High-Frequency Electrothermal Characterization of TSV-Based Power Delivery Network

In this paper, high-frequency electrothermal characteristics of the power delivery network (PDN) are investigated for through-silicon-via (TSV)-based 3-D ICs by utilizing a self-developed electrothermal co-simulation solver. The solver circularly solves the full-wave electromagnetic equation and the steady heat conduction equation using the finite-element method. The preconditioned biconjugate gradient method combined with the element-by-element approximate factorization method is employed to speed up the simulation and save memory cost. Based on the solver, the impacts of the excitation condition and dielectric loss tangent are analyzed for a one-chip power grid, while the influence of TSV location is studied for a two-chip PDN structure. In the modeling, both the conductor and dielectric losses are taken into account, and the temperature dependence of material parameters is treated appropriately. As results, PDN impedance and self-heating-induced temperature rise are emphatically analyzed in a wide frequency range, and the electric field and temperature distributions of several resonance modes are presented. The results would be beneficial for the design and thermal management of 3-D PDNs.