Front-tracking finite element methods for a void electro-stress migration problem

Continued research in electronic engineering technology has led to a miniaturisation of integrated circuits. Further reduction in the dimensions of the interconnects is impeded by the presence of small cracks or voids. Subject to high current and elastic stress, voids tend to drift and change shape in the interconnect, leading to a potential mechanical failure of the system. This thesis investigates the temporal evolution of voids moving along conductors, in the presence of surface diffusion, electric loading and elastic stress. 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. We first give a general overview about geometric evolution equations, which define the motion of a hypersurface by prescribing its normal velocity in terms of geometric quantities. We briefly describe the three main approaches that have been proposed in the literature to solve numerically this class of equations, namely parametric approach, level set approach and phase field approach. We then present in detail two methods from the parametric approach category for the void electro-stress migration problem. We first introduce an unfitted method, where bulk and interface grids are totally independent, i.e. no topological compatibility between the two grids has to be enforced over time. We then discuss a fitted method, where the interface grid is at all times part of the boundary of the bulk grid. A detailed analysis, in terms of existence and uniqueness of the finite element solutions, 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 for both approaches. Several numerical simulations, both two- and three-dimensional, are performed in order to test the accuracy of the methods.Open Acces