Solid Modeling and Analysis of MEMS Structures · COSMOS ® SOLID MODELING AND ANALYSIS OF MEMS STRUCTURES no. 2 • 3D visualization facilitates communication within the organization

----W H I T E P A P E R

COSMOS®

Solid Modeling and Analysis ofMEMS Structures

SolidWorks Corporation

C O N T E N T S

Introduction 1

3D visualization 1-2

Sub-micron featuredefinition 2

Patterns and creation ofpatterns of patterns 3

The power of configurationmanagement 3-4

Complex assemblydesign support 5

Associative photomaskdefinition 6-7

Finite element analysis(FEA) of MEMS structuresfor thermomechanical,electrostatic, and fluidflow behavior 79

Design Re-Use 10

Ease of use 11

Collaboration tools 11-12

Tightly integratedcomplementaryapplications 13-14

One standard CAD toolto design everything 16

COSMOS®

S O L I D M O D E L I N G A N D A N A LY S I S O F M E M S S T R U C T U R E S no. 1

Solid Modeling tools are helping MEMS designers streamline their design

process and leverage the availability of finite element analysis (FEA) software.

Associative mask definition gives the MEMS designer even more power, letting

the designer concentrate on refining micron-scale structures in 3D and letting

the mask follow the design.

Your choice of solid modeling tools is critical to achieving results in the MEMS

world. SolidWorks® is easily mastered, even by part-time designers. SolidWorks

allows the designer to design the MEMS structure, analyze it, generate the

photomasks, and design all the related product packaging and assembly

equipment. This guide identifies key issues and explains advantages of

SolidWorks 3D modeling software for MEMS designers.

3D Visualization

• 3D visualization provides MEMS designers a first check of design intent,

proper operation, collision avoidance, and package stack-up.

• MEMS designers have created impressive structures, frequently using layout

software that is inherently two-dimensional. These accomplishments are

impressive, but true 3D tools offer MEMS designers better design

visualization. This gives designers a clear and accurate review of parts and

assemblies early in the design cycle.

• SolidWorks provides true solid modeling capability, avoiding the need to

acquire extremely expensive high-end specialty design software marketed

strictly for MEMS design and analysis.

I N T R O D U C T I O N

Figure 1

This microtransformer was

designed in 3D with

SolidWorks and fabricated

with MEMGen Corporation’s

EFAB™ technology.

Figure 2

As microfabrication techniques

extend our grasp into the realm

of microns, as with this fiber

positioner, SolidWorks guides the

way with sub-micron solid

modeling and analysis.

COSMOS®


• 3D visualization facilitates communication within the organization and

beyond. Not only is the MEMS designer more able to explain design intent to

colleagues, but scholarly presentations, articles and requests for funding

benefit from showing 3D features.

• To shorten time-to-market for your MEMS designs, you need to identify

potential problems early in the design cycle, before committing to a mask or

processing wafers. SolidWorks Office Professional includes PhotoWorks™,

SolidWorks Animator, and 3D Instant Website software, that enable excellent

visualization capabilities by providing photorealistic rendering, full-motion

animation, and webbased presentation of the finished design.

• Clearance design rules can be particularly important for surface

micromachining to ensure proper etching and separation of parts during

lift-off processes. SolidWorks enables checks for interferences or specific

clearances between components using Dynamic Assembly Motion and

Collision Detection. Any interference will stop motion between parts that

contact and the point of interference will be highlighted by changing color.

Physical Simulation takes motion checking to the next level by presenting

meshing parts, such as meshing gears, and showing their operation in the

assembly.

Sub-Micron Feature Definition

• SolidWorks solid modeling software provides MEMS designers with

sub-micron feature generation capability. In fact, the user can choose to work

in microns, nanometers, or even angstroms as appropriate.

• Features in most MEMS devices are several microns or tens of microns.

SolidWorks allows designers to work on this scale and still define

sub-micron features in structures (such as die-mounted, packaged

assemblies) with dimensions of tens of millimeters.

• This sub-micron definition capability means that certain types of optical

gratings may be described fully as a solid model, with all the power that

SolidWorks can bring to such entity creations.

3D VISUALIZATION/SUB-MICRON FEATURE DEFINITION

Figure 3

This gear, designed in SolidWorks,

is 10 microns thick and 120

microns in diameter. The detail

shows a fiducial which is 0.4

microns wide and 10 microns long,

etched to a depth of 0.5 micron.

Patterns and Patterns of Patterns

• SolidWorks saves designers time and simplifies model construction by

allowing patterns of model features. Bosses and cuts are just two of the

features that may be patterned within a part. Patterns may be linear,

rectangular, or defined by a curve.

• Patterns may also be employed within an assembly. Several component parts

may be dragged into an assembly, or the designer can simply define a

pattern of components.

• Patterns of patterns may also be defined. Using the gear patterns at left as

an example, the pattern of six gears may be defined as an element, then

patterning the pattern creates a photomask to produce a large number of

such gears.

• Circular patterns of linear patterns are supported, as are linear patterns of

circular patterns. In fact, the pattern definition and pattern-of-a-pattern

definition are independent. Each may be constructed from: linear, circular, or

curve geometries.

Configuration Management

• Configuration Management is the ability to control design variations from

within a single file or document. This applies to parts and assemblies, with

the effects propagating to drawings, including photomask drawings.

• Configuration Management enables the generation of multiple versions of

parts, assemblies, and drawings in a single document with a minimal

amount of time and effort. Configurations make use of design tables, derived

design data, component properties, relationships, viewing states, and other

attributes, storing part and assembly information in one area for greater

efficiency. SolidWorks offers multilevel configurations, called nested

configurations, to optimize the power, organization, and efficiencies of

configurations.

• SolidWorks Configuration Management gives you maximum flexibility in

creating multiple design variations covering a wide range of needs. New

configurations are easily developed from previously created designs to

further speed development and meet market needs for data reuse.

COSMOS®


PATTERNS AND CREATION OF PATTERNS OF PATTERNS

Figure 4

Each gear above contains a pattern of

holes and extruded cuts. A radial

pattern of such gears may be defined as

at left, then a rectangular pattern of

such patterns may be defined, as shown

at right. Defining patterns in this fashion

eases photomask creation.

COSMOS®


THE POWER OF CONFIGURATION MANAGEMENT

• A simple application of this capability would be to create various versions of

MEMS structures that automatically scale both surface feature size and etch

depth as dimensions increase. The various versions of this MEMS design can be

created within a single SolidWorks model file for simplicity and easy design

control. “What if” scenarios for different design requirements such as film

thickness and modulus can be quickly explored by turning on and off various

configurations of a part or assembly. Etched well dimensions and sizing of

cutouts can be tied to design data for each chip size. As the chip requirements

change, the necessary wafer level dimensions automatically update to reflect

the new design.

• Components involving multistage processing, such as surface micromachining

or LIGA, can easily be documented by using multiple configurations of a single

part. Configuration Management techniques can generate a discrete version of

a part or assembly as necessary to reflect a separate version or in-process

state. These versions help you compare designs, track expected performance,

and develop process plans.

• Because change and flexibility are keys to effective design, the importance of

configurations to the designer cannot be overstated and SolidWorks is the only

product among powerful, easy-to-use 3D CAD products that offers

configurations for both parts and assemblies.

Figure 6

Two design variations for an

etched silicon well structure.

A design table offers agile feature

re-definition during preliminary

design studies. Design

tables together with the

Configuration Manager tree

provide defined configurations

that can be called up as

needed.

Figure 5

Design tables are Microsoft®

Excel spreadsheets embedded

within the drawing.

COSMOS®


COMPLEX ASSEMBLY DESIGN SUPPORT

Complex Assembly Design Support

• The ability to handle assemblies with thousands of parts without compromising

performance is a requirement of 3D CAD solutions for designing wafers full of

MEMS devices such as accelerometers, orifices, mirrors for Micro-Opto-

Electro-Mechanical Systems (MOEMS), or arrays of Micro-Structure Technology

(MST) devices, such as miniature gears.

• The ability to manage large assemblies easily allows product designers to take

on a broader range of projects and gain greater flexibility in solving design

problems.

• The challenges associated with large-assembly MEMS device design are often

unpredictable and complex. SolidWorks 3D modeling software, with its Large

Assembly Mode, offers unparalleled performance for applications involving a

large number of parts, allowing product designers to design and assemble tens

of thousands of components and evaluate complete assemblies.

• SolidWorks provides built-in tools for evaluating assembly designs, including

motion simulation and visualization (Physical Simulation), interference

checking, collision detection, clearance information, and creation of envelopes

for defining the full range of motion for an assembly. Clearance design rules

can be set for micromachining operations. These tools help MEMS designers

identify necessary changes in assembly development, which can be easily made

using simple drag-and-drop assembly structure reorder operations.

• Many organizations accelerate development through concurrent design

approaches where several designers or teams work at the same time on

separate components or subassemblies of a large assembly. SolidWorks 3D

modeling software supports concurrent design, providing powerful capabilities

that enable Configuration Management, top-down design techniques, and

design collaboration.

Figure 7

Assembly level configurations

can pull together etch depth

and film thickness.

Figure 8

A large MEMS array could contain tens

of thousands of elements. The solid

model pictured here contains a 10 x 10

array of tiny diving board structures.

Analysis of models such as this, and

significantly larger, can be readily

achieved on common desktop

computers or workstations.

COSMOS®


ASSOC IAT IVE PHOTOMASK DEF IN IT ION

Associative Photomask Definition

• For MEMS device design, fully associative assemblies are critical for

effectively using bottom-up and top-down assembly design techniques.

Associativity guarantees that all elements of a model are electronically

associated or connected, including assembly models, components, and

drawings. This means that when a change is made to any SolidWorks file,

that change is automatically made in all associated files.

• After surveying numerous MEMS designers actively working in the field, we

have received feedback that mask definition should be associative to model

changes. SolidWorks developers have put in place powerful tools that will

streamline mask generation in GDS II file formats from associative DXF files,

which link directly to model definition changes.

• Bottom-up associative design encompasses the creation of new components

and integration of these with existing components into assemblies. This is

important when components must be designed based on strict limitations

imposed on component properties, then checked for integration in the

context of the overall assembly. Each of these parts can be edited within the

assembly as needed.

Figure 9

This positive photomask was generated associatively from

a solid model. Below is the corresponding negative photomask.

Figure 10

Because the drawing dimensions

are associative, they

automatically propagate

throughout the model, drawings,

and configuration tables.

• Top-down associative design involves working with an existing assembly to

develop new components for use with that assembly. Because new

components reference existing parts in the assembly, any changes made to

any of the parts are reflected throughout the design. In the MEMS arena, this

means that a component can be created or modified within the context of the

overall device model, allowing real-time modification for fit and function.

Modifications automatically propagate throughout the assembly and

drawings, maintaining design intent.

• Examples of top-down design include developing a package for a MEMS

device that realizes a certain stack height and footprint, generating a

maximum envelope (length, width, and height) for a chip within a required

finished package size. Configuration Management enables the new parts to

be linked through the assembly and to the photomask definition drawing file.

Integrated Finite Element Analysis (FEA): Thermal, Mechanical,

Electrostatic, and Fluid Flow

• Designers can now run initial stress analysis checks on MEMS designs

up-front using COSMOSXpress™ FEA software that is included with every

license of SolidWorks. Furthermore, COSMOS products in the

COSMOSWorks™ analysis software product line enable thermal, stress,

deflection, buckling, non-linear, and electromagnetic analysis. Partners such

as MSC.Software (MSC.visualNastran FEA for SolidWorks) also provide

Certified Gold Product Solution analysis products for use with SolidWorks.

COSMOSFloWorks™ from COSMOS provides CFD (computational flow

dynamics) analysis for flow and heat transfer applications.

• Reliability is a key factor that differentiates various MEMS device

technologies and designs. Companies that are able to build in reliability from

the initial design stage will have an advantage in gaining market acceptance.

COSMOSWorks facilitates early-on reliable design by allowing MEMS

designers to perform a range of FEA on initial designs. From thermal

analysis to static analysis, COSMOS ensures device behavior will be within

design limits, avoiding thermal or stress-induced failure.

COSMOS®


F IN ITE ELEMENT ANALYS IS (FEA ) OF MEMS STRUCTURES

Figure 11

COSMOSWorks brings highend performance

to desktop computer users. This mesh,

which features over 130,000 nodes, was

automatically generated by the standard

COSMOS mesher, utilizing controls that

increased resolution where needed.

• Thermal analysis is critically important for MEMS package design.

It also plays a pivotal role in predicting device operation for certain

technologies, such as thermo-optic planar waveguides and resistor

arrays. Using the SolidWorks solid model as a starting point, COSMOS

can perform steady-state or transient thermal analysis on parts or

assemblies. After meshing the design, the designer sets any relevant

constraints (for example, the underside of a substrate may be

considered clamped to a certain temperature because it is intimately

bonded to a thermoelectric cooler), then the designer sets power or

heat flux conditions associated with a geometrical feature of the

model. Because component material properties include thermal

conductivity, coefficient of thermal expansion, and heat capacity, the

designer gets a realistic prediction of temperature distributions under

prescribed conditions.

• By coupling the power of FEA studies with Configuration Management,

the designer can quickly converge on the best-form design solution

over many degrees of freedom. For example, a range of epoxy bond

layer thicknesses may be studied in coordination with evaluating a

broad range of epoxy thermal conductivities.

COSMOS®



Figure 12

Thermal analysis of a

MEMS subassembly.

Figure 13

Deflection and stress profiles

are easily computed with

COSMOSWorks.

Figure 14

COSMOSEMS was used to analyze

performance of this cantilever beam

under various voltages. (The aqua-colored

volume represents air.)

COSMOS®



• COSMOS Static analysis capability is a tool that empowers the MEMS

designer to avoid catastrophic immediate or long-term failure modes.

The diving board analysis at left, for example, showed that although

desirable deflection distances could be achieved with a shallow (5

micron) etch and a thin (1 micron) diving board, the resultant stress in

the moving element would result in early failure. After several

permutations were analyzed, a balance between risk and performance

was achieved. In some cases, designers will learn that changing preset

variables is insufficient to resolve the tradeoff, then re-design of one or

more core elements will be necessary. COSMOS then guides the way in

conjunction with Configuration Management.

• For most MEMS devices, and particularly those whose performance

depends on electrostatic performance (such as piezoelectrics or

deformable mirrors), electrostatic analysis capability is necessary to fully

predict device performance. The simple cantilever beam model shown

here was solved to model beam deflection under different potentials

between the stationary and moving elements. The results can then be

compared to the effects of shock and vibration to optimize performance

under real world conditions.

• Fluid flow analysis is important across a range of MEMS applications.

Whether you’re trying to get heat out of a package, and therefore need to

determine which heat exchanger has the best properties; or you’re

designing a MEMS orifice or pump whose operability is directly tied to

fluid handling, COSMOSFloWorks™ offers high-powered computational

flow dynamics analysis in a straightforward interface.

Figure 16

COSMOSFloWorks was used

to model the air flow through this

circuit board environment, allowing

the designer to optimize package

characteristics such as chassis

cut-outs or heat exchanger

configuration.

Figure 15

COSMOSEMS computed the

potential distribution shown

at top. The predicted deflection

is shown in the lower plot.

Design Re-Use

• MEMS designers frequently have a large amount of legacy data (data

created from previous projects or fab runs).

• Legacy data may form a starting point for new designs or can contribute

key elements to the development process, including projects based on

collaborator-supplied CAD data. Unfortunately it is often available in

various 2D and 3D formats. The ability to use these varying formats

helps designers leverage legacy data, work sideby- side with designers

who use other CAD systems, speed development, respond to market

needs, and increase financial returns.

• SolidWorks 3D CAD software offers the widest number of data

translation formats of any CAD solution. A list of the supported formats

is provided on the SolidWorks datasheet. Designers migrating to

SolidWorks from 2D CAD will greatly benefit from new functionality

including view folding, which enables legacy DWG or DXF™ drawing

views to be used more efficiently to create new 3D models. A new import

wizard with an AutoCAD-oriented help system also streamlines the

migration process.

• After 3D legacy data is imported into SolidWorks, the FeatureWorks®

feature recognition product (a component of SolidWorks Office

Professional) further speeds design work by searching the incoming file

data for features, such as bosses, holes, ribs, sheetmetal features, and

fillets. These features are then converted into native SolidWorks features

and inserted in the SolidWorks FeatureManager® design tree for easy

modification, reordering, and other standard SolidWorks operations.

• Feature Palette is a powerful tool for designers who have already

accumulated a large arsenal of SolidWorks parts or assemblies. The

Feature Palette, shown at left, operates as an “always on top” window

holding frequently used SolidWorks file. The designer can save time by

simply dragging required components for a new assembly directly from

the Feature Palette and dropping them into the new design.

COSMOS®


DES IGN RE -USE

COSMOSFloWorks can also

determine whether the performance

of the oven will be more efficient if

the designer adds air flow

deflectors.

Figure 17

Feature Palette speeds up design

by keeping a handy set of

prior design elements at the

user’s disposal. The elements

can be fresh designs, or converted

from legacy data.

Figure 18

This model was imported from an IGES

file to SolidWorks. With FeatureWorks

feature recognition software, imported

geometry can easily be turned into an

editable, parameterized feature-based

solid model.

Ease of Use

• MEMS designers need and want powerful functionality from their 3D

CAD software, but it must be easy to learn and use since they are not

using it all the time. If the software is powerful yet easy to use then the

designer can be productive even with only occasional use.

• SolidWorks is gaining favor with MEMS designers worldwide as they

come to appreciate the fit between SolidWorks capabilities and their

requirements.

Collaboration Tools

• Design collaboration has become an increasingly important part of the

development process, enabling designers to share designs easily with

anyone, anywhere.

• Collaboration tools offer new ways for product designers to work more

effectively with other members of the development team. The ability to

share design resources over the Internet can benefits MEMS designers,

from independent consultants to engineers in large multinational

corporations.

• SolidWorks collaboration tools enable the MEMS designer to convey 2D

and 3D product design information to colleagues, customers, funding

agencies, and suppliers easily and efficiently.

eDrawings Professional is the first email-enabled communication tool

that dramatically eases the review of 2D and 3D design information

across your extended product development teams. With eDrawings

Professional you can generate accurate representations of 2D and 3D

models that anyone can view, mark up, and measure without having to

purchase their own markup tools. eDrawings files provide an effective

means of communicating 2D and 3D design information to customers,

vendors, collaborators, production personnel, and everyone else involved

in the product development process. www.solidworks.com/edrawings/

COSMOS®


EASE OF USE/COLLABORAT ION TOOLS

Figure 19

DXF files and DWG files can be easily imported and

incorporated into sketches and drawings.

COSMOS®


COLLABORAT ION TOOLS

3D Instant Website provides the capability to publish product design data

to a live web site of interactive 3D design content. A few simple mouse

clicks from within SolidWorks allow a designer to publish a SolidWorks

model to a web site and communicate the design to the entire work team,

including other designers, manufacturing staff, marketing management,

purchasing agents, suppliers, and customers. Visitors to the site can easily

view, rotate, zoom, and evaluate the design as well as offer comments.

www.solidworks.com/3dinstantwebsite/

Figure 20

eDrawings allow the MEMS

designer to communicate designs,

such as this variable

capacitor, readily to colleagues,

customers, or vendors.

A micrograph of the

capacitor appears below.

Figure 21

3D Instant Website enables

design communication worldwide.

You can publish to a hosted web

site instantly.

Integrated Solution Partner Products

• Available best-in-class partner solutions are fully integrated into the core

SolidWorks 3D modeling software to offer a complete, singlewindow

approach to medical product design.

• SolidWorks software development focuses solely on 3D design tools to

ensure continuous innovation. CAD companies that build strong ties to

Solution Partners for best-in-class, extended solutions — such as finite

element analysis (FEA), computer-aided manufacturing (CAM), product data

management (PDM), and kinematics — make sure that development is done

by the companies best suited for the job. The results are more complete

product design and development solutions.

• SolidWorks provides an unmatched selection of Solution Partner products

plus the highest level of add-on product integration in the industry. Certified

Gold Products offer the look-and-feel of SolidWorks software, simplifying

learning and use and extending best-in-class functionality. All Certified Gold

Products offer singlewindow integration with SolidWorks, are fully

associative, and undergo a rigorous testing and certification process by

SolidWorks to ensure compatibility with every release of SolidWorks.

• Several SolidWorks partners have demonstrated efficient use of SolidWorks

in conjunction with COSMOSWorks for the design, analysis, and fabrication

of MEMS structures and MEMS-related materials.

• Elsyca NV markets software for modeling electrochemical reactions. Elsyca

has supplied the electronics industry with custom electrochemical

deposition analysis tools that model reaction cell behavior during deposition

processes on silicon wafers. One of their electrochemical cell design

evaluations, with deposition current spatial characteristics appears at left.

COSMOS®


T IGHTLY INTEGRATED COMPLEMENTARY APPL ICAT IONS

Figure 22

SEM photoof the RF filter, also

featured above in the 3D Instant

Website.

Figure 23

A scanning micro-mirror. A

broad range of fabrication

techniques benefit from solid

modeling with SolidWorks.

A scanning micro-mirror. A

broad range of fabrication

techniques benefit from solid

modeling with SolidWorks.

COSMOS®



• Another SolidWorks partner, MEMGen Corporation, uses SolidWorks to

design MEMS devices, which they fabricate for customers in a captive fab

facility using their exclusive license to EFAB™ technology. The photos at

left illustrate the accurate predictive nature of the SolidWorks model for

this technology.

Electronic-oriented tools: CircuitWorks from Zeal Solutions offers a

SolidWorks Certified Gold Product solution that enables the merging of 2D

IDF format PCB data and component 3D data to build complete 3D models

of PCB assemblies. These exact models result in optimized packaging

designs with minimum envelope sizes.

Kinematics tools: Kinematics analysis is helpful for developing products

requiring complex motion including many MEMS devices. COSMOS

(COSMOSMotion™) and Certified Gold Product Solution Partner Solid

Dynamics (MotionWorks) offer these type of analysis tools.

For a complete listing of SolidWorks Solution Partner products, please

refer to the “Partner” section of the SolidWorks web site at

www.solidworks.com.

Figure 24

Elsyca models electrochemical

wafer deposition and etching

processes.

Figure 25

MEMGen Corporation uses

EFAB™ technology to produce

MEMS devices defined with

SolidWorks.

COSMOS®



• SolidWorks offers a unique degree of integration with add-on solutions,

supplying valuable functionality beyond that found in the core CAD product.

These solutions operate from within SolidWorks and can be added at any

time to meet new or existing needs.

• SolidWorks Office Professional combines the full functionality of

SolidWorks CAD software with the following design communication,

CAD productivity tools, and data management tools: SolidWorks Office

Professional Design Communication Tools Demonstrate more

effectively how products look and perform with SolidWorks design

communication tools:

SolidWorks Animator — animation software for creating compelling AVI

files from SolidWorks parts and assemblies. PhotoWorks — rendering

software for creating photorealistic images.

3D Instant Website — an easy-to-use tool for publishing live web sites with

3D interactive content.

eDrawings Professional — tools necessary to visualize, interpret,

measure, mark up, and expedite the review of 2D and 3D product designs

across your extended design team.

Figure 26

CircuitWorks allows realistic

PC board layout visualization,

as in this packaged MEMS device

mounted onto a board

populated with other ICs, SMT

capacitors, and resistors.

COSMOS®


ONE STANDARD CAD TOOL TO DES IGN EVERYTH ING

One Tool for all Design Needs

• As organizations increasingly struggle to run leaner and increase

productivity, solutions that optimize their existing capital and human

resource investments become more imperative. This paradigm applies to

research organizations and for-profit corporations alike. Fortunately,

SolidWorks is an investment that has broad application for MEMS design.

• SolidWorks handles design at the sub-micron level, assembles thousands

of components in assemblies, provides native FEA that can be easily

enhanced with tightly integrated analysis products, and designs structures

measuring many tens of meters, including packaging automation

equipment.

Making the Decision

• When weighing information to decide between high-end, specialized

design software specifically targeting MEMS design vs. SolidWorks, which

is an effective single tool for myriad applications, a number of features

should be considered. Features that recommend SolidWorks include:

• Ease of use, so even part-time users can maintain productivity

• Ease of learning, allowing new users to quickly contribute to collaborative

design efforts

• Associativity, from assembly through component parts to mask definition

• Efficient Power, FEA of complex assemblies running easily on standard

desktop computers

• Agility, SolidWorks can be used both to design sub-micron MEMS features

and packaging line equipment measuring tens of meters

Figure 27

This automated packaging cell was

designed with SolidWorks. Design the

MEMS device with SolidWorks, then

output the mask, design the packaging,

and even the automation to put it all

together. Solid modeling across several

dimensional decades ensures everything

fits, everything works.

For additional information about COSMOS products, check out the COSMOS website http://www.cosmosm.com.

SolidWorks Corporation

300 Baker Avenue Concord, MA 01742 USA Phone: 1 800 693 9000 Outside the US: +1 978 371 5011 Fax: +1 978 371 7303 Email: [email protected]

SolidWorks Europe

Phone: +33 4 42 15 03 85 Fax: +33 4 42 75 31 94 Email: [email protected]

SolidWorks Asia/Pacific

Phone: +65 6866 3885 Fax: +65 6866 3838 Email: [email protected]

SolidWorks Latin America

Phone: +55 11 3818 0980 Fax: +55 11 3818 0977 Email: [email protected]

COSMOS

3000 Ocean Park Boulevard, Suite 2001 Santa Monica CA 90405Phone: 1 800 469 7287 Outside the US: +1 310 309 2800 Fax: +1 310 207 2774 Email: [email protected]

SolidWorks CorporationSolidWorks is a registered trademark of SolidWorks Corporation. COSMOS is a registered trademark of Structural Research and Analysis Corporation. All other company and product names are trademarks or registered trademarks of their respective owners. ©2006 Structural Research and Analysis Corporation. All rights reserved.

COSMOS®

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Solid Modeling and Analysis of MEMS Structures · COSMOS ® SOLID MODELING AND ANALYSIS OF MEMS STRUCTURES no. 2 • 3D visualization facilitates communication within the organization