Inductive coupling effects in large TSV arrays

The effects of inductive coupling among TSVs within large TSV arrays are investigated in this paper. A comparison of the equivalent inductance of a paired TSV model and arrayed TSV macromodel is presented for three TSV distribution topologies, grouped, lined, and uniform, within the power network. Modified closed-form expressions are proposed to determine the equivalent inductance of a TSV in these large TSV arrays. Simulation results show that this method achieves hundred times speed improvement as compared to an electromagnetic field solver while maintaining accuracy within 7%.