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.