Constitutive modelling of copper films on silicon substrate

In order to characterize the material behavior of copper films deposited on silicon substrate, wafer curvature experiments were performed. The samples were exposed to repeated cycles in the range between -50°C to 400°C. The diagrams of film stress versus temperature show linear film behavior followed by plastic flow. In fact, a pronounced Bauschinger effect was observed which is attributed to back-stress arising from the dislocation structure in copper films. For better understanding of the underlying mechanisms, a new statistical dislocation model was developed which can nicely be fitted to experiments. However, the algorithm of the dislocation model appeared to be very time consuming during computation. Therefore, a second model was developed which can refit the experimental data with high accuracy using a fast algorithm. We call this model pressure dependent combined isotropic and kinematic hardening. This model was implemented in ANSYS with user-subroutine usermat.