Elastic and elastic-plastic analysis of multilayer thin films: Closed-form solutions

The stress and curvature induced by temperature fluctuation in multilayer thin film structures have been investigated extensively in the past. However, most of the previous efforts were focused on the elastic deformation range. In this paper, first we propose a simple approach to derive the closed-form solutions in multilayer thin film structures in the elastic range. Subsequently, approximate solutions are obtained for very thin multilayer films. The condition that the film stress is of the same sign is identified for bilayer cases. The investigation is then extended into the elastic-plastic deformed films in bilayer structures. Closed-form solutions of the maximum, average, and minimum film stresses and curvatures are obtained for plastically deformed films. It is concluded that for an error within +/-10% as compared with that of Stoney equation, it is required that the thickness ratio should be about 0.1 or less for whatever elastic or elastic-plastic analysis. In addition, the result of a case study reveals that the yield start point may be estimated as a linear function of temperature in the elastic-plastic deformation range. (C) 2004 American Institute of Physics.