Interfacial coherency stress distribution in TiN/AlN bilayer and multilayer films studied by FEM analysis

The development of interfacial coherency stresses in TiN/AlN bilayer and multilayer films was investigated by finite element method (ABAQUS) using the four-node bilinear quadrilateral axisymmetric element CAX4R. The TiN and AlN layers are always in compression and tension at the interface, respectively, as may be expected from the fact TiN has larger lattice parameter than AlN. Both, the bi-layer and the multilayer stacks bend due to the coherency stresses. For the TiN/AlN bilayer system, the curvature of the bending is largest for the TiN/AlN thickness ratios ∼0.5 and ∼2 (at which one of the two layers is fully in compression or tension), while it is smaller for the layers with the same thickness (at which both layers posses regions with compressive as well as tensile stresses). This stress distribution over the bi-layer thickness is shown to be strongly influenced by the presence and the properties of a substrate. Furthermore, the coherency stress profile and specimen curvature of a TiN/AlN multilayer system was studied as a function of the top-most layer thickness. The curvature is maximum for equal number of TiN and AlN layers, and decreases with increasing the number of TiN/AlN periods. Within the growth of an additional TiN/AlN bilayer, the curvature first decreases to zero for a vertically symmetrical geometry over the layers when the TiN layer growth is finished (e.g. for (n + 1) layers of TiN and n layers of AlN). At this stage, the coherency stresses in TiN and AlN are same in each layer type (independent on the layer position). The growth of the second half of the TiN/AlN bi-layer (i.e. the AlN) to finish the period, again bends the specimen, and generates a non-uniform stress distribution. This suggests that the top layer as well as the overall specimen geometry plays a critical role on the actual coherency stress profile.