Optimization for thermal and electrical performance for a flip-chip package using physical-neural network modeling

This paper reports a novel approach which combines concurrent thermal and electrical analysis with Artificial Neural Networks (ANNs). The application vehicle chosen to demonstrate this concept is a typical flip-chip electronic package. First, the thermal calculations are performed by solving the steady heat conduction equation in a three dimensional domain. The temperature profiles and chip-to-case thermal resistances are obtained for different number and sizes of thermal vias. This thermal data set is used to “train” an ANN model. Our “simple to complex” and simultaneous testing and training procedure is used to develop an appropriate network with best predictive capabilities. Then, an algebraic expression for the electrical wiring density on the chip is derived as a function of the via number and size for a typical wiring layout. Using this expression along with the ANN model for the thermal resistance, we illustrate a method where the maximum wiring density is determined for a prescribed chip-to-case thermal resistance