research-article

Open access

Recent Progress in the Analysis of Electromigration and Stress Migration in Large Multisegment Interconnects

Authors:

Nestor Evmorfopoulos,

Mohammad Abdullah Al Shohel,

Olympia Axelou,

Pavlos Stoikos,

Vidya A. Chhabria,

Sachin S. SapatnekarAuthors Info & Claims

ISPD '23: Proceedings of the 2023 International Symposium on Physical Design

Pages 115 - 123

https://doi.org/10.1145/3569052.3578919

Published: 26 March 2023 Publication History

Abstract

Traditional approaches to analyzing electromigration (EM) in on-chip interconnects are largely driven by semi-empirical models. However, such methods are inexact for the typical multisegment lines that are found in modern integrated circuits. This paper overviews recent advances in analyzing EM in on-chip interconnect structures based on physics-based models that use partial differential equations, with appropriate boundary conditions, to capture the impact of electron-wind and back-stress forces within an interconnect, across multiple wire segments. Methods for both steady-state and transient analysis are presented, highlighting approaches that can solve these problems with a computation time that is linear in the number of wire segments in the interconnect.

References

[1]

J. Lienig, "Electromigration and its impact on physical design in future technologies," in Proceedings of the International Symposium on Physical Design, pp. 33--40, 2013.

[2]

J. Lienig and M. Thiele, "The pressing need for electromigration-aware physical design," in Proceedings of the International Symposium on Physical Design, pp. 144--151, 2018.

[3]

S. S. Sapatnekar, "Electromigration-aware interconnect design," in Proceedings of the International Symposium on Physical Design, pp. 83--90, 2019.

[4]

S. M. Alam, et al., "Circuit-level reliability requirements for Cu metallization," IEEE Transactions on Devices and Materials Reliability, vol. 5, no. 3, pp. 522--531, 2005.

[5]

C. Auth, et al., "A 10nm high performance and low-power CMOS technology featuring 3rd generation FinFET transistors, self-aligned quad patterning, contact over active gate and cobalt local interconnects," in IEEE International Electronic Devices Meeting, pp. 29.1.1-29.1.4, 2017.

[6]

I. A. Blech, "Electromigration in thin aluminum films on titanium nitride," Journal of Applied Physics, vol. 47, no. 4, pp. 1203--1208, 1976.

[7]

J. R. Black, "Electromigration failure modes in aluminum metallization for semiconductor devices," Proceedings of the IEEE, vol. 57, no. 9, pp. 1587--1594, 1969.

[8]

R. Rosenberg and M. Ohring, "Void formation and growth during electromigration in thin films," Journal of Applied Physics, vol. 42, no. 13, pp. 5671--5679, 1971.

[9]

M. Schatzkes and J. R. Lloyd, "A model for conductor failure considering diffusion concurrently with electromigration resulting in a current exponent of 2," Journal of Applied Physics, vol. 59, pp. 3890--3893, 1986.

[10]

J. J. Clement and J. R. Lloyd, "Numerical investigations of the electromigration boundary value problem," Journal of Applied Physics, vol. 71, pp. 1729--1731, 1992.

[11]

M. A. Korhonen, et al., "Stress evolution due to electromigration in confined metal lines," Journal of Applied Physics, vol. 73, no. 8, pp. 3790--3799, 1993.

[12]

V. Sukharev, "Beyond Black's equation: Full-chip EM/SM assessment in 3D IC stack," Microelectronic Engineering, vol. 120, pp. 99--105, 2014.

[13]

H.-B. Chen, et al., "Analytical modeling and characterization of electromigration effects for multibranch interconnect trees," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 35, no. 11, pp. 1811--1824, 2016.

Digital Library

[14]

Y. J. Park, et al., "New electromigration validation: Via node vector method," in Proceedings of the IEEE International Reliability Physics Symposium, pp. 698--704, 2010.

[15]

V. Mishra and S. S. Sapatnekar, "Predicting electromigration mortality under temperature and product lifetime specifications," in Proceedings of the ACM/IEEE Design Automation Conference, pp. 43:1--43:6, 2016.

[16]

V. Sukharev, et al., "Postvoiding stress evolution in confined metal lines," IEEE Transactions on Devices and Materials Reliability, vol. 16, no. 1, pp. 50--60, 2016.

[17]

S. Chatterjee, et al., "Power grid electromigration checking using physics-based models," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 37, pp. 1317--1330, July 2018.

[18]

H.-B. Chen, et al., "Analytical modeling of electromigration failure for VLSI interconnect tree considering temperature and segment length effects," IEEE Transactions on Devices and Materials Reliability, vol. 17, no. 4, pp. 653--666, 2017.

[19]

V. Mishra and S. S. Sapatnekar, "The impact of electromigration in copper interconnects on power grid integrity," in Proceedings of the ACM/IEEE Design Automation Conference, pp. 88:1-88:6, 2013.

[20]

B. Li, et al., "Statistical evaluation of electromigration reliability at chip level," IEEE Transactions on Devices and Materials Reliability, vol. 11, pp. 86--91, Mar. 2011.

[21]

J. Gambino, "Process technology for copper interconnects," in Handbook of Thin Film Deposition (K. Seshan and D. Schepis, eds.), ch. 6, pp. 147--194, Amsterdam, The Netherlands: Elsevier, 3rd ed., 2018.

[22]

L. Zhang, et al., "Grain size and cap layer effects on electromigration reliability of cu interconnects: Experiments and simulation," in AIP Conference Proceedings, vol. 1300, 3, 2010.

[23]

S. P. Riege, et al., "A hierarchical reliability analysis for circuit design evaluation," IEEE Transactions on Electron Devices, vol. 45, pp. 2254--2257, Oct. 1998.

[24]

J. J. Clement, et al., "Methodology for electromigration critical threshold design rule evaluation," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 18, pp. 576--581, May 1999.

Digital Library

[25]

H. Haznedar, et al., "Impact of stress-induced backflow on full-chip electromigration risk assessment," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 25, pp. 1038--1046, June 2006.

Digital Library

[26]

E. Demircan and M. Shroff, "Model based method for electro-migration stress determination in interconnects," in Proceedings of the IEEE International Reliability Physics Symposium, pp. IT5.1-IT5.6, 2014.

[27]

P. Gibson, et al., "Electromigration analysis of full-chip integrated circuits with hydrostatic stress," in Proceedings of the IEEE International Reliability Physics Symposium, pp. IT.2.1-IT.2.7, 2014.

[28]

F. Najm and V. Sukharev, "Electromigration simulation and design considerations for integrated circuit power grids," Journal of Vacuum Science & Technology B, vol. 38, pp. 063204:1-12, Nov/Dec 2020.

[29]

M. A. A. Shohel, et al., "A new, computationally efficient "Blech criterion' for immortality in general interconnects," in Proceedings of the ACM/IEEE Design Automation Conference, 2021.

[30]

M. A. A. Shohel, et al., "A linear-time algorithm for steady-state analysis of electromigration in general interconnects," in arXiv:2112.13451 [cs.AR], 2021.

[31]

Z. Sun, et al., "Fast electromigration immortality analysis for multisegment copper interconnect wires," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 37, pp. 3137--3150, Dec. 2018.

Digital Library

[32]

M. A. A. Shohel, et al., "Analytical modeling of transient electromigration stress based on boundary reflections," in Proceedings of the IEEE/ACM International Conference on Computer-Aided Design, 2021.

[33]

O. Axelou, et al., "A novel semi-analytical approach for fast electromigration stress analysis in multi-segment interconnects," in Proceedings of the IEEE/ACM International Conference on Computer-Aided Design, 2022.

[34]

K. Daloukas, et al., "Parallel fast transform-based preconditioners for large-scale power grid analysis on graphics processing units (gpus)," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 35, no. 10, pp. 1653--1666, 2016.

Digital Library

[35]

C. Van Loan, Computational Frameworks for the Fast Fourier Transform. USA: Society for Industrial and Applied Mathematics, 1992.

[36]

H. Qian and S. S. Sapatnekar, "Fast poisson solvers for thermal analysis," in 2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pp. 698--702, 2010.

[37]

S. R. Nassif, "Power grid analysis benchmarks," in Proceedings of the Asia-South Pacific Design Automation Conference, pp. 376--381, 2008.

[38]

K.-D. Lee, "Electromigration recovery and short lead effect under bipolar- and unipolar-pulse current," in Proceedings of the IEEE International Reliability Physics Symposium, pp. 6B.3.1-6B.3.4, 2012.

[39]

A. H. Al-Mohy and N. Higham, "Computing the action of the matrix exponential, with an application to exponential integrators," SIAM Journal of Scientific Computing, vol. 33, no. 2, pp. 488--511, 2011.

Digital Library

[40]

P. Stoikos, et al., "A fast semi-analytical approach for transient electromigration analysis of interconnect trees using matrix exponential," in Proceedings of the Asia-South Pacific Design Automation Conference, 2023.

[41]

L. Chen, et al., "Fast analytic electromigration analysis for general multisegment interconnect wires," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 28, no. 2, pp. 421--432, 2019.

[42]

L. Chen, et al., "A fast semi-analytic approach for combined electromigration and thermomigration analysis for general multisegment interconnects," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 40, no. 2, pp. 350--363, 2021.

Digital Library

[43]

X. Wang, et al., "Fast physics-based electromigration analysis for full-chip networks by efficient eigenfunction-based solution," IEEE Transactions on Computer- Aided Design of Integrated Circuits and Systems, vol. 40, no. 3, pp. 507--520, 2021.

[44]

C. Cook, et al., "Fast electromigration stress evolution analysis for interconnect trees using Krylov subspace method," IEEE Transactions on VLSI Systems, vol. 26, no. 5, pp. 969--980, 2018.

[45]

M. N. Özişik, Heat Transfer: A Basic Approach. New York, NY: McGraw-Hill, 1985.

[46]

F. N. Najm, "Equivalent circuits for electromigration," Microelectronics Reliability, pp. 114200-1-114200-16, Aug. 2021.

Cited By

Vutukuru MEmmert JJha R(2024)A Survey of Electromagnetic Radiation Based Hardware Assurance and Reliability Monitoring Methods in Integrated CircuitsIEEE Access10.1109/ACCESS.2024.347992912(150623-150638)Online publication date: 2024
https://doi.org/10.1109/ACCESS.2024.3479929

Index Terms

Recent Progress in the Analysis of Electromigration and Stress Migration in Large Multisegment Interconnects
1. General and reference
  1. Cross-computing tools and techniques
    1. Reliability
2. Hardware

Recommendations

An Interconnect Reliability-Driven Routing Technique for Electromigration Failure Avoidance

As VLSI technology enters the nanoscale regime, design reliability is becoming increasingly important. A major design reliability concern arises from electromigration which refers to the transport of material caused by ion movement in interconnects. ...
Circuit reliability: from physics to architectures
ICCAD '12: Proceedings of the International Conference on Computer-Aided Design

In the period of extreme CMOS scaling, reliability issues are becoming a critical problem. These problems include issues related to device reliability, in the form of bias temperature instability, hot carrier injection, time-dependent dielectric ...
Reliability computer-aided design tool for full-chip electromigration analysis and comparison with different interconnect metallizations

We have developed a set of methodologies for thermal aware circuit-level reliability analysis with either Al or Cu metallization in a circuit layout and implemented it in a public domain reliability CAD tool, SysRel. SysRel utilizes a hierarchical ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

ISPD '23: Proceedings of the 2023 International Symposium on Physical Design

March 2023

278 pages

ISBN:9781450399784

DOI:10.1145/3569052

General Chair:
David Chinnery
Siemens Digital Industries Software, USA
,
Program Chair:
Iris Hui-Ru Jiang
National Taiwan University, Taiwan

Copyright © 2023 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Sponsors

SIGDA: ACM Special Interest Group on Design Automation

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 March 2023

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

National Science Foundation
SPAWAR

Conference

ISPD '23

Sponsor:

SIGDA

ISPD '23: International Symposium on Physical Design

March 26 - 29, 2023

Virtual Event, USA

Acceptance Rates

Overall Acceptance Rate 62 of 172 submissions, 36%

Upcoming Conference

ISPD '25

Sponsor:
sigda

International Symposium on Physical Design

March 16 - 19, 2025

Austin , TX , USA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

1
Total Citations
View Citations
372
Total Downloads

Downloads (Last 12 months)220
Downloads (Last 6 weeks)31

Reflects downloads up to 22 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

Vutukuru MEmmert JJha R(2024)A Survey of Electromagnetic Radiation Based Hardware Assurance and Reliability Monitoring Methods in Integrated CircuitsIEEE Access10.1109/ACCESS.2024.347992912(150623-150638)Online publication date: 2024
https://doi.org/10.1109/ACCESS.2024.3479929

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Table of Contents