Analysis of the Resistance of TSV in TSV-Based Inductors with Air Core

An analytical method is presented for determining the resistance of through-silicon via (TSV) in TSV-based inductors with air core. Firstly, integral equations are established by the boundary condition. Secondly, we solve integral equations by an approximate method of undetermined coefficients, and obtain the current density. Thirdly, the resistance calculated by current density are compared with the result got from the full-wave simulator in Ansys HFSS, which shows that error is less than 7%.