Torsion Mirror Research Articles

Design of planar comb-driven MEMS torsional mirror

The MEMS torsional mirror is an important MEMS optical device, and its related applications are very wide, including LiDAR, projection equipment, optical communication, and so on. At present, the electrostatically driven MEMS torsional mirror mainly adopts a vertical comb driver to achieve torsional motion, which has some disadvantages such as a complicated manufacturing process, low yield, and high driving voltage. In this paper, a novel MEMS torsional mirror structure is proposed, which provides flexible elastic constraint points for the torsional mirror with the bottom support rod structure as the center, and relies on the combination of planar comb and support rod to form a tie rod structure to achieve torsion, and achieves a torsion Angle of ±15.55° under the driving voltage of 65 V. The use of a planar comb instead of a vertical comb greatly reduces the difficulty of manufacturing. Finally, it is verified that the system stability is good, the correlation drift does not affect the results within the range, the fifth-order modes are within the reasonable range, and the maximum stress is 671 MPa, which is controlled within the range of fracture stress of silicon material.

Fracture strength of silicon torsional mirror resonators fully coated with submicrometer-thick PECVD DLC film

In this work, we attempted to enhance the torsional fracture strength of single crystal silicon (SCS) resonators for micro mirrors application by introducing a 300 nm-thick diamond-like carbon (DLC) coating. The SCS torsional beams of the resonators were 20 μm long, 9 μm wide and 9 μm thick, and fully coated with DLC films using plasma enhanced chemical vapor deposition (PECVD) at three different deposition bias voltages. The resonators were driven by a piezoelectric actuator and their angular amplitude was measured by a custom-made torsional test system. Average nominal torsional fracture strength of DLC coated resonators was 11.1–30.0% higher than that of bare SCS, reaching a value of 2.93 GPa. The torsional fracture strength of resonators exhibited a good agreement with the tensile fracture strength. Deviations in torsional strength were reduced with increasing deposition bias voltage due to the compressive residual stress of DLC films.

Tensile Strength of Silicon Nanowires Batch-Fabricated into Electrostatic MEMS Testing Device

The tensile strength of a silicon nanowire (SiNW) that had been integrated into a silicon-on-insulator (SOI)-based microelectromechanical system (MEMS) device was measured using electrostatic actuation and sensing. SiNWs of about 150 nm diameter and 5 μm length were batch-fabricated into a 5-μm-thick SOI device layer. Since there was no interface between the SiNW and the MEMS device and the alignment was perfect, the SiNW integration into an SOI-MEMS was expected to be useful for developing highly sensitive biochemical sensors or highly reliable torsional mirror devices. The SiNW was tensile tested using the electrostatic MEMS testing device. The integration was achieved using a combination of anisotropic and an isotropic dry etching of silicon, with an inductively coupled plasma reactive ion etching. A fabricated silicon beam of 800 nm square was thinned by a sacrificial oxidation process. The tensile strength of the wire was 2.6–4.1 GPa, which was comparable to that of microscale silicon MEMS structures. The reliability of such a thin device was successfully verified for future applications of the device structures.

A Silicon Microsystem for Generation of Infrared Patterned Light

The use of patterned light for three-dimensional (3D) imaging and movement tracking has been in the last decade object of experimental investigations for industrial, scientific, and consumer applications. In this paper, we demonstrate the functionality of a compact silicon microsystem for patterned light generation suitable for 3D imaging. It incorporates a single-axis torsional MEMS mirror for steering a near-infrared beam on a diffractive silicon microstructure that projects light patterns on the target. We, here, report images, acquired with a CMOS camera, of the detected light patterns realized with different diffractive elements. As an example of application, we have illuminated 3D objects with a generated line pattern and then detected the deformation of the projected lines with the same camera. By image processing, from the line deformation, we have estimated the object depth that was found in agreement with the geometrical size.

Improving the nonlinear proportional-derivative control for an MEMS torsional mirror with parametric uncertainties

Fast settling, accurate positioning, and a large tilt angle range are important for MEMS mirrors. Here, residual vibration and the pull-in phenomenon—both major problems affecting the performance of an electrostatically actuated mirror—are investigated. Based on the analysis of a nonlinear proportional-derivative (PD) control with parametric uncertainties, a closed-loop feedback control strategy with a combined control scheme is proposed. This method, combining nonlinear PD control and sliding mode control (SMC), not only inherits the virtue of a good dynamic performance from the nonlinear PD control, but also further improves the robustness with SMC for such MEMS mirrors. Furthermore, this method can be convenient when tuning design gains of the controller to obtain a faster error convergence rate. Numerical simulation results show that with this combined control scheme not only the transient response of the MEMS mirror is improved but the influence of parametric uncertainties and external disturbance is also reduced.

The squeeze-film air damping of circular and elliptical micro-torsion mirrors

This paper proposes an analytical solution to calculate the squeeze-film air damping of circular and elliptical micro-torsion mirrors. To derive the expressions of squeeze-film air-damping torque, the nonlinear Reynolds equation, which governs the air behavior of torsion mirror, is solved by the method of eigenfunction expansions in polar coordinate and elliptical coordinate, respectively. The series solutions are integrated and summed up to deduce the damping torque of circular and elliptical torsion mirrors. The formulas of circular mirror and elliptical mirror are deduced independently, and their results match when the eccentricity of the elliptical mirror approaches zero. Besides, the results of the formulas are consistent with numerical simulation. Both of them verifies the damping torque formulas in this paper.

An Equivalent Circuit Model for Semiparallel Plate Electrostatic Torsion Mirror

SUMMARYAn equivalent circuit model for a semiparallel plate electrostatic torsion mirror has been developed based on an electrical circuit simulator. An analytical model for the electrostatic torque has been translated into a nonlinear dependent current source as a function of the input voltages that interpret the drive voltages and the mirror angle. Use of the suspension width as a fitting parameter explained well the experimental results on frequency response and the mirror's static deflection. © 2013 Wiley Periodicals, Inc. Electron Comm Jpn, 97(1): 37–47, 2014; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.11486

Efficient Numerical Evaluation of Semianalytical Models for Squeeze Film Damping for Torsion Mirrors

Abstract In the semianalytical models for squeeze film damping, the coefficient of damping torque is expressed as an infinite double series. To work with these models, methods for the efficient numerical evaluation of these double series are important, because, as has been pointed out, the results are given by complicated equations; the application of the results is difficult. This paper presents a transformation of the equations that allows a fast and reliable numerical evaluation of the coefficient of damping torque for torsion mirrors. We give precise error bounds and present examples that illustrate that approximations with one or two terms are often sufficient in practice.

Strain analysis in Si micro-electromechanical systems by dynamical X-ray diffraction

Long-range strain in nearly perfect crystalline materials can be detected by dynamical X-ray diffraction. Long-range strain due to uniform bending or torsion is undetectable by conventional methods when the specimen is vertical in a symmetrical Laue setting, but it can be detected by rotating the specimen along the scattering vector. This method is applied to Si devices for a resonating torsion mirror in a micro-electromechanical system. X-ray transmission topography clearly reveals local strain concentrations as enhancements or reductions in the diffraction intensity where non-uniform strain exists. In conjunction with reflection plane-wave topography, a model of local strain is proposed and the strain qualitatively analysed.

An Equivalent Circuit Model for Semi-parallel Plate Electrostatic Torsion Mirror

An equivalent circuit model for the semi-parallel plate electrostatic torsion mirror has been developed based on the electrical circuit simulator. An analytical model for the electrostatic torque has been translated into a nonlinear dependent current source as a function of input voltages that interpret the drive voltages and the mirror angle. A use of the suspension width as a fitting parameter explained well the experimental results of frequency response and the mirror's static deflection.

Novel fabrication process for a monolithic PMMA torsion mirror and vertical comb actuator

This paper presents a novel fabrication process for monolithic PMMA (polymethylmethacrylate) vertical comb-drive actuators utilizing hot embossing, surface-activated direct bonding and elliptical vibration cutting. The robustness and capability of the method are demonstrated through the fabrication of sophisticated PMMA freestanding microstructures, such as a rotation mirror device integrated with vertical comb actuators. The fabrication process consists of silicon mold fabrication by deep-RIE, PMMA microstructure formation by hot embossing, PMMA–PMMA direct bonding by surface activation, releasing or removal of a PMMA layer remaining after hot embossing by elliptical vibration cutting, and finally, metallization by sputtering to form electrodes. An efficient technique to protect the PMMA microstructures during the release process using reinforcement material is applied. A monolithic PMMA torsion mirror driven by a vertical comb actuator has been fabricated successfully.

Design and Analysis of a Dual-Mode MEMS Micromirror

In this paper, the design and simulation of a dual-mode Aluminum MEMS micromirror device are proposed. The dual-mode micromirror can work in either torsional or piston modes, depending on the voltage scheme applied to the bottom driving electrodes. The working principle and performance of the micromirror are analyzed. Based upon the analysis, a set of optimized micromirror design parameters is suggested, and the corresponding performance of the micromirror design is reported. According to the analysis, the mirror can deflect for a maximum controllable displacement of 1.3μm in its piston mode, and rotate for a maximum controllable angle of ±3.6° in its torsional mode. If the micromirror works in digital operation in its torisional mode, a maximum rotation angle of ±7.8° can be achieved. ANSYS FEM method is used to simulate the first five vibrational modes and the corresponding resonant frequencies of the micromirror. The micromirror is to be fabricated with thick photoresist sacrificial layer technique. The proposed micromirror can be used to modulate the phase as well as the direction of the incident light due to its dual-mode modes. Keywords: Microelectromechanical Systems (MEMS), Spatial Light Modulator (SLM), micromirror, piston mirror, torsional mirror

A semi-analytical model for squeeze-film damping including rarefaction in a MEMS torsion mirror with complex geometry

A semi-analytical approach is presented to model the effects of complicated boundary conditions and rarefaction on the squeeze-film damping dependent quality factor in a double-gimballed MEMS torsion mirror. To compute squeeze-film damping in a rectangular torsion mirror with simple boundaries, compact models derived by solving the conventional Reynolds equation with zero pressure boundary conditions on the edges of the plate are generally used. These models are not applicable if the air-gap thickness is comparable to the length of the plate. To extend the validity of the existing models in devices with large air-gap thickness and complicated boundaries, we present a procedure that requires the computation of the effective length of the structure and uses this length for the computation of damping in all flow regimes using a modified effective viscosity model. The effective length is computed by comparing the damping obtained from a numerical solution of Navier–Stokes equations with that obtained from a Reynolds-equation-based compact model. To capture the effect of rarefaction in different flow regimes, we use two different approaches: the effective viscosity approach which is valid for continuum, slip, transition and molecular flow regimes, and an approach based on the free molecular model which is valid only in a molecular flow regime. We show that the effective length obtained for complicated structures in the continuum regime may still be used to capture the rarefaction effect in the slip, transition and molecular regimes. On comparing different empirical models based on the effective viscosity approach with experimental results, we find some anomaly in the region between the molecular regime and the intrinsic regime where non-fluid damping dominates. To improve modelling in the rarified regimes, we modify the best model among the existing models by minimizing error obtained with respect to the experimental results. We find that the proposed model captures the rarefaction effect not only in the slip, transition and molecular regimes but also couples well with the non-fluid damping in the intrinsic regime and captures the transition to purely intrinsic losses.

1×8 fiber-optic switch based on an innovative waveguide converter and a micro torsion mirror

This paper reports a 1x8 fiber-optic switch based on an innovative waveguide converter and a micro torsion mirror. A compact 9-fiber collimator is implemented with the waveguide converter. With the micro torsion mirror aligned to the 9-fiber collimator, light from the central fiber can be steered to any of the other 8 fibers. The introduction of the waveguide converter enables a smaller and faster micro torsion mirror. The switch shows good performance, insertion loss, nonuniformity, and cross talk is <3.02 dB, <0.4 dB, and <-35 dB respectively. Improvements of performance are expected after further optimization.

Squeeze film effects on dynamic performance of MEMS μ-mirrors-consideration of gas rarefaction and surface roughness

The squeeze film behavior of MEMS torsion mirrors is modeled, analyzed and discussed. Effects of gas rarefaction (first-order slip-flow model with non-symmetric accommodation coefficients, ACs) and surface roughness are considered simultaneously by using the average Reynolds type equation (ARTE). Based on the operating conditions with small variations in film thickness and pressure, the ARTE is linearized. A coordinate transformation, by stretching or contracting the axes by referring to the roughness flow factors, is proposed to transform the linearized ARTE into a diffusion type modal equation. The dynamic coefficients (stiffness and damping coefficients) are then derived and expressed in analytical form. The results show that the tilting frequency (or Γ0 squeeze number), roughness parameters (γ Peklenik numbers, σ standard deviation of composite roughness) and gas rarefaction parameters (D inverse Knudsen number, $$\alpha_{1}, \alpha_{2}:$$ ACs) are all important parameters on analyzing the dynamic performance of MEMS torsion mirrors.

Influence of Boundary Conditions on the Dynamic Characteristics of Squeeze Films in MEMS Devices

Micromechanical structures that have squeeze-film damping as the dominant energy dissipation mechanism are of interest in this paper. For such structures with narrow air gap, the Reynolds equation is used for calculating squeeze-film damping, which is generally solved with trivial pressure boundary conditions on the side walls. This procedure, however, fails to give satisfactory results for structures under two important conditions: 1) for an air gap thickness comparable to the lateral dimensions of the microstructure and 2) for nontrivial pressure boundary conditions such as fully open boundaries on an extended substrate or partially blocked boundaries that provide side clearance to the fluid flow. Several formulas exist to account for simple boundary conditions. In practice, however, there are many micromechanical structures such as torsional microelectromechanical system (MEMS) structures that have nontrivial boundary conditions arising from partially blocked boundaries. Such boundaries usually have clearance parameters that can vary due to fabrication. These parameters, however, can also be used as design parameters if we understand their role on the dynamics of the structure. We take a MEMS torsion mirror as an example device that has large air gap and partially blocked boundaries due to static frames. We actuate the device and experimentally determine the quality factor Q from the response measurements. Next, we model the same structure in ANSYS and carry out computational fluid dynamics analysis to evaluate the stiffness constant K, the damping constant D, and the quality factor Q due to the squeeze film. We compare the computational results with experimental results and show that without taking care of the partially blocked boundaries properly in the computational model, we get unacceptably large errors.

Squeeze-film air damping of a torsion mirror at a finite tilting angle

This paper proposes an analytical model for calculating the squeeze-film air damping of a rectangular torsion mirror at finite normalized tilting angles. The general Reynolds equation is first modified to a nonlinear equation for the condition. Based on the nonlinear equation, the damping pressure, the damping torque and the coefficient of the damping torque are derived as functions of the tilting angle and the aspect ratio of the mirror plate. To show the relation clearly and for the ease of application, the coefficient of the damping torque is given in curves in addition to complicated analytical expressions. The results show that the damping torque coefficient is a highly nonlinear function of the tilting angle and basically a linear function of the aspect ratio of the mirror. The coupling between the two factors is appreciable but not very strong. When the tilting angle is reduced to zero, the result of this paper agrees perfectly well with those of previous papers, which have been verified by experiments and/or numerical calculation. The analytical results are effective for normalized tilting angles up to 0.7.

Micro torsion mirror actuated by compound electrostatic driving structure

We report on a novel micro torsion mirror actuated by a compound electrostatic driving structure. The compound driving structure is made up of a planar plate drive and a vertical comb drive. The device is fabricated in SOI substrate by using a bulk-and-surface mixed silicon micromachining process. As demonstrated by experiment, the novel driving structure can actuate the mirror to achieve large-range continuous rotation as well as spontaneous 90° rotation induced by the pull-in effect in a voltage control fashion. The continuous rotating range of the micro torsion mirror is increased to about 46° at an increased threshold voltage. The measured threshold voltage ranges of the mirrors with torsion springs of 1μm and 0.5μm in thickness are 390–410V and 140–160V, respectively. Theoretical modeling is carried out to compare with the experiment. The optical insertion loss has also been measured to be −1.98dB when the mirrors serve as digital optical switches in a 2×2 array form.

Monolithic 2-D scanning mirror using self-aligned angular vertical comb drives

We have demonstrated microfabricated, monolithic two degrees of freedom (two-dimensional) electrostatic torsional mirrors using a three-mask process on silicon-on-insulator wafer with a single plastic deformation step. The mirror operated independently in two orthogonal directions as controlled by two sets of self-aligned angular vertical combs. The measured dynamic performance showed resonant frequencies of 10.56 and 1.54 kHz with optical scanning angles up to 27/spl deg/ and 20/spl deg/ in the two orthogonal axes, respectively, under driving voltages of 20 V/sub dc/ plus 15 V/sub pp/. A 90-day continuous mirror operation at peak resonance, in equivalent to 80 and 12.1 billion cycles on the two orthogonal axes, showed negligible performance variations.

Damping of a micro-resonator torsion mirror in rarefied gas ambient

Damping in resonating MEMS mirrors has a profound effect on the dynamical behavior. The validity of the existing theories is investigated in this work by theoretical and experimental means. The squeeze-film model with artificial viscosity and the molecular dynamics model are adapted for the case of a torsion mirror under a wide range of vacuum levels. The considered ambient pressure varies from atmospheric to a pressure under which structural damping prevails. High resolution experiments have been conducted on dedicated devices. Two independent experimental damping extraction methods have been employed for substantiating the validity of the measured parameters. Although the theoretical models agree favorably with the experimental data, it appears they provide slightly different predictions under different operating regimes.