Thermally induced viscoelastic stresses in multilayer thin films

摘要

This paper presents a viscoelastic analysis of the thermal stress in multilayer thin-film structures. In this analysis the viscoelastic field was calculated utilizing the Laplace transform. The thermal stress equation in the Laplace transform space can be numerically inverted to obtain the time domain. In the case of a single-layer film the stress of the thin film at any time can be obtained analytically. In a bilayer system, the normalized viscoelastic stress of the thin film is affected by the relaxation times, the biaxial moduli ratio, and the ratio of thickness between the film layer and the substrate. The effects of different ratio values of thickness on the normalized viscoelastic stress were analyzed. Viscoelastic stress can also be calculated if the elastic behavior in either the film or the substrate is considered. Furthermore, when both the substrate and film's relaxation times approach infinity, they begin to exhibit elastic behavior, and then the residual stress in the film can be determined. The residual stress results were shown to be identical to those results obtained by the elastic analysis.