Approximate Mechanical Properties of Clamped–Clamped Perforated Membranes From $In-Situ$ Deflection Measurements Using a Stylus Profiler

Surface micromachined membranes such as RF-MEMS switches are widely adopted in the field of telecommunication devices and represent nowadays the lowest loss devices for switching and routing RF signals. The knowledge of specific properties of structural materials is crucial for a reliable design of devices with optimized performance. Material properties, like Young's modulus and stress, strongly determine the mechanical behavior of MEMS devices. In this paper, Si
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thin film membranes, of different sizes and porosities, were fabricated by unconventional low temperature PECVD, using surface micromachining approach. The tri-layer was characterized by nanoindentation and stress measurements based on wafer curvature method. On the possibility to extract mechanical properties from deflection measurements, to the best of our knowledge, literature seems to lack of analytical solutions of the nonlinear large deflection problem of such membranes. Finite element analysis was used to model the load-deflection response of double-clamped membranes, in agreement with measured data. An approximate empirical function was proposed and validated, for describing the maximum deflection under quasi-point loads. The function was used to determine the stress of the investigated membranes; the relative error between predicted and calculated stress values was in the range 2.1%-8.5% for membranes with lower porosity.