Level set modeling of transient electromigration grooving

A numerical investigation of grain-boundary (GB) grooving by means of the l evel set (LS) method is carried out. GB grooving is emerging as a key eleme nt of electromigration (EM) drift in polycrystalline microelectronic (ME) i nterconnects, as evidenced by a number of recent studies. The purpose of th e 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 EM drift velocity as well as on the morphology of the affected regions. An idealized polycrys talline interconnect which consists of grains separated by parallel GBs ali gned normal to the average orientation of interconnect's surface is conside red. Surface and GB diffusions are the only diffusion mechanisms assumed. T he 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 the electrostatic problem at a given time step, a full model bas ed on the solution of Laplace's equation for the electric potential is empl oyed. The resulting set of linear algebraic equations (from the finite diff erence discretization of the equation) is solved with an effective multigri d iterative procedure. The details of transient slit and ridge formation pr ocesses are presented and compared with theoretical predictions on steady-s tate grooving (C) 2001 Elsevier Science B.V. All rights reserved.