Electromigration (EM) becomes one of the most challenging reliability issues for current and future ICs in 10-nm technology and below. In this article, a novel method is proposed for the EM hydrostatic stress analysis on 2-D multibranch interconnect trees, which is the foundation of the EM reliability assessment for large-scale on-chip interconnect networks, such as on-chip power grid networks. The proposed method, which is based on an eigenfunction technique, could efficiently calculate the hydrostatic stress evolution for multibranch interconnect trees stressed with different current densities and nonuniformly distributed thermal effects. The proposed method solves the partial differential equations of transient EM stress more efficiently since it does not require any discretization either spatially or temporally, which is in contrast to numerical methods, such as the finite difference method and finite element method. The accuracy of the proposed transient analysis approach is validated against the analytical solution and commercial tools. The convergence of the proposed method is demonstrated by numerical experiments on practical power/ground networks, showing that only a small number of eigenfunction terms are necessary for the accurate solution. Thanks to its analytical nature, the proposed method is also utilized in efficient EM analysis techniques, such as searching for the void nucleation time by a modified bisection algorithm. The numerical results show that the proposed method is 10X-100X faster than the finite difference method and scales better for larger interconnect trees.

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'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, Critical EM Voltage, VCrit,EM. We show that the VCrit,EM is essentially the natural, but important, extension of the Blech limit 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.

Electromigration (EM) becomes one of the most challenging reliability issues for current and future ICs in 10nm technology and below. In this paper, we propose a new analyses method for the EM hydrostatic stress evolution for multi-branch interconnect trees, which is the foundation of the EM reliability assessment for large scale on-chip interconnect networks, such as power grid networks. The proposed method, which is based on eigenfunctions technique, could efficiently calculate the hydrostatic stress evolution for multi-branch interconnect trees stressed with different current densities and non-uniformly distributed thermal effects. The new method can also accommodate the pre-existing residual stresses coming from thermal or other stress sources. The proposed method solves the partial differential equations of EM stress more efficiently since it does not require any discretization either spatially or temporally, which is in contrast to numerical methods such as finite difference method and finite element method. The accuracy of the proposed transient analysis approach is validated against the analytical solution and commercial tools. The efficiency of the proposed method is demonstrated and compared to finite difference method. The proposed method is 10X~100X times faster than finite difference method and scales better for larger interconnect trees.

In this paper, we propose a new approach for cross-layer electromigration (EM) induced reliability modeling and optimization at physics, system and datacenter levels. We consider a recently proposed physics-based electromigration (EM) reliability model to predict the EM reliability of full-chip power grid networks for long-term failures. We show how the new physics-based dynamic EM model at the physics level can be abstracted at the system level and even at the datacenter level. Our datacenter system-level power model is based on the BigHouse simulator. To speed up the online optimization for energy in a datacenter, we propose a new combined datacenter power and reliability compact model using a learning based approach in which a feed-forward neural network (FNN) is trained to predict energy and long term reliability for each processor under datacenter scheduling and workloads. To optimize the energy and reliability of a datacenter, we apply the efficient adaptive Q-learning based reinforcement learning method. Experimental results show that the proposed compact models for the datacenter system trained with different workloads under different cluster power modes and scheduling policies are able to build accurate energy and lifetime. Moreover, the proposed optimization method effectively manages and optimizes data-center energy subject to reliability, given power budget and performance.

In this article, we propose a new dynamic reliability management (DRM) techniques at the system level for emerging low power dark silicon manycore microprocessors operating in near-threshold region. We mainly consider the electromigration (EM) failures. To leverage the EM recovery effects, which was ignored in the past, at the system-level, we propose a new equivalent DC current model to consider recovery effects for general time-varying current waveforms so that existing compact EM model can be applied. The new equivalent DC current is calculated in two steps: firstly, the equivalent square waveform is calculated so that peak and terminal stresses are matched, secondly, the parameterized equivalent DC current is derived in terms of the parameters of the periodic fitted square waveforms from the first step. The new recovery EM model can allow EM-induced lifetime to be better managed at the system level. The system level energy optimization problem considering EM lifetime subject to power and performance constraints is framed by seeking the best dark silicon cores' voltage and on/off status. The resulting problem is solved by the State-Action-Reward-State-Action (SARSA) reinforcement learning algorithm. Experimental results on a 64-core near-threshold dark silicon processor show that the new equivalent EM DC currents can fully exhibit the recovery effects at the system-level so that trade-off between EM lifetime and energy/performance can be easily made. We further show that the proposed learning-based energy optimization can effectively manage and optimize energy subject to reliability, given power budget and performance limits. When the recovery effects are considered, the new optimization method can achieve 8.6× longer lifetime at the costs of 2.0× more energy and 3.3× more performance degradation.