  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.
