Development of compact thermal models for advanced electronic packaging: methodology and experimental validation for a single-chip CPGA package
A methodology for creating compact thermal models of a single-chip CPGA package was developed and rigorously evaluated. Detailed package thermal models were exposed to a set of "hard" boundary conditions representing directional cooling scenarios. Studies were performed to compare the predicted temperature distributions in the package first when the metallic/ceramic sub-layers of the substrate and each pin in the array were individually modeled and secondly by combining the sub-layers as well as the pins and interstitial air into smeared layers. The smeared layer approach was found to be quite reasonable The detailed model was experimentally validated using a novel apparatus that allowed imposing temperature boundary conditions on the pin grid array and on the other surfaces, one at a time. Thermal response data were generated with the experimentally validated detailed model for a set of eight boundary conditions that were derived from a design of experiments approach using the minimum and maximum values of average heat transfer prevailing on the package external surfaces. Compact models of three different network topologies were generated utilizing a nonlinear programming algorithm. The simplest, five-resistor star-shaped network was unable to capture either the junction temperatures or the heat flows leaving the prime lumped areas within the required accuracy. Shunted networks with and without a floating node were also optimized, both topologies yielding good accuracy for both the junction temperatures and heat flows.