An official website of the United States government
Electromigration (EM) analysis for complicated interconnects requires the solving of partial differential equations, which is expensive. In this paper, we propose a fast transient hydrostatic stress analysis for EM failure assessment for multi-segment interconnects using generative adversarial networks (GANs). Our work is inspired by the image synthesis and feature of generative deep neural networks. The stress evaluation of multi-segment interconnects, modeled by partial differential equations, can be viewed as time-varying 2D-images-to-image problem where the input is the multi-segment interconnects topology with current densities and the output is the EM stress distribution in those wire segments at the given aging time. We show that the conditional GAN can be exploited to attend the temporal dynamics for modeling the time-varying dynamic systems like stress evolution over time. The resulting algorithm, called {\it EM-GAN}, can quickly give accurate stress distribution of a general multi-segment wire tree for a given aging time, which is important for full-chip fast EM failure assessment. Our experimental results show that the EM-GAN shows 6.6\% averaged error compared to COMSOL simulation results with orders of magnitude speedup. It also delivers $$8.3 \times$$ speedup over state-of-the-art analytic based EM analysis solver.
more »
« less
This content will become publicly available on July 31, 2026
An Analytical Solution for Transient Electromigration Stress in Multisegment Straight-line Interconnects Based on a Stress-wave Model
This work presents an analytical approach for analyzing electromigration (EM) in modern technologies that use copper dual damascene (Cu DD) interconnects. In these technologies, due to design rule and methodology constraints, wires are typically laid out unidirectionally in each metal layer; since EM in Cu DD interconnects do not cross layer boundaries, the problem reduces to one of analyzing EM in multisegment interconnect lines. In contrast with traditional empirical methodologies, our approach is based on physics-based modeling, directly solving the differential equations that model EM-induced stress. This article places a focus on interconnect lines, for reasons described above, and introduces the new concept of boundary reflections of stress flux that ascribes a physical (wave-like) analogy to the transient stress behavior in a finite multisegment line. This framework is used to derive analytical expressions of transient EM stress for lines with any number of segments, which can also be tailored to include the appropriate number of terms for any desired level of accuracy. The approach is applied to both the nucleation phase and the postvoiding phase on large power grid benchmarks. These experiments demonstrate excellent accuracy as compared to accurate numerical solution, as well as linear complexity with the number of segments for evaluating stress at a specified point and time.
more »
« less
- PAR ID:
- 10617910
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- ACM Transactions on Design Automation of Electronic Systems
- Volume:
- 30
- Issue:
- 4
- ISSN:
- 1084-4309
- Page Range / eLocation ID:
- 1 to 31
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Electromigration (EM) becomes a major concern for VLSI circuits as the technology advances in the nanometer regime. With Korhonen equations, EM assessment for VLSI circuits remains challenged due to the increasing integrated density. VLSI multisegment interconnect trees can be naturally viewed as graphs. Based on this observation, we propose a new graph convolution network (GCN) model, which is called {\it EMGraph} considering both node and edge embedding features, to estimate the transient EM stress of interconnect trees. Compared with recently proposed generative adversarial network (GAN) based stress image-generation method, EMGraph model can learn more transferable knowledge to predict stress distributions on new graphs without retraining via inductive learning. Trained on the large dataset, the model shows less than 1.5% averaged error compared to the ground truth results and is orders of magnitude faster than both COMSOL and state-of-the-art method. It also achieves smaller model size, 4X accuracy and 14X speedup over the GAN-based method.more » « less
-
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
-
As the technology node of VLSI designs advances to sub10 nm, two interconnect-centric metrics of a circuit, the interconnect complexity (either number of interconnects or wirelength/WL) and congestion, become critically important across all design stages alongside conventional resource or function-unit (FU)-centric metrics like area/number-of-FUs and leakage power. High Level synthesis (HLS), one of the earliest and most impactful design stages, rarely monitors interconnect metrics, which makes their recovery at later stages very difficult. HLS algorithms and tools typically perform FU-centric minimization via operation scheduling, module selection (S&MS) and binding. As a consequence, it mostly overlooks interconnect-based metrics. In this paper, we explore whether this can adversely affect interconnect metrics, and in general explore the correlation between FU-centric optimization in S&MS, and the resulting interconnect metrics co-optimized (along with FU metrics) in the later binding stage(s). For this purpose we develop a probabilistic analysis for post-scheduling binding to estimate interconnect metrics, and verify its accuracy by comparison to empirical results across different scheduling techniques that generate different degrees of FU optimization. Based on both empirical and analytical results we predict how interconnects metrics will pan out with different degrees of FU optimization. Finally, based on our analysis, we also provide suggestions to improve interconnect metrics for whatever FU optimization degree an available S&MS technique can achieve.more » « less
-
Interconnect materials play the critical role of routing energy and information in integrated circuits. However, established bulk conductors, such as copper, perform poorly when scaled down beyond 10 nm, limiting the scalability of logic devices. Here, a multi‐objective search is developed, combined with first‐principles calculations, to rapidly screen over 15,000 materials and discover new interconnect candidates. This approach simultaneously optimizes the bulk electronic conductivity, surface scattering time, and chemical stability using physically motivated surrogate properties accessible from materials databases. Promising local interconnects are identified that have the potential to outperform ruthenium, the current state‐of‐the‐art post‐Cu material, and also semi‐global interconnects with potentially large skin depths at the GHz operation frequency. The approach is validated on one of the identified candidates, CoPt, using both ab initio and experimental transport studies, showcasing its potential to supplant Ru and Cu for future local interconnects.more » « less
