As the size of hybrid microelectronics is reduced, the power density increases and thermal interaction between heat-producing devices becomes significant. A nondimensional model is developed to investigate the effects of heat source interaction on a substrate. The results predict the maximum temperature created by a device for a wide range of device sizes, substrate thicknesses, device spacings, and external boundary conditions. They can be used to assess thermal interaction for preliminary design and layout of power devices on hybrid substrates.

Previous work in this area typically deals with semi-infinite regions or finite regions with isothermal bases. In the present work, the substrate and all heat dissipating mechanisms below the substrate are modeled as two separate thermal resistances in series. The thermal resistance at the base of the substrate includes the bond to the heat sink, the heat sink, and convection to a cooling medium. Results show that including this external resistance in the model can significantly alter the heat flow path through the substrate and the spreading resistance of the substrate. Results also show an optimal thickness exists to minimize temperature rise when the Biot number is small and the device spacing is large.

Tables are presented which list nondimensional values for maximum temperature and spreading resistance over a wide range of substrate geometries, device sizes, and boundary conditions. A design example is included to demonstrate an application of the results to a practical problem. The design example also shows the error that can result from assuming an isothermal boundary at the bottom of the substrate rather than a finite thermal resistance below the substrate.

Several other models are developed and compared with the axisymmetric model. A one-dimensional model and two two-dimensional models are simpler than the axisymmetric model but prove to be inaccurate. The axisymmetric model is then compared with a full three-dimensional model for accuracy. The model proves to be accurate when sources are symmetrically spaced and when sources are asymmetrical under certain conditions. However, when the sources are asymmetrical the axisymmetric model does not always predict accurate results.