During the manufacturing, thin slender Si wafers are coated with thin metal layers at high temperatures. When this composite is cooled down to room temperature, stresses are developed due to different thermal expansion coefficients of silicon and metal, leading to the deformation of the wafer. The aim of this master thesis is to develop and validate the appropriate modelling approaches for this classical thin-film-on-substrate problem for thin slender Si wafers using FEA program ANSYS.
Stoney's approach is modified for circular plates with anisotropic substrates subjected to thermal mismatch for the purpose of theoretical calculations. Further, considering the limitations of Stoney's approach, an analytical approach is developed based upon large deformation theory to predict the behaviour of thin slender wafers. In order to calculate the curvature from FE results, two analytical approaches based upon least square method and second order differential approximations are developed in program MATHEMATICA.
The problem is solved in two subsequent steps. In the first step, a moderately thick plate is analysed for isotropic and anisotropic substrates. Several modelling approaches based upon varying element types, element sizes, contact formulations and number of timesteps are examined in this step. In the second step, this study is extended to the thin slender wafers and studied in different regimes of in-plane film stress - curvature relationships. Bifurcation phenomenon, an important characteristic of geometrical nonlinearity is also examined.
The limitations of Stoney's approach for large deformations are mentioned. Analytical approach based upon large deformation theory is found to be serving a strong base for the purpose of comparison of FE results. The use of layered shell elements for anisotropy, large deformations and optimum calculation efforts is also examined.