Thermal Spreading Resistance and Heat Source Temperature in Compound Orthotropic Systems With Interfacial Resistance

In this paper, a new and more general solution for thermal spreading resistance in compound, orthotropic systems with interfacial resistance is considered. This new solution, which extends beyond previously published results, is obtained for a finite rectangular heat source of uniform strength arbitrarily located on a rectangular substrate. By means of superposition, one can obtain the temperature field in the source plane for multiple heat sources as well as the source mean and centroid temperatures. By means of orthotropic transformations, systems containing orthotropic materials can be easily modeled. Extension of the present solutions using a computationally efficient influence coefficient method is also given, such that the effects of large numbers of heat sources are superimposed. The application of these closed-form expressions for the temperature rise is demonstrated with calculations for Gallium nitride (GaN) high electron mobility transistors (HEMTs). These solutions are shown to be more flexible than previously reported analytical expressions and much more computationally efficient than 3-D finite element analysis, especially for a large number of discrete heat sources associated with multifinger GaN HEMTs.