Surface stress effects on the resonance properties of cantilever sensors

The effect of surface stress on the resonance frequency of a cantilever sensor is modeled analytically by incorporating strain-dependent surface stress terms into the equations of motion. This mechanistic approach can be equated with a corresponding thermodynamic description, allowing basic equations to be derived that link the analysis to experimentally determined parameters. Examples are shown for the cases of a pure surface stress and an adsorption-induced surface stress, and indicate that frequency measurements may be useful for fundamental understanding of surface and adsorption-induced stresses on metals, semiconductors, and nanoscale structures. Application to biomolecular adsorption sensors appears unlikely.

Figure 1

Schematic view of the free-body diagram of the end part of a cantilever.

Figure 2

Schematic showing the general cases considered for (a) a cantilever with uniform surface stress on upper and lower surfaces and no adsorption; (b) the cantilever of (a) with adsorption on one side of the cantilever, causing a surface stress difference between the upper and lower surfaces.