Admittance extraction and analysis for through silicon vias near edge and at corner of silicon substrate

Due to the charge at the interfaces between the silicon substrate and its outer region, the admittance of the through silicon vias (TSVs) near the edge and at the corner of the silicon is different from that of the centre case, which is hardly calculated by conventional empirical formulas. Utilising the method of moment combined with the image method in this study, those admittances can be easily extracted. The difference on the admittance between edge/corner and centre cases is discussed with the frequency and the wave propagation mode. The influence of the distance to the silicon-outer region interfaces and pitches of the TSVs on the admittance are also evaluated and compared in edge and corner cases. The scope of the conventional empirical formulas is also given for the admittance calculation of TSVs in edge/corner case, in order to offer help for the TSVs design.