Analytical and experimental study of mismatch strain-induced microcantilever behavior during deposition

A model of mechanical behavior of microcantilever due to mismatch strain during deposition of MEMS structures is analytically derived and experimentally verified. 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 throughthickness variation of the mismatch strain is derived. Second, the deposition analysis is experimentally verified by electroplating of nickel onto an AFM cantilever beam. The deflection of the AFM cantilever is measured in-situ as a function of the deposited thin film thickness through the optical method of Atomic Force Microscopy and the mismatch strain with the through-thickness variation is determined from the experiment results. The usefulness of these equations is that they are indicative of the real time behavior of the structures, i.e. it predicts the deflection of the beam continuously during deposition process.