THERMAL-ANALYSIS OF MICROELECTRIC PACKAGES AND PRINTED-CIRCUIT BOARDS USING AN ANALYTIC SOLUTION TO THE HEAT-CONDUCTION EQUATION

This paper provides an overview of the solution and application of the three-dimensional heat conduction equation for a rectangular-shaped, multilayer structure with discrete surface heat sources. A Fourier series expansion is used to represent both the heat source function and temperature solution. Trigonometric terms are used for the two planar coordinates whereas the Fourier coefficient for the temperature expansion provides the dependence in the direction of the substrate thickness. Boundary conditions consist of insulated edges and Newtonian surface cooling. Application possibilities are numerous. A computer program based on this method has been used to analyze simple heat sinking chassis panels and finned extrusions with mounted power transistors. More elegant solutions are provided for many types of single and multi-chip packages, including hybrid circuit substrates. The prediction of printed circuit board conduction effects is also possible. Although the theory and a variety of applications of the resultant computer codes have been previously published in technical journals and symposia proceedings, this paper presents the most unified and complete review to date.