Kimberly L. Turner

Five parametric resonances in a microelectromechanical system

The Mathieu equation governs the forced motion of a swing, the stability of ships and columns, Faraday surface wave patterns on water,, the dynamics of electrons in Penning traps, and the behaviour of parametric amplifiers based on electronic or superconducting devices. Theory predicts that parametric resonances occur near drive frequencies of 2ω0/n, where ω0 is the systems natural frequency and n is an integer ⩾1. But in macroscopic systems, only the first instability region can typically be observed, because of damping and the exponential narrowing of the regions with increasing n. Here we report parametrically excited torsional oscillations in a single-crystal silicon microelectromechanical system. Five instability regions can be measured, due to the low damping, stability and precise frequency control achievable in this system. The centre frequencies of the instability regions agree with theoretical predictions. We propose an application that uses parametric excitation to reduce the parasitic signal in capacitive sensing with microelectromechanical systems. Our results suggest that microelectromechanical systems can provide a unique testing ground for dynamical phenomena that are difficult to detect in macroscopic systems.

Design and Modeling of a High-Speed AFM-Scanner

A new mechanical scanner design for a high-speed atomic force microscope (AFM) is presented and discussed in terms of modeling and control. The positioning range of this scanner is 13 mum in the X- and Y-directions and 4.3 mum in the vertical direction. The lowest resonance frequency of this scanner is above 22 kHz. This paper is focused on the vertical direction of the scanner, being the crucial axis of motion with the highest precision and bandwidth requirements for gentle imaging with the AFM. A second- and a fourth-order mathematical model of the scanner are derived that allow new insights into important design parameters. Proportional-integral (Pl)-feedback control of the high-speed scanner is discussed and the performance of the new AFM is demonstrated by imaging a calibration grating and a biological sample at 8 frames/s.

Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Abstract Parametric resonance has been well established in many areas of science, including the stability of ships, the forced motion of a swing and Faraday surface wave patterns on water. We have previously investigated a linear parametrically driven torsional oscillator and along with other groups have mentioned applications including mass sensing, parametric amplification, and others. Here, we thoroughly investigate the design of a highly sensitive mass sensor. The device we use to carry out this study is an in-plane parametrically resonant oscillator. We show that in this configuration, the nonlinearities (electrostatic and mechanical) have a large impact on the dynamic response of the structure. This result is not unique to this oscillator—many MEMS oscillators display nonlinearities of equal importance (including the very common parallel plate actuator). We report the effects of nonlinearity on the behavior of parametric resonance of a micro-machined oscillator. A nonlinear Mathieu equation is used to model this problem. Analytical results show that nonlinearity significantly changes the stability characteristics of parametric resonance. Experimental frequency response around the first parametric resonance is well validated by theoretical analysis. Unlike parametric resonance in the linear case, the jumps (very critical for mass sensor application) from large response to zero happen at additional frequencies other than at the boundary of instability area. The instability area of the first parametric resonance is experimentally mapped. Some important parameters, such as damping co-efficient, cubic stiffness and linear electrostatic stiffness are extracted from the nonlinear response of parametric resonance and agree very well with normal methods.

Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators

This review provides a summary of the work completed to date on the nonlinear dynamics of resonant micro- and nanoelectromechanical systems (MEMS/NEMS). This research area, which has been active for approximately a decade, involves the study of nonlinear behaviors arising in small scale, vibratory, mechanical devices that are typically integrated with electronics for use in signal processing, actuation, and sensing applications. The inherent nature of these devices, which includes low damping, desired resonant operation, and the presence of nonlinear potential fields, sets an ideal stage for the appearance of nonlinear behavior, and this allows engineers to beneficially leverage nonlinear dynamics in the course of device design. This work provides an overview of the fundamental research on nonlinear behaviors arising in micro/nanoresonators, including direct and parametric resonances, parametric amplification, impacts, selfexcited oscillations, and collective behaviors, such as localization and synchronization, which arise in coupled resonator arrays. In addition, the work describes the active exploitation of nonlinear dynamics in the development of resonant mass sensors, inertial sensors, and electromechanical signal processing systems. The paper closes with some brief remarks about important ongoing developments in the field.

The nonlinear response of resonant microbeam systems with purely-parametric electrostatic actuation

Electrostatically-actuated resonant microbeam devices have garnered significant attention due to their geometric simplicity and broad applicability. Recently, some of this focus has turned to comb-driven microresonators with purely-parametric excitation, as such systems not only exhibit the inherent benefits of MEMS devices, but also a general improvement in sensitivity, stopband attenuation and noise rejection. This work attempts to combine each of these areas by proposing a microbeam device which couples the inherent benefits of a resonator with purely-parametric excitation with the simple geometry of a microbeam. Theoretical analysis reveals that the proposed device exhibits desirable response characteristics, but also quite complex dynamics. Of particular note is the fact that the devices nonlinear frequency response is found to be qualitatively dependent on the systems ac excitation amplitude. While this flexibility can be desirable in certain contexts, it introduces additional design and operating limitations. While the principal focus of this work is the proposed systems nonlinear response, the work also contains details pertaining to model development and device design.

Tunable Microelectromechanical Filters that Exploit Parametric Resonance

Background: This paper describes an analytical study of a bandpass filter that is based on the dynamic response of electrostatically-driven MEMS oscillators. Method of Approach: Unlike most mechanical and electrical filters that rely on direct linear resonance for filtering, the MEM filter presented in this work employs parametric resonance. Results: While the use of parametric resonance improves some filtering characteristics, the

Linear and Nonlinear Tuning of Parametrically Excited MEMS Oscillators

Microelectromechanical oscillators utilizing noninterdigitated combdrive actuators have the ability to be parametrically excited, which leads to distinct advantages over harmonically driven oscillators. Theory predicts that this type of actuator, when dc voltage is applied, can also be used for tuning the effective linear and nonlinear stiffnesses of an oscillator. For instance, the parametric instability region can be rotated by using a previously developed linear tuning scheme. This can be accomplished by implementing two sets of noninterdigitated combdrives, choosing the correct geometry and alignment for each, and applying ac excitation voltages to one set and proportional dc tuning voltages to the other set. Such an oscillator can also be tuned to display a desired nonlinear behavior: softening, hardening, or mixed nonlinearity. Nonlinear tuning is attained by carefully designing combdrive geometry, flexure geometry, and applying the correct dc voltages to the second set of actuators. Here, two oscillators have been designed, fabricated, and tested to prove these tuning concepts experimentally

Tin-oxide-nanowire-based electronic nose using heterogeneous catalysis as a functionalization strategy.

An electronic nose (e-nose) strategy is described based on SnO(2) nanowire arrays whose sensing properties are modified by changing their operating temperatures and by decorating some of the nanowires with metallic nanoparticles. Since the catalytic processes occurring on the metal nanoparticles depend on the identity of the metal, decorating the semiconducting nanowires with various metal nanoparticles is akin to functionalizing them with chemically specific moieties. Other than the synthesis of the nanowires, all other steps in the fabrication of the e-nose sensors were carried out using top-down microfabrication processes, paving the way to a useful strategy for making low cost, nanowire-based e-nose chips. The sensors were tested for their ability to distinguish three reducing gases (H(2), CO, and ethylene), which they were able to do unequivocally when the data was classified using linear discriminant analysis. The discriminating ability of this e-nose design was not impacted by the lengths or diameters of the nanowires used.

Chaos for a Microelectromechanical Oscillator Governed by the Nonlinear Mathieu Equation

A variety of microelectromechanical (MEM) oscillators is governed by a version of the Mathieu equation that harbors both linear and cubic nonlinear time-varying stiffness terms. In this paper, chaotic behavior is predicted and shown to occur in this class of MEM device. Specifically, by using Melnikovs method, an inequality that describes the region of parameter space where chaos lives is derived. Numerical simulations are performed to show that chaos indeed occurs in this region of parameter space and to study the systems behavior for a variety of parameters. A MEM oscillator utilizing non interdigitated comb drives for actuation and stiffness tuning was designed and fabricated, which satisfies the inequality. Experimental results for this device that are consistent with results from numerical simulations are presented and convincingly show chaotic behavior.

Silicon oxide thickness-dependent growth of carbon nanotubes

Recent discovery of substrate-selective growth of carbon nanotubes on SiO2 in exclusion to Si, has opened up the possibility of organizing nanotubes on Si/SiO2 patterns in premeditated configurations for building devices. Here, we report the strong dependence of nanotube growth on the SiO2 layer thickness, and the utility of this feature to build three-dimensional architectures. Our results show that there is no detectable nanotube growth on SiO2 layers with thickness (TSiO2) less than ∼5–6 nm. For 6 nm 50 nm. We grew nanotubes with multiple lengths at close proximity in a single step by using substrates with regions of different TSiO2. Such processing strategies would be attractive for creating nanotube mesoscale architectures for device applications.