On the micromechanics of micro-cantilever sensors: Property analysis and eigenstrain modeling

Micro-cantilevers can be utilized as sensors primarily due to their low stiffness/high flexibility and high resonance frequency. The cantilever system is therefore very sensitive to small changes of properties that can be detected either as change of deflection, or of resonance frequency. The development of small forces in the near-surface layers results in significant property changes of micro-cantilevers allowing their use for the detection of very small effects, e.g. associated with the adsorption of biological or chemical substances on the cantilever surfaces. While many experiments providing proof of principle deformation have been reported in the literature, quantitative analysis of the cantilever transduction effect requires precise characterization of the device deflection in response to known forces, i.e. detector calibration. The present paper addresses two aspects of this issue: property evaluation of micro-cantilever components, particularly the coating layer, and the use of analytical and numerical models of cantilever deformation using the concept of eigenstrain, a term that is used in residual stress theory to describe inelastic deformation. The analytical model proposed here accounts for the presence of surface tension and thermal mismatch effects, and predicts the resulting cantilever curvature. The numerical model presented is developed within the framework of finite element analysis, and allows the prediction of effects of cantilever attachment to the chip on complete cantilever deflection. Comparisons of model predictions with the experimental data on cantilever deflection due to changes in temperature obtained using optical interferometry show good agreement.