Arthur Morris, Stephen Bart, Derek Kane, Gunar Lorenz and Vladimir Rabinovich.: A design flow for. MOEMS, SPIE Photonics East 2000. 2. Gunar Lorenz, Arthur ...
Design and Simulation of MOEMS Gunar Lorenza, Issam Lakkisb 1. INTRODUCTION MOEMS are emerging from the laboratory to provide unparalleled functionality in optical telecommunications applications. While the ultimate speed of these devices is unlikely to compete with solid-state or electro-optic devices, the transparency that can be achieved with MOEMS contributes negligible degradation to optical channels and thus enables long range flexible all-optical networks. Beam steering has been shown to be the optimum approach for scaling optical cross-connect switching to large port counts and MOEMS have proven to be the method of choice for compact implementations of this concept. Other telecommunication applications include smaller switches, variable attenuators, equalizers, modulators, and polarization and dispersion compensators. Applications outside optical communications for MOEMS include scanning, projection, display, printing, sensing, and data storage. In these optical subsystems, the choice of the “right” MOEMS device for a given application is driven by the MOEMS device interaction with the rest of the system. This includes free-space and guided-wave optical elements, MOEMS packaging, opto-electronics, and the control system for the MOEMS. To evaluate these interactions, the designer must be able to simultaneously model all of these areas in sufficient detail to enable tradeoffs to be made without requiring such extensive computation that interactive design is impossible. The environment must also be able to perform more detailed analyses when required to evaluate second order effects and then incorporate these results back into the system-level simulation. This work describes such an integrated design flow and illustrates its value through examples.
2. OUTLINE OF THE DESIGN FLOW A highly capable design system that enables the designer to work both top-down and bottom-up is illustrated in Figure 1. The initial set of MOEMS system requirements is used to select a design and fabrication approach. Choices made at this point could include digital vs. analog control, surface vs. bulk micromachining, actuation method (thermal, electrostatic, magnetic, fluidic, etc.), and range of motion required. An initial system model of the MOEMS component is then built from predefined parametric primitives in a schematic. The system model enables the user to quickly explore a large design space and reduce the amount of finite element analysis needed to create an initial design that considers the device’s interaction with the surrounding system. A first pass accurate simulation is possible in a matter of minutes, enabling design investigation with Sensitivity and Monte Carlo algorithms. Once the simulation is complete to the designer’s satisfaction, a device layout can be generated from the high level description in the context of the chosen process. If the design is simple enough, this may be sufficient to tape out for fabrication. The more likely path involves detailed 3-D PDE (partial differential equations) analysis to perform selective verifications – including finite element (FEM), boundary element (BEM), optical beam propagation and finite difference analyses and make any corrections necessary for interactions not included in the parametric models1. A detailed PDE analysis is usually needed to investigate the stress distribution in the chosen materials or second order effects like plate bending and optical scalar diffraction effects which are neglected in the system models.
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Manager, Libraries and Top-down design methodology, Coventor Senior Corporate Engineer, Coventor
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Entry Point for Bottom-Up Design
Figure 1: MOEMS design flow combining top-down and bottom-up
3. TOP DOWN DESIGN FLOW The top-down design flow evolves from a system model where the system architect makes design tradeoffs and determines the individual component specifications. In a high-level simulation, users work with libraries of individual components with symbols that can be connected and configured to solve most MEMS problems. From this level, the design team moves to higher levels of detail as appropriate. The system modeling approach rests on two component libraries provided for the MOEMS design flow. The first is a parametric model library for the design of mechanical structures and actuators. The second is a Gaussian beam optics model library for capturing the optical interaction with the MEMS structures as well as the interaction of the light with surrounding components and packaging.
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3.1. Parametric electromechanical elements The electromechanical components for the MOEMS design flow are part of Coventor’s electromechanical library (see Figure 2). The electro-mechanical library has been developed to allow rapid creation of 6-DOF (degree of freedom) electromechanical models of micro machined devices such as mirrors2, RF switches, resonators, accelerometers and gyros 3,4.
Electromechanical library Electromechanical components
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Figure 2: Electromechanical components for the MOEMS design
The elements of the electromechanical library provide quite general geometry including rigid and flexible segments for rectangular, triangular and pie shaped geometries. They are fully parametric in material properties and dimensional scaling. A particular emphasis has been placed on the modeling of geometrical properties caused by the manufacturing process such as material stress, stress gradients, stress related surface bending, sidewall angles etc. The influence of manufacturing tolerances, surface stress, stress gradients and the interaction of different system components can be investigated with just one model using the frequency or transient analysis tools of commercial network simulators such as Architect from Coventor. The electrostatically driven torsion mirror on the left hand side of Figure 3 serves as a simple example to illustrate the modeling approach. The corresponding schematic on the right hand side consists of two torsion beams, a rigid plate and two electrodes. Each library component represents the electromechanical behavior of a certain substructure in the device. The substructure’s geometry and position in the common substrate coordinate system are defined via the parameters of the corresponding schematic symbol. On the schematic level, the different symbols are mechanically linked by six wires. The connected mechanical wires refer to a 6 DOF defining of the modeled subcomponent in a common coordinate system. The cross variables (voltages) of the wires refer to the component’s displacement and rotation. The through variables (currents) are interpreted as the corresponding forces and torques. The libraries include underlying code that expresses how the individual components behave when subjected to electrical, mechanical, or other domain stimuli. A high level of accuracy is maintained because the developed code is closely correlated with the differential equations used by FEM and BEM tools. Simulations times are typically orders of magnitude smaller, however, because the simulations run using reduced-order models instead of FEM based or BEM-based partial differential equation models.
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The graph in Figure 4 shows the 0.35 actuation curve for the mirror of Figure FEM/BEM with 1176 elements 3. The mirror’s tilting angle versus 0.3 FEM/BEM with 682 voltage (applied to only one electrode) System Model was determined by an Architect DC 0.25 transfer simulation. For verification a 3D solid model (Figure 3(a)) was built by 0.2 importing the device layout into 0.15 Coventor’s Designer, and two meshes of different densities were constructed. 0.1 Mirror actuation using the two meshes was simulated using CoSolve (a 0.05 coupled FEM/BEM solver). In this example, results of the system level 0 simulations proved to be more accurate 0 100 200 300 400 than those of the FEM/BEM for the Voltage coarse mesh. As seen in Table 1, the Figure 4: Verification of the pull-in rotation angle (node rx) high level simulator greatly reduced the computation time while maintaining high accuracy.
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Table 1: Simulation time comparison (750 MHZ PC with 1G RAM)
Simulation approach FEM/BEM using 682 elements FEM/BEM using 1176 elements ARCHITECT system model
Simulation time for the DC transfer simulation (no contact) 2.5 hours 8 hours < 2 seconds!!!
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3.2. Parametric optical elements The optics library described in Figure 5 includes first-order models that consider ideal optical behavior, with light assumed to propagate as Gaussian beams. Because many systems in telecommunications use lasers and single-mode fibers, Gaussian beam models provide a good approximation.
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Lasers
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Figure 5: Optical components for MOEMS design
The library components model the effect on an impinging Gaussian beam and obtain an outgoing Gaussian beam. Some devices are only sources of optical beams (lasers, fiber outputs, etc.), and others are only sinks for optical power in the beam (detectors, fiber inputs, etc.). The models account for direction changes, polarization changes, astigmatism, (de)focusing effects, clipping and optical losses due to the finite aperture of the component and possible absorption. Unlike ray tracing or physical optics codes, the presented approach enables optical simulation simultaneously with 3-D displacements and rotations providing arbitrary motions in space. The advantage of using Gaussian beam analysis is the fast computational speed in which light is modeled and propagated, allowing for interactive system-level design. The position and orientation of each of the optical elements is completely arbitrary. The dynamic position is set by the same 6 DOF connections used in the electromechanical model libraries. This enables the designer to create complex optical systems including the motion of the MOEMS themselves.
4. OPTICAL CROSS CONNECT DESIGN EXAMPLE
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Two-axis gimbaled mirror array Figure 6: Large Scale Optical Cross Connect Drawing
Both qualitative and quantitative tradeoffs among the system subdomains shall be demonstrated with the following example. Consider an optical cross-connect utilizing twoaxis mirrors for beam steering. One implementation of such a system is shown in Figure 6. This involves detailed design of the MEMS twoaxis mirrors, optical system design, optical packaging and alignment, and control electronics for the mirror movement. We begin with the concept of the circular gimbaled mirror. A system model of the gimbal, the mirror and the electrodes can be quickly constructed using the components of the parametric electromechanical library (see Figure 2). In the system
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model (similar to Figure 3), important design and process parameters such as the mirror radius, the width of suspension beams, beam length, layer thickness, material data etc. are saved globally for easy access and manipulation during the design process. An initial pull-in analysis revealed that pull-in occurs at a mirrorelectrode voltage of 233 volts. The angular rotation at pull-in is 0.2025 rad. The operation voltage is expected to be less than 233 volts for safety reasons. Let’s assume that the operation voltage is 225 volts at which the mirror rotation is 0.15 rad. In order to investigate the sensitivity of the mirror rotation angle at the 225 volts mirror-electrode operation voltage we perform a Sensitivity Analysis, one of the most powerful features of a system simulator like ARCHITECT. Performing the sensitivity analysis for parameter perturbations of 1%, 2%, 3%, 4% and 5% on the design and material parameters yields the graph in Figure 7. Mirror rotational angle vs % perturbation -0.1 0 -0.11 -0.12
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Assuming that a precision of 0.01 radian is needed, the threshold deviations can be summarized Table 2. Table 2: Threshold deviations based on the graph in Figure 7
nominal value mirror_radius mBeamWidth mBeamLength sacrlayer_h mechlayer1_h mechlayer1_E
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6.6 0.024 2.15 3.36 >0.2 >0.08E+11
The width of the mirror beams (parameter name mBeamWidth) is clearly the most sensitive dimension and appears to be most critical design parameter. The mirror beam width must be fabricated to within a tolerance of 0.011 µm in order for mirror rotation (at 225 volts) to be 0.15 ± 0.01 rad. Several such simulations are usually needed to converge towards a robust design that meets all the requirements of the initial system specification. Similar simulations are also used to calculate yield estimations based on fabrication tolerances.
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After completing the verification and the optimization of the electro-mechanical behavior of the mirror system model, a hierarchical symbol for the model is created which enables multiple instantiation of the model as well as varying the dimensions using parameters at the higher level. These electro-mechanical mirrors are then used together with optical and electronic elements to create a schematic of a cross connect system shown in Figure 8(a). The optical beam starts from a laser at the upper left, is focused by a lens, and then reflected by a MEMS mirror. Note the 6-DOF connections between the electromechanical mirror and the optical mirror. Next the large fixed mirror reflects the beam. At this point, we run the same beam information to two different locations in the system. This beam is sampled both by the intended second MEMS mirror for evaluation of channel loss and alignment sensitivity as well as another MEMS mirror for evaluation of crosstalk. Since these mirrors can be placed parametrically anywhere in the MEMS array, the performance of any combination of mirrors can be studied with this simple schematic. In Figure 8 (b), the signal from the intended channel is plotted versus the focal length of the lenses at a sequence of lens positions. These results can be used to minimize the optical loss of the system while simultaneously minimizing the sensitivity to variations. In Figure 8(c), the same signal is plotted as a function of the x-axis actuation voltage at y-axis voltages from 30 to 40 volts. The required mirror electrode voltages for maximum signal are easy to determine and the performance sensitivity to voltage variation can be evaluated.
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Figure 8:(a) Cross Connect System Schematic (a) and Simulation Results (b and c)
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5. BOTTOM-UP DESIGN FLOW The bottom-up approach begins with the available processes and involves detailed layout of the device, either generated from a system model or created with traditional layout tools. The layout and process are used to generate a 3D solid model of the component for visual debugging. This solid model is automatically meshed for PDE simulation (e.g. finite element, boundary element, finite difference, etc.). The main drawback of the bottom-up approach is that initial investigations of these devices to determine basic design parameters usually involve numerically intensive PDE simulations. It is also highly likely that additional simulations are needed to include the effect of systems interactions. 1.
Electro-thermal-mechanical numerical analysis
Detailed numerical analysis of MEMS electro-mechanical behavior is done using CoSolve; a coupling of the boundary element method (BEM) for electrostatics and the finite element method (FEM) for mechanics. This optimal combination of numerical methods provides accurate results with reasonable simulation times. The tools are designed to input design and boundary conditions in a MEMS context, enable easy parametric variations and provide meaningful visualization of the results. Detailed analyses could include various actuation mechanisms, eigen modes, stress distortions, and optical behavior among many others. Examples pertinent to optical devices include surface deformations due to actuation, temperature, and/or material stresses and stress gradients. 2.
Optical numerical analysis
Depending on the problem at hand and the objectives, different types of optical analyses may be required. One of these is the need to examine the diffractive effects SM Fiber of non-uniform surfaces and Fixed Mirror Beam Waist apertures. A scalar diffraction Collimator Plane Mirror Plane 250 um module has been developed for Intensity Collimator Intensity this purpose. It takes a 15mm specified input wave and Centered separation examines the effects of between 10° fixed and clipping and phase shifts movable 50% Offset optics caused by MOEMS surfaces. An example of this is shown in 100% Offset Figure 9, where clipping of a Two-axis mirror – 420um dia Gaussian beam by a circular mirror is examined for three -25 dB 0 dB -50 dB offsets of the beam center relative to the mirror center. Figure 9: Diffractive effects of beam clipping by finite mirror size and beam offsets. Note the sharp fringes that are present in the aligned case while the misaligned case generates a secondary peak along with a general increase in the wide-angle energy but without the sharp fringes. This is due to the phase curvature of the incident Gaussian beam at the mirror surface. Other general optical simulation needs could include ray-tracing, free-space and guided-wave beam propagation, and full-wave electromagnetics. Our approach to providing these capabilities is to create links to several of the most capable optical simulation tools on the market. Other specialized needs could include the general treatment of diffraction gratings and thin-film coatings for filters, mirrors, and anti-reflection coatings.
6. DESIGN EXAMPLE GRATING-LIGHT-VALVE PIXEL The Grating Light Valve (GLV) technology is suitable for a wide variety of imaging applications, ranging from front or rear projection systems, to portable communication devices, printers and optical fiber communications. GLV technology offers high operation speed, reliability, and low cost at production
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volumes. GLV arrays were designed by Silicon Light Machines (acquired by Cypress) in 1992 and fabricated using MEMS fabrication technology. In 2000, Sony took an exclusive license to develop, manufacture and market display devices and products based on this technology. 1
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Grating Light Valve technology is based on 3 4 representing the on and off states of a pixel by 5 6 diffractive interference patterns of two configurations of a phase grating. A typical GLV pixel is made up of an even number of parallel doubly supported beams, Figure 10: GLV pixel as shown in Figure 10 A typical design for a 25µ pixel consists of six beams (each 3µ wide, 100µ long, and 0.1µ thick) suspended above a thin air gap (typically about 650 nm), allowing them to move vertically relative to the plane of the surface. Each of the active (2nd, 4th, and 6th beams, from left to right) is actuated by an electrode situated below it on the substrate. In their unactuated (or unaddressed) state, these “active” beams assume a straight line, forming a flat surface between the two anchored ends. Let’s call the 1st, 3rd, and 5th beam the “inactive” beams referring to the fact that no electrode is directly situated under any of these beams. To address a pixel, a potential difference is applied between the beams and the electrodes. The electrostatic force deflects each of the active beams towards the electrode below it as depicted in Figure 11. Control of the vertical displacement of the beam can be achieved by balancing this electrostatic attraction against the restoring force of the beam. The dependence of the electrostatic force on the inverse of Figure 11: GLV pixel operation the square of the air gap allows for large accelerations to be achieved. This, in addition to achieving large restoring accelerations by having a very strong tensile restoring force designed into the beams, produces an extremely fast switching speed (20 ns). In the unaddressed state, the surfaces of the beams collectively function as a mirror. When a GLV pixel is addressed, alternate beams are deflected and their surfaces function as a square-well diffraction (phase) grating. This grating introduces phase offsets between the wave fronts of light reflected off active and inactive beams at angles θ, where æ mλ ö (1) θ m = arcsinç ÷ è Λ ø where Λ is the period between deflected beams and m is the order of diffraction. The diffracted intensity achieves it maximum Imax when the grating depth δ is equal to a quarter of the wavelength of the incident light, i.e. δ = λ/4. The dependence of the 1st order diffraction lobes on the grating depth δ is æ 2πδ ö I1 = I max sin 2 ç (2) ÷ è λ ø By varying the drive voltage applied—and thus the grating depth—at each pixel, one can achieve analog control over the proportion of light that is reflected or diffracted. By blocking reflected light and collecting diffracted light, contrast ratios up to up to 1,000:1 can be achieved. Note that the gaps between beams degrade optical efficiency.
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Analysis of a Red Pixel Design using CoventorWare
We consider the pixel configuration shown in Figure 12.
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Electrostatic actuation
We employ CoSolve to simulate electrostatic actuation of the “active beams” (2nd, 4th, and 6th from left). The objective is to get the electrode voltage-beam deflection relationship. We are specifically interested in the voltage that deflects the actuated beams a distance one quarter of the wavelength below the unactuated beams. Due to the fact that the central parts of the beams (comprising the mirror) do not stay planar upon deflection, the average relative deflection of the actuated beams is expected to be slightly less than that of the beam center. The maximum (center) deflection δmax and average deflection δave are plotted in Figure 13 versus the voltage. The average deflection is obtained from equation (2), where the intensity ratio I1/Imax was numerically measured at the center of the first diffraction lobe using the optics simulation results discussed next. Diffraction of a plane wave
In the optics part of the analysis, we use MemOptics to simulate the reflection and diffraction of a plane wave from the actuated pixel configuration. The light source is a plane wave of wavelength λ = 0.64µ (red light) and is situated on the z-axis of the mirror at z = 1000µ. The actuated pixel geometries for different actuation voltages obtained from CoSolve are used as input to the optics solver. The detection screen, located at z = 1000µ, has the dimensions Length_X=1000 µ and Length_Y=100 µ (the detection screen is selected to have a large x-dimension because diffraction effects due to the pixel configuration of beams along the y-coordinate would be
Maximum Deflection versus Voltage 0.35 Maximum deflection Average deflection
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prominent along the x-coordinate.) According to equation (1), we expect the wave fronts of light to be reflected off the grating at angles θ1 = arcsin(λ/Λ) = 3.938 degrees. The separation between the detection screen and the pixel is ∆Z = Z(DS) – Z(mirror) = 1000 – 1.86 = 998.14µ. Thus, the position of the first order diffraction lobe on the detection screen is X1st lobe = ∆z tan θ1=68.7µ. The positions of the second to sixth order diffraction lobes are respectively 138.4, 210.2, 285.2, 365, 451.5, and 547.3. Figure 14 shows the intensity distribution on the detection screen for voltage values of 0, 0.5 and 1 volt. The vertical lines mark positions of the first to sixth lobes obtained according to equation (1). The top picture corresponds to diffraction due to a square mirror of size W = Lpixel = 6w + 5s = 27.46µ. The impact of the beam separation s may be observed by comparing between top two images in Figure 14. Square mirror
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X1 X6 X5 X4 X3 X2 Figure 14: Intensity distributions on the DS for (a) square mirror and (b) actuated pixel for voltage values of 0, 0.5 and 1. X1, X2, …, X6 are the positions of the first to sixth diffraction lobes.
The pixel design tested differs from the SLM design in two major ways. First, in our test configuration, the beams are made up of Aluminum, whereas in the SLM design, they are made of Silicon Nitride. Silicon Nitride has larger tensile strength and is more durable. Second, the SLM subjected the beams to pre-stress,
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1.2 1.0 I/Imax at x=-66.25
Figure 15 shows the normalized intensity I/Imax at the center of the first lobe plotted against the actuation voltage. The empty symbols correspond to solutions obtained from equation (2) where δ is the maximum deflection numerically measured in the electrostatic simulation.
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7. CONCLUSIONS We have presented a comprehensive capability for the design and analysis of optical MEMS systems. Our new top-down approach starts with system requirements and uses parametric elements for initial design entry and experimentation. Optical, electronic, and mechanical aspects of the systems can be simulated simultaneously, enabling true system level design of applications incorporating optical MEMS. This provides rapid evaluation of the system performance and reserves intense numerical analyses for evaluating second order effects and couplings in a bottom-up verification/design centering step. Comprehensive FEM
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and BEM analysis capabilities are available for these evaluations and can also be exercised to extract precise behavioral models for final inclusion in system simulations.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
Arthur Morris, Stephen Bart, Derek Kane, Gunar Lorenz and Vladimir Rabinovich.: A design flow for MOEMS, SPIE Photonics East 2000 Gunar Lorenz, Arthur Morris, Issam Lakkis; A top-down flow for MOEMS, DTIP 2001 Teegarden, D.; Lorenz, G. and Neul, R.: How to model and simulate microgyroscope systems. IEEE Spectrum, July 1998, pp. 66-75. Reinhard Neul, Gunar Lorenz and Stefan Dickmann: Modelling and Simulation of Micro Electromechanical Sensor Systems, Proceedings of the VDE World Microtechnologies Congress MICRO.tec 2000 September 25th - 27th, 2000, Hannover, Germany, Volume 2, pp. 67 - 72. Lorenz, G.: Netzwerksimulation mikromechanischer Systeme. Dissertation, Universität Bremen, Shaker Verlag, 1999. Lorenz, G.; Neul, R.: Network-Type Modeling of Micromachined Sensor Systems. Proc. Int. Conf. on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, MSM98, Santa Clara, April 1998, pp. 233-238. Coventor, http://www.coventor.com Kurzweg, et al., Proceedings of Modeling and Simulation of Microsystems, 768-773, June 2000. Walker and Nagel, “Optics & MEMS,” Naval Research Lab, NRL/MR/6336—99-7975.
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