Thermal properties of the multilayer infinite plate structure

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Abstract
Using the double Fourier integral transform method, the analytical temperature solutions to the single-layer and multilayer structures with infinite lateral dimensions have been derived. For the single-layer structure, temperature dependence of the thermal conductivity has been taken into account using the Kirchhoff transformation. The use of discrete rectangular heat sources rather than circular heat sources on the top surface of the structure makes this model particularly useful for the thermal analysis of common solid-state and integrated circuit devices and packages. For studying the thermal properties of a large class of solid-state device geometries, this model can be utilized to approximate actual devices with reasonable accuracy. The general device geometries for which this model can be employed to represent the actual devices are determined. Compared with the model where the finite extent of the chip lateral dimensions is considered, the present model is much more computationally efficient for cases where the heat source size is much smaller than the substrate or package size.

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