The effect of some composite structures on the thermal resistance of substrates and integrated circuit chips

An exact three-dimensional solution to the differential equation for steady-state heat transfer in composite media has been derived. Detailed results for 0.050-in-square chips mounted on 1- and 2-in-square substrates show that the thermal resistance of alumina substrates may be expected to increase by as much as 80 percent upon application of a glaze to the surface. The thermal resistances of beam lead chips varying in size from 0.050-to 0.150-in square are determined for chip-substrate interface distances from 0.0005 to 0.002 in, both with and without a thermal conducting compound as the interface media.