Capacitance and Conductance of Through Silicon Vias With Consideration of Multilayer Media and Different Shapes

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This paper evaluates the capacitance and conductance of the through silicon vias (TSVs) with consideration of the multilayer media along the vertical direction and different shapes. According to the moment method, the capacitance and conductance of the straight and two types of tapered TSVs are calculated and compared with those of the conventional 2-D method. It is shown that the capacitance calculated by the 2-D method for the straight TSVs will produce a large error when the radius and pitch of the TSVs become larger. For the two types of tapered TSVs, their capacitance decreases with the increase in the slop angle and the pitch due to less surface area and capacitance coupling, respectively. Therefore, the tapered TSVs with larger slop angle and pitch are beneficial to reduce the propagation delay. With the increase in the pitch, the conductance of both the straight and the tapered TSVs increases slightly at low frequency, while it decreases at high frequency. All the results by the method in this paper agree well with those of the electromagnetic simulations up to 40 GHz.