Transient Thermal Grating Technique Research Articles

Unsteady ballistic heat transport in two-dimensional harmonic graphene lattice

We study the evolution of initial temperature profiles in a two-dimensional isolated harmonic graphene lattice. Two heat transfer problems are solved analytically and numerically. In the first problem, the evolution of a spatially sinusoidal initial temperature profile is considered. This profile is usually generated in real experiments based on the transient thermal grating technique. It is shown that at short times the amplitude of the profile decreases by an order magnitude and then it performs small decaying oscillations. A closed-form solution, describing the decay of the amplitude at short times is derived. It shows that due to symmetry of the lattice, the anisotropy of the ballistic heat transfer is negligible at short times, while at large times it is significant. In the second problem, a uniform spatial distribution of the initial temperature in a circle is specified. The profile is the simplest model of graphene heating by an ultrashort localized laser pulse. The corresponding solution has the symmetry of the lattice and many local maxima. Additionally, we show that each atom has two distinct temperatures corresponding to motions in zigzag and armchair directions. Presented results may serve for proper statement and interpretation of laboratory experiments and molecular dynamics simulations of unsteady heat transfer in graphene.

Radiative contribution to thermal grating decay

The decay of a spatially sinusoidal temperature perturbation (thermal grating) via thermal transport by both conduction and radiation is analyzed theoretically. The intrinsic non-radiative conduction is described by the heat diffusion equation while radiative transport is described by the radiation transport equation for a non-scattering absorbing medium. We solve the coupled equations analytically and obtain the thermal grating decay rate, which leads to an explicit expression for the radiative contribution to the effective thermal conductivity measured with the laser-induced transient thermal grating technique. We find that at a given thermal grating period, the radiative contribution to thermal transport is maximized when the absorption length of thermal radiation is about 1/4 of the period. We present the expression for an upper bound for the radiative contribution and discuss the results for representative materials. We conclude that in a typical transient grating measurement with the grating period in the micrometer range, the radiative contribution is negligible, but it may be significant if the grating period is in the millimeter or centimeter range. Our analysis also provides a Fourier-domain Green's function that can be used to find the temperature field produced by an arbitrary spatiotemporal distribution of heat sources.

Direct observation of large electron\u2013phonon interaction effect on phonon heat transport

As a foundational concept in many-body physics, electron–phonon interaction is essential to understanding and manipulating charge and energy flow in various electronic, photonic, and energy conversion devices. While much progress has been made in uncovering how phonons affect electron dynamics, it remains a challenge to directly observe the impact of electrons on phonon transport, especially at environmental temperatures. Here, we probe the effect of charge carriers on phonon heat transport at room temperature, using a modified transient thermal grating technique. By optically exciting electron-hole pairs in a crystalline silicon membrane, we single out the effect of the phonon–carrier interaction. The enhanced phonon scattering by photoexcited free carriers results in a substantial reduction in thermal conductivity on a nanosecond timescale. Our study provides direct experimental evidence of the elusive role of electron–phonon interaction in phonon heat transport, which is important for understanding heat conduction in doped semiconductors. We also highlight the possibility of using light to dynamically control thermal transport via electron–phonon coupling.

Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell

We study thermal processes in infinite harmonic crystals having a unit cell with an arbitrary number of particles. Initially, particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main goal is to calculate spatial distribution of kinetic temperatures, corresponding to degrees of freedom of the unit cell, at any moment in time. An expression for the temperatures is derived from solution of lattice dynamics equations. It is shown that the temperatures are represented as a sum of two terms. The first term describes high-frequency oscillations of the temperatures caused by local transition to thermal equilibrium at short times. The second term describes slow changes in the temperature profile caused by ballistic heat transport. It is shown that during heat transport, local values of temperatures, corresponding to degrees of freedom of the unit cell, are generally different. Analytical findings are supported by results of numerical solution of lattice dynamics equations for diatomic chain and graphene lattice. Strong anisotropy of ballistic heat transport in graphene is demonstrated. Presented theory may serve for description of unsteady ballistic heat transport in real crystals with low concentration of defects. In particular, solution of the problem with sinusoidal initial temperature profile can be used for proper interpretation of experimental data obtained by the transient thermal grating technique.

Reduced thermal conductivity of epitaxial GaAs on Si due to symmetry-breaking biaxial strain

Epitaxial growth of III-V semiconductors on Si is a promising route for silicon photonics. Threading dislocations and the residual thermal stress generated during growth are expected to affect the thermal conductivity of the III-V semiconductors, which is crucial for efficient heat dissipation from photonic devices built on this platform. In this work, we combine a non-contact laser-induced transient thermal grating technique with ab initio phonon simulations to investigate the in-plane thermal transport of epitaxial GaAs-based buffer layers on Si, employed in the fabrication of III-V quantum dot lasers. Surprisingly, we find a significant reduction of the in-plane thermal conductivity of GaAs, up to 19%, as a result of a small in-plane biaxial stress of 250 MPa. Using ab initio phonon calculations, we attribute this effect to the enhancement of phonon-phonon scattering caused by the in-plane biaxial stress, which breaks the cubic crystal symmetry of GaAs. Our results indicate the importance of eliminating the residual thermal stress in the epitaxial III-V layers on Si to avoid the reduction of thermal conductivity and facilitate heat dissipation. Additionally, our results showcase potential means of effectively controlling thermal conductivity of solids with external strain/stress.

Thermal conductivity reduction in highly doped mesoporous silicon: The effect of nano-crystal formation

The study of heat transfer properties in mesoporous silicon, fabricated from highly doped p-type and n-type silicon wafers, is presented. Measurements were performed by a laser induced transient thermal grating technique, which allowed us to determine the effective (in-plane) thermal conductivity. It is shown that the thermal conductivity undergoes a significant decrease with respect to bulk values mainly due to a reduction of the phonon mean free path of the solid matrix. This reduction can be ascribed to the formation of nano-crystalline domains, which are a consequence of the wet etching fabrication method. Additionally, the in-plane thermal conductivity was analyzed by employing a modified effective medium approach, which includes the phonon mean free path reduction due to the presence of both the nanometric pores and the nano-crystalline domains. The theoretical analysis shows good agreement with our measurements, indicating that the inclusion of phonon mean free path reduction to an effective medium approach is a well-suited method for studying the thermal conductivity of porous silicon.

Gas-pressure chemical vapor transport growth of millimeter-sized c-BAs single crystals with moderate thermal conductivity

We have grown c-BAs single crystals up to 1000 μm size by the chemical vapor transport (CVT) technique using combined As and I2 transport agents with the As:I ratio of 1:3 under gas pressures of up to 35 atm. Raman spectroscopy revealed a very sharp (∼2.4 cm−1) P1 phonon mode and an interesting splitting behavior of P1 from detailed polarization studies. Electron paramagnetic resonance (EPR) experiments revealed no evidence for EPR active growth-related defects under the experimental resolution. Finally, a moderate thermal conductivity value of ∼132 W/m-K was obtained using a transient thermal grating technique. These results suggest that although the high As gas vapor pressure environment in CVT growth can increase the transport rate of c-BAs significantly, it may not be efficient in reducing the defects and enhancing the thermal conductivity in c-BAs significantly.

Thermal Switching of Thermoresponsive Polymer Aqueous Solutions.

Thermal switches are of great importance to thermal management in a wide variety of applications. However, traditional thermal switches suffer from being large and having slow transition rates. To overcome these limitations, we took advantage of abrupt second-order phase transitions in thermoresponsive polymer aqueous solutions to enable fast thermal switching. While thermoresponsive polymers have been widely studied for biomedical applications, their thermal switching capability has not been studied. In this work, we used poly(N-isopropylacrylamide) (PNIPAM) as a model system to demonstrate abrupt thermal conductivity changes of thermoresponsive polymer aqueous solutions across their transition temperatures by using a powerful approach, the transient thermal grating technique, which has high sensitivity. We observed a thermal switching ratio up to 1.15 in dilute PNIPAM aqueous solutions (up to 0.025 g/mL) across the transition. This work may provide new opportunities to engineer thermal switches using second-order phase transitions of thermoresponsive polymer aqueous solutions or abrupt higher-order phase transitions in general.

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.

Non-diffusive thermal transport in GaAs at micron length scales

We use a transient thermal grating technique in reflection geometry to measure the effective thermal diffusivity in GaAs as a function of heat transfer distance at three temperatures. Utilizing heterodyne detection, we isolate the “amplitude” grating contribution of the transient grating signal, which encodes the thermal transport dynamics. As the thermal grating period decreases, and thus the heat-transfer distance, we observe a reduction in the effective thermal diffusivity, indicating a departure from diffusive behavior. Non-diffusive behavior is observed at room temperature, as well as low temperature (180 K) and high temperature (425 K). At the shortest thermal grating period measured corresponding to a heat transfer distance of approximately 1 μm, the effective diffusivity drops to a value roughly 50% of the bulk thermal diffusivity. These measurements show the utility of the reflection transient thermal grating technique to measure thermal transport properties of opaque materials.

Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes

Knowledge of the mean-free-path distribution of heat-carrying phonons is key to understanding phonon-mediated thermal transport. We demonstrate that thermal conductivity measurements of thin membranes spanning a wide thickness range can be used to characterize how bulk thermal conductivity is distributed over phonon mean free paths. A noncontact transient thermal grating technique was used to measure the thermal conductivity of suspended Si membranes ranging from 15--1500 nm in thickness. A decrease in the thermal conductivity from 74--13% of the bulk value is observed over this thickness range, which is attributed to diffuse phonon boundary scattering. Due to the well-defined relation between the membrane thickness and phonon mean-free-path suppression, combined with the range and accuracy of the measurements, we can reconstruct the bulk thermal conductivity accumulation vs. phonon mean free path, and compare with theoretical models.

Phase-controlled, heterodyne laser-induced transient grating measurements of thermal transport properties in opaque material

The methodology for a heterodyned laser-induced transient thermal grating technique for non-contact, non-destructive measurements of thermal transport in opaque material is presented. Phase-controlled heterodyne detection allows us to isolate pure phase or amplitude transient grating signal contributions by varying the relative phase between reference and probe beams. The phase grating signal includes components associated with both transient reflectivity and surface displacement whereas the amplitude grating contribution is governed by transient reflectivity alone. By analyzing the latter with the two-dimensional thermal diffusion model, we extract the in-plane thermal diffusivity of the sample. Measurements on a 5 μm thick single crystal PbTe film yielded excellent agreement with the model over a range of grating periods from 1.6 to 2.8 μm. The measured thermal diffusivity of 1.3 × 10−6 m2/s was found to be slightly lower than the bulk value.

Experimental Evidence of Non-Diffusive Thermal Transport in Si and GaAs

ABSTRACTThe length-scales at which thermal transport crosses from the diffusive to ballistic regime are of much interest particularly in the design and improvement of nano-structured materials. In this work, we demonstrate that the departure from diffusive transport has been observed in Si and GaAs using an optical transient thermal grating technique where an arbitrary, experimentally set length scale can be imposed on a material. In a transient thermal grating experiment, crossed laser pulses interfere creating a well-defined periodic absorption and temperature profile. A probe beam is diffracted from this transient grating and length-scale dependent thermal transport properties can be determined from the signal decay. As the length scale is decreased to lengths shorter than the mean free paths of heat carrying phonons, quasi-ballistic heat transport effects become apparent allowing us to map out length scales and mean free paths relevant to nondiffusive thermal transport in Si and GaAs.

Thermal diffusivity of La0.6Sr0.4MnO3thin film investigated by transient thermal grating technique

We investigate thermal diffusivity a of La 0.6 Sr 0.4 MnO 3 thin film by means of transient thermal grating technique. The transient thermal grating signal is analysised by Green's functions, and the thermal diffusivity a of La 0.6 Sr 0.4 MnO 3 film is determined to be 0.92 mm 2 s -1 . Comparison with that (∼1 mm 2 s -1 ) of the ceramic material, the smaller α-value is ascribed to the mismatch of lattice for the film material.

Optimised method of thermal diffusivity determination of thin films by means of laser-induced dynamic gratings

The transient thermal grating (TTG) technique in transmitting geometry has been applied to the characterisation of thin-film thermal diffusivity. The thermal grating is initially formed in a film surrounded by two substrates The theoretical background and experimental data for diffraction active and nonactive substrates are described. A one-dimensional model of heat diffusion in a three-layer structure fits the experimental data of TTG decay well if the film thickness is less than the thermal grating period. In addition, film thickness, light absorption coefficient in a film, and thermal properties of substrates influence the TTG relaxation time. The optimum experimental conditions have been selected, and the method of thermal diffusivity characterisation of thin films has been devised.

Numerical simulation and error analysis for thermal diffusivity measurements using laser-induced thermal grating technique

The laser-induced thermal grating technique has been used to determine the thermal diffusivity of liquids and liquid mixtures. But the dynamic behaviour of the transient thermal grating has not yet been thoroughly investigated, and the systematic errors, which result from the departures from one-dimensional heat conduction, have scarcely been studied quantitatively. In this paper. a three-dimensional numerical simulation and results of the transient thermal grating technique are presented, which enable a good understanding of the dynamic behaviour of the transient thermal grating. The results of this simulation are important for the proper design of the experimental setup to keep the systematic errors for the diffusivity measurement small. Based on the simulation method, the systematic errors were analyzed quantitatively. Here, the following effects were studied: (I) sample thickness, (2) intersection angle, (3) absorption, (4) Gaussian beam intensity distribution and focusing of heating laser beam, and (5) heating pulse duration and laser power. This error analysis makes it possible to specify the criteria for optimum measuring conditions, to correct the measured thermal-diffusivity values for systematic errors, and to estimate the accuracy of the measurements.