Design of circular heat spreaders on semi-infinite heat sinks in microelectronics device applications

Using the rigorous analytical solutions, we discuss design aspects in terms of thermal resistance and temperature uniformity for the canonical heat dissipation configuration consisting of a circular heat spreader on a semi-infinite heat sink. Regarding the optimized size of the heat spreader, we have found that the minimum temperature thickness of the spreader depends on the thermal conductivity values of the spreader and the sink, in contrast to the results published previously by other researchers. In addition, a new design formula d=0.44 b for the selection of spreader thickness d from the spreader radius b is proposed to replace the commonly used rule d=b/3. Our results have confirmed the design rule b=5 a for the selection of the spreader radius b from a given heat source radius a. To facilitate the complete design of the heat spreaders, we present two nomographs in the form of contour plots for the normalized thermal resistance and the normalized temperature uniformity.