Mechanical behavior of mismatch strain-driven microcantilever

A model of mechanical behavior of microcantilever due to mismatch strain during deposition of MEMS structures is derived. First, a microcantilever, modeled as an Euler-Bernoulli beam, is subjected to deposition of another material and a linear ordinary differential equation which considers the through-thickness variation of the mismatch strain is derived. Second, the deposition analysis is experimentally realized by electroplating of nickel onto an atomic force microscope (AFM) cantilever beam. Young's modulus of the electroplated nickel film is determined by using Sader's method and elementary beam theory. The deflection of the AFM cantilever is in-situ measured as a function of the electroplated thin film thickness through the optical method of AFM and the mismatch strain with the through-thickness variation is determined from the experiment results.