Time-domain thermoreflectance (TDTR) measurements of anisotropic thermal conductivity using a variable spot size approach

Anisotropic Thermal Conductivity Enhancement of the Aligned Metal-Organic Framework under Water Vapor Adsorption

Metal-organic frameworks (MOFs) exhibit high adsorption and catalytic activities for various gas species. Because gas adsorption can cause a temperature increase in the MOF, which decreases the capacity and adsorption rate, a strict evaluation of its effect on the thermal conductivity of MOFs is essential. In this study, the thermal conductivity measurement of the MOF under water vapor adsorption was performed using an oriented film of copper tetrakis(4-carboxyphenyl)porphyrin (Cu-TCPP) MOF. A recently developed bidirectional 3ω method enabled the anisotropic thermal conductivity measurement of layered Cu-TCPP while maintaining its ordered structure. The water adsorption was found to increase the thermal conductivity in both in-plane and cross-plane directions with different trends and magnitudes, owing to the structural anisotropy. Molecular dynamics simulations suggest that additional vibrational modes provided by the adsorbed water molecules were the reason for the thermal conductivity enhancement.

Impact of Graphitization Degree on the Electrochemical and Thermal Properties of Coal

Coal-based cryptocrystalline graphite is an intermediate phase formed during the transformation of highly metamorphic anthracite into crystalline graphite. In order to explore the relationship between the graphitization degree of coal-based cryptocrystalline graphite and its physical properties from macromolecular structure to provide a theoretical basis for industrial application, samples were tested by X-ray diffraction, electrochemistry, and thermal conductivity and compared with standard graphite (SG) and artificial thermal simulation graphitized samples. The results show that with the increase of graphitization degree and the growth of microcrystalline structure, the electrical impedance of cryptocrystalline graphite decreases, the conductivity increases, the specific capacity of initial discharge increases, and the thermal conductivity increases, which gradually approach the electrical and thermal properties of crystalline graphite. The linear equations between impedance and La and Lc are y = -0.42x + 70.44 and y = -1.87x + 70.62, and the correlation coefficients are 0.93 and 0.88. The linear equations between thermal conductivity and the horizontal extension length (La) and vertical stacking thickness (Lc) are y = 0.09x + 1.36 and y = 0.4x + 0.76, the correlation coefficients are 0.82 and 0.84., and the reduction of microcrystalline parameters d002 and the increase of La and Lc lead to a direct improvement of physical properties. Artificial thermal simulation samples also show the same regularity, but their physical properties are lower than those of natural evolution samples. Short-term high-temperature simulation is different from long-term magma heat and pressure, and the growth of graphite microcrystals is more complete under long-term geological conditions, resulting in better physical properties.

Organic Conjugated Small Molecules with High Thermal Conductivity as an Effective Coupling Layer for Heat Transfer

As the features of electronics are miniaturized, the need for interfacial thermal coupling layers to enhance their thermal transfer efficiency and improve device performance becomes critical. Organic conjugated small molecules possess a unique combination of periodic crystal structures and conjugated units with π electrons, resulting in notable thermal conductivities and molecular structure orientation that facilitates directed heat transfer. Nevertheless, there is a noticeable gap in literatures regarding the thermal properties of organic conjugated small molecules and their potential applications in nanoscale thermal management. Herein, we report the fabrication of high-quality thin films of organic conjugated small molecules. The result reveals that the 2D organic conjugated small molecule thin films exhibit a high cross-plane thermal conductivity of 3.2 W/m K. The increased thermal conductivity is attributed to the well-organized lattice structure and existence of π-electrons induced by conjugated systems. The studied conjugated small molecules engage in π-π stacking interactions with carbon materials and efficiently exchange energy with electrons in metals, promoting rapid interfacial heat transfer. These molecules act as coupling layers, significantly enhancing thermal transfer efficiency between graphite-based thermal pads and copper heat sinks. This pioneering research represents the inaugural investigation of the thermal performance of conjugated organic small molecules. These findings highlight the potential of conjugated small molecules as thermal coupling layers, offering tunable combinations of desirable properties.

High Thermal Conductivity of Submicrometer Aluminum Nitride Thin Films Sputter-Deposited at Low Temperature

Aluminum nitride (AlN) is one of the few electrically insulating materials with excellent thermal conductivity, but high-quality films typically require exceedingly hot deposition temperatures (>1000 °C). For thermal management applications in dense or high-power integrated circuits, it is important to deposit heat spreaders at low temperatures (<500 °C), without affecting the underlying electronics. Here, we demonstrate 100 nm to 1.7 μm thick AlN films achieved by low-temperature (<100 °C) sputtering, correlating their thermal properties with their grain size and interfacial quality, which we analyze by X-ray diffraction, transmission X-ray microscopy, as well as Raman and Auger spectroscopy. Controlling the deposition conditions through the partial pressure of reactive N2, we achieve an ∼3× variation in thermal conductivity (∼36-104 W m-1 K-1) of ∼600 nm films, with the upper range representing one of the highest values for such film thicknesses at room temperature, especially at deposition temperatures below 100 °C. Defect densities are also estimated from the thermal conductivity measurements, providing insight into the thermal engineering of AlN that can be optimized for application-specific heat spreading or thermal confinement.

Frequency-domain probe beam deflection method for measurement of thermal conductivity of materials on micron length scale

Time-domain thermoreflectance and frequency-domain thermoreflectance (FDTR) have been widely used for non-contact measurement of anisotropic thermal conductivity of materials with high spatial resolution. However, the requirement of a high thermoreflectance coefficient restricts the choice of metal coating and laser wavelength. The accuracy of the measurement is often limited by the high sensitivity to the radii of the laser beams. We describe an alternative frequency-domain pump-probe technique based on probe beam deflection. The beam deflection is primarily caused by thermoelastic deformation of the sample surface, with a magnitude determined by the thermal expansion coefficient of the bulk material to measure. We derive an analytical solution to the coupled elasticity and heat diffusion equations for periodic heating of a multilayer sample with anisotropic elastic constants, thermal conductivity, and thermal expansion coefficients. In most cases, a simplified model can reliably describe the frequency dependence of the beam deflection signal without knowledge of the elastic constants and thermal expansion coefficients of the material. The magnitude of the probe beam deflection signal is larger than the maximum magnitude achievable by thermoreflectance detection of surface temperatures if the thermal expansion coefficient is greater than 5 × 10^-6 K^-1. The uncertainty propagated from laser beam radii is smaller than that in FDTR when using a large beam offset. We find a nearly perfect matching of the measured signal and model prediction, and measure thermal conductivities within 6% of accepted values for materials spanning the range of polymers to gold, 0.1-300 W/(m K).

Hexagonal Boron Nitride for Next-Generation Photonics and Electronics

Hexagonal boron nitride (h-BN), an insulating 2D layered material, has recently attracted tremendous interest motivated by the extraordinary properties it shows across the fields of optoelectronics, quantum optics, and electronics, being exotic material platforms for various applications. At an early stage of h-BN research, it is explored as an ideal substrate and insulating layers for other 2D materials due to its atomically flat surface that is free of dangling bonds and charged impurities, and its high thermal conductivity. Recent discoveries of structural and optical properties of h-BN have expanded potential applications into emerging electronics and photonics fields. h-BN shows a very efficient deep-ultraviolet band-edge emission despite its indirect-bandgap nature, as well as stable room-temperature single-photon emission over a wide wavelength range, showing a great potential for next-generation photonics. In addition, h-BN is extensively being adopted as active media for low-energy electronics, including nonvolatile resistive switching memory, radio-frequency devices, and low-dielectric-constant materials for next-generation electronics.

Deep Neural Network-Evaluated Thermal Conductivity for Two-Phase WC-M (M = Ag, Co) Cemented Carbides

DNN (Deep Neural Network) is one kind of method for artificial intelligence, which has been applied in various fields including the exploration of material properties. In the present work, DNN, in combination with the 10-fold cross-validation, is applied to evaluate and predict the thermal conductivities for two-phase WC-M (M = Ag, Co) cemented carbides. Multi-layer DNNs were established by learning the measured thermal conductivities for the WC-Ag and WC-Co systems. It is observed that there are local-minimum regions for the loss functions during training and testing the DNNs, and the presently utilized Adam optimizer is valid for breaking the local-minimum regions. The good agreements between the DNN-evaluated thermal conductivities and the measured ones manifest that the DNNs were well trained and tested. Moreover, another 1000 input data points were randomly generated for the established DNNs to predict the thermal conductivities for WC-Ag and WC-Co systems, respectively. Compared with the thermal conductivities predicted by the previously developed physical model, the presently established DNNs show similarly robust predicting ability. Concerning the efficiency, it is demonstrated in the present work that machine learning is promising to explore the material properties, especially in the high-dimensional parameter space, more efficiently than previous models, and thus can considerably contribute to the corresponding material design with less time consumption and costs.

Anisotropic thermoreflectance thermometry: A contactless frequency-domain thermoreflectance approach to study anisotropic thermal transport

We developed a novel contactless frequency-domain thermoreflectance approach to study thermal transport, which is particularly convenient when thermally anisotropic materials are considered. The method is based on a line-shaped heater geometry, produced with a holographic diffractive optical element, instead of using a spot heater as in conventional thermoreflectance. The heater geometry is similar to the one used in the 3-omega method, however, keeping all the technical advantages offered by non-contact methodologies. The present method is especially suitable to determine all the elements of the thermal conductivity tensor, which is experimentally achieved by simply rotating the sample with respect to the line-shaped optical heater. We provide the mathematical solution of the heat equation for the cases of anisotropic substrates, thin films, and multilayer systems. This methodology allows an accurate determination of the thermal conductivity and does not require complex modeling or intensive computational efforts to process the experimental data, i.e., the thermal conductivity is obtained through a simple linear fit ("slope method"), in a similar fashion to the 3-omega method. We demonstrate the potential of this approach by studying isotropic and anisotropic materials in a wide range of thermal conductivities. In particular, we have studied the following inorganic and organic systems: (i) glass, Si, and Ge substrates (isotropic), (ii) β-Ga₂O₃ and a Kapton substrate (anisotropic), and (iii) a 285 nm thick SiO₂ thin film deposited on a Si substrate. The accuracy in the determination of the thermal conductivity is estimated as ≈5%, whereas the temperature uncertainty is ΔT ≈ 3 mK.

Reducing the uncertainty caused by the laser spot radius in frequency-domain thermoreflectance measurements of thermal properties

In a frequency-domain thermoreflectance (FDTR) experiment, the phase lag between the surface temperature response and the applied heat flux is fit with an analytical solution to the heat diffusion equation to extract an unknown thermal property (e.g., thermal conductivity) of a test sample. A method is proposed to reduce the impact of uncertainty in the laser spot radius on the resulting uncertainty in the fitted property that is based on fitting to the quotient of the test sample phase and that of a reference sample. The reduction is proven analytically for a semi-infinite solid and was confirmed using numerical and real experiments on realistic samples. When the spot radius and its uncertainty are well known, the reference phase can be generated numerically. In this situation, FDTR experiments performed on Au-SiO₂-Si and PbS nanocrystal test samples demonstrate 32% and 82% reductions in the overall uncertainty in thermal conductivity. When the spot radius used in the test sample measurement is not well known, a real reference sample, measured under conditions that lead to the same unknown spot radius, is required. Although the real reference sample introduces its own uncertainties, the total uncertainty in the fitted thermal conductivity can still be reduced. A reference sample can also be used to reduce uncertainty due to other sources, such as the transducer properties. Because frequency-domain solutions to the heat diffusion equation are the basis for time-domain thermoreflectance (TDTR) analysis, the approach can be extended to TDTR experiments.

Control of Thermal Conductance across Vertically Stacked Two-Dimensional van der Waals Materials via Interfacial Engineering

A comprehensive understanding of the roles of various nanointerfaces in thermal transport is of critical significance but remains challenging. A two-dimensional van der Waals (vdW) heterostructure with tunable interface lattice mismatch provides an ideal platform to explore the correlation between thermal properties and nanointerfaces and achieve controllable tuning of heat flow. Here, we demonstrate that interfacial engineering is an efficient strategy to tune thermal transport via systematic investigation of the thermal conductance (G) across a series of large-area four-layer stacked vdW materials using an improved polyethylene glycol-assisted time-domain thermoreflectance method. Owing to its rich interfacial mismatch and weak interfacial coupling, the vertically stacked MoSe₂-MoS₂-MoSe₂-MoS₂ heterostructure demonstrates the lowest G of 1.5 MW m^-2 K^-1 among all vdW structures. A roadmap to tune G via homointerfacial mismatch, interfacial coupling, and heterointerfacial mismatch is further demonstrated for thermal tuning. Our work reveals the roles of various interfacial effects on heat flow and highlights the importance of the interfacial mismatch and coupling effects in thermal transport. The design principle is also promising for application in other areas, such as the electrical tuning of energy storage and conversion and the thermoelectricity tuning of thermoelectronics.

Review on Techniques for Thermal Characterization of Graphene and Related 2D Materials

The discovery of graphene and its analog, such as MoS2, has boosted research. The thermal transport in 2D materials gains much of the interest, especially when graphene has high thermal conductivity. However, the thermal properties of 2D materials obtained from experiments have large discrepancies. For example, the thermal conductivity of single layer suspended graphene obtained by experiments spans over a large range: 1100-5000 W/m·K. Apart from the different graphene quality in experiments, the thermal characterization methods play an important role in the observed large deviation of experimental data. Here we provide a critical review of the widely used thermal characterization techniques: the optothermal Raman technique and the micro-bridge method. The critical issues in the two methods are carefully revised and discussed in great depth. Furthermore, improvements in Raman-based techniques to investigate the energy transport in 2D materials are discussed.

Thermal conductivity measurements of sub-surface buried substrates by steady-state thermoreflectance

Measuring the thermal conductivity of sub-surface buried substrates is of significant practical interests. However, this remains challenging with traditional pump-probe spectroscopies due to their limited thermal penetration depths. Here, we experimentally and numerically investigate the TPD of the recently developed optical pump-probe technique steady-state thermoreflectance (SSTR) and explore its capability for measuring the thermal properties of buried substrates. The conventional definition of the TPD (i.e., the depth at which temperature drops to 1/e value of the maximum surface temperature) does not truly represent the upper limit of how far beneath the surface SSTR can probe. For estimating the uncertainty of SSTR measurements of a buried substrate a priori, sensitivity calculations provide the best means. Thus, detailed sensitivity calculations are provided to guide future measurements. Due to the steady-state nature of SSTR, it can measure the thermal conductivity of buried substrates that are traditionally challenging by transient pump-probe techniques, exemplified by measuring three control samples. We also discuss the required criteria for SSTR to isolate the thermal properties of a buried film. Our study establishes SSTR as a suitable technique for thermal characterizations of sub-surface buried substrates in typical device geometries.

Mapping Elevated Temperatures with a Micrometer Resolution Using the Luminescence of Chemically Stable Upconversion Nanoparticles

The temperature-sensitive luminescence of nanoparticles enables their application as remote thermometers. The size of these nanothermometers makes them ideal to map temperatures with a high spatial resolution. However, high spatial resolution mapping of temperatures >373 K has remained challenging. Here, we realize nanothermometry with high spatial resolutions at elevated temperatures using chemically stable upconversion nanoparticles and confocal microscopy. We test this method on a microelectromechanical heater and study the temperature homogeneity. Our experiments reveal distortions in the luminescence spectra that are intrinsic to high-resolution measurements of samples with nanoscale photonic inhomogeneities. In particular, the spectra are affected by the high-power excitation as well as by scattering and reflection of the emitted light. The latter effect has an increasing impact at elevated temperatures. We present a procedure to correct these distortions. As a result, we extend the range of high-resolution nanothermometry beyond 500 K with a precision of 1-4 K. This work will improve the accuracy of nanothermometry not only in micro- and nanoelectronics but also in other fields with photonically inhomogeneous substrates.

Thermoelectric Properties of Cu2Se Nano-Thin Film by Magnetron Sputtering

Thermoelectric technology can achieve mutual conversion between thermoelectricity and has the unique advantages of quiet operation, zero emissions and long life, all of which can help overcome the energy crisis. However, the large-scale application of thermoelectric technology is limited by its lower thermoelectric performance factor (ZT). The thermoelectric performance factor is a function of the Seebeck coefficient, electrical conductivity, thermal conductivity and absolute temperature. Since these parameters are interdependent, increasing the ZT value has always been a challenge. Here, we report the growth of Cu₂Se thin films with a thickness of around 100 nm by magnetron sputtering. XRD and TEM analysis shows that the film is low-temperature α-Cu₂Se, XPS analysis shows that about 10% of the film’s surface is oxidized, and the ratio of copper to selenium is 2.26:1. In the range of 300–400 K, the maximum conductivity of the film is 4.55 × 10⁵ S m⁻¹, which is the maximum value reached by the current Cu₂Se film. The corresponding Seebeck coefficient is between 15 and 30 µV K⁻¹, and the maximum ZT value is 0.073. This work systematically studies the characterization of thin films and the measurement of thermoelectric properties and lays the foundation for further research on nano-thin-film thermoelectrics.

Dual Laser Beam Processing of Semiconducting Thin Films by Excited State Absorption

We present a unique dual laser beam processing approach based on excited state absorption by structuring 200 nm thin zinc oxide films sputtered on fused silica substrates. The combination of two pulsed nanosecond-laser beams with different photon energies-one below and one above the zinc oxide band gap energy-allows for a precise, efficient, and homogeneous ablation of the films without substrate damage. Based on structuring experiments in dependence on laser wavelength, pulse fluence, and pulse delay of both laser beams, a detailed concept of energy transfer and excitation processes during irradiation was developed. It provides a comprehensive understanding of the thermal and electronic processes during ablation. To quantify the efficiency improvements of the dual-beam process compared to single-beam ablation, a simple efficiency model was developed.

Anisotropic thermal conductivity measurement of organic thin film with bidirectional 3ω method

Organic thin film materials with molecular ordering are gaining attention as they exhibit semiconductor characteristics. When using them for electronics, the thermal management becomes important, where heat dissipation is directional owing to the anisotropic thermal conductivity arising from the molecular ordering. However, it is difficult to evaluate the anisotropy by simultaneously measuring in-plane and cross-plane thermal conductivities of the film on a substrate because the film is typically as thin as tens to hundreds of nanometers and its in-plane thermal conductivity is low. Here, we develop a novel bidirectional 3ω system that measures the anisotropic thermal conductivity of thin films by patterning two metal wires with different widths and preparing the films on top and extracting the in-plane and cross-plane thermal conductivities using the difference in their sensitivities to the metal-wire width. Using the developed system, the thermal conductivity of spin-coated poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) with thickness of 70 nm was successfully measured. The measured in-plane thermal conductivity of PEDOT:PSS film was as high as 2.9 W m^-1 K^-1 presumably due to the high structural ordering, giving an anisotropy of 10. The calculations of measurement sensitivity to the film thickness and thermal conductivities suggest that the device can be applied to much thinner films by utilizing metal wires with a smaller width.

High-performance wearable thermoelectric generator with self-healing, recycling, and Lego-like reconfiguring capabilities

Thermoelectric generators (TEGs) are an excellent candidate for powering wearable electronics and the "Internet of Things," due to their capability of directly converting heat to electrical energy. Here, we report a high-performance wearable TEG with superior stretchability, self-healability, recyclability, and Lego-like reconfigurability, by combining modular thermoelectric chips, dynamic covalent polyimine, and flowable liquid-metal electrical wiring in a mechanical architecture design of "soft motherboard-rigid plugin modules." A record-high open-circuit voltage among flexible TEGs is achieved, reaching 1 V/cm² at a temperature difference of 95 K. Furthermore, this TEG is integrated with a wavelength-selective metamaterial film on the cold side, leading to greatly improved device performance under solar irradiation, which is critically important for wearable energy harvesting during outdoor activities. The optimal properties and design concepts of TEGs reported here can pave the way for delivering the next-generation high-performance, adaptable, customizable, durable, economical, and eco-friendly energy-harvesting devices with wide applications.

Anisotropic thermal conductivity of the nanoparticles embedded GaSb thin film semiconductor

The prior theoretical model shows that GaSb is one of the few non-alloy semiconductors showing phonons ballistic effect in the thermal conductivity. However, no previous literature had been reported on the experimental measurements on the quasi-ballistic thermal transport of the GaSb thin film. In this paper, we employed the time-domain thermoreflectance (TDTR) to study the thermal transport of nanoparticles embedded GaSb thin film. Our measurements results provide first experimental evidence to verify the quasi-ballistic effect in the thermal transport of the GaSb thin film. The apparent cross-plane thermal conductivity of pure GaSb sample drops ∼15% when the pump laser modulation frequency is increased from 0.8 MHz to 10 MHz at room temperature. To further understand the thermal transport mechanism, Tempered Lévy analysis is employed to study the quasi-ballistic effect of the GaSb thin film. The model shows that GaSb thin film thermal transport has a superdiffusion exponent, [Formula: see text] = 1.51 ± 0.23 and Lévy-Fourier transition length, r _LF = 0.19 ± 0.13 µm. Both obtained values via Tempered Lévy indicates the quasi-ballistic transport phenomena in GaSb thin film. However, this frequency dependence of the cross-plane thermal conductivity will disappear in the presence of the 3%-20% ErSb nanoparticles. Another thermal transport mechanism, i.e. anisotropic thermal transport, can be observed in GaSb thin film. The ratio of in- to cross-plane thermal conductivity varies from ∼0.2 to ∼0.7 in the 0%-20% ErSb nanoparticles volume concentrations. Detailed temperature dependence of the in-plane thermal conductivity of ErSb:GaSb samples with 0%-20% are also included in the paper for the understanding of the scattering mechanism in the thin film thermal transport. With enhanced understanding of the quasi-ballistic and anisotropic thin film thermal transport, our results might improve the thermal management efficiency of the GaSb devices.

Accurate measurement of in-plane thermal conductivity of layered materials without metal film transducer using frequency domain thermoreflectance

Measuring anisotropic thermal conductivity has always been a challenging task in thermal metrology. Although recent developments of pump-probe thermoreflectance techniques such as variable spot sizes, offset pump-probe beams, and elliptical beams have enabled the measurement of anisotropic thermal conductivity, a metal film transducer enabled for the absorption of the modulated pump laser beam and the detection of the thermoreflectance signal. However, the existence of the transducer would cause in-plane heat spreading, suppressing the measurement sensitivity to the in-plane thermal conductivity. In addition, the transducer film also adds complexity to data processing, since it requires careful calibration or fitting to determine extra parameters such as the film thickness and conductivity, and interface conductance between the transducer and the sample. In this work, we discussed the methodology for measuring in-plane thermal conductivity of layered semiconductors and semimetals without any transducer layer. We show that the removal of transducer results in the dominantly large sensitivity to in-plane thermal conductivity compared with other parameters, such as cross-plane thermal conductivity and the absorption depth of the laser beams. Transducerless frequency-domain thermoreflectance (FDTR) measurements are performed on three reference layered-materials, highly ordered pyrolytic graphite, molybdenum disulfide (MoS₂), and bismuth selenide (Bi₂Se₃) and demonstrated using the analytical thermal model that the measured in-plane thermal conductivity showed much-improved accuracy compared with conventional FDTR measurement with a transducer.

Halide Perovskites: Thermal Transport and Prospects for Thermoelectricity

The recent re-emergence of halide perovskites has received escalating interest for optoelectronic applications. In addition to photovoltaics, the multifunctional nature of halide perovskites has led to diverse applications. The ultralow thermal conductivity coupled with decent mobility and charge carrier tunability led to the prediction of halide perovskites as a possible contender for future thermoelectrics. Herein, recent advances in thermal transport of halide perovskites and their potentials and challenges for thermoelectrics are reviewed. An overview of the phonon behavior in halide perovskites, as well as the compositional dependency is analyzed. Understanding thermal transport and knowing the thermal conductivity value is crucial for creating effective heat dissipation schemes and determining other thermal-related properties like thermo-optic coefficients, hot-carrier cooling, and thermoelectric efficiency. Recent works on halide perovskite-based thermoelectrics together with theoretical predictions for their future viability are highlighted. Also, progress on modulating halide perovskite-based thermoelectric properties using light and chemical doping is discussed. Finally, strategies to overcome the limiting factors in halide perovskite thermoelectrics and their prospects are emphasized.

Nanosecond transient thermoreflectance method for characterizing anisotropic thermal conductivity

A method is presented to characterize the anisotropic thermal properties of materials based on nanosecond transient thermoreflectance (TTR). An analytical heat transfer model is derived for the TTR signal, showing that the signal is sensitive to out-of-plane and in-plane heat conductions at distinct time scales. This sensitivity feature can be exploited to simultaneously determine the out-of-plane and in-plane thermal conductivities. Examples are given for molybdenum disulphide, hexagonal boron nitride, and highly oriented pyrolytic graphite to assess the validity of this method.

A new elliptical-beam method based on time-domain thermoreflectance (TDTR) to measure the in-plane anisotropic thermal conductivity and its comparison with the beam-offset method

Materials lacking in-plane symmetry are ubiquitous in a wide range of applications such as electronics, thermoelectrics, and high-temperature superconductors, in all of which the thermal properties of the materials play a critical part. However, very few experimental techniques can be used to measure in-plane anisotropic thermal conductivity. A beam-offset method based on time-domain thermoreflectance (TDTR) was previously proposed to measure in-plane anisotropic thermal conductivity. However, a detailed analysis of the beam-offset method is still lacking. Our analysis shows that uncertainties can be large if the laser spot size or the modulation frequency is not properly chosen. Here we propose an alternative approach based on TDTR to measure in-plane anisotropic thermal conductivity using a highly elliptical pump (heating) beam. The highly elliptical pump beam induces a quasi-one-dimensional temperature profile on the sample surface that has a fast decay along the short axis of the pump beam. The detected TDTR signal is exclusively sensitive to the in-plane thermal conductivity along the short axis of the elliptical beam. By conducting TDTR measurements as a function of delay time with the rotation of the elliptical pump beam to different orientations, the in-plane thermal conductivity tensor of the sample can be determined. In this work, we first conduct detailed signal sensitivity analyses for both techniques and provide guidelines in determining the optimal experimental conditions. We then compare the two techniques under their optimal experimental conditions by measuring the in-plane thermal conductivity tensor of a ZnO [11-20] sample. The accuracy and limitations of both methods are discussed.

Anisotropic thermal conductivity measurement using a new Asymmetric-Beam Time-Domain Thermoreflectance (AB-TDTR) method

Anisotropic thermal properties are of both fundamental and practical interests, but remain challenging to characterize using conventional methods. In this work, a new metrology based on asymmetric beam time-domain thermoreflectance (AB-TDTR) is developed to measure three-dimensional anisotropic thermal transport by extending the conventional TDTR technique. Using an elliptical laser beam with controlled elliptical ratio and spot size, the experimental signals can be exploited to be dominantly sensitive to measure thermal conductivity along the cross-plane or any specific in-plane directions. An analytic solution for a multi-layer system is derived for the AB-TDTR signal in response to the periodical pulse, elliptical laser beam, and heating geometry to extract the anisotropic thermal conductivity from experimental measurement. Examples with experimental data are given for various materials with in-plane thermal conductivity from 5 W/m K to 2000 W/m K, including isotropic materials (silicon, boron phosphide, and boron nitride), transversely isotropic materials (graphite, quartz, and sapphire), and transversely anisotropic materials (black phosphorus). Furthermore, a detailed sensitivity analysis is conducted to guide the optimal setting of experimental configurations for different materials. The developed AB-TDTR metrology provides a new approach to accurately measure anisotropic thermal phenomena for rational materials design and thermal applications.

Probing Growth-Induced Anisotropic Thermal Transport in High-Quality CVD Diamond Membranes by Multifrequency and Multiple-Spot-Size Time-Domain Thermoreflectance

The maximum output power of GaN-based high-electron mobility transistors is limited by high channel temperature induced by localized self-heating, which degrades device performance and reliability. Chemical vapor deposition (CVD) diamond is an attractive candidate to aid in the extraction of this heat and in minimizing the peak operating temperatures of high-power electronics. Owing to its inhomogeneous structure, the thermal conductivity of CVD diamond varies along the growth direction and can differ between the in-plane and out-of-plane directions, resulting in a complex three-dimensional (3D) distribution. Depending on the thickness of the diamond and size of the electronic device, this 3D distribution may impact the effectiveness of CVD diamond in device thermal management. In this work, time-domain thermoreflectance is used to measure the anisotropic thermal conductivity of an 11.8 μm-thick high-quality CVD diamond membrane from its nucleation side. Starting with a spot-size diameter larger than the thickness of the membrane, measurements are made at various modulation frequencies from 1.2 to 11.6 MHz to tune the heat penetration depth and sample the variation in thermal conductivity. We then analyze the data by creating a model with the membrane divided into ten sublayers and assume isotropic thermal conductivity in each sublayer. From this, we observe a two-dimensional gradient of the depth-dependent thermal conductivity for this membrane. The local thermal conductivity goes beyond 1000 W/(m K) when the distance from the nucleation interface only reaches 3 μm. Additionally, by measuring the same region with a smaller spot size at multiple frequencies, the in-plane and cross-plane thermal conductivities are extracted. Through this use of multiple spot sizes and modulation frequencies, the 3D anisotropic thermal conductivity of CVD diamond membrane is experimentally obtained by fitting the experimental data to a thermal model. This work provides an improved understanding of thermal conductivity inhomogeneity in high-quality CVD polycrystalline diamond that is important for applications in the thermal management of high-power electronics.

High temperature thermal management with boron nitride nanosheets

The rapid development of high power density devices requires more efficient heat dissipation. Recently, two-dimensional layered materials have attracted significant interest due to their superior thermal conductivity, ease of production and chemical stability. Among them, hexagonal boron nitride (h-BN) is electrically insulating, making it a promising thermal management material for next-generation electronics. In this work, we demonstrated that an h-BN thin film composed of layer-by-layer laminated h-BN nanosheets can effectively enhance the lateral heat dissipation on the substrate. We found that by using the BN-coated glass instead of bare glass as the substrate, the highest operating temperature of a reduced graphene oxide (RGO) based device could increase from 700 °C to 1000 °C, and at the same input power, the operating temperature of the RGO device is effectively decreased. The remarkable performance improvement using the BN coating originates from its anisotropic thermal conductivity: a high in-plane thermal conductivity of 14 W m^-1 K^-1 for spreading and a low cross-plane thermal conductivity of 0.4 W m^-1 K^-1 to avoid a hot spot right underneath the device. Our results provide an effective approach to improve the heat dissipation in integrated circuits and high power devices.

Probing Anisotropic Thermal Conductivity of Transition Metal Dichalcogenides MX2 (M = Mo, W and X = S, Se) using Time-Domain Thermoreflectance

Transition metal dichalcogenides (TMDs) are a group of layered 2D semiconductors that have shown many intriguing electrical and optical properties. However, the thermal transport properties in TMDs are not well understood due to the challenges in characterizing anisotropic thermal conductivity. Here, a variable-spot-size time-domain thermoreflectance approach is developed to simultaneously measure both the in-plane and the through-plane thermal conductivity of four kinds of layered TMDs (MoS₂ , WS₂ , MoSe₂ , and WSe₂ ) over a wide temperature range, 80-300 K. Interestingly, it is found that both the through-plane thermal conductivity and the Al/TMD interface conductance depend on the modulation frequency of the pump beam for all these four compounds. The frequency-dependent thermal properties are attributed to the nonequilibrium thermal resistance between the different groups of phonons in the substrate. A two-channel thermal model is used to analyze the nonequilibrium phonon transport and to derive the intrinsic thermal conductivity at the thermal equilibrium limit. The measurements of the thermal conductivities of bulk TMDs serve as an important benchmark for understanding the thermal conductivity of single- and few-layer TMDs.