Study of mechanical properties of RF MEMS switches by nanoindentation: characterization and modeling of electro-mechanical behavior

This paper presents a thorough methodology to evaluate the mechanical properties of RF MEMS switches. It includes an analytical electro-mechanical model and nanoindentation characterizations which allow explaining the electrostatic behavior of the MEMS switches.Experimental and theoretical aspects are compared through two runs of ohmic electrostatic switches which are different from geometric and process flow standpoint.The switch is modeled as a clamped-clamped beam with mobile vertical loads, two stretching axial forces and two reaction moments in the anchors.The mechanical properties are characterized by nanoindentation technique; specific test protocol for measuring very low stiffness has been specially implemented with an adapted continuous stiffness measurement method. The measured values of the stiffness at the membrane center are respectively 79 and 137 N/m for the two runs, and they remain in good agreement with the theoretical model. The difference between these two runs is explained by the difference of the tensile residual stress.Moreover, the nanoindentation data turn out to be useful to evaluate the contact quality: dimple deformation due to twisting of the beam (contact in multiple steps), or inhomogeneous surface (stiffness is increasing while in contact).The fitted model is also used to approximate the restoring and contact forces and to point out the influence of the mechanical properties on the electrostatic behavior. A simple model with two parallel-plate capacitors in parallel, used for calculation of the up- and down-state capacitances, shows no discrepancy with experimental values.Finally, it may be concluded that the electrostatic behavior of the switches (pull-in voltage, up- and down-state capacitances, and probability of stiction) can be better understood thanks to the mechanical characterizations made by nanoindentation.