Stationary Temperature Profiles and Heat Flux Distribution in a Plastic-encapsulated Circuit Package
by J. A. Paivanas
Thermal characteristics that are important to structural integrity are analyzed herein for a TTL, plastic-encapsulated package. By assuming that total module heat during operation is engendered at idealized junctions between lead wires and the chip surface, an analysis of its dissipation has been undertaken to determine internal steady-state temperature profiles and heat flux distribution. Based on junction heat sources of equal strength and on certain adiabatic assumptions, the multi-wire package has been modeled as a single-wire "composite" incorporating postulated heat dissipation mechanisms in representative plastic-to-wire and chip-to-lead frame thermal circuits. These circuits are treated, respectively, by axisymmetric and one-dimensional analyses. Instead of a partial differential equation approach in the former treatment, a less complicated method is devised which leads to characterization by a pair of linear ordinary differential equations. Their closed-form solution gives expressions for calculating two-dimensional temperature profiles and heat flux fractions. The resultant analyses are applied to a module containing 14 lead wires and operating at a given power level. The plastic and wire temperature profiles are seen to be nonlinear in the neighborhood of the chip surface and to coalesce axially into a common, essentially linear form in the outlying regions of the module. Constituent heat fluxes are also calculated for each thermal circuit, and some implications of the overall results to thermal stress are qualitatively discussed.