Gravity and Film Stress Analysis for Mems Deformable Mirror with Electrostatic Piston Array

We report on the development of a new class of electrostatic MEMS deformable mirror (DM) fabricated through a combination of bulk micromachining, wafer bonding, and surface micromachining. The combination of these fabrication technologies introduces four major improvements over previous MEMS DMs, which are fabricated using surface micromachining alone. First, the MEMS DM structural components (mirror surface and actuator array) are made entirely of single crystalline silicon by use of the device layer of a whole 4-inch silicon-on-insulator (SOI) wafer bonded together via anodic bonding. Unlike current MEMS DMs fabricated entirely using surface micromachining, bulk micromachining steps in this fabrication process require no etch access holes, print through is inexistent, and no polishing steps are required. This leads to reduced diffraction of light from the mirror surface, improved mirror surface optical quality, and elimination of manufacturing processing steps. Second, through-wafer interconnects are used to connect the densely-packed electrostatic actuator array to driver electronics. This eliminates the need for wirebonding at the periphery of the DM, increasing the surface area available for actuators and removes the need for bulky wire bundles to connect the device to its driver. Third, by using the full area of a silicon wafer for each mirror, these MEMS DMs offer a larger optical aperture than any previously-reported MEMS DM. The larger aperture will achieve higher angular resolution, providing larger wavefront correction. Finally, the mirror and actuator thicknesses are not limited to several micrometers, unlike in surface micromachining. The thickness limits using this fabrication process is prescribed by the device layer thickness in SOI wafers, which vary between several micrometers to several hundred of microns.

The Lynx X-ray Observatory concept, under study for the 2020 NASA Decadal Survey, will require a telescope with ∼2 m2 of effective area and a point-spread function (PSF) with ∼0.5-arc sec half-power diameter (HPD) to meet its science goals. This requires extremely accurate thin grazing-incidence mirrors with a reflective x-ray coating. A mirror coating, such as 15-nm-thick iridium, can exhibit stress exceeding 1 GPa, significantly deforming segmented mirrors and blurring the PSF. The film stress and thickness are neither perfectly repeatable nor uniform. We use finite element analysis and ray tracing to quantify the effects of integrated stress inaccuracy, nonrepeatability, nonuniformity, and postmounting stress changes on segmented mirrors. We find that if Lynx uses segmented mirrors, it will likely require extremely small film stress (∼10 MPa) and nonuniformity (<1 % ). We show that realigning mirrors and matching complementary mirror pairs can reduce the HPD from uniform film stress by a factor of 2.3 × and 5 × , respectively. Doubling mirror thickness produces much less than the 4 × HPD reduction that would be expected from a flat mirror. The x-ray astronomy community has developed numerous methods of reducing the PSF blurring from film stress, and Lynx may require several of these in combination to achieve 0.5 arc sec HPD using segmented mirrors.

The three-dimensional (3D) processing maps of cast Mg-9.0Gd-3.0Y-2.0Zn-0.5Zr alloy were established based on isothermal compression tests and dynamic material model (DMM). The stable and power-efficient forming domains were determined by considering both the instability and power dissipation efficiency maps. Multi-directional forging (MDF) was then simulated by employing finite element (FE) analysis in the Deform-3D software, using the 3D power dissipation efficiency maps as input. The optimal forging parameters were thus obtained for a large-scale ingot with 430 mm in diameter and 440 mm in height, i.e., a forging temperature of 450 °C and forging speed of 10 mm/s. Finally, a Mg-9.0Gd-3.0Y-2.0Zn-0.5Zr cake-shaped forged part with 900 mm in diameter and 100 mm in height was produced. After T6-heat treatment, the edge and center of the forged part exhibit homogeneous microstructure and relatively consistent properties, with the tensile strength, yield strength, and elongation being about 400 MPa, 320 MPa, and 14.0%, respectively. Using transmission electron microscopy, the main strengthening phases were revealed to be the dense nano-scale β′ phases that are uniformly distributed inside the material.

Deformable membrane mirrors are promising MOEMS devices for focus control and aberration correction in vital microscopy, offering high speed focus adjustment in an optical system that can be miniaturized for in vivo use. This paper describes mirrors comprising metalized polymer membranes suspended over three concentric circular electrodes for electrostatic actuation. The membranes are 2-μm thick and 3 mm in diameter, made from the fully cross-linked photoset epoxy SU-8 2002. A layer of SU-8 2025 is used to establish a 30-μm thick air gap between the electrodes and the membrane mirror. The membranes are actuated by applying voltage to each electrode individually to achieve displacement as large as 12 μm while minimizing spherical aberration. Surface deflection is studied using phase-shift interferometry under both static and dynamic excitation. Using the deformable MOEMS mirror for focus control in an optical microscope we demonstrate the ability to adjust the location of the focal plane by 85 μm using an N.A. = 0.75 optical system.

Using a transmission electron microscopy-based orientation and phase mapping technique we examine effects of film stress and geometry on texture development before and after the martensitic transformation in a nanocrystalline Co thin film. Specimens are annealed for various times at 873 K (600 °C), which is above the equilibrium martensitic transformation temperature [~693 K (~420 °C)], and then cooled to room temperature. The cooled specimens are used for texture analysis. The martensitic transformation is observed to be incomplete, and fcc and hcp structures coexist in all the specimens examined. It is deduced from the crystallographic orientation relationship of the martensitic transformation of Co that, during prolonged annealing at 873 K (600 °C), the major texture in the fcc phase is {101}, followed by {111}. In the cooled structure, the major texture component in the hcp phase is (0001), followed by {2 $$ \overline{1} \overline{1} $$ 0}. The {101} texture is clarified by assuming that the film system is perfect elastic–plastic with the help of the concept of the Taylor factor. We conclude that the (0001) texture is produced by the surface energy minimization, which, however, does not elucidate the development of the {2 $$ \overline{1} \overline{1} $$ 0} texture. The formation of the texture component is understood by considering the strain energy provided by a constraint imposed by neighboring grains. As annealing time increases, the hcp phase expands its area, dominating over the fcc phase after prolonged annealing, which is also clarified by allowing for the geometrical constraint effect. The expansion of the hcp phase supports the possibility of surface nucleation of martensites.

To study the effect of stress on SMR devices, SMR resonator is designed and fabricated on 8-inch wafers. According to the test results, the $k_{eff}^2$ distribution of the SMR device on 8-inch wafer is obtained. It was shown that $k_{eff}^2$ in the device varied from 4.8% to 3.6% due to stress inhomogeneity across the wafer, and it was positively correlated with the tensile stress of the piezoelectric film.

SUMMARYIn this report, we constructed a simple mathematical analysis model for a new MEMS deformable mirror using an electrostatic piston array. The deformable mirror has been developed as a wavefront compensation device in adaptive optics for retinal observation. The device realizes a large convex deformation with a low operation voltage because of moving bottom electrodes on the pistons. The constructed model is based on the plate theory and simple superposition of the actuation components. The calculated deformation analyzed using this model agrees well with that analyzed using the finite element method not only in deformation shape but the peak‐valley deformations. In addition, the calculation time is much shorter, so the model can be used for design optimization of the device.

Focus on sensors

Membrane mirrors are advantageous in several applications due to their light weight and potential for deployability. Desired optical performance often requires dynamic actuation, however, and electrostatic actuators are frequently employed for this purpose. This paper investigates a variable area/constant voltage method for electrostatic actuation of small circular membrane mirrors designed to meet specified performance requirements for a beam steering and focus/defocus application. The proposed technique involves selective application of a constant voltage to area segments that together make up an electrode pad. The paper shows that a lumped parameter model for this system also has the property of differential flatness (similar to variable voltage/constant area systems), based on which the reference trajectory for membrane deflection can be specified in phase space. The phase space trajectory is derived from the required transient response characteristics (rise time, settling time, etc.). A closed loop system comprised of a controller and an observer is devised using a Lyapunov function-based approach. A `quad cell' beam position finder is used to detect the beam angular deflection and intensity. The overall system is simulated numerically in this paper. The control system is found to provide efficient trajectory tracking for both symmetric and antisymmetric mode excitation. Although the area changes for the proposed system are discrete, the present simulations only consider continuously-variable area actuation.

Thickness and film stress effects on the martensitic transformation temperature in equi-atomic NiTi thin films

Due to the high power density and local temperature increase on nanoscopic asperities of solid metal contacts, traditional MEMS contact switches suffer from contact welding, pitting, electromigration and oxidation. Particularly, when MEMS switches are used to handle high power, solid metal contacts pose serious limitation on the contact reliability. A self-healing RF MEMS switch, which utilizes liquid gallium contacts to take the place of the traditional solid metal-to-metal contacts, is proposed in this paper. Electrostatic actuation is used to drive a silicon nitride bridge with upper electrodes. When the bridge is pulled down, liquid gallium droplets work as an interface between the upper and lower contact electrodes. The loss of the gallium droplets can be avoided due to the unwettability of the material surrounding the contact electrodes. The switch is fabricated using a surface micromachining process. A coupled-field finite element analysis (FEA) is used to model the electric current, heating and thermal conduction of the contacts. The model includes deformable gallium droplets with 4 μm base diameter. The two sides of the droplets are connected to the upper and lower solid metal contact electrodes, respectively. By using the FEA models, the electric and thermal characteristics of the gallium droplets featuring a variety of geometric parameters have been studied. 1 A current handling capability of the liquid gallium contact is verified by the FEA models.

This diploma thesis investigates the analysis and design of gravity retaining walls. More specifically, it aims at: a) developing a complete numerical tool in excel spreadsheet to analyze and design both in geotechnical and structural engineering terms and b) to compare the Rankine earth pressures analysis with the numerical finite element analysis (FEA) results for a range of soil types. Chapter 1 presents the advance of Retaining Walls throughout the human history and the types which we construct today. Chapter 2 describes and presents the regulation of the analysis and design of gravity walls in Europe – Eurocode 7(EC7). Next, Chapter 3 presents the theoretical framework about the earth pressures which is the basis of the analysis of a retaining work. Chapter 4 describes the types of Concrete Retaining Walls and their failure behaviors. Moreover, in Chapter 5 an excel sheet was successfully programmed for the complete conventional analysis and design of a reinforced concrete retaining wall (Type L) with load on the backfill . Chapter 6 involve extensive numerical modeling on a range of non-cohesive sands and cohesive clays scenarios with FEA, using a linear elastic – perfectly plastic Mohr Coulomb constitutive model. In Chapter 7, a comparison of the earth pressures calculated with the Rankine method and the FEA for sands and clays for a concrete gravity wall, is presented. The FEA included the complete structure sequence. The main conclusion is that Rankine method underestimated the soil earth pressures as in FEA there was no generalized soil failure, which depends on soil strength (c΄, φ΄). As a result, soil movements were lower than expected for Rankine failure. Elasticity modulus (E) had little on earth earth pressures because Poison’s ratio is the main influential parameter.

Calculation and properties of thermal stress of monolayer film and solution of thermal stress of multilayer infrared antireflection coating by finite element analysis

Erosive wear often occurs on heavy machinery operating under extreme conditions. This research utilizes the Finite Element Analysis (FEA) method with the Cowper-Symonds strain rate model to analyze the erosion behavior of high-Cr cast iron (HCCI) under different impact angles and compare it to other materials of different characteristics, such as 6061-T6 Aluminium, GH4720Li Superalloy, and Stainless Steel 304 Annealed. A single particle erosion model was made for this study. The erodent particle size used is 0.7 mm in diameter, with the target material measuring 1 x 1 x 0.5 mm. The particle velocity is kept constant at 25 m/s. Based on the simulation results, it can be known that HCCI performs the best at every impact angle. Moreover, from the model's cross-section, it's evident that the material's stress concentration aligns with the direction of movement of the erodent particle. Therefore, it can be concluded that these factors, along with others such as contact time, plastic strain, and surface deformation lead to variations in surface mechanics.

Operational characteristics of a miniature loop heat pipe with flat evaporator