Thermal conductivity of metal-matrix composites

The thermal conductivity of metal-matrix composites, which are potential electronic packaging materials, is calculated using effective medium theory and finite-element techniques. The thermal boundary resistance, which occurs at the interface between the metal and the included phase (typically ceramic particles), has a large effect for small particle sizes. It is found that SiC particles in Al must have radii in excess of 10 μm to obtain the full benefit of the ceramic phase on the thermal conductivity. Bimodal distributions of particle size are considered, since these are often used to fabricate high-volume fraction composites. It is found that if the small particles (in a bimodal distribution) have a radius less than 2.5 μm in SiC/Al their addition reduces the thermal conductivity of the composite. Diamond-containing composites, which have large thermal boundary resistance effects, are analyzed. Comparison of the effective medium theory results to finite-element calculations for axisymmetric unit-cell models in three dimensions and to simulation results on disordered arrays of particles in two dimensions confirms the validity of the theory.