Torsional Micromirror Research Articles

A Method for Improving Heat Dissipation and Avoiding Charging Effects for Cavity Silicon-on-Glass Structures

Anode bonding is a widely used method for fabricating devices with suspended structures, and this approach is often combined with deep reactive-ion etching (DRIE) for releasing the device; however, the DRIE process with a glass substrate can potentially cause two critical issues: heat accumulation on the suspended surface and charging effects resulting from the reflection of charged particles from the glass substrate. In particular, for torsional bars with narrow widths, the heat accumulated on the suspended surface may not dissipate efficiently, leading to photoresist burning and, subsequently, resulting in the fracture of the torsional bars; moreover, once etching is finished through the silicon diaphragm, the glass surface becomes charged, and incoming ions are reflected towards the back of the silicon, resulting in the etching of the back surface. To address these issues, we proposed a method of growing silicon oxide on the back of the device layer. By designing, simulating, and fabricating electrostatic torsional micromirrors with common cavity silicon-on-glass (SOG) structures, we successfully validated the feasibility of this approach. This approach ensures effective heat dissipation on the suspended surface, even when the structure is over-etched for an extended period, and enables the complete etching of torsional bars without adverse effects due to the overheating problem; additionally, the oxide layer can block ions from reaching the glass surface, thus avoiding the charging effect commonly observed in SOG structures during DRIE.

Parametric amplification of a resonant MEMS mirror with all-piezoelectric excitation

We report a resonant torsional micro-mirror with all-piezoelectric driving and tunable spring stiffness. Stiffness modulation finds two practical applications. First is tuning of the resonance frequency, achieved by applying DC bias voltage to the stiffness modulating structures. A tuning rate was found to be 0.95 Hz V−1 with up to 20 Hz of usable frequency range. Second, when direct excitation of the torsional mode is combined with the harmonic modulation of the spring stiffness, an optical scan angle is shown to be increased by more than 4° through 2:1 degenerate parametric amplification. By varying the phase of the parametric pump with respect to the direct excitation, the Q-factor is tuned between 617 and 898, corresponding to the minimum and maximum parametric gain factors of 0.84× and 1.21×, respectively, achieved at a nominal unpumped optical scan angle of 16.3°. Increasing the pump amplitude shows a moderate increase in the amplifier's gain with clear saturation at 1.43× in the superthreshold pumping regime, indicating a presence of the third order stiffness nonlinearity. The results show potential to apply parametric amplification to future piezo-micro-electro-mechanical-system actuators for large frequency and large-stroke mechanical response achieved at ambient pressure.

Controllable electromechanical stability of a torsional micromirror actuator with piezoelectric composite structure under capillary force

Various types of micro/nano functional devices are being widely designed as optical switches, micro scanners, micromirrors and other core optical devices. The continuing miniaturization of the functional devices makes the size dependence of electromechanical property significant in micro/nano scale due to the sharp increase of surface interactions such as capillary force from liquid bridge, van der Waals and Casimir forces from quantum fluctuations. The surface interactions can cause the pull-in instability, adhesion between parts, and even failure of device. This work provides an active control method to avoid the pull-in instability of an electrostatically driven circular micromirror by applying voltage on a torsional piezoelectric composite structure. The influences of the three types are compared of dispersion forces on the electromechanical stability of the micromirror actuator. A comprehensive electromechanical model of a torsional piezoelectric beam was established to numerically investigate the electromechanical coupling of the micromirror. The results show that the influence of capillary force on the stability of the micromirror is as significant as van der Waals force and Casimir force. By introducing piezoelectric nanoplates into the laminated torsional structure, the micromirror stability can be controlled based on the piezoelectric effect of the torsional piezoelectric composite structure. This work can contribute to the structural optimization design and manufacture of micromirror systems. Cited as: Liu, M., Chen, Y., Cheng, W., Chen, S., Yu, T., Yang, W. Controllable electromechanical stability of a torsional micromirror actuator with piezoelectric composite structure under capillary force. Capillarity, 2022, 5(3): 51-64. https://doi.org/10.46690/capi.2022.03.02

Open-loop control of electrostatic levitation actuators to enhance the travel-range of optical switches

Command shaping is a driving technique for handling the large settling time of the high-Q-MEMS actuators. The strong nonlinearity due to the electrostatic actuation limits the linear operation range in cantilevered or torsional micro-mirrors where command shaping techniques can be applied for positioning. Experimental and simulation results of this research demonstrate the effectiveness of using electrostatic levitation to overcome the actuation nonlinearities and a significant increase in the operation range. The motivation for this research is that applying the nonlinear command shaping causes complexity in command manipulation and requires an accurate knowledge of the nonlinear terms involved in the system model. The large linear operation range generated by the levitating force allows using the practical simple command shaping methods for open-loop control.

Stability analysis of quasicrystal torsion micromirror actuator based on the strain gradient theory

Stability analysis of quasicrystal torsion micromirror actuator based on the strain gradient theory

Coupled effects of surface interaction and damping on electromechanical stability of functionally graded nanotubes reinforced torsional micromirror actuator

This paper demonstrated the coupled surface effects of thermal Casimir force and squeeze film damping (SFD) on size-dependent electromechanical stability and bifurcation of torsion micromirror actuator. The governing equations of micromirror system are derived, and the pull-in voltage and critical tilting angle are obtained. Also, the twisting deformation of torsion nanobeam can be tuned by functionally graded carbon nanotubes reinforced composites (FG-CNTRC). A finite element analysis (FEA) model is established on the COMSOL Multiphysics platform, and the simulation of the effect of thermal Casimir force on pull-in instability is utilized to verify the present analytical model. The results indicate that the numerical results well agree with the theoretical results in this work and experimental data in the literature. Further, the influences of volume fraction and geometrical distribution of CNTs, thermal Casimir force, nonlocal parameter, and squeeze film damping on electrically actuated instability and free-standing behavior are detailedly discussed. Besides, the evolution of equilibrium states of micromirror system is investigated, and bifurcation diagrams and phase portraits including the periodic, homoclinic, and heteroclinic orbits are described as well. The results demonstrated that the amplitude of the tilting angle for FGX-CNTRC type micromirror attenuates slower than for FGO-CNTRC type, and the increment of CNTs volume ratio slows down the attenuation due to the stiffening effect. When considering squeeze film damping, the stable center point evolves into one focus point with homoclinic orbits, and the dynamic system maintains two unstable saddle points with the heteroclinic orbits due to the effect of thermal Casimir force.

Dynamic Modeling and Anti-Disturbing Control of an Electromagnetic MEMS Torsional Micromirror Considering External Vibrations in Vehicular LiDAR.

Micromirrors based on micro-electro-mechanical systems (MEMS) technology are widely employed in different areas, such as optical switching and medical scan imaging. As the key component of MEMS LiDAR, electromagnetic MEMS torsional micromirrors have the advantages of small size, a simple structure, and low energy consumption. However, MEMS micromirrors face severe disturbances due to vehicular vibrations in realistic use situations. The paper deals with the precise motion control of MEMS micromirrors, considering external vibration. A dynamic model of MEMS micromirrors, considering the coupling between vibration and torsion, is proposed. The coefficients in the dynamic model were identified using the experimental method. A feedforward sliding mode control method (FSMC) is proposed in this paper. By establishing the dynamic coupling model of electromagnetic MEMS torsional micromirrors, the proposed FSMC is evaluated considering external vibrations, and compared with conventional proportion-integral-derivative (PID) controls in terms of robustness and accuracy. The simulation experiment results indicate that the FSMC controller has certain advantages over a PID controller. This paper revealed the coupling dynamic of MEMS micromirrors, which could be used for a dynamic analysis and a control algorithm design for MEMS micromirrors.

Design and Development of a Double-Bridge Micromirror With Bending and Twisting Cantilevers for Multiobject Spectroscopy

This article presents the design, development, and characterization of a double-bridge electrostatically actuated micromirror for multiobject spectroscopy (MOS). The proposed structure is an improvement over single-bridge micromirrors in terms of aperture size, pull-in voltage, degrees of freedom, and fill factor. The two-axis symmetric rotation mechanism of the proposed micromirror is achieved by bending and twisting action of the suspended cantilevers which is contrary to the twisting cantilevers of a conventional one-axis torsional micromirror. The placement of anchor and cantilevers under the mirror plate results in a high fill factor when arranged in a 2-D array. The analytical modeling, design optimization, and static and dynamic analysis are done using finite-element method (FEM) in Coventorware. An optimized design is fabricated using a simple approach of surface micromachining and electroplating. For a micromirror of size $200\,\,\mu \text{m}\,\,\times 200\,\,\mu \text{m}$ and the actuation gap of $2.5~\mu \text{m}$ , the device exhibits a tilt angle of 1.5° at a pull-in voltage of 23.1 V, a switching time of $38~\mu \text{s}$ , and the resonance frequency of 35.23 kHz. A ${3} \times {3}$ array of the micromirror is demonstrated with a fill factor of more than 95%. The deflection range can be increased by simply increasing the thickness of the sacrificial layer and without any major process modification.

Twisting sliding mode control of an electrostatic MEMS micromirror for a laser scanning system

In this paper, we present a twisting control scheme with proportional-integral-derivative &#x0028 PID &#x0029 sliding surface for a two-axis electrostatic torsional micromirror, and the utilization of the proposed scheme in a laser scanning system. The experimental results of set-point regulation verify that the proposed scheme provides enhanced transient response and positioning performance as compared to traditional sliding mode control. To evaluate the tracking performance of the closed-loop system, triangular waves with different frequencies are used as desired traces. With the proposed scheme the experimental results verified that the closed-loop controlled micromirror follows the given triangular trajectories precisely. A micromirror-based laser scanning system is developed to obtain images. When compared with open-loop control, the experimental results demonstrated that the proposed scheme is able to reduce the distortion of the raster scan, and improve the imaging performance in the presence of cross-coupling effect.

Estimation of Air Damping in Out-of-Plane Comb-Drive Actuators.

The development of new compliant resonant microsystems and the trend towards further miniaturization have recently raised the issue of the accuracy and reliability of computational tools for the estimation of fluid damping. Focusing on electrostatically actuated torsional micro-mirrors, a major dissipation contribution is linked to the constrained flow of air at comb fingers. In the case of large tilting angles of the mirror plate, within a period of oscillation the geometry of the air domain at comb-drives gets largely distorted, and the dissipation mechanism is thereby affected. In this communication, we provide an appraisal of simple analytical solutions to estimate the dissipation in the ideal case of air flow between infinite plates, at atmospheric pressure. The results of numerical simulations are also reported to assess the effect on damping of the finite size of actual geometries.

Interactive Modelling and Simulation of Micromirror MEMS Devices

This paper presents an interactive software package for the modelling and simulation of microelectromechanical system (MEMS) devices utilizing the MATLAB high-level programming language and its interactive environment. The package provides a dynamic analysis and frequency responses of a 1-D torsional micromirror electrostatically actuated with staggered vertical comb-drives. Applying a frequency sweep to the micromirror equation, the torsional mode natural frequency may be estimated. The developed package consists of several graphical user interfaces used for modeling MEMS devices. The software package is useful for computing the forces and torques for different micromirror geometries.

Design and simulation of a MEMS analog micro-mirror with improved rotation angle

This paper presents design and simulation of a MEMS analog torsional micro-mirror with improved rotation angle. The working range and consequently the rotation angle limitation of electrostatically actuated torsional micro-mirror due to pull-in instability are solved. Pedestal and suspension beams are presented to achieve electrostatically actuated torsional micro-mirror with extended working range. In the electrostatically actuated torsional micro-mirror, increasing the applied voltage decreases the equivalent stiffness of the structure and leads the system to an unstable condition by undergoing to a saddle node bifurcation. In the proposed structure to eliminate pull-in instability and increase the rotation angle range, mechanical stiffness of the structure is increased by adding a pedestal and locating auxiliary fixed-free beams in the free ends of the micro-mirror. The governing equations in relation to the proposed structure are derived. To verify, the numerical results are compared with simulated results.

A design method and its CAD prototype system for surface micromachined MEMS devices

Now the MEMS design method of “bottom–up” (mask-to-shape-to-function) has been adopted widely. However, it is complicated, time-consuming and not straightforward and can’t meet the demand of MEMS development. In this paper, a 3D MEMS aided design method is studied for surface micromachined MEMS devices, which adopts the design procedure of function-to-shape-to-mask. With this method, 3D geometric models of surface micromachined MEMS devices are built by selecting 3D MEMS features from the developed feature database after functional requirement analysis and concept design have been made. After the geometric model is analyzed with FEM analysis tools, 2D candidate masks and process flow are automatically generated by analyzing geometric information and material information of the model. Meanwhile, a 3D MEMS CAD prototype system of this method is developed based on SolidWorks. Finally a torsional micromirror is designed to verify the validity of the design method and its CAD prototype system. The practical example shows that 3D MEMS design method can help designers develop MEMS devices straightforwardly and obtain 2D masks and process flow automatically, and the developed 3D MEMS CAD prototype system based on SolidWorks can make MEMS device design easily.

A Fast Multiobjective Optimization Strategy for Single-Axis Electromagnetic MOEMS Micromirrors

Micro-opto-electro-mechanical (MOEMS) micromirrors are an enabling technology for mobile image projectors (pico-projectors). Low size and low power are the crucial pico-projector constraints. In this work, we present a fast method for the optimization of a silicon single-axis electromagnetic torsional micromirror. In this device, external permanent magnets provide the required magnetic field, and the actuation torque is generated on a rectangular multi-loop coil microfabricated on the mirror plate. Multiple constraints link the required current through the coil, its area occupancy, the operating frequency, mirror suspension length, and magnets size. With only rather general assumptions about the magnetic field distribution and mechanical behavior, we show that a fully analytical description of the mirror electromagnetic and mechanical behavior is possible, so that the optimization targets (the assembly size, comprising the mirror and magnets, and the actuation current) can be expressed as closed functions of the design parameters. Standard multiobjective optimization algorithms can then be used for extremely fast evaluation of the trade-offs among the various optimization targets and exploration of the Pareto frontier. The error caused by model assumptions are estimated by Finite Element Method (FEM) simulations to be below a few percent points from the exact solution.

The Normal Condition of Squeeze-film Damping Model for Torsion Micro-Resonators

The prediction of squeeze-film damping plays a significant role in the design of high Q MEMS devices. This paper presents an analytical solution for the effect of squeeze film damping on a rectangular torsion micro-mirrors whose torsion axis exists in different positions. We defined a variable l to represent the distance which torsion axis departs from its central axis. The double sine solution is derived from the linearized Reynolds equation to obtain the pressure distribution under the vibrating plate, and then calculate the analytical expression of the damping constant. Comparing the results with the finite element method(FEM), the accuracy of the model can be verified.

Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness.

Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach.

Parametric Resonance in Electrostatically Actuated Micromirrors

We consider an electrostatically actuated torsional micromirror, a key element of recent optical microdevices. The mechanical response is analyzed with specific emphasis on its nonlinear features. We show that the mirror motion is an example of parametric resonance, activated when the drive frequency is twice the natural frequency of the system. The numerical model, solved with a continuation approach, is validated with very good accuracy through an extensive experimental campaign.

A Squeeze Film Damping Model for a Torsion Micro-mirror with Coupling Effect Between Torsion and Bending

The prediction of squeeze film damping is very significant in designing high Q MEMS devices. In the past, there have been many analytical models studying the squeeze film damping of torsion micro-mirrors. However, the previous models didn’t consider the coupling motion of torsion and bending. This paper presents an analytical model for squeeze film damping considering the coupling motion of torsion and bending. In this paper, the modified Reynolds equation is solved by using the double sine series and the pressure distribution in the gap is derived, then the squeeze film damping force and torque applied to the micro-plate are derived. By solving the coupled equations of torsion and bending, the expression of the quality factor of the model is obtained. The accuracy of the present model is verified by comparing its results with the finite element method(FEM) solutions. The limitations and conclusions of the model are presented at the final state.

Active Disturbance Rejection Control of a 2D MEMS Micromirror with Sidewall Electrodes

This study proposes the active disturbance rejection control (ADRC) for a second degree of freedom (2D) electrostatic torsional micromirror with sidewall electrodes. The main idea is to use the linear extended state observer (LESO) to estimate the external disturbance and the angular velocity of the micromirror, and a feedback controller is further applied to achieve the position control of the micromirror. The effectiveness of the LESO in the estimation of the external disturbance and angular velocity is demonstrated. The proposed novel control scheme provides the micromirror with high positioning accuracy and disturbance rejection.

复合结构磁扭转微镜光纤电流传感器的研究

复合结构磁扭转微镜光纤电流传感器的研究