilize and extend the McKelvey-Shockley (McK-S) flux method, a simple and accurate framework, to investigate ballistic effects in transient phonon transport submitted to a spatially sinusoidal heating profile, simulating a transient thermal grating. We begin by extending a previous McK-S formulation to include inelastic scattering, then obtain an analytical solution in the single phonon energy case (gray approximation), and after show how this approach can readily support a full phonon dispersion and mean-free-path distribution. The results agree with experimental data and compare very well to solutions of the phonon Boltzmann transport equation in the diffusive and weakly quasi-ballistic transport regimes. We discuss the role of ballistic and non-equilibrium physics, and show that inelastic scattering is key to retrieving the heat equation solution in the diffusive limit. Overall the McK-S flux method, which takes the form of a diffusion-like equation, proves to be a simple and accurate framework that is applicable from the ballistic to diffusive transport regime.

Heat transport in semiconductor crystals under large temperature gradients

We analyze and discuss the fundamental behavior of the nonlocal/nonlinear contributions to heat transport by phonons in bulk cubic semiconductor (SC) crystals subject to large temperature gradients. The calculation approach is based on solving steady-state Boltzmann-Peierls Transport Equation (BPTE) by expanding the phonon distribution function in a series of temperature gradients. We work out the modeling within the framework of the single relaxation time approximation and using modified Debye-Callaway model in which both longitudinal and transverse phonon modes are included explicitly. The SC system is treated as a continuum, elastic, isotropic and dispersionless medium. The frequency and temperature dependences of three-phonon anharmonic Normal and Umklapp scattering processes are kept the same for all SC crystals. Our model allows us to obtain compact expressions for the first three nonlocal/nonlinear thermal coefficients to which we limit our calculations. We assume these three coefficients to be the leading ones over the whole temperature range considered in our study. Their fundamental behaviors are studied by changing ambient temperature, longitudinal and transverse Grüneisen parameters as well as the mass-fluctuation parameter. In the simplest case of the grey spectrum approximation, we shed light on a very interesting result regarding the expression of the effective thermal conductivity κeff of the bulk SC crystal when the latter is subject to a space-periodic temperature profile that is typically encountered in Transient Thermal Grating (TTG) experiments. We find an expression that undoubtedly proves both nonlocality and nonlinearity to be a sound and robust explanation of the reduced measured thermal conductivity that was reported in TTG experiments.

Thermal transport in suspended silicon membranes measured by laser-induced transient gratings

Studying thermal transport at the nanoscale poses formidable experimental challenges due both to the physics of the measurement process and to the issues of accuracy and reproducibility. The laser-induced transient thermal grating (TTG) technique permits non-contact measurements on nanostructured samples without a need for metal heaters or any other extraneous structures, offering the advantage of inherently high absolute accuracy. We present a review of recent studies of thermal transport in nanoscale silicon membranes using the TTG technique. An overview of the methodology, including an analysis of measurements errors, is followed by a discussion of new findings obtained from measurements on both “solid” and nanopatterned membranes. The most important results have been a direct observation of non-diffusive phonon-mediated transport at room temperature and measurements of thickness-dependent thermal conductivity of suspended membranes across a wide thickness range, showing good agreement with first-principles-based theory assuming diffuse scattering at the boundaries. Measurements on a membrane with a periodic pattern of nanosized holes (135nm) indicated fully diffusive transport and yielded thermal diffusivity values in agreement with Monte Carlo simulations. Based on the results obtained to-date, we conclude that room-temperature thermal transport in membrane-based silicon nanostructures is now reasonably well understood.

Compact stochastic models for multidimensional quasiballistic thermal transport

The Boltzmann transport equation (BTE) has proven indispensable in elucidating quasiballistic heat dynamics. The experimental observations of nondiffusive thermal transients, however, are interpreted almost exclusively through purely diffusive formalisms that merely extract “effective” Fourier conductivities. Here, we build upon stochastic transport theory to provide a characterisation framework that blends the rich physics contained within the BTE solutions with the convenience of conventional analyses. The multidimensional phonon dynamics are described in terms of an isotropic Poissonian flight process with a rigorous Fourier-Laplace single pulse response P(ξ→,s)=1/[s+ψ(∥ξ→∥)]. The spatial propagator ψ(∥ξ→∥), unlike commonly reconstructed mean free path spectra κΣ(Λ), serves as a genuine thermal blueprint of the medium that can be identified in a compact form directly from the raw measurement signals. Practical illustrations for transient thermal grating and time domain thermoreflectance experiments on respectively GaAs and InGaAs are provided.

Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films

The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.

Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring non-diffusive transport. By utilizing the known Fourier solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime.

The determination of the elastic constants of isotropic solids by means of transient thermal surface gratings

Starting from the coupled thermoelastic equations, an analytic formula is obtained for the surface deformation of a semi-infinite homogeneous and isotropic solid in an impulsive stimulated scattering (ISS) experiment. The surface ripple consists of a transient diffusive grating and a standing Rayleigh wave. The time evolution of the diffusive part directly reveals the thermal diffusivity. The oscillatory part then reveals the elastic properties, and explicit formulae are presented for retrieving the elastic moduli as a function of the frequency and amplitude of the standing Rayleigh wave. The analytic formulae not only allow to avoid time-consuming and delicate numerical integration but they also demonstrate the uniqueness of the inversion from signal to material parameters and offer direct insight into the error propagation. The formulae are applied to real experimental data, illustrating the strength and the limitations of the ISS technique.

Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation

The relaxation of an one-dimensional transient thermal grating (TTG) in a medium with phonon-mediated thermal transport is analyzed within the framework of the Boltzmann transport equation (BTE), with the goal of extracting phonon mean free path (MFP) information from TTG measurements of non-diffusive phonon transport. Both gray-medium (constant MFP) and spectrally dependent MFP models are considered. In the gray-medium approximation, an analytical solution is derived. For large TTG periods compared to the MFP, the model yields an exponential decay of grating amplitude with time in agreement with Fourier's heat diffusion equation, and at shorter periods, phonon transport transitions to the ballistic regime, with the decay becoming strongly non-exponential. Spectral solutions are obtained for Si and PbSe at 300 K using phonon dispersion and lifetime data from density functional theory calculations. The spectral decay behaviors are compared to several approximate models: a single MFP solution, a frequency-integrated gray-medium model, and a “two-fluid” BTE solution. We investigate the utility of using the approximate models for the reconstruction of phonon MFP distributions from non-diffusive TTG measurements.

Anisotropy of the Thermal Conductivity in GaAs/AlAs Superlattices

We combine the transient thermal grating and time-domain thermoreflectance techniques to characterize the anisotropic thermal conductivities of GaAs/AlAs superlattices from the same wafer. The transient grating technique is sensitive only to the in-plane thermal conductivity, while time-domain thermoreflectance is sensitive to the thermal conductivity in the cross-plane direction, making them a powerful combination to address the challenges associated with characterizing anisotropic heat conduction in thin films. We compare the experimental results from the GaAs/AlAs superlattices with first-principles calculations and previous measurements of Si/Ge SLs. The measured anisotropy is smaller than that of Si/Ge SLs, consistent with both the mass-mismatch picture of interface scattering and with the results of calculations from density-functional perturbation theory with interface mixing included.

Finite element analysis of three-dimensional laser-induced transient thermal grating in diamond/ZnSe system

This paper uses finite element method to obtain the three-dimensional temperature field of laser-induced transient thermal grating (TTG) for two-layered structure of diamond film on ZnSe substrate. The numerical results indicate that unique two-times heating process is gradually experienced in the area between two adjacent grating stripes. However, there is a little change for the temperature field along the depth direction for the diamond film due to its great thermal conductivity. It further finds that the thickness of the diamond film has a significant influence on the temperature field in diamond/ZnSe system. The results are useful for the application of laser-induced TTG technique in film/substrate system.

Characterizing the Thermal Properties of Solid Materials with Weakly Absorption by the Transient Thermal Grating Method

In this paper, a perpendicularly overlapped transient thermal grating (TTG) method is proposed to characterize the weakly absorptive or poorly reflective materials. Based on the Kirchhoff’s law and thermal elastic theory, the theoretical distribution of the diffraction light in space, which modulated by the overlapped TTG method and TTG method, have been given. As the simulation results shows, the diffraction ability of the perpendicularly overlapped TTG is much better than that of the TTG method, and much suitable to characterize the thermal properties of opaque sample with weak absorptivity or poor reflectivity.