Random network percolation models for particulate thermal interface materials

Abstract

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.

On refining the parameters of a Random Network Model for determining the effective thermal conductivity of particulate thermal interface materials

“…In a subsequent study [11], we found that the earlier model [2] using a cylindrical region to approximate the thermal transport within the filler particles as being less accurate when the polydispersivity of the particulate system increases. We developed a novel semi-spherical approximation to the conductance of fillers as an alternative to the cylindrical region approximation used in reference [2].…”

“…But the classical models are often inaccurate at larger volume fractions (up to 80%) and when SDUWLFOHV DUH LQ ³QHDU SHUFRODWLRQ´ DUUDQJHPHQWV ,Q WKHLU VWXG\ D random network model (RNM [2]) was developed and applied to evaluate the effective thermal conductivity of particulate thermal interface materials. The heat transport between the filler particles ZDV DFFXUDWHO\ FDSWXUHG E\ LPSOHPHQWLQJ %DWFKHORU ¶V [6] estimate of the conductance between two spherical particles in near contact.…”

“…RNM [2] has the advantage of being able to handle random particle size variations compared to the percolation models as they are classically used [7][8][9]. In the RNM [2], the heat conductance between the spherical filler particles was approximated by cylindrical zones. The network model was used to evaluate the bulk conductivities of random microstructures.…”

“…We developed a novel semi-spherical approximation to the conductance of fillers as an alternative to the cylindrical region approximation used in reference [2]. The revised model showed a better agreement with experimental data than the model of reference [2].…”

The Effect of Polydispersivity on the Thermal Conductivity of Particulate Thermal Interface Materials

“…The goal of the present paper is to study the effect of polydispersivity on the effective thermal transport in polymeric composites using a computationally efficient random network model developed earlier by the authors [20,21]. The network model was demonstrated in our prior work to capture accurately (for composites with a very high contrast in the constituent thermal conductivities) the effect of random spatial distribution of the particles as well the constituent thermal conductivities on the effective thermal conductivity of the composite.…”