Browsing by Subject "probabilistic"

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    Electromigration-Induced Interconnect Aging and its Repercussions on the Performance of Nanometer-Scale VLSI Circuits
    (2016-06) Mishra, Vivek
    Modern electronic machines are powered by the integrated-circuit (IC), a semiconductor device consisting of compact electronic circuits on a silicon substrate. ICs can contain over a billion fundamental computing elements (transistors) that are connected by a network of metal wires called interconnects. Presently, interconnects constitute a primary bottleneck in achieving required IC performance. One of the major hurdles towards achieving good interconnect performance is electromigration (EM), a physical wear-out mechanism that occurs in metal wires carrying electrical current. EM is projected to limit the performance in future generations of ICs, especially for the wires carrying unidirectional (DC) currents, and is becoming a growing concern in on-chip interconnects across applications ranging from mobile computing to automotive domains. EM results in redistribution of metal atoms in interconnects that may result in the formation of either voids (empty spaces inside the wire) or extrusions (metal accumulation into the dielectric), and for modern copper-based interconnects, experimental works have observed that failure happens typically through the formation and growth of voids. For modern interconnects carrying large current densities, EM-induced voids can cause a resistance increase in the wire, rendering a wire EM-mortal. The resistance increase in these mortal interconnects can potentially result in circuit performance failure within the lifetime of a product. The classical methods for EM circuit analysis that are used in the industry to design EM-safe ICs do not capture the reality of EM physics in the realm of modern copper-based interconnects. IC designers use simple, deterministic, empirical EM models and there is a significant gap between such empirical models and the physics-based models that accurately capture the effect of EM in interconnects. The focus of this thesis is to attempt to reduce this gap by combining the two types of models efficiently, capturing the essence of physics-based models into the IC design, thereby enabling the design of EM-robust IC in future technologies. Unlike the classical EM analysis methods that rely on determining failure by extrapolating the EM characteristics of isolated single wires to IC operating conditions, the approach described in this thesis captures the circuit context and uses system failure rather than single-wire failure as the criterion for determining the lifetime of a circuit. The first part of the thesis proposes a statistical framework to evaluate the circuit performance degradation in on-chip wires through circuit level analysis. Typical on-chip power grids are inherently robust to EM due to redundancies in the interconnect network structure. In these grids, where interconnects typically carry unidirectional currents, the traditional approach to EM analysis is based on the weakest link model, whereby a single wire failure causes the grid to fail. It is shown here that the power grid can maintain supply integrity even under multiple elemental failures, and this can result in longer and more realistic lifetime predictions as compared with classical approaches. The next part of the thesis addresses signal interconnects that carry bidirectional (AC) currents as they transport logic signals within the digital system. For these wires, it is shown that EM is not only a catastrophic failure problem, but is also capable of causing parametric shifts in circuit performance over time. We perform HSPICE-based Monte Carlo simulations on a standard on-chip structure to quantify the impact of EM on circuit performance degradation. Although the damage due to EM degradation under bidirectional currents is reduced relative to the unidirectional current case due to partial EM recovery, it is demonstrated that, depending on the level of recovery, the circuit performance may degrade beyond acceptable limits and can be comparable to other transistor degradation mechanisms. The third part of the thesis addresses the issue of EM mortality in interconnects. A wire may be prevented from being mortal under EM if the maximum stress build-up, corresponding to the equilibrium between the current-induced forward stress and the back stress due to the gradient in atomic concentration along the wire, does not exceed the critical stress due to void nucleation. Alternatively, it may also not be mortal if the stress build-up does not exceed the critical stress over the lifetime of the circuit. A new efficient approach, based on multiple filters, is developed for determining the mortality of wires in a circuit. These filters greatly reduce circuit analysis time by predicting which wires can never be mortal over the circuit lifetime under its operating conditions so that detailed analysis must only be performed over a small subset of all interconnects. The final part of the thesis studies the effect of EM on via arrays, which redundantly connect the wires in multiple levels of metal in an IC. A stress analysis technique for via arrays is proposed, accounting for differential coefficients of thermal expansion in the materials that make up these structures. The combined impact of thermomechanical stress and redundancy on the via array is determined, and a new model for the impact on the failure of a larger interconnect network is developed. Using the new model, we analyze the EM-induced performance degradation in via arrays of an industrial power grid benchmark circuit.