Random network percolation models for particulate thermal interface materials

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 enables 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 mil-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-fall-shake 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.