Spreading Resistance in Multilayered Orthotropic Flux Channels With Different Conductivities in the Three Spatial Directions

In the microelectronics industry, the multilayered structures are found extensively where the microelectronic device/system is manufactured as a compound system of different materials. Recently, a variety of new materials have emerged in the microelectronics industry with properties superior to Silicon, enabling new devices with extreme performance. Such materials include β-Gallium-oxide (β-Ga₂O₃), and black phosphorus (BP), which are acknowledged to have anisotropic thermal conductivity tensors. In many of these devices, thermal issues due to self-heating are a problem that affects the performance, efficiency, and reliability of the devices. Analytical solutions to the heat conduction equation in such devices with anisotropic thermal conductivity tensor offer significant computational savings over numerical methods. In this paper, general analytical solutions for the temperature distribution and the thermal resistance of a multilayered orthotropic system are obtained. The system is considered as a multilayered three-dimensional (3D) flux channel consisting of N-layers with different thermal conductivities in the three spatial directions in each layer. A single eccentric heat source is considered in the source plane while a uniform heat transfer coefficient is considered along the sink plane. The solutions account for the effect of interfacial conductance between the layers and for considering multiple eccentric heat sources in the source plane. For validation purposes, the analytical results are compared with numerical solution results obtained by solving the problem with the finite element method (FEM) using the ANSYS commercial software package.