Efficient Modeling of Crosstalk Noise on Power Distribution Networks for Contactless 3-D ICs

An efficient and frequency-dependent model describing the crosstalk noise on power distribution networks due to inductive links in contactless 3-D ICs is presented. A two-step approach is followed to model the crosstalk effect. During the first step, the mutual inductance between the power distribution network and the inductive link is analytically determined. Due to the weak dependence of mutual inductance to frequency, a magnetostatic model is proposed for this step. The model includes the physical and electrical characteristics of both the on-chip inductor and the wires of the power distribution network. In this way, different power network topologies can be modeled facilitating noise analysis in the vicinity of the on-chip inductor. This approach is justified by the typical use of regular power network topologies in modern integrated circuits. In the second stage, the noise is assessed with SPICE simulations, considering the mutual inductance between the two structures from the first step and the resistance variations due to high frequency effects. Thus, an efficient, scalable, and accurate method for the analysis of the crosstalk effects due to inductive links is provided, without resorting on computationally expensive and time consuming full-wave simulations. Compared with the full-wave simulations, the induced noise is evaluated four orders of magnitude faster with the proposed model. The accuracy of the proposed model is within 10% of the respective noise computed with a commercial electromagnetics simulator using the finite element method. An analysis including the effect of substrate resistivity on the crosstalk noise is also presented.