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In this paper, the electrical-thermal co-simulation of 3D systems with Joule heating, fluidic cooling and air convection effects is proposed. The finite-volume method formulations of voltage distribution equation, heat equations for both fluid flow and solid medium with nonuniform mesh are explained in detail. Based on the proposed iterative co-simulation method, package temperature distribution and voltage drop with Joule heating and fluidic cooling effects can be estimated. Several packaging examples are simulated and the results show that with micro-channel fluidic cooling in high power density 3D integrated packages, the thermal effect on voltage drop is reduced by 10% which is much less than that of using a traditional heat sink.
Xie et al. (Mon,) studied this question.