Gradient residual stress induced elastic deformation of multilayer MEMS structures

Abstract

Multilayered structures are widely used as sensing or actuating components in MEMS devices. Since the thin films of multilayered structures are always subject to residual stresses, it is important to model the relation between these residual stresses and the resultant elastic deformation. The main purpose of this paper is to explore two different approaches to addressing this issue when the residual stress in each thin film is not necessarily uniform throughout the thickness. These two approaches are first briefly introduced and then used to arrive at identical solutions for a monolayer cantilever and a bilayer cantilever, both with arbitrary residual strain distributions throughout the thickness. The analytical formulas for a bilayer cantilever are further verified by the numerical simulation of a special case. After the discussion on the errors induced by assuming the gradient residual strains in the bilayer cantilevers are uniform, the relation between the bending plane and the neutral plane in bilayer cantilevers is also explored. Finally, we present an approach to characterizing residual stresses in thin films by using micromachined bilayer cantilevers in conjunction with the theory developed in this paper.