A novel semi-analytical approach for fast electromigration stress analysis in multi-segment interconnects

Olympia Axelou, Nestor Evmorfopoulos, George Floros, George Stamoulis, Sachin S. Sapatnekar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

As integrated circuit technologies move below 10 nm, Electromigration (EM) has become an issue of great concern for the longterm reliability due to the stricter performance, thermal and power requirements. The problem of EM becomes even more pronounced in power grids due to the large unidirectional currents flowing in these structures. The attention for EM analysis during the past years has been drawn to accurate physics-based models describing the interplay between the electron wind force and the back stress force, in a single Partial Differential Equation (PDE) involving wire stress. In this paper, we present a fast semi-analytical approach for the solution of the stress PDE at discrete spatial points in multi-segment lines of power grids, which allows the analytical calculation of EM stress independently at any time in these lines. Our method exploits the specific form of the discrete stress coefficient matrix whose eigenvalues and eigenvectors are known beforehand. Thus, a closed-form equation can be constructed with almost linear time complexity without the need of time discretization. This closed-form equation can be subsequently used at any given time in transient stress analysis. Our experimental results, using the industrial IBM power grid benchmarks, demonstrate that our method has excellent accuracy compared to the industrial tool COMSOL while being orders of magnitude times faster.

Original languageEnglish (US)
Title of host publicationProceedings of the 41st IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781450392174
DOIs
StatePublished - Oct 30 2022
Event41st IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2022 - San Diego, United States
Duration: Oct 30 2022Nov 4 2022

Publication series

NameIEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD
ISSN (Print)1092-3152

Conference

Conference41st IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2022
Country/TerritoryUnited States
CitySan Diego
Period10/30/2211/4/22

Bibliographical note

Funding Information:
This research has been co-financed by the European Regional Development Fund of the European Union and Greek national funds through the Operational Program “Competitiveness, Entrepreneurship and Innovation”, under the call “Research – Create – Innovate” (project code: T2EDK-00609).

Publisher Copyright:
© 2022 Association for Computing Machinery.

Keywords

  • Analytical Solution
  • Electromigration
  • Korhonen s PDE
  • Longterm Reliability
  • Stress Diffusion

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