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A three-dimensional inverse heat conduction problem is solved in the present study by using the conjugate gradient method (CGM) and the general-purpose commercial code CFD - ACE+ to estimate the strength of the unknown heat generation for an encapsulated chip in a three-dimensional irregular domain. The advantage of calling CFD - ACE+ code as a subroutine in the present inverse calculation lies in that many difficult but practical 3D inverse problem can be solved under this construction since the general-purpose commercial code has the ability to solve the direct problem easily. The results obtained by using the CGM to solve this 3D inverse problem are justified based on the numerical experiments using the simulated exact and inexact measurements. It is concluded that reliable heat generation can be estimated by the present inverse algorithm. [DOI: 10.1115/1.4000720]

A finite element method was developed to predict the effective thermal conductivity of particle filled epoxy composites. Three-dimensional models, which considered the effect of filler geometry, filler aspect ratio, conductivity ratio of filler to matrix, and interfacial layer were used to simulate the microstructure of epoxy composites for various filler volume fractions up to 30%. The calculated thermal conductivities were compared with results from existing theoretical models and experiments. Numerical estimation of ellipsoids-in-cube model accurately predicted thermal conductivity of epoxy composites with alumina filler particles. The number of length division during mesh process and particle numbers used in the finite element analysis affect the accuracy of calculated results. At a given value of filler content, the numerical results indicated a ratio of conductivity of filler to matrix for achieving the maximum thermal conductivity. [DOI: 10.1115/1.4000210] Keywords: composite materials, thermal analysis, encapsulant, underfill, finite element method

This paper reports the design study performed on a heat conduction panel having several heat sources at separate locations and a heat sink on one of the panel corners. The panel is given a thickness distribution so as to provide spatially varying heat conduction paths from the heat sources to the heat sink. The objective of thickness distribution design is to reduce the variation among heat source temperatures and the maximum heat source temperature simultaneously. The genetic algorithm is used to search for an optimum thickness distribution. The problem is a generic representation of the situations that are becoming common in a compact electronic equipment. [DOI: 10.1115/1.2993137] Keywords: heat conduction path design, multiple heat sources, displaced heat sink, genetic algorithm application

An analytical model is developed to estimate the heat transfer performance of printed circuit board (PCBs). The PCB under study is the substrate for a ball-grid-array (BGA) package. Under the BGA, the PCB has a belt of densely populated through-vias that penetrate the laminate of horizontal copper and resin; outside the BGA-covered area the board is a copper/resin laminate and its surfaces are exposed to cooling air. Calculations are performed on a sample board having the dimensions 11 x 11 [cm.sup.2] (footprint) x 1.26 mm (thickness). The model of the board has two internal layers of continuous copper (0.03 mm thick) and through-vias under a 4.4 x 4.4 [cm.sup.2] BGA package. The impacts of board design parameters on the temperature and the heat flow are presented; the parameters are the width of the insulation gap around the via, the area of copper coverage at the via bottom, and the population of vias. [DOI: 10.1115l/1.2993126] Keywords: printed circuit board, heat conduction, analytical modeling, through-vias, copper/rein laminate

Over upcoming electronics technology nodes, shrinking feature sizes of on-chip interconnects and correspondingly higher current densities are expected to result in higher temperatures due to self-heating. This study describes a finite element based compact thermal modeling approach to investigate the effects of Joule heating on complex interconnect structures. In this method, interconnect cross section is assumed to be isothermal and conduction along the interconnect is retained. A composite finite element containing both metal and dielectric regions is used to discretize the interconnect stack. The compact approach predicts the maximum temperature rise in the metal to within 5-10% of the detailed numerical computations, while requiring only a fraction of elements. Computational time for the compact model solution is several seconds, versus many hours for the detailed solutions obtained through successive mesh refinement until grid independence is achieved. For a comparable number of elements, the compact model is in general much more accurate than the traditional finite element approach. To validate the simulations, temperature rise in a 500-link two-layer interconnect with a via layer was measured at several current densities. The compact method predicts the temperature rise of the 500-link chain to within 5% of the measurements thereby validating the method. The approach described here could be an efficient technique for full chip Joule heating simulations and for clock signal propagation simulations, which are performed as part of designing next generation chip architectures. [DOI: 10.1115/1.2957318]

We report the first use of a bimetallic buckling disk as a thermal conduction switch. The disk is used to passively alter the thermal resistance of the package of a chip scale atomic clock. A vertical-cavity surface-emitting laser and a cesium vapor cell, contained in the clock, must be maintained at 70 [+ or -] 0.1[degrees]C even under an ambient temperature variation of -40[degrees]C to 50[degrees] C. A thermal test vehicle has been developed to characterize a sample package with a thermal conduction switch. Three cases are presented for the temperature control of the test vehicle under different load placements and environmental conditions: (1) a heating load with a good conduction path to the switch in a vacuum package; (2) the same loading as in Case 1, but packaged in air; and (3) a heating load insulated from the switch, in a vacuum package. At 38[degrees]C, the switch snaps upward to reduce the package's thermal resistance. As a result, the heating power needed to maintain a constant temperature, 63.9 [+ or -] 0.1[degrees]C, is increased from 118 to 200 mW for Case 1. Such a significant change of the thermal resistance demonstrates the effectiveness of the thermal switch. However, the switch becomes less effective with air filling the gap, as in Case 2, and the switch is not effective at all if the heating load does not have a good conduction path to the switch as in Case 3. The steady state response of this novel thermal conduction switch has been well characterized through experimentation and finite element analysis. [DOI: 10.1115/1.2912187]

Traditionally, large quantities of ceramic fillers are added to polymers in order to obtain high thermally conductive polymer composites, which are used for electronic encapsulants. However, that is not cost effective enough. In this study, [Si.sub.3][N.sub.4] particle filled epoxy composite with a novel structure was fabricated by a processing method and structure design. Epoxy resin used in particle form was obtained by premixing and crushing. Different particle sizes were selected by sieving. High thermal conductivity was achieved at relative low volume fraction of the filler. The microstructure of the composites indicates that a continuous network is formed by the filler, which mainly completes the heat conduction. Thermal conductivity of the composites increases as the filler content increases, and the samples exhibit a highest thermal conductivity of 1.8 W/m K at 30% volume fraction of the filler in the composites using epoxy particles of 2 mm. The composites show low dielectric constant and low dielectric loss. [DOI: 10.1115/1.2804097] Keywords: thermal conductivity, polymer composite, ceramic filler, dielectric properties

This paper presents the results of an analytical study of steady state heat conduction in multiple rectangular domains. Any finite number of domains that are equally sized (in plane) may be considered in the current analysis. The thermal conductivity and thickness of these domains may be different. The entire geometry composed of these connected domains is considered as adiabatic on the lateral surfaces and can be subjected to a wide range of thermal boundary conditions at the top and bottom. For example, the bottom of the stack may be adiabatic, while the top of the stack may be exposed to a uniform heat transfer coefficient. Spatially varying heat generation rates can be applied in each of the domains. The solutions are found to be in agreement with known solutions for simpler geometries. The analytical solution presented here is very general in that it takes into account the interface resistances between the layers. One application of this analytical study relates to the thermal management of three-dimensional stacks of computer devices and interconnect layers. The devices would have spatially nonuniform power dissipation within them, and the interconnect layers would have a significantly lower thermal conductivity than the devices. Interfacial defects, such as delamination or air voids, between the devices and the interconnect layers may be included in the model Another possible application is to the study of hot spots in a chip stack with nonuniform heat generation. Many other potential applications may also be simulated. [-DOI: 10.1115/1.2804094]

The thermal design of plate fin heat sinks can benefit from optimization procedures where all design variables are simultaneously prescribed, ensuring the best thermodynamic and air flow characteristic possible. While a cursory review of the thermal network established between heat sources and sinks in typical plate fin heat sinks would indicate that the film resistance at the fluid-solid boundary dominates, it is shown that the effects of other resistance elements, such as the spreading resistance and the material resistance, although of lesser magnitude, play an important role in the optimization and selection of heat sink design conditions. An analytical model is presented for calculating the best possible design parameters for plate fin heat sinks using an entropy generation minimization procedure with constrained variable optimization. The method characterizes the contribution to entropy production of all relevant thermal resistances in the path between source and sink as well as the contribution to viscous dissipation associated with. fluid flow at the boundaries of the heat sink. The minimization procedure provides a fast, convenient method for establishing the 'best case' design characteristics of plate fin heat sinks given a set of prescribed boundary conditions. It is shown that heat sinks made of composite materials containing nonmetallic constituents, with a thermal conductivity as much as an order of magnitude less that typical metallic heat sinks, can provide an effective alternative where performance, cost, and manufacturability are of importance. It is also shown that the spreading resistance encountered when heat flows from a heat source to the base plate of a heat sink, while significant, can be compensated for by making appropriate design modifications to the heat sink. [DOI: 10.1115/1.2429713]

The increased heat generation in power electronic components can greatly reduce the reliability of the components and increase the chances of malfunction to the components. A good understanding of the thermal behavior of these components can help in deciding an effective thermal management scheme. Recognizing the inherent need for the thermal design of the active integrated power electronics modules, this paper assesses various possibilities of integrated thermal management for integrated power electronics modules. These integrated thermal management strategies include employing high thermal conductivity materials as well as structural modifications to the current module structure while not adding complexity to the fabrication process to reduce the cost. [DOI: 10.1115/1.2429703]

An experimental study was conducted to determine the performances of silicon microheat pipes (MHPs) filled with different fluids. The MHP arrays are made of 27 triangular microchannels chemically etched in a silicon wafer. This wafer is closed by molecular bonding of a bulk oxidized silicon wafer. The results show that the use of MHPs with low liquid charges can increase the effective thermal conductivity of the array. The best improvement of the effective thermal conductivity of the MHP array is equal to 41%for methanol and pentane, 12% for ethanol and nil for water and FC72. [DOI: 10.1115/1.2229233] Keywords: microheat pipe, experiment, heat transfer, silicon technology, effective thermal conductivity

Power dissipation in electronic devices is projected to increase over the next 10 years to the range of 150-250 W per chip for high performance applications. One of the primary obstacles to the thermal management of devices operating at such high powers is the thermal resistance between the device and the heat spreader or heat sink that it is attached to. Typically the in situ thermal conductivity of interface materials is in the range of 1-4 W/mK, even though the bulk thermal conductivity of the material may be significantly higher. In an attempt to improve the effective in situ thermal conductivity of interface materials nanoparticles and nanotubes are being considered as a possible addition to such interfaces. This paper presents the results of a numerical study of transport in a thermal interface material that is enhanced with carbon nanotubes. The results from the numerical solution are in excellent agreement with an analytical model (Desai, A., Geer, J., and Sammakia, B., 'Models of Steady Heat Conduction in Multiple Cylindrical Domains,' J. Electron. Packaging (to be published)) of the same geometry. Wide ranges of parametric studies were conducted to examine the effects of the thermal conductivity of the different materials, the geometry, and the size of the nanotubes. An estimate of the effective thermal conductivity of the carbon nanotubes was used, obtained from a molecular dynamics analysis (Mahajan, S., Subbarayan, G., Sammakia, B. G., and Jones, W., 2003, Proceedings of the 2003 ASME International Mechanical Engineering Congress and Exposition, Washington, D.C., Nov. 15-21). The numerical analysis was used to estimate the impact of imperfections in the nanotubes upon the overall system performance. Overall the nanotubes are found to significantly improve the thermal performance of the thermal interface material. The results show that varying the diameter of the nanotube and the percentage of area occupied by the nanotubes does not have any significant effect on the total temperature drop. [DOI: 10.1115/1.2161231] Keywords: thermal management, carbon nanotubes, thermal interface material (TIM), numerical modeling, analytical modeling, molecular dynamic simulations

An analytical model of steady state heat conduction in multiple cylindrical domains is presented and discussed. The domains are axisymmetric, contiguous, and coaxial. Three domains are considered in the current study. The thermal conductivities, thicknesses, and radii of the domains may be different. The entire geometry composed of the three connected domains is considered as adiabatic on its lateral surfaces and is subjected to uniform convective cooling at one end. The other end of the geometry is subjected to a constant heat flux, while uniform heat generation is imposed in one of the domains. The analytical solution of the model is found and special cases of it are shown to be in agreement with known solutions for simpler geometries. One application of this model relates to the thermal management of computer chips that are attached to a heat sink or a heat spreader. The three layers could simulate the chip, the thermal adhesive and the heat sink. Another application is the simulation of a nanotube or nanocylinder connecting a region of the chip to a region of the heat sink. Many other potential applications may be simulated using the different possible configurations for the solution presented. [DOI: 10.1115/1.2159003]

A finite element method (FEM)formulation for the prediction of unknown steady boundary conditions in heat conduction for multidomain three-dimensional (3D) solid objects is presented. The FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown, provided such quantities are sufficiently overspecified on other boundaries. An inverse finite element program has been previously developed and successfully tested on 3D simple geometries. The finite element code uses an efficient sparse matrix storage scheme that allows treatment of realistic 3D problems on personal computer. The finite element formulation also allows for very straightforward treatment of geometries composed of many different materials. The inverse FEM formulation was applied to the prediction of die-junction temperature distribution in a simple ball grid array electronic package. Examples are presented with simulated measurements, which include random measurement errors. Regularization was applied to control numerical error when large measurement errors were added to the overspecified boundary conditions.

Experiments involving several types of thermally conductive adhesives are conducted to determine the fracture toughness and bond strength of the materials at varying temperatures. These include the Emerson and Cumming LX 3739, the Dow Corning 6325 and 6632. Results show that the J-integral values of adhesives considered as hyperelastic materials jive with those derived from linear-elastic materials.

Instead of the classic Fourier equation based on diffusion, a hyperbolic equation based on a wave model has been used to predict the rapid transient heat conduction in IC chips. The peak temperature, spatial difference, and time variation of temperature, which are critical to thermal reliability of the chip, are given and compared with that obtained from the Fourier equation. Analytical and numerical results show that non-Fourier effects, including the higher peak temperature and thermal stress, greater temperature difference between components, and stronger thermal noise, are significant to IC chip reliability.

A numerical analysis on the heat conduction characteristics of concentric cylinders is presented. The study is relevant to heat transfer in electronic equipment wherein cylindrical electrical conductors or thermal vias (typically characterized by high thermal conductivities) are surrounded by electrical insulators having a different thermal conductivity. The heat conduction equation is solved using a control-volume finite-difference technique. Results are presented in terms of the thermal spreading resistance, the heat removal contribution of the inner cylinder (pin) and the heat spreading contribution of the surrounding material for a wide range of governing parameters. In particular, the effects of the thermal conductivities of the cylinders and the geometric dimensions on the heat spreading characteristics are investigated. It is shown that there is no spreading when the ratio of the conductivity of the pin to the conductivity of the surrounding material (k/K) is larger than about 1000; as found in copper pins surrounded by Teflon or Fr-4 type of a dielectric material. Substantial reduction in the overall thermal resistance is obtained with k/K less than 10, which could be practically achieved by using silicon carbide or aluminum nitride as the surrounding material.

Exact series solutions for three-dimensional temperature distribution in two-layer bodies subject to various types of boundary conditions are presented. Special consideration is given to the case when one layer is a thin diamond film. The computation emphasizes the temperature effect of an embedded thin heat source of the type used in electronic devices. The mathematical formulation employs the Green's function solution method. The solution is time partitioned in order to achieve a high degree of accuracy. Time partitioning greatly improves the convergence of three-dimensional heat conduction solutions. Time-partitioned series solutions with a reduced number of terms yield highly accurate temperature data. A two-layer model is chosen for simplicity of presentation; however, the method can be extended to more than two layers.

The electrical current carrying capability of a surface or buried trace located within a fiberglass printed circuit board (PCB), is of important interest in the microelectronics industry. The maximum allowable trace power, hence local integrity and maximum allowable operating temperature, will depend on several parameters including the circuit board thermal conductivity, thickness, trace size and location. A two-dimensional, steady-state thermal conduction analysis is made on a finite, plane homogeneous medium (PCB), to examine the trace behavior. The trace is modeled as a zero-thickness, strip heat source with specified uniform temperature, and it's position in the medium is varied. A two-dimensional thermal analysis is also performed on a multilayered cell model with finite heat source, to establish an accurate, effective thermal conductivity for a typical PCB. Results are tabulated and presented graphically for both the two-dimensional trace and effective conductivity models.

The passive cooling, including the transient start-up process, of a leadless chip carrier package mounted on a vertical substrate in a liquid filled cubic enclosure is investigated numerically. A relatively detailed thermal model of the electronic package is included. The governing three-dimensional unsteady equations for natural convection within the fluid and for the coupled heat conduction in the package are solved numerically using a finite difference method. The transient heat up of the system can be characterized by four stages: 1) initial heat up of the chip with some conduction through the package and the surrounding fluid; 2) increased conduction characterized by symmetric thermal spreading through the substrate, accompanied by the development of the natural convection flow field; 3) increased convection effects, as the buoyant driving force reaches its peak level, leading to asymmetric spreading through the substrate and a strong plume above the package; 4) gradual approach to steady state as the fluid in the enclosure is slowly heated, with reduced buoyant driving force and hence decreasing velocities. Steady-state conditions are characterized by thin boundary layers along the hot and cold surfaces, well stratified temperature in the core, a strong plume above the package, and oval shaped isotherms along the substrate surface. With FC-75 as the coolant, a large fraction of the heat generated in the chip is conducted to the substrate and then transferred to the fluid, due to the high thermal conductivity of the substrate relative to that of the fluid. Even when the upper lid of the package is removed, exposing the chip directly to the fluid, the chip temperature drops only by 5 percent, indicating the importance of substrate conduction. Use of a chip that has twice the cross-sectional area as the base case results in a 25 percent drop in chip temperature, with little effect on the remainder of the flow. When water is used as the coolant instead of FC-75, the nondimensional temperature of the chip increases, due to the lower Rayleigh number and lower ratio of substrate-to-fluid thermal conductivity. In dimensional units, however, the actual chip temperature is 25 [degrees] C cooler., The passive cooling of a leadless chip carrier package in a liquid-filled enclosure is analyzed. The finite difference method is used to solve the three-dimensional equations of the natural convection in the enclosure and the coupled conduction in the package and substrate. Using FC-75 as the coolant conducts a large amount of heat from the chip to the substrate which is then transferred to the fluid. Water used as the coolant increases the nondimensional temperature of the chip.

A numerical and experimental study of conduction heat transfer from low power magnetic components with gull wing leads was conducted to determine the effects of distributing the power loss between the core, the winding and the thermal underfill on the thermal resistance. The numerical study was conducted in the power loss ratio range of 0.5 [is less than or equal to] PR [is less than or equal to] 1.0, where the only active power loss was from the winding at PR=1. In addition, the effect of the thermal underfill material between the substrate and the lower surface of the magnetic package on the thermal performance of the magnetic device was also examined. For comparison, a test was conducted on a magnetic component at PR=1, without thermal underfill. This comparison revealed good agreement between the numerical and experimental results. Finally, a general model was proposed for conduction heat transfer from the surface mount power magnetic packages. The agreement between the model and the experimental results was within 8 percent. [S1043-7398(00)00704-0]

Sodium silicate based thermal interface pastes give higher thermal contact conductance across conductor surfaces than polymer based pastes and oils, due to their higher fluidity and the consequent greater conformability. Addition of hexagonal boron nitride particles up to 16.0 vol. percent further increases the conductance of sodium silicate, due to the higher thermal conductivity of BN. However, addition beyond 16.0 vol. percent BN causes the conductance to decrease, due to the decrease in fluidity. At 16.0 vol. percent BN, the conductance is up to 63 percent higher than those given by silicone based pastes and is almost as high as that given by solder. Water is almost as effective as sodium silicate without filler, but the thermal contact conductance decreases with time due to the evaporation of water. Mineral oil and silicone without filler are much less effective than water or sodium silicate without filler. [S1043-7398(00)00402-3]