Thermal conductivity assessment in a low dimension structure

The present work describes the method by which the thermal resistance of a flat heat pipe spreader can be more accurately computed. The total effectiveness of the heat spreader is dependent on the one-dimensional (R1D) thermal resistance and the thermal spreading resistance (Rs). Recently developed more accurate methods from the literature were used to calculate the spreading resistance by taking into account all the multiple layers of the heat pipe. Both R1D and Rs depend to a large extent on the effective thermal conductivity of the wick. The calculation of effective thermal conductivity of wick is demonstrated using well-defined silicon micropillars. The effect of interfacial heat transfer resistance, which is usually neglected on the wick's thermal resistance is also discussed. Finally, the effective thermal conductivity of a flat heat pipe as a function of vapor chamber size and effective wick thermal conductivity is calculated. As the overall device performance strongly depends on the estimation of wick thermal resistance, the results of this study show that an effective thermal conductivity that is equal to or better than diamond can be attained with proper design. Furthermore, this work provides design tools that can be used to optimize the overall device level thermal performance.

Abstract. Phonon transport in a two-dimensional thin silicon film is considered and the effect of heat source size and the film thickness on the transport characteristics is examined. Frequency dependent Boltzmann equation is incorporated in the analysis to account for the contribution of the ballistic phonons to the energy transport. Equivalent equilibrium temperature is introduced to assess the thermal resistance during the phonon transport in the film. The numerical scheme with the appropriate boundary conditions is used to predict the transport properties, including the effective thermal conductivity, of the thin film. It is found that the heat source size and the film thickness influence the thermal resistance of the film almost equally. The ballistic phonons reduce the film thermal resistance while suppressing the effective thermal conductivity in the thin film.

Significant reductions in both the in-plane and cross-plane thermal conductivities of superlattices, in comparison to the values calculated from the Fourier heat conduction theory using bulk material properties, have been observed experimentally in recent years. Understanding the mechanisms controlling the thermal conductivities of superlattice structures is of considerable current interest for microelectronic and thermoelectric applications. In this work, models of the thermal conductivity and phonon transport in the direction perpendicular to the film plane of superlattices are established based on solving the phonon Boltzmann transport equation (BTE). Different phonon interface scattering mechanisms are considered, including elastic vs inelastic, and diffuse vs specular scattering of phonons. Numerical solution of the BTE yields the effective temperature distribution, thermal conductivity, and thermal boundary resistance (TBR) of the superlattices. The modeling results show that the effective thermal conductivity of superlattices in the perpendicular direction is generally controlled by phonon transport within each layer and the TBR between different layers. The TBR is no longer an intrinsic property of the interface, but depends on the layer thickness as well as the phonon mean free path. In the thin layer limit, phonon transport within each layer is ballistic, and the TBR dominates the effective thermal conductivity of superlattices. Approximate analytical solutions of the BTE are obtained for this thin-film limit. The modeling results based on partially specular and partially diffuse interface scattering processes are in reasonable agreement with recent experimental data on GaAs/AlAs and Si/Ge superlattices. From the modeling, it is concluded that the cross-plane thermal conductivity of these superlattices is controlled by diffuse and inelastic scattering processes at interfaces. Results of this work suggest that it is possible to make superlattice structures with thermal conductivity totally different from those of their constituting materials.

III-Nitrides promise to offer high-frequency power amplifiers at higher power densities. This is attractive for realizing device platforms for 5G and beyond. It also enables integrating Si-based electronics to complement functionalities. However, to obtain the full potential of III-Nitrides one must operate these transistors at higher power densities, for which thermal management is crucial.Due to the continuous need for higher performance in various applications ranging from DC to W-band frequencies, semiconductor devices are pushed to higher power densities. This results in a higher junction temperature owing to the Joule heating in the channel resulting in device performance degradation and premature failure. Using devices based on wide-bandgap (WBG) semiconductors such as Gallium Nitride (GaN) and Gallium Oxide (GaOx) with a larger critical electric field and high-temperature tolerance, one could increase the power density. However, in order to increase the output power to the levels that is promised by these wide bandgap materials, junction temperature reduction through device-level cooling is critical. We are actively researching thermal management at device, circuit and packaging level using synthetic polycrystalline (PC) diamond. PC-diamond, at an appropriate grain size offers a TC is higher than any competing thermal vias with metals without interfering the electrical performance. Over the past 5 years we have demonstrated the potential of integrating diamond with GaN and recently achieving a record low diamond/GaN thermal boundary resistance (TBR) along with a relatively high diamond thermal conductivity (TC). This remarkable thermal performance was be achieved by maintaining the electrical performance, as demonstrated by the unharmed channel charge and mobility results.There are two key requirements for thermal management using heat spreading from the channel: first, a low thermal boundary resistance (TBR) between the hot spot in the channel and the heat spreader is required (in this study between GaN channel and diamond). Second, a low thermal resistance path to the heat-sink is crucial from the diamond layer which is directly proportional to diamond’s thermal conductivity (TC). In collaboration with Univ of Bristol, we have reported a TBR of ~3 m2K/GW, to date, known to be the lowest reported TBR for GaN HEMT technology. Diamond-GaN TBR depends strongly on the interface smoothness and the thickness of interfacial Si3N4 layer. A thinner Si3N4 resulted in lower TBR and allowed superior phonon coupling from the channel to the spreader. We have also measured a remarkably high TC for a 2 μm-thick diamond layer yielding over 650 W/m.K. The diamond grains are near isotropic in shape that allows excellent in-plane and cross-plane thermal conductivity. Achieving high TC within a thin film of diamond, grown heterogeneously, underscores the importance of our technique, since it reduces the residual stress when integrating with different materials that involves many thin layers like GaN/AlGaN HEMT epi-layers.β-Ga2O3 is an emerging ultra-wide bandgap material showing promises for both power and RF devices. However, the material’s low thermal conductivity poses to be a challenge for efficient power delivery (at any frequencies). PC diamond was successfully grown on (‾¯201)β-Ga2O3 using proper nucleation technique and thermal characterizations were conducted. A thermal conductivity (diamond + nucleation) and thermal boundary resistance at the diamond/β-Ga2O3 interface of 110 ± 33 W/mK and 30.2 ± 1.8 m2K/GW, respectively were measured.Our current results demonstrates a very promising roadmap for wide bandgap semiconductors via diamond integration.

We measured thermal boundary resistance at organic-inorganic interface to calculate the effective thermal conductivity by changing the thickness of both PEDOT:PSS and Bismuth Telluride in multi-layered thin films system. The total thermal resistance of the films as a function of thickness were measured by using a differential 3ω method. Thermal boundary resistance was calculated from the measured thermal resistance of the films at nonzero intercept. The measured PEDOT:PSS-Bismuth Telluride thermal boundary resistance was 1.4±0.3×10-7( m2·K ) / W. The measured high thermal boundary resistance can explain the low value of effective thermal conductivity of organic-inorganic composite film.

Thermal boundary resistance (TBR), which measures an interface's resistance to the thermal flow, is of critical importance among various areas, such as electronics cooling and thermoelectric materials. As for measuring TBR, electrical techniques are generally less sensitive compared to optical ones, but they are easily operable and compatible with the measurement of other electric properties; thus, it is highly desirable to develop electrical methods with higher accuracy and larger measurement range. Here, a two-sensor 3ω-2ω method with a novel experimental procedure design is proposed, which can well address those deficiencies in the conventional 3ω method. Two parallel metal sensors are fabricated, with one of them being wide and the other being narrow. The temperature changes of these two sensors are measured by detecting the 3ω and 2ω signals, respectively. The measurement includes three steps: (1) obtain thin film's thermal conductivity from the wide sensor's 3ω thermal response; (2) obtain substrate thermal conductivity from the narrow sensor's 2ω thermal response; and (3) derive an effective TBR from the narrow sensor's 3ω thermal response. Moreover, it is found the TBRs of metal/dielectric and dielectric/substrate interfaces are distinguishable due to the considerable difference between their contact areas, which enables us to separate these two TBRs by varying the contact area (heater's width). Then, our method is employed to probe the TBRs between the Al2O3 nanofilm and Si as well as SiC substrates at room temperature and good agreement with the previous measurements is achieved, verifying its feasibility. Our present scheme will be helpful for the experimental study of interfacial thermal transport.

Sensitive analysis on the effective soil thermal conductivity of the Thermal Response Test considering various testing times, field conditions and U-pipe lengths

Thermal resistance and phonon scattering at the interface between carbon nanotube and amorphous polyethylene

Thermal rectification refers to the phenomenon that heat fluxes or equivalent thermal conductivities are different under the same temperature difference when temperature gradient directions are different. The nature of the thermal rectification is that the structure has different effective thermal conductivities in different directions. Most of previous studies focused on thermal rectification of temperature-dependent thermal conductivity materials or variable cross section area structure, and the effect of thermal contact resistance at the interface was investigated very rarely. In the present paper we present the analytical and finite element numerical solution of temperature field and thermal rectification ratios of a composite structure with variable cross section area and thermal conductivity under different interface thermal contact resistances. The prescribed temperature boundary condition is introduced by penalty method, and the temperature jump condition at the interface is implemented by the definition of thermal contact resistance directly. The nonlinear heat conduction problem caused by temperature-dependent thermal conductivity and interface thermal contact resistance is then solved with a direct iteration scheme. Comparisons between experimental results and the present theoretical and numerical results show the feasibility of the proposed model. Then parameter investigations are also conducted to reveal the effect of some key geometric and material parameters. Numerical results show that thermal contact resistance plays an important role in the temperature field and thermal rectification ratio of the two-segment thermal rectifier. With the increase of the length ratio, thermal ratification ratio increases first and decreases then, and the optimal length ratio varies with both thermal contact resistance and cross-section radius change rate of the two segments. In general, the existence of thermal contact resistance can increase the total thermal resistance of the rectifier and magnify the distinction of the heat flux in forward and reverse cases. However, if the thermal contact resistance is too large, this distinction will decrease and correspondingly the thermal rectification ratio becomes low. With the increase of the boundary temperature difference, thermal rectification ratio increases due to the effect of temperature-dependent thermal conductivity. In the present study, we propose a theoretical and numerical approach to designing and optimizing the length ratio, cross-section radius change rate, thermal conductivity, boundary temperature difference and interface thermal contact resistance to obtain the maximal thermal rectification ratio of a bi-segment thermal rectifier, as well as the manipulation of thermal flux in engineering applications.

Simultaneous measurement of infrared absorption coefficient of Carbon doped Al0.33Ga0.67As thin film and thermal boundary resistance between thin film and heavily Zn doped GaAs substrate using spectrally-resolved modulated photothermal infrared radiometry

Non-monotonously tuning thermal conductivity of graphite-nanosheets/paraffin composite by ultrasonic exfoliation

Effective thermal conductivity of nonlinear composite media with contact resistance

The contrasting effect of compression on the ability of gas diffusion layer (GDL) in polymer electrolyte membrane fuel cell to conduct fluid, heat and electron implies that there is an optimal clamping force for cell performance. For a given GDL, understanding its associated optimal compression needs to know how its conductive ability changes with compressive pressure. In this paper we investigated the impact of compression on the effective diffusion coefficient and thermal conductivity of a carbon‐cloth GDL. The interior microstructures of the GDL under different compressions were acquired using X‐ray tomography; microscopic models were then developed to simulate gas diffusion and heat transfer in the microstructures in both in‐plane and through‐plane directions. The effective diffusion coefficient and thermal conductivity were calculated by volumetrically averaging the simulated gas diffusive and thermal flux rates at micron scale. The results show that both effective diffusion coefficient and thermal conductivity were anisotropic and their values in the in‐plane direction were higher than in the through‐plane direction. With porosity decreasing under the compression, the effective diffusion coefficient decreased faster in the through‐plane direction than in the in‐plane direction; the formula derived by Nam and Kaviany was capable of describing the change of the effective diffusion coefficient with porosity in the in‐plane direction but not in the through‐plane direction. For heat transfer, as the porosity decreased, the thermal conductivity increased faster in the through‐plane direction than in the in‐plane direction, and the increase in both directions could fit to the formula of Das et al.

Medium voltage vacuum interrupters are high-performance current interruption devices in the contemporary energy transition and electrification. The current interruption performance is directly correlated to the properties of their electrical contacts made of Cu-Cr alloys. Therefore, enhancing their performance to respond to the continuously increasing demand for higher current, higher power, and high voltage applications inherently requires the optimization of the microstructure of the Cu-Cr alloys to increase their electrical and thermal conductivity. Herein, we unveil the microstructural features governing the effective thermal conductivity of Cu-25Cr sintered composites, a subject of much less scientific attention than their electrical conductivity due to the complex microstructure-thermal conduction relationships. We coupled advanced 3D characterization techniques, namely X-ray computed tomography and atom probe tomography, with experimental and full-field numerical investigation of the effective thermal conductivity for three Cu-25Cr sintered composites having different final relative density (94, 96, and 98%). We demonstrate the synergistic effect of solid solution, interfacial thermal resistance, phase distribution on the effective thermal conductivity. Interfacial pores hinder the thermal conduction across phases. The effective thermal conductivity also decreases due to elements in solid-solution that diffused in the Cu matrix during sintering, along with interfacial thermal resistance across Cu/Cr phases. Using a full-field numerical approach, we unravel a microstructure heterogeneity-induced heat flux anisotropy contributing to the anisotropy in effective thermal conductivity.

The significance of interfacial thermal resistance in the thermal conductivity of nanofluids is not well understood, in part because of the absence of measurements of this quantity. Here, we study the interfacial thermal resistance for metal-oil nanofluids of interest as heat transfer fluids for concentrating solar power, using density functional theory and molecular dynamics simulations. Insights on the role of chemical interactions in determining the interfacial thermal resistance are revealed. The results presented here showcase a general picture in which the stronger the chemical interactions between species at the interface, the lower the associated interfacial thermal resistance. The implications toward nanofluid design are discussed. We show that, for this important family of metal-oil nanofluids, the interfacial thermal resistance values are low enough so that it is possible to afford a reduction in particle size, minimizing stability and rheological issues while still offering enhancement in the effective thermal conductivity with respect to the base fluid.