Effect of Surface Stress on Resonance Frequency of Microcantilever Sensors

This paper models the effect of surface stress on the cantilever flexural vibrations based on the balance equations for the transverse forces and bending moments, and seeks solutions within normal mode representation. The purpose is to resolve certain ambiguities and inconsistencies in the existing models, and to present an accurate description. The work is important for interpretation of data from the chemical and biological micro/nano cantilever sensors where the transduction processes are dominated by the changes in surface stress associated with the analyte sorption/binding. Modeling these effects up to second order in the beam slope it is found that the primary effect is an equivalent axial load similar to previous theories with some correction. However, there occurs second order effects associated with the shearing and bending influences of the axial load due to finite beam curvature. In normal sensing conditions with small amplitude oscillations these second order influences are negligibly small. However, in operations under externally imposed static bending and/or large amplitudes the latter may influence changes in resonance frequency by a few percent.