Effect of undercut on the resonant behaviour of silicon nitride cantilevers

We present a systematic investigation of the dynamic properties of silicon nitride cantilevers in air. The thermal noise spectra of cantilevers have been measured using a home-made optical deflection setup. Torsional and flexural resonances up to the seventh mode are observed. The dependence of resonance frequencies on the dimensions and mode number is studied in detail. It is found that undercut increases the effective length of the cantilever by a value Delta L, which depends on the undercut distance and the resonance mode shape, but not on the cantilever length. Finite element modelling confirms these experimental findings. A simple model is suggested for the shape of the undercut region, which agrees well with experimental findings. Using this model, the undercut cantilever can be approximated by a stepped beam, where the clamp distance depends on the underetch duration and the mode shape.