On The Correlation Between Multiple Hot Blocks And Package Thermal Resistance

A flip-chip package with square die is considered in this study. Up to four square non-intersecting hot blocks are imposed on the die´s otherwise uniform power distribution. Block locations on the die outline are randomly chosen with uniform probability. The power density of a given block is a random parameter, and is permitted to be as high as 10times the baseline uniform bulk power density. Additionally, the size of any block is also treated as a random parameter and is permitted to be as high as 10 % of the die area. A 6000-tuple Monte Carlo study of the packages is conducted, and the package thermal resistance (R_jc) noted in each case. A variety of models are fit to the R_jc using the block characteristics as key variables, and their quality is characterized using the statistical correlation coefficient as a model metric. The results suggest a 96 % correlation between R_jc and the largest product of local power ratio and square of effective local power density ratio among the blocks- providing a simple and useful method to immediately identify blocks with the most impact on R_jc in a die floorplan.