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.

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.

Frequency domain thermoreflectance technique for measuring the thermal conductivity of individual micro-particles.

The thermal properties of micron scale particles are an important factor in the design of composite materials and other applications. Here we present an optical technique based on frequency domain thermoreflectance (FDTR) that is capable of measuring the thermal conductivity of individual particles a few microns across. In addition, the technique can provide values for a particle's effective volume which is a new capability compared to conventional FDTR applied to multilayer samples. We also show and explain the response of systems that constrain heat flow along the in-plane direction due to a boundary. We tested this technique with natural diamond and doped silicon particles of different sizes. For the diamond particles, the thermal conductivity values obtained were within the range of reported literature values, while for the silicon particles, the thermal conductivities were slightly lower than the bulk sample they were fabricated from, possibly due to defects introduced during the fabrication process.

Unusual high thermal conductivity in boron arsenide bulk crystals.

Conventional theory predicts that ultrahigh lattice thermal conductivity can only occur in crystals composed of strongly bonded light elements, and that it is limited by anharmonic three-phonon processes. We report experimental evidence that departs from these long-held criteria. We measured a local room-temperature thermal conductivity exceeding 1000 watts per meter-kelvin and an average bulk value reaching 900 watts per meter-kelvin in bulk boron arsenide (BAs) crystals, where boron and arsenic are light and heavy elements, respectively. The high values are consistent with a proposal for phonon-band engineering and can only be explained by higher-order phonon processes. These findings yield insight into the physics of heat conduction in solids and show BAs to be the only known semiconductor with ultrahigh thermal conductivity.

Uncertainty analysis of thermoreflectance measurements.

We derive a generally applicable formula to calculate the precision of multi-parameter measurements that apply least squares algorithms. This formula, which accounts for experimental noise and uncertainty in the controlled model parameters, is then used to analyze the uncertainty of thermal property measurements with pump-probe thermoreflectance techniques. We compare the uncertainty of time domain thermoreflectance and frequency domain thermoreflectance (FDTR) when measuring bulk materials and thin films, considering simultaneous measurements of various combinations of thermal properties, including thermal conductivity, heat capacity, and thermal boundary conductance. We validate the uncertainty analysis using Monte Carlo simulations on data from FDTR measurements of an 80 nm gold film on fused silica.

Thermal property microscopy with frequency domain thermoreflectance.

A thermal property microscopy technique based on frequency domain thermoreflectance (FDTR) is presented. In FDTR, a periodically modulated laser locally heats a sample while a second probe beam monitors the surface reflectivity, which is related to the thermal properties of the sample with an analytical model. Here, we extend FDTR into an imaging technique capable of producing micrometer-scale maps of several thermophysical properties simultaneously. Thermal phase images are recorded at multiple frequencies chosen for maximum sensitivity to thermal properties of interest according to a thermal model of the sample. The phase versus frequency curves are then fit point-by-point to obtain quantitative thermal property images of various combinations of thermal properties in multilayer samples, including the in-plane and cross-plane thermal conductivities, heat capacity, thermal interface conductance, and film thickness. An FDTR microscope based on two continuous-wave lasers is described, and a sensitivity analysis of the technique to different thermal properties is carried out. As a demonstration, we image ~3 nm of patterned titanium under 100 nm of gold on a silicon substrate, and simultaneously create maps of the thermal interface conductance and substrate thermal conductivity. Results confirm the potential of our technique for imaging and quantifying thermal properties of buried layers, indicating its utility for mapping thermal properties in integrated circuits.

Measurement of carbon nanotube microstructure relative density by optical attenuation and observation of size-dependent variations.

Engineering the density of carbon nanotube (CNT) forest microstructures is vital to applications such as electrical interconnects, micro-contact probes, and thermal interface materials. For CNT forests on centimeter-scale substrates, weight and volume can be used to calculate density. However, this is not suitable for smaller samples, including individual microstructures, and moreover does not enable mapping of spatial density variations within the forest. We demonstrate that the relative mass density of individual CNT microstructures can be measured by optical attenuation, with spatial resolution equaling the size of the focused spot. For this, a custom optical setup was built to measure the transmission of a focused laser beam through CNT microstructures. The transmittance was correlated with the thickness of the CNT microstructures by Beer-Lambert-Bouguer law to calculate the attenuation coefficient. We reveal that the density of CNT microstructures grown by CVD can depend on their size, and that the overall density of arrays of microstructures is affected significantly by run-to-run process variations. Further, we use the technique to quantify the change in CNT microstructure density due to capillary densification. This is a useful and accessible metrology technique for CNTs in future microfabrication processes, and will enable direct correlation of density to important properties such as stiffness and electrical conductivity.

Coherent phonon heat conduction in superlattices.

The control of heat conduction through the manipulation of phonons as coherent waves in solids is of fundamental interest and could also be exploited in applications, but coherent heat conduction has not been experimentally confirmed. We report the experimental observation of coherent heat conduction through the use of finite-thickness superlattices with varying numbers of periods. The measured thermal conductivity increased linearly with increasing total superlattice thickness over a temperature range from 30 to 150 kelvin, which is consistent with a coherent phonon heat conduction process. First-principles and Green's function-based simulations further support this coherent transport model. Accessing the coherent heat conduction regime opens a new venue for phonon engineering for an array of applications.

Nuclear reactor pulse calibration using a CdZnTe electro-optic radiation detector.

A CdZnTe electro-optic radiation detector was used to calibrate nuclear reactor pulses. The standard configuration of the Pockels cell has collimated light passing through an optically transparent CdZnTe crystal located between crossed polarizers. The transmitted light was focused onto an IR sensitive photodiode. Calibrations of reactor pulses were performed using the CdZnTe Pockels cell by measuring the change in the photodiode current, repeated 10 times for each set of reactor pulses, set between 1.00 and 2.50 dollars in 0.50 increments of reactivity.

A frequency-domain thermoreflectance method for the characterization of thermal properties.

A frequency-domain thermoreflectance method for measuring the thermal properties of homogenous materials and submicron thin films is described. The method can simultaneously determine the thermal conductivity and heat capacity of a sample, provided the thermal diffusivity is greater, similar3x10(-6) m(2)/s, and can also simultaneously measure in-plane and cross-plane thermal conductivities, as well the thermal boundary conductance between material layers. Two implementations are discussed, one based on an ultrafast pulsed laser system and one based on continuous-wave lasers. The theory of the method and an analysis of its sensitivity to various thermal properties are given, along with results from measurements of several standard materials over a wide range of thermal diffusivities. We obtain specific heats and thermal conductivities in good agreement with literature values, and also obtain the in-plane and cross-plane thermal conductivities for crystalline quartz.

Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump-probe transient thermoreflectance.

The relationship between pulse accumulation and radial heat conduction in pump-probe transient thermoreflectance (TTR) is explored. The results illustrate how pulse accumulation allows TTR to probe two thermal length scales simultaneously. In addition, the conditions under which radial transport effects are important are described. An analytical solution for anisotropic heat flow in layered structures is given, and a method for measuring both cross-plane and in-plane thermal conductivities of thermally anisotropic thin films is described. As verification, the technique is used to extract the cross-plane and in-plane thermal conductivities of highly ordered pyrolytic graphite. Results are found to be in good agreement with literature values.