Large Angle Silicon-on-Insulator Tilting Actuator with Kinematic Excitation and Simple Integrated Parallel-Plate Electrostatic Transducer

Abstract

We report on the novel architecture and operational principle of an electrostatically actuated large angle tilting microelectromechanical (MEMS) actuator with kinematic excitation. The device transforms and amplifies small linear out-of-plane motion of a parallel-plate transducer into a large angular motion of a tilting element attached to the transducer with a certain offset using an elastic torsion axis. The actuator, which is distinguished by the single layer robust architecture and incorporating the simple integrated electrostatic transducer, was fabricated from a silicon-on-insulator (SOI) substrate using a common deep reactive ion etching (DRIE) based process. Detailed modeling of the device was followed by the experimental characterization of the actuator. Large tilting angles were observed in experiments, consistenty with the theoretical prediction. An optical peak to peak angle of 37.5° was measured under relatively low actuation voltages. Our theoretical and experimental results collectively demonstate the feasibility of the suggested apporach and show that simple electrostatic actuation combined with the dynamic amplification results in efficient large amplitude operation of tilting devices.

Torsional Resonators Based on Inorganic Nanotubes

“…Discrepancies between measured peak positions and calculated resonance frequencies can be explained by the simplicity of the model, which does not take into account the complexity of the inner structure of the nanotubes and its anisotropy, as well as defects and imperfections appearing during the fabrication process. Also, the normal mode designated as "torsion" does in fact contain a small component of bending motion, 18 and likewise, the normal mode designated as "out-of-plane" in fact contains a small component of torsional motion, each mode having a different contribution from all the walls (solid rod case) or only from the outer wall (hollow cylinder case). In principle, our experimental setup is not designed to actuate nor detect in-plane motion (referred to in Figure 3 as "in plane bending" and "in plane rotation"), so these modes are ideally not expected to appear in the spectra.…”

“…This is typical of linear oscillators, 11 and allows for a linear approximation of the resonant behavior. 18 The results for all the CNT-, BNNT-and WS 2 NT-based resonators are summarized in Tables S1, S2 and S3 (Supporting Information), respectively. A total of 25 devices were measured: 11 of CNTs, 9 of BNNTs, and 5 of WS 2 NTs.…”

Nanoscale displacement measurement of microdevices via interpolation-based edge tracking of optical images

“…Note that although the algorithm was implemented in this study on linear or weakly nonlinear displacements, its implementation on more complicated functions is possible as well. As was previously demonstrated, the implementation of the basic algorithm does not depend on the shape of the tracked function [9,10], while as shown above, the quality of the averaging depends on different operational parameters. We also note that while the current analysis was carried out on a single line of pixels, an arbitrary number of lines could be monitored either in situ or ex situ; thus the algorithm could be used to detect more complicated shape changes and motion paths.…”

“…Another study used curve fitting of the edge intensity levels using a hyperbolic tangent function [7]. The interpolation-based edge-tracking algorithm demonstrated high-resolution measurement of the tilting of optical MEMS devices based on the position of a reflected laser beam [8,9]. It has also been applied to track the displacement of quasi-statically [10] or dynamically vibrating microstructures [11].…”

Self-Sensing WS2 Nanotube Torsional Resonators

“…The electrostatic force and moment applied to the paddle were extracted from the capacitance, by calculating the derivatives of the electrostatic co-energy U = CV 2 /2, where C is the capacitance and V is the excitation voltage, with respect to the linear deflection and the rotational motions (similar calculations were demonstrated elsewhere , ), such that The equations of motion derived from variational principles are where I and m are the mass moment of inertia and the mass of the paddle, respectively, e is the offset of the nanotube from the paddle center of mass (Figure c), and c θ and c u are the coefficients of damping associated with motion in the θ and u directions, respectively. Importantly, the equations of motion demonstrate the coupling between the two degrees of freedom due to the offset e , which implies that under dynamic excitation of the device both θ and u appear.…”