Determination of the Anisotropy of Young´s Modulus Using a Coupled Microcantilever Array

This paper reports a simple technique to measure the anisotropy of the Young´s modulus of MEMS materials using coupled cantilevers. The technique is demonstrated in single-crystal silicon with an array of cantilevers fabricated in (100) silicon following a “wagon wheel” configuration. The long axis of the cantilevers had different angular orientations to the [110] direction. The parasitic coupling due to undercut below the cantilevers, which is often observed during etching of MEMS, led to a collective behavior in the frequency response of the cantilevers. This collective behavior was used in association with an inverse eigenvalue analysis to obtain the Young´s moduli for the different orientations. Further analysis of the technique relating to accuracy and precision required in the resonance frequency measurement has also been presented.