Simulation of physical vapor deposition into trenches and vias: Validation and comparison with experiment

We have performed 2D and 3D (axisymmetric) numerical simulations of physical vapor deposition (PVD) into high aspect ratio trenches and vias used for modern VLSI interconnects. The topographic evolution is modeled using (continuum) level set methods. The level set approach is a powerful computational technique for accurately tracking moving interfaces or boundaries, where the advancing front is embedded as the zero level set (isosurface) of a higher dimensional mathematical function. We have validated both codes against analytic formulae for step coverage. First, we study the 2D case of long rectangular trenches including 3D out-of-plane target flux. The 3D flux can be obtained from molecular dynamics computations, and hence our approach represents a hybrid atomistic/continuum model. Secondly, we report results of axisymmetric 3D simulations of high aspect ratio vias, which we compare with experimental data for Ti/TiN barrier layers. We find that the simulations (using a cosine angular distribution for the flux from the target) over-predict bottom coverage in some cases by approximately 20%-30% for both collimated and uncollimated deposition, but in other cases provide a reasonably accurate comparison with experiment.