Anurag Garg

Direct measurements and numerical simulations of gas charging in microelectromechanical system capacitive switches

Gas breakdown in microelectromechanical system capacitive switches is demonstrated using high resolution current measurements and by particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. Measurements show an electric current through a 3 μm air gap increasing exponentially with voltage, starting at 60 V. PIC/MCC simulations with Fowler-Nordheim [Proc. R. Soc. London, Ser. A 119, 173 (1928)] field emission reveal self-sustained discharges with significant ion enhancement and a positive space charge. The effective ion-enhanced field emission coefficient increases with voltage up to about 0.3 with an electron avalanche occurring at 159 V. The measurements and simulations demonstrate a charging mechanism for microswitches consistent with earlier observations of gas pressure and composition effects on lifetime.

A study of field emission process in electrostatically actuated MEMS switches

Abstract A study of field emission process in MEMS-based capacitor/switch-like geometries is presented. High resolution current–voltage characteristics up to breakdown have been obtained across micro-gaps in fixed–fixed Metal–Air–Metal and Metal–Air–Insulator–Metal structures. In metallic devices the I–V dependence reveals Fowler–Nordheim theory effects. In the presence of insulator the process is found to be limited by the film conductivity following Poole–Frenkel dependence. The data analysis reveals the major importance of surface asperities on the onset of the field emission process while it is also presented that charge transfer may occur between metal and insulator surfaces even in the presence of micrometer scale gaps.

Estimating residual stress, curvature and boundary compliance of doubly clamped MEMS from their vibration response

Structural parameters of doubly clamped microfabricated beams such as initial curvature, boundary compliance, thickness and mean residual stress are often critical to the performance of microelectromechanical systems (MEMS) and need to be estimated as a part of quality control of the microfabrication process. However, these parameters couple and influence many metrics of device response and thus are very difficult to disentangle and estimate using conventional methods such as the M-test, static mechanical tests, pull-in measurements or dynamic mechanical tests. Here we present a simple, non-destructive experimental method to extract these parameters based on the non-contact measurement of the natural frequencies of the lowest few eigenmodes of the microfabricated beam, and knowledge of Youngs modulus and plan dimensions of the beam alone. The method exploits the fact that certain eigenmodes are insensitive to some of these structural parameters which enable a convenient decoupling and estimation of the parameters. As a result, the method does not require complicated finite element analysis, is insensitive to the gap height and introduces no contact wear or dielectric charging effects. Experiments are performed using laser Doppler vibrometry to measure the natural frequencies of doubly clamped, nickel, RF-MEMS capacitive switches and the method is applied to extract the residual stress, beam thickness, boundary compliance and post-release curvature.

Direct measurement of field emission current in E-static MEMS structures

Direct experimental evidence of field emission currents in metallic MEMS devices is presented. For the first time, high resolution I–V curves have been demonstrated for micro-gaps in MEMS-based capacitor/switch-like geometries. The I–V dependence shows a good agreement with the Fowler-Nordheim theory, supporting the hypothesis that field emission plays a significant role in charging phenomena in MEMS switches. The data has been used to extract effective values of the field enhancement factor, β, for the metallic structures fabricated under typical MEMS processes.

Impact of sacrificial layer type on thin-film metal residual stress

In this paper we study the impact of two sacrificial layers on the final residual stress of thin gold films. In particular, we comapre a typical photoresist layer (Shipley SC1827) to single-crystalline silicon. We fabricate and measure cantilever beams on both sacrificial layers and study their residual stresses by analyzing the final displacement profile of the released beams. All samples were fabricated at the same time and under identical conditions. The study clearly shows that the induced stress on thin films is dependent on the sacrificial layer. The gold film deposited over the single-crystalline silicon shows nearly zero gradient stress after release. On the other hand, gradient stress dominates the gold film deposited during the same run but over a photoresist layer. Such results are very useful in designing and fabricating a wide variety of low-stress actuators and sensors.

Electrostatically tunable analog single crystal silicon fringing-field MEMS varactors

This paper reports on the design of a new analog MEMS varactor that uses electrostatic fringing-field actuation and is based on a single-crystal silicon movable structure coated with a thin metallic layer. Electrostatic fringing-field actuation allows for an analog displacement with no pull-in instability that yields a much larger tuning ratio compared to conventional electrostatic designs. In addition, total lack of dielectric layers and the use of single crystal silicon for the moving membrane significantly enhances the robustness of our proposed varactor by making it devoid of dielectric charging and stiction, insensitive to process variations, amenable to high yield manufacturing and less susceptible to hysteresis and creep. Based on this idea, we present example designs and the associated fabrication processes for varactors that exhibit a tuning ratio of 4.5∶1 with capacitance values in the range of 43–200 fF achieved with DC voltages of 0–55 V. Such varactors are key elements in MEMS matching networks, tunable filters and reconfigurable antennas in the K/Ka/W-bands.

Residual Stress Extraction of Surface-Micromachined Fixed-Fixed Nickel Beams Using a Wafer-Scale Technique

This paper reports on the extraction of residual stress in surface-micromachined nickel thin films of electrostatically actuated fixed-fixed beams using a wafer-scale technique. The distribution of residual stress for 87 beams on a 4-in quarter wafer piece is presented. The residual stress (σ0) is determined from the best fit of the displacement-voltage curves predicted by a computationally efficient model to the experimental data. The nondestructive and automated measurements are taken at room temperature and directly at the beam itself without any additional test structures. The model employed incorporates the nonideal effects of inclined supports, nonflat initial beam profiles, and fringing fields. The extracted residual stress values vary between -12.8 and 13.6 MPa (negative values are for compressive stresses and positive ones for tensile stresses). The residual stresses for these 87 beams follow a nearly normal distribution with a mean value of -1.7 MPa and a standard deviation of 5.9 MPa, which represents the variability of the residual stresses across the wafer. Detailed uncertainty analysis has been conducted, and it reveals that inaccurate modeling of the nonideal effects will result in significant errors in the extracted residual stress. Although demonstrated on nickel thin films, this technique can be applied to other metallic thin films.

Electrostatic fringing-field actuation for pull-in free RF-MEMS analogue tunable resonators

This paper presents the design, fabrication and measurement of the first pull-in free tunable evanescent-mode microwave resonator based on arrays of electrostatically actuated fringing-field RF-MEMS tuners. Electrostatic fringing-field actuation (EFFA) is the key on achieving a wide tunable frequency range that is not limited by the conventional pull-in instability. Furthermore, total lack of dielectric layers and no overlap between the pull-down electrode and movable beams significantly enhance the robustness of our proposed tuning mechanism by making it devoid of dielectric charging and stiction and amenable to high-yield manufacturing. The proposed electrostatic fringing-field tuners are demonstrated in a highly loaded evanescent-mode cavity-based resonator. The measured unloaded quality factor is 280?515 from 12.5 to 15.5?GHz. In addition, a 10? improvement in switching time is demonstrated for the first time for EFFA tuners in a tunable microwave component by employing dc-dynamic biasing waveforms. With dynamic biasing, the measured up-to-down and down-to-up switching times of the resonator are 190 and 148 ?s, respectively. On the other hand, conventional step biasing results in switching times of 5.2 and 8?ms for up-to-down and down-to-up states, respectively.

An equation-based nonlinear model for non-flat MEMS fixed–fixed beams with non-vertical anchoring supports

Anchor supports in MEMS beams are often far from the ideally assumed built-in or step-up conditions. Practical fabrication processes often result in non-vertical anchoring supports (referred to as inclined supports in the following text) which significantly influence the post-release performance of the beam. This paper brings attention to the presence of the inclined supports in surface micromachined fixed–fixed beams and models the mechanical and electromechanical effects of inclined supports for the first time. Specifically, we calculate and validate the effects of residual stress and loading on the post-release beam behavior including their nonlinear large-displacement characteristics. In addition the model accounts for non-flat beam profiles caused by residual stress and/or a non-flat sacrificial layer profile. Inclined supports are modeled as cantilever beams connected to a horizontal beam. The Euler–Bernoulli equations for all beams are simultaneously solved to calculate the axial stress of the horizontal beam and the axial, translational, and rotational compliance of the supports. Nonlinear effects due to stretching and residual stress are also included. The calculated beam displacements agree with FEM models to within 1.1% in both the linear and nonlinear regimes. Furthermore, experimentally-obtained displacements of six fabricated beams with inclined supports agree to within 5.2% with the presented model.

Post-Release Displacement Uncertainty of Micro-Cantilevers Due to Anchor Over/Under Etching

In this paper we follow an analytical and finite element modeling approach to study the effect of anchor over/under-etch on the post-release tip displacement of MEMS cantilever beams. We show that the last release step is particularly critical in controlling the beam’s post-release displacement, which is of primary importance in a variety of applications. In this paper we isolate the effects of mean stress and imperfect anchor. We assume negligible gradient stress since its effect has been studied in detail in the literature. Beams with perfect anchors and zero under-etch are also presented for comparison. The results emphasize that through careful control of the fabrication parameters and anchor structure, the initial displacement profile and thus performance of micro-cantilevers can be accurately controlled.Copyright