Size effects on the thermal conductivity of polymers laden with highly conductive filler particles

Polymer-based composite materials are being used extensively in semiconductor packaging as thermal interface materials. In the flip-chip technology these materials are inserted between the chip and the heat spreader and also between the heat spreader and heat sink. The composites generally have a polymer base and highly conducting ceramic particles as fillers. The size of the filler particles affects the impact of the thermal boundary resistance between the particles and the matrix, R_b, and hence the overall thermal conductivity of the composite, k. We have modeled the composite using percolation theory to study the dependence of thermal conductivity and percolation threshold on the particle Biot number, which is a way to take into account the effect of particle size and R_b on k. The temperature dependence of R_b and the critical diameter are also studied using the acoustic mismatch model (AMM) for a polyethylene matrix with alumina particles as filler. The results indicate that R_b is most important below the percolation threshold, but also that increasing R_b tends to increase the percolation threshold. The presence of R_b leads to a critical Biot number such that as the Biot number is increased above 1, the composite thermal conductivity is reduced to below that of the matrix, until the percolation threshold is reached.