Coefficients of thermal expansion of metal-matrix composites for electronic packaging

Finite element analyses of the effective coefficient of thermal expansion (CTE) of metal-matrix composites are presented, with a focus on composites with potential for use in electronic packaging applications. The analyses are based on two-dimensional plane strain and axisymmetric unit-cell models. The brittle phase is characterized as an isotropic elastic solid with isotropic thermal expansion. The possibility of plastic deformation, described by an isotropic-hardening flow rule, is allowed for in the ductile phase. A wide range of reinforcement volume fractions is considered. The effects of phase geometry, phase contiguity, ductile phase material properties, processing-induced residual stresses, and brittle particle fracture are considered. The CTE is found to be much less sensitive to phase distribution effects than is the tensile stiffness. The results show that there is a significant dependence of the overall CTE on the phase contiguity (i.e., on whether the brittle or the ductile phase is continuous).