Fast Electromigration Immortality Analysis for Multisegment Copper Interconnect Wires

In this paper, we present a novel and fast electromigration (EM) immortality check for general multisegment interconnect wires. Instead of using current density as the key parameter, as in traditional EM analysis methods based on Black&#x2019;s equation and the Blech limit, the new method estimates the EM-induced steady-state stress in general multisegment copper interconnect wires based on a novel parameter, <italic>Critical EM Voltage</italic>, <inline-formula> <tex-math notation="LaTeX">${V_{\mathrm { Crit,EM}}}$ </tex-math></inline-formula>. We show that the <inline-formula> <tex-math notation="LaTeX">${V}_{\mathrm { Crit,EM}}$ </tex-math></inline-formula> is essentially the natural, but important, extension of the <italic>Blech limit</italic> concept, which describes the EM immortality condition for a single segment wire, to more general multisegment interconnect wires. The proposed method, called voltage-based EM (VBEM) method, mitigates the problem of current-density-based EM criteria, which can only be applied to a single wire. The new VBEM method can naturally comprehend the impact of the topology of the wire structure on EM-induced stress. As a result, this new VBEM analysis method is very amenable to addressing EM violations, as it brings new optimization capabilities to the physical design flow. The VBEM stress estimation method is based on the fundamental steady-state stress equations. This approach avoids computationally intensive numerical methods and can be implemented in CAD tools very easily, as we demonstrate on real design examples. We also show that the proposed VBEM analysis method agrees with results from the finite difference method in the steady state through one example and also agrees with one published closed-form expression of steady-state stress for a special 3-terminal wire case. Furthermore, we compare VBEM against the COMSOL finite element analysis tool and another published EM numerical simulator XSim, validated by measured results, which shows that VBEM agrees with both of them very well in terms of accuracy and thus further validates the proposed method. We also study the impact of current crowding in practical interconnect wires on the estimated steady-state stress, which are shown to be not significant if the length of the wire is much greater than its width. An extension of the VBEM method to consider the significant current crowding effects is also shown and additionally, we analyze mesh-structured interconnect wires and demonstrate that the proposed VBEM method is correct and accurate on such structures.