Analytical model of the DC actuation of electrostatic MEMS devices with distributed dielectric charging and nonplanar electrodes

This paper gives a new insight into the problem of the irreversible stiction of RF microelectromechanical systems (MEMS) attributed to the dielectric charging. We present a model for the electrostatic actuation of MEMS devices taking into account the nonuniform distributions of the air gap and the charges in the dielectric layer. The major result of our study is the impossibility to invoke the sole uniform dielectric charging phenomenon to explain the irreversible stiction of electrostatic MEMS devices. In the absence of other forces, a nonzero variance of the charge distribution is required to explain the stiction of the device. Considering only uniform residual charge densities, previous reported works could only account for a drift of the actuation characteristics as a whole. In case of a uniform air-gap distribution, our analytical model can already account for an increase of the up-capacitance, a shift of the C-V, its narrowing, and the stiction by a closure of the pull-out window. We further show that the combined nonuniformities of air gaps and charges break the symmetry of the actuation characteristics. The asymmetry can be such that one of the pull-in points disappears, which is replaced by a continuous tuning range while the other pull-in point still exists.