**8. Conclusion**

228 Microelectromechanical Systems and Devices

by the following parameters: gap between bridge and floating metal *g*=2.85 µm, SiO2 dielectric thickness on the central conductor of the CPW *d*=0.1 µm, beam thickness *t*=4 µm (grown by electroplating). By using the above values and those given in Fig. 19, we get an actuation voltage V=40 V ca. for the lateral actuation. The experimental value was Vexp=(41±2) V by using ten devices measured onto the same wafer in different positions

Fig. 18. Simulated deformation for the same bridge experimentally tested with a higher value of the residual stress (σ=60 MPa). An actuation voltage around 95 volt has been

Fig. 19. Shunt capacitive switch manufactured by means of the eigth mask process

developed at FBK-irst. Dimensions are in µm.

predicted.

Analytical and numerical modelling for the mechanical response of a shunt capacitive RF MEMS switch have been compared by using an uni-dimensional theory, and 2D and 3D simulations performed by means of a commercial software package (COMSOL Multiphysics). Two actual configurations have been experimentally studied to validate the proposed model.

As a result, it has been demonstrated that RF MEMS mechanics can be predicted in a convenient way by uni-dimensional phenomenological models if evaluations about switching times, threshold voltage and preliminary dynamics have to be studied, without involving cumbersome simulations with a computer. In fact, the most part of the previous quantities depend on the equations to be used for the correct definition of the spring constant, and we demonstrated that the analytical approach based on the knowledge of the materials and of the geometry fulfils the most part of the quantities to be obtained. The actuation velocity and the switching times have been also defined and predicted by means of the analytical approach based on the Mechanical Energy considerations, including the applied DC voltage.

2D and 3D simulations are really useful for configurations having a very peculiar shape, especially for combining mechanical and RF predictions, being based on the same geometry, and this will be very useful to get a figure of merit for the RF MEMS technology (not yet available) based on different input conditions. Concerning the evaluation of the actuation voltage, the main parameter to be defined is the residual stress of the structure, because it dramatically influences the mechanical response of the bridge. On the other hand, with the proper knowledge of the technology used, the evaluation can be easily based on the unidimensional approach by defining effective quantities for simple configurations. The relative influence of surface forces and charging contributions has been discussed, to demonstrate that, under proper geometrical and material constraints, only charging effects can be really responsible for un-reliable structures, and a very simple solution to prevent this contribution is to tailor the switch in order to have contact-less actuation pads.
