The role of fabrication techniques on the performance of widely tunable micromachined capacitors

Coventorware 2001.1^® is used to identify key vertical dimensions for the low voltage operation of a two-gap widely tunable capacitor. Using identical masking stages, two varieties of tunable capacitor are presented. Nickel structures are demonstrated which have a tuning ratio of 5.1:1 from an initial capacitance of 0.7 pF. Gold devices exhibit a tuning ratio of 7.3:1 from an initial capacitance of 1.5 pF. These are the most widely tunable devices reported to date.     

Fabrication and dynamic analysis of the electrostatically actuated MEMS variable capacitor

Future microwave networks require miniature high-performance tunable elements such as switches, inductors, and capacitors. In this paper, high performance variable capacitor was fabricated by simple microelectromechanical systems (MEMS) technology. The capacitance and quality (Q) factor at 1 GHz are 0.792 pF and 51.6. The pull-in voltage is 13.5 V and the tuning ratio of the capacitor is more than 1.31:1. A reduced-order model for the dynamic characteristics of the capacitor is established based on the equilibrium among the plate flexibility.     

A novel MEMS tunable antenna with wide tuning range of frequency

In this paper a novel MEMS tunable CPW antenna with wide tuning range of frequency is presented. The antenna’s frequency tuning range increment is achieved by loading three novel large tuning range capacitors at radiation edge of antenna patch. Two techniques are employed for increasing the capacitors tuning range. First, dual gap technique is used to overcome the pull-in limitation and then two lateral beams are added in order to parallel movement of capacitive plate which increases the capacitance value. The simulation result shows that the resonance frequency tuning range of antenna increased from 1.96 GHz loaded by traditional capacitor to 6.89 GHz using the new capacitor structure. Also in resonance frequency, the antenna has a good impedance matching with transmission line even in high capacitance values.     

Large tuning ratio high aspect ratio variable capacitors using leveraged bending

Variable capacitors are a key component in Radio Frequency Micro Electro-Mechanical Systems (RF MEMS). They comprise fixed and flexible electrodes. Deformation, or actuation, of the flexible electrode changes the capacitance of the capacitor. This way, electrical properties of high frequency circuits can be modified. Traditionally, variable capacitors are based on a planar layout architecture, while a newer, vertical-wall, quasi three-dimensional approach theoretically enables increased device performance. Such devices depend on high aspect ratios, i.e. relatively high micro structures with very thin walls and gaps. A few vertical-wall variable capacitors made of nickel or gold have been fabricated to date, using deep X-ray lithography and subsequent electroplating (Achenbach et al. 2006; Klymyshyn et al. 2007, 2010) as the fabrication approach. They feature, amongst others, excellent quality factors of Q ≤ 95 at 5.6 GHz with 50 Ω reactance, but suffer from a very limited tuning range of the capacitance value (tuning ratio of, e.g., 1.38:1). The devices presented here exploit the same architecture and materials selection, resulting in similar, excellent Q-factors, but feature a different electrode layout approach, referred to as leveraged-bending. This layout is based on pulling a flexible electrode sideways, towards a fixed electrode, increasing the capacitance when actuating the variable capacitor. The leveraged bending approach theoretically enables infinitely high tuning ratios for components with perfect structure accuracy. To date, a significantly increased tuning ratio of 1.9:1 has been demonstrated. Limiting factors are an electrically non-ideal layout geometry chosen as a compromise to increase the fabrication yield, and structure deviations of ~1.6 μm from CAD layout to the electroplated component. Electrostatic actuation requires voltages between 0 and 72 V for capacitance values on the order of C = 0.3 pF at device dimensions of about 1.5 mm overall length, 5–10 μm gap and wall widths, and 100 μm metal height. Device performance measured with a vector network analyzer is in 97 % agreement with simulation results based on two-dimensional electrostatic-structural coupling (ANSYS Multiphysics) and three-dimensional electromagnetic field simulations (Ansoft HFSS). These simulations also indicate that an optimized gap geometry will allow to reduce the actuation voltage required by up to 40 %.     

Design and investigation of a low insertion loss,broadband, enhanced self and hold down power RF-MEMS switch

This paper presents a low insertion loss capacitive shunt RF-MEMS switch. In the presented design, float metal concept is utilized to reduce the capacitance in up-state of the device. Float metal switch shows an insertion loss <0.11 dB, a return loss below 26.27 dB up to 25 GHz as compared to 0.81 dB insertion, 8.67 dB return loss for the conventional switch without float metal. OFF state response is same for the both devices. Further pull-in voltage of 12.75 V and switching time of 69.62 µs have been observed in case of the conventional switch whereas device with float metal have 11.75 V and 56.41 µs. Improvement of around 2.5 times in bandwidth and 4 times in input power has been observed without self actuation, hold down problem. The designed switch can be useful at device and sub-system level for multi-band applications.     

Linear Bilayer ALD Coated MEMS Varactor With High Tuning Capacitance Ratio

A curl-up-plate microelectromechanical system (MEMS) varactor with an almost linear response and high tuning capacitance ratio is presented. The curl-up in the top plate is realized by the residual stress in the two layers that construct the top plate of the varactor. The linear response is achieved by having the curl-up plate designed to relax on the bottom plate and by having unanchored cantilever beams that prevent the pull-in, while applying a dc bias voltage. The developed varactor exhibits a low parasitic capacitance through etching the lossy substrate underneath the varactor's plates. A thin alumina dielectric layer of 100-nm thickness is deposited using an atomic-layer-deposition technique to provide electrical isolation between the two plates. This MEMS varactor exhibits an almost linear capacitance with a tuning ratio of 5 : 1. $hfill$[2008-0161]      

Pull-In Analysis of Torsional Scanners Actuated by Electrostatic Vertical Combdrives

This paper presents pull-in analysis of torsional MEMS scanners actuated by electrostatic vertical combdrives with general comb gap arrangements and cross sections. The analysis is based on a 2-DOF actuator with a single voltage control. Three failure modes of the scanners are identified as in-plane twist, transversal motion, and out-of-plane twist. For each failure mode, analytical expressions of pull-in deflection are obtained by applying 2D analytical capacitance models to the derived pull-in equations. From these, the dominant pull-in mechanism is shown to be in-plane twist for scanners with high-aspect-ratio torsional springs. The analytical calculations for both symmetric and asymmetric capacitances are shown to be in good agreement with simulation results. The optimum scanner design is achieved when the pull-in deflection matches the capacitance maximum angle. The condition can be expressed in terms of the ratio of the comb thickness to the comb gap, which is smaller than the typical aspect ratio of deep reactive ion etching. The optimum tradeoff between the maximum deflection angle and the number of movable combs is achieved by adjusting the overlap of the movable and fixed combs and the distance of the comb sets from the axis of the rotation.     

Surface micromachined high-performance RF MEMS inductors

High-performance three-dimensional (3-D) microinductors with air-core and polyimide-core were fabricated by using simple MEMS technology. Both inductors have electroplated copper coils to minimize resistance to obtain high quality factor. The measurement results show that both inductors have high Q-factors over wide range of operating frequency. The maximum Q-factor of the polyimide-core is 36.5 and the inductance is 1.42 nH at 4.5 GHz, while the maximum Q-factor of the air-core inductor is 22.9 and the inductance is 1.17 nH at 5.5 GHz. The series resistance/parasitic capacitance of the polyimide-core inductor and air-core inductor is 1.05 Ω/1.07 pF and 1.82 Ω/0.57 pF respectively at the peak-Q frequency.     

Analysis of a novel RF MEMS switch using different meander techniques

In this paper, two types of RF MEMS switches namely step structure and Normal beam structure are designed and analyzed using different meander techniques. Three techniques namely plus, zigzag and three-square meander were used to lower the pull-in voltage. The actuating beam is designed with the rectangular perforations affects the performance of a switch by lowering the pull-in voltage, switching speed and results in better isolation. In this paper a comparative analysis is done for all three meander techniques with and without perforations on the beam. Total six structures have been designed with the combination three meanders and two different beam structures. The proposed stepdown structure exhibits high performance characteristics with a very low pull-in voltage of 1.2 V having an airgap of 0.8 µm between the actuation electrodes. The gold is used as beam material and HfO₂ as the dielectric material such that the upstate and downstate capacitance is seen as 1.02 fF and 49 fF. The FEM analysis is done to calculate the spring constant and thereby the pull-in voltage and behavior of the switch is studied with various parameters. The switch with a step structure and three-square meander configuration has shown best performance of all by requiring a pull-in voltage of 1.2 V and lower switching time of 0.2 µs. The proposed switch also exhibits good RF performance characteristics with an insertion loss below − 0.07 dB and return loss below − 60 dB over the frequency range of 1–40 GHz. At 28 GHz a high isolation of − 68 dB is exhibited.

     

A novel high tuning ratio MEMS cantilever variable capacitor

This paper presents a novel cantilever-type MEMS variable capacitor with high tuning ratio. In previous works, the cantilever is used as a switch but in our design, it is applied as a variable capacitor. For increasing the maximum achievable capacitance of the cantilever, the suspended capacitive plate should be moved as parallel with fixed plate. The parallel movement can be obtained using the novel structure which utilized two additional lateral beams. Also to overcome the pull-in phenomenon in new structure, the different membrane thickness technique is used. The novelty of our design is adding the lateral beams to make parallel movement of the suspended plate to increase the variable capacitor of the cantilever. The new device is designed on a thick silicon substrate with a thin poly silicon membrane. The results show the tuning range of tunable capacitor with initial capacitance of 560.1 fF can be improved from 6:1 for conventional cantilever to 22.5:1 for the new cantilever. In other words the capacitance tuning range increased three times.     

MEMS tunable capacitors with fragmented electrodes and rotational electro-thermal drive

This paper reports on the design, simulation and fabrication of tunable MEMS capacitors with fragmented metal (AlSi 4%) electrodes. We examine a rotational electro-thermal actuation. An analytic model of the rotational effect thermal actuator was established in order to show the periodicity of the capacitance when the angle increases. Evaluation of the impact of fringing fields on the capacitance has been carried out using finite element analysis (FEA). The MEMS capacitors were fabricated using metal surface micromachining with polyimide sacrificial layer. The maximum rotation, corresponding to a maximum angle of 7°, was obtained near 1.2 V and 299 mA. The proposed capacitor has a practical tuning range of 30%. FEA has shown that this figure can be improved with design optimization. The MEMS architecture based on rotational effect and fragmented electrodes does not suffer from the pull in effect and offers a practical solution for future above-IC capacitors.     

On the tunability of a MEMS based variable capacitor with a novel structure

In this work a novel MEMS based variable capacitor has been presented. To increase the tunability and decrease the applied voltage, the conventional fixed-fixed beam used in CPW lines has been changed to a fixed-simple supported beam. The proposed structure is a simple cantilever micro-beam in the first step of deflection and is changed to a fixed-simple supported micro-beam in the second step of motion. In the capacitive micro-structures increasing the applied voltage decreases the equivalent stiffness of the structure and leads the system to an unstable condition by undergoing to a saddle node bifurcation. In the proposed structure to avoid pull-in instability and increase the capacitance tuning range, mechanical stiffness of the structure is increased by changing boundary conditions by locating a pedestal in the end of the cantilever beam. The governing nonlinear equation for static deflection of the micro-beam, based on Euler–Bernoulli micro-beam theory has been presented. The results show that the proposed structure increases the capacitance tuning range and decreases the applied voltage. The results also show that the position of the pedestal affects the tunability and the threshold voltage of the structure.     

Resonant Pull-In Condition in Parallel-Plate Electrostatic Actuators

Electrostatic parallel-plate actuators are a common way of actuating microelectromechanical systems, both statically and dynamically. In the static case, the stable actuation voltages are limited by the static pull-in condition, which indicates that the travel range is approximately limited to 1/3 of the initial actuation gap. Under dynamic actuation conditions, however, the stable voltages are reduced, whereas the travel range can be much extended. This is the case with the dynamic pull-in and the resonant pull-in conditions (RPCs). Using energy analysis, this paper extends the study of pull-in instability to the resonant case and derives the analytical RPC. This condition predicts snapping or pull-in of the structure for a given domain of dc and ac actuation voltages versus quality factor, taking into account the nonlinearities due to large amplitudes of oscillation. Experimental results are presented to validate the analytically derived RPC.     

Design,modeling, and mechanical characterizations of micromachined InP-based actuator for tunable MOEMS applications

A novel InP-based microactuator, which is actuated by electrostatic means, has been proposed, designed, fabricated, and characterized for tuning applications in the 1.5 μm wavelength domains. Its structural design is based on the global optimization method. The tunable device is a big square membrane, which is supported by four identical cantilever beams. The three alternating layers Si₃N₄/SiO₂ as a distributed Bragg reflector (DBR) mirror, which were previously reported, have been formed on the top of the membrane. Based on the optical interferometric measurements, the proposed Fabry–Perot filter has demonstrated a maximum deflection of ∼321 nm with an applied voltage up to 12 V, an average sensitivity of ∼27 nm/V, a pull-in voltage of 12.7 V, and a release voltage of 10.7 V. It is also observed that its natural frequency is 88.4 kHz. This measured frequency implies that the tuning speed of our device is fast for optical operations within 0.01 ms. In addition, our device’s mirror remains so flat with a good planarity of 0.07°, which is strictly required for the filter’s optical performance. This optical performance can be achieved, when the micromachined structure has a tuning displacement up to ∼38 nm with a low tuning voltage up to 5 V. When compared with the finite element models (FEM), which were generated by the commercialized software, Coventor™, our experimental results agree well in terms of the natural frequency, pull-in voltage and deflections. Thus, our tunable filter, which is based on the optimized design, enables better performances including reduced actuation voltages, large pull-in voltage, improved device reliability, and fast switching times. Our device can also quickly snap back to the original position. In addition, the undesired spring-softening effect has been reduced.     

Dynamic response of a torsional micromirror to electrostatic force and mechanical shock

In this paper dynamic characteristics of a capacitive torsional micromirror under electrostatic forces and mechanical shocks have been investigated. A 2DOF model considering the torsion and bending stiffness of the micromirror structure has been presented. A set of nonlinear equations have been derived and solved by Runge–Kutta method. The Static pull-in voltage has been calculated by frequency analyzing method, and the dynamic pull-in voltage of the micromirror imposed to a step DC voltage has been derived for different damping ratios. It has been shown that by increasing the damping ratio the dynamic pull-in voltage converges to static one. The effects of linear and torsional shock forces on the mechanical behavior of the electrostatically deflected and undeflected micromirror have been studied. The results have shown that the combined effect of a shock load and an electrostatic actuation makes the instability threshold much lower than the threshold predicted, considering the effect of shock force or electrostatic actuation alone. It has been shown that the torsional shock force has negligible influence on dynamic response of the micromirror in comparison with the linear one. The results have been calculated for linear shocks with different durations, amplitudes, and input times.     

RMS voltage sensor based on a variable parallel-plate capacitor made of electroplated copper

We present an advanced RMS voltage sensor based on a variable parallel-plate capacitor using the principle of electrostatic force. The device is fabricated in a micromechanical surface process with a high-aspect ratio actuator, reinforced by copper electroplating employing a sacrificial photo-resist layer. Another copper layer with a coplanar waveguide below the actuator provides separated excitation and sensing electrodes. Flip-chip technology is employed for low-loss electrical connectivity. The presented design has a plate area of up to 3 × 3 mm² and an initial gap distance of only 1.5 μm. We present results achieving a pull-in voltage below 1 V at frequencies from DC up to 1 GHz and sensitivities up to 1 fF/mV.     

Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.     

Pull-in study of an electrostatic torsion microactuator

Pull-in study of an electrostatic microactuator is essential for making the electrostatic actuation more effective. In this paper, pull-in analysis is presented for an electrostatic torsion microactuator. The torsion microactuator can be used as a microtorsion mirror. A polynomial algebraic equation for the pull-in voltage and pull-in angle of a torsion microactuator is derived. Two types of microactuators fabricated using bulk micromachining are presented. Measurements done on the fabricated microactuators are reported, showing deviations within 1% error from the calculations     

A methodology and model for the pull-in parameters of electrostaticactuators

This paper presents a generalized model for the pull-in phenomenon in electrostatic actuators with a single input, either charge or voltage. The pull-in phenomenon of a general electrostatic actuator with a single input is represented by an algebraic equation referred to as the pull-in equation. This equation directly yields the pull-in parameters, namely, the pull-in voltage or pull-in charge and the pull-in displacement. The model presented here permits the analysis of a wide range of cases, including nonlinear mechanical effects as well as various nonlinear, nonideal, and parasitic electrical effects. In some of the cases, an analytic solution is derived, which provides physical insight into how the pull-in parameters depend upon the design and properties of the actuator. The pull-in equation can also yield rapid numerical solutions, allowing interactive and optimal design. The model is then utilized to analyze analytically the case of a Duffing spring, previously analyzed numerically by Hung and Senturia, and captures the variations of the pull-in parameters in the continuum between a perfectly linear spring and a cubic spring. Several other case studies are described and analyzed using the pull-in equation, including parallel-plate and tilted-plate (torsion) actuators taking into account the fringing field capacitance, feedback and parasitic capacitance, trapped charges, an external force, and large displacements     

Extending the travel range of analog-tuned electrostatic actuators

The pull-in instability limits the travel distance of elastically suspended parallel-plate electrostatic microactuators to about 1/3 of the undeflected gap distance. In this paper, we examine the “leveraged bending” and “strain-stiffening” methods for extending the travel range of electrostatic actuators. The leveraged bending effect can be used to achieve full gap travel at the cost of increased actuation voltage. The strain-stiffening effect can be used to minimize actuation voltage for a given travel range. An analytical approximation shows that the strain-stiffening effect can be used to achieve a stable travel distance up to about 3/5 of the gap. A tunable reflective diffraction grating known as the polychromator has been designed using these actuation techniques, and selected designs have been fabricated and tested for actuation behavior. Gratings with 1024 flat, closely packed grating-element actuators have been fabricated with over 1-cm-long mirrors, achieving stable vertical travel distances of more than 1.75 μm out of a 2-μm gap