Stochastic multiphysics modeling of RF MEMS switches

摘要

Micro-Electro-Mechanical (MEM) devices like switches, varactors and oscillators have shown great potential for use in communication devices, sensors and actuators. Electrostatically actuated switches in particular have been shown to have superior performance characteristics over traditional semiconductor switches. However, their widespread insertion in integrated electronics is critically dependent on a thorough understanding of two broad issues - manufacturing process variations and failure mechanisms. Variations during fabrication lead to uncertain material and/or geometric parameters causing a significant impact on device performance. Such uncertainties need to be accounted for during the robust design of these switches. In terms of failure mechanisms limiting the lifetime of MEMS switches, dielectric charging is considered to be the most critical. It can cause the switch to either remain stuck after removal of the actuation voltage or to fail to contact under application of voltage. There is a need for accurate and computationally efficient, multi-physics CAD tools for incorporating the effect of dielectric charging. In this work, we have attempted to address some of the aforementioned challenges. We have come up with new algorithms for improving the effciency of coupled electro-mechanical simulations done in existing commercially available software like ANSYS. The gains in efficiency are accomplished through eliminating the need for repeated mesh update or re-meshing during finite element electrostatic modeling. This is achieved through the development of a `map' between the deformed and un-deformed geometries. Thus only one finite element discretization on the original undeformed geometry is needed for performing electrostatic analysis on all subsequent deformed geometries. We have generalized this concept of `mapping' to perform stochastic electrostatic analysis in the presence of geometric uncertainties. The different random realizations of geometry are considered as deformed geometries. The electrostatic problem on each of these random samples is then obtained using the `mapping' and the finite element simulation on the mean geometry. Statistics such as the mean and standard deviation of the desired system response such as capacitance and vertical force are efficiently computed. This approach has been shown to be orders of magnitude faster than standard Monte Carlo approaches. Next, we have developed a methodology for the model order reduction of MEMS devices under random input conditions to facilitate fast time and frequency domain analyses. In this approach, the system matrices are represented in terms of polynomial expansions of input random variables. The coefficients of these polynomials are obtained by deterministic model order reduction for specific values of the input random variables. These values are chosen `smartly' using a Smolyak algorithm. The stochastic reduced order model is cast in the form of an augmented, deterministic system. The proposed method provides significant efficiency over standard Monte Carlo.Finally, we have developed a physics based, one dimensional macroscopic model for the quantitative description of the process of dielectric charging. The fidelity of the model relies upon the utilization of experimentally-obtained data to assign values to model parameters that capture the non-linear behavior of the dielectric charging process. The proposed model can be easily cast in the form of a simple SPICE circuit. Its compact, physics-based form enables its seamless insertion in non-linear, SPICE-like, circuit simulators and makes it compatible with system-level MEMS computer-aided analysis and design tools. The model enables the efficient simulation of dielectric charging under different, complex control voltage waveforms. In addition, it provides the means for expedient simulation of the impact of dielectric charging on switch performance degradation. It is used to demonstrate failure of a switch in Architect. We conclude with a description of how this one dimensional model can be combined in a detailed two dimensional coupled electro-mechanical framework.