Modeling TSV interposer considering depletion capacitance and substrate effects

摘要

In a method for modeling electromagnetic effects in a planar circuit that employs a plurality of through-silicon vias in a domain, a region around each through-silicon via is described in terms of a cylindrical accumulation mode basis function. The cylindrical accumulation mode basis function is incorporated into an equivalent circuit that describes selected electrical characteristics of each through-silicon via. A plurality of localized intervals around each through-silicon via is selected. A multilayer Green's function is approximated for I^MN_zz′ (wherein M and N identify selected layers and wherein zz′ designates layer boundaries in a layer through which the through-silicon via passes) in each localized interval without approximating the Green's function over the entire domain. Coefficients I^MN_zz′ are approximated over a predetermined range of frequencies (ω). Admittance parameters based on of I^MN_zz′ are calculated over a frequency sweep.