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Miniaturized electrochemical impedance-based biochemical sensors have been extensively used for detection of chemical and biological agents at extremely low concentrations. The majority of the sensors presented in the literature have a two-dimensional (planar) geometry and use two interdigitated electrodes that are exposed to an aqueous solution for deteciotn. In this work, a novel three-dimensional sensor is presented that uses a parallel-plate geometry for sensor structure. The sensor has a digitated electrode patterned on the substrate and a planar and porous electrode suspended above the fixed electrode. The sensor is fabricated using PolyMUMPs and diethylhexyl phthalate (DEHP) is used to demonstrate the ability of the sensor for biochemical detection. The measurement results show that the sensor has distinct Nyquist responses for 0.02 ppm, 0.2 ppm, 2 ppm and 10 ppm concentrations of the DEHP. Different electrochemical phenomena such as double-layer capacitance formation and charge transport at high frequencies, and diffusion at low frequencies are detected using Nyquist plots. The experimental results show that, for 3D parallel-plate sensors, in contrast to interdigitated geometry, the electrostatic effect is noticeable, and the parallel-plate capacitance due to the dielectric effect of the solution notably affects the Nyquist response. This is an important effect, specially for biological detection.

This paper presents a new design for MEMS capacitive pressure sensor that helps to linearize the capacitance-pressures response of the sensor. Capacitive pressure sensors have two electrodes, one often fixed and one is deformed as the ambient pressure changes. In general, the two electrodes are made of flat thin films. The proposed sensor design is based on a corrugated membrane, where circular ridges and grooves are made in the membrane altering its deformation as the pressure is applied. The sensor design is analyzed using finite element simulations, and ANSYS coupled-field multiphysics solver is used to model and obtain the response of a conventional and corrugated pressure sensor as the ambient pressure changes. The simulation results show that, as expected, the sensor displays high sensitivity at lower pressure and as the pressure increases and the contact area between the membrane and fixed electrode expands, the sensitivity of the capacitance-pressure (C-P) response decreases for both sensors. However, the sensor with corrugated membrane displays high linearity at lower pressures. The response for proposed design at this pressure range is nearly a perfect line, while the conventional design exhibits nonlinearity that is visually noticeable. To quantitatively evaluate the level of linearity of the C-P responses, a linearity factor as the coefficient of linear correlation between the capacitance and pressure is used. The simulation results show that at low pressure of 0.2–1.0 MPa, the sensor with corrugated membrane has high linearity of 0.999 compared to 0.987 for conventional sensor, where for pressure range 0–1.0 MPa these values are 0.997 and 0.983, respectively. The quantitative comparison of the linearity factors for the two design show a notable improvement in the linearity of the C-P response providing nearly a constant sensitivity over the pressure range of 0.2 to 1.0 MPa.

Integrated micro-biosensors and microfluidic systems have been recently used for detection of cells, proteins, and other biomarkers for a wide range of applications. In this work, open micro-channel flows driven by capillary force designed for food safety applications are studied. The micro-channels are used to deliver the nutrients (extracts of different fresh produce) to the sensing site where pathogens reside. The presence of nutrients, simulating the condition that micro-organisms experience in real food materials, allow us to investigate their behavior in real time. Open channels studied in this work are partially covered to allow for etching of the sacrificial layer that creates the channel and use of capillary force to create a self-driven microfluidic system in which fluid flow is actuated by surface tension and wall adhesion. Numerical simulations are used to investigate the fluid flow regime in micro-channels using ANSYS FLUENT. The volume of fraction (VOF) method is used to simulate the dynamics of fluid flow in microchannels made of polycrystalline silicon with a thin layer coating of native silicon dioxide. The effects of channel size and different geometries (open channel, T-junction, and L-junction) on a flow rate of water in the channel are investigated. Our study shows that adding T- and L-junctions to the flow path would create a small delay in the fluid flow in the channel, and the number of junctions directly affect the delay, however, it does not prevent the fluid transfer by capillary force. The (partially covered) open channel geometry presented in this work is compatible with conventional surface micromachining process.

MEMS tunable capacitors have applications in tunable filters and RF circuits where high tunability and Q-factor are desired. Conventional parallel-plate tunable capacitors have a highly nonlinear capacitance-voltage (C-V) response and limited tunability of up to 50% due to fundamental limitation and structural instability. In this work, we present a novel design idea for a parallel-plate tunable capacitor that increases the tuning ratio and provides a smoother (more linear) response. The design uses two modes of deformation, rigid-body displacement of a curved moving electrode before pull-in and deforming the plate after pull-in, and exploits nonlinear structural stiffness to improve the linearity (and the tunability) of the tunable parallel-plate capacitor. The capacitor structure is designed such that when actuation voltage is applied, first the beams holding the moving electrode deform, and capacitance increase similar to conventional design up to pull-in. After the pull-in, the top electrode (which has a curved geometry) is deformed and further increases the capacitance, as the voltage increases. The design may provide an overall simulated tunability of more than 380%, and also has a more linear C-V response. The design is modeled and simulated using ANSYS coupled-field multiphysics solver and the effect of different design parameters are investigated. The simulation results show much high tunability and better linearity than conventional parallel-plate capacitors.

This work presents the surface modification of silicon chips as a platform for silicon-based biosensors with applications aiming for the detection of foodborne bacteria in aqueous solution. The detection requires high selectivity as the solution may contain a variety of biological species, which affect the outcome of the sensing process. The silicon surface is functionalized by a self-assembled monolayer (SAM) with thiol groups followed by immobilizing a thiol-linked DNA aptamer. The DNA aptamer used in this work has reported to recognize a biological species, E. coli ATCC 25922. The presence of DNA aptamer on the sensor surface allows the capture of the specific E. coli cells on the surface, while other potential biological (and chemical) species would not attach to the sensor surface, thus improving the selectivity of the sensor. The uniform formation of the SAM on the surface is an important step toward uniformly coating the sensor surface with the desired DNA aptamer. The SAM is created on the silicon surface by surface modification with the MPTS (3-mercaptopropyl trimethoxy silane) solution. Then the aptamer DNA solution is applied as droplets on the chip followed by a cure process. The attachment of the SAM and DNA aptamers are verified by atomic force microscopy (AFM). The surface functionalization presented in this work can be used for sensors made of silicon coated with a thin layer of native oxide, and can be adopted for detection of other cells and biological agents using the proper SAM and DNA aptamer.

Presence of toxic chemicals in food products due to the use of different synthetic materials in food packages may cause long-term health hazard. Addition of chemical components such as phthalate family (for instance, Di(2-ethylhexyl) phthalate, DEHP) to plastics may result in diffusion of these materials in food specially in liquids such as bottled soft drink, water and juice. In this work, we present a chemical sensor that can detect DEHP in orange juice at extremely low concentrations. The sensor is made of two interdigitated electrodes, and electrochemical impedance spectroscopy (EIS) is used for the detection. Sensors with different overall dimensions and finger/gap sizes were fabricated using a polycrystalline silicon standard foundry. For simplification of the experiments, low concentration of citric acid in water (similar to orange juice) is used to represent the orange juice. The sensors are exposed to different concentrations of DEHP and their Nyquist and impedance-frequency plots are studied. The experimental data shows that the sensors can distinctly capture low concentrations of DEHP in the juice solution. An electrical model is developed that can simulate the frequency response of the system containing the sensor and the solution. The model includes dynamic physical parameters such as double-layer capacitance, solution resistance and Warburg impedance that can be used in detection. EIS curves fit to experimental data shows that the model well fits the experimental data.

The present work introduces a novel design that linearizes the characteristic capacitance-pressure (C-P) response of the pressure sensor in contact mode. The design relies on patterning the insulating (dielectric) layer that separates the two electrodes of the device when the device is in contact mode. Since the capacitance is inversely proportional to the gap between the electrodes and the dielectric constant of the insulating layer is several times more than that of air (or vacuum), the contact region of the two electrodes makes more significant contribution to the overall capacitance of the system. Therefore, if the dielectric layer is properly patterned, the shape of C-P response can be controlled. In this work, we focus on linearity of the sensor response, and design and optimize dielectric pattern to achieve the highest linearity. Finite element simulations are used to demonstrate the applicability of the design concept. Different sensor designs are modeled and simulated using ANSYS® Multiphysics solver and their responses are compared to that of a conventional capacitive pressure sensor. Coefficient of linear correlation between pressure and capacitance is used as a quantitative measure for improvement of linearity. The simulation results show that the linearity of the C-P response improves from 0.930 in a 600 μm-diameter conventional design to 0.978 for a sensor with patterned dielectric layer. Moreover, a smaller sensor with 300 μm diameter display linearity of 0.999 over a 1.25 MPa – 5.0 MPa pressure range.

This research presents the numerical analysis of the triply coupled flap-wise, cord-wise and torsional vibrations of flexible rotating blades. Euler-Bernoulli bending and St. Venant torsion beam theories are considered to derive the governing differential equations of motion. Based on Finite Element Methodology (FEM), the cubic "Hermite" shape functions are implemented where the solution of the equations results in a linear engine problem. Then, the Dynamic (frequency dependent) Trigonometric Shape Functions (DISF's) for beam's uncoupled displacements are derived. The application of the Dynamic Finite Element (DFE) approach to the solution of the governing equations is then presented. The DFE formulation, based on the weighted residual method and the DTSF's results in a nonlinear engine problem representing eigenvalues and engine modes of the system. The applicability of the DFE method is then demonstrated by illustrative examples, where a Wittrick-Williams root counting technique is used to find the system's natural frequencies. The DFE approach, an intermediate method between FEM and "Exact" formulation, is characterized by higher convergence rates, and can be advantageously used when multiple natural frequencies and/or higher modes of beam-like structures are to be evaluated.

A new design concept for MEMS capacitive pressure sensors is presented that can be used to improve the linearity of the capacitance-pressure (C-T) response of the sensor. The sensor uses an extra dimple mask and etching step in the fabrication process of the device to create small bumps under the pressure sensitive and flexible membrane. Different designs, including a conventional sensor, are modeled and simulated using FEM coupled-field multiphysics solver in ANSYS®. Polycrystalline silicon is used as the structural material in the simulations. Coefficient of linear correlation between device capacitance and ambient pressure is used as the linearity factor to quantitatively compare the performance of different sensors. The finite element analysis show that the linearity factor improves from 0.938 for a conventional design to 0.973 for a design with a central bump. For a design with five bumps (one at the center of membrane and four off-center) the linearity factor increases to 0.997 for bumps of 1.5 μm thickness for wide pressure range of 0.0–4.0 MPa. The proposed design can be tailored for different applications that require certain sensor materials or different pressure ranges by using optimized sensor dimensions.

Chemical and biological detection using Electrochemistry Impedance Spectroscopy (EIS) highly depends on the electrical characteristics of the electrodes used in the measurement process. In this work, the effect of surface coating on behavior of interdigitated impedance-based biochemical sensors is studied. Two interdigitated sensors with the same geometry and different electrode materials are fabricated using a standard process. One electrode is made of gold and the other electrode is made of polycrystalline silicon covered with a thin layer of native silicon dioxide. Different concentrations of di(2-ethylhexyl) phthalate (DEHP) in water are used and the Nyquist responses of the two sensors exposed to these solutions are obtained. The measurement results show that at high frequency both sensors form double-layer capacitance values on their electrode surfaces, however, the silicon sensor has a much lower double-layer capacitance values, because formation of oxide layer adds to the gap between charges at the interface of the electrode and the solution. Moreover, comparing the low frequency regions of the Nyquist plots for two sensors shows that the presence of oxide layer affects the Warburg effect and the charge diffusion near the surface of the electrode, creating an extra capacitive element in series with the diffusion effect. The results of this work may be extended to other interdigitated biochemical sensors that may have other sources of contamination on their surfaces.

A novel design for laterally actuated nanoelectromechanical (NEM) relays with flexible source-drain contact is presented. The design uses a thin curved source that can provide expandable contact area between the source and the drain in ON-STATE position. The presence of the thin film curved source creates a local nonlinear stiffness in addition to the main stiffness of the source beam. This additional stiffness not only controls the contact area with over-drive voltage after the pull-in, but can also generate repulsive force when the actuation voltage is removed to separate the two contacting surfaces. The additional repulsive force creates a “peel-off” separation mechanism and can overcome relatively large adhesion forces. Finite element simulations are used to verify the applicability of this design and ANSYS® APDL structural solver and contact technology is used to determine the nonlinear stiffness of the curved source and also to simulate the stiction and repulsive forces generated in the curved source. Curved source structures with different curvatures are simulated to examine the applicability of the design idea in overcoming the adhesion between source and drain. FEM results demonstrate that secondary structural stiffness created at the source-drain contact can overcome large adhesion stress and allow the separation in a peel-off mechanism after the actuation voltage is removed.

A novel structure for capacitive MEMS pressure sensors is presented that can be used for a wide range of pressure sensing applications. The sensor is designed such that its characteristic capacitance-pressure (C-P) response is highly linear and could cover a wide range of working pressure. A capacitive pressure sensor includes two capacitive electrodes, one patterned on the substrate and the other one suspended creating a sealed cavity. The suspended electrode acts as the pressure sensitive membrane in the device and undergoes out-of-plane deformation when there is a change in ambient pressure, resulting in a change in the device’s capacitance. The design presented in this work uses a wavy-shape membrane with controlled deformations to provide a highly linear C-P response. The wavy shape of the membrane can be fabricated using grey-scale mask and lithography. ANSYS APDL multiphysics solver is used to model and simulate the pressure sensor and optimize its response. The material used in the design and simulations of the pressure sensor is silicon carbide making this design suitable for harsh environment applications. The simulation results show that if the size and the shape of the wave form in the membrane are optimized, highly linear C-P response can be achieved and also its working pressure range can be extended.

The effect of long-term contact on adhesion force between MEMS silicon surfaces is investigated. A test structure is developed that can initiate the contact between the two surfaces without actuation. Therefore, the surfaces may remain in contact for a long period of time. The contacting surfaces are separated using a thermal actuator and the adhesion force is determined utilizing FEM simulations. Freshly released and long-time stored devices were tested, and their adhesion force is determined. The test results show that the adhesion force for devices in contact for a long time is drastically larger than those with short-term contact. Adhesion force values as large as 2.9 μN for long-term contact and as small as 0.4 μN for fresh contact were measured. The large adhesion force associated with long-term contact is believed to be attributed to the formation of native oxide at contacting nano-asperities and formation of covalent bonds between the surfaces, requiring larger force to break the bonds.

Three-dimensional biochemical sensors are developed that can be used for chemical and biological detection in aqueous solutions and suspensions. The sensors are fabricated using a standard polycrystalline silicon process, PolyMUMPs, and can detect chemicals and biomarkers in low concentrations in near real time. The sensors made of a stack of electrodes allowing the solution to occupy the space between the layers of electrodes and have a larger interface with the electrodes. The sensors use electrochemistry impedance spectroscopy (EIS) for detection and therefore increasing the solution-electrode interface improves the sensitivity of the sensor. To demonstrate the applicability of the proposed sensor design, experimental measurements are used to characterize and compare the 3D sensors with conventional 2D interdigitated sensors. Diethylhexyl phthalate (DEHP) solution is used as the target chemical, and the 2D and 3D biochemical sensors are exposed to different concentrations of DEHP solution. An LCR meter is used to sweep the frequency and determine the impedance of the sensor-solution combination. The test results show that the three-dimensional sensors have higher sensitivity than 2D interdigitated ones verifying the advantage of the new sensor design over existing conventional sensors. The proposed sensors can also be used for detection of biological markers such as cells, proteins and enzymes in aqueous solutions.

A MEMS capacitive temperature sensor is presented that displays high sensitivity over a specific temperature range using out-of-plane thermal actuators and capacitive electrodes. The sensor is suitable for applications that require high precision in relatively small temperature range, such as biomedicine, food processing and food safety. The device uses a combination of bilayer, rigid and flexible beams to create a nonlinear capacitance-temperature response over a short temperature range. The bilayer beams act as the out-of-plane thermal actuator and move the top electrode of the sensor up and down to change the capacitance. The capacitance is inversely proportional to the electrodes' gap and a decrease in the gap increases the sensitivity of the capacitance-temperature (C-T) response. Sensors with different geometries have been simulated using ANSYS to show the possibility of geometric modification to shift the temperature range with high sensitivity. Fabricated sensors are used in an experimental set up to demonstrate the applicability of the proposed design concept. The measured data verify the simulation results and demonstrate that the proposed sensor design can provide high sensitivity of 20 fF/°C in a desired range of ambient temperature where low sensitive region display noticeably smaller sensitivity of 5 fF/°C.

A novel design for MEMS capacitive pressure sensors is presented that can effectively eliminate the temperature drift in sensor for high temperature applications. The design uses a bilayer membrane made of a thin metal film deposited on the top of membrane to balance the deformation the membrane experiences when the ambient temperature changes. The thermal expansion mismatch of the metal layer and the membrane results in out-of-plane bending if the temperature changes. This deformation can compensate the deformation in the membrane due to the temperature change. By optimizing the dimensions of the top metal layer (shape and thickness), it is possible to minimize the change in the device capacitance due to temperature rise. A coupled-field multiphysics solver in ANSYS® APDL is used for design, simulation and optimization of the sensor’s structure and to solve the governing equations of the coupled electrostatic and structural physics. The membrane material is silicon carbide (SiC), the top metal layer is nickel (Ni) and the substrate is a single-crystal silicon wafer. The thickness and dimensions of top metal layer is optimized using FEM simulations. The results display a very stable capacitance value for a large pressure range and over a wide range of ambient temperature (0–600°C), demonstrating the proposed design can effectively eliminate the temperature effect. Different pressure values ranging from 0.0 to 20 bars have been examined in the simulations and for most of the pressure range, a highly stable capacitance value is observed with less than 0.5% error over 600 °C temperature range.

Internalization of pathogens inside pores and channels of fresh produce and formation of polymeric biofilm around their colonies are important phenomena in food safety due to complications they create for removal and inactivation of pathogens. The practical challenges does not allow for monitoring the pathogen-produce interaction in real time and under different ambient conditions. The present work introduces a biomimetic biosensing platform that simulates the actual produce and can detect the presence, growth and internalization of microorganisms and also potential formation of biofilm. The system consists of layers of capacitive electrodes made of polycrystalline silicon which are designed based on a standard foundry process (PolyMUMPs). The electrodes form multiple impedance-based biosensors and can simulate porous medium of the produce surface. As the cells reside on the surface of the top layer or penetrate inside the system, the capacitance value of each electrode pair changes. Monitoring the capacitance change of each biosensor allows us to determine where the microorganisms are and also whether their population is increasing. To demonstrate the applicability of our proposed biosensing system, a comprehensive FEM simulation is performed using ANSYS® APDL. The simulation results show that each pair of electrodes displays a specific pattern of capacitance change when cells reside on the system’s surface, move inside, grow or produce polymeric biofilm, because the electrostatic properties of cells and biofilm polymers are different from those of the solution. Analyzing the capacitance patterns allows us to determine that cells are at which stage of growth or internalization, and how far they have moved inside the system.

This paper describes the improvement of pull-in stability, contact properties, and reliability of laterally actuated nanoelectromechanical relays by partitioning the mechanical and electrostatic domains in the relay structure. Separation of the two physics allows us to individually optimize the structural stiffness and the actuation voltage to increase the contact pressure and reduce the ON-state resistance without applying excessive drain voltage. The devices can tolerate more than 200% overdrive gate voltage, resulting in near 100% increase in contact force, and reducing the contact resistance from $\sim 10$ G $\Omega $ to $\sim 23$ K $\Omega $ . For a given overall device dimension, tailoring the mechanical and electrostatic elements independently also enables us to control the pull-in and pull-out voltages, which have different design requirements for different applications. The measurement results show that the pull-in/pull-out hysteresis could vary between 30% and 60% of the actuation (pull-in) voltage. Increasing the mechanical force without affecting the device actuation voltage improves the relay reliability by reducing the possibility of failure due to source–drain stiction when the relay is switched ON. As a proof of concept, mechanical relays are fabricated using polycrystalline silicon coated by a titanium nitride layer deposited via plasma enhanced atomic layer deposition. [2014-0018]

An impedance-based interdigitated biochemical sensor is presented in this work that is designed for, and fabricated using a standard polycrystalline silicon process. The sensor provides a near real time, non-invasive, label free and rapid detection technique to quantify chemicals and biomarkers in aqueous solutions. The combination of sensor structure and aqueous solution creates an equivalent electrical circuit comprised of constant and variable capacitive and resistive elements such as solution resistance and double-layer capacitance formed at the interface of the electrodes surface and the solution. The equivalent circuit and its elements are used to quantify the concentration of chemicals in an aqueous solution using the impedance of the system. Diethylhexyl phthalate (DEHP) solution is utilized to characterize and analyze the sensor's response via electrochemical impedance spectroscopy (EIS). Finite element analysis (FEA) and experimental data are used to determine the components of the equivalent circuit. The experimental results show that the sensor is able to detect the concentration of DEHP as low as 0.02 ppm. Using the circuit model and experimental data, the change of double-layer capacitance and solution resistance of the system for different solution concentrations are obtained. The results show that the double-layer capacitance increases with solution concentration, while the solution resistance decreases. The experimental results also verify the electrical circuit model used for the sensing system.

Laterally actuated polycrystalline silicon nanoelectromechanical (NEM) relays with enhanced electrical properties are presented. Due to surface oxidation of polysilicon in room ambient conditions, the relays have a high contact resistance (> 1 GΩ) that requires high drain bias (3-5 V) to break through. The addition of a platinum sidewall coating reduces the on-resistance and the required drain bias to as low as 3 kΩ and 0.1 V, respectively. The platinum coating's stability is demonstrated by two tests: first, a contact-and-hold test where the relay passes current (~1μA) for up to 155 min and, second, a hot cycling test where the relay survives for over 108cycles . The NEMS relays are simulated using finite-element analysis, and the models are verified against experimental tests. Furthermore, the relays are configured and tested as a 2 : 1 multiplexer to show their potential as a digital logic component.

Microstructures with flexible and stretchable properties display tremendous potential applications including integrated systems, wearable devices and bio-sensor electronics. Hence, it is essential to develop an effective method for fabricating curvilinear and flexural microstructures. Despite significant advances in 2D stretchable inorganic structures, large scale fabrication of unique 3D microstructures at a low cost remains challenging. Here, we demonstrate that the 3D microstructures can be achieved by grayscale lithography to produce a curved photoresist (PR) template, where the PR acts as sacrificial layer to form wavelike arched structures. Using plasma-enhanced chemical vapor deposition (PECVD) process at low temperature, the curved PR topography can be transferred to the silicon dioxide layer. Subsequently, plasma etching can be used to fabricate the arched stripe arrays. The wavelike silicon dioxide arch microstructure exhibits Young modulus and fracture strength of 52 GPa and 300 MPa, respectively. The model of stress distribution inside the microstructure was also established, which compares well with the experimental results. This approach of fabricating a wavelike arch structure may become a promising route to produce a variety of stretchable sensors, actuators and circuits, thus providing unique opportunities for emerging classes of robust 3D integrated systems.

New microstructures for the measurement of the interfacial adhesion force between polycrystalline silicon surfaces in micro- and nanoelectromechanical systems and at elevated temperatures are introduced. The devices consist of bilayer cantilever beams with different coefficients of thermal expansion, which carry a rigid plate with a dimple as one of the contacting surfaces. A landing pad patterned on the substrate serves as the second contact surface. Thermal actuation and structural force stored in the beams initiate and terminate, respectively, the contact between the dimple and the landing pad. The presented designs eliminate the effect of the electrostatic force caused by trapped charges at the contact surfaces and drastically reduce the capillary force caused by ambient humidity, both of which may contribute to the adhesion forces measured by other techniques. This allows us to separately measure different sources of adhesion force. The measurement results show that in the absence of electrostatic and capillary forces, the value of the adhesion force is notably reduced and is independent of contact area over the examined range.

This paper introduces a modified structure for parallel-plate-based MEMS tunable capacitors. The capacitor has triangular electrodes with geometric and structural asymmetry, which enhances its performance. The device structure is also equipped with a set of cantilever beams between capacitor's electrodes, called middle beams. These beams provide extra stiffness as tuning voltage increases and delay the pull-in which results in a higher tunability. They also reduce the high sensitivity of the capacitance to the voltage change and linearize the C-V response. An analytical model is developed to optimize the capacitor's dimensions for maximum linearity of the response. Numerical simulations demonstrate tunabilities over 150% where more than 2/3 of which is highly linear. Capacitors fabricated with PolyMUMPs verify that the design technique proposed in this paper can improve the linearity of the device and increase the maximum tunability. The proposed design has a simple geometry and is fabricated using three structural layers, and therefore, it can be easily integrated in tunable filters or other RF circuits.

The application of a Refined Dynamic Finite Element (RDFE) technique to triply coupled vibration of centrifugally stiffened beams is presented. The proposed method is a fusion of the “Galerkin weighted residual” formulation and the Dynamic Stiffness Matrix (DSM) method, where the basis functions of approximation space are assumed to be the closed form solutions of the differential equations governing uncoupled bending and torsional vibrations of the beam. The use of resulting dynamic trigonometric interpolation (shape) functions leads to a frequency dependent stiffness matrix, representing both mass and stiffness properties of the beam element. Assembly of the element matrices and the application of the boundary conditions then leads to a frequency dependent nonlinear eigenproblem. The Wittrick–Williams algorithm is used as a solution technique to compute the natural frequencies and modes of five illustrative example beam configurations, exhibiting doubly and triply coupled vibrations. The discussion of results is followed by some concluding remarks.

Intrinsic uncertainties of MEMS fabrication processes can severely affect the performance of devices because the tolerance ranges of these processes are relatively large and improvement of process accuracy is very expensive. Therefore, the analysis of fabrication uncertainties and their outcome on a device performance is a vital task before finalizing the design. In this paper, the effects of process inaccuracy on the performance of MEMS tunable capacitors are studied. Design parameters such as dimensions of electrodes and the initial gap between them and the stiffness of supporting beams are considered as random variables. The variation of these parameters within tolerance ranges drastically alters the capacitor's actual response from the desired one and results in low yield. Hence, design optimization with the objective of maximizing yield in early steps becomes very important. An effective method for yield optimization of MEMS capacitors under given fabrication uncertainties is introduced. The method utilizes aspects of the advanced first-order second-moment (AFOSM) reliability method to find a linearized feasible region to estimate the yield. The yield is calculated directly using the joint cumulative distribution function (CDF) over the tolerance box requiring no numerical integration and avoiding computational complexity. The optimal design verified by Monte-Carlo (M-C) simulation exhibits a significant increase in the yield. The main advantage of this method comparing to other design optimization methods is that the proposed method does not change the design topology or fabrication accuracy. It increases the yield by finding the optimum design variables as demonstrated in this paper.

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 plate's 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.

Accurate prediction of growth of undesirable organisms (e.g., Pseudomonas fluorescens) in perishable foods (e.g., milk), held under sub-ideal storage conditions, can help ensure the quality and safety of these foods at the point of consumption. In this investigation, we inoculated sterile milk with P. fluorescens (~10(3) cfu/mL) and monitored inoculum growth behavior at constant and fluctuating storage temperatures. Three storage temperatures, 4 °C, 15 °C and 29 °C, were selected to simulate proper refrigeration conditions (4 °C) and temperature abuse, respectively. To simulate temperature fluctuation, milk held at 4 °C was subjected to temperature shifts to 15 °C or 29 °C for 4 to 6h. A modified logistic model was used to obtain the best-fit curve for the microbial growth under constant storage temperature. The specific growth rates at 4 °C, 15 °C, and 29 °C, obtained from experimental data, were 0.056 ± 0.00, 0.17 ± 0.05, and 0.46 ± 0.02 h(-1), respectively, and the lag time values were 29.5 ± 4.2, 12.7 ± 4.4, and 2.8 ± 0.3h, respectively. A model predicting bacterial growth under different temperature fluctuations was obtained using the growth parameters extracted from constant temperature experiments. Growth behavior predicted by the fluctuating temperature model and that obtained experimentally were in good agreement. Lag time exhibited a larger variation compared with specific growth rate, suggesting that it depends not only on growth temperature but also on the sample population and temperature gradient. Additionally, experimental data showed that changing the temperature during the lag phase induced an additional lag time before growth; however, no significant lag time was observed under the temperature fluctuation during the exponential phase. The results of this study provide information for precise shelf-life determination and reduction of food waste, particularly for milk and milk-containing food products.

A microinstrument with electrostatic actuation and capacitive readout for the measurement of adhesion force is introduced that can be used in packaged systems for the in-line characterization and monitoring of fabricated devices. The test results for different apparent contact areas obtained using these devices are in agreement with previously reported values for adhesion force obtained via optical readout and display a weak correlation between the apparent contact area and the adhesion force.

Capacitive microinstruments with compliant electrodes for accurate determination of small adhesion force between polycrystalline silicon surfaces are presented. The test structures can determine the adhesion force as low as 60nN. Using these devices, the effects of fabrication and release variations on the adhesion force are investigated. The measurement results show that the adhesion force does not depend on the apparent contact area over the range of parameters examined. Moreover, a distinct difference between adhesion force values measured on wafers with different fabrication processes is observed that is attributed to different surface topography. The distribution of adhesion force in 8" wafers is also studied and is found not uniform throughout a single wafer.

The adhesion force between polycrystalline silicon surfaces in MEMS structures is studied using three different test structures. Electrostatic and thermal actuations are used to bring the two surfaces into contact and mechanical force stored in the structures is used to separate them. In particular, the devices consist of (i) double-clamped beam that is actuated electrostatically and measured optically, (ii) suspended plate that is actuated electrostatically and measured capacitively, and (iii) thermally actuated and optically measured beams. The devices are fabricated using PolyMUMPs® process. The results show that the adhesion force in tested structures has little or no dependence on the apparent contact surface and is highly affected by the test environment and the actuation methods. The test results at high temperatures (100-130 °C) show that in absence of capillary and electrostatic forces, the adhesion force drastically decreases and mainly depends on the number of contacting asperities.

Laterally actuated nanoelectromechanical relays with compliant source-drain contacts are presented. The relay sidewalls are coated with a 30 nm-thick conductive layer of titanium nitride (TiN) deposited using atomic layer deposition (ALD). By hollowing the tip of the relay, a flexible sidewall is formed from the thin TiN that results in a larger contact area and therefore improves the contact properties of the relay. This modification improves the on-state resistance (RON) and also provides better stability over a larger number of switching cycles compared to a rigid contact. The results of life-time tests show that the contact resistance increases with the number of switching cycles possibly due to degradation of the contact material. However, flexible contacts show improved contact resistance stability under cyclic contact.

A new structure for the measurement of interfacial adhesion force between polycrystalline silicon (polysilicon) surfaces in M/NEMS and at elevated temperature is introduced. The device consists of bilayer cantilever beams with different coefficients of thermal expansion (CTE), which carry a rigid plate with a dimple. Thermal actuation and structural force stored in the beam, respectively, initiate and terminate the contact between the two surfaces under study. The proposed design can eliminate the effect of secondary forces such as electrostatic force caused by trapped charges at contact surfaces, which may contribute to the adhesion forces measured using other techniques.

This paper reports on the modeling, fabrication, and testing of cantilever- and parallel plate-based laterally actuated platinum-coated polysilicon nanoelectromechanical (NEM) relays. The polysilicon acts as the structural layer, while the platinum serves as a conducting contact material, as well as a local routing layer. The two-part cantilever design utilizes a source made of a compliant beam in series with a stiff bridged perimeter electrode to reduce the secondary pull-in of the source to the gate. The parallel-plate-based relay also uses stiffened electrodes in addition to serpentine structures that reduce the actuation voltage. Overdrive gate voltage in excess of 100% without failure and sharp release of the relay from output are achieved for polysilicon relays with 50nm platinum coating and 500nm actuation gap.

A capacitive temperature sensor with separate thermal actuation and capacitive readout is introduced. A bi-layer plate with fixed-free boundary condition is used for the thermal actuation to change the gap between two parallel electrodes used for capacitance measurement. Different coefficients of thermal expansion (CTE) of the two layers in actuator cause out-of-plane deformations in the plate when the temperature changes. The proposed design has the capability to control the response of the sensor by increasing its sensitivity in a given temperature range. To obtain the desired characteristic C-T curve, the design utilizes asymmetric geometries. Different design parameters such as the size of the bi-layer plate and the sense electrodes are considered as design variables. ANSYS® FEM simulations are used to extract the C-T responses of different geometries. The results of the FEM simulations show that for a given fabrication process and material properties, the design can be modified to provide the highest sensitivity and linearity in the C-T response for a given temperature range. This temperature sensor can be used for remote and on-chip temperature measurement or temperature compensation.

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.

A MEMS heart rate monitor has been designed for a three-structural-layer fabrication process such as PolyMUMPs. The device size is just over 400 mum times 400 mum. It uses a movable top plate in order to create a variable capacitance in conjunction with a coil for an inductance in order to create a resonant tank circuit. The circuit resonant frequency changes depending on the deflection of the top plate. The device is powered via the sensor coil by a magnetic field produced by an external coil. The resonant frequency is also monitored using magnetic coupling. The capacitance change has been calculated to be about 70.5% corresponding to a 45.8% change in resonant frequency. The reflected impedance magnitude and phase are monitored on the external coil.

This research presents a novel linearly tunable MEMS capacitor with flexible electrode and modified structural stiffness. The capacitor is designed for PolyMUMPs as a standard three-structural-layer fabrication process. The moving electrode is divided into segments interconnected through torsional springs. Under each connecting point (node) two flexible and rigid steps are located. The flexible steps are cantilever beams, and as the bias voltage increases, they touch their corresponding nodes and consequently their stiffnesses are added to the total structural stiffness. This is the core idea of the proposed design to linearize the capacitance-voltage (C-V) response. An analytical model is developed to investigate the behavior of the new capacitor. In this model, the governing equations of the capacitor are numerically solved to obtain the system’s C-V response. An optimization problem with different design variables, such as dimensions of the segments or the beams stiffness coefficients, is solved to maximize the linearity of the C-V curves. The numerical results demonstrate drastic improvement in capacitors performance, where a highly linear C-V response and a maximum tunability of 94% is reached.Copyright © 2008 by ASME

In conventional MEMS parallel-plate capacitor designs, the moving electrode is commonly modeled as a rigid plate with flexible boundary conditions provided by a set of supporting beams. Such a capacitor generates limited tuning ratio up to 1.5 and its capacitance-voltage response is nonlinear. This paper presents novel designs where the moving electrodes are fixed-edge flexible plates. The plate displacement is selectively limited by a set of rigid steps, located between two electrodes, to generate a smooth and linear response and high tunability. Three different step heights are considered in the design and the linearity of the C-V curve is maximized by modifying the geometry of the plate, and changing the location and order of steps. Since the analytical solution for coupled electrostatic-structural physics in this case does not exist, ANSYS® FEM simulation is performed to obtain the C-V curves and optimize the design. Two designs with different electrode shapes, rectangular and circular, are developed. For rectangular-plate capacitors, tunabilities ranging from 120% to 140% and high linearity are achieved. Circular-plate designs, on the other hand, generate lower tunabilities and an extremely linear region in C-V curves. Design methodology introduced in this research is not limited to proposed geometries and can be extended to different topologies to obtain a combination of high tunability and linearity.Copyright © 2008 by ASME

MEMS parallel-plate tunable capacitors have high Q-factors and fast responses to the actuation and therefore are desired for RF applications. However, conventional designs have low tuning ratios and nonlinear capacitance-voltage (C-V) responses which are highly sensitive to the voltage change near pull-in. In this research, a novel structure for parallel-plate-based capacitors is introduced. The capacitor has electrodes with triangular shape and uneven supporting beams and is equipped with a set of middle beams which increases the structural stiffness of the capacitor as bias voltage increases. Because the asymmetric design alters the parallelness of the plates, the stiffness of each middle beam is added to the system at a different voltage causing a smooth increment in structural stiffness. To analyze the capacitor and optimize the design, an analytical model is developed to solve the coupled electrostatic-structural physics. The results of numerical simulations reveal that if the stiffness coefficients of supporting and middle beams are optimized, a highly linear C-V response is obtained. Moreover, since the structural rigidity is gradually increased with voltage, the sensitivity of the response to the voltage change is also improved and a higher tunability over 150% is achieved. The proposed design has a simple geometry and can be fabricated by a three-structural-layer process such as PolyMUMPs.Copyright © 2008 by ASME

This paper presents a novel geometry and modified structural stiffness for electrostatically actuated MEMS tunable capacitors. The design is based on parallel-plate configuration and four triangular plates are put together to form a butterfly shape flexible moving electrode. Each triangle is suspended by three uneven supporting beams. The capacitor is also equipped with extra beams, called here the “middle beams”, located under the triangles’ corners (nodes). An analytical model is developed to solve the governing equations of a triangular-plate electrode with uneven sides and supporting beams, where the stiffness of the middle beams is gradually added to the system as actuation voltage increases. The numerical simulations reveal that each triangle can be individually tuned up to 150% and the capacitance-voltage (C-V) response is broken into small sections due to added middle beams. Using the model developed in this paper and by design optimization, a linear C-V response is obtained, where the tunability in linear region reaches 100%. The simplicity of the proposed design allows the device to be fabricated using a three-structural-layer process such as PolyMUMPs and could therefore be monolithically integrated with other RF devices and ICs. Moreover, adding additional insulator layer on top of the fixed electrode increases the tunability to over 200% displaying a smooth and low sensitive response.Copyright © 2008 by ASME

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 © 2007 by ASME

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 © 2007 by ASME

MEMS parallel-plate tunable capacitors are widely used in different devices such as tunable filters and resonators because of their simple structures, high Q-factors and small sizes. However, these capacitors have low tuning range with nonlinear and highly sensitive capacitance-voltage (C-V) responses. In this paper the development of novel tunable capacitor designs exhibiting highly linear C-V responses, is presented. The designs use segmentation technique to produce lumped flexibility in capacitor’s structure. A numerical model is developed to simulate the behavior of the capacitor. When a actuation voltage is applied, the structural rigidity of the plate produces resistive force which balances the electrostatic force, causes nodal displacements and changes the capacitance. It is shown that by optimizing the shape of segments (from rectangular to trapezoidal) and adding flexible steps located under the segments, a low sensitive linear C-V response could be achieved, while maintaining high tunability. The results of numerical simulation for the capacitors designed for PolyMUMPs process demonstrate that by optimization of the segments shape and structural stiffness a combination of high tunability over 100% and highly linear C-V response is achievable.

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 © 2006 by ASME