Time-domain Thermoreflectance Measurements Research Articles

Covalent bonding modulated graphene-metal interfacial thermal transport.

We report the covalent bonding enabled modulation of the interfacial thermal conductance between graphene and metals Cu, Al, and Pt by controlling the oxidation of graphene. By combining comprehensive X-ray photoelectron spectroscopy (XPS) analysis and time-domain thermoreflectance measurements, we quantify the effect of graphene oxidation on interfacial thermal conductance. It was found that thermal conductance increases with the degree of graphene oxidation until a peak value is obtained at an oxygen/carbon atom percentage of ∼7.7%. The maximum enhancement in thermal conductance was measured to be 55%, 38%, and 49% for interfaces between oxidized graphene and Cu, Al, and Pt, respectively. In situ XPS measurements show that oxygen covalently binds to Cu and graphene simultaneously, forming a highly efficient bridge to enhance the thermal transport. Our molecular dynamics simulations verify that strong interfacial covalent bonds are the key to the thermal conductance enhancement. This work provides valuable insights into the mechanism of functionalization-induced thermal conductance enhancement and design guidelines for graphene-based devices.

Measuring Phonon Mean Free Path Distributions by Probing Quasiballistic Phonon Transport in Grating Nanostructures.

Heat conduction in semiconductors and dielectrics depends upon their phonon mean free paths that describe the average travelling distance between two consecutive phonon scattering events. Nondiffusive phonon transport is being exploited to extract phonon mean free path distributions. Here, we describe an implementation of a nanoscale thermal conductivity spectroscopy technique that allows for the study of mean free path distributions in optically absorbing materials with relatively simple fabrication and a straightforward analysis scheme. We pattern 1D metallic grating of various line widths but fixed gap size on sample surfaces. The metal lines serve as both heaters and thermometers in time-domain thermoreflectance measurements and simultaneously act as wire-grid polarizers that protect the underlying substrate from direct optical excitation and heating. We demonstrate the viability of this technique by studying length-dependent thermal conductivities of silicon at various temperatures. The thermal conductivities measured with different metal line widths are analyzed using suppression functions calculated from the Boltzmann transport equation to extract the phonon mean free path distributions with no calibration required. This table-top ultrafast thermal transport spectroscopy technique enables the study of mean free path spectra in a wide range of technologically important materials.

Limits to Fourier theory in high thermal conductivity single crystals

We report the results of time-domain thermoreflectance (TDTR) experiments that examine the ability of Fourier theory to predict the thermal response in single crystals when heater dimensions are small. We performed TDTR measurements on Al-coated diamond, 6H-SiC, GaP, Ge, MgO, GaAs, and GaSb single crystals with a wide range of laser spot size radii, 0.7 μm < w0 < 12 μm. When the laser spot-size is large, w0 ≈ 12 μm, TDTR data for all crystals are in agreement with predictions of Fourier theory with bulk thermal conductivity values. When the laser spot-size is small, w0 < 2 μm, there are significant differences between the predictions of Fourier theory and TDTR data for all crystals except MgO.

Thermal conductance of metal-diamond interfaces at high pressure.

The thermal conductance of interfaces between metals and diamond, which has a comparatively high Debye temperature, is often greater than can be accounted for by two-phonon processes. The high pressures achievable in a diamond anvil cell (DAC) can significantly extend the metal phonon density of states to higher frequencies, and can also suppress extrinsic effects by greatly stiffening interface bonding. Here we report time-domain thermoreflectance measurements of metal-diamond interface thermal conductance up to 50 GPa in the DAC for Pb, Au0.95Pd0.05, Pt and Al films deposited on type 1A natural [100] and type 2A synthetic [110] diamond anvils. In all cases, the thermal conductances increase weakly or saturate to similar values at high pressure. Our results suggest that anharmonic conductance at metal-diamond interfaces is controlled by partial transmission processes, where a diamond phonon that inelastically scatters at the interface absorbs or emits a metal phonon.

Size effects in the thermal conductivity of gallium oxide (β-Ga2O3) films grown via open-atmosphere annealing of gallium nitride

Gallium nitride (GaN) is a widely used semiconductor for high frequency and high power devices due to of its unique electrical properties: a wide band gap, high breakdown field, and high electron mobility. However, thermal management has become a limiting factor regarding efficiency, lifetime, and advancement of GaN devices and GaN-based applications. In this work, we study the thermal conductivity of beta-phase gallium oxide (β-Ga2O3) thin films, a component of typical gate oxides used in such devices. We use time domain thermoreflectance to measure the thermal conductivity of a variety of polycrystalline β-Ga2O3 films of different thicknesses grown via open atmosphere annealing of the surfaces of GaN films on sapphire substrates. We show that the measured effective thermal conductivity of these β-Ga2O3 films can span 1.5 orders of magnitude, increasing with an increased film thickness, which is indicative of the relatively large intrinsic thermal conductivity of the β-Ga2O3 grown via this technique (8.8 ± 3.4 W m−1 K−1) and large mean free paths compared to typical gate dielectrics commonly used in GaN device contacts. By conducting time domain thermoreflectance (TDTR) measurements with different metal transducers (Al, Au, and Au with a Ti wetting layer), we attribute this variation in effective thermal conductivity to a combination of size effects in the β-Ga2O3 film resulting from phonon scattering at the β-Ga2O3/GaN interface and thermal transport across the β-Ga2O3/GaN interface. The measured thermal properties of open atmosphere-grown β-Ga2O3 and its interface with GaN set the stage for thermal engineering of gate contacts in high frequency GaN-based devices.

Examining thermal transport through a frequency-domain representation of time-domain thermoreflectance data.

Laser-based time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance (FDTR) techniques are widely used for investigating thermal transport at micro- and nano-scales. We demonstrate that data obtained in TDTR measurements can be represented in a frequency-domain form equivalent to FDTR, i.e., in the form of a surface temperature amplitude and phase response to time-harmonic heating. Such a representation is made possible by using a large TDTR delay time window covering the entire pulse repetition interval. We demonstrate the extraction of frequency-domain data up to 1 GHz from TDTR measurements on a sapphire sample coated with a thin layer of aluminum, and show that the frequency dependencies of both the amplitude and phase responses agree well with theory. The proposed method not only allows a direct comparison of TDTR and FDTR data, but also enables measurements at high frequencies currently not accessible to FDTR. The frequency-domain representation helps uncover aspects of the measurement physics which remain obscured in a traditional TDTR measurement, such as the importance of modeling the details of the heat transport in the metal transducer film for analyzing high frequency responses.

Nonlocal theory for heat transport at high frequencies

We develop a nonlocal theory for heat conduction under high-frequency temperature fields and apply the theory to explain reductions of the apparent thermal conductivity observed in recent experiments. Our nonlocal theory is an analytical solution of the Boltzmann transport equation for phonons in a semi-infinite solid, similar to a prior nonlocal theory for heat conduction under a high-temperature gradient but subjected to periodic heating at the surface. The boundary condition of periodic heating, as opposed to prior calculations of heating by a single laser pulse, better mimics time-domain thermoreflectance (TDTR) and broadband frequency-domain thermoreflectance (BB-FDTR) measurements. We find that, except for pure crystals at high frequencies, the effective thermal conductivity derived using the nonlocal theory compares well with calculations of a modified Callaway model that includes an upper limit on the phonon mean-free path at twice the thermal penetration depth. For pure crystals, however, the effective thermal conductivity derived from the out-of-phase calculations are independent of frequency, in agreement with prior TDTR measurements, due to the countereffect of reduced heat flux and diminished relative phase between the heat flux and temperature oscillations at high frequencies. Our results suggest that empirical interpretation of ballistic phonons not contributing to heat conduction is not general and can only be applied to measurements on alloys and not pure crystals, even when a large laser spot size is used in the experiments and the interfacial thermal resistance is negligible.

Pump-probe measurements of the thermal conductivity tensor for materials lacking in-plane symmetry.

We previously demonstrated an extension of time-domain thermoreflectance (TDTR) which utilizes offset pump and probe laser locations to measure in-plane thermal transport properties of multilayers. However, the technique was limited to systems of transversely isotropic materials studied using axisymmetric laser intensities. Here, we extend the mathematics so that data reduction can be performed on non-transversely isotropic systems. An analytic solution of the diffusion equation for an N-layer system is given, where each layer has a homogenous but otherwise arbitrary thermal conductivity tensor and the illuminating spots have arbitrary intensity profiles. As a demonstration, we use both TDTR and time-resolved magneto-optic Kerr effect measurements to obtain thermal conductivity tensor elements of <110> α-SiO2. We show that the out-of-phase beam offset sweep has full-width half-maxima that contains nearly independent sensitivity to the in-plane thermal conductivity corresponding to the scanning direction. Also, we demonstrate a Nb-V alloy as a low thermal conductivity TDTR transducer layer that helps improve the accuracy of in-plane measurements.

Thermal Conductivity of Mechanically Joined Semiconducting/Metal Nanomembrane Superlattices

The decrease of thermal conductivity is crucial for the development of efficient thermal energy converters. Systems composed of a periodic set of very thin layers show among the smallest thermal conductivities reported to-date. Here, we fabricate in an unconventional but straightforward way hybrid superlattices consisting of a large number of nanomembranes mechanically stacked on top of each other. The superlattices can consist of an arbitrary composition of n- or p-type doped single-crystalline semiconductors and a polycrystalline metal layer. These hybrid multilayered systems are fabricated by taking advantage of the self-rolling technique. First, differentially strained nanomembranes are rolled into three-dimensional microtubes with multiple windings. By applying vertical pressure, the tubes are then compressed and converted into a planar hybrid superlattice. The thermal measurements show a substantial reduction of the cross-sectional heat transport through the nanomembrane superlattice compared to a single nanomembrane layer. Time-domain thermoreflectance measurements yield thermal conductivity values below 2 W m(-1) K(-1). Compared to bulk values, this represents a reduction of 2 orders of magnitude by the incorporation of the mechanically joined interfaces. The scanning thermal atomic force microscopy measurements support the observation of reduced thermal transport on top of the superlattices. In addition, small defects with a spatial resolution of ∼100 nm can be resolved in the thermal maps. The low thermal conductivity reveals the potential of this approach to fabricate miniaturized on-chip solutions for energy harvesters in, e.g., microautonomous systems.

Thermal conductivity control by oxygen defect concentration modification in reducible oxides: The case of Pr0.1Ce0.9O2−δ thin films

We demonstrate the impact on thermal conductivity of varying the concentration of oxygen vacancies and reduced cations in Pr0.1Ce0.9O2−δ thin films prepared by pulsed laser deposition. The oxygen vacancy concentration is controlled by varying the oxygen partial pressure between 1 × 10−4 and 1 atm at 650 °C. Corresponding changes in the oxygen non-stoichiometry (δ) are monitored by detecting the lattice parameters of the films with high-resolution X-ray diffraction, while the thermal properties are characterized by time-domain thermoreflectance measurements. The films are shown to exhibit a variation in oxygen vacancy content, and in the Pr3+/Pr4+ ratio, corresponding to changes in δ from 0.0027 to 0.0364, leading to a reduction in the thermal conductivity from k = 6.62 ± 0.61 to 3.82 ± 0.51 W/m-K, respectively. These values agree well with those predicted by the Callaway and von Baeyer model for thermal conductivity in the presence of point imperfections. These results demonstrate the capability of controlling thermal conductivity via control of anion and cation defect concentrations in a given reducible oxide.

Two-channel model for nonequilibrium thermal transport in pump-probe experiments

We present an analytic solution for heat flow in a multilayer two-channel system for the interpretation of time-domain thermoreflectance (TDTR) experiments where nonequilibrium effects are important. The two-channel solution is used to analyze new room temperature TDTR measurements of Al/Cu and Al/Si${}_{0.99}$Ge${}_{0.01}$ systems. Cu and Si${}_{0.99}$Ge${}_{0.01}$ are examples of materials well suited for analysis with a two-channel model because thermal excitations responsible for the vast majority of the heat capacity in these solids contribute little to their thermal conductivity. Nonequilibrium effects are found to be unimportant for the interpretation of the Al/Cu TDTR data but dramatic for the Al/Si${}_{0.99}$Ge${}_{0.01}$ TDTR data. The two-channel model predicts a significant reduction in the effective thermal conductivity of Si${}_{0.99}$Ge${}_{0.01}$ in a region within 150 nm of the Al/Si${}_{0.99}$Ge${}_{0.01}$ interface. The extra thermal resistance in this region is a result of the disparate heat flux boundary conditions for low- and high-frequency phonons in combination with weak coupling between low- and high-frequency phonons. When the experimental data are analyzed with a single-channel model, both the conductance and thermal conductivity appear to depend on pump-modulation frequency, consistent with the two-channel model's predictions. Finally, we compare the results of our diffusive two-channel model to a nonlocal description for steady-state heat flow near a boundary and show they yield nearly identical results.

Mean Free Path Effects on the Experimentally Measured Thermal Conductivity of Single-Crystal Silicon Microbridges

Accurate thermal conductivity values are essential for the successful modeling, design, and thermal management of microelectromechanical systems (MEMS) and devices. However, the experimental technique best suited to measure the thermal conductivity of these systems, as well as the thermal conductivity itself, varies with the device materials, fabrication processes, geometry, and operating conditions. In this study, the thermal conductivities of boron doped single-crystal silicon microbridges fabricated using silicon-on-insulator (SOI) wafers are measured over the temperature range from 80 to 350 K. The microbridges are 4.6 mm long, 125 μm tall, and either 50 or 85 μm wide. Measurements on the 85 μm wide microbridges are made using both steady-state electrical resistance thermometry (SSERT) and optical time-domain thermoreflectance (TDTR). A thermal conductivity of 77 Wm−1 K−1 is measured for both microbridge widths at room temperature, where the results of both experimental techniques agree. However, increasing discrepancies between the thermal conductivities measured by each technique are found with decreasing temperatures below 300 K. The reduction in thermal conductivity measured by TDTR is primarily attributed to a ballistic thermal resistance contributed by phonons with mean free paths larger than the TDTR pump beam diameter. Boltzmann transport equation (BTE) modeling under the relaxation time approximation (RTA) is used to investigate the discrepancies and emphasizes the role of different interaction volumes in explaining the underprediction of TDTR measurements.

Phonon and electron transport through Ge2Sb2Te5 films and interfaces bounded by metals

While atomic vibrations dominate thermal conduction in the amorphous and face-centered cubic phases of Ge2Sb2Te5, electrons dominate in the hexagonal closed-packed (hcp) phase. Here we separate the electron and phonon contributions to the interface and volume thermal resistances for the three phases using time-domain thermoreflectance and electrical contact resistance measurements. Even when electrons dominate film-normal volume conduction (i.e., 70% for the hcp phase), their contribution to interface heat conduction is overwhelmed by phonons for high-quality interfaces with metallic TiN.

Simultaneous measurement of thermal conductivity and heat capacity of bulk and thin film materials using frequency-dependent transient thermoreflectance method

The increasing interest in the extraordinary thermal properties of nanostructures has led to the development of various measurement techniques. Transient thermoreflectance method has emerged as a reliable measurement technique for thermal conductivity of thin films. In this method, the determination of thermal conductivity usually relies much on the accuracy of heat capacity input. For new nanoscale materials with unknown or less-understood thermal properties, it is either questionable to assume bulk heat capacity for nanostructures or difficult to obtain the bulk form of those materials for a conventional heat capacity measurement. In this paper, we describe a technique for simultaneous measurement of thermal conductivity κ and volumetric heat capacity C of both bulk and thin film materials using frequency-dependent time-domain thermoreflectance (TDTR) signals. The heat transfer model is analyzed first to find how different combinations of κ and C determine the frequency-dependent TDTR signals. Simultaneous measurement of thermal conductivity and volumetric heat capacity is then demonstrated with bulk Si and thin film SiO2 samples using frequency-dependent TDTR measurement. This method is further testified by measuring both thermal conductivity and volumetric heat capacity of novel hybrid organic-inorganic thin films fabricated using the atomic∕molecular layer deposition. Simultaneous measurement of thermal conductivity and heat capacity can significantly shorten the development∕discovery cycle of novel materials.

Microcrystalline diamond micromechanical resonators with quality factor limited by thermoelastic damping

Thin-film microcrystalline diamond micromechanical resonators with mechanical quality factor limited by thermoelastic dissipation in the diamond film are demonstrated. Surface micromachined double ended tuning fork resonators were fabricated from in-situ boron doped microcrystalline diamond films deposited using hot filament chemical vapor deposition. Time-domain thermoreflectance measurements show thermal conductivity of 110 W m−1 K−1 for heat transport through the thickness of the diamond film. Measurement of the quality factor of resonators spanning a frequency range 0.5–10 MHz shows a maximum Q = 81 646 and demonstrates good agreement with quality factor limited by thermoelastic dissipation using 100 W m−1 K−1 for the in-plane thermal conductivity of the diamond film.

Interpreting picosecond acoustics in the case of low interface stiffness

Analysis of data acquired in time-domain thermoreflectance (TDTR) experiments requires accurate measurements of the thickness of the metal film optical transducer that absorbs energy from the pump optical pulse and provides a temperature dependent reflectivity that is interrogated by the probe optical pulse. This thickness measurement is typically accomplished using picosecond acoustics. The presence of contaminants and native oxides at the interface between the sample and transducer often produce a picosecond acoustics signal that is difficult to interpret. We describe heuristics for addressing this common difficulty in interpreting picosecond acoustic data. The use of these heuristics can reduce the propagation of uncertainties and improve the accuracy of TDTR measurements of thermal transport properties.

Role of phonon anharmonicity in time-domain thermoreflectance measurements

Using ab-initio calculations, we argue that the apparent frequency dependence of the thermal conductivity measured by time-domain thermoreflectance (TDTR) is majorly determined by the balance between harmonic (elastic) and anharmonic (inelastic) phonon channels, and not by ballistic phonons. The match between this theory and experiment is closer than that obtained with previous models. Concrete trends in frequency and temperature dependence are predicted. Reinterpreting frequency modulated time-domain thermoreflectance in terms of elastic vs. inelastic channels explains the markedly different behavior between alloys and non-alloys, and the approach can in principle be applied to other nanostructured material systems.

Low Thermal Resistances at GaN–SiC Interfaces for HEMT Technology

The temperature rise in AlGaN/GaN high-electron-mobility transistors depends strongly on the GaN-substrate thermal interface resistance (TIR). We apply picosecond time-domain thermoreflectance measurements to GaN-SiC composite substrates with varying GaN thickness to extract both the TIR and the intrinsic GaN thermal conductivity at room temperature. Two complementary data extraction methodologies yield 4-5 for the GaN-SiC TIR and 157-182 for the GaN conductivity. The GaN-SiC interface resistance values reported here, as well as the TIR experimental uncertainties documented in this letter, are substantially lower than those reported previously for this material combination.

Structural and Thermal Properties of Single Crystalline Epitaxial Gd2O3 and Er2O3 Grown on Si(111)

Lattice mismatch with a substrate and difference in coefficient of thermal expansion to the substrate induces stress and deformations in crystalline structure of epitaxially grown layers. In this work, we present results of structural study of gadolinium oxide and erbium oxide grown on silicon (111) substrate applying X-ray diffraction at room temperature and during in-situ heating up to 1273 K. The layers are almost fully relaxed at room temperature. Only minor tetragonal distortion of the crystal lattice was indirectly detected. No thermal induced stress relaxation occurs in the oxide layer during the in-situ heating and cooling procedure though strong tetragonal distortion of the oxide lattice due to thermal expansion difference with silicon. The time-domain thermo-reflectance measurements reveal that thermal conductivity of the rare earth oxides is approximately five times higher than that of silicon dioxide.

Assessing the thermal conductivity of non-uniform thin-films: Nanocrystalline Cu composites incorporating carbon nanotubes

We demonstrate a procedure for measuring the thermal conductivity of non-ideal thin-films with significant non-uniformity. By spatially mapping the thermal transport with time-domain thermoreflectance measurements, followed by statistical analysis, we determined the thermal conductivity of Cu composite films containing dispersed carbon nanotubes (CNTs). The thermal conductivity of the composite decreased from 188 to 60 W/m K as 1.8 wt. % of multi-walled CNTs was incorporated into nanocrystalline Cu. We compared the decreasing trend with that calculated from a scattering model to find out that the CNTs scatter the heat carriers in Cu.