Barry E. DeMartini

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.

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

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.

A single input-single output coupled microresonator array for the detection and identification of multiple analytes

This work reports the experimental demonstration of single input-single output, multianalyte detection and identification using a coupled array of microresonators. A prototype sensor with four frequency-mistuned microbeam sensors, each coupled to a common shuttle mass resonator, is presented. Tailored localized modes of vibration in this coupled system are exploited to embed all requisite resonance shift information into the response of the common shuttle. Four standard polymers are applied to the microbeams to functionalize them for vapor detection. Toluene and methanol vapors, as well as toluene/methanol mixtures, are detected and identified using a single input signal and a single output signal.

Design and modeling of a high-speed scanner for atomic force microscopy

A new scanner design for a high-speed atomic force microscope (AFM) is presented and discussed in terms of modeling and control. The lowest resonance frequency of this scanner is above 22 kHz. The X and Y scan ranges are 13 micrometers and the Z range is 4.3 micrometers. The focus of this contribution is on the vertical positioning direction of the scanner, being the crucial axis of motion with the highest bandwidth and precision requirements for gentle imaging with the atomic force microscope. A mathematical model of the scanner dynamics is presented that will enable more accurate topography measurements with the high-speed AFM system

Exploiting Nonlinearity to Provide Broadband Energy Harvesting

Energy harvesters are a promising technology for capturing useful energy from the environment or a machine’s operation. In thispaperwehighlight ideasthatmight leadtoenergyharvesters that more efficiently harvest a portion of the considerable vibrational energy that is present for human-made devices and environments such as automobiles, trains, aircraft, watercraft, machinery, and buildings. Specifically, we consider how to exploit ideas based on properties of nonlinear oscillators with negative linear stiffness driven by periodic and stochastic inputs to design energy harvesters having large amplitude response over a broad range of ambient vibration frequencies. Such harvesters could improve upon proposed harvesters of vibrational energy based on linear mechanical principles, which only give appreciable response if the dominant ambient vibration frequency is close to the resonance frequency of the harvester.

Modeling of parametrically excited microelectromechanical oscillator dynamics with application to filtering

A model for the dynamics of an emerging class of electrostatically driven microelectromechanical oscillators, parametrically excited MEM oscillators, has been developed. The equation of motion for these devices is a nonlinear version of the Mathieu equation, which gives rise to rich dynamics. A standard perturbation analysis, averaging, has been adopted to analyze this complicated system. Numerical bifurcation analysis was employed and successfully verified these analytical results. Using the analytical and numerical tools developed for this model, along with the experimental results for such a device, parameters for the system are identified. This model is a pivotal design tool for the development of parametrically excited MEM filters

NONLINEAR RESPONSE OF PARAMETRICALLY-EXCITED MEMS

Due to the position-dependent nature of electrostatic forces, many microelectromechanical (MEM) oscillators inherently feature parametric excitation. This work considers the nonlinear response of one such oscillator, which is electrostatically actuated via non-interdigitated comb drives. Unlike other parametricallyexcited systems, which feature only linear parametric excitation in their equation of motion, the oscillator in question here exhibits parametric excitation in both its linear and nonlinear terms. This complication proves to significantly enrich the system’s dynamics. Amongst the interesting consequences is the fact that the system’s nonlinear response proves to be qualitatively dependent on the system’s excitation amplitude. This paper includes an introduction to the equation of motion of interest, a brief, yet systematic, analysis of the equation’s nonlinear response, and experimental evidence of the predicted behavior as measured from an actual MEM oscillator.

Frequency resolution of a multi degree of freedom resonator

This paper outlines the process for estimating measurable parameters in a multi degree of freedom micro resonator. Thermal mechanical noise provides a baseline limit for frequency resolution of micro resonators. We develop the likelihood function for a linear regression model of 2 degree of freedom resonator. Using the Cramer-Rao inequality we determine the minimum possible covariance to estimate parameters, such as the natural frequency of the system.

A SISO, Multi-Analyte Sensor Based on a Coupled Microresonator Array

This work details a preliminary analytical and experimental investigation of a new class of resonant, single input - single output (SISO) microsensors, which are capable of detecting multiple analytes. The key feature of these sensors is that they exploit vibration localization in a set of N microbeams, coupled indirectly through a common shuttle mass, to allow for the detection of N distinct resonance shifts (induced by the presence of up to N distinct analytes) using solely the shuttle mass’ response. The work includes a brief overview of the proposed sensor design, the formulation and subsequent analysis of a representative lumpedmass model of the sensor, and details of a recently-completed simulated mass detection experiment, which verified the feasibility of the proposed sensor design. Where appropriate, practical design issues, essential to sensor development, are described.