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Development of Measurement Method for Microscale Distribution and 2-D Mapping of Thermal Contact Resistance Using Lock-in Thermography Periodic Heating Methodロックインサーモグラフィ周期加熱法による マイクロスケール界面熱抵抗分布計測 および二次元マッピング手法の開発
Abstract
In order to evaluate the local relationship between thermal resistance and its factors at a realistic solid contact interface, we developed a method to measure the thermal contact resistance distribution by combining periodic heating method and lock-in thermography. For a two-layer sample with thermal resistance as low as the order of 10⁻⁶ m²⋅K/W, the thermal resistance distribution was evaluated by two different approaches: direct observation of the temperature wave change from the transverse direction and obtaining phase lag distribution from the vertical direction. As a result, a line profile along the interface was obtained at a super high resolution of 2.5 μm, and it was clarified that there was a difference of about 30% within a range of 2.5 mm. Furthermore, the two-dimensional distribution was obtained at a high resolution of about 70 μm, and the difference in thermal resistance due to the interface geometry was visualized quantitatively.
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Enhancement of polymer thermal conductivity using nanographene fillers and clarification of its molecular-scale mechanisms are of great concern in the development of advanced thermal management materials. In the present study, molecular dynamics simulation was employed to theoretically show that the in-plane aspect ratio of a graphene filler can have a significant impact on the effective thermal conductivity of paraffin/graphene composites. Our simulation included multiple graphene fillers aggregated in a paraffin matrix. The effective thermal conductivity of a paraffin/graphene composite, described as a second-rank tensor in the framework of equilibrium molecular dynamics simulation, was calculated for two types of graphene fillers with the same surface area but in-plane aspect ratios of 1 and 10. The filler with the higher aspect ratio was found to exhibit a much higher thermal conductivity enhancement than the one with the lower aspect ratio. This is because a high in-plane aspect ratio strongly restricts the orientation of fillers when they aggregate and, consequently, highly ordered agglomerates are formed. On decomposing the effective thermal conductivity tensor into various molecular-scale contributions, it was identified that the thermal conductivity enhancement is due to the increased amount of heat transfer inside the graphene filler, particularly along the longer in-plane axis. The present result indicates a possibility of designing the heat conduction characteristics of a nanocomposite by customizing the filler shapes so as to control the aggregation structure of the fillers.
The addition of surfactants to polymer-based thermal interface materials applied to improve the heat dissipation efficiency of chip surfaces in contact has attracted attention for the microelectronic processing technology. In the present study, the mechanism by which a long-chain surfactant affects heat transfer across the interface between solid surface and polymer liquid was investigated by non-equilibrium molecular dynamics simulation. We constructed a system where tetracosane was used as a solvent and contained alcohol molecules as a surfactant, and they were placed between two flat silica surfaces under a thermal gradient. The effect of the hydrophilicity of silica surface, the concentration of the surfactant, and chain length of the surfactant on silica–liquid interfacial thermal resistance Rb were examined. Alcohol surfactant molecules preferred to adsorb onto the hydrophilic silica (Si–OH) surface due to hydrogen bonding between alcohol and silanol hydroxyl groups. It was found that Rb reduced not only with the adsorption amount of alcohol molecules but also with the chain length of alcohol. The van der Waals interaction contribution was dominant for solid–liquid and liquid–liquid heat conduction near the interface. The hydroxyl terminals of alcohol molecules were vertically adsorbed onto the Si–OH surface due to hydrogen bonds, which produced a heat path from silanols to the hydroxyl groups of alcohol. Furthermore, heat was also exchanged between alcohol hydroxyl and alkyl groups via intramolecular interaction and between the alcohol alkyl groups and nearby solvent molecules via van der Waals (vdW) intermolecular interaction. This resulted in an efficient heat path from solid surface silanols to liquid bulk. As the alcohol chain length increased without changing the number of adsorbed alcohol molecules, the heat transfer through this heat path increased, which led to a decrease in Rb. These results provided insight toward the guiding principle for the molecular design of complex surfactants to enhance the interfacial heat transfer.
This study proposes a new method for measuring thermal contact resistance using lock-in thermography. By using lock-in thermography with an infrared microscope, the dynamic and spatially resolved temperature behavior of the contact interface was visualized on a microscale with one measurement. In addition, a new thermal contact resistance measurement principle was constructed after solving the three-dimensional thermal conduction equation in the cylindrical coordinates by considering a periodic heat source with a Gaussian intensity distribution and the relative position of the heating point to the sample edge, in the presence of thermal resistance at the contact interface. Consequently, the discontinuous behaviors of the temperature wave, amplitude, and phase lag at the contact interface were observed on a microscale. From that discontinuity, the local thermal contact resistance was analyzed as a fitting parameter by matching the theoretical curve to the measured amplitude and phase lag. Furthermore, the simultaneous analysis of the material thermal diffusivity was demonstrated and the validity of the measurements was confirmed.
In this study, we carried out molecular dynamics simulations of a cylindrical Lennard-Jones droplet on a flat and smooth solid surface, and showed that Young's equation as the relation among solid-liquid, solid-vapor, and liquid-vapor interfacial tensions $\gamma_{sl}$, $\gamma_{sv}$, and $\gamma_{lv}$, respectively, was applicable only under a very restricted condition.
Using the fluid stress-tensor distribution, we examined the force balance in the surface-lateral direction exerted on a rectangular control volume set around the contact line. As the mechanical route, the fluid stress integrals along the two control surfaces normal to the solid-fliuid interface were theoretically connected with
$\gamma_{sl}$ and $\gamma_{sv}$ relative to the solid-vacuum interfacial tension $\gamma_{s0}$ by Bakker's equation extended to solid-related interfaces via a thought experiment, for which the position of the solid-fluid interface plane was defined at the limit that the fluid molecules could reach. On the other hand, the fluid stress integral along the control surface lateral to the solid-fluid interface was connected with $\gamma_{lv}$ by the Young-Laplace equation.
Through this connection, we showed that Young's equation was valid for a system in which the net lateral force exerted on the fluid molecules from the solid surface was zero around the contact line.
Furthermore, we compared $\gamma_{sl}-\gamma_{s0}$ and $\gamma_{sv}-\gamma_{s0}$ obtained by the mechanical route
with the solid-liquid and solid-vapor works of adhesion obtained
by the dry-surface method as one of the thermodynamic routes
, and showed that both routes resulted in a good agreement. In addition, the contact angle predicted by Young's equation with these interfacial tensions corresponded well to the apparent droplet contact angle determined by using the previously defined position of the solid-fluid interface plane; however, our theoretical derivation indicated that this correspondence was achieved because the zero-lateral force condition was satisfied in the present system with a flat and smooth solid surface. These results indicated that the contact angle should be
predicted not only by the interfacial tensions but also by the pinning force exerted around the contact line.
This paper considers the resistance to the flow of heat between two thick solid bodies in contact in a vacuum. Existing analyses of single idealized contacts are summarized and compared, and then applied, together with results of recent electrolytic analog tests, to predict the conductance of multiple contacts. "appropriately" or "inappropriately" distributed at the interface. Reconsideration of the theory of interaction between randomly rough surfaces shows how the parameters required to predict heat transfer can be determined in principle by simple manipulation of typical profiles of the mating surface, together with an approximation from deformation theory. It is also shown that this process depends more crucially than had been realized upon the distribution of the few high peaks of the surfaces, where the assumption of Gaussian distribution of heights is suspect. In place of that assumption, the use of describing functions is suggested. The few experimental data relevant to these theories are examined and compared with predictions of theory.
The thermal conductivity and thermoelectric power of a single carbon nanotube were measured using a microfabricated suspended device. The observed thermal conductivity is more than 3000 W/K m at room temperature, which is 2 orders of magnitude higher than the estimation from previous experiments that used macroscopic mat samples. The temperature dependence of the thermal conductivity of nanotubes exhibits a peak at 320 K due to the onset of umklapp phonon scattering. The measured thermoelectric power shows linear temperature dependence with a value of 80 microV/K at room temperature.
Since smaller thermal-resistance design is indispensable for automotive IGBT modules, the double-sided cooling power module and stacked cooler have been developed. However, it has not known that the FS-IGBT played an extremely important role in exquisite combination of. Therefore, we have reviewed the bottlenecks from the viewpoint of the power semiconductor chips in the power module, named as “Power-Card”, followed by the basic functions the chips should have. Further, we have recognized that the paradigm shift from “Power semiconductor device first” to “Power module first” has strongly pushed forward realization.
Thermal contact resistance (TCR) between individual carbon fibers (CFs) can dominate heat dissipation rates in CF-based composite materials. Here, we develop a totally non-contact “laser-flash Raman mapping” method to simultaneously measure the TCR at the CF-CF junction and their thermal conductivities. Laser power is used to heat the sample and the laser absorptivity is experimentally determined by a transient laser-flash Raman technique. The laser heating positions are changed along two connected CFs, and the change of temperature rise with varying positions is in-situ measured from the temperature dependent Raman band shifts. The high spatial resolution of the micro-Raman mapping allows direct observation of the abrupt jump of thermal resistance at the CF-CF junction, from which we extracted the TCR as well as the thermal conductivity. The laser absorptivity of the 11 μm-diameter CFs is measured to be 0.12 ± 0.03, the thermal conductivities of the individual CFs are around 200 W/mK, and the TCR of the CF-CF junction is (2.98 ± 0.92) × 10⁵ K/W. This work provides indispensable knowledge for the design of CF-based composite for thermal management, and the novel non-contact measurement method can stimulate characterization and manipulation of contact/interface heat conduction between various micro- and nano-materials.
Thermal contact resistance (TCR) plays an importance role in thermal management, which can strongly affect heat dissipation across interfaces, especially as devices are becoming smaller and smaller in size. This paper presents a review of commonly used experimental characterization methods for TCR including the steady-state method, the T-type method, micro-thermometry, Raman-based techniques, infrared thermography measurements, laser-flash measurements, photoacoustic techniques, the 3ω method and transient thermoreflectance techniques. Conventional steady-state measurements are still an acknowledged technique for measuring TCR for bulk materials, and recent modifications and improvements are increasing their measurement accuracy and reliability. Transient methods are diverse and widely applied to both bulk and low dimension materials. We describe in detail the principles and developments of both the steady-state and transient methods and summarize new applications for different material level and the features of each test methodology for TCR. Finally, we discuss the challenges facing TCR characterization and identify possible future research directions.
The Laser Photothermal Method (LPM), which is a transient non-contact technique, was employed to measure the thermal physical parameters of Stainless Steel 304 (SS304), Oxygen-Free Copper (OFC) and Aluminum Nitride (AlN) ceramics. The thermal diffusivity of SS304, OFC and AlN ceramic were measured by the LPM and some explanations for the tendency with the temperature were given. Compared with the reference values, it showed that the LPM is reliable in measuring thermal parameters. Following, the thermal contact resistances (TCRs) of OFC-AlN ceramic, SS304-AlN, SS304-SS304 and AlN ceramic were measured in the temperature range from 70 K to 300 K and the contact pressure was on the order of 0.10 MPa. Some explanations were given to make clear the changing trend of TCRs with the increase of temperature. Moreover, some empirical formulas of the TCRs were established. The accuracy of the establishing empirical formulas had been validated by the experiment, and the error was smaller than 9%.
Thermal conductance of an interface, between aluminum surfaces, was measured at pressures ranging from 0.172 to 2.76 MPa. The conductance was measured for a bare interface as well as with several commercial thermal interface materials (TIMs) applied. A steady state TIM characterization device was developed in house. A total of six different TIMs were tested using this device: Tgrease 880, Tflex 720, Tmate 2905c, Tpcm HP105, Cho-Therm 1671, and Cho-Therm T500. The characterized TIMs showed a very strong dependence on clamping pressure. The conductance of samples at 2.76 MPa were shown to be between 135% and 515% greater than the conductance at 0.172 MPa. Many of the samples showed a near linear increase in conductance while others leveled off at higher pressures. The steady state characterization device was found to have high experimental uncertainty when characterizing high conductance TIM samples (specifically Tgrease 880). It was determined that this uncertainty was mainly the result of inadequate cooling.
Optical-based techniques have been used to characterize thermal energy transport in materials for a few decades. To implement these techniques, a modulated heat source (either pulse or continuous wave) is always employed to excite a periodic temperature variation, which subsequently causes variation of temperature within the material and various other parameters that are a function of temperature. Ambient pressure, surface infrared properties, and radiation are all affected by the temperature variation and serve as indicators to indirectly detect the temperature change. To extract the properties of interest, theoretical models and solutions are necessary. In this work, we propose a general heat transfer model in multilayer structures. We also derived general solutions in the frequency domain using recursive matrix relationships. The recursive matrix simplifies the heat transfer analysis by only considering key parameters within the adjacent layers. In addition, the general analytical solution is only composed of a group of equivalent resistances that yield the contribution to the overall phase shift from each interface and can be used to directly calculate the phase difference within similar configurations. We applied this model and the associated solutions to analyze the data from the phase-sensitive transient thermoreflectance (PSTTR) technique. In contrast with typical thermoreflectance techniques, in the PSTTR technique, the pump and probe beams are applied on the opposite surfaces of the sample. We conducted PSTTR measurements on different multilayer structures, and then determined the thermal/physical properties of interest by fitting the theoretical solutions to the experimental data. The thermal conductivity of thermal grease (TC-5022) was determined to be 3.5 W/(m K). Where appropriate, the fitted results were in excellent agreement with results from the literature, which validates this general model and the solution methodology. As another example of a multilayer structure, a novel direct-bonded interface that contains four layers, was studied. Its overall thermal resistance was 0.46 mm2 K/W, including the Al-Al contact resistance of 0.33 mm2 K/W and Al-Si contact resistance of 0.06 mm2 K/W. Using this general model along with the PSTTR technique, an in-depth understanding of the interfacial resistance was achieved by investigating the contributions from each component in the interface.
In Chapters 21 to 23 we were mainly concerned with the total power radiated by sources and fiber nonuniformities, rather than the distribution of radiation throughout the fiber. This distribution describes the spatial transient between the source of excitation of the radiation fields and the spatial steady state further along the fiber, where essentially only bound modes propagate. The spatial transient and the spatial steady state were discussed in Section 8-1, and for a source on the endface, the situation is depicted schematically in Fig. 8-1. Within the region of the spatial transient, both bound modes and the radiation fields are necessary to fully describe light propagation. The duration of the spatial transient depends on the degree to which the fiber retains radiation from the source prior to its eventual escape, or leakage, from the core. The purpose of this chapter is to introduce a class of modes, called leaky modes, to describe the portion of the radiation field which travels comparatively long distances along and close to the fiber axis.
A novel method combining experimental test and heat transfer modeling was developed to determine the thermal contact conductance (TCC) between thin metal sheets as a function of contact pressures. In the experiment, thin metal samples were sandwiched between one white light transparent and one infrared (IR) transparent glass disks pressed together under different pressure levels. The metal stack was then heated up from the white light transparent side by an intense short pulse of flash light. The temperature transient on the other side was measured by an IR camera. To obtain a value of TCC, two separate experiments having different layers of thin sheet materials were performed and the values of maximum temperature rise were measured. Numerical heat transfer modeling was used to calculate the temperature evolution in the stack-up comprised of metal layers sandwiched between two glass disks. The heat transfer calculation results showed that TCC had a strong correlation to the ratio of maximum temperature rise between the two experiment configurations, but it was insensitive to the variations of other thermal properties. Thus, for a given pair of metal sheets in contact, a unique correlation between the TCC and the ratio of temperature rise was established using the heat transfer calculation. Such correlation allows the direct determination of the TCC value from the ratio of the experimentally measured temperature rise. The TCC between three types of thin metal sheets (i.e., 0.2-mm-thick Al, 0.2-mm-thick Cu and 0.9-mm-thick Cu) were measured and compared with the available literature data. Published by Elsevier Ltd.
The effect of the waviness on thermal contact resistance is examined. The experiments performed on a simplified model of waviness show that the thermal contact resistance is roughly said to be the sum of the resistances for roughness and waviness in series. Long before investigating the theoretical analyses shown in the previous reports, we have obtained experimentally a practical method of estimating the thermal contact resistance. That is, on the assumption that the thermal contact resistance is the resultant of resistances to metalmetal and metal-medium-metal parallel heat flows and the additional resistance attached in series to the metal-metal heat flow, this additional resistance may be taken to be constant for each metal. This fact will be verified theoretically.
Thermal models are needed when designing power converters for Wind Turbines (WTs) in order to carry out thermal and reliability assessment of certain designs. Usually the thermal models of Insulated Gate Bipolar Transistors (IGBTs) are given in the datasheet in various forms at component-level, not taking into account the thermal distribution among the chips. This is especially relevant in the case of Press-Pack (PP) IGBTs because any non-uniformity of the clamping pressure can affect the chip-level thermal impedances. This happens because the contact thermal resistances in the thermal impedance chains are clamping pressure dependent. In this paper both component-level and chip-level dynamic thermal models for the PP IGBT under investigation are developed. Both models are developed using geometric parameters and material properties of the device. Using the thermal models, the thermal impedance curves under various mechanical clamping conditions are derived. Moreover, the deformation of the internal components of the PP IGBT under operating-like conditions is investigated with the help of the thermal models and the coefficient of thermal expansion (CTE) information.
During measuring the thermal contact resistance (TCR) of solids by using traditional steady-state test methods, it is observed that the measured results are unavoidable to be impacted by the direction of exerting heat flux between dissimilar and similar metals. Such a directional effect has also been found for the cases between two solids of identical material with the same surface properties. Uncertainty analysis shows that the directional effect between two solids may result from the additive errors. In order to improve the measurement precision, we propose a method by using harmonic mean value of TCR in two directions of exerting heat flux to diminish the effect. Meanwhile, a modified experimental apparatus has been designed and established to high-precisely measure TCR between two solids of the identical material. To verify the accuracy of the method, the TCRs of samples of 99.999% standard pure copper and Elkonite copper-tungsten alloy 30W3 are measured and discussed in detail. The results show that the present method has high precision and can be used in a relatively wide range of TCR measurement for identical solids and the characterization of thermal interface materials.
We have measured the low-temperature thermal conductivity and specific heat of CdGeAs2 to investigate the influence of coordination number on the thermal properties of amorphous solids. CdGeAs2 is tetrahedrally bonded in the crystalline state and strong evidence exists that this local order is preserved in the amorphous state. The thermal conductivity of the amorphous material was measured from 0.1 to 300 K. It displays the same behavior as all other glasses: a T2 dependence below 1 K, a wide range of temperature over which the conductivity is approximately temperature independent, and a thermal conductivity at high temperatures that approaches the minimum thermal conductivity as described by Slack. The specific heats of c-CdGeAs2 and a-CdGeAs2 were measured from 0.1 to 50 K. Below 1 K, the amorphous material shows the excess specific heat that is characteristic of amorphous solids. Above 1 K, the specific heat of the amorphous material, when compared to the Debye model, closely resembles the specific heat of the crystal. We have also measured the thermal conductivity of a sputtered film of a-Ge from 30 to 300 K and compare our results to previous measurements of the thermal properties of a-Si and a-Ge. On the basis of our experimental findings, we conclude that the thermal properties of amorphous solids do not depend on the coordination number.
Interfacial thermal transport via van der Waals interaction is quantitatively evaluated using an individual multi-walled carbon nanotube bonded on a platinum hot-film sensor. The thermal boundary resistance per unit contact area was obtained at the interface between the closed end or sidewall of the nanotube and platinum, gold, or a silicon dioxide surface. When taking into consideration the surface roughness, the thermal boundary resistance at the sidewall is found to coincide with that at the closed end. A new finding is that the thermal boundary resistance between a carbon nanotube and a solid surface is independent of the materials within the experimental errors, which is inconsistent with a traditional phonon mismatch model, which shows a clear material dependence of the thermal boundary resistance. Our data indicate the inapplicability of existing phonon models when weak van der Waals forces are dominant at the interfaces.
The paper presents the data reduction analysis for measurements of the transient thermal interface resistance between two
bonded metal bodies using the laser-flash method. By using two different mathematical models, i.e., a two-layered and a three-layered
model, whose complete analytical solutions for realistic conditions are provided, different results for final values and their
uncertainties can be obtained. The analysis has been applied to experimental data measured from samples prepared with three
different bonding materials, cyanoacrylate, metal epoxy resin, and silicone rubber.
We report measurements of the solid‐solid thermal boundary resistance R bd , spanning the temperature range from 1 to 300 K. Below 30 K, R bd is found to be in agreement with the prediction of the acoustic mismatch model. The influence of diffuse scattering at the interface is found to have a very minor influence on R bd . Above 30 K, R bd decreases less rapidly with increasing temperature than predicted by the theory. Phonon scattering in thin (∼30 Å) disordered layers near the interface is shown to be a possible explanation. Implications for heat removal from integrated circuits are discussed.
Modifying Beam Profiles with Multimode Fibers
- Thorlabs
Thorlabs, "Modifying Beam Profiles with Multimode Fibers,"
Application Note. (2015) 1-10.
Certified Reference Material Catalog
NMIJ; "Certified Reference Material Catalog," (2023) 41-43,
The National Institute of Advanced Industrial Science and
Technology.