Mohammad Shavezipur

A novel linearly tunable butterfly-shape MEMS capacitor

A new MEMS tunable capacitor with linear capacitance-voltage (C-V) response is introduced. The design is developed based on a parallel-plate configuration and uses the structural lumped flexibility and geometry optimization to obtain a linear response. The moving electrode is divided into two segments connected to one another by a torsional spring. There are extra beams located between the two plates, which constrain the displacement of the moving plate. The resulting nonlinear structural rigidity provides the design with higher tunability than the parallel-plate ones. Furthermore, because the plates displacement is controlled, the shape of C-V curve changes in such a way that high linearity is achieved. The proposed design can be fabricated by a three-structural-layer process such as PolyMUMPs. The results of analytical solution and experimental measurements verify that the new capacitor can produce tunability of over 100% with high linearity. The introduced design methodology can further be extended to flexible plates and beams to obtain smooth C-V curves.

Development of parallel-plate-based MEMS tunable capacitors with linearized capacitance–voltage response and extended tuning range

This paper presents a design technique that can be used to linearize the capacitance?voltage (C?V) response and extend the tuning range of parallel-plate-based MEMS tunable capacitors beyond that of conventional designs. The proposed technique exploits the curvature of the capacitors moving electrode which could be induced by either manipulating the stress gradients in the plates material or using bi-layer structures. The change in curvature generates a nonlinear structural stiffness as the moving electrode undergoes out-of-plane deformation due to the actuation voltage. If the moving plate curvature is tailored such that the capacitance increment is proportional to the voltage increment, then a linear C?V response is obtained. The larger structural resistive force at higher bias voltage also delays the pull-in and increases the maximum tunability of the capacitor. Moreover, for capacitors containing an insulation layer between the two electrodes, the proposed technique completely eliminates the pull-in effect. The experimental data obtained from different capacitors fabricated using PolyMUMPs demonstrate the advantages of this design approach where highly linear C?V responses and tunabilities as high as 1050% were recorded. The design methodology introduced in this paper could be easily extended to for example, capacitive pressure and temperature sensors or infrared detectors to enhance their response characteristics.

Development of novel segmented-plate linearly tunable MEMS capacitors

In this paper, novel MEMS capacitors with flexible moving electrodes and high linearity and tunability are presented. The moving plate is divided into small and rigid segments connected to one another by connecting beams at their end nodes. Under each node there is a rigid step which selectively limits the vertical displacement of the node. A lumped model is developed to analytically solve the governing equations of coupled structural-electrostatic physics with mechanical contact. Using the analytical solver, an optimization program finds the best set of step heights that provides the highest linearity. Analytical and finite element analyses of two capacitors with three-segmented- and six-segmented-plate confirm that the segmentation technique considerably improves the linearity while the tunability remains as high as that of a conventional parallel-plate capacitor. Moreover, since the new designs require customized fabrication processes, to demonstrate the applicability of the proposed technique for standard processes, a modified capacitor with flexible steps designed for PolyMUMPs is introduced. Dimensional optimization of the modified design results in a combination of high linearity and tunability. Constraining the displacement of the moving plate can be extended to more complex geometries to obtain smooth and highly linear responses.

A probabilistic design optimization for MEMS tunable capacitors

This paper presents a design optimization method for MEMS parallel-plate capacitors under fabrication uncertainties. The objective of the optimization problem is to maximize the production yield considering the fabrication tolerances. The method utilizes aspects of the advanced first-order second-moment (AFOSM) reliability method in probabilistic design to find a linearized feasible region for performance functions and uses an analytical double-bounded-probability distribution function (DB-PDF) to approximate the distribution of random variables. Then, it attempts to place the tolerance box in such a way that the portions of the box with higher yield lies in the feasible region. The yield is directly estimated using the joint cumulative distribution function (CDF) over the tolerance box requiring no numerical integration and saving considerable computational complexity for multidimensional problems. For this reason, any arbitrary distribution can be considered for random parameters and the problem is not restricted to normality assumptions. Numerical examples, verified by Monte-Carlo simulations, demonstrate that optimal designs significantly increase the yield. The advantage of the proposed design optimization method is that the yield can be maximized in early design stages without tightening tolerances or increasing the fabrication cost and complexity. The application of the presented method is not limited to tunable capacitors and can be extended to other MEMS devices.

Eliminating the galvanic effect for microdevices fabricated with PolyMUMPs

The galvanic effect may notably damage associated micro-electro-mechanical devices fabricated with processes involving electrochemical steps. This effect is commonly observed when a significant amount of gold is used to design MEMS devices that are fabricated using PolyMUMPsreg. To study and overcome the galvanic effect on these devices, three methods are proposed: (1) connecting the device to a poly0 ring; (2) increasing the device surface area and (3) grounding the device to the substrate. The three methods are compared for their effectiveness in preventing galvanic corrosion. It is observed that although all three methods can considerably restrain the galvanic effect, grounding the device to the substrate is the best solution.

Design and Modelling of Novel Linearly Tunable Capacitors

MEMS-based tunable capacitors with electrostatic actuation are well-known for their wide tuning ranges, high Q-factors, fast responses, and small sizes. However, tunable capacitors exhibit very high sensitivity near pull-in voltage which counters the concept of tunability. In this research, two novel designs are presented that improve the high sensitivity in capacitance-voltage (C-V) curve. In the first design, the nonlinear deformation of supporting beams is studied to develop a new nonlinear spring. The variable stiffness coefficients of such springs improve the linearity of the C-V curve, and by delaying the pull-in, the maximum tunability is also increased without using complex geometries. In the second design, an asymmetric non-parallel-plate capacitor is introduced, in which the C-V response has lower sensitivity at high voltages. The design concept can be applied to highly tunable capacitors to improve the sensitivity and maintain high tunability. The numerical results demonstrate low sensitivity and high linearity and tunability for the new designs.Copyright

Linearization and tunability improvement of MEMS capacitors using flexible electrodes and nonlinear structural stiffness

This paper proposes solutions for high nonlinearity and structural instability in electrostatically actuated MEMS capacitors. The proposed designs use the flexibility of the moving electrode and nonlinear structural stiffness to control the characteristic capacitance–voltage (C–V) response. The moving plate displacements are selectively constrained by mechanical stoppers to prevent sudden jumps in the capacitance and to eliminate the pull-in. A symmetric double-humped electrode shape is utilized which results in a fairly constant sensitivity in the C–V curve and therefore a linearized response. An analytical and a finite-element coupled-field model are developed to study the behavior of the proposed capacitors and to optimize their design for maximum linearity. The experimental results verify that the designs introduced in this paper improve the linearity of the C–V response and increase the maximum tunability by three times compared to conventional MEMS parallel-plate capacitors. At the same time, they also eliminate the pull-in hysteresis of the response.

The application of structural nonlinearity in the development of linearly tunable MEMS capacitors

Electrostatically actuated parallel-plate tunable capacitors are the most desired MEMS capacitors because of their smaller sizes and higher Q-factors. However, these capacitors suffer from low tunability and exhibit high sensitivity near the pull-in voltage which counters the concept of tunability. In this paper, a novel design for parallel-plate tunable capacitors with high tunability and linear capacitance–voltage (C–V) response is developed. The design uses nonlinear structural rigidities to relieve intrinsic electrostatic nonlinearity in MEMS capacitors. Based on the force–displacement characteristic of an ideally linear capacitor, a real beam-like nonlinear spring model is developed. The variable stiffness coefficients of such springs improve the linearity of the C–V curve. Moreover, because the structural stiffness increases with deformations, the pull-in is delayed and higher tunability is achieved. Finite element simulations reveal that capacitors with air gaps larger than 4 µm and supporting beams thinner than 1 µm can generate highly linear C–V responses and tunabilities over 120%. Experimental results for capacitors fabricated by PolyMUMPs verify the effect of weak nonlinear geometric stiffness on improving the tunability for designs with a small air gap and relatively thick structural layers.

Design and Optimization of a New Highly Linear Tunable MEMS Capacitor

In this paper, a novel linearly tunable MEMS capacitor with high tunability is introduced. The characteristic air gap-voltage curve for an ideally linear tunable capacitor is studied. This curve is considered as a target for new designs. A three-structural layer process is used to develop the capacitor. The actuation and sense gaps in the three-plate capacitor are selected in such a way that for a voltage interval (between zero and pull-in), the gap-voltage response for sense electrodes becomes similar to the ideal curve. The resulting capacitance-voltage response of the new design demonstrates a combination of high linearity and tunability up to 250%. For processes which have fixed layer thickness and the sense and actuation gaps cannot be optimized, the design is modified by adding nonlinear springs and asymmetric geometry. The results of numerical simulation for a capacitor designed for PolyMUMPs process verify the improvement of linearity and tunability.Copyright

Novel Highly Tunable MEMS Capacitors With Flexible Structure and Linear C-V Response

MEMS parallel-plate tunable capacitors are widely used in different areas such as tunable filters, resonators and communications (RF) systems for their simple structures, high Q-factors and small sizes. However, these capacitors have relatively low tuning range (50%) and are subjected to highly sensitive and nonlinear capacitance-voltage (C-V) responses. In this paper novel designs are developed which have C-V responses with high linearity and tunability and low sensitivity. The designs use the flexibility of the moving plates. The plate is segmented to provide a controllable flexibility. Segments are connected together at end nodes by torsional springs. Under each node there is a step which limits the vertical movement of that node. An optimization program finds the best set of step heights that provides the highest linearity. Two numerical examples of three-segmented- and six-segmented-plate capacitors verify that the segmentation of moving plate can considerably improve the linearity without decreasing the conventional tunability. A two-segmented-plate capacitor is then designed for standard processes which cannot fabricate steps of different heights. The new design uses a flexible step (spring) under middle node. The simulation of a capacitor with flexible middle step, designed for PolyMUMPs process, demonstrates a C-V response with high tunability and linearity and low sensitivity.Copyright