The role of the substrate in determining heat dissipation in high power electronics is calculated, subject to convective cooling in the small Biot number regime. Analytical models that exploit the large aspect ratio of the substrate to justify approximations are shown to predict the behavior with good accuracy over a wide range of configurations. The solutions distinguish heat spreading effects’ that enable high chip-level power densities from insulation effects that arise at large chip densities. In the former, the attributes of high thermal conductivity are apparent, especially when the substrate dimensions are optimized. Additional benefits that derive from a thin layer of a high thermal conductivity material (such as diamond) are demonstrated. In the insulating region, which arises at high overall power densities, the substrate thermal conductivity has essentially no effect on the heat dissipation. Similarly, for compact multichip module designs, with chips placed on both sides of the substrate, heat dissipation is insensitive to the choice of the substrate material, unless advanced cooling mechanisms are used to remove heat around the module perimeter.
High thermal conductivity diamond-doped silver paste for power electronics packaging
