Thermal Aware IR drop using Mesh Conforming Electro-Thermal Co-Analysis

PI engineers designing Power Distribution Networks (PDNs) apply electric IR drop analysis tools in order to optimize the supply voltage margins for the ICs mounted on the board. The IR drop is affected by the thermal conditions due to the temperature dependency of the material properties. Hence, including thermal effects in the IR drop analysis is important. Both the electric power dissipation inside the IC's and the Joule loss in the copper contribute to the generated heat. We use a finite element discretization technique to solve the coupled electric and thermal steady-state equations simultaneously. Our solution combines H(div) Whitney face elements with electro-thermal mesh conformity, preserving all geometrical details in both domains. The exchange of electric data (power loss) and thermal data (temperature) happens at the mesh level speeding up the solution process and increasing the accuracy of the simulations. The electro-thermal co-analysis technique is validated using a via test board and applied to the PandaBoard to demonstrate the significance of thermal aware IR drop.