Fast admittance computation for TSV arrays

A fast method to calculate the admittance matrix of Through Silicon Vias (TSVs) is proposed in this paper. The silicon dioxide layers are equivalently modelled using the bound charge on the conductor surfaces as well as on the dielectric interface between the silicon dioxide and the silicon regions. Unknown surface densities of both the free and bound charge are expanded using the axial harmonics. Galerkin's method is then applied to obtain the capacitance and conductance matrices. The proposed method is validated with a full-wave 2D cross-sectional analysis tool for a typical TSV pair structure. Comparisons with popular closed-form expressions are also discussed.