Beam model for calculating magnetostriction strains in thin films and multilayers

A standard technique to measure the magnetostriction strain in thin films involves measurement of the end deflection or slope of cantilever beams using optical deflectometry or capacitive methods. This article presents a general beam model for inferring magnetostriction strain from the end deflection or slope data. This model greatly extends the range of applicability over existing shell models, allowing for inference of magnetostriction strains for practical film/substrate thickness ratios that are important in microelectromechanical systems (MEMS) and bio-microelectromechanical systems (bio-MEMS). If the properties of individual layers are known, the beam theory can be used to design multilayer MEMS or bio-MEMs beams over a full range of thickness ratios.