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Summary The air-stable layered semiconductor Bi2O2Se has recently attracted extensive interest because of its potential application in electronics, optoelectronics, ferroelectrics, and thermoelectrics. For many of these applications, thermal transport in Bi2O2Se is of great importance, but a complete understanding of the process remains elusive. Here, we perform a combined experimental and theoretical study of the anisotropic thermal conductivity of single-crystalline Bi2O2Se in comparison with Bi2Se3. Bi2O2Se exhibits relatively higher through-plane thermal conductivity but lower in-plane thermal conductivity, resulting in substantially smaller thermal anisotropy. This behavior originates from the stronger interlayer electrostatic interaction in Bi2O2Se compared with the typical van der Waals coupling in layered materials, making the phonon isoenergy surfaces less anisotropic and, thus, weakening phonon focusing in the in-plane directions. Our study advances the fundamental understanding of thermal anisotropy in layered materials with various interlayer interactions and will facilitate application of Bi2O2Se in electronics and thermoelectrics.

Recent developments of the pump-probe thermoreflectance methods (such as the beam-offset and elliptical-beam approaches of the time-domain and frequency-domain thermoreflectance techniques) enabled measurements of the thermal conductivities of in-plane anisotropic materials. Estimating the temperature rise of anisotropic layered structures under surface heating is critically important to make sure that the temperature rise is not too high to alias the signals in these experiments. However, a simple formula to estimate the temperature rise in three-dimensional (3D) anisotropic layered systems heated by a non-circular laser beam is not available yet, which is the main problem we aim to solve in this work. We first re-derived general formalisms of the temperature rise of a multilayered structure based on the previous literature work by solving the 3D anisotropic heat diffusion equation in the frequency domain. These general formalisms normally require laborious numerical evaluation; however, they could be reduced to explicit analytical expressions for the case of semi-infinite solids. We then extend the analytical expressions to multilayered systems, taking into account the effect of the top layers. This work not only enhances our understanding of the physics of temperature rise due to surface laser heating but also enables quick estimation of the peak temperature rise of 3D anisotropic layered systems in pump-probe thermoreflectance experiments and thus greatly benefits the thermoreflectance experiments in choosing the appropriate heating power intensity for the experiments.

Scattering of phonons at boundaries of a crystal (grains, surfaces, or solid/solid interfaces) is characterized by the phonon wavelength, the angle of incidence, and the interface roughness, as historically evaluated using a specularity parameter p formulated by Ziman [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. This parameter was initially defined to determine the probability of a phonon specularly reflecting or diffusely scattering from the rough surface of a material. The validity of Ziman's theory as extended to solid/solid interfaces has not been previously validated. To better understand the interfacial scattering of phonons and to test the validity of Ziman's theory, we precisely measured the in-plane thermal conductivity of a series of Si films in silicon-on-insulator (SOI) wafers by time-domain thermoreflectance (TDTR) for a Si film thickness range of 1 - 10 {\mu}m and a temperature range of 100 - 300 K. The Si/SiO2 interface roughness was determined to be 0.11+/-0.04 nm using transmission electron microscopy (TEM). Furthermore, we compared our in-plane thermal conductivity measurements to theoretical calculations that combine first-principles phonon transport with Ziman's theory. Calculations using Ziman's specularity parameter significantly overestimate values from the TDTR measurements. We attribute this discrepancy to phonon transmission through the solid/solid interface into the substrate, which is not accounted for by Ziman's theory for surfaces. We derive a simple expression for the specularity parameter at solid/amorphous interfaces and achieve good agreement between calculations and measurement values., Comment: 4 figures, submitted to PRB

Hexagonal boron nitride (h-BN) has received great interest in recent years as a wide bandgap analog of graphene-derived systems. However, the thermal transport properties of h-BN, which can be critical for device reliability and functionality, are little studied both experimentally and theoretically. The primary challenge in the experimental measurements of the anisotropic thermal conductivity of h-BN is that typically sample size of h-BN single crystals is too small for conventional measurement techniques, as state-of-the-art technologies synthesize h-BN single crystals with lateral sizes only up to 2.5 mm and thickness up to 200 {\mu}m. Recently developed time-domain thermoreflectance (TDTR) techniques are suitable to measure the anisotropic thermal conductivity of such small samples, as it only requires a small area of 50x50 {\mu}m2 for the measurements. Accurate atomistic modeling of thermal transport in bulk h-BN is also challenging due to the highly anisotropic layered structure. Here we conduct an integrated experimental and theoretical study on the anisotropic thermal conductivity of bulk h-BN single crystals over the temperature range of 100 K to 500 K, using TDTR measurements with multiple modulation frequencies and a full-scale numerical calculation of the phonon Boltzmann transport equation starting from the first principles. Our experimental and numerical results compare favorably for both the in-plane and through-plane thermal conductivities. We observe unusual temperature-dependence and phonon-isotope scattering in the through-plane thermal conductivity of h-BN and elucidate their origins. This work not only provides an important benchmark of the anisotropic thermal conductivity of h-BN but also develops fundamental insights into the nature of phonon transport in this highly anisotropic layered material., Comment: 18 pages, 5 figures, submitted to Physical Review Materials

Measuring thermal properties of materials is not only of fundamental importance in understanding the transport processes of energy carriers (electrons and phonons) but also of practical interest in developing novel materials with desired thermal conductivity for applications in energy, electronics, and photonic systems. Over the past two decades, ultrafast laser-based time-domain thermoreflectance (TDTR) has emerged and evolved as a reliable, powerful, and versatile technique to measure the thermal properties of a wide range of bulk and thin film materials and their interfaces. This tutorial discusses the basics as well as the recent advances of the TDTR technique and its applications in the thermal characterization of a variety of materials. The tutorial begins with the fundamentals of the TDTR technique, serving as a guideline for understanding the basic principles of this technique. A diverse set of TDTR configurations that have been developed to meet different measurement conditions are then presented, followed by several variations of the TDTR technique that function similarly as the standard TDTR but with their own unique features. This tutorial closes with a summary that discusses the current limitations and proposes some directions for future development., Comment: 82 pages, 23 figures, invited tutorial submitted to Journal of Applied Physics

Silicon carbide (SiC) is a wide bandgap (WBG) semiconductor with promising applications in high-power and high-frequency electronics. Among its many useful properties, the high thermal conductivity is crucial. In this letter, the anisotropic thermal conductivity of three SiC samples, n-type 4H-SiC (N-doped 1 × 1019 cm−3), unintentionally doped (UID) semi-insulating (SI) 4H-SiC, and SI 6H-SiC (V-doped 1 × 1017 cm−3), is measured using femtosecond laser based time-domain thermoreflectance (TDTR) over a temperature range from 250 K to 450 K. We simultaneously measure the thermal conductivity parallel to ( k r ) and across the hexagonal plane ( k z ) for SiC by choosing the appropriate laser spot radius and the modulation frequency for the TDTR measurements. For both k r and k z , the following decreasing order of thermal conductivity value is observed: SI 4H-SiC > n-type 4H-SiC > SI 6H-SiC. This work serves as an important benchmark for understanding thermal transport in WBG semiconductors.

β-Ga2O3 has attracted considerable interest in recent years for high power electronics, where the thermal properties of β-Ga2O3 play a critical role. The thermal conductivity of β-Ga2O3 is expected to be three-dimensionally (3D) anisotropic due to the monoclinic lattice structure. In this work, the 3D anisotropic thermal conductivity tensor of a (010)-oriented β-Ga2O3 single crystal was measured using a recently developed elliptical-beam time-domain thermoreflectance method. Thermal conductivity along any direction in the (010) plane as well as the one perpendicular to the (010) plane can be directly measured, from which the 3D directional distribution of the thermal conductivity can be derived. Our measured results suggest that at room temperature, the highest in-plane thermal conductivity is along a direction between [001] and [102], with a value of 13.3 ± 1.8 W m−1 K−1, and the lowest in-plane thermal conductivity is close to the [100] direction, with a value of 9.5 ± 1.8 W m−1 K−1. The through-plane thermal conductivity, which is along the [010] direction, has the highest value of 22.5 ± 2.5 W m−1 K−1 among all the directions. The temperature-dependent thermal conductivity of β-Ga2O3 was also measured and compared with a theoretical model calculation to understand the temperature dependence and the role of impurity scattering.

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., 35 pages, 12 figures, submitted to RSI

Despite recent progress in the first-principles calculations and measurements of phonon mean-free-paths (MFPs), contribution of low-energy phonons to heat conduction in silicon is still inconclusive, as exemplified by the discrepancies between different first-principles calculations. Here we investigate the contribution of low-energy phonons with MFP>0.8 um by accurately measuring the cross-plane thermal conductivity of crystalline silicon films by time-domain thermoreflectance (TDTR), over a wide range of film thickness 1-10 um and temperature 100-300 K. We employ a dual-frequency TDTR approach to improve the accuracy of our cross-plane thermal conductivity measurements. We find from our cross-plane thermal conductivity measurements that phonons with MFP>0.8 um contribute 53 W/m-K (37%) to heat conduction in Si at 300 K while phonons with MFP>3 um contribute 523 W/m-K (61%) at 100 K, >20% lower than the first-principles predictions by Lindsay et al. of 68 W/m-K (47%) and 695 W/m-K (77%), respectively. Using a relaxation times approximation (RTA) model, we demonstrate that macroscopic damping (e.g., Akhieser's damping) eliminates the contribution of phonons with mean-free-paths >30 um at 300 K, which contributes 15 W/m-K (10%) to heat conduction in Si according to Lindsay et al. Thus we propose that omission of the macroscopic damping for low-energy phonons in the first-principles calculations could be one of the possible explanations for the observed discrepancy between our measurements and calculations by Lindsay et al. Our work provides an important benchmark for future measurements and calculations of the distribution of phonon mean-free-paths in crystalline silicon.

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.

It is challenging to characterize thermal conductivity of materials with strong anisotropy. In this work, we extend the time-domain thermoreflectance (TDTR) method with a variable spot size approach to simultaneously measure the in-plane (Kr) and the through-plane (Kz) thermal conductivity of materials with strong anisotropy. We first determine Kz from the measurement using a larger spot size, when the heat flow is mainly one-dimensional along the through-plane direction, and the measured signals are sensitive to only Kz. We then extract the in-plane thermal conductivity Kr from a second measurement using the same modulation frequency but with a smaller spot size, when the heat flow becomes three-dimensional, and the signal is sensitive to both Kr and Kz. By choosing the same modulation frequency for the two sets of measurements, we can avoid potential artifacts introduced by the frequency-dependent Kz, which we have found to be non-negligible, especially for some two-dimensional layered materials like MoS2. After careful evaluation of the sensitivity of a series of hypothetical samples, we provided a guideline on choosing the most appropriate laser spot size and modulation frequency that yield the smallest uncertainty, and established a criterion for the range of thermal conductivities that can be measured reliably using our proposed variable spot size TDTR approach. We have demonstrated this variable spot size TDTR approach on samples with a wide range of in-plane thermal conductivity, including fused silica, rutile titania (TiO2 [001]), zinc oxide (ZnO [0001]), molybdenum disulfide (MoS2), hexagonal boron nitride (h-BN), and highly ordered pyrolytic graphite (HOPG)., 24 pages, 6 figures, 1 table, submitted to Review of Scientific Instruments

Accurate measurements of the cross-plane thermal conductivity {\Lambda}_cross of a high-thermal-conductivity thin film on a low-thermal-conductivity ({\Lambda}_s) substrate (e.g., {\Lambda}_cross/{\Lambda}_s>20) are challenging, due to the low thermal resistance of the thin film compared to that of the substrate. In principle, {\Lambda}_cross could be measured by time-domain thermoreflectance (TDTR), using a high modulation frequency f_h and a large laser spot size. However, with one TDTR measurement at f_h, the uncertainty of the TDTR measurement is usually high due to low sensitivity of TDTR signals to {\Lambda}_cross and high sensitivity to the thickness h_Al of Al transducer deposited on the sample for TDTR measurements. We observe that in most TDTR measurements, the sensitivity to h_Al only depends weakly on the modulation frequency f. Thus, we performed an additional TDTR measurement at a low modulation frequency f_0, such that the sensitivity to h_Al is comparable but the sensitivity to {\Lambda}cross is near zero. We then analyze the ratio of the TDTR signals at f_h to that at f_0, and thus significantly improve the accuracy of our {\Lambda}cross measurements. As a demonstration of the dual-frequency approach, we measured the cross-plane thermal conductivity of a 400-nm-thick nickel-iron alloy film and a 3-{\mu}m-thick Cu film, both with an accuracy of ~10%. The dual-frequency TDTR approach is useful for future studies of thin films., Comment: 23 pages, 5 figures