Fast and accurate electro-thermal analysis of three-dimensional power delivery networks

Power delivery networks (PDNs) are essential to the optimal performance of the circuits. Reliable design of three-dimensional (3D) PDNs faces several challenges due to parasitics of each tier PDN and Through-Silicon-Vias (TSVs). Furthermore, as 3D integration enables high circuit densities, it induces large current demand from the PDN. Because of these attributes, 3D PDNs can suffer from excessive non-uniform voltage drop and temperatures. These are further exacerbated from electro-thermal coupling, as parasitics are temperature dependent. Already 2D PDNs are challenging to analyze due to their large granularity. 3D PDNs pose additional challenge due to multi tier PDNs connected together with TSVs resulting in even larger granularities. Thus, the objective of this work is to develop fast and accurate electro-thermal models and analysis for 3D PDNs. Electro-thermal duality is exploited to develop compact electrical and thermal analytical models for 3D PDNs and TSVs. Simulation results demonstrate the accuracy of the proposed analysis method.