Effect of biaxial curvature on the resonance frequency of uncoated microcantilevers

[Display omitted] •SiO2 MCs of various dimensions with inherent biaxial curvature (Kx, Ky) were successfully fabricated.•Experimentally measured resonance frequency values were compared with FEM simulated ones.•(Kx, Ky) values were extracted from MC initial bending measurements.•Presence of Ky is shown to significantly influence the resonance frequencies of MCs.•Our experiments revealed that curvature induced resonance frequency shift critically depends on MC dimensions. Microcantilevers (MCs) are extensively studied as physical, chemical and biological sensors in dynamic mode, where the shift in resonance frequency due to the adsorption of target analytes/biomolecules on their surface is measured. However, surface stress generated during adsorption or microfabrication induced curvature inherently present in MCs can influence the observed frequency shift, introducing significant errors in the quantification of the analyte sensing response. In spite of several studies over the past four decades, the role of surface stress/curvature on the stiffness and thus resonance frequency of MCs is not well established. Interestingly, this effect also depends on MC dimensions and is not completely understood. In the present work, we address this problem and demonstrate that the presence of transverse curvature significantly influences the resonance frequency and this effect critically depends on width by length ratio (W/L) of MCs. For this purpose, we have fabricated uncoated SiO2 MCs of various dimensions with inherent biaxial curvature. Our experiments on these devices revealed that when W/L of MCs is < 0.16, resonance frequency shift is independent of curvature whereas it is directly proportional to the same when W/L is between 0.16 and 0.35. These results are explained on the basis of curvature induced nonlinear stiffening of MCs and clamping geometric effects. Interestingly, a further increase in W/L (>0.4) was found to marginally reduce the observed frequency shift and is attributed to the presence of competing non-linear plate softening effects at these dimensions. Finally, we have compared our results with various experimental studies and theoretical models reported in the literature.