Dynamic electrothermal macromodeling: An application to signal integrity analysis in highly integrated electronic systems

The problem of dynamic electrothermal equivalent extraction for system level and signal integrity analysis is considered in the framework of standard macromodeling tech- niques. The self-heating and mutual thermal impedances of the embedded elements of the system—preliminarily evaluated via 3-D thermal simulations—are reduced with passive identification methods, and equivalent electrical models are realized with a Foster multiport synthesis scheme. The identification is pursued with a convex optimization approach, which is found to be well suited for the thermal problem. As a case study, the coupled electrothermal analysis of an ultra-thin chip-stacking module including two thinned silicon chips interconnected by a copper line is fully carried out in SPICE.