Random network model for heat transfer in high contrast composite materials

Thermal management of future generations of integrated circuits will require the use of packages with higher thermal conductivity and greater areas of contact between particles. In this paper, we introduce a novel percolation computational model of the most commonly suggested design: polymer filled with highly conductive ceramic (e.g., boron nitride) particles. The effective conductivity of random networks of spherical conductors with different degree of: fill, polydispersity, conductivity, and interface contact were determined by solving systems of Kirchoff's equations for cubic resistor network. It was found that above the percolation threshold (approximately 0.36, all cases), the effective conductivity is almost a linear function of the amount of fill or contact area between particles. Also, monodispersed filler yielded significantly higher effective conductivity than systems with three filler sizes. The model shows that if any spatial periodic arrangement is used, then effective conductivity much higher than that of the polymer matrix cannot be reached by increasing the conductivity of the filler. Thus periodic composites below maximal packing volume fraction yield the effective conductivity comparable to that of the polymer. We show that for nonperiodic (random) arrays the conductivity does improve significantly with increasing fill volume above the percolation threshold. Also, in agreement with recent experimental work, we find the key to significant improvement in thermal conductivity is an increase in contact area between particles. This last result suggests an explanation for recent experimental reports that boron nitride-filled polymers provide for higher conductivity than polymers filled with harder materials. Our model allows for quantitative estimation of the the effective conductivity as a function of the contact area, polydispersity and the volume fraction.