An Improved Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials Available to Purchase

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.