This work examines the effect of microstructure upon microcantilever bending stiffness. An existing beam theory model, based upon an isotropic Hooke's law constitutive relationship, is compared to a model based upon a micropolar elasticity constitutive model. The micropolar approach introduces a bending stiffness relation which is a function of any two independent elastic constants of the Hooke's law model (e.g., the elastic modulus and the Poisson's ratio), and an additional material constant (called γ). A consequence of the additional material constant is the prediction of an increased bending stiffness as the cantilever thickness decreases—a stiffening due to the material microstructure which becomes measurable at micron-order thicknesses. Polypropylene microcantilevers, which have a non-homogeneous microstructure due to their semi-crystalline nature, were fabricated via injection molding. A nanoindenter was used to measure their stiffness. The nanoindenter-determined stiffness values, which include the effect of the additional micropolar material constant, are compared to stiffness values obtained from beam theory. The nanoindenter stiffness values are seen to be at least four times larger than the beam theory stiffness predictions. This stiffening effect has relevance in future MEMS applications which employ materials with non-homogeneous microstructures instead of the conventional MEMS materials (e.g., silicon, silicon nitride), which have a very uniform microstructure.

This work presents a model to predict the effect of surface stresses on the ith-mode bending resonant frequency of microcantilevers and its experimental validation. With this model, one can calculate the surface stress acting upon the microcantilever solely by measuring resonant frequencies whereas previously one needed to measure the deflection. Resonant frequency measurement has distinct advantages in terms of ease and accuracy of measurement.

The mechanical response of a multiwalled carbon nanospring was examined with an atomic force microscope. Cantilever deflection, oscillation amplitude, and resonance were simultaneously monitored during the cycled movement of the scanner. A nonlinear response of the nanospring was observed, consistent with compression and buckling of the nanospring. This is the first reported measurement of a shift in the cantilever resonance frequency as a result of the interaction of a nanospring-tipped cantilever with the substrate.

A method is presented to determine the geometry of tipless microcantilevers by measuring the resonance frequencies of at least one of their bending, lateral and torsional resonance modes, and having knowledge of the beam's elastic modulus, Poisson's ratio and density. Once the geometry is known, the beam's stiffness and mass can be calculated. Measurement of multiple modes allows for multiple estimates of cantilever geometry. Multiple data points from the experimental results show that this approach yields dimensional values accurate to roughly 2.5% as compared to SEM-determined length, width and thickness. Stiffness values determined with this new technique are roughly 4.7% and 6.5% less than two existing characterization methods (i.e., Sader's method and Euler–Bernoulli beam theory predictions), and roughly 16% greater than Hutter and Bechhoefer's stiffness determination method.

An important figure of merit in atomic force microscopy is the spring constant of the cantilever probe. To create high aspect ratio tips, cantilever probe manufacturers commonly use dynamic etch techniques that modify the shape and dimensions of both the tip and the beam. Most of the methods used to determine beam stiffness assume a rectangular cross section even though the commonly used etches produce beams with trapezoidal cross sections. We present herein an improved method for determining beam stiffness that takes into account the actual geometry of the cantilever.