chapter 10 moems mems cad and simulation

Chapter 10

MOEMS/MEMS CAD AND

SIMULATION

Ridha Hamza, Jean Michel Karam, Philippe Nachtergaele

10.1 Introduction

The design of optical systems involves the interdisciplinary efforts of a team, andhence a computer-aided design (CAD) system must be integrated, yet flexibleenough to be able to be used by optical engineers, mechanical engineers,electrical engineers, etc. The creation of a typical optical system involves the sim-ultaneous design and optimization of new microelectromechanical system(MEMS) processes, actuators, optical components, electronics, and packaging.The CAD system must encompass all of these design activities. Micro-optoelectromechanical systems (MOEMS) design is still the domain of experts,handcrafting the overall system using detailed knowledge. CAD tools can beused to promote information sharing between design teams working on differentaspects of a complex MOEMS design. The domain experts must communicateand cooperate, and CAD, can help them perform this task. In addition, MOEMSdesign involves innovations at the process and device level as well as in system-level architectures, implying that a top-down design flow is often not possible.Rather than the top-down approach, MEMS design is more like a spiral wherethe partitioning of requirements between ease of electronics design, optical per-formance, and mechanical constraints must often be iterated. The design flowfor realizing optical MEMS systems is often unique to a given organization. TheCAD tool suites must be able to support many different design flows.MOEMS designs are often based on custom processes, materials, and device

types. Hence, the library-based designs of the very large scale integration (VLSI)world, where system designers can use the results of precharacterized cells basedon standard processes, are not available today. MEMS are three-dimensional (3D)structures and must be analyzed and visualized in 3D. The detailed physics must besimulated with high-fidelity 3D computations solving a coupled set of physical

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constitutive equations in several energy domains. Yet, structures consisting ofseveral MEMS components must be simulated, along with packaging effects. Sosystem simulations using approximate, high-level models must be provided.CAD for MOEMS must then span the gamut from full-wave optical simulationto behavioral simulation.The needs of MOEMS designers depend on the kind of device they design and

the technology they have developed. Models and simulation tools depend on thedimensions of the devices to be built, on the optical phenomena to take intoaccount and the actuation mechanisms, and on the degree of accuracy that isneeded for the simulations. Designers want tools in order to predict performanceand operating range, to optimize devices with respect to process parameters,device dimensions, and manufacturability constraints, and to understand behaviorwith respect to operating conditions. They also need to explore failure mechanismsand to understand the effect of device failure on system performance, includingtime-dependent device degradation. They need material databases that are relevantto the materials used in MOEMS.Design tools must capture the designer’s intent and provide links to manufactur-

ing. Mask layout tools are needed to draw masks. Optical computations are neededin 3D, and different and more computation-intensive tools are needed, dependingon the wavelength assumptions made. System-level tools include simulation ofpackaging, electronics, and optical components, as well as MEMS actuators. Ver-ification tools are needed to ensure that the designed structure matches thedesigner’s intention and that the design is manufacturable. Design rule checkersverify that the mask designs comply with manufacturing rules for spacing andwidth of structures.It is important that simulation models be hierarchical, scalable, parametric,

composable, Q1and consistent. Results at one level of simulation should not bemerely shifted from those at a lower level. Models must be functions ofperformance, fabrication process parameters, and device dimensions that aredetermined only statistically. Devices models and simulation results beaccompanied by some idea of their accuracy. The tools should support alsopopular formats such as those used by mask vendors. The tools should be inter-operable and compatible with other tools. For example, the same 3D modelformat should be able to be used for optical solving and electromechanicalsimulation.There also need to be links and information sharing between the tools used by

the system engineer and by the component engineer. Information must be trans-ferred from the physical design environment to the system design environment.The system engineer uses tools for schematic capture, simulation, layout,design-rule checking, and cross-section viewing. The component engineer usesfinite-element modeling (FEM) and process simulation. These results may betranslated to a behavioral model to enable validation of full system functionality,and libraries at various levels that are tied to the schematic driven layout feature ofthe system engineer.1 Unfortunately, there is no single CAD system incorporatingall elements needed for MOEMS design.

474 Ridha Hamza, Jean Michel Karam, Philippe Nachtergaele

10.2 3D device simulation

10.2.1 Introduction

As described before, MOEMS devices must be analyzed and visualized in 3D toensure design validation. The detailed physics must be simulated with high-fidelity3D computations solving a coupled set of physical constitutive equations in severalenergy domains. The starting point for these simulations is the geometrical masklayers, fabrication process descriptions, material properties, and boundary con-ditions. Process modeling can produce geometry in a 3D description. CAD toolscan also enable the automatic creation of 3D models from a simplified fabricationprocess definition and two-dimensional (2D) masks. This method is faster compu-tationally than process modeling, but less accurate. The 3D model is then visual-ized, and used for visual verification, meshing, and 3D simulations. Many CADtools have been developed to automate the preparation and performance of thesesimulations.2–12 The next sections will provide a more detailed understandingof these processes of 3D analysis and design.

10.2.2 Process simulation

As described before, much of the innovation in MOEMS comes from the noveldesign of the fabrication process for creating the optical structures. CAD toolsmust be provided to simulate the effect of different processing steps. Before thecreation of MEMS-specific process simulation, some process tools were availablefrom the integrated circuit (IC) industry and used to simulate semiconductor pro-cessing.13–16 Modeling programs that were used for studying the structuralreliability of thin films were also used. Process steps such as lithography, depo-sition of thin films, various types of etching, oxidation, and other chemicalreactions, planarization, and diffusion need to be simulated for the design ofMOEMS structures. Process modeling solvers use finite-element or finite-difference techniques to solve the semiconductor transport equations. The simu-lations are parameterized by process variables such as temperature, pressure,etch rates, and doping, and the inputs are the 2D layouts representing themask’s geometries. The outputs are 3D material shapes and material properties.Since MEMS are inherently 3D devices, visualizing with high quality models is

important to understanding the device and checking the fabrication processes.Dynamic simulation of the as-processed device can also be important, forMEMS are moving structures as well. Dynamic simulation is important to checkfor collision avoidance and ensure clearance for the moving structures. The 3Dprocess simulation can then be passed to solid modeling, meshing, and finite-element or boundary-element method (BEM) simulations. In addition to thegeometries, process simulation provides information about material propertiesand the device initial state, which is also needed for device performance

MOEMS/MEMS CAD and Simulation 475

simulation. Properties such as the initial stress state, surface conditions, chemicalcompositions, and material structure can be calculated.Orientation-dependent etching occurs when wet etchants attack a silicon

substrate. The etch rate depends on the wafer’s orientation and material type.An important problem for designers is to predict the behavior of the etch rate atconvex corners where underetching occurs. Designers often must adjust themask design to achieve the needed 3D profile. Many simulators calculate accurate1D or 2D profiles, but only a few 3D simulators exist.17–20 Figure 10.1 shows twoexamples of etching simulations—a 2D interpretation of the etching wavefrontsuperimposed on the 2D layout geometry, and a 3D description.18 The etchingprofiles are calculated from the chemical mixture ratio, its etching diagram, theetch time, and the etched structure material composition.A currently unsolved problem is to determine the mask necessary to produce a

given shape. Researchers19 have applied genetic algorithms to try to synthesize amask for a given 3D shape. Other approaches are repeated characterization embo-died as simple formulas. For example, the design of the membrane for pressuresensors has been well studied through repeated trial and error. The results aremade available in spreadsheets and simple formulas.Several CAD tools create 3D descriptions from mask layouts and a simplified

process description.3,10,23,24 Here the process is not simulated, but emulated forreasons of speed. The geometrical effects of a process step are used to create a3D solid representation of the as-processed material. So, for example, an oxidedeposition will be characterized by a thickness as opposed to process variablessuch as temperature and pressure of the deposition. Typically a viewer is providedfor arbitrary 3D transformations and cross-sectioning. Figure 10.2 shows a typicalgeometrical characterization for a typical process step. These geometrical tech-niques lack the detail to capture many important process artifacts, but they arecomputationally fast enough to allow mask changes to be quickly transformed to

Figure 10.1: 2D21 and 3D22 etching tools.


3D models for simulation and viewing. Simulation errors will result, since the gen-erated model may not capture some effects such as scalloped edges in deep reac-tive ion etching (DRIE) nonhomogeneous sputtering, voids, chamfered edges,curved surfaces, and nonvertical edges.12 Another approach is based on creatinghigh-fidelity geometric models of MEMS using finite-element techniques.25

Unfortunately, even process-simulation-based models assume ideal physics,which is computationally complex in itself.After generation of the 3D model for viewing, defeaturing of the model is often

done to simplify the geometries for meshing and simulation. Corners may berounded, details that are unimportant may be removed, etc. Often, many simu-lation points must be calculated where the model geometry has detail, so simpli-fying the model may save computation time at the expense of solution accuracy.The allowed simplifications will vary with the physics to be calculated. Forexample, detail not needed for a capacitance calculation may be critical for astress computation. Care and experience are needed to determine the optimumapproach.

10.2.3 FEM and BEM simulation

10.2.3.1 Introduction

MOEMS design usually involves some type of actuation. Normally, the actuator isdesigned separately and then the system interactions are analyzed. MOEMS mayuse any of many physical principles for actuation, and coupled physics must besimulated, as multiple energy domains are involved in the actuation. Types ofactuators include electrostatic (comb drives and beams), bimetallic, magnetic,piezoelectric, bimorphs, and motors. A complete review of actuators is given inChapter 4. Mirrors may have flexures and hinges whose mechanical propertiesneed evaluation. Mirrors need also to be modeled for properties such as flatness,tilt, and stresses during their deformation. The output of a MOEMS CAD toolsimulating the coupled physics of micromirrors can be the input into an opticalsimulation program that provides the optical system performance of the wholeMOEMS micromirror. The outputs can also be used to design the electronicsand electrodes for the mirror’s movement control and actuations.

Figure 10.2: Example of the geometric representation of a typical process step.21


All of these simulations are done in 3D, using discretization methods such asfinite elements or boundary elements or both, which simulate coupling and conser-vation laws. High-fidelity simulations need to be done because of the complexshapes used in MEMS and MOEMS devices. Simple analytical formulas oftendo not work for these cases. As a start, mechanical CAD tools used for thedesign of macroscopic structures have been adapted for MEMS. Simulations ofmicrosystems with high surface-to-volume ratios and thin layers often requiretweaks to mechanical CAD programs. For electrostructural problems, the finite-element technique is used to solve the structural problem, and the boundary-element technique is usually used for the electrostatic domain. Boundary elementsare preferred for electrostatic solving because the air volume does not need to bemeshed, requiring less memory. Multiphysics solvers are available from industryand academia.2–10,12,26–28 For the moment, two of the limitations on our ability tomodel microsystems are that we do not understand the underlying physics and thatwe do not have the tools to measure test structures with enough resolution tocharacterize them for simulation.

10.2.3.2 FEM simulation

Most of the calculations of interest in 3D for predicting the response of MOEMSstructures involve the computation of a field and its spatial derivative or potential.These fields are usually described with differential equations and then transformedby the finite-element method into algebraic ones. The modeling process starts byoperating on a geometric model of the device, which is subdivided or meshed intosmaller, simple shaped pieces called elements, which are connected at nodes. Foreach element, the physical equations are written for that simple shape and approxi-mated using a Rayleigh or Ritz approximation. The equations are formulated sothat energy is conserved. This is done by minimizing the expression for theenergy function. The minimum is described by setting the derivative of theenergy function with respect to the potential equal to zero, as the minimum haszero slope. Normally, a very simple variation of the potential is assumed, sothat simple equations are solved. The functions of the potential assumed foreach element are called shape functions. These shape functions are generallylow-order polynomials. The higher the order of the polynomial, the more accuratethe solution is for each element.The number of elements is chosen to achieve sufficient accuracy. Adaptive tech-

niques are used to refine the solution if the number of elements chosen is notenough for a given solution accuracy. Depending on the physics represented,a number of unknowns are used for representing the potential’s degrees offreedom. For example, in a mechanical problem, six positional degrees offreedom may be used—three displacements and three rotations. Each element’sequations are represented by a matrix of order equal to the number of unknownsfor the element. The total solution to the field problem is performed by assemblingthe matrices for each element. Next, the material behavior and the boundaryconditions are applied to each element, and constraints are applied. Boundary


conditions can be placed on volumes or surfaces or at points. Hence, they areapplied to the nodes or within the elements. Constraints can be given for someor all of the degrees of freedom. Finally, the matrix equation is solved.A number of analyses can be performed on an FEMmodel. If time variation is to

be described, a general equation is used:

MN½ �d2

dt2XNf g þ DN½ �

d

dtXNf g þ KN½ � XNf g ¼ FNf g,

where

. MN , DN , KN are square N � N matrices, usually referred to as the mass,damping, and stiffness matrices;

. XN is the vector containing the degrees of freedom describing the FEMmodel;

. FN is the load vector applied to the device.

The damping matrix results from motion through a fluid such as air. For MOEMSdevice analysis, calculation of damping is very important, as it affects the accuracyof the calculation of the speed of operation and the quality factor for the response.A transient analysis can be performed in which a numerical time integration

algorithm is used to step forward through time. As a special case, if the input isa sine wave, harmonic analysis may be done if the system is linear. A modal analy-sis is done to calculate the natural frequencies and mode shapes of the system.These model shapes can be used to formulate an efficient transient analysis algor-ithm. In a modal transient analysis, instead of using the potentials as unknowns, thesolution is written in terms of the natural frequencies of the system. First, a suffi-cient number of natural frequencies are calculated. Then, the equations of motionare recast to be a sum of contributions from each natural frequency and solved.This method is much faster than a direct transient analysis.Many of the analyses needed for MOEMS require solution for one or more phys-

ical behaviors at the same time. Some of the elements can conveniently be writtento describe multiple physical equations. For coupled electrostatic-mechanicalproblems, however, this method usually is not efficient and the meshes are notthe same. In this case, the solutions to each physical problem may be calculatedseparately and iterated. Typically, an electrostatic simulation is solved, and thesolved electrostatic gradient is used as an input to calculate a mechanical solutionincluding displacements. The new displacement is then input to a new electrostaticsolution, and solutions are iterated until convergence.12

A variety of special-purpose analysis techniques are used with the FEM forMOEMS devices. One such technique is used to calculate contact forces asdevices come together. Another allows the computation of damping parameters.The arbitrary Lagrangian Eulerian (ALE) formulation allows the modeling ofmoving structures. Both lift and drag forces can be computed. Equivalentreduced-order resistance and damping terms can be extracted.29 Figure 10.3shows the mesh and resulting fluid field computation for a moving electrostaticallyactuated micromirror. The mirror is modeled as a plate suspended in a fluid.


10.2.3.3 BEM analysis

In contrast to the finite element method, the boundary-element method uses a meshonly on the boundary of a problem domain, as shown in Fig. 10.4. It uses a surfacemesh instead of a volume mesh for 3D problems. It is based on the idea offormulating the solution equations by applying a load at node j and observingthe effect at node i to form a set of influence coefficients Hij and Gij .

31 Given aset of point boundary conditions u and slope boundary conditions q, the methodsolves the formulation:32

H � u ¼ G � q:

The BEM calculates very accurate solutions to partial differential equations(PDEs). There are three sources of error in these calculations: numerical inte-gration inaccuracy, geometric modeling inaccuracy, and mesh discretization inac-curacy.12 The boundary-element and finite-element methods are practical only forsmall problems. MOEMS devices usually require large numbers of elements for anaccurate solution. Hence a method must be used to reduce the problem size. An

Figure 10.3: Mesh and fluid field for a moving micromirror.30

Figure 10.4: BEM geometrical description.32


elegant solution was developed for the BEM by considering that nodes far from agiven node do not contribute as much to the solution as nodes that are close to it.Since the method proceeds by summing the elements’ contributions, at a suffi-ciently large distance the interaction of a group of nodes can be represented bytheir average contribution. This concept is illustrated in Fig. 10.5.If the BEM formulation is subdivided in this way, the new formulation

becomes:32

Hnear þ Hfarð Þu ¼ Gnear þ Gfarð Þq:

If the average contributions are used, then the system reduces to:32

HnearuþMu ¼ GnearqþMq

where Mu and Mq represent the far-field contributions to the solution.

10.2.3.4 Comparison of FEM and BEM

The boundary-element method and finite-element method can both be used for avariety of 3D simulation problems. As described previously, typically BEM isused for electrostatics and FEM for mechanical problems. Coupled solutions canuse both, utilizing independent meshes and solvers, whose solutions are iterated.Figure 10.6 shows a comparison between FEM and BEM methods.

Figure 10.5: Near-field and far-field interactions in a BEM calculation.32


10.2.3.5 Meshing

In order to perform finite-element analysis, the MEMS structure is discretized ormeshed in an appropriate form for the type of analysis to be performed. Both2D and 3D meshing must be supported. In a simple case, a 2D mesh may beswept to produce a volume mesh. The geometry to be meshed may be automati-cally created from the solid modeling tool from mask geometry and a fabricationprocess description as described earlier. Automated meshing can be used in somecases, and the mesh can usually be refined automatically and locally to meet errorestimates. Normally, the mesher will use more finite elements where the geometryis complex. In an automatic mesh refinement, an initial mesh is created and solved,and then the results are examined with respect to error criteria. If the mesh needs to

Figure 10.6:

Q1

Comparison of BEM and FEM.32


be refined, the size of elements can be reduced or the shape function orders can beincreased,12 and the process iterated either locally or globally. As the structuremoves, the mesh must be updated, and local algorithms may be used to updatethe mesh locally if possible. Because surface-micromachined MEMS mayconsist of very thin layers, the meshing techniques that were used for more sym-metric volumes are not efficient. New techniques must be applied.33

10.2.4 Noncontinuum methods

Non continuummethods are needed to address the calculation of physical phenom-ena for MOEMS on even a smaller scale than that handled with FEM and BEM.These methods must be used when the scale of the phenomena being studied isof order of the characteristic device length. Researchers have started the develop-ment ofMonte Carlo techniques to treat gasdynamic damping and thermal transportin the noncontinuum limit.34 Because of the small scale and large surface-to-volume ratio of MOEMS devices, new methods must be used to create volume-averaged properties from spatially varying ones. Large surface-to-volume ratiosalso increase the dominance of surface forces, making the evaluation of suchsurface phenomena as adhesion, stiction, friction, surface tension, and surface elec-trostatic charges very important for MOEMS devices. Some of the physics to beexplored must be done by simulations of atomic- and molecular-scale processes.For example, molecular dynamics is used to study the behavior of self-assemblingmonolayers that are used as coatings on MEMS surfaces to reduce stiction.

10.3 Actuator design and simulation

10.3.1 Introduction

ForMOEMS applications, it is important to have an actuator that can be driven withstandard electronics. However, the actuator must be robust and be able to produceenough force to move the optical component, and hencemany of the earlyMOEMSdevices were driven by high-voltage electronics. It is also sometimes desirable tohave a greater force in one direction than in the other—for example, a differencefor opening and closing a contact or switch. Another important consideration isthe size of the actuator, as arrays of optical devices may require that the actuatorsmatch the pitch of the array. In this section, we will discuss the principles of FEMand CAD simulation for design of two major actuators. To gain more knowledge inMOEM actuator design and performance, readers should refer to Chapter 4.

10.3.2 Simulation of thermal actuators

An important actuator used in MOEMS is the thermal actuator.35–37 An examplethermal actuator that is made from polysilicon is shown in Fig. 10.7. This actuator


consists of two arms, one thick and one thin, connected to electrical pads. Thethermal actuator works on the basis of a differential thermal expansion betweenthe thin and the thick arm. The structure is usually pinned at one point and operatesas a lever. As heat is introduced, the thermal actuation force overcomes internalspring forces. As the system cools, the return force eventually equals theapplied force due to heating plus the internal spring force. The temperatureincrease adds kinetic energy to the system, and the material expansion providesforce and displacement. Thermal actuators can be made of two different materialsor have different arm geometries (a bimorph) or both.35 Arrays of thermal actua-tors can be made and have been used to move optical components.A potential difference applied across the electrical connection pads induces a

current to flow through the two arms. The current flow through the resistance ofthe polysilicon produces Joule heating in the arm. The current in the thin arm isgreater than the current in the thick arm because it is thinner and hence more resis-tive. The thin arm heats up more than the thick arm, which causes the actuator tobend towards the thick arm. The maximum deflection occurs at the tip. The amountof tip deflection is a direct function of the applied potential difference.A coupled-field multiphysics analysis is required to simultaneously solve for the

coupling between the thermal, electric, and structural fields. FEM analysis can beused to compute the arm tip deflection for an applied potential difference across theelectrical connection pads. Temperature, voltage, and displacement can be calcu-lated in 3D, and the current and heat flow can also be calculated. Figure 10.8 showsa plot from FEM analyses results for the displacement of the thermal actuator for a5-V difference in potential across the device.2

Figure 10.7: Polysilicon thermal actuator example.21


Thermal actuation has the advantage that it gives a large force per unit area com-pared to electrostatic Q3actuation and has a linear response. Disadvantages include itshigh power consumption and that its speed of operation is limited by the time ittakes to cool the actuator, so that thermal actuators can be quite slow. There hasbeen some work using FEM techniques to optimize the geometry of thermal actua-tors by figuring out exactly how material should be added or removed to create theoptimal deflection.38

10.3.3 Simulation of electrostatic actuators

For electrostatic actuators a voltage control is used to convert electrostatic energyinto mechanical motion. In the simplest actuator, parallel plate electrodes are used.An example of such a device is shown in Fig. 10.9. The electrostatic actuation canbe used in an analog sense to move mirrors into a variety of positions, or in adigital sense to move the mirror to one of several fixed positions. An exampleof the digital method of actuation is the Texas Instruments micromirror, theDMD.39 In a DMD, two landing pads are used, and the mirror electrodes arebiased to attract the mirror to either pad, depending on the tilt angle required forthe mirror (see Chapter 8 for details).A more complex actuator is the scratch drive, where an array of electrostatically

actuated plates crawls in a horizontal direction. Another important electrostaticactuator is the comb drive, shown in Figure 10.10. Here, two electrodes are

Figure 10.8: Thermal actuator analysis results from FEM.2


formed from an overlapping array of fingers. As a voltage difference is applied tothe two electrodes, the extent of the fingers’ overlaps changes. The device ismodeled as a set of variable capacitors. An advantage of the comb drive is thatthe capacitance changes as a linear function of the overlap, whereas in the parallelplate actuator, the capacitance is nonlinear in the moving-plate distance.A typical calculation of interest for an electrostatic actuator is the motion pro-

duced versus the voltage applied. For this type of actuator, this computationinvolves the calculation of force and capacitance. For a parallel plate actuator,when the plates are far apart and the plates begin to move together with anapplied electrostatic force, this force is balanced by the spring force of thematerial. At some plate distance, the electrostatic force overwhelms the springforce and the plates snap together. This point is usually referred to as the pull-inpoint and is an important parameter to be calculated. Numerically, it is hard toevaluate, because the electrostatic force becomes large. Designers use FEM andBEM software to calculate this parameter and other important parameters of theactuator; as noted, BEM is often the preferred method.

Figure 10.9: Example of an electrostatically actuated optical device from Silicon Light

Machines.40

Figure 10.10: SEM of a comb-drive actuator.


Electrostatic actuators are in general faster than thermal actuators. In addition tothe deflection and force, the designer needs to look at the resonant frequency anddamping of the actuator. If an actuator is going to be used for an optical communi-cation system, switching time is also important. Calculations of stress and strain onthe actuator may also be needed. To create a system model for the device so thatthe actuator can be simulated with electronics, calculation of the capacitance isneeded. Figure 10.11 depicts an example of a series of coupled simulation stepsof the Texas Instruments micromirror.12 The electrostatically driven actuatorrequires a coupled electrostatic-mechanical simulation. As described previously,this computation requires that simulations must be iterated to converge to afixed point. The figure shows the stages and computations required.

10.4 Optical solvers

10.4.1 Introduction

As with a standard optical design, the design of a MOEMS device involves choos-ing the device dimensions and the optical characteristics of the materials fromwhich it is fabricated to achieve the required optical performance. There are no

Figure 10.11: Coupled simulation results for the TI micromirror.12


general optical solvers available that can handle all the types of simulationsneeded. The solver used depends on the approximation made for the behavior ofthe optical signal, the type and materials of the structure, and the device dimen-sions. Many classical optical solvers are not designed to handle the device struc-tures and materials used in MOEMS. When the dimensions of the structure areclose to the wavelength and/or diffraction effects cannot be neglected, it is necess-ary to simulate the propagation of the electromagnetic field on a micro scale. Forsome MOEMS systems, a simplified approach using classical optics can be used.This approach works well for devices where the wavelength in the optical spec-trum is still short compared to the lateral dimensions of the MEMS device. ForMOEMS devices of size 10–100 mm, sometimes diffraction effects are negligible.For other devices, this is not the case. MOEMS-specific CAD tool suites are justnow beginning to incorporate the optical solvers from the optical world into trueMOEMS tools.

10.4.2 Propagation phenomena

In a free-space optical system such as an optical switching system, opticalelements modify the propagation of the light beam by reflection, transmission,and refraction. The light beam passes through lenses, is reflected by mirrors,and may be divided by beamsplitters, in free space during travel between inputfiber and output fiber. The wavelength varies from visible to IR. For some ofthe computations for IR free-space propagation, diffraction effects can be neg-lected and the theory of Gaussian optics can be used. Propagations in guided-wave structures such as a waveguide, fiber optics, or resonant cavities usuallyrequire simulation at a finer scale. Fine-scale simulations are used when the dimen-sions of the devices are close to the wavelength used or when the material iscomplex, such as a photonic crystal. Fine-scale simulation is needed forexample in devices such as a waveguide coupler, a Fabry-Perot cavity in atunable filter, a vertically oriented surface cavity lasers (VCSEL), or a variableoptical attenuator (VOA).

10.4.3 Optical theories

In geometrical optics, the propagation of an optical beam is based on geometricalrules and can be used only to study the propagation of light into macroscopicsystems. In Gaussian optics, the power of the beam spot has a Gaussian profile,and the propagation of a light beam through an optical element is given by amatrix operation. Both theories enable fast calculation, but they are limited inthat they do not take into account the propagation of light on a micron scale.Scalar theory is used when dimensions of elements are about 10 to 100 timeslarger than the wavelength and is based on the Helmholtz equation, where assump-tions are made on the direction of propagation. In vectorial theory, Maxwell’s


equations are solved directly and no assumptions are made. Maxwell’s equationsare used when dimensions are very close to the wavelength.

10.4.4 Mathematical techniques and approximations

No single simulator has been written to handle all optical phenomena, and anumber of different numerical techniques are used. Figure 10.12 shows a hierarchyof approximations used in optical modeling.41

Scalar diffraction solutions make the assumptions that the diffracting structuresare large compared with the wavelength of the light and that the observation pointis reasonably far from the diffracting structure. The Fraunhofer technique is validwhen the light at the observation point can be assumed to be a plane wave. Thisassumption is valid in the far field, where the light has propagated to a distancefar from the aperture, and the diffraction pattern looks like that calculated at infin-ity. Quick simulations can be done with the fast Fourier transform (FFT). TheFresnel approximation uses a spherical wave model and is valid in the near andfar field. The wavefront must be explicitly integrated. Because of the wavelengthsused and the dimensions of optical MEMS structures, Fresnel and Fraunhoferapproximations are usually not precise enough to model diffraction effects thatappear in free-space optical MEMS systems.The Rayleigh-Sommerfeld and Fresnel-Kirchoff formulations provide more rig-

orous analyses of diffractive effects, because they explicitly integrate the complexwavefront. Unlike the Fresnel-Kirchoff formulation, the Rayleigh-Sommerfeld islimited to planar components. These formulations also share the limitation thatthe propagation distance should be greater than the wavelength of the light. TheRayleigh-Sommerfeld formulation has been implemented to model the propa-gation of the light in a free-space 2D optical switch.41 Full-wave solutions, thoughthe most accurate are computationally very complex and hence are avoided whenpossible because they lead to extreme simulation times.

Figure 10.12: Hierarchy of validity of approximations used for optical modeling based on

distance from the source.42


10.4.5 Codes

The beam propagation method (BPM) is based on Helmholtz’s equation, for whichassumptions on the direction of propagation are made and polarization effects areneglected. Its input data are the real or complex-valued refraction index distri-bution, an input field distribution, and the wavelength of the light. The techniquepropagates the field distribution through a series of time steps. Only paraxialpropagation can be studied. For a 2D model, polarization, anisotropic and non-linear effects are not taken into account. This model is much faster than morecomplicated methods like finite-time-difference techniques, and the model isable to handle micron-scale phenomena, but it cannot handle multidirectionalwave propagation.Other, more complicated techniques arise from directly discretizing Maxwell’s

equation. No assumptions are made on the type of solution. With these techniques,multidirectional wave propagation can be studied, and they can show the timeevolution of the electromagnetic field. This technique consumes a lot of simulationtime, but is more accurate than the BPM. It can be used for complex geometricalproblems and complex materials. This technique is often implemented usingparallel computing.There are several simulators implementing each of the optical computation

methods.43–47

10.5 System-level simulations

Analog circuits are used for the sensing and control of the MEMS and opticalelements. Typically, electronics are simulated with electronics simulators suchas SPICE or high-level language simulators. Systems of MEMS devices, optics,and electronics are simulated with several different approaches.48–53 Oneapproach attempts to model the MEMS elements in a system-modelingprogram. These programs can simulate differential equations or flowgraphs, butdo not have electronic design environments. Another method is to use a system-level simulator based on electronics. There are several options, which differ intheir ability to represent the MOEMS models. High-level languages such asVerilog-A, VHDL-AMS, or System C allow the representation of multidomainsignals. SPICE simulators use an equivalent circuit representation. Some SPICEsimulators have been adapted to allow models written in the C language, whichthen do not require an equivalent circuit to be represented. The limitation ofthese simulators is in their ability to represent the spatial extent of the opticalwaveform. They represent the optical system as a coupled set of nonlinear ordinarydifferential equations (not partial differential equations). A lumping approximationis used to model the distributed MEMS system. At a very simplistic level, someMOEMS calculations are even done by spreadsheet.The approach taken by some system-level codes is to use a schematic driven

front end to capture mixed-technology circuit diagrams where the opticalsymbols represent multidomain components. Figure 10.13 presents two examples


of parameterized component libraries. Transistors can be simulated from standardelectronics libraries. A netlist is extracted, which references behavioral models,which are then simulated with a standard IC simulation engine. Using thesesystem simulators, the MOEMS devices can be simulated with their electroniccontrol circuitry, signal conditioning circuits, and packaging. Specific stimulimay be applied with mechanical and optical sources to simulate environmentand boundary conditions.The types of analyses that can be performed are similar to those that can be done

with FEM and BEM methods—alternating current (ac), transient, and directcurrent (dc). Parameter sweeps can be performed to explore dependence on geo-metrical or process parameters. Deflections, resonant mechanical modes, and har-monic responses may all be calculated. Due to the model’s simplicity andnumerical efficiency, larger numbers of elements can be simulated and muchlarger time windows can be simulated, along with strong nonlinearities, thanwith 3D simulation programs. There is necessarily a loss in accuracy due to the

Figure 10.13: System-level MOEMS library elements.21,54


fact that the partial differential equation is replaced by an ordinary differentialequation, limiting the spatial resolution. Behavioral CAD will lose accuracywhere the spatial variation must be modeled on a small scale. But system- andbehavioral-level performance parameters are not necessarily calculated with lessaccuracy. A problem with FEM or BEM is that the process parameters must beknown with great accuracy, whereas system simulators often work with higher-order measured parameters. As a result, the calculation of the resonant frequencyfor a resonator, for example may not be less accurate with behavioral simulationthan with FEM and BEM methods. Behavioral-level methods are also limitedwhere the physics is unknown and there are no good model.Failure modes (fatigue, fracture, buckling, etc.) are examples of phenomena that

may be poorly modeled at the behavioral level. These types of processes must bededuced by 3D simulations or in some cases cannot be modeled at all. Figure 10.14shows a typical calculation that can be performed with a behavioral-level simu-lator. The figure shows how the displacement of a MEMS actuator behaves as afunction of spring length. The spring length change causes a shift in resonantfrequency as expected.The simplest method for modeling MOEMS describes nonelectrical energy

domain behavior with electrical analogs, utilizing standard SPICE electrical primi-tives: resistors, capacitors, inductors, transistors, etc. For example, the reactingforce of a mechanical spring may be modeled in SPICE using a resistor.However, the standard SPICE elements often are limited to simple linear elementsand polynomial sources. The MOEMS designer is forced to make model approxi-mations that may lead to nonconservation. Model codes based on the C language or

Figure 10.14: Parameter sweep of the spring length, showing the displacement behavior

dependence.55


other high-level programming languages allow representations of devices with anunlimited number of device terminals by equations relating through and acrossvariables, as in a hardware description language.Table-based models allow the use of tabular data to form macro-models. These

data may come from 3D FE/BE analysis or from experiments. For experimentaldata tables, a monotonicity checker is used to verify the model’s consistency.Data tables provide a modeling mechanism when the functional form of themodel is unknown. Another use of tables is for simulation speedup.Performance-based models using high-level parameters such as spring constants

and damping coefficients are used for prototyping. Geometrically parameterizedmodels are used to perform more detailed simulations with parameters such asspring lengths, widths, and thicknesses. Optimization is employed to map perform-ance goals and model parameters to geometrical structures for synthesis.

10.5.1 Optimization

Given a parameterized library of devices, optimization algorithms can be utilizedto specify device geometries and process parameters, given a set of system-levelconstraints and performance goals. An example is the automatic determinationof the spring lengths, plate geometries, and number of comb teeth in a resonatorstructure given displacement and area constraints. Technology exploration canalso be done with optimization tools. Comparison of actuation methods can bequickly explored given a set of technology constraints. Technology comparisonof process steps and parameters can also be done. The problems can be posed asmaximum or minimum problems—for example, minimizing actuation voltagesor maximizing displacement.To enable optimization, a set of hierarchical composable models must be

created with representations that are parameterized in terms of design geometricalparameters and process parameters. The models must have multidomain signalsand cover the physics of interest. Optimization is achieved by running iterativesimulations over a constrained set of selected parameters. In order to specify anoptimization, the inputs are a list of parameters to vary, a set of constraints, theoptimization goals, and a choice among analysis and optimization algorithms.Most optimization procedures employ a gradient-following technique. Measure-ments are used to specify goals—for example, a switching-time measurementmight be made Q1by counting signal crossings, or an area could be the sum of aset of geometrical measurements. Optimized parameter values can be used in sub-sequent analyses of the same model. This allows for incremental optimization:some parameters can be optimized while others are held fixed; later, otherparameters can be optimized based on the results of the earlier optimization.Multiple analyses can be supported: dc analyses, ac analyses, and transient ana-lyses. Multiparameter nonlinear optimization is necessary. Optimization can beperformed with FEM or BEM simulations and at the system level. Optimizationof MOEMS devices is a challenge due to the multiple scales and the strong thenonlinearities in the device behavior. As in most optimizations, avoidance of


local minima is an issue. If the analytical models have links to geometry generatorsthe design procedure shown in Fig. 10.15 can be executed automatically to producea mask layout from the specification of performance goals.

10.5.2 Statistical analysis

Statistical analysis can be used for considering process and mask variation indesign and for design centering—choosing mask designs that maximize yieldand are the most tolerant to variation. A designer can explore, for example, howresonant frequency varies with polysilicon thickness. Statistical analysis can beperformed at the system level or the device level. Device and process parametersmust be described with statistical distributions. Sensitivity analysis can be used todetermine the parameters with the largest effect on system performance, and para-metric variation can be explored. A set of worst-case scenarios and process cornerscan be developed for testing designs.Yield analysis is a very important statistical function for MOEMS designers.

MOEMS fabrication vendors do not typically supply process corners, as is doneroutinely in the VLSI world. The CAD tool must extract variational data from pro-cesses via critical monitors, build a statistical model of the variations, and thencreate models that relate system functions to process and mask variations.The most common numerical method is Monte Carlo simulation, where

repeated simulations are run using a random sampling of the parameter probabilitydistributions. Various methods can be used to sample, such as the Latin hypercubeor design of experiments (DOE) methods. The Monte Carlo method is general andnot dependent on the physics; therefore, the assumption made is that the limited

Figure 10.15: Design optimization with automatic layout generation.55


number of simulation loops is statistically representative. This assumption can beverified using confidence limits on the data. The individual simulation loops areinherently independent; that makes Monte Carlo simulation techniques ideal forparallel processing. Data models can then be created using techniques such asresponse-surface modeling. Fig. 10.16 shows an example of a Monte Carlo analy-sis using statistical data from a MEMS foundry.

10.5.3 Dedicated MOEMS simulation and cosimulation

In many important optical systems, the cosimulation of the optical devices, thecontrol electronics, and the MEMS devices is important for the system analysis.The system-level description of the optical system is limited to a few points inspace, and hence the system-level model may be too coarse to capture the opticalbehavior adequately. Some mixed approaches are possible where the partial differ-ential equations that are used to simulate the spatial extent of the optical signal arelinked to the differential equations used to model the MEMS and system elec-tronics. One such simulation technique embeds the beam prop method inSPICE.57 Other numerical methods attempt to link a behavioral simulator withan optical simulator to perform co simulation where results are passed betweentwo distinct numerical engines.58

The simulation systems described so far have involved the combination of stan-dard simulators used for IC simulation and/or simulators for optical systems anddevices. Work has been done41 on an optical system simulator dedicated toMOEMS. These tools encompass numerical algorithms that have been tailoredto model the optical devices found in MOEMS along with the nonlinear electronicdevice models. An example of the system modeling is shown in Fig. 10.17.

Figure 10.16: Monte Carlo analysis showing the shift in resonant frequency of a MEMS

resonator as a function of polysilicon thickness variation.56


10.5.4 System simulation example—pull-in computation

An example of a coupled electrical-mechanical system model simulation is devel-oped in this section. A device representative of an electrostatically actuated micro-mirror is shown in Fig. 10.18. The device is represented as two plates where theupper plate is connected by a long thin beam to an anchor. A voltage differenceis applied between the two plates and actuates the upper plate.To simulate the actuator system, the overall system was decomposed into

models for the beam, the anchor, and the plates. The beam is described as anelemental stiffness matrix relating the beam forces and moments to its displace-ments. The anchor fixes the mechanical position. A gap functional model describesthe force and moment generated between the two plates with coupling between themechanical and electrostatic equations. Figure 10.19 gives a schematic represen-tation of the system.Figure 10.20 shows the dc sweep analysis of this device for the following con-

ditions and parameters: a beam length of 150 mm, a beam width of 2 mm, a gaplength of 100 mm, an initial gap distance of 2 mm, and the width of the top gapplate of 6 mm. A transient analysis is also shown for a pulse input voltage. Thegraph on the left shows a plot of the plate deflection at its end versus thevoltage between the two plates. The figure illustrates the pull-in phenomenon.As the voltage is increased beyond a certain point, the plates come togetherrapidly. This effect is due to the electrostatic force overwhelming the spring

Figure 10.17: System modeling with Chatoyant.41

Figure 10.18: Physical representation of an electrostatic actuator.59


force of the plates. The plot on the right shows the deflection in response to achange in voltage. Note the bouncing of the actuator for some time before itsettles on its final position.Several important modeling issues are the accuracy of the model equations in

capturing the essential physics, errors due to geometry measurement, and theinability to accurately extract process parameters and capture process variation.In order to simulate MOEMS devices accurately, the model equations mustcapture the correct dependence on physical mask dimensions, which may be diffi-cult for serpentine and complicated 3D etched structures. Models used in systemsimulation are often simplified to 1D and may neglect important cross-axis inter-actions. Test structures to measure process parameters will become a keycomponent of model creation.

10.5.5 Packaging simulation

Packaging is an important issue for MOEMS design. Simulations must be done inorder to take into account packaging effects on the actuator and optical system.MOEMS packages are usually not standard and hence often are designed fromscratch, requiring intensive simulation for validation of new packaging concepts.

Figure 10.19: Schematic representation of the electrostatic actuator.59

Figure 10.20: Dc and transient analysis of the actuator.59


Of particular importance is the simulation of stress and thermal effects. Thepackage must be simulated at several levels of detail. Typically, finite-elementmodels are created to simulate the detailed thermal and mechanical behavior ofthe package in 3D. System-level models are used to evaluate the effect of thepackage on the sensor or optics, and the packaging effects are added as parasiticelements. Shown in Fig. 10.21 is a design flow for incorporating packagingeffects into a MOEMS and electronics simulation.

10.5.6 Reduced-order modeling

Good models for MEMS devices are needed at the system level that are computa-tionally efficient but that maintain the accuracy needed to describe the relevantdevice behavior. Describing MEMS devices by full dynamic finite-element simu-lation is prohibitively expensive. In addition, system designers need access tohigh-fidelity models in order to simulate systems of MEMS, electronics, andpackaging. The need exists to create behavioral models that provide accurate har-monic and time-domain solutions in a fast and efficient manner. Previously, beha-vioral models were created by hand through doctoral theses. But with the numberof new device types expanding rapidly, an automatic way of creating behavioralmodels is necessary. Currently, techniques exist to automatically reduce thenumber of degrees of freedom in an FEM model to produce an equivalentreduced-order model.12,60–62 The programs can handle the reduction of coupledelectrostatic, thermal, and mechanical systems.Typically, a user creates an FEM model and simulates it under the boundary

conditions expected in the behavioral simulation. The user must indicate themaster degrees of freedom that should be retained to create load conditionsunder which the model is to be exercised. The user must also explore thesimulation space under which the model will be run in the system simulation.

Figure 10.21: Packaging simulation flow.


Various FEM or BEM runs analyzing the device in the physical domains of interestmust be done, including coupled physics simulations. For example, for a reduced-order model of a moving optical device, typically, mechanical, fluidic, and electro-static analyses must be done. The reduced-order modeling (ROM) algorithmcreates a simplified model based on matrix reduction techniques and numericaldata fitting. The model is then output in a format compatible with a system simu-lator in a suitable behavioral modeling language. Figure 10.22 shows an equivalentcircuit for a coupled electrostatic-mechanical reduced-order model.In addition, the reduced model can be hooked directly to full FEM models that

capture the physics of devices that cannot be accurately modeled by lumpedelements, and a mixed-mode analysis can be performed using the two types ofmodels. Most of the reduced-order modeling systems deal with a fixed geometryand hence are not easily parameterizable. Creating parameterized reduced-ordermodels is a current important area of research.As described previously, in 3D simulators the general dynamic behavior of a

structural model may be described in terms of the mass matrix the dampingmatrix and the stiffness matrix. The model reduction procedure consists inselecting a reduced set of degrees of freedom (DOFs), Xr , representative ofthe system behavior and usually including the DOFs to be output or sensed. Thesystem behavior is reexpressed in terms of these variables. Reduced-order model-ing generates a new set of matrices and a new load vector (Mr , Dr , Kr , and Fr).After this procedure, the new system formulation is

Mr½ �d2

dt2Xrf g þ Dr½ �

d

dtXrf g þ Kr½ � Xrf g ¼ Frf g:

Figure 10.22: Reduced-order model equivalent circuit.


Note that the number of equations is now equal to the new number of DOFs. Fromthe MOEMS system designer’s point of view, in many practical cases, only a smallnumber of real model DOFs are of interest for capturing the behavior of the devicewhen simulating with electronics or packaging. The DOFs retained, may be at con-nection points or outputs. For example, the center or tip of a mirror may be retainedas a DOF.

10.5.6.1 Example application: Reduction of a micromirror

In this example, reduced-order modeling is used to describe an electrostaticallyactuated micromirror. The mirror is shown in Fig. 10.23 and consists of a plateconnected to a beam. The beam mainly behaves as a torsional spring. The topface of the plate is covered by a metal deposit to obtain desired optical properties.Undeformed, the lower side of the plate is parallel to a surface connected to anelectrical ground plane.In the simulation of the micromirror, the electrostatic forces applied to the struc-

ture depend on the deformation. A coupled analysis is required. In order to demon-strate the model reduction formulation, only one DOF is considered. For thisexample, the master DOF for the reduction was chosen as the displacement,normal to the ground plane, of the point located at the end of the lower side ofthe plate. In this configuration, the model behavior can be reduced to the following

Figure 10.23: Micromirror model.


structural and electrical equations:

md2Xr

dt2þ d

dXr

dtþ kXr ¼ fcoupling(V , Xr),

I ¼ @t CGVð Þ,

where I is the current. The reduced electrostatic coupling loads array fcoupling(V, Xr), is expressed in terms of the capacitanceCG and the conductor’s bias voltage:

fcoupling ¼ @xrCG

� �V2

2:

The capacitance value CG(Xr) can be computed by polynomial fitting. Fitting pointsare obtained by generating a set of deformed configurations of the complete model.For each configuration, the capacitance is computed by solving the complete FEMmodel electrical equations. This operation yields a numerical table of CG values forgiven Xr values. A least-squares fitting routine yields CG in the form

CG(Xr) ¼1

PNi¼0 aiX

ir

:

The reduction algorithm leads to an approximation of the system eigenfrequency.In order to match this eigenfrequency, a correction of the reduced system mass canbe done using an eigenfrequency simulation. In the case of single-DOF systems, theeigenfrequency is proportional to the square root of the reduced stiffness divided bythe reduced mass. On computing the eigenfrequency of the complete model byrunning a modal analysis and considering the reduced stiffness, the eigenfrequencycalculation yields a corrected reduced mass. This correction produces a reducedmodel whose eigenfrequency matches exactly the eigenfrequency of interest ofthe full model. Output in the form of a behavioral modeling language wascreated, and the model was simulated with a system simulator. Figure 10.24 containsa comparison between full FEM simulation and the output of the micromirrorreduced-order model for a transient simulation for the same load conditions ineach simulator. The figure shows simulations of the response after eigenfrequencycorrection. The agreement between the two curves could be enhanced by increasingthe number of fitting points.Fitting has been performed on the reciprocals of the force and capacitance

values, using a fourth-order polynomial approximation. Results from steadystate analyses as well as transient analyses performed on the full and reducedmodels show good accord. The capacitance as a function of micromirror gap pos-ition is shown in the Fig 10.25.

10.6 Physical tools and verification

Mask layout is typically done with mask layout programs from the IC industry orthe mechanical computer-aided design industry.22 Optical design tools alsoencompass mask layout tools. Mechanical CAD programs, although possessing


rich geometric representations and flexibility, have no higher-level semantics forrepresenting transistors or electronic devices for integrated MEMS. IC-basedtools have little native support for curves, but have sophisticated links to physicalverification tools such as design rule checkers and parasitic extractors.

Figure 10.25: Capacitance plot as a function

Q1

of displacement for the micromirror structure.

Figure 10.24: Transient analysis of the ROM model and full FEM simulation with

eigenfrequency correction.


CAD tools contain libraries (see, e.g., Fig. 10.26) of geometrical Q1primitives per-tinent to optical designers. These libraries include scalable primitives for drawingsuch optical devices as mirrors and lenses. The libraries often contain predesignedMEMS devices such as electrostatic, thermal, and magnetic actuators. Macros arealso available for generating arrays of devices for mirror arrays or polar arrays ofoptical elements. Optical design programs usually include the physical design ofgeometrical structures based on optical performance criteria. In these design pro-grams dimensions are often automatically calculated from simple formulas, andthe tools provide links to simulations.

10.6.1 Design rule checking, extractors, layout Q1versusschematic, and parasitics

Manufacturable MOEMS must obey foundry design rules such as spacing, overlap,and minimum-width rules. Optical structures also must have certain minimum ormaximum dimensions. Some rules are context-dependent and depend on the typeof MEMS structure being designed. For example, there may be a minimum distancefrom the ground plane to the stator of a motor or the number and placement of etchholes on a plate that is to be released. These rules can be automatically checked withdesign rule checkers that process the 2D mask layouts looking for violations. So far,design rule checking (DRC) has not been a priority, due to the simplicity of the struc-tures designed. However, this is no longer true with larger integrated systems.Design rule checkers for MEMS have been adopted from the IC industry.Because the VLSI checkers were created for mostly 90-deg-angle designs, theyare not very efficient and accurate at checking MEMS designs, which are highlycurvilinear. The VLSI checkers often report false errors at curved segments.

Figure 10.26: MOEMS physical

Q1

design library elements.55


In VLSI systems, a netlist describing the devices used along with their dimensionsand their interconnections can be derived from the physical layout. This is possiblebecause rules for recognizing the primitive devices from mask objects have beencreated for the commonly used devices—transistors, capacitors, resistors, and induc-tors. MEMS offer a rich set of primitives, and so far no robust recognition algorithmshave been put forth. Another, more pragmatic approach treats theMEMS device as ablack box where the connections to other devices may be extracted but the deviceitself must be specified by hand. Layout-versus-schematic (LVS) checks have alsobeen extended to MEMS where the comparison is made for multidomain netlists.In addition to the intended devices created in the layout, extractors can be used torepresent elements forming parasitic devices present in the layout. For example, inelectrical layouts unwanted capacitances, resistances, and inductances are oftenpresent. In MEMS these parasitics must be generalized to multiple domains.System simulation must be run on the netlist with parasitics to verify any changesin system function due to the presence of parasitics.

10.7 Material, process, and reliability issues

Processes and materials must be understood to produce commercial MOEMS. Theaccuracy of device simulations depends on accurate values of material properties.Material property databases are supported by the CAD tools, but material propertiesare very dependent on exact fabrication conditions and hence cannot be reliably rep-resented by standardized tables. The properties may be nonlinear and anisotropic.The size of MEMS devices and the thin film materials used imply that the bulkmaterial properties of materials often cannot be used. The material microstructuresize (for example, grain size) can be on the same order as the device dimensions.Material properties must be entered at the system level and the FEM level, andmust be consistent. Often units are not even consistent between the two types of pro-grams. Statistical data must also be available. Today, in the world ofMOEMS, thereare no standard processes, material parameter exchange mechanisms, or test struc-tures; however, this issue is being addressed.63 Figure 10.27 shows some of the teststructures used to measure material properties of MOEMS devices.One of the issues involved in productization is reliability testing. An important

roadblock is the lack of available understanding and modeling of failure mechan-isms. To some extent, CADmust wait for the availability of these models. Materialdatabases allow users to predict mechanical, electrical, thermal, physical, optical,and other material properties of thin film materials as a function of fabricationmachine settings and processing parameters based on measured data. Many ofthe data used to populate the databases must come from measured data capturedfrom diagnostic techniques as opposed to simulation.

10.8 Conclusions

An important issue for the future is the interoperability of CAD tools and standardsfor data exchange. Lack of standards has and will continue to hamper the adoption


of CAD tools. Lack of standard fabrication processes, in the short term, allowsMEMS foundries to have more added value, but makes it difficult for systemdesigners and fabless design houses to utilize MOEMS quickly and efficiently.In the integrated circuit industry, model parameters are exchanged in a standardfashion. Making progress in this area will require the collaboration of foundries,CAD tool vendors, and users. Because MOEMS is still the domain of expertsand involves the collaboration of a large, multidisciplinary team, there is no stan-dard design and workflow. Unlike the top-down design flow found in the design oflarge digital systems, MOEMS design is more like a spiral where requirements areiterated between package, MEMS, optical elements, and electronics designs.Design may begin with innovation at process, device, or system level, andhence the CAD tool must be flexible enough to handle multiple entry points anddesign flows. Because of the variety of MOEMS devices, the lack of standardiz-ation, and the value added in the details of the device design, system designerscannot currently take advantage of predefined, characterized libraries as is donein digital design. This state of affairs allows for richness in device design, butmakes it hard for system designers to innovate, as they must possess a lot ofdevice-specific knowledge. This is reflected in the CAD tools, as libraries arejust beginning to be adopted and are rather at the stage of being examples.CAD tools can allow the transfer of knowledge from experts to nonexperts or the

encapsulation of knowledge created at the device level for use at the system levelof design. Libraries will allow system designers to have access to the technology.Design principles based on CAD will hopefully replace empirical knowledge fromdomain experts. Although we do not see device designers giving up their freedomto standard libraries and processes in the near term future, there is a migration path.Designers can capture their own ideas into in-house process-specific libraries fordesign reuse. Pressure from system-level designers will push the library

Figure 10.27: Test structures for deriving

Q2

material properties.55


concept, which will be necessary if MOEMS is to proliferate into a large-scaleindustry. Time-to-market issues and cost will drive the need for reusability of pre-vious process and structures.

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chapter 10 moems mems cad and simulation

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