Quantification of Uncertainty in the Modeling of Creep in RF MEMS Devices
2020-07-29T01:06:28Z (GMT) by
Permanent deformation in the form of creep is added to a one-dimensional model of a radio-frequency micro-electro-mechanical system (RF-MEMS). Due to uncertainty in the material property values, calibration under uncertainty is carried out through comparison to experiments in order to determine appropriate boundary conditions and material property values. Further uncertainty in the input parameters, in the form of probability distribution functions of geometric device properties, is included in simulations and propagated to the device performance as a function of time. The effect of realistic power-law grain size distributions on the creep response of thin RF-MEMS films is examined through the use of a finite volume software suite designed for the computational modelling of MEMS. It is seen that the use of a realistic height-dependent power-law distribution of grain sizes in the film in place of a uniform grain size has the effect of increasing the simulated creep rate and the uncertainty in its value. The effect is seen to be the result of the difference between the model with a homogeneous grain size and the model with a non-homogeneous grain size. Realistic variations in the grain size distribution for a given film are seen to have a smaller effect. Finally, in order to incorporate variations in thickness in manufactured devices, variation in the thickness of the membrane across the length and width is considered in a 3D finite element model, and variation of thickness along the length is added to the earlier one-dimensional RF-MEMS model. Estimated uncertainty in the film profile is propagated to selected device performance metrics. The effect of film thickness variation along the length of the film is seen to be greater than the effect of variation across the width.