A theoretical study of the effect of thermal annealing on curvature changes in multilayered structures

During the manufacturing of thin-film heterostructures, a post-deposition thermal anneal may be needed to reduce deposition and thermal stresses. Relaxation due to viscous flow results in a net decrease in stress in the structure. However, there is an associated change in curvature of the structure which may be significant to consider in many applications. Moreover, the curvature may either increase or decrease depending on the film-to-substrate thickness ratio, material properties, and deposition stresses. A numerical model has been developed to determine the time-dependent change in stress and curvature during thermal annealing. Parametric studies of different layer thicknesses and elastic moduli were conducted to determine whether the structure flattens or curves more. Results indicate a transition point at which this change in curvature switches direction. This transition point can be defined with a simple relation between the ratio of film to substrate thickness as well as the ratio of their elastic moduli. © 1995