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 inter-particle 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 fullfield 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 inter-particle 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 [26]. 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.Keywords: Thermal interface materials, network models, full-field simulations.
Thermal Interface Materials (TIMs) are widely used in the microelectronics industry to adequately expel the waste heat generated in the chips, by reducing the contact resistance between the chip and the heat sink. A critical need in developing these TIMs is apriori modeling using fundamental physical principles to predict the effect of particle volume fraction and arrangements on effective behavior. Such models will enable one to optimize the structure and arrangement of the material. The existing analytical descriptions of thermal transport in particulate systems under predict (as compared to the experimentally observed values) the effective thermal conductivity since these models do not accurately account for the effect of inter-particle interactions, especially when particle volume fractions approach the percolation limits of approximately 50% -60%. Another crucial drawback in the existing analytical as well as the network models is the inability to model random size distributions of the filler material particles, which is what one obtains when particulates are produced. While full-field simulations (using the finite element method) are possible for such systems, they are computationally expensive. In the present paper, we develop efficient network models that capture the inter-particle interactions and also allow random size distributions. Fifteen microstructural arrangements of alumina as well as aluminum particles in silicone matrix were first experimentally characterized. Microstructures that are representative of the experimentally tested systems were simulated using a drop-fallshake algorithm implemented in java.Thirty such microstructural arrangements were evaluated through both full field simulations as well as the network models. In all cases, it is shown that the full-field simulations of effective behavior are accurate to within 10% of the experimentally measured values and the random network models are accurate to within 10% of the full field simulations. The random network models were efficient since they required a few minutes to run, while the full field simulations required 4-5 hours on an average to complete.
Thermal Interface Materials (TIMs) are particulate composite materials widely used in the microelectronics industry to reduce the thermal resistance between the device and heat sink. Predictive modeling using fundamental physical principles is critical to developing new TIMs since it can be used to quantify the effect of particle volume fraction and arrangements on the effective thermal conductivity. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of inter-particle interactions, especially in the intermediate volume fractions of 30%–80%. An efficient Random Network Model (RNM) that captures the near-percolation transport in these particle-filled systems, taking into account the inter-particle interactions and random size distributions, was previously developed by the authors. The RNM is computationally efficient compared to full field simulations and was demonstrated to match to within 5% of the full field simulations and to within 15% of the experimentally measured values. The RNM approach uses a cylindrical region to approximate the thermal transport within the filler particles and to capture the inter-particle interactions. This approximation is less accurate when the polydispersivity of the particulate system increases. In the present paper, a novel semi-spherical approximation to the conductance of the fillers is presented as an alternative to the cylindrical region approximation used earlier. The new semi-spherical model is compared to the cylindrical model in two and three dimensions. In two dimensions, the semi-spherical model and the cylindrical model were compared with Finite Element Model (FEM) results. The comparison showed that the temperature distribution of the semi-spherical model matched more closely to the FEM model than the temperature distribution of the cylinder model when the radius ratio of the two particles increases. In three dimension microstructures, the semi-spherical model and the cylindrical model were compared under various volume fractions. The comparison showed that thermal conductivities of the semi-spherical model were always higher than thermal conductivities of the cylindrical model and were in better agreement with existing experimental data for particulate TIMs at 58% volume loading.
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