Phase-Field-Crystal Model for Electromigration in Metal Interconnects

We propose an atomistic model of electromigration (EM) in metals based on a recently developed phase-field-crystal (PFC) technique. By coupling the PFC model's atomic density field with an applied electric field through the EM effective charge parameter, EM is successfully captured on diffusive...

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Bibliographic Details
Published in:Physical review letters 2016-10, Vol.117 (15), p.155901-155901, Article 155901
Main Authors: Wang, Nan, Bevan, Kirk H, Provatas, Nikolas
Format: Article
Language:English
Subjects:
Diffusion
Electric fields
Electromigration
Failure
Mathematical models
Migration
Time
Voids
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Summary:We propose an atomistic model of electromigration (EM) in metals based on a recently developed phase-field-crystal (PFC) technique. By coupling the PFC model's atomic density field with an applied electric field through the EM effective charge parameter, EM is successfully captured on diffusive time scales. Our framework reproduces the well-established EM phenomena known as Black's equation and the Blech effect, and also naturally captures commonly observed phenomena such as void nucleation and migration in bulk crystals. A resistivity dipole field arising from electron scattering on void surfaces is shown to contribute significantly to void migration velocity. With an intrinsic time scale set by atomic diffusion rather than atomic oscillations or hopping events, as in conventional atomistic methods, our theoretical approach makes it possible to investigate EM-induced circuit failure at atomic spatial resolution and experimentally relevant time scales.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.117.155901