Sequentially formed underfills: Thermo-mechanical properties of underfills at full filler percolation

To ensure functionality and integrity of electronic package interconnects, underfill materials are designed to meet a desired stiffness that bridges the thermal expansion behavior of die, substrates and interconnects. The underfill protects the interconnects from thermal strains and environmental influences. Recently, the thermal conductivity became a critical parameter too, to efficiently dissipate heat from 3D chip stacks. Accordingly, the particle loading is increased beyond the percolation threshold, which was demonstrated by sequentially fabricated materials with a 5fold thermal conductivity improvement. This paper explores the thermo-mechanical properties of the novel percolating thermal underfills considering alumina filler particles. The changing behavior of underfill composites has been well described for various fillers and matrices both theoretically and experimentally. But percolation was excluded so far for lack of relevance. We compare the numerical predictions of composites´ Young´s moduli around the filler percolation threshold to known effective-medium approximation bounds of polydisperse materials. The simulations were based on 3D unit cells of the face centered cubic packing in different lattice orientations and consider both filler and matrix materials. A significant change in characteristics is observed close to percolation. However, the 100 and the 110 lattice orientations give a 5% Young´s modulus difference only. The numerical predictions are within effective-medium approximation bounds, but appear closer to either upper or lower bounds depending on the filler fraction. The presented results extend the possible thermo-mechanical parameter space of conventional underfills to percolating composites.