Determination of the spring constants of the higher flexural modes of microcantilever sensors

A method for the simultaneous calibration of the spring constants of all flexural modes of microcantilevers is presented. It is based on a flow of gas from a microchannel that interacts with the microcantilever. The gas flow causes a measurable shift in the resonance frequencies of thermal noise spectra of the flexural modes. From the magnitude of the frequency shifts of the individual modes the spring constants can be determined with high accuracy and precision. The method is non-invasive and does not risk damage to the cantilever. Experimental data is presented for several V-shaped and rectangular cantilevers with nominal fundamental spring constants in the range of 0.03-1.75 N/m. The spring constants of the fundamental modes compare favorably to those obtained using the Sader method. The higher modes of oscillation are readily calibrated with experimental uncertainties of 5-10%.