Investigation of the Dynamics of a 2-DoF Actuation Unit Cell for a Cooperative Electrostatic Actuation System

The mechanism of the inchworm motor, which overcomes the intrinsic displacement and force limitations of MEMS electrostatic actuators, has undergone constant development in the past few decades. In this work, the electrostatic actuation unit cell (AUC) that is designed to cooperate with many other counterparts in a novel concept of a modular-like cooperative actuator system is examined. First, the cooperative system is briefly discussed. A simplified analytical model of the AUC, which is a 2-Degree-of-Freedom (2-DoF) gap-closing actuator (GCA), is presented, taking into account the major source of dissipation in the system, the squeeze-film damping (SQFD). Then, the results of a series of coupled-field numerical simulation studies by the Finite Element Method (FEM) on parameterized models of the AUC are shown, whereby sensible comparisons with available analytical models from the literature are made. The numerical simulations that focused on the dynamic behavior of the AUC highlighted the substantial influence of the SQFD on the pull-in and pull-out times, and revealed how these performance characteristics are considerably determined by the structure’s height. It was found that the pull-out time is the critical parameter for the dynamic behavior of the AUC, and that a larger damping profile significantly shortens the actuator cycle time as a consequence.

A Feasibility Study of a Vibrotactile System based on Electrostatic Actuators for Touch Bar Interfaces: Experimental Evaluations

Vibrotactile feedback is a very desirable feature for many touchscreen applications, creating a more engaging and effective user experience. Although it is common in small electronic devices, this feedback is often absent in large touchscreen devices because it is difficult to provide vibration sensations and control the magnitude throughout the display. Because of their long shape (over 20 cm), touch bar displays are susceptible to the same challenges that other large display types face. Thus, there is a need for a vibrotactile actuation system capable of generating a freely positionable and fully controllable point of stimulation with satisfying force output at any point of a touch bar display. This study proposes a new spring boundary condition vibrotactile system as a way to provide such feedback in touch bar interfaces. A prototype system was created using two electrostatic resonant actuators and a thin, narrow aluminum beam to study the effect of different actuator excitation parameters on the beam′s response. By varying the number of actuators excited, magnitude, excitation frequency, and signal duration, a minimum vibration of 24.5 m/s2 could be created in the beam, with the majority of the beam able to exceed 40 m/s2. These results show that a targeted vibrotactile response at a given location in the beam can be achieved and sustained. This demonstrates a promising potential for generating a freely positionable and fully controllable point of vibrotactile stimulation at any point of a touch bar display.

High-Output Micro-Machined Electrostatic Actuators

This work presents a new class of micromachined electrostatic actuators capable of producing output force and displacement unprecedented for MEMS actuators. The actuators feature submicron high aspect ratio transduction gaps lined up in two-dimensional arrays inspired by the cellular structure of animal muscle tissue. Such arrangement of micro-scale actuator cells, allows addition of force and displacements of a large number of cells (up to 7600 in one array demonstrated), leading to displacements in the hundreds of microns range and several gram-forces of axial force. For 50 µm thick actuators with horizontal dimensions in the 1-4 millimeters range, out of plane displacement of up to 678 µm, bending moment of up to 2.0 µNm i.e. 0.08 N (~8 gram-force) of axial force over the 50 µm by 2 mm cross-sectional area of the actuator (800 kPa of electrostatically generated stress), and energy density (mechanical work output per stroke per volume) up to 1.42 mJ/cm3 have been demonstrated for the actuators.

Development and Proof of Concept of a Miniaturized MEMS Quantum Tunneling Accelerometer Based on PtC Tips by Focused Ion Beam 3D Nano-Patterning

Most accelerometers today are based on the capacitive principle. However, further miniaturization for micro integration of those sensors leads to a poorer signal-to-noise ratio due to a small total area of the capacitor plates. Thus, other transducer principles should be taken into account to develop smaller sensors. This paper presents the development and realization of a miniaturized accelerometer based on the tunneling effect, whereas its highly sensitive effect regarding the tunneling distance is used to detect small deflections in the range of sub-nm. The spring-mass-system is manufactured by a surface micro-machining foundry process. The area of the shown polysilicon (PolySi) sensor structures has a size smaller than 100 µm × 50 µm (L × W). The tunneling electrodes are placed and patterned by a focused ion beam (FIB) and gas injection system (GIS) with MeCpPtMe3 as a precursor. A dual-beam system enables maximum flexibility for post-processing of the spring-mass-system and patterning of sharp tips with radii in the range of a few nm and initial distances between the electrodes of about 30–300 nm. The use of metal–organic precursor material platinum carbon (PtC) limits the tunneling currents to about 150 pA due to the high inherent resistance. The measuring range is set to 20 g. The sensitivity of the sensor signal, which depends exponentially on the electrode distance due to the tunneling effect, ranges from 0.4 pA/g at 0 g in the sensor operational point up to 20.9 pA/g at 20 g. The acceleration-equivalent thermal noise amplitude is calculated to be 2.4–3.4 mg/. Electrostatic actuators are used to lead the electrodes in distances where direct quantum tunneling occurs.

Coulomb-actuated microbeams revisited: experimental and numerical modal decomposition of the saddle-node bifurcation

Electrostatic micromechanical actuators have numerous applications in science and technology. In many applications, they are operated in a narrow frequency range close to resonance and at a drive voltage of low variation. Recently, new applications, such as microelectromechanical systems (MEMS) microspeakers (µSpeakers), have emerged that require operation over a wide frequency and dynamic range. Simulating the dynamic performance under such circumstances is still highly cumbersome. State-of-the-art finite element analysis struggles with pull-in instability and does not deliver the necessary information about unstable equilibrium states accordingly. Convincing lumped-parameter models amenable to direct physical interpretation are missing. This inhibits the indispensable in-depth analysis of the dynamic stability of such systems. In this paper, we take a major step towards mending the situation. By combining the finite element method (FEM) with an arc-length solver, we obtain the full bifurcation diagram for electrostatic actuators based on prismatic Euler-Bernoulli beams. A subsequent modal analysis then shows that within very narrow error margins, it is exclusively the lowest Euler-Bernoulli eigenmode that dominates the beam physics over the entire relevant drive voltage range. An experiment directly recording the deflection profile of a MEMS microbeam is performed and confirms the numerical findings with astonishing precision. This enables modeling the system using a single spatial degree of freedom.

Development of electrostatic actuators with large out-of-plane deflection and its application in scanning display

Electrostatic out-of-plane microactuators have been widely used in applications of variable capacitors, optical attenuators, optical switches and scanning displays due to their small size, low cost, simple and diverse structure, low power consumption and high compatibility with semiconductor process. The large out-of-plane displacement of the microactuator with high reliability is preferred in order to increase the tuning range, tunability and the display size. However, the “pull-in” instability associated with conventional attractive-force electrostatic microactuators significantly limits the out-of-plane displacement and lowers the operation stability. A repulsive-force microactuator has been previously developed which can achieve large out-of-plane rotation and does not suffer from the “pull-in” instability. However, a larger rotation angle of the repulsive-force actuator is highly desired in order to improve its performance in the applications such as increasing the tunability and the scanning angle. In this thesis two novel repulsive-force actuators, i.e., two-row interdigitating-finger and two-width-finger (TWF) actuators are developed which output much larger out-of-plane rotation than the previous repulsive-force actuator without suffering from the “pull-in” instability. The mathematical models are established for both actuators using a hybrid approach. The actuators require only two thin layers and are suitable for surface micromachining process. The measured results show that the two microactuators can achieve rotation angles of 11.5° and 7.5° at 150 V respectively. The improvements are 100% and 35% in comparison to the previous repulsive-force actuator with the same size, stiffness and driving voltage. A 2D scanning micromirror has been developed and fabricated based on the two-row-finger (TRF) actuator. Experimental results show the micromirror has larger rotation angle and faster response speed than those of the micromirror driven by the previous repulsive-force microactuator. The vector scanning display based on the micromirror is demonstrated. An advanced display approach is developed to generate displays with less distortion and higher refreshing rate compared to the previous generic display approach. The automotive Head-up Display (HUD) based on the micromirror and advanced display approach has been constructed for both real and virtual image configurations, which has advantages of small size, low cost, large viewing angle and good visibility over those HUDs in the market.

Development of electrostatic actuators with large out-of-plane deflection and its application in scanning display

Electrostatic out-of-plane microactuators have been widely used in applications of variable capacitors, optical attenuators, optical switches and scanning displays due to their small size, low cost, simple and diverse structure, low power consumption and high compatibility with semiconductor process. The large out-of-plane displacement of the microactuator with high reliability is preferred in order to increase the tuning range, tunability and the display size. However, the “pull-in” instability associated with conventional attractive-force electrostatic microactuators significantly limits the out-of-plane displacement and lowers the operation stability. A repulsive-force microactuator has been previously developed which can achieve large out-of-plane rotation and does not suffer from the “pull-in” instability. However, a larger rotation angle of the repulsive-force actuator is highly desired in order to improve its performance in the applications such as increasing the tunability and the scanning angle. In this thesis two novel repulsive-force actuators, i.e., two-row interdigitating-finger and two-width-finger (TWF) actuators are developed which output much larger out-of-plane rotation than the previous repulsive-force actuator without suffering from the “pull-in” instability. The mathematical models are established for both actuators using a hybrid approach. The actuators require only two thin layers and are suitable for surface micromachining process. The measured results show that the two microactuators can achieve rotation angles of 11.5° and 7.5° at 150 V respectively. The improvements are 100% and 35% in comparison to the previous repulsive-force actuator with the same size, stiffness and driving voltage. A 2D scanning micromirror has been developed and fabricated based on the two-row-finger (TRF) actuator. Experimental results show the micromirror has larger rotation angle and faster response speed than those of the micromirror driven by the previous repulsive-force microactuator. The vector scanning display based on the micromirror is demonstrated. An advanced display approach is developed to generate displays with less distortion and higher refreshing rate compared to the previous generic display approach. The automotive Head-up Display (HUD) based on the micromirror and advanced display approach has been constructed for both real and virtual image configurations, which has advantages of small size, low cost, large viewing angle and good visibility over those HUDs in the market.