4.3.5 Mesh Refinement at Material Interfaces and Grain Boundaries

In order to obtain an appropriate resolution for the local vacancy dynamics at grain boundaries and interfaces formed by the interconnect metal with the surrounding layers, an appropriately fine FEM mesh has to be provided at these locations. Therefore, a simple local mesh refinement procedure was implemented. The procedure first detects the elements with nodes connected to more than one segment. If the tetrahedron volume is larger than a given value, the corresponding tetrahedron is refined. This procedure can be executed recursively, until all tetrahedrons connected to the interface have a volume smaller than the specified one. Figure 4.4 shows the mesh refinement obtained at a grain boundary and at the metal/capping layer interface of a typical dual-damascene interconnect.

Figure 4.4: Mesh refinement at a grain boundary and at a material interface.