Topological design of channels for squeeze flow optimization of thermal interface materials

Performance of thermal interface materials (TIMs) used between a microelectronic device and its associated heat spreader is largely dependent on the bulk thermal conductivity of the TIM, but the bond-line thickness (BLT) of the applied material as well as the interfacial contact resistances are also significant contributors to overall performance. Hierarchically Nested Channels (HNCs), created by modifying the surface topology of the chip or the heatsink with hierarchical arrangements of microchannels in order to improve flow, have been proposed to reduce both the required squeezing force and the final BLT at the interfaces. In the present work, a topological optimization framework that enables the design of channel arrangements is developed. The framework is based on a resistance network approximation to Newtonian squeeze flow. The approximation, validated against finite element (FE) solutions, allows efficient, design-oriented solutions for squeeze flow in complex geometries. A comprehensive design sensitivity analysis exploiting the resistance network approximation is also developed and implemented. The resistance approximation and the sensitivity analysis is used to build an automated optimal channel design framework. A Pareto optimal problem formulation for the design of channels is posed and the optimal solution is demonstrated using the framework.