Empirical and theoretical characterisation of electrostatically driven MEMS structures with stress gradients

This paper investigates the influence of residual stress on the characteristics of electrostatic actuators. This is first done empirically by mechanical characterisation of a set of RF-MEMS switches with varying geometries. The mechanical measurements are performed on a Dektak surface profilometer. In addition, low-frequency electrical characterisation is performed. The measurement results allow for fine-tuning of the analytical relationship between pull-in voltage and geometrical parameters. This generally applicable method therefore reduces the need for more advanced but time-consuming electromechanical simulations to predict the electrostatic switching behaviour of a large range of (RF-)MEMS devices with various geometries. Next, an analytical formula is derived, relating the deformation of the actuator due to stress and stress gradients to the electrostatic pull-in voltage. The results obtained with this formula are in good agreement with the measurements.