Capacitance calculation of TSVs using an integral equation method based on partial capacitances

An integral equation method based on partial capacitances is used to extract the capacitance between two through-silicon-vias (TSVs). The unrealistic assumption of equal potential along the vertical interface of silicon dioxide (SiO₂) coating of TSVs in the analytical method has been removed by introducing unknown equivalent charges. The Galerkin method is used here to solve the unknown charge densities in the integral equation and thus, the capacitance between two TSVs can be efficiently calculated. The results are validated by comparing the extracted capacitances with commercial software based on the finite element method. The accuracy and efficiency have been demonstrated.