skip to main content


Title: Reliable power grid network design framework considering EM immortalities for multi-segment wires
This paper presents a new power grid network design and optimization technique that considers the new EM immortality constraint due to EM void saturation volume for multi-segment interconnects. Void may grow to its saturation volume without changing the wire resistance significantly. However, this phenomenon was ignored in existing EM-aware optimization methods. By considering this new effect, we can remove more conservativeness in the EM-aware on-chip power grid design. Along with recently proposed nucleation phase immortality constraint for multi-segment wires, we show that both EM immortality constraints can be naturally integrated into the existing programming based power grid optimization framework. To further mitigate the overly conservative problem of existing immortality-constrained optimization methods, we further explore two strategies: first we size up failed wires to meet one of immorality conditions subject to design rules; second, we consider the EM-induced aging effects on power supply networks for a targeted lifetime, which allows some short-lifetime wires to fail and optimizes the rest of the wires. Numerical results on a number of IBM and self-generated power supply networks demonstrate that the new method can reduce more power grid area compared to the existing EM-immortality constrained optimizations. Furthermore, the new method can optimize power grids with nucleated wires, which would not be possible with the existing methods.  more » « less
Award ID(s):
1854276
NSF-PAR ID:
10148024
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proc. Asia South Pacific Design Automation Conference (ASP-DAC’20)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Electromigration (EM) is still the most important reliability concern for VLSI systems, especially at the nanometer regime. EM immortality check is an important step for full-chip EM signoff analysis. In this paper, we propose a new electromigration (EM) immortality check method for multi-segment interconnect considering the impacts of Joule heating induced temperature gradient. Temperature gradients from metal Joule heating, called thermal migration, can be a significant force for the metal atomic migrations, and these impacts get more significant as technology scales down. Compared to existing methods, the new method can consider the spatial temperature gradient due to Joule heating for multi-segment wires for the first time. We derive the analytic solution for the resulting steady-state EM-thermal migration stress distribution problem. Then we develop the new temperature-aware voltage-based EM immortality check method considering the multi-segment temperature migration effects, which carries all the benefits of the recently proposed voltage-based EM immortality method for multi-segment interconnects. Numerical results on an IBM power grid and self synthesized power delivery networks show that the proposed temperature-aware EM immortality check method is much more accurate than recently proposed state of the art EM immortality method. 
    more » « less
  2. In this paper, we propose a new spatial temperature aware transient EM induced stress analysis method. The new method consists of two new contributions: First, we propose a new TM-aware void saturation volume estimation method for fast immortality check in the post-voiding phase for the first time. We derive the analytic formula to estimate the void saturation in the presence of spatial temperature gradients due to Joule heating. Second, we developed a fast numerical solution for EM-induced stress analysis for multi-segment interconnect trees considering TM effect. The new method first transforms the coupled EM-TM partial differential equations into linear time-invariant ordinary differential equations (ODEs). Then extended Krylov subspace-based reduction technique is employed to reduce the size of the original system matrices so that they can be efficiently simulated in the time domain. The proposed method can perform the simulation process for both void nucleation and void growth phases under time-varying input currents and position-dependent temperatures. The numerical results show that, compared to the recently proposed semi-analytic EM-TM method, the proposed method can lead to about 28x speedup on average for the interconnect with up to 1000 branches for both void nucleation and growth phases with negligible errors. 
    more » « less
  3. Electromigration (EM) is a major failure effect for on-chip power grid networks of deep submicron VLSI circuits. EM degradation of metal grid lines can lead to excessive voltage drops (IR drops) before the target lifetime. In this paper, we propose a fast data-driven EM-induced IR drop analysis framework for power grid networks, named {\it GridNet}, based on the conditional generative adversarial networks (CGAN). It aims to accelerate the incremental full-chip EM-induced IR drop analysis, as well as IR drop violation fixing during the power grid design and optimization. More importantly, {\it GridNet} can naturally leverage the differentiable feature of deep neural networks (DNN) to {\it obtain the sensitivity information of node voltage with respect to the wire resistance (or width) with marginal cost}. {\it GridNet} treats continuous time and the given electrical features as input conditions, and the EM-induced time-varying voltage of power grid networks as the conditional outputs, which are represented as data series images. We show that {\it GridNet} is able to learn the temporal dynamics of the aging process in continuous time domain. Besides, we can take advantage of the sensitivity information provided by {\it GridNet} to perform efficient localized IR drop violation fixing in the late stage design and optimization. Numerical results on 36000 synthesized power grid network samples demonstrate that the new method can lead to $10^5\times$ speedup over the recently proposed full-chip coupled EM and IR drop analysis tool. We further show that localized IR drop violation fix for the same set of power grid networks can be performed remarkably efficiently using the cheap sensitivity computation from {\it GridNet}. 
    more » « less
  4. Abstract

    This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the recent development of distributed algorithms for nonconvex programs, highly complicated constraints still pose a significant challenge in theory and practice. We first identify some difficulties with the existing algorithms based on the alternating direction method of multipliers (ADMM) for dealing with such problems. We then propose a reformulation that enables us to design a two-level algorithm, which embeds a specially structured three-block ADMM at the inner level in an augmented Lagrangian method framework. Furthermore, we prove the global and local convergence as well as iteration complexity of this new scheme for general nonconvex constrained programs, and show that our analysis can be extended to handle more complicated multi-block inner-level problems. Finally, we demonstrate with computation that the new scheme provides convergent and parallelizable algorithms for various nonconvex applications, and is able to complement the performance of the state-of-the-art distributed algorithms in practice by achieving either faster convergence in optimality gap or in feasibility or both.

     
    more » « less
  5. Abstract The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting ill-posed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the superiority of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with the quadratic regularization, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid. 
    more » « less