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 Blot 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.