An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials
ABSTRACT Particulate composites are commonly used in microelectronics applications. One example of such materials is thermal interface materials (TIMs) that are used to reduce the contact resistance between the chip and the heat sink. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of interparticle interactions, especially in the intermediate volume fractions of 30%-80%. Another crucial drawback in the existing analytical as well as the network models is the inability to model size distributions (typically bimodal) of the filler material particles that are obtained as a result of the material manufacturing process. While full-field simulations (using, for instance, the finite element method) are possible for such systems, they are computationally expensive. In the present paper, we develop an efficient network model that captures the physics of interparticle interactions and allows for random size distributions. Twenty random microstructural arrangements each of Alumina as well as Silver particles in Silicone and Epoxy matrices were generated using an algorithm implemented using a Java language code. The microstructures were evaluated through both full-field simulations as well as the network model. The full-field simulations were carried out using a novel meshless analysis technique developed in the author's (GS) research . In all cases, it is shown that the random network models are accurate to within 5% of the full field simulations. The random network model simulations were efficient since they required two orders of magnitude smaller computation time to complete in comparison to the full field simulation.
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ABSTRACT: Point contact models for the effective thermal conductivity of porous media with uniform spherical inclusions have been briefly reviewed. The model of Zehner and Schlunder (1970) has been further validated with recent experimental data over a broad range of conductivity ratio from 8 to 1200 and over a range of solids fraction up to about 0.8. The comparisons further confirm the validity of Zehner-Schlunder model, known to be applicable for conductivity ratios less than about 2000, above which area contact between the particles becomes significant. This validation of the Zehner-Schlunder model has implications for its use in the prediction of the effective thermal conductivity of water frost (with conductivity ratio around 100) which arises in many important areas of technology.Journal of Porous Media 01/2011; 14(10). · 0.47 Impact Factor
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ABSTRACT: Thermal conduction of the particulate composites or granular materials can be widely used in porous materials and geotechnical engineering. And it has continued to develop "effective thermal conductivity" of medium by modeling energy relationship among particles in medium. This study focuses on the development of the effective thermal conductivity at the unsaturated conditions of soils using the modified network model approach assisted by synthetic 3D random packed systems (DEM method, Discrete Element Method) at the particle scale. To verify the network model, three kinds of glass beads and the Jumunjin sand are used to obtain experimental values at various unsaturated conditions. The PPE (Pressure Plate Extractor) test is then performed to obtain SWCC (Soil-Water Characteristic Curve) of soil samples. In the modified network model, SWCC is used to adjust the equivalent radius of thermal cylinder at contact area between particles. And cutoff range parameter to define the effective zone is also adjusted according to the SWCC at given conditions. From a series of laboratory tests and the proposed network model, the modified network model which adopts a SWCC shows a good agreement in modeling thermal conductivity of granular soils at given conditions. And an empirical correlation between the fraction of the mean radius () and thermal conductivity at given saturated condition is provided, which can be used to expect thermal conductivity of the granular soils, to estimate thermal conductivity of granular soils.Journal of the Korean Geotechnical Society. 01/2013; 29(1).
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ABSTRACT: An innovative approach for electrical chip to substrate and chip to chip interconnects is proposed. The coexistence of solder balls and rails on a chip is discussed, supporting power delivery and heat removal for high-performance flip-chip-onboard and 3D stack applications. The concept enables further bandwidth and current density scaling at a high count of interconnects for signaling, but also at a high solder area fill factor for power delivery and heat removal. The rail-shaped solder joints are also compatible with the current floorplans of microprocessors with voltages arranged in lines. After reflow, solder rails compared to balls can result in a much larger maximal solder width relative to their pads. Therefore, a staggered array arrangement was proposed to minimize shorting risk. In addition, a solder height engineering strategy utilizing modulated pad shapes is discussed to yield equal solder heights for balls and rails present on the same device. However, improper rail design was found to lead to two instability types: 1) Balling and 2) Asymmetric Solder Accumulation. The first is the result of a solder height to width ratio of larger than approximately 0.6 considering long rail lines. The second occurs due to fabrication imperfections. The initial non-symmetric pad/solder shape can cause the accumulation of solder at one rail end (typically the end with the larger area) after reflow. The stability of Bow Tie Rails against Asymmetric Solder Accumulation was investigated to provide design rules for a robust rail design. Accordingly, a solder shape phase diagram indicating the parameters of the three identified phases is compiled. Experimental investigations of reflown solder shapes were complemented with numerical results using a surface energy minimization tool called Surface Evolver. A prediction quality of better than 9% was identified indicating the applicability of the tool to perform solder shape designs. The solver was also capable to predict the men- ioned instabilities, rendering the tool even more valuable. Finally, a thermal interface resistance benchmark of ball and rail-like interconnects is performed in a bulk thermal tester. The rail interface with a solder fill factor of 57% yielded a 7 times reduced interface resistance.Electronic Components and Technology Conference (ECTC), 2013 IEEE 63rd; 01/2013