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

Ioannis A. Papistas, Vasilis F. Pavlidis
2018 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
An efficient and frequency-dependent model 1 describing the crosstalk noise on power distribution networks 2 due to inductive links in contactless 3-D ICs is presented. A two-3 step approach is followed to model the crosstalk effect. During the 4 first step, the mutual inductance between the power distribution 5 network and the inductive link is analytically determined. Due 6 to the weak dependence of mutual inductance to frequency, 7 a magnetostatic model is proposed for this step. The model 8
more » ... includes the physical and electrical characteristics of both the 9 on-chip inductor and the wires of the power distribution network. 10 In this way, different power network topologies can be modeled 11 facilitating noise analysis in the vicinity of the on-chip inductor. 12 This approach is justified by the typical use of regular power 13 network topologies in modern integrated circuits. In the second 14 stage, the noise is assessed with SPICE simulations, considering 15 the mutual inductance between the two structures from the 16 first step and the resistance variations due to high frequency 17 effects. Thus, an efficient, scalable, and accurate method for 18 the analysis of the crosstalk effects due to inductive links is 19 provided, without resorting on computationally expensive and 20 time consuming full-wave simulations. Compared with the full-21 wave simulations, the induced noise is evaluated four orders of 22 magnitude faster with the proposed model. The accuracy of the 23 proposed model is within 10% of the respective noise computed 24 with a commercial electromagnetics simulator using the finite 25 element method. An analysis including the effect of substrate 26 resistivity on the crosstalk noise is also presented. 27 Index Terms-Mutual inductance, crosstalk noise, inductive 28 links, power distribution networks, high frequency, contactless 29 3-D systems. 30 1549-8328 89 tors, such as power distribution interconnects, which operate as 90 accidental antennas. Subsequently, undesirable voltage fluctu-91 ations develop on the power distribution network (PDN), that 92 can hinder power integrity and degrade the robustness of the 93 system. 94 In [18] and [19], the crosstalk noise effects are explored 95 for different power distribution network topologies and arrays 96 of multiple inductors. For example, the noise caused by an 97 inductive link array in a 65 nm process node can reach up to 98 320 mV (e.g. 26% of the nominal V D D ); though proper PDN 99 placement can reduce the noise up to 70% [18]. Furthermore, 100 the sensitivity of PDN topologies to noise depend upon the 101 geometry of each topology [19]. These results demonstrate 102 that noise due to inductive links affects the power distribution 103 network, thereby compromising power integrity if ignored. 104 Nevertheless, proper allocation of the PDN wires in the 105 vicinity of the inductor mitigates the induced noise. Therefore, 106 placement of the PDN in close proximity to the on-chip 107 inductor is feasible, resulting in a small increase in the I R drop 108 noise but mitigating the overall noise. 109 To determine the appropriate PDN placement for minimis-110 ing the aggregate noise, the crosstalk noise should accurately 111 be evaluated. This noise depends upon the relative position 112 of the PDN and the on-chip inductors. The mutual induc-113 tance between the coupled structures is therefore required, 114 which can be determined with electromagnetic simulations. 115 However, full-wave electromagnetic simulations 1 cost in time 116 and computing resources and typically are limited to a specific 117 inductor-PDN structure. Additionally, simulating the inves-118 tigated structures for each location of the PDN conductors 119 in the vicinity of the inductor entails excessive delay in the 120 design process. Furthermore, commercial IC design tools do 121 not support inductance extraction for multi-tier systems and 122 different process nodes. Thus, there is a lack of effective means 123 to determine the vital mutual inductance for inductive-based 124 3-D ICs. 125 Based on these observations, the contributions of this paper 126 are: 127 • A methodology to describe the induced crosstalk noise 128 on on-chip interconnects without the need for full-wave 129 electromagnetic simulations. 130 • A scalable, efficient, and accurate magnetostatic model 131 for the evaluation of the mutual inductance as part of 132 this methodology. The spatial position and geometry of 133 the on-chip inductor and the topology of the nearby 134 interconnects are considered for the evaluation of the 135 mutual inductance. 136 • A SPICE-based noise model to rapidly and accurately 137 evaluate the induced noise on the PDN. 138 The proposed model improves power integrity, without requir-139 ing excessive computational resources. 140 The remainder of this paper is organised as follows. A mag-141 netostatic model for the evaluation of the mutual inductance 142 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: REGULAR PAPERS 1 Abstract-An efficient and frequency-dependent model 1 describing the crosstalk noise on power distribution networks 2 due to inductive links in contactless 3-D ICs is presented. A two-3 step approach is followed to model the crosstalk effect. During the 4 first step, the mutual inductance between the power distribution 5 network and the inductive link is analytically determined. Due 6 to the weak dependence of mutual inductance to frequency, 7 a magnetostatic model is proposed for this step. The model 8 includes the physical and electrical characteristics of both the 9 on-chip inductor and the wires of the power distribution network. 10 In this way, different power network topologies can be modeled 11 facilitating noise analysis in the vicinity of the on-chip inductor. 12 This approach is justified by the typical use of regular power 13 network topologies in modern integrated circuits. In the second 14 stage, the noise is assessed with SPICE simulations, considering 15 the mutual inductance between the two structures from the 16 first step and the resistance variations due to high frequency 17 effects. Thus, an efficient, scalable, and accurate method for 18 the analysis of the crosstalk effects due to inductive links is 19 provided, without resorting on computationally expensive and 20 time consuming full-wave simulations. Compared with the full-21 wave simulations, the induced noise is evaluated four orders of 22
doi:10.1109/tcsi.2018.2791498 fatcat:wncu76nhzjgobbpekkosv3o2le