Quantitative Boundary Support Characterization for Cantilever MEMS

Microfabrication limitations are of concern especially for suspended Micro-Electro-Mechanical-Systems (MEMS) microstructures such as cantilevers. The static and dynamic qualities of such microscale devices are directly related to the invariant and variant properties of the microsystem. Among the invariant properties, microfabrication limitations can be quantified only after the fabrication of the device through testing. However, MEMS are batch fabricated in large numbers where individual testing is neither possible nor cost effective. Hence, a suitable test algorithm needs to be developed where the test results obtained for a few devices can be applied to the whole fabrication batch, and also to the foundry process in general. In this regard, this paper proposes a method to test MEMS cantilevers under variant electro-thermal influences in order to quantify the effective boundary support condition obtained for a foundry process. A non-contact optical sensing approach is employed for the dynamic testing. The Rayleigh-Ritz energy method using boundary characteristic orthogonal polynomials is employed for the modeling and theoretical analysis.