A METHOD FOR DEFINING INITIAL STRESS IN PROGRESSIVELY DEPOSITED FILM ON A SUBSTRATE

Abstract

The initial stress is induced during film formation and is partially counterbalanced through curvature changes. Therefore, it is commonly evaluated by the measured residual stress. Initial stress may directly affect the film formation rather than residual stress in progressively deposited films. In the present work, we introduced a multiple layer model for progressively deposited films to obtain a quantitative solution for estimating the initial stress. The results showed that residual stress in the last layer is equal to the initial stress when layer number approaches infinity. In particular, the initial stress, σi in deposited film could be determined using the equation, σi = σSt/β, in which σSt is the averaged residual stress in films calculated by Stoney formula and β is the correction factor. The value of β varied between 0 and 1, depending on relative modulus and relative thickness of film and substrate. Finally, using element birth and death technique, a finite element model was presented to verify the analytical multiple layer model. Good agreement was obtained between the analytical and FE results.