Predicting multilayer film's residual stress from its monolayers

Abstract Multilayer film's residual stress was deduced from Stoney formula. A simple stress formula, which means that multilayer residual stress can be given by the weighted average of each monolayer's residual stress, was proposed and verified through experiments on gradient diamond-like carbon (DLC) and CrN/DLC multilayers prepared by cathodic vacuum arc technology. Typical stress formulas for alternating multilayers were also investigated on corresponding DLC multilayers. Multilayer samples, together with monolayers existed in multilayers, were prepared and studied. Surface profilometry and film stress tester were used to measure films' thicknesses and residual stresses, respectively. Cross-sectional morphologies of multilayers were observed by scanning electron microscope. Results showed that the proposed stress formula was correct and could provide useful instructions on multilayer design. The formula's accuracy of predicting multilayer's residual stress through its monolayers was also investigated. In the present paper, relative errors of theoretical values were in the range of 0.2% to 10.7%, which had a strong relationship with the substrate–film interfaces. In addition, as to alternating multilayer film, its residual stress is a constant value as the number of monolayers is even; while this number is odd, multilayers' residual stress gets close to the constant value gradually and monotonously.