Spatial-mode analysis of micromachined optical cavities using electrothermal mirror actuation

The performance of optical microcavities is limited by spectral degradation resulting from thermal deformation and fabrication imperfections. In this paper, we study the spatial-mode properties of micromirror optical cavities with respect to commonly seen aberrations. Electrothermal actuation is used to slightly adjust the shape and position of micromirrors and study the effects this has on the spatial-mode structure of the cavity spectrum. The shapes of the micromirrors are changed using Joule heating with thermal expansion deformation. Significant differences in mirror tilt, curvature, and astigmatism are measured, but the tilt has by far the biggest impact on cavity finesse and resolution. We demonstrate that unwanted higher order spatial modes can be suppressed electrically and an amplitude reduction for the higher order modes of over 60% has been obtained with a tuning current of 5.5 mA. A fundamental mode finesse of approximately 60 is maintained throughout tuning. These tunable cavities have great potential in applications using cavity arrays or requiring dynamic mode control.     

Robust control of the electrostatic torsional micromirrors

In order to simplify the sensors subsystems of the electrostatic torsional micromirrors (ETMs), the output feedback control for the ETM systems is investigated in this paper. The dynamics of the systems is established by combining the dynamics of both the mechanical and electronic subsystems, and it is proved that the dynamics of the overall system with uncertainties in electrical parameters can be exactly transformed into the third order linear system. Then an output feedback finite-time stabilizing (FTS) controller is presented by composing of a full state FTS observer and a state feedback FTS controller for the third order linear systems, such that the ETM systems can be stabilized in its full travel range by merely measuring the tilt angle. Some numerical simulations demonstrate the stability of the proposed output feedback FTS controller.     

Design, fabrication and characterization of a high fill-factor micromirror array for wavelength selective switch applications

This paper presents the design, fabrication and characterization of a high fill-factor micromirror array in application of wavelength selective switch (WSS). The micromirror array consists of 52 independent micromirrors. Each micromirror is composed of a cantilever-type micromirror plate (800 μm × 120 μm) with a bumper and an eight-terraced bottom electrode with a limiting plane. A cantilever beam is designed to obtain the rotation angle of micromirror plate and achieve a high fill-factor for the micromirror array. Meanwhile, the bumper and limiting plane are used to prevent the damage possibly caused by the pull-in effect or some vibration instance. An eight-terraced electrode is utilized for reducing the driving voltage. The micromirror array with a high fill-factor in excess of 97% has been successfully achieved using the bulk micromachining technologies. The measured static and dynamic characteristics show that the micromirror can achieve a maximal rotation angle of 0.87° with a Direct Current (DC) driving voltage of 156 V. The turn-on responding time is 0.57 ms, and the turn-off responding time is 4.36 ms. Furthermore micromirror plate can be easily released from the pull-in state without damaged due to the novel bumper design. The switching function between the two output ports of a WSS optical system has also been demonstrated.     

Using dynamic voltage drive in a parallel-plate electrostatic actuator for full-gap travel range and positioning

The nonlinear dynamics of the parallel-plate electrostatically driven microstructure have been investigated with the objective of finding a dynamic voltage drive suitable for full-gap operation. Nonlinear dynamic modeling with phase-portrait presentation of both position and velocity of a realistic microstructure demonstrate that instability is avoided by a timely and sufficient reduction of the drive voltage. The simulation results are confirmed by experiments on devices fabricated in an epi-poly process. A 5.5-V peak harmonic drive voltage with frequency higher than 300 Hz allows repetitive microstructure motion up to 70% of gap without position feedback. The results of the analysis have been applied to the design of a new concept for positioning beyond the static pull-in limitation that does include position feedback. The measured instantaneous actuator displacement is compared with the desired displacement setting and, unlike traditional feedback, the voltage applied to the actuator is changed according to the comparison result between two values. The "low" level is below the static pull-in voltage and opposes the motion, thus bringing the structure back into a stable regime, while the "high" level is larger than the static pull-in voltage and will push the structure beyond the static pull-in displacement. Operation is limited only by the position jitter due to the time delay introduced by the readout circuits. Measurements confirm flexible operation up to a mechanical stopper positioned at 2 /spl mu/m of the 2.25 /spl mu/m wide gap with a 30 nm ripple.     

Analysis of the dynamic behaviour of a torsional micro-mirror

In this paper, the results of the dynamic pull-in voltage characteristics of a micro-mirror using electrostatic actuation are analyzed. Based on torsional dynamic theory, appropriate equations are developed that allowed to give insight into the actuating voltage, switching time and other dynamic parameters. The analytical results are discussed in detail without and with considering air squeeze film damping, respectively. This is equivalent to assuming the mirror is operated in vacuum or at ambient pressure. When the effect of the damping is considered, the movement trajectory of the cantilever beam is changed, and the calculated results of the pull-in voltage and switching time are considerably different compared to those without considering damping. Therefore, the effect of the air squeeze film damping is an important factor in the design and fabrication of micro-electro-mechanical systems. Finally, the experimental results in the air environment are discussed and compared to the theoretical analysis.     

Modeling, Design, Fabrication, and Demonstration of a Digital Micromirror With Interdigitated Cantilevers

We present the modeling, design, fabrication, and measurement results of a novel digital micromirror based on a new actuator called interdigitated cantilevers. In contrast to conventional micromirrors that rotate through the twisting actuation of a hinge, this micromirror has a symmetric bidirectional rotation through a bending actuation of interdigitated cantilevers hidden under a mirror plate. For the static and dynamic characteristics of the proposed micromirror, analytical models were developed first on the basis of the Euler–Bernoulli beam equation, as well as both distributed- and lumped-parameter models. The results of the developed analytical models are in good agreement with those of a finite-element-method (FEM) simulation, having just a 10% deviation. On the basis of these analytical models, we successfully designed, fabricated, and evaluated a micromirror with a mirror size of $16 muhbox{m} times 16 muhbox{m}$. The fabricated micromirror has a mechanical rotation angle of $pm 10^{circ}$, a pull-in voltage of 54 V, a resonant frequency of 350 kHz, and a switching response time of 17 $muhbox{s}$. The measurement results compare favorably with those of analytical models and FEM simulations, with deviations of less than 15% and 10%, respectively. $hfill$[2009-0139]      

Testing of "Venetian-Blind" silicon microstructures with optical methods

In this paper, we illustrate the design and testing of new silicon microstructures, fabricated by means of a conventional planar process. These "Venetian-blind" structures consist of arrays of narrow, rectangular suspended masses (width =31 /spl mu/m, length =400 /spl mu/m, thickness =15 /spl mu/m), which can be tilted using electrostatic actuation. Characterization of their static and dynamic behavior was performed with optical methods. The diffraction patterns in monochromatic light were analyzed and vibration measurements were performed by means of semiconductor laser feedback interferometry: experimental data on the tilt angle as a function of the applied voltage and on the resonance frequencies are reported. A maximum tilt angle of approximately 1.9/spl deg/ was obtained with a driving voltage in the range of 70-95 V. All the tested devices showed resonance frequencies higher than 80 kHz, which is fast enough (i.e., switching time in the millisecond range) for future use in optical interconnections. Numerical analyses were performed to evaluate the coupled electromechanical behavior of the microstructures, confirming the observed experimental behavior.     

Position control of parallel-plate microactuators for probe-based data storage

In this paper, we present the use of closed-loop voltage control to extend the travel range of a parallel-plate electrostatic microactuator beyond the pull-in limit. Controller design considers nonlinearities from both the parallel-plate actuator and the capacitive position sensor to ensure robust stability within the feedback loop. Desired transient response is achieved by a pre-filter added in front of the feedback loop to shape the input command. The microactuator is characterized by static and dynamic measurements, with a spring constant of 0.17 N/m, mechanical resonant frequency of 12.4 kHz, and effective damping ratio from 0.55 to 0.35 for gaps between 2.3 to 2.65 /spl mu/m. The minimum input-referred noise capacitance change is 0.5 aF//spl radic/Hz measured at a gap of 5.7 /spl mu/m, corresponding to a minimum input-referred noise displacement of 0.33 nm//spl radic/Hz. Measured closed-loop step response illustrates a maximum travel distance up to 60% of the initial gap, surpassing the static pull-in limit of one-third of the gap.     

Static and electrically actuated shaped MEMS mirrors

A novel digitally-actuated shaped micromirror for on-off optical switch applications is described. Reflective static spherical mirrors were designed and fabricated using conventional surface micromachining and the MultiPoly process, a technique for depositing multilayers of LPCVD polysilicon in order to control the overall stress and stress gradient. The resulting mirrors were measured to have radii of curvature of approximately 9 mm in agreement with design predictions. Based upon these static mirrors, an actuatable micromirror (diameter=500 /spl mu/m, static radius curvature=6.4 mm) was designed for snap action. This mirror was simulated using an electromechanical coupled-field model and fabricated using the MultiPoly process. Its performance was measured dynamically using an interferometer. A curved-to-flat digital actuation of the mirror was successfully achieved with a pull-in voltage of 38 V.     

Towards a stable low-voltage torsional microscanner

Torsional micromirrors emerged recently as an effective means of light manipulation. Their fast response, low wavelength sensitivity, and easy mass production have made them an attractive technology to implement optical switching and scanning applications. In this work, we developed a rigorous model of an electrically-actuated torsional micromirror. We verified the model against experimental data and conducted a convergence analysis to determine the minimum size of a reduced-order model (ROM) capable of representing the microscanner response accurately. We used the optimal ROM to study the dynamics of a microscanner. We found that the microscanner response exhibits a softening-type nonlinearity whose magnitude increases as the magnitude of the bias voltage increases. This nonlinearity results in multiple stable solutions at excitation frequencies close to but less than the natural frequency of the first mode. Operating the mirror in this region can cause abrupt jumps in the mirror response, thereby degrading the scanner performance. Furthermore, for a certain voltage range, we observed a two-to-one internal resonance between the first two modes. Due to this internal resonance, the mirror exhibits complex dynamic behavior, which degrades the microscanner’s performance. We formulated a simple design rule to avoid this problem.     

Pull-in study of an electrostatic torsion microactuator

Pull-in study of an electrostatic microactuator is essential for making the electrostatic actuation more effective. In this paper, pull-in analysis is presented for an electrostatic torsion microactuator. The torsion microactuator can be used as a microtorsion mirror. A polynomial algebraic equation for the pull-in voltage and pull-in angle of a torsion microactuator is derived. Two types of microactuators fabricated using bulk micromachining are presented. Measurements done on the fabricated microactuators are reported, showing deviations within 1% error from the calculations     

Design, Simulation, Fabrication, and Characterization of a Digital Variable Optical Attenuator

In this paper, we present the design, simulation, fabrication, and some measurement and characterization of a novel 16-bit digital variable optical attenuator (VOA) that attenuates by switching individual mirror of an array as an attempt to achieve input voltage variation independence and output linearization. The design was aided by a simulation package that features coupled electrostatic and mechanical solver. The mirror array spans an area of 1500$,times,$1500$mu m^2$and contains 16 equal-length rectangular micromirrors. Each mirror is suspended by two torsion beams. Experiments on beam design and width variations are conducted. Assuming Gaussian distribution, the mirror widths computed by an iteration algorithm vary from about 40 to 250$mu m$. Based on silicon-on-insulator (SOI) technology, two fabrication schemes to open the backside optical entrance were investigated. A hydrofluoric (HF) acid vapor-phase-etching (VPE) setup built to release the microstructure anhydrously is the key to achieve high yield especially for fragile components. Surface flatness, resonance frequencies, and tilt angles of selected mirrors were characterized. Quartz chips patterned with aluminum electrodes and 10$mu m$-high SU8 spacer columns were fabricated and assembled to corresponding device chips. Optical performance adversely affected by mirror bending is believed to originate from the intrinsic stress of the SOI wafer. 1271     

Nonlinear Control of an Electrostatic Micromirror Beyond Pull-In With Experimental Validation

This paper is aimed at demonstrating the potential benefits of applying nonlinear control techniques to a type of microelectromechanical system, namely, electrostatic micromirrors, in order to extend their stable operation range, enhance the system's performance, and allow controller tuning and system operation to be performed in a systematic manner. A nonlinear tracking control based on feedback linearization and trajectory planning has been developed. Aspects essential to the implementation, such as the prevention of devices from destruction due to contact, modeling and sensing schemes, the influence of the dynamics of the driving circuit on performance, and the device characterization, have been thoroughly addressed, and practical solutions have been proposed. The experimentation is performed on a setup built with low-cost commercial off-the-shelf instruments and components in a laboratory environment. The experimental results show that the developed control system can achieve stable operation beyond the pull-in position for both set-point and scanning controls.$hfill$ [2008-0268]      

On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources

This study considers the dynamic response of electrostatic actuators with multiple degrees of freedom that are driven by multiple voltage sources. The critical values of the applied voltages beyond which the dynamic response becomes unstable are investigated. A methodology for extracting a lower bound for this dynamic pull-in voltage is proposed. This lower bound is based on the stable and unstable static response of the system, and can be rapidly extracted because it does not require time integration of momentum equations. As example problems, the dynamic pull-in of two prevalent electrostatic actuators is analyzed.     

Current drive methods to extend the range of travel ofelectrostatic microactuators beyond the voltage pull-in point

When a voltage source drives an electrostatic parallel plate actuator, the well-known pull-in instability limits the range of displacement to 1/3 of the gap. Different strategies have been reported to overcome this limitation. More recently, experimental results have been presented using a capacitor in series with the actuator. Nevertheless, this strategy requires higher voltage than the pull-in voltage value to achieve full range of travel. In order to reduce the operating voltage, a switched-capacitor configuration has been also proposed. In this paper, two different approaches are introduced to control charge in the actuator by means of current driving. Theoretical equations derived for each method show that full range of travel can be achieved without voltage penalty. Both approaches are based on the use of current pulses injecting the required amount of charge to fix the position of the movable plate. Experimental measurements, showing that displacement beyond the pull-in point can be achieved, are in good agreement with the theoretical and the predicted simulated behavior     

Rotary electrostatic micromirror switches using wafer-scale processing and assembly

The design, micromachining process, wafer-scale assembly, and experimental characterization of our rotary electrostatic micromirrors for optical switching applications are reported in this paper. Some of the proposed microelectromechanical systems (MEMS) optical switches utilize surface-micromachined thin films as the reflection micromirrors which might result in optical degradation due to dynamic warping. Some of these devices fabricated by bulk micromachining highly rely on a delicate post-assembly process to assemble the micromirrors onto the top of MEMS actuators. In this research, we focus on developing rotary electrostatic micromirror switches without the requirement of delicate post-assembly processes. We use the spin-on-glass, which is used as an intermediate layer in a 280°C low-temperature wafer-bonding process, to fabricate our rotary optical switches with a wafer-scale assembly process. The rotary electrostatic actuator and the vertical micromirror are fabricated simultaneously by the same deep RIE process in our design. We have successfully demonstrated the rotary electrostatic micromirror switches via the wafer-scale assembly process with a yield rate of above 70%. Experimental results show that our rotary vertical micromirrors rotate about 1.5° under an applied voltage of 150 V for steady-state measurements. For dynamic measurements, the rotary vertical micromirrors rotate about 3.6° under an applied voltage of 30 V at the resonant frequency. The first vibration mode of our rotary switch is an in-plane rotational mode and appears around 3.4 kHz, which is characterized via a Polytec laser doppler vibrometer.

---

Arrays of large-area, tip/tilt micromirrors for use in a high-contrast projector

Arrays of two-degree of freedom analog micromirrors are designed for use within an high-contrast projector and fabricated using a multi-user MEMS fabrication process. We demonstrate a novel way of optimizing the tradeoffs between tilt angle and mirror size by subdividing the mirrors into smaller functional subsections that move synchronously. The mirror design employs multiple mirrors within a gimbal frame. The frame rotates around one axis, and each mirror within the frame rotates around a perpendicular axis, resulting in two-degree of freedom rotation. The design employs specific electrode shapes to allow one-layer connections. Using these fabricated mirrors, simultaneous actuation of mirrors within a composite structure is achieved. A prototype array of fabricated mirrors is described, with 6 × 5 mirrors each of 160 μm × 160 μm forming one composite mirror of an array, giving total active area of 960 μm × 800 μm. The mirrors can achieve a maximum tilt angle of 2.25°. The fill factor of this design is 68%.     

车载环境下MEMS微镜长期可靠性及控制方法

作为一种新型微光机电系统,MEMS微镜可完成微尺度下的光调控工作,在光电通信、医疗成像、民用投影、雷达探测等领域应用广泛.近年来,以微镜为核心部件的MEMS激光雷达因其体积小和功耗低等优势,有望成为更具竞争力的辅助驾驶传感器之一.然而,鉴于车载应用特殊性,MEMS微镜在温湿、电磁、振动和冲击等复杂多物理场耦合环境下的各类可靠性问题严重制约了MEMS激光雷达的工程应用.本文立足MEMS微镜可靠性研究领域,综述其在高频振动、温湿循环、电磁耦合等极端环境下的分层翘曲、结构断裂、静电吸合、短路烧毁等复杂失效形式及失效机制,总结了MEMS微镜常见动力学建模理论及控制方法,讨论并展望了MEMS激光雷达车规化面临的主要挑战和发展趋势.     

Analysis of a novel RF MEMS switch using different meander techniques

In this paper, two types of RF MEMS switches namely step structure and Normal beam structure are designed and analyzed using different meander techniques. Three techniques namely plus, zigzag and three-square meander were used to lower the pull-in voltage. The actuating beam is designed with the rectangular perforations affects the performance of a switch by lowering the pull-in voltage, switching speed and results in better isolation. In this paper a comparative analysis is done for all three meander techniques with and without perforations on the beam. Total six structures have been designed with the combination three meanders and two different beam structures. The proposed stepdown structure exhibits high performance characteristics with a very low pull-in voltage of 1.2 V having an airgap of 0.8 µm between the actuation electrodes. The gold is used as beam material and HfO₂ as the dielectric material such that the upstate and downstate capacitance is seen as 1.02 fF and 49 fF. The FEM analysis is done to calculate the spring constant and thereby the pull-in voltage and behavior of the switch is studied with various parameters. The switch with a step structure and three-square meander configuration has shown best performance of all by requiring a pull-in voltage of 1.2 V and lower switching time of 0.2 µs. The proposed switch also exhibits good RF performance characteristics with an insertion loss below − 0.07 dB and return loss below − 60 dB over the frequency range of 1–40 GHz. At 28 GHz a high isolation of − 68 dB is exhibited.

     

Optical switch with auto-aligning fibers and latching micro-mirrors

This paper presents an innovative device for self-aligning in a V-groove and a self-latching vertical mirror on the suspension diaphragm using the out of plane fiber-optical switch array technique. The self-aligning offers integrating the optical fiber and mirror within the same optical switch. The self-latching vertical mirror is supported on the suspension diaphragm by four cantilever beams. The theoretical analysis includes a dynamic simulation using the ANSYS software and corner compensation using the IntelliCAD software. The fabrication process consists of wet etching micromachining, lithography, and excimer laser ablation. This proposed process is simpler than those proposed in other works. An electrostatic driving voltage is used to operate the optical switch. The mirror is made of a photoresist coating with gold film as the switching element. The reflectivity of the gold film mirror is higher than 85% using a wavelength of 1310 nm. The micro-optical switch has a maximum displacement of 48 m and the switching time is below 0.4 ms with a driving voltage of 100 VDC.This work was supported by the National Science Council (series no. NSC90-2218-E-005-005) and the Ministry of Economic Affairs of Taiwan. Thanks are due to the MIRLs colleagues at ITRI for preparing the etching solutions and operating the excimer laser.