2000/05/02 by Mikhail Khenner, M. Khenner, Khenner, M. +10
Engineering · Materials Science · Physics and Astronomy · #Advancements in Photolithography Techniques #Computational Physics (physics.comp-ph) #Copper Interconnects and Reliability #Electronic Packaging and Soldering Technologies #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #cond-mat.mtrl-sci #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.cond-mat/0005045
19 pages, 9 PS figures; submitted to Computational Materials Science
arxiv created 2000/05/02 · openalex publication_date 2000/05/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A numerical investigation of grain-boundary (GB) grooving by means of the Level Set (LS) method is carried out. GB grooving is emerging as a key element of electromigration drift in polycrystalline microelectronic interconnects, as evidenced by a number of recent studies. The purpose of the present study is to provide an efficient numerical simulation, allowing a parametric study of the effect of key physical parameters (GB and surface diffusivities, grain size, current density, etc) on the electromigration drift velocity as well as on the morphology of the affected regions. An idealized polycrystalline interconnect which consists of grains separated by parallel GBs aligned normal to the average orientation of interconnect's surface is considered. Surface and grain-boundary diffusion are the only diffusion mechanisms assumed. The diffusion is driven by surface curvature gradients and by an externally applied electric field. The corresponding mathematical system is an initial boundary value problem for a two-dimensional Hamilton-Jacobi type equation. To solve for the electrostatic problem at a given time step, a full model based on the solution of Laplace's equation for the electric potential is employed. The resulting set of linear algebraic equations (from the finite difference discretization of the equation) is solved with an effective multigrid iterative procedure. The details of transient slit and ridge formation processes are presented and compared with theoretical predictions on steady-state grooving.