A two-port analytical model for thermal characterization boards

Thermal characteristics of packaged semiconductor devices are difficult to compare, especially between suppliers and sometimes even across packages from the same supplier. Yet at a fundamental level, "standard" thermal test boards are relatively simple thermal systems characterized by just a few critical parameters, and they should respond simply and consistently to thermal inputs (that is, a heat source of certain dimensions and power level). There should be a means by which data taken on one style of board could be extrapolated quickly and reasonably accurately to any other type of standard test board. To this end, an axisymmetric thermal model (essentially a 1D cylindrical "fin") is developed and its closed-form solution expressed as a two-port network (heat flow and temperature, in and out). The resulting two-port network is utilized to describe a more complex thermal model consisting of multiple regions of differing thermal properties. Its application to thermal characterization of semiconductor devices is discussed, as an example demonstrating the relationship between so called "min pad" and "1-inch pad" device characteristics. The model is also compared to other experimental data, where the "best fit" of the axisymmetric model shows a reasonable correlation with the normalized temperature values of the experiment.