Thermal Spreading Resistance Research Articles

Analytical Solutions for Transient Thermal Spreading Resistance of a 3-D Flux Channel

Analytical Solutions for Transient Thermal Spreading Resistance of a 3-D Flux Channel

Thermal Spreading Resistance of Near Surface Localized Heating-Induced Size Effects in Semiconductors

Abstract Localized heating is encountered in various scenarios, including the operation of transistors, light-emitting diodes, and some thermal spectroscopy techniques. When localized heating occurs on a scale comparable to the mean free path of the dominant energy carriers, additional thermal resistance is observed due to ballistic effects. The main objective of this study is to find a relation between this resistance, problem geometry, and material thermal properties in situations involving localized heating. Models based on the solution of the Fourier heat diffusion equation and the gray phonon Boltzmann Transport Equation are solved simultaneously to calculate the additional thermal resistances that arise from localized heating. Subsequently, the results are analyzed to derive the desired relationship. It is noted that in the context of localized heating resistance, the effects of geometrical variables are non-linear and substantial, particularly when the Knudsen numbers for the boundary and heat source exceed certain thresholds. Specifically, when the Knudsen number for the heat source becomes comparable to 1 localized heating resistance is observed. However, when the Knudsen number based on heat source height and width surpasses 8 and 20, respectively the heat source behaves akin to a point source, no longer significantly affecting the localized heating resistance. At this juncture, the maximum resistance limit is reached.

Optimization of embedded cooling for hotspots based on compound plate thermal spreading model

Heat fluxes of GaN-based high electron mobility transistors (HEMTs) can reach dozens of kilowatts per square centimeter, and the heat is generated only within a small area with feature size of micrometer to millimeter length scales, which poses a huge challenge for thermal management. In this study, an embedded microfluidic cooling solution is proposed to dissipate heat from the hotspots, and thermal test vehicles are fabricated using the Micro-Electro-Mechanical System (MEMS) process. Cooling performances of hotspots with sizes ranging from 40 × 40 μm2 to 500 × 500 μm2 and varying locations are demonstrated. Thermal resistances of the test samples are analysed and the heat transfer coefficient can achieve 1.5 × 105 W/(m2∙K) using embedded microchannel cooling. We propose a compound plate spreading thermal resistance model to demonstrate the effect of the dielectric layer and the size of the heat source on heat dissipating capability of the microfluidic cooling system. Based on the thermal spreading model, when the heat source is small, integrating high thermal conductivity materials near the heat source can reduce its total thermal resistance by two orders of magnitude. By balancing the heat spreading resistance with the convective resistance of microchannel cooling, we find that ∼1 mm can be considered as the critical length for distinguishing the primary thermal management approach for different sized hotspots. This paper provides useful design guidelines for embedded microchannel cooling of devices with localized heat generation patterns, such as HEMT devices.

Transient Thermal Spreading Resistance from Isothermal Source in a Circular Flux Tube

An analytical expression is developed for transient thermal spreading resistance from an isothermal circular source in a cylindrical flux tube as a function of constriction ratio and time. The flux tube is semi-infinite. The spreading resistance expression is obtained from the temperature expression by solving the heat equation. For short times, the dimensionless transient spreading resistance is proportional to dimensionless time based on the square root of the source area. For long times, the dimensionless spreading resistance approaches the values of the corresponding steady-state expression in the literature. For small constriction ratios, dimensionless spreading resistance approaches the classic isothermal half-space limit. A numerical analysis is presented which shows excellent agreement with the analytical solution. Approximate correlations for dimensionless resistance are also presented for both the isothermal and the isoflux cases.

Transient Thermal Spreading From a Circular Heat Source in Polygonal Flux Tubes

Abstract This study develops a numerical simulation to assess transient constriction resistance in various semi-infinite flux channel geometries, including circle on circle, triangle, square, pentagon, and hexagon, which are derived from various heat source arrangements in a large domain. Using both isothermal and isoflux circular heat sources in polygonal flux channels, and employing a finite volume method, the study evaluates transient constriction resistance. The research confirms that for different geometries, similar nondimensionalized constriction resistance results are obtained, particularly when using the square root of the source area as the characteristic length and the square root of the constriction area ratio. The study reveals that flux tube shape has a minimal impact on thermal spreading resistance, with the circle-on-triangle configuration displaying the largest deviation from a simple circle-on-circle model. These insights advance our understanding of thermal spreading resistance in polygonal flux channels and their applications in thermal engineering, especially in contact heat transfer problems.

Thermal Spreading/Constriction From an Isothermal Source Into a Multilayer Orthotropic Semi-Infinite Flux Tube

Abstract Thermal spreading and constriction have been widely studied due to relevance in heat transfer across interfaces with imperfect contact and problems such as microelectronics thermal management. Much of the past work in this field addresses an isoflux source, with relatively lesser work on the isothermal source problem, which is of much relevance to heat transfer across rough interfaces. This work presents an analytical solution for thermal spreading/constriction resistance that governs heat flow from an isothermal source into a multilayer orthotropic semi-infinite flux tube. The mixed boundary condition due to the isothermal source is accounted for by writing a convective boundary condition with an appropriately chosen spatially-varying Biot number. A series solution for the temperature field is derived, along with a set of linear algebraic equations for the series coefficients. An expression for the nondimensional thermal spreading resistance is derived for Cartesian and cylindrical problems. It is shown that, depending on the values of various nondimensional parameters, heat transfer in either the thin film or the flux tube may dominate and govern the overall thermal spreading resistance. Results for a single-layered isotropic flux tube are derived as a special case of the general result, for which, good agreement with past work is demonstrated. An easy-to-use polynomial fit for this special case is presented. This work contributes a novel technique for solving mixed boundary problems involving an isothermal source, and may also help solve practical problems related to interfacial heat transfre and thermal management.

Heat transfer and spreading in a finite-thickness cylinder with spatially varying convective cooling along the side wall

Thermal spreading and constriction resistance play an important role in thermal management of a variety of engineering systems, including semiconductor devices. Moreover, thermal contact resistance at interfaces between materials is also governed by spreading and constriction processes. Most of the past literature on theoretical modeling of thermal spreading from a source into a larger body assumes an adiabatic side wall, whereas several recent thermal management problems involve active cooling at the side wall. This work addresses such scenarios by solving the thermal spreading problem in a finite thickness cylinder with spatially varying convective heat transfer on the side wall. An eigenfunction-based series solution for the temperature field is written, the coefficients of which are shown to be governed by a set of coupled algebraic equations. Results are shown to agree well with past work for special cases of the general analysis presented here. Thermal spreading resistance is computed for a number of practical scenarios, including step function, periodic and sinusoidal convective cooling on the side wall. In each case, it is shown that the temperature distribution is consistent with the nature of the spatially varying boundary condition. A key theoretical insight from this work is that under certain conditions, the classical definition of thermal spreading resistance may become negative due to the presence of two heat sinks in the problem. Therefore, analysis based on total resistance may be more appropriate. This work offers a significant generalization of past papers, making it possible to analyze realistic thermal management problems, in which, side wall cooling plays an important role.

Thermal spreading resistance from an isothermal source into a finite-thickness body

Thermal spreading resistance is encountered during two-dimensional thermal conduction from a hot surface into a body. Thermal spreading and the opposite problem of thermal constriction resistance are of much technological relevance in the design of heat sinks and thermal spreaders for thermal management of microelectronics and other heat-generating devices. Much of the past work in the theoretical analysis of thermal spreading is based on a source with given heat flux. In contrast, the isothermal source problem presents difficulties due to the resulting mixed nature of the boundary condition, due to which, only approximate solutions are available. This work derives the steady-state thermal spreading resistance from an isothermal source into a finite-thickness slab or cylinder. The mixed boundary condition is handled by posing it in the form of a spatially varying convective boundary condition, with a sufficiently large Biot number over the source to represent its isothermal nature. A series solution for the problem is derived, along a sufficient set of linear algebraic equations to determine the series coefficients. Results are shown to agree well with finite-element simulations. Results are compared with previously-reported approximate solutions within the parametric range of validity of the approximate solutions. The impact of key non-dimensional parameters on thermal spreading resistance is quantified. It is shown that thermal spreading resistance increases with decreasing size of the isothermal heat source, as expected. A third-order polynomial correlation with very good accuracy is proposed. This work advances the theoretical understanding of a problem for which only approximate solutions have been reported in the past. Results presented here offer a practical tool for thermal design and optimization of a variety of practical thermal management problems involving spreading or constriction.

Numerical optimization and experimental validation of vapor chambers having an outwardly protruding boss

The purpose of vapor chamber (VC) is to spread heat from small concentrated heat sources. In practice, a protruding boss surface on the VC is used to meet the layout of printed circuit board assembly. This study numerically examines the effect of outwardly protruding boss on the performance of the VC subject to various geometrical design parameters under varying heat load conditions. The overall thermal resistance, spreading resistance, and temperature distribution are monitored to characterize the thermal performance. The experimentally validated numerical model is used to undertake parametric studies of the VC. It is found that the compound pillars and the area ratio in the boss region have significant effect on the thermal performance of the VC. The shape of compound pillars in the peripheral region, and the impact of the height of the vapor region are also studied. Pillar diameter and the number of pillars in the boss region impose the maximum effect on the performance of the VC as they directly influence the evaporative heat transfer and the surface temperature. The optimal design based on the compound pillar structures and area ratio in the boss region reduces overall thermal and spreading resistances by 18.2% and 18.9%, respectively.

The thermal analysis of the heat dissipation system of the charging module integrated with ultra-thin heat pipes

• A hybrid heat dissipation system of charging module is performed. • An application of ultra-thin heat pipes (UTHPs) in charging module. • Effects of heat dissipation factors are compared quantitatively. • The HTUPs greatly improve the temperature uniformity. Electric vehicles (EV) played an important role fighting greenhouse gas emissions that contributed to global warming. The construction of the charging pile, which was called as the "gas station" of EV, developed rapidly. The charging speed of the charging piles was shorted rapidly, which was a challenge for the heat dissipation system of the charging pile. In order to reduce the operation temperature of the charging pile, this paper proposed a fin and ultra-thin heat pipes (UTHPs) hybrid heat dissipation system for the direct-current (DC) charging pile. The L-shaped ultra-thin flattened heat pipe with ultra-high thermal conductivity was adopted to reduce the spreading thermal resistance. ICEPAK software was used to simulate the temperature and flow profiles of the new design. And various factors that affected the heat dissipation performance of the system were explored. Simulation results showed that the system had excellent heat dissipation capacity and achieved good temperature uniformity. Rather than solely relied on the fans, this new design efficiently dissipated heat with a lower fan load and less energy consumption.

Analytical thermal resistance network model for calculating each mean die temperature of the multi-chips module combined with quad flat no-leads packaging

With the rapid advancement of next-generation communication technology, traditional Quad Flat No-leads (QFN) packaging is facing challenges to meet functional requirements. Due to its high integration and excellent thermal performance, the Multi-chips Module combined with Quad Flat No-leads (MCM-QFN) packaging is gaining popularity. However, the structural complexity of MCM-QFN packaging and the thermal coupling effect between multiple dies make it challenging to analyze the steady-state thermal distribution of MCM-QFN packaging, which is necessary for assessing the reliability and optimizing the layout design of the multi-chips module. By analyzing the heat dissipation path from each die to the ambient, this paper proposes an analytical thermal resistance network model for calculating each mean die temperature of MCM-QFN packaging. The thermal coupling effect among the multi-chips, the thermal spreading resistance between critical layers, and the boundary conditions and cooling conditions are all considered. All thermal resistances in the model are expressed analytically, and the mean temperature of each chip can be calculated within 0.1 s using MATLAB programming. To validate the accuracy of the proposed model, finite element method (FEM) simulations are conducted to provide a reference for the mean temperature of each chip under four sets of thermal conditions. The data comparison demonstrates that the analytical model is fast and accurate in calculating each mean die temperature of MCM-QFN packaging, with a maximum error of 3.72%, and the calculation speed increased by about 600× compared to that of FEM simulation. Furthermore, the analytical model is able to offer a direction for optimizing the layout design and material selection of MCM-QFN packaging.

Near-junction phonon thermal spreading in GaN HEMTs: A comparative study of simulation techniques by full-band phonon Monte Carlo method

Accurate thermal simulation is essential for the near-junction thermal management and electro-thermal co-design of GaN HEMTs. While various methods have been employed to simulate phonon thermal transport in GaN, a comprehensive evaluation of their performance and reliability has yet to be conducted. In this work, first-principle-based steady-state full-band phonon tracing Monte Carlo (MC) simulations are conducted to study the thermal spreading resistance in GaN HEMTs. The results of full-band MC serve as a standard against which the applicability, accuracy, and computational efficiency of three widely-used approaches to simulate the near-junction phonon transport in GaN are thoroughly examined. The simulation techniques compared in this study include MC simulations with empirical isotropic phonon dispersion (isotropic MC), MC simulations with gray-medium approximation (gray MC), and finite-element methods (FEM) with effective thermal conductivities (FEM with keff). It is found that isotropic MC largely overestimates the thermal resistance due to the empirical model’s overestimation of phonon mean free path (MFP) distributions. By selecting an appropriate average MFP, gray MC can approximate the full-band results well, but due to its inability to reflect the contributions of different phonon modes, discrepancies are inevitable for some geometric parameters. For FEM-based analysis, although the diffusive nature of Fourier’s law precludes the reproduction of channel temperature distributions, the influence of phonon ballistic effects on the junction temperature can be accurately reflected in the well-chosen effective thermal conductivities. The comparison highlights the importance of directly incorporating first-principles-calculated phonon properties into device thermal simulations, and the paper can provide a clearer understanding of near-junction thermal transport in GaN and can be useful for thermal simulations of GaN-based devices.

A theoretical study of thermal management of FBAR considering thickness- and temperature-dependent thermal conductivity of AlN

Reliable and long-term operation of thin film bulk acoustic resonators (FBARs) under high power relies on the optimization of thermal resistance. In this work, thermal design strategies for high power FBARs are explored theoretically. For accurate estimation of the thermal characteristics of FBARs, the thermal conductivity of the AlN epilayer with temperature and thickness dependence is included in the finite element simulation model, of which AlN thermal conductivity is calculated through normal-process, Umklapp, and boundary scattering. To further reduce thermal resistance and improve power capacity, the effects of aspect ratio, AlN thickness, the number of resonators, and pitch distance on thermal resistance are investigated. Compared with FBARs with a square electrode, the thermal resistance of the FBAR-on-diamond device is decreased by 43% at an aspect ratio of three. Meanwhile, the optimal AlN thickness is 2 µm, which maintains the balance between thermal resistance and electric performance. The power capacity is increased by 1.93 dB by substituting six resonators for four resonators. The improvement in power handling ability is attributed to the reduced thermal spreading resistance and lower power density. Our study can provide detailed thermal design strategies for high power FBARs toward high throughput data transmission.

Optimizing the heat source layout of chips using bionic method: Reduction of junction temperature

Optimizing the heat source layout to reduce the junction temperature is an important topic in the thermal design field of chips. However, the relationship between the heat source layout and the junction temperature is still ambiguous, and the optimization method suitable for actual chips is still rare, while it is quite desirable in engineering. In this work, we propose a feasible strategy to optimize the heat source layout using bionic method, and demonstrate the strategy by a flip chip ball grid array (FCBGA) case. The optimized layout can reduce the junction temperature and thermal spreading resistance by 2.38 K and 30.94%, respectively. The mechanism can be attributed to the heat dissipation advantage at the corner and edge positions of the heat source surface and the low temperature coupling between heat sources in the optimization process. This work illustrates a great promising potential of the bionic optimization method in the design of the CPU and GPU chips.

Reduced graphene oxide films for reducing hotspot temperatures of electronic devices

The increase in the number of transistors in electronic circuits has increased the power density of electronic devices, which leads to the formation of hotspots on the microchips of the electronic devices. Hotspots deteriorate the lifespan and reliability of electronic devices. With the advantages of high thermal conductivity (κ), low cost, and feasibility for mass production, reduced graphene oxide (rGO) films have become a promising candidate for dispersing the excessive heat at the hotspots and alleviating the adverse effects caused by the hotspots. In this study, a chemical–thermal method combining the chemical reduction and thermal annealing process at a relatively low temperature of 1200 °C was utilized for the synthesis of rGO films. The synthesis method lowered the annealing temperature and yielded a high-quality rGO film. A high κ of 1653.9 ± 214.7 W/m-K was derived for the rGO film annealed at 1200 °C for 90 min. In addition, by bonding the rGO film on the Si chip, the hotspot temperature and thermal spreading resistance were reduced by 12 °C and 20%, respectively. The results indicate that the rGO films synthesized in this study retain a superior thermal property and can be employed for the thermal management of electronic devices.

Spectral Thermal Spreading Resistance of Wide-Bandgap Semiconductors in Ballistic-Diffusive Regime

To develop efficient thermal management strategies for wide-bandgap (WBG) semiconductor devices, it is essential to have a clear understanding of the heat transport process within the device and accurately predict the junction temperature. In this article, we use the phonon Monte Carlo (MC) method with the phonon dispersion of several typical WBG semiconductors, including GaN, SiC, AlN, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> -Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , to investigate the thermal spreading resistance in a ballistic-diffusive regime. This work shows that when compared with Fourier’s law-based predictions, the increase in the thermal resistance caused by the ballistic effects is strongly related to the phonon dispersion. Based on the model derived under the gray-medium approximation and the results of dispersion MC, we obtained a thermal resistance model that can well address the issues of thermal spreading, ballistic effects, and the influence of phonon dispersion. The model can be easily coupled with finite-element method (FEM)-based thermal analysis and applied to different materials. This article can provide a clearer understanding of the influence of phonon dispersion on the thermal transport process, and it can be useful for the prediction of junction temperatures and the development of thermal management strategies for WBG semiconductor devices.

Deep neural network prediction for effective thermal conductivity and spreading thermal resistance for flat heat pipe

PurposeThis study aims to introduce a deep neural network (DNN) to estimate the effective thermal conductivity of the flat heat pipe with spreading thermal resistance.Design/methodology/approachA total of 2,160 computational fluid dynamics simulation cases over up to 2,000 W/mK are conducted to regress big data and predict a wider range of effective thermal conductivity up to 10,000 W/mK. The deep neural networking is trained with reinforcement learning from 10–12 steps minimizing errors in each step. Another 8,640 CFD cases are used to validate.FindingsExperimental, simulational and theoretical approaches are used to validate the DNN estimation for the same independent variables. The results from the two approaches show a good agreement with each other. In addition, the DNN method required less time when compared to the CFD.Originality/valueThe DNN method opens a new way to secure data while predicting in a wide range without experiments or simulations. If these technologies can be applied to thermal and materials engineering, they will be the key to solve thermal obstacles that many longing to overcome.

Numerical case study and modeling for spreading thermal resistance and effective thermal conductivity for flat heat pipe

Flat heat pipe, vapor chamber, thermal ground plane, and heat spreader have been emerging topics for various thermal applications such as electric battery packs and high-power computer chips. In this study, computational fluid dynamics is used to model the effective thermal conductivity of a vapor chamber and thermal ground plane. From various literature, simulation conditions are obtained for different flat heat pipe geometries. With the commercial code Fluent (Ansys Inc.), 4,800 cases have been used to examine the spreading thermal resistance tendencies for the different heat sink areas, heat source area, thickness, and heat transfer coefficient. In conclusion, the effective thermal conductivity increases when the thickness decreases or the heat sink area becomes greater with the same spreading thermal resistance value. In particular, the modified model of spreading thermal resistance is proposed for a better accuracy targeting various effective thermal conductivity, based on the original analytical model. A good agreement with a better accuracy is found between the model and the numerical results. This study will be able to provide the thermal system guideline for flat heat pipes.

Vacuum null-point scanning thermal microscopy: Simultaneous quantitative nanoscale mapping of undisturbed temperature and thermal resistance

Null-point scanning thermal microscopy (NP SThM) quantitatively measures undisturbed temperature without the influence of changes in physical properties and surface topography of the specimen. Simultaneously NP SThM measures the ratio of the sum of the tip-specimen contact thermal resistance and the spreading thermal resistance of the specimen to the effective thermal resistance of the SThM probe. Hence, arguably, NP SThM is an ideal SThM that meets all the requirements of SThM. However, in practice, the use of NP SThM has been limited to one-dimensional profiling only, and two-dimensional extension of NP SThM has been virtually impossible so far. This is because NP SThM is very difficult to implement and ensure a sufficient measurement sensitivity. In this study, we enable two-dimensional extension of NP SThM with almost a 20-fold improvement in measurement sensitivity even under mild vacuum conditions (<10−3 Torr). Through rigorous analysis of the two-dimensional imaging results of vacuum NP SThM (VNP SThM), we demonstrate the ideal characteristics and performance of VNP SThM. With the ideal measurement characteristics, and the greater sensitivity and convenience, VNP SThM is proven to be an essential tool in the analysis of nanoscale energy transport and conversion occurring inside nanodevices and nanomaterials.

Thermal spreading resistance of hollow hemi-sphere with internal convective cooling

The 2-D steady-state heat transfer in a hollow hemi-sphere subjected to an arbitrary general heat flux on its pole, and convective cooling at the inner surface, is studied analytically. Closed-form mathematical expressions for temperature distribution and non-dimensional thermal resistance as a function of radii ratio, contact angle, and the Biot number, are derived and presented for two cases that simulate the flux distribution from isoflux and isothermal heat sources. The analytical solution is verified by using a finite-element numerical solution, developed in a commercially-available software, and comparing the results. Moreover, it is demonstrated that the present fundamental analysis provides a general solution for other problems found in the literature, including spreading resistance in hollow spheres with insulated walls, as well as the heat source on a half-space and infinite disk with an isothermal end.