{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T16:52:55Z","timestamp":1779295975583,"version":"3.51.4"},"reference-count":39,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1714805, CCF-2212345, CCF-2437795"],"award-info":[{"award-number":["CCF-1714805, CCF-2212345, CCF-2437795"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000185","name":"Defense Advanced Research Projects Agency","doi-asserted-by":"publisher","award":["IDEA Program"],"award-info":[{"award-number":["IDEA Program"]}],"id":[{"id":"10.13039\/100000185","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Louise Dosdall"},{"DOI":"10.13039\/100008025","name":"Fulbright Foundation, Greece","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008025","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Des. Autom. Electron. Syst."],"published-print":{"date-parts":[[2025,7,31]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1145\/3734796","type":"journal-article","created":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T06:57:03Z","timestamp":1746514623000},"page":"1-31","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["An Analytical Solution for Transient Electromigration Stress in Multisegment Straight-line Interconnects Based on a Stress-wave Model"],"prefix":"10.1145","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6845-4306","authenticated-orcid":false,"given":"Mohammad Abdullah Al","family":"Shohel","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3273-0724","authenticated-orcid":false,"given":"Vidya A.","family":"Chhabria","sequence":"additional","affiliation":[{"name":"School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6968-0222","authenticated-orcid":false,"given":"Nestor","family":"Evmorfopoulos","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Thessaly, Volos Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5353-2364","authenticated-orcid":false,"given":"Sachin S.","family":"Sapatnekar","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis United States"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,6,5]]},"reference":[{"key":"e_1_3_3_2_2","unstructured":"The OpenROAD Project. (n.d.). Retrieved March 26 2025 from https:\/\/github.com\/The-OpenROAD-Project"},{"key":"e_1_3_3_3_2","unstructured":"PDNSim. (n.d.). Retrieved March 26 2025 from https:\/\/github.com\/The-OpenROAD-Project\/PDNSim"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICCAD51958.2021.9643570"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICCAD57390.2023.10323810"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TDMR.2005.853507"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1969.7340"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.322842"},{"key":"e_1_3_3_9_2","unstructured":"C. Chan T. Huang and M. Liang. 2002. Integrated Circuit Design Incorporating a Power Mesh. (Nov. 122002). US Patent 6 480 989 B2."},{"key":"e_1_3_3_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2013.2264686"},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2017.2666723"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2016.2523898"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/TDMR.2017.2746660"},{"key":"e_1_3_3_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/ASP-DAC47756.2020.9045303"},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.351204"},{"key":"e_1_3_3_16_2","doi-asserted-by":"publisher","DOI":"10.1119\/1.9699"},{"key":"e_1_3_3_17_2","volume-title":"Tables of Integral Transforms","author":"Erd\u00e9lyi A.","year":"1954","unstructured":"A. Erd\u00e9lyi (Ed.). 1954. Tables of Integral Transforms. McGraw-Hill, New York, NY."},{"key":"e_1_3_3_18_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3357161"},{"key":"e_1_3_3_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-812311-9.00006-2"},{"key":"e_1_3_3_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2005.855941"},{"key":"e_1_3_3_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2023.3283937"},{"key":"e_1_3_3_22_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1845840"},{"key":"e_1_3_3_23_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2017.2706520"},{"key":"e_1_3_3_24_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.354073"},{"key":"e_1_3_3_25_2","doi-asserted-by":"publisher","DOI":"10.1109\/APCCAS50809.2020.9301690"},{"key":"e_1_3_3_26_2","doi-asserted-by":"publisher","DOI":"10.1145\/2463209.2488842"},{"key":"e_1_3_3_27_2","doi-asserted-by":"publisher","DOI":"10.1145\/2897937.2898070"},{"key":"e_1_3_3_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.microrel.2021.114200"},{"key":"e_1_3_3_29_2","doi-asserted-by":"publisher","DOI":"10.1109\/IEDM19573.2019.8993548"},{"key":"e_1_3_3_30_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICECS.2014.7050077"},{"key":"e_1_3_3_31_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1659998"},{"key":"e_1_3_3_32_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.336731"},{"key":"e_1_3_3_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48206-4"},{"key":"e_1_3_3_34_2","volume-title":"Proceedings of the ACM\/IEEE Design Automation Conference","author":"Shohel M. A. Al","year":"2021","unstructured":"M. A. Al Shohel, V. A. Chhabria, and S. S. Sapatnekar. 2021. A new, computationally efficient \u201cBlech Criterion\u201d for immortality in general interconnects. In Proceedings of the ACM\/IEEE Design Automation Conference. IEEE, Piscataway, NJ, 913\u2013918."},{"key":"e_1_3_3_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mee.2013.08.013"},{"key":"e_1_3_3_36_2","doi-asserted-by":"publisher","DOI":"10.1109\/TDMR.2015.2508447"},{"key":"e_1_3_3_37_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2018.2801221"},{"key":"e_1_3_3_38_2","doi-asserted-by":"publisher","DOI":"10.1109\/IRPS48227.2022.9764511"},{"key":"e_1_3_3_39_2","first-page":"3","volume-title":"AIP Conference Proceedings","author":"Zhang L.","year":"2010","unstructured":"L. Zhang, M. Kraatz, O. Aubel, C. Hennesthal, E. Zschech, and P. S. Ho. 2010. Grain size and cap layer effects on electromigration reliability of Cu interconnects: Experiments and simulation. In AIP Conference Proceedings. AIP Publishing, Melville, NY, 3\u201311."},{"key":"e_1_3_3_40_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2018.2861358"}],"container-title":["ACM Transactions on Design Automation of Electronic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3734796","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3734796","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3734796","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:56:56Z","timestamp":1750298216000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3734796"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,5]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,7,31]]}},"alternative-id":["10.1145\/3734796"],"URL":"https:\/\/doi.org\/10.1145\/3734796","relation":{},"ISSN":["1084-4309","1557-7309"],"issn-type":[{"value":"1084-4309","type":"print"},{"value":"1557-7309","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,5]]},"assertion":[{"value":"2024-05-25","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-04-25","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-06-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}