Maximum Temperatures in Diamond Heat Spreaders Using the Surface Element Method

Diamond heat spreaders are very attractive for lowering the temperature of laser diodes and computer chip components. The use of diamonds as heat spreaders is very advantageous because its thermal conductivity is so large, about four times that of copper. The diamond heat spreader is mounted on a semi-infinite heat sink. The purposes of this paper are to present (a) a surface element method for the analysis of such composite systems, (b) a set of convenient algebraic equations for the maximum temperatures, (c) optimal geometry conditions and (d) some accurate numerical results. The analysis method is an adaptation of the unsteady surface element method but is different because the present problem is a steady-state one. The surface element method with one node gives a relatively simple algebraic solution, which contains all the important dimensionless groups. The one-node solution is simple, accurate, and has a form that can give deep insight into the effects of various parameters; for example, it premits derivation of the optimal geometry corresponding to the minimal temperature at the hot spot. The study shows that the optimal geometry of the thickness to radius aspect ratio of the diamond heat spreaders is about 0.4. In addition to the single-node analysis, a multinode analysis is developed and very accurate results are presented. These results show that the single-node analysis is generally within 2 percent.