A fitted finite element method for the numerical approximation of void electro-stress migration
File(s)NurnbergS15preprint.pdf (1012.05 KB)
Accepted version
Author(s)
Nurnberg, R
Sacconi, A
Type
Journal Article
Abstract
Microelectronic circuits usually contain small voids or cracks, and if those defects are large enough to sever the line, they cause an open circuit. A fully practical finite element method for the temporal analysis of the migration of voids in the presence of surface diffusion, electric loading and elastic stress is presented. We simulate a bulk–interface coupled system, with a moving interface governed by a fourth-order geometric evolution equation and a bulk where the electric potential and the displacement field are computed. The method presented here follows a fitted approach, since the interface grid is part of the boundary of the bulk grid. A detailed analysis, in terms of experimental order of convergence (when the exact solution to the free boundary problem is known) and coupling operations (e.g., smoothing/remeshing of the grids, intersection between elements of the two grids), is carried out. A comparison with a previously introduced unfitted approach (where the two grids are totally independent) is also performed, along with several numerical simulations in order to test the accuracy of the methods.
Date Issued
2015-09-25
Date Acceptance
2015-09-07
Citation
Applied Numerical Mathematics, 2015, 104, pp.204-217
ISSN
1873-5460
Publisher
Elsevier
Start Page
204
End Page
217
Journal / Book Title
Applied Numerical Mathematics
Volume
104
Copyright Statement
© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Fitted
Finite element method
Electro-stress migration
PHASE FIELD MODEL
GENERIC GRID INTERFACE
SURFACE-DIFFUSION
ELECTROMIGRATION
COMPUTATION
MESHES
EQUATIONS
EVOLUTION
PARALLEL
DESIGN
Numerical & Computational Mathematics
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0802 Computation Theory And Mathematics
Publication Status
Published