Assessment of micromechanically-induced uncertainties in the electromechanical response of MEMS devices

Microelectromechanical systems (MEMS) have been already successfully commercialized for around 20 years. The design of novel MEMS sensors currently target two important features: smaller dimensions and higher reliability. As the characteristic size of the mechanical components of the devices decreases, uncertainties in the mechanical and geometrical properties induced by the microfabrication process become more and more important. To address these issues, an on-chip testing device has been proposed by the authors to avoid any visual inspection for the read-out. As the device has been obtained with a standard MEMS fabrication process, the experimentally tested conditions can be rather similar to those featured by the application systems. The spreading of the mentioned mechanical and geometrical features has been assessed thanks to a thin micro-cantilever, so as to magnify the effects of the microstructure on the overall MEMS behavior.

The electromechanical responses of ten nominally identical specimens have been recorded, and experimental data have shown a significant scattering due to the presence of the relevant uncertainty sources. To interpret the response of the device, an analytical reduced-order model and a finite element model of the whole device have been developed. The effects of random film morphology and of (over)etch depth have been then assessed through a Monte Carlo analysis. A genetic algorithm has been eventually adopted to identify features of the probability distributions of the mechanical and geometrical uncertainties in the batch of test structures.