AVS2016 Session MN-WeM: Multiscale Phenomena & Emerging Technologies in Micro- and Nano-Systems

Research on mobile microrobots has been ongoing for the last 20 years, but the few robots that have walked have done so at slow speeds on smooth silicon wafers. However, ants can move at speeds over 40 body lengths/second on surfaces from picnic tables to front lawns. At larger scales, bio-inspired robots have taken advantage of a wide array of materials to provide passive mechanical properties used by insects to locomote effectively. We have developed a micro-molding process to incorporate materials with widely varying moduli and functionality along with traditional silicon MEMS for similar complexity in smaller packages. Mechanisms useful for locomotion like legs and energy storage elements are demonstrated, including a 4mm jumping mechanism that can be launched approximately 35 cm in height. In addition, magnetic materials can be incorporated in this process and we have used press-fit, commercially available NdFeB magnets down to 250 um in size to provide untethered, off-board actuation of these robotic mechanisms. Both magnetic and molded materials have been characterized to better model robot mechanisms using this process. In addition, magnetic actuation is used to characterize legged locomotion in a 25 mg 6-legged microrobot over flat and rough terrain with speeds demonstrated up to 5.9 body lengths/second.

Lead zirconate titanate (PZT) films are used in micro electro mechanical systems (MEMS) due to the self-generating sensing, large actuation amplitude with low voltage, and compatibility to integrated circuit process. PZT films exhibit higher values of effective transverse piezoelectric coefficient (e_31,f) and effective longitudinal piezoelectric coefficient (d_33,f), compared to any other available piezoelectric materials, both of which are important properties for such applications. Further improvement in the piezoelectric coefficients of PZT films is still being investigated.

In our previous work, the effect of Pb content and solution concentration of lead titanate (Pb_xTiO₃) seed layer on the texture and electric properties of Pb_1.1(Zr_0.52,Ti_0.48)O₃ thin films (190 nm) was investigated. The results indicated that 0.02 M Pb_xTiO₃ favors (100)/(001) orientation and suppresses (111) orientation in PZT films, thereby improving the electrical properties. The optimized conditions of the seed layer were further used to prepare thicker PZT films. Seed layer of 0.02 M Pb_xTiO₃ with varying Pb content ( x= 1.0, 1.05, 1.1, 1.2) was used to prepare 1.3 µm PZT films by chemical solution deposition method . From the results, it was observed that PZT films deposited on seed layer with 1.0 Pb content exhibit maximum {100}-texture, highest remnant polarization (50.25 µC/cm²), coercive field (38.20 kV/cm), and permittivity (2086). However, maximum transverse piezoelectric coefficient of -13.3 C/m² was obtained for films with 1.05 Pb content in the seed layer. Thus use of a seed layer is a promising route to promote {100}-textured PZT films, thereby improving the electrical properties and effective transverse piezoelectric coefficient of PZT films required for actuators and/or sensors.

In resonant micro and nanoelectromechanical sensors (MEMS/NEMS), the excitation of vibratory motion is usually achieved through implementation of electrostatic, piezoelectric, magnetic, thermal or optical transduction. Most of these methods require additional conductive layers, which broaden the vibrational characteristics of the device and induce residual stresses. In addition, often nonlinear actuation forces may alter the spectral characteristics of the structure. Inertial excitation by an external shaker is widely used for mechanical dynamic characterization. However, simultaneous electrical excitation and detection requires wire bonding and packaging, which is not always suitable at the initial stages of characterization or for wafer level testing. In this work we report on a methodology for efficient electromechanical characterization of resonant micro structures using a combination of acoustic and fringing electrostatic fields. We show that omnidirectional acoustic excitation of unpackaged, electrically connected using micromanipulators, devices is a convenient alternative to inertial excitations.

Using deep reactive ion etching (DRIE), 500 μm long and 16 μm wide cantilevers were fabricated from silicon on insulator (SOI) wafers with 5 μm and 2 μm thick device and buried thermal silicon dioxide layers, respectively. A cavity was etched within the handle of the wafer to allow for high unobscured out-of-plane vibrational amplitudes. An actuating electrode was fabricated from the device layer and was located symmetrically at the two sides of the beam. First, in order to investigate the mechanical response, flexural out-of-plane vibrations of microcantilevers were excited by a miniature acoustic speaker. The transducer frequency band was chosen near the fundamental mode of the cantilevers. Resonant frequencies and quality factors of the devices were measured optically with a laser Doppler vibrometer (LDV). An acoustic field was simultaneously monitored by a microphone located in a proximity of the cantilever. The microphone output, after re-normalization, was subtracted from the LDV output in order to eliminate the influence of the spectral characteristics of the transducer itself. Next the devices were operated simultaneously by the acoustic and electrostatic fields. The distributed electrostatic force acts in the direction opposite to the deflection and serves as an effective elastic foundation. As a result, the stiffness of the cantilever increases with increasing voltage. By applying a steady DC voltage of 100 V we demonstrate that the fundamental frequency of the beam harmonically excited by an acoustic field can be tuned upward by 2.5%.

Micro- and nano-electromechanical systems (M/NEMS) have enormous potential in and provide new opportunities for applications such as detection of mass, force and energy, microwave amplification, optomechanics, and energy harvesting. Micro and nanoscale mechanical resonators offer significant advantages over their macroscopic counterparts, including their low mass, high mechanical quality factor, Q, and compatibility with integrated electronics. Architectures consisting of interacting M/NEMS arrays exhibit rich dynamical phenomena. For instance, excitations in periodic, strongly-interacting nonlinear systems give rise to wave propagation and intrinsically localized modes. The dynamics of these systems are highly sensitive to local changes in their environment which makes them an attractive platform for realizing ultra-sensitive chemical, biological, and force sensors. In our work, we report experimental observations of parametric electrostatic excitation, synchronization and abrupt transitions between standing wave patterns in the interacting cantilever array systems.

Interdigitated, electrostatically-actuated cantilever devices were fabricated using a silicon‑on‑insulator (SOI) wafer with a highly-doped single-crystal silicon device layer. First, Au electrodes with a Cr adhesion layer were defined using lift-off with a bilayer resist process. The devices, consisting of two sets of 100 interdigitated cantilevers, were lithographically defined and etched using deep reactive ion etching (DRIE). The two structures were electrically isolated by the underlying ≈ 3 micrometer thick buried silicon dioxide layer (BOX). Using an aligned backside exposure, the silicon handle wafer was bulk etched within the active array area. This allowed the excitation of nonlinear vibrations with large amplitudes by eliminating the possibility of impacts between the cantilevers and the substrate. Interactions between cantilevers take place via both fringing electrostatic fields within the overlap region and mechanical coupling through the overhang. The out of plane, translational motion was directly visualized using a high resolution CMOS camera at a frame rate of ≈ 30 s^-1. Device dynamics were first measured in vacuum at a pressure of ≈ 2 × 10^‑3 Pa and then under ambient air conditions. In vacuum, where mechanical quality factors are high, the drive voltage was significantly lower than in air where considerable damping occurs. Our results show distinct propagation bands, abrupt transitions between standing wave patterns, and the influence of missing-beam defects on system dynamics.

MEMS and NEMS oscillators have been proposed as frequency generators to replace quartz as timing components in applications that require low power and a small footprint. The accuracy of a time measurement using a frequency generator is related to the fluctuations in both the generator amplitude and frequency. In many oscillators, the relative magnitude of frequency fluctuations is suppressed by increasing the vibration amplitude and choosing an operating point before the onset of non-linear response. Operating in a nonlinear region is generally avoided, primarily due to an additional contribution to the frequency fluctuations arising from the conversion of amplitude fluctuations into frequency fluctuations. However, we demonstrate a non-linear frequency generator that suppresses frequency fluctuations through means of an internal resonance. An internal resonance is accompanied by a pronounced transfer of energy between two coupled modes of a resonant structure [1,2]. For our frequency generator, the primary mode of operation is an in-plane flexural mode, which is actively controlled, and the second mode is a torsional mode with an eigenfrequency about three times larger than the flexural mode, which is passively coupled to the flexural mode. We present a theoretical model of the modal coupling and show, from our model and experimental observations, that the frequency fluctuations are reduced by several orders of magnitude due to a broad range of near-zero dispersion, i.e., near independence of the vibration frequency on the amplitude imposed by the presence of internal resonance. Within this near-zero dispersion region, a subset of operating conditions is found where frequency fluctuations are reduced even further due to a zero-dispersion point created by relationships of the parameters of the coupled equations. We present data on the stability of the frequency as a function of time (Allan deviation) and the spectrum of the frequency fluctuations (phase noise versus offset frequency) at different operating points of the generator. We also discuss the prospect of further increasing the frequency stability of MEMS/NEMS oscillators by reducing the noise floor of the system and approaching the thermomechanical noise limit of such systems.

[1] A. H. Nayfeh and D. T. Mook, Nonlinear oscillations (John Wiley & Sons, 2008).

[2] D. Antonio, D. H. Zanette, and D. Lopez, Nature communications 3 806 (2012).

This paper presents an investigation into the resonant frequency behavior of large area diaphragms made from silicon carbide thin films and the development of a plate-under-tension model to determine the Young’s modulus and residual stress from resonant frequency data. Test specimens consisted of single crystalline (100) 3C-SiC, polycrystalline (111) 3C-SiC and amorphous SiC thin films that were fabricated into nominally 1 x 1 mm² diaphragms by silicon bulk micromachining. Single crystalline diaphragms ranged in thickness from ~1.5 µm to 125 nm while the polycrystalline and amorphous diaphragms were held in the 1.5 µm thickness range. A thin (~50 nm) Si₃N₄ diaphragm was also included in the study. Test specimens were excited into resonance using a PZT crystal and interferometry was used to detect the vibrational modes. Testing was performed in vacuum to eliminate damping.

Initial testing involved measurement of resonant frequencies between 50 kHz and 2 MHz at various drive amplitudes. Each diaphragm exhibited at least 50 resonant peaks in this range, with at least one diaphragm having 250 peaks. Every diaphragm exhibited at least 5 peaks with quality factors (Q) > 10,000. The highest quality factor, as well as the largest number of high Q peaks, was observed in the diaphragm with the highest residual stress.

A method to determine the Young’s modulus and residual stress of a diaphragm from the resonant frequency data using a plate-under-tension model was proposed and developed. This method, which relies on the identification of numerous high order modes, was shown to be effective for the thicker films in the study (> 1 µm); however, the technique was only able to determine the residual stress for the submicron-thick films. Based on these observations, an equation that relates the Young’s modulus and residual stress to diaphragm thickness, side lengths and mode number was derived to identify diaphragm parameters that are well suited for this method.

Quantitative calorimetric studies of minute amount of material is a notoriously sophisticated task. It requires a high-resolution calorimeter design that contributes a negligible background signal (addenda). The issue is further complicated when the electronic specific heat of a sample is concerned, e.g. in the case of characterising the superconducting phase transition of a superconductor in thin film form. Over a wide temperature range, the electronic specific heat in most materials is one or two orders of magnitude lower than its lattice counterpart, raising even more stringent requirements on the resolution and accuracy of calorimetric measurements.

In this work, we describe a state-of-the-art, microelectromechanical system (MEMS)-based differential calorimeter operating in the ac steady-state mode that addresses this challenge. The calorimeter cell, consisted of two 150-nm-thick SiN_x windows placed side by side, is fabricated with a batch processing routine utilising silicon bulk micromachining techniques. Active components of the calorimeter include a gold-germanium resistive thermometer, an AC heater for delivering a well-defined alternating power to the sample, and a DC heater for locally heating the sample above the base temperature. They are defined using UV lithography and deposited onto the centre of the membrane window in the form of a stack of thin film layers [1]. The addenda of the calorimeter cell are as low as a few tens of nJ/K at room temperature, and further decrease down to 10 pJ/K at 1 K. Calorimetric measurements are carried out in a sample-in-vacuum ³He cryostat, under an automatic frequency adjusting, true differential-mode using custom-designed FPGA-based advanced electronics [2]. This provides both absolute accuracy and high resolution, where the addenda from the calorimeter cell are largely eliminated.

Thin films of superconducting niobium and tantalum in the range of hundreds of nanometers are used in demonstrating the capability of our calorimeter. They are deposited onto prefabricated silicon nitride windows, sculptured with a focused ion beam, and then transferred onto one of the calorimeter windows with a micromanipulator under an optical microscope. Specific heat jumps at the respective superconducting phase transition are still found to display an excellent signal-to-noise ratio while in-field measurements allow quantitative studies of the suppression of superconducting order parameters by applied magnetic fields.

[1] S. Tagliati, V. M. Krasnov, and A. Rydh, Rev. Sci. Instrum. 83 (2012) 055107.