Analysis of heat flow in modified transient plane source (MTPS) measurements of the thermal effusivity and thermal conductivity of materials.

An iterative algorithm for the diffusion of heat in layered structures is solved in cylindrical coordinates for the geometry used in measurements of thermophysical properties of materials by the modified transient plane source (MTPS) method. This solution for the frequency-domain temperature response is then used to model the transient temperature excursion and evaluate the accuracy of the measurements. We evaluate when the MTPS method is capable of separately determining the thermal conductivity and heat capacity per unit volume of a material. For a typical sensor design, data acquisition, and data analysis, the MTPS measurement has a small sensitivity to the thermal diffusivity of the sample when the thermal diffusivity is <5 mm2 s-1. We analyze the propagation of errors from uncertainties in the thermal contact between the sensor and the sample and evaluate the limitations of the MTPS method in accurately measuring samples with extremely low thermal effusivity, e.g., low density foam insulation. We find that uncertainties in the thickness of the contact region limit the accuracy of MTPS measurements when the data are analyzed in a conventional manner based on a single parameter, m-1, the inverse of the slope of the temperature excursion as a function of the square root of time.

Ionic Peltier effect in Li-ion electrolytes.

The coupled transport of charge and heat provide fundamental insights into the microscopic thermodynamics and kinetics of materials. We describe a sensitive ac differential resistance bridge that enables measurements of the temperature difference on two sides of a coin cell with a resolution of better than 10 µK. We use this temperature difference metrology to determine the ionic Peltier coefficients of symmetric Li-ion electrochemical cells as a function of Li salt concentration, solvent composition, electrode material, and temperature. The Peltier coefficients Π are negative, i.e., heat flows in the direction opposite to the drift of Li ions in the applied electric field, large, -Π > 30 kJ mol-1, and increase with increasing temperature at T > 300 K. The Peltier coefficient is approximately constant on time scales that span the characteristic time for mass diffusion across the thickness of the electrolyte, suggesting that heat of transport plays a minor role in comparison to the changes in partial molar entropy of Li at the interface between the electrode and electrolyte. Our work demonstrates a new platform for studying the non-equilibrium thermodynamics of electrochemical cells and provides a window into the transport properties of electrochemical materials through measurements of temperature differences and heat currents that complement traditional measurements of voltages and charge currents.

Hybrid achromatic microlenses with high numerical apertures and focusing efficiencies across the visible.

Compact visible wavelength achromats are essential for miniaturized and lightweight optics. However, fabrication of such achromats has proved to be exceptionally challenging. Here, using subsurface 3D printing inside mesoporous hosts we densely integrate aligned refractive and diffractive elements, forming thin high performance hybrid achromatic imaging micro-optics. Focusing efficiencies of 51-70% are achieved for 15µm thick, 90µm diameter, 0.3 numerical aperture microlenses. Chromatic focal length errors of less than 3% allow these microlenses to form high-quality images under broadband illumination (400-700 nm). Numerical apertures upwards of 0.47 are also achieved at the cost of some focusing efficiency, demonstrating the flexibility of this approach. Furthermore, larger area images are reconstructed from an array of hybrid achromatic microlenses, laying the groundwork for achromatic light-field imagers and displays. The presented approach precisely combines optical components within 3D space to achieve thin lens systems with high focusing efficiencies, high numerical apertures, and low chromatic focusing errors, providing a pathway towards achromatic micro-optical systems.

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).

Topological Metal MoP Nanowire for Interconnect.

The increasing resistance of copper (Cu) interconnects for decreasing dimensions is a major challenge in continued downscaling of integrated circuits beyond the 7 nm technology node as it leads to unacceptable signal delays and power consumption in computing. The resistivity of Cu increases due to electron scattering at surfaces and grain boundaries at the nanoscale. Topological semimetals, owing to their topologically protected surface states and suppressed electron backscattering, are promising candidates to potentially replace current Cu interconnects. Here, we report the unprecedented resistivity scaling of topological metal molybdenum phosphide (MoP) nanowires, and it is shown that the resistivity values are superior to those of nanoscale Cu interconnects <500 nm2 cross-section areas. The cohesive energy of MoP suggests better stability against electromigration, enabling a barrier-free design . MoP nanowires are more resistant to surface oxidation than the 20 nm thick Cu. The thermal conductivity of MoP is comparable to those of Ru and Co. Most importantly, it is demonstrated that the dimensional scaling of MoP, in terms of line resistance versus total cross-sectional area, is competitive to those of effective Cu with barrier/liner and barrier-less Ru, suggesting MoP is an attractive alternative for the scaling challenge of Cu interconnects.

Angstrom-scale imaging of magnetization in antiferromagnetic Fe2As via 4D-STEM.

We demonstrate a combination of computational tools and experimental 4D-STEM methods to image the local magnetic moment in antiferromagnetic Fe2As with 6 angstrom spatial resolution. Our techniques utilize magnetic diffraction peaks, common in antiferromagnetic materials, to create imaging modes that directly visualize the magnetic lattice. Using this approach, we show that center-of-mass analysis can determine the local magnetization component in the plane perpendicular to the path of the electron beam. Moreover, we develop Magnstem, a quantum mechanical electron scattering simulation code, to model electron scattering of an angstrom-scale probe from magnetic materials. Using these tools, we identify optimal experimental conditions for separating weak magnetic signals from the much stronger interactions of an angstrom-scale probe with electrostatic potentials. Our techniques should be useful for characterizing the local magnetic order in systems such in thin films, interfaces, and domain boundaries of antiferromagnetic materials, which are difficult to probe with existing methods.

Odd-even effect on the thermal conductivity of liquid crystalline epoxy resins.

Rapid developments in high-performance computing and high-power electronics are driving needs for highly thermal conductive polymers and their composites for encapsulants and interface materials. However, polymers typically have low thermal conductivities of ∼0.2 W/(m K). We studied the thermal conductivity of a series of epoxy resins cured by one diamine hardener and seven diepoxide monomers with different precise ethylene linker lengths (x = 2-8). We found pronounced odd-even effects of the ethylene linker length on the liquid crystalline order, mass density, and thermal conductivity. Epoxy resins with even x have liquid crystalline structure with the highest density of 1.44 g/cm3 and highest thermal conductivity of 1.0 W/(m K). Epoxy resins with odd x are amorphous with the lowest density of 1.10 g/cm3 and lowest thermal conductivity of 0.17 W/(m K). These findings indicate that controlling precise linker length in dense networks is a powerful route to molecular design of thermally conductive polymers.

High thermal conductivity in wafer-scale cubic silicon carbide crystals.

High thermal conductivity electronic materials are critical components for high-performance electronic and photonic devices as both active functional materials and thermal management materials. We report an isotropic high thermal conductivity exceeding 500 W m-1K-1 at room temperature in high-quality wafer-scale cubic silicon carbide (3C-SiC) crystals, which is the second highest among large crystals (only surpassed by diamond). Furthermore, the corresponding 3C-SiC thin films are found to have record-high in-plane and cross-plane thermal conductivity, even higher than diamond thin films with equivalent thicknesses. Our results resolve a long-standing puzzle that the literature values of thermal conductivity for 3C-SiC are lower than the structurally more complex 6H-SiC. We show that the observed high thermal conductivity in this work arises from the high purity and high crystal quality of 3C-SiC crystals which avoids the exceptionally strong defect-phonon scatterings. Moreover, 3C-SiC is a SiC polytype which can be epitaxially grown on Si. We show that the measured 3C-SiC-Si thermal boundary conductance is among the highest for semiconductor interfaces. These findings provide insights for fundamental phonon transport mechanisms, and suggest that 3C-SiC is an excellent wide-bandgap semiconductor for applications of next-generation power electronics as both active components and substrates.

Role of Thin Film Adhesion on Capillary Peeling.

The capillary force can peel off a substrate-attached film if the adhesion energy (Gw) is low. Capillary peeling has been used as a convenient, rapid, and nondestructive method for fabricating free-standing thin films. However, the critical value of Gw, which leads to the transition between peeling and sticking, remains largely unknown. As a result, capillary peeling remains empirical and applicable to a limited set of materials. Here, we investigate the critical value of Gw and experimentally show the critical adhesion (Gw,c) to scale with the water-film interfacial energy (≈0.7γfw), which corresponds well with our theoretical prediction of Gw,c = γfw. Based on the critical adhesion, we propose quantitative thermodynamic guidelines for designing thin film interfaces that enable successful capillary peeling. The outcomes of this work present a powerful technique for thin film transfer and advanced nanofabrication in flexible photovoltaics, battery materials, biosensing, translational medicine, and stretchable bioelectronics.

Extremely anisotropic van der Waals thermal conductors.

The densification of integrated circuits requires thermal management strategies and high thermal conductivity materials1-3. Recent innovations include the development of materials with thermal conduction anisotropy, which can remove hotspots along the fast-axis direction and provide thermal insulation along the slow axis4,5. However, most artificially engineered thermal conductors have anisotropy ratios much smaller than those seen in naturally anisotropic materials. Here we report extremely anisotropic thermal conductors based on large-area van der Waals thin films with random interlayer rotations, which produce a room-temperature thermal anisotropy ratio close to 900 in MoS2, one of the highest ever reported. This is enabled by the interlayer rotations that impede the through-plane thermal transport, while the long-range intralayer crystallinity maintains high in-plane thermal conductivity. We measure ultralow thermal conductivities in the through-plane direction for MoS2 (57 ± 3 mW m-1 K-1) and WS2 (41 ± 3 mW m-1 K-1) films, and we quantitatively explain these values using molecular dynamics simulations that reveal one-dimensional glass-like thermal transport. Conversely, the in-plane thermal conductivity in these MoS2 films is close to the single-crystal value. Covering nanofabricated gold electrodes with our anisotropic films prevents overheating of the electrodes and blocks heat from reaching the device surface. Our work establishes interlayer rotation in crystalline layered materials as a new degree of freedom for engineering-directed heat transport in solid-state systems.

Thermal Visualization of Buried Interfaces Enabled by Ratio Signal and Steady-State Heating of Time-Domain Thermoreflectance.

Thermal resistances from interfaces impede heat dissipation in micro/nanoscale electronics, especially for high-power electronics. Despite the growing importance of understanding interfacial thermal transport, advanced thermal characterization techniques that can visualize thermal conductance across buried interfaces, especially for nonmetal-nonmetal interfaces, are still under development. This work reports a dual-modulation-frequency time-domain thermoreflectance (TDTR) mapping technique (1.61 and 9.3 MHz) to visualize the thermal conduction across buried semiconductor interfaces for ß-Ga2O3-SiC samples. Both the ß-Ga2O3 thermal conductivity and the buried ß-Ga2O3-SiC thermal boundary conductance (TBC) are visualized for an area of 200 × 200 µm simultaneously. Areas with low TBC values (≤20 MW/m2·K) are identified on the TBC map, which correspond to weakly bonded interfaces caused by high-temperature annealing. Additionally, the steady-state temperature rise induced by the TDTR laser, usually ignored in TDTR analysis, is found to be able to probe TBC variations of the buried interfaces without the typical limit of thermal penetration depth. This technique can be applied to detect defects/voids in deeply buried heterogeneous interfaces nondestructively and also opens a door for the visualization of thermal conductance in nanoscale nonhomogeneous structures.

Good Solid-State Electrolytes Have Low, Glass-Like Thermal Conductivity.

Thermal management in Li-ion batteries is critical for their safety, reliability, and performance. Understanding the thermal conductivity of the battery materials is crucial for controlling the temperature and temperature distribution in batteries. This work provides systemic quantitative measurements of the thermal conductivity of three important classes of solid electrolytes (SEs) over the temperature range 150 < T < 350 K. Studies include the oxides Li1.5 Al0.5 Ge1.5 (PO4 )3 and Li6.4 La3 Zr1.4 Ta0.6 O12 , sulfides Li2 S-P2 S5 , Li6 PS5 Cl, and Na3 PS4 , and halides Li3 InCl6 and Li3 YCl6 . Thermal conductivities of sulfide and halide SEs are in the range 0.45-0.70 W m-1  K-1 ; thermal conductivities of Li6.4 La3 Zr1.4 Ta0.6 O12 and Li1.5 Al0.5 Ge1.5 (PO4 )3 are 1.4 and 2.2 W m-1  K-1 , respectively. For most of the SEs studied in this work, the thermal conductivity increases with increasing temperature, that is, the thermal conductivity has a glass-like temperature dependence. The measured room-temperature thermal conductivities agree well with the calculated minimum thermal conductivities indicating that the phonon mean-free-paths in these SEs are close to an atomic spacing. The low, glass-like thermal conductivity of the SEs investigated is attributed to the combination of their complex crystal structures and the atomic-scale disorder induced by the materials processing methods that are typically needed to produce high ionic conductivities.

Effect of Linker Length and Temperature on the Thermal Conductivity of Ethylene Dynamic Networks.

Dynamic covalent networks are a class of polymers containing exchangeable bonds. The influence of the thermodynamics and kinetics of dynamic bond exchange on the thermal conductivity and mechanical properties of dynamic networks is important for understanding how they differ from thermoplastics and thermosets. In this work, a series of ethylene dynamic networks are synthesized from benzene diboronic acid and alkane diols with different precise ethylene linker lengths. The thermal conductivity of these ethylene dynamic networks at 40 °C decreases from 0.19 to 0.095 W/(m K) when the ethylene linker length increases from 4 to 12 carbons. The thermal conductivity also has a strong temperature dependence, decreasing by a factor of 3 over the temperature range from -80 °C to 100 °C. The minimum thermal conductivity model predicts these trends of the thermal conductivity with variations in ethylene linker length and temperature.

Microscale, bendable thermoreflectance sensor for local measurements of the thermal effusivity of biological fluids and tissues.

Measurements of the thermal transport properties of biological fluids and tissues are important for biomedical applications such as thermal diagnostics and thermal therapeutics. Here, we describe a microscale thermoreflectance sensor to measure the thermal effusivity of fluids and biological samples in a minimally invasive manner. The sensor is based on ultrafast optical pump-probe techniques and employs a metal-coated optical fiber as both a photonic waveguide and a local probe. Calibration of the sensor with five liquids shows that the percentage deviation between experimentally measured effusivity and literature values is on average <3%. We further demonstrate the capability of the sensor by measuring the thermal effusivity of vegetable oil, butter, pork liver, and quail egg white and yolk. We relate the thermal effusivity of the samples to their composition and water content, and establish our technique as a powerful and flexible method for studying the local thermal transport properties of biological materials.

Condensation Induced Blistering as a Measurement Technique for the Adhesion Energy of Nanoscale Polymer Films.

Polymeric coatings having micro-to-nanoscale thickness show immense promise for enhancing thermal transport, catalysis, energy conversion, and water collection. Characterizing the work of adhesion (G) between these coatings and their substrates is key to understanding transport physics as well as mechanical reliability. Here, we demonstrate that water vapor condensation blistering is capable of in situ measurement of work of adhesion at the interface of polymer thin films with micrometer spatial resolution. We use our method to characterize adhesion of interfaces with controlled chemistry such as fluorocarbon/fluorocarbon (CFn/CFm, n, m = 0-3), fluorocarbon/hydrocarbon (CFn/CHm), fluorocarbon/silica (CFn/SiO2), and hydrocarbon/silica (CHn/SiO2) interfaces showing excellent agreement with adhesion energy measured by the contact angle approach. We demonstrate the capability of our condensation blister test to achieve measurement spatial resolutions as low as 10 µm with uncertainties of ∼10%. The outcomes of this work establish a simple tool to study interfacial adhesion.

Ultrahigh thermal conductivity in isotope-enriched cubic boron nitride.

Materials with high thermal conductivity (κ) are of technological importance and fundamental interest. We grew cubic boron nitride (cBN) crystals with controlled abundance of boron isotopes and measured κ greater than 1600 watts per meter-kelvin at room temperature in samples with enriched 10B or 11B. In comparison, we found that the isotope enhancement of κ is considerably lower for boron phosphide and boron arsenide as the identical isotopic mass disorder becomes increasingly invisible to phonons. The ultrahigh κ in conjunction with its wide bandgap (6.2 electron volts) makes cBN a promising material for microelectronics thermal management, high-power electronics, and optoelectronics applications.

Anomalous spin-orbit torques in magnetic single-layer films.

The spin Hall effect couples charge and spin transport1-3, enabling electrical control of magnetization4,5. A quintessential example of spin-Hall-related transport is the anomalous Hall effect (AHE)6, first observed in 1880, in which an electric current perpendicular to the magnetization in a magnetic film generates charge accumulation on the surfaces. Here, we report the observation of a counterpart of the AHE that we term the anomalous spin-orbit torque (ASOT), wherein an electric current parallel to the magnetization generates opposite spin-orbit torques on the surfaces of the magnetic film. We interpret the ASOT as being due to a spin-Hall-like current generated with an efficiency of 0.053 ± 0.003 in Ni80Fe20, comparable to the spin Hall angle of Pt7. Similar effects are also observed in other common ferromagnetic metals, including Co, Ni and Fe. First-principles calculations corroborate the order of magnitude of the measured values. This work suggests that a strong spin current with spin polarization transverse to the magnetization can be generated within a ferromagnet, despite spin dephasing8. The large magnitude of the ASOT should be taken into consideration when investigating spin-orbit torques in ferromagnetic/non-magnetic bilayers.