M. Niessner

Modeling and fast simulation of RF-MEMS switches within standard IC design frameworks

We present a macromodel of an electrostatically actuated and viscously damped ohmic contact RF-MEMS switch suitable for direct implementation in standard IC design frameworks. The physics-based and multi-energy domain coupled model is systematically derived on the basis of a hierarchical modeling approach. The very good agreement with measurements proves the capability of the model to predict the behavior of the RF-MEMS switch. Especially effects due to the nonlinear coupling of the different energy domains are correctly reproduced. The accurate reproduction of heavily contact-related situations within acceptable computing time is identified as an issue for future research.

Experimentally validated and automatically generated multi-energy domain coupled model of a RF-MEMS switch

We present a computationally efficient multi-energy domain coupled system-level model of an electrostatically actuated RF-MEMS switch exposed to squeeze film damping. The physically-based model is systematically derived and calibrated on the basis of a hierarchical modeling approach. The model shows excellent agreement with both static and dynamic measurements performed with a white light interferometer. Especially coupling effects, that are the increased damping and the spring softening whilst actuation, are correctly reproduced by the model. This demonstrates the power of our modeling approach and, in particular, the predictiveness w.r.t. “real world” experiments. Furthermore, the automatically generated model is suitable for direct implementation into standard EDA tools for ICs, like Cadence™ and Mentor Graphics®.

A reconfigurable impedance matching network entirely manufactured in RF-MEMS technology

In this work we present a reconfigurable impedance matching network for RF (Radio Frequency) applications, entirely manufactured in MEMS technology (RF-MEMS). The network features four impedance sections. The way they load the RF line (i.e. in series or shunt configuration) as well as the type of impedance they realize (purely capacitive, inductive, or both in parallel) are reconfigured by means of RF-MEMS cantilever-type ohmic switches. A few specimen of the network have been fabricated using the RF-MEMS technology platform available at FBK and experimentally characterized. In particular, the electromechanical characteristic of the RF-MEMS switches is observed, and the upward bending of the switches contact tips made the characterization of the RF behavior impossible. The non-planarity is due to the accumulation of residual stress within the suspended Gold layer during the release of suspended structures, and is currently being mitigated by performing a low-temperature release step. Electromagnetic simulations (S-parameters) of the RF-MEMS network are also reported in this paper, showing the wide range of impedance transformations enabled by such a complex device based on MEMS technology.

Extraction of Physically Based High-Level Models for Rapid Prototyping of MEMS Devices and Control Circuitry

We present a novel MATLAB toolbox that, starting from discretized FEM device models, allows for the automated generation of physically based high-level system models. Our methodology is based on the mixed-level approach presented previously, which has proven to be a powerful method to tackle couplings between the electrostatic, fluidic, and mechanical energy domain. The resulting reduced-order models are formulated as state space models amenable to direct use in standard design tools. Due to its nature, the impact of design variations and environmental effects on the system performance can be quickly evaluated, which considerably facilitates full system optimization. The simulation of a micromirror demonstrates the power of our method, in particular the predictiveness w.r.t. experiments.

Mixed-level modeling of squeeze film damping in MEMS: Simulation and pressure-dependent experimental validation

We present the first results of a systematic study of squeeze film damping (SQFD) in MEMS, in which we compare the measured and simulated quality factors of a series of specifically designed devices at varying pressure. Three models are employed to calculate the quality factor: an analytical-heuristic compact model by Veijola, a numerical mixed-mode model by Veijola and a mixed-level model by the authors of this work. At normal pressure the mixed-level model produces, with a maximum error of only 7%, the most accurate results for the specimens considered demonstrating the predictive power of this rigorously physics-based modeling approach. The Veijola models produce maximum errors of up to 38% and 84%, respectively. Versus pressure, the highest errors occur in the transition regime between the continuum and the molecular gas regime.

A measurement procedure of technology-related model parameters for enhanced RF-MEMS design

The accurate design of Micro-Electro-Mechanical-Systems (MEMS) for Radio Frequency (RF) architectures (e.g., reconfigurable transceivers) relies on suitable models describing the static and, above all, the dynamic electromechanical and electromagnetic behaviour of moveable structures. Such models usually include multiple parameters, whose values depend on the adopted manufacturing technology, as well as the uncertainty sources affecting the process itself. As a consequence, measuring the technology-related model parameters of a given class of MEMS structures is essential to estimate and to reduce, at an early design stage, possible mismatches between simulation results and device performances. In order to address this issue, in this paper we describe a procedure to measure the parameters describing the behaviour of RF-MEMS switches that are most severely affected by residual mechanical stress and surface roughness. The validity of the proposed methodology is confirmed by the good accordance between simulation and experimental results.

Mechanical Contact in System-level Models of Electrostatically Actuated RF-MEMS Switches: Experimental Analysis and Modeling

Three different multi-energy domain coupled system-level models are used to simulate the closing and opening transients of a respective ohmic contact type RF-MEMS switch. The comparison of simulated and measured data shows that, due to the presence of multiple structural modes, none of the system-level models is able to capture exactly the initial closing and contact phase whilst dynamic pull-in. The system-level model, that uses a mechanical submodel based on modal superposition, produces the result closest to the real situation. Notably, the effective residual air gap, assumed whilst contact between the membrane with high surface roughness and the contact pads of the switch, is the most influential parameter in the simulation of the closing transient, as this parameter strongly affects the air damping on the device during pull-in. This finding demonstrates that a reliable model of air damping is a vital prerequisite for the predictive simulation of pull-in and pull-out transients.

Experimental analysis and modeling of the mechanical impact during the dynamic pull-in of RF-MEMS switches

The dynamic pull-in and pull-out of an electrostatically actuated and viscously damped ohmic contact RF-MEMS switch is both measured and simulated. Three different models are used for the simulations and evaluated w.r.t. measurements performed with a white light interferometer and a laser vibrometer. The evaluation shows that all models fail in predicting the initial contact phase of the membrane correctly. Further analysis reveals that this is due to the presence of a higher eigenmode that is activated during the first impact of the membrane.

Reduced-order modeling of capacitive MEMS microphones using mixed-level simulation

The authors demonstrate a reduced-order modeling methodology based on the mixed-level simulation approach that allows for the rapid evaluation of microphone design variations with arbitrary arrangement and shape of the acoustic holes. The resulting reduced-order models take multiply coupled energy domains into account and are capable of describing the effects caused by non-linear fluidic damping. The methodology is easily approachable, as the generation of the reduced-order models is automated by the use of a MATLAB toolbox

Automated Extraction of Multi-Energy Domain Reduced-Order Models Demonstrated on Capacitive MEMS Microphones

We present a methodology to systematically extract efficient and physically-based reduced-order models based on a mixed-level simulation approach and demonstrate its practicality for the design of a capacitive MEMS microphone. The method has been implemented in a MATLAB toolbox which starting from a FEM discretization, enables the automated generation of mixed-level VHDL-AMS based macro- models, which can be straightforwardly fed into a standard circuit simulator. The extracted models are highly efficient and moreover, in contrast to other equivalent network approaches, physically-based, thus allowing for the predictive simulation of microstructures with complex geometry.