Thermal Micromechanisms for Out-of-Plane Actuation

Thermal Micromechanisms for Out-of-Plane Actuation

Key Words: MEMS, Thermal, Asymmetric, Vertical, Out-of-Plane, Actuators, Adaptive Optics

Brian Patrick TreaseUniversity of Michigan

Advisor: Prof. Sridhar KotaDepartment of Mechanical Engineering

Thomas Zipperian, Manager (Org. 01769)James Allen, Technical Advisor (Org. 01769)

Tuesday, August 7, 2001

Special thanks to Daryl Dagel and Michael Baker of SandiaNational Laboratories for their technical conversations, review, and advice.

reviewer

Text Box

Note: This paper has been neither peer-reviewed nor published.

B.P. Trease Thermal Micromechanisms for Out-of-Plane Actuation - 2

ABSTRACT

Many currently “hot” Micro-Electro-Mechanical System (MEMS) applications, such as micro-optics, require high-displacement, high-resolution out-of-plane actuation. We are specificallyfocusing on the control of adaptive optics via deformable mirror manipulation. Our goal is todevelop electrically-heated thermal microactuators capable of at least 12 microns out-of-planemotion with 25 nanometer resolution. While many thermal actuators use bimaterial technology(i.e. unequal expansion due to different coefficients of thermal expansion), we desire to fabricatesolely in polysilicon, simplifying the process steps and creating compatibility with theSUMMiT VTM Process, Sandia’s 5-layer polysilicon fabrication technology. The new actuatordesigns share the principles already seen in in-plane devices: unequal thermal expansion (due todifferent cross-sections) of connected parallel beams, resulting in tip displacement. After thedevelopment of an analytical model as a design tool, these actuators will be combined within aleverage scheme leading to several feasible designs. An array of candidate devices will bemodeled in computer-aided design software, undergo thermo-mechanical analysis in finiteelement analysis software, and be submitted for fabrication in the SUMMiT VTM process. Theresults of this work will aid in the expansion of MEMS technology from simple planar motion tocomplex 3-dimensional mechanisms.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed MartinCompany, for the United States Department of Energy under Contract DE-AC04-94AL85000.


TABLE OF CONTENTS

SUMMARY.................................................................................................................................... 4

1. INTRODUCTION................................................................................................................. 4

1.1. SCOPE OF RESEARCH........................................................................................................ 41.2. BACKGROUND.................................................................................................................. 4

1.2.1. Adaptive Optics Background................................................................................... 41.2.2. MEMS Background ................................................................................................. 5

1.3. DESIGN GOALS FROM A MEMS PERSPECTIVE ................................................................. 5

2. TECHNOLOGIES FOR MIRROR ACTUATION ........................................................... 6

2.1. ALTERNATIVES FOR OUT-OF-PLANE MOTION .................................................................. 62.2. THERMAL ACTUATORS..................................................................................................... 7

2.2.1. Bimaterial................................................................................................................ 72.2.2. Single Material........................................................................................................ 8

2.2.2.1. In-Plane Actuators........................................................................................... 82.2.2.2. Out-of-Plane Actuators ................................................................................... 9

3. PRELIMINARY PROTOTYPES AND RESULTS......................................................... 10

3.1. DEVICE DESCRIPTION..................................................................................................... 103.2. METHODS AND EQUIPMENT............................................................................................ 113.3. RESULTS......................................................................................................................... 11

4. ACTUATOR MODELING ................................................................................................ 13

4.1. FOURIER’S LAW ............................................................................................................. 134.2. THERMAL EXPANSION.................................................................................................... 154.3. FORCE METHOD ............................................................................................................. 154.4. VIRTUAL WORK ............................................................................................................. 164.5. FINITE ELEMENT ANALYSIS ........................................................................................... 16

5. NEW DESIGNS................................................................................................................... 16

6. FUTURE WORK ................................................................................................................ 17

7. CONCLUSIONS ................................................................................................................. 18

BIBLIOGRAPHY ....................................................................................................................... 18


Summary

Thermal micro-electro-mechanical devices are being investigated for their potential as sources ofout-of-plane actuation. Experimental prototypes have given absolute displacements of greaterthan 16 microns (13 microns of dynamic displacement) with 12V applied across the devices.This has further motivated our development of analytical models to predict such displacements.Several new device designs await to be evaluated with the new analytical tools. One of the newdesigns is presented for the reader. The devices are to be fabricated in the SUMMiT VTM

Process, Sandia National Laboratories’ 5-layer polysilicon fabrication technology.

1. Introduction

Where will the field of adaptive optics find new technologies to assist in mirror manipulationwith very high resolution? Several potential solutions exist and it is the purpose of this paper toexplore devices based on Micro-Electro-Mechanical Systems (MEMS). DevelopingMEMS-based adaptive optics is very important in realizing inexpensive and lightweight laserimaging systems and space telescopes. Furthermore, by exploiting the basic theory of thermalactuation, we will arrive at simplicity and robustness not found in other adaptive opticsstrategies. Aside from the applications in optics, out-of-plane actuation is becoming arequirement in many other MEMS applications. With much of the need for in-plane actuationbeing met by current devices, the next logical step is to explore 3-dimensional motion.

1.1. Scope of Research

To address the topic of mirror control for adaptive optics, out-of-plane thermal actuators arebeing investigated. This prompts the question: How can high-displacement out-of-planeactuation (also referred to as vertical actuation) in MEMS devices be achieved while maintainingthe high resolution required for adaptive optics applications? In pursuit of an answer, prototypeactuators have already been fabricated and tested. Mathematical models have been and arecontinuing to be developed. Combined with finite element analysis information, an array of newdevices is being designed for fabrication by Sandia National Laboratories’ multi-layerpolysilicon fabrication technology, the SUMMiT VTM Process (Sandia Ultra-planar, Multi-levelMEMS Technology for Five levels).

1.2. Background

1.2.1. Adaptive Optics Background

Adaptive Optics (AO) is the field of imaging correction via deformable mirrors, acousto-opticand electro-optic modulators, or nonlinear crystals. Corrections are needed for a variety ofoptical aberrations, both those internal to the optical system and those external, such asatmospheric conditions. Adaptive optics is currently applied to both ground-based and space-based telescopes, and to laser imaging and focusing systems. Today, space telescopes use heavy,fixed, rigid mirrors that are usually impervious to significant deformations. However, theoriginal, flawed mirrors of the Hubble Space Telescope provide a striking counter-example. Had


the Hubble mirror been of an adaptive and deformable nature, no second repair mission wouldhave been required. The space program would have been saved from spending an enormousamount of funds and from a great deal of public embarrassment.

Initial adaptive optics schemes included piezoelectric1 actuators used to deform continuousmembrane mirrors made of glass. Piezoelectric mirrors are usually assembled into macro-scaledevices and are thus too large and heavy for applications such as a space telescope. The numberof mirrors can range from hundreds to thousands. As the number increases, the cost offabrication likewise increases, as does the likelihood of flawed parts.

The particular adaptive optics project that motivates this research [1] seeks to reduce the weightof a primary telescope mirror to less than 10 kg/m2 (cf. Hubble’s 250 kg/m2), thereby attractingMEMS as a possible solution. While movable plates corresponding to the facets of the primarywill be driven by piezoelectrics for coarse adjustment (~10s of microns of motion), an array ofmicromirrors is embedded in each plate for fine adjustment. These micromirrors are required tocorrect root-mean-square distortions down to a value of 1/20th of the incident wavelength. Thesignificance of these requirements to a MEMS designer is described below.

1.2.2. MEMS Background

The field of MEMS is a relatively new area of science and engineering, combining aspects ofmechanical engineering, electrical engineering, chemistry, physics, and many other fields.Device fabrication is based on the same lithographic techniques developed to create integratedcircuits; as a result, all mechanisms are initially fabricated in the plane of a silicon chip. Theycan have an area of more than 1mm2, but thickness is limited to around 10 microns. Thus, mostMEMS devices that have been developed are highly planarized. Some technology exists for out-of-plane assembly, such as pop-up mirrors, but very few designs exist for repeatable out-of-planeactuation.

MEMS fabrication is a batch process; each wafer can contain hundreds or thousands of devices.Since the cost of producing a single wafer is constant, the high volumes distribute the overheadcosts. Therefore, as the number of required actuators increases, batch fabrication makes MEMSmore favorable than piezoelectrics.

1.3. Design Goals from a MEMS Perspective

The design goals desired for an adaptive optics system have already been stated in Section 1.2.1.From a MEMS application perspective, the specifications translate into another set ofperformance goals. Bulk motion for positioning may still be provided by larger actuators (e.g.piezoelectrics) moving a plate containing hundreds of micromirrors. The micromirrors will thenbe responsible for fine adjustment. The mirror rotation specifications require at least 3 actuatorscapable of at least 12 microns piston (vertical) displacement. For fine imaging, 9-bit resolutionis required. This is defined as stroke divided by 29, which is 12µm ÷ 512 = 24nm resolution. In

1 Piezoelectric materials deform when voltage is applied across them, providing a source of actuation.


addition, the actuators are to be actively controlled per changing optical conditions, at speeds upto 300 Hz.

Another goal is 99% surface coverage with mirrors. This can only be achieved by placing theactuators entirely underneath the mirrors. This goal is very feasible and well-suited for Sandia’sSUMMiT VTM process, which allows for 5 individual levels of polysilicon, more than any otherexisting fabrication process.

2. Technologies for Mirror Actuation

2.1. Alternatives for Out-of-Plane Motion

The first alternative to using thermal microactuators is to not use MEMS devices at all. Fixedmirrors and meso-scale adaptive optics are found in most of today’s optical imagingtechnologies, but both are expensive and heavy. Meso-scale adaptive optics includes those thatare actuated by piezoelectrics. Further, while fixed mirrors can solve the problem of not creatingtheir own aberrations, there is no way for them to correct for image distortions due toatmospheric conditions.

Some work has been done on vertical actuation in MEMS, but many designs have onlyintermittent positional control, such as on/off switching. Such mirrors have been mounted onelectrostatic plates that tilt back and forth in seesaw fashion. (eg. Texas Instruments’ DigitalMicromirror Device (DMD) for projectors)

Another scheme for vertical actuation is the 4-bar slider-crank mechanism used for pop-upmirrors. These are typically used for one time assembly or on/off switching, not for precisioncontrol under dynamic operation. The joints used in these devices are not pin joints butoverlapping planar beams that intersect each other in square-hole-and-peg fashion. There is a lotof clearance and sloppiness inherent in these joints, making them ill-suited for precision control.

Buckled beams provide another source of out-of-plane motion for micro-devices. Long, thinbeams can be fabricated in plane. When axially loaded by an in-plane actuator, they will buckleout of plane. Quevy et al. [2], have fabricated scratch-drive driven, buckled-beam mechanismsthat provide 90 microns of vertical motion, but only for one-time assembly. These beams requireexcessive amounts of voltage and force for initial buckling. However, after buckling, only smallchanges in force should be required to cause further displacement, and the potential of theseactuators is still being explored.

Finally, some researchers have been experimenting with vertical out-of-plane actuators, theimpetus and subject of this research. Burns and Bright [3] have fabricated a device 200µm longused to rotate a mirror out of plane. By applying 14.2 volts for 5 seconds they induced 20microns of permanent out-of-plane deformation. This was a one-time actuation for assembly,and the displacement was not to credit, but the great force that it exerted which was leveraged topush the mirror. For active mirror control, Chiou and Lin [4] fabricated a similar device. Over10 microns of vertical displacement was achieved by applying only 8 volts. The principles ofthermal actuation that drive both of the above devices will be discussed in the next section.


2.2. Thermal Actuators

Most thermal actuators are driven on the principle of unequal thermal expansion of parallelplates, beams, or discs. This has already been demonstrated and proven useful in bimaterialactuators and in-plane MEMS devices.

2.2.1. Bimaterial

Bimaterial actuators, also known as bimorphs, have been around for some time. In fact, this isthe technology behind the common thermostat. Two beams or plates of different materials,usually two metals, are firmly bonded along their common interface. Having differentcoefficients of thermal expansion (α), each beam tends to deform to a different length when theentire structure is heated. Because of the geometric constraint imposed by their connectedboundaries, they cannot freely expand as they naturally would and instead cause the beam todeflect. The beam deflects as a curve, with the tip rotating away from the longer beam, i.e. thelonger beam is on the outside of the curve.

Figure 2-1 Principle of thermal actuation in bimaterial structures

Except for metal processing issues, this might be an ideal approach for a MEMS thermalactuator. While metallization steps are common in many fabrication schemes, they add a greatamount of process difficulty and cost. Further, the SUMMiT VTM process that we will use forfabrication uses only polysilicon for all 5 of its layers.


2.2.2. Single Material

2.2.2.1. In-Plane Actuators

Due to the difficulties of fabricating with more than one material, an alternate actuatortechnology has been developed. Based on parallel beams of different cross sections, theseactuators are sometimes called “asymmetric thermal actuators” or “unimorphs”. These havebeen fairly well developed for in-plane actuators, and the same principles can be used in creatingout-of-plane motion, provided enough structural layers exist.

By connecting two asymmetric beams together at their free cantilever ends and fixing their otherends to separate electrical contacts on the chip substrate (see Figure 2-2), an electrical circuit isformed.

Figure 2-2 Layout of a basic asymmetric parallel beam in-plane thermal actuator [5]

When an electrical current is passed through the device via the contacts, resistive heating occurs.Also known as Joule heating, the heating intensity is directly related to the resistance of eacharm. The resistance, R, is related to the inherent resistivity of the given material (ρ), the area(A), and the length (L) of the beam, as seen in the following formula: R = ρ ∗(L/A). Thenarrower beam’s smaller cross-sectional area yields a higher resistance. Joule heating is relatedto resistance by the following formula: Q (heating in Watts) = I2 R. The result is greater heatingof the thin beam, causing it to expand more than the thick beam despite their equal coefficient ofthermal expansion. The disparate thermal expansions have the same effect as bimorphsstructures, resulting in curvature of the tip toward the cooler beam.

Another simple, although not often used, thermal actuator design exists, which provides furtherdesign flexibility. Two parallel beams are also used in this approach, but rather than havingvaried cross-sections, they are of different lengths, as depicted in Figure 2-3.


Figure 2-3 Layout of a length-varied thermal thermal actuator.A motion-amplifying extended jaw is shown at the tip. [6]

Here, even with an outside source equally heating the entire device, the longer beam willdisplace more because of its initial starting length: �∆L (deformation) = αL(∆T). Furthermore,in this constant cross-section case, one treats the entire device as one beam with one resistance.Fourier’s Law for internal heat generation predicts the hottest spot to be in the center, which willnaturally be located in the longer beam segment. Therefore, the longer beam will not only behotter, but will also have a greater response for any given temperature change. Combining thisknowledge with the principle of asymmetric beams allows the engineer an additional designvariable.

2.2.2.2. Out-of-Plane Actuators

Similar to in-plane single-material electro-thermal actuators, vertical thermal actuators also workon the principle of disparate thermal expansion. As mentioned above, several devices havealready been fabricated [3],[4]. In these devices, a thick beam is stacked directly over a thinbeam.

Figure 2-4 Diagram of an out-of-plane thermal actuator

Current

They are parallel, connected to separate electrical contacts at one end and connected by a thinflexure at the other end, electrically linking the beams in series. This electro-thermo-mechanicalcircuit works in the same manner as observed for in-plane actuators, giving an upwarddisplacement of the free end when actuated. The research of both devices has provided valuabledata and demonstrates the potential for out-of-plane actuation. However, the actuators stillrequire more design work and analysis and have yet to be incorporated into further leveragingschemes.


3. Preliminary Prototypes and Results

3.1. Device Description

To evaluate the potential of fabricating useful out-of-plane thermal actuators via the SUMMiTTM

Process, three proof-of-concept devices have already been fabricated and tested. These are verysimple ad hoc designs that were laid out with little engineering and no design calculations.Evidence of any motion at all was desired before spending time developing models anddesigning. The first design tested is the “scissor-leg table”, which is basically two asymmetricthermal actuators merged together, as shown in Figure 3-1 and Figure 3-2.

Figure 3-1 Top-view of "Scissor-leg Table" vertical thermal actuator

Figure 3-2 Side-view of displaced vertical thermal actuator

Two sets of thin, hot beams are connected to opposite ends of the same thick, cold beam(considered a plate here). When actuated, both beams try to deflect their ends upward, resultingin nearly level lifting of the plate. A second design was a modification of the first, but with thesections of the thin beams located near their grounded ends made even thinner. These thinnersections act as flexures, allowing more mobility of the deflecting beams, but at a risk of loweringthe threshold voltage for material breakdown. The third design was similar to both of the above,except that one of the thin beams was stacked over the thick beam, as seen in Figure 3-3.


Figure 3-3 Top-view of vertically rotating thermal actuator

Therefore, the end of the thick beam connected to the thin beams below it will deflect upward,and the other end (connected to the thin beam above) will deflect downward. Thus, the purposeof the third design is to produce a high-torque rotation.

3.2. Methods and Equipment

The proof-of-concept devices were analyzed on microscope probe stations with a voltage sourcecapable of delivering high currents. Out-of-plane deflection was measured using the focus dialon the microscope, which was calibrated to 1 micron. DC Voltage was applied across thedevices in 1 volt increments until they failed. Between each increment, the voltage was turnedoff completely. Amperage through the devices was recorded at each increment. A video wasalso made to capture the motion of the devices.

3.3. Results

For descriptions and graphs of complete results, please refer to the appendix.

These small structures, about 200µm in length, produced large amounts of displacement, furtherdriving the pursuit of this technology. The results for the first design, the thick-flexure “scissor-leg table”, are included in Figure 3-4. The three curves represent the absolute deflection whenthe voltage is on, the permanent deformation from the original fabricated position, and therelative displacement between the two (which is the amount of actual movement for thatparticular actuation.)


Figure 3-4 Out-of-Plane Displacement of the Thick Flexure "Scissor-leg Table" Actuator

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12Voltage (V)

Out

-of-

Pla

ne D

ispl

acem

ent (

mic

rons

)

Absolute Disp. with Voltage Applied

Permanent Deformation after Voltage Removed

Relative Motion per Actuation (difference)

Presented in Figure 3-5 is the plot of milliamps versus volts for this device. While the plot ismonotonically increasing, it is not as linear as one would desire or expect for resistive heating ofsuch a simple structure. Several sources for the nonlinearities are being investigated: change ofmaterial properties, change of resistance via changes in geometry, and possibly convection andradiation heat losses. Based on previous finite element models, the last two are typicallyconsidered insignificant in MEMS. Due to the unexplained nonlinearities, they are still inquestion here as potential factors.

Figure 3-5 Current vs. Voltage for the Thick Flexure "Scissor-Leg Table" Actuator

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12

Volts

mill

iAm

ps

While this device was able to produce up to 16 microns of absolute displacement (13 micronsrelative) at 12V and 7mA, the thin flexure device displaced a maximum of 14.5 microns absolute(10 microns relative) at 12V and 6.3mA. The rotating beam design produced highly nonlinear


results due to large permanent deformation (17 microns on one end!). At higher voltages, thedevice performed in reverse; the applied voltage acted to return the structure from itspermanently deformed position back to its original position. At most, it produced 6.5 microns ofrelative displacement and 5.2 degrees of relative rotation at 13V and 4.2mA.

4. Actuator Modeling

To better understand and predict the operation of these thermal actuators, analytical models arebeing investigated. Such models will serve as useful design tools in creating new actuators.

4.1. Analytical Model

4.1.1. Fourier’s Law

First, the internal temperature profile of the beams needs to be determined form Fourier’s heattransfer laws. Internal heat generation is actually more complex than heat flow analysis underexternal heating, where circuit analogies simplify analysis. Fourier’s heat equation is a second-order differential equation with, in this case, non-constant coefficients.

k

xq

dx

Td )(2

2

−=

We have solved this step of the solution for an N element structure by writing equations for eachelement (q is constant over each element) and then constraining the temperatures andtemperature gradients to be equal at each boundary. The equation for the ith element is foundbelow:

If the total current through the device (I) is known, the heat generation can be found for eachelement i:

2

2

2 ii A

Iq

ρ=

However, if only the voltage is known, then the voltage across each element (Vi) mustfirst be calculated. This can be done using R = ρ(Li/Ai) and simple circuit analysis.

2

2

i

ii L

Vq

ρ=

element i TiTi-1

Li

Tsubststrate TsubststrateT1 Tn-1


Allowing each element to have its own coordinate system, we can set the following boundaryconditions:

T(0)i = Ti-1

T(Li )i = Ti

where T(x)i is the temperature distribution for each element. Solving Fourier’s equation thenyields the following formula for temperature distribution:

xL

TTxLx

k

qxT

i

iii

ii

12 )()( −−++−=

This formula can be written for each element, but solving the system of equations requiresanother set of equalities. Not only must the temperatures at each interface be equal, but thetemperature slopes must also be equal. Since all heat generation is finite, the first derivative oftemperature must be continuous throughout the structure. This is accomplished through thefollowing equality:

11

)0()( ++

= ii

iii dx

dTL

dx

dT

The general solution to the above equation is shown here:

+

++++=

+

+++

+

+−+

1

111

1

111

2 ii

iiiiii

ii

iiiii LL

LqLq

k

LL

LL

LTLTT

Writing the above equation for I from 1 to N-1 gives us a system of linear equations that caneasily be solved for T1 through TN-1, which are all the internal nodes. We have done this with amatrix solution, first rewriting the above formula as follows:

iiiiii CTBTAT ++= +− 11

where

1

1

+

+

+=

ii

ii LL

LA

; 1++

=ii

ii LL

LB

;

+

+=+

+++

1

111

2 ii

iiiiiii LL

LqLq

k

LLC

The N equations can now be written in matrix format:

−

−

=

−−

−−

−−

−

−−

−

−

−

−

−−

NNN

N

i

N

N

i

N

NN

ii

TBC

C

C

C

TAC

T

T

T

T

T

A

BA

BA

BA

B

11

2

2

011

1

2

2

1

1

22

22

1

...

...

...

...

100000

10000

0...1...000

00100

000...1...0

00001

000001

or more simply as[ ] [ ] [ ]CTAB = .


T0 and TN are known; they are both equal to the substrate temperature, TS. [AB] is band diagonaland easily invertible, giving us the solution:

[ ] [ ] [ ]CABT 1−=

4.1.2. Thermal Expansion

With the thermal profile of each beam known, the respective theoretical expansion of eachrespective beam is easily calculated from

( )∫ −=∆ dxTxTL substrateii )(α

Substituting equation 4-1 and the values of Ti into the above equations gives the individual beamelongations:

−++=∆ −

Sii

iii

i TTT

LLkA

IL

21213

2

2ρα

The calculation is theoretical because each beam is assumed to be free to expand withoutconstraint. Knowing these theoretical expansions, one can find the actual forces in the structurethrough a process described in the next section.

4.1.3. Force Method

Our problem is statically indeterminate; it has more variables to solve for than it does equationsto do so. A common technique to solve this type of problem is the Force Method. If we assumethat one end of our structure is free (e.g. the connection of the thick beam to the ground), then wecan predict the displacement of that point using only the simple thermal expansions obtainedabove. The forces and moments (torques) required to take this structure back to its originalconfiguration can now be calculated using conventional methods. These forces are taken to bethe same forces required to hold in place the original completely constrained structure – theforces and moments that we seek.

Huang and Lee employed this method for a simple parallel beam structure. Refer to their workfor a complete description [5]. One drawback of this method is that, the compliance matrixwould need to be reformulated for every different basic structure. The follow-up work of thisreport will include an example based on the structures used in our prototype testing.

For devices where there is one continuous path for electricity from electrode to electrode with noother structural members, a more systematic solution can be found for a generic N-elementstructure. This is in the next phase of this research, and will be an analytical solution based on afinite-element technique where Hermite polynomials represent the shape functions of the beams.Hermite polynomials automatically include both the end displacements and rotations of thebeams, eliminating the need to manually create a compliance matrix by inspection of the designlayout.


4.1.4. Virtual Work

Knowing the forces and moments in a structure, one can use the Virtual Work Method [7] to findany given displacement. First, a dummy load at the point of interest is assumed and the forcesand moments it would introduce are calculated. By multiplying these and the actual internalforces in the structure (determined above), displacements can be found. The follow-up work tothis project will also include an example of this method, continuing from the results of the ForceMethod example, as stated above.

4.2. Finite Element Analysis

Finally, as verification of the analytic models and for higher fidelity results, Finite ElementAnalysis (FEA) will be performed on the structures. This is a numerical solution of the posedproblem, performed on a computer. The structure is broken up into many small segments forwhich a computer can create a large matrix. The electrical, thermal, and mechanical analysis foreach element can then be easily performed by the computer and combined for the total output.

There exists a trade-off of usefulness and accuracy between analytical solutions and FEAsolutions depending on the complexity of the problem. For complex structures with coupledbehavior (i.e. electro-thermo-mechanical), analytical solutions usually require many moresimplifying assumptions than an FEA model. In that case, an FEA model can be significantlymore accurate, but at the same time cost considerably more computing time. Also, because anFEA solution cannot be represented by a single simple formula, it does not provide the designtool convenience of an analytical solution. Finally, analytical formulas are much moreconvenient to use in optimization schemes, which will be of interest in the later design stages ofthis project.

5. New Designs

Once all of the design tools are in place, a number of new potential actuator designs will beinvestigated and laid out for fabrication. As an example, one new design that is a building blockfor many designs is described. The concept is to create a device with good deflection but zerotip rotation, so that other similar devices can be arranged in parallel or series, connecting at thecommon zero degree angle.

Figure 5-1 Diagram of proposed thermal actuator building block

This can be done by connecting two out-of-plane thermal actuators in series – one inverted withrespect to the other (see Figure 5-1). If only the first is considered, then its tip deflection andangle can be calculated. However, since its tip is connected to another actuator, the secondactuator displaces the same amount (in the same direction), but rotates the same amount in theopposite direction, thus canceling the final tip rotation (see Figure 5-2).


Figure 5-2 Deflection curve for new actuator building block

By connecting two of these building blocks tip-to-tip, the force characteristics improve. In aparallel configuration, as seen in Figure 5-3(a), the force is doubled. In addition, the symmetryprovides extra balance and resistance to external loads. On the other hand, by stacking thesedevices on top of each other (in series as shown in Figure 5-3(b)), a possibility in theSUMMiT VTM Process, the displacement can be multiplied. Such a building block could becomea standard component used in many applications.

Figure 5-3 (a) Building blocks arranged in parallel. (b) Building blocks arranged in parallel and series.

(a) (b)

The above design and additional designs will be laid out on a custom CAD system built on top ofAutoCAD 2000i, a computer-aided design software package. All of the design work mustconform to the rules of the already-established SUMMiT VTM surface micromachining process.The CAD model can be converted to a solid model for FEA analysis in the Nastran softwarepackage and for kinematic (motion) analysis in Working Model software.

6. Future Work

The research is still incomplete, but we hope to fabricate an array of numerous devices forphysical testing to verify our analytical models and see which designs perform best. TheAutoCAD files described in the previous section will be converted into the required number of2-dimensional photolithography masks, which will then be submitted to the fabrication center ofSandia National Laboratories’ Microelectronics Development Laboratory. Fabrication takes 3 to4 months, after which the devices will be tested in Sandia’s MEMS Performance Labs. Thelengthy time for fabrication will allow us to further develop both the analytic and finite element


electro-thermo-mechanical models. The analytical solutions may also be used for designoptimization during that time.

The physical post-fabrication test results will be valuable in validating and modifying the modelsonce again. The improved models will be used to create another iteration of improved actuators.The modeling, designing, fabricating, and testing cycle will continue until the performance goalsare met.

7. Conclusions

Prototype out-of-plane thermal actuators have been fabricated and tested to realize their potentialfor adaptive optics applications. The initial results are very promising – up to 17µm of absolutemotion and 13µm of relative motion with only 12-14 applied volts. These devices are only“rough drafts” and our development of new design tools should increase performancesignificantly. New discoveries will aid in determining if MEMS-based devices are a suitablechoice for continuing research in adaptive optics. In general, the continuing results of thisresearch will assist in the transition of MEMS actuation from mostly 2-dimensional planardevices to those which can perform complex 3-D motion.

Bibliography

[1] B. Sweatt, “3-Meter, Ultra-Lightweight Telescopes with MEMS-Based Phase-FrontCorrection”, Sandia National Laboratories Internal Proposal, LDRD 02-0096, 2001

[2] E. Quevy, L. Buchaillot, and D. Collard, “Realization and Actuation of Continuous-membrane by an Array of 3D Self-assembling Micro-mirrors for Adaptive Optics”, 14thIEEE International Conference on MEMS, IEEE, pp. 329-332, 2001

[3] D. Burns and V. Bright, “Design and performance of a double hot arm polysilicon thermalactuator”, SPIE vol. 3224, pp. 296-306, 1997

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Appendix – Summary of Test Result Figures

The following is an outline describing the charted test results contained in the appendix. Fordescription of the experiment, please refer to the original report, Section 3.

Nomenclature

In viewing the graphs, several types of data may be included at once. Those marked as LS or RSrefer to the left-side and right-side of the actuator, respectively. As seen in Figure 3-1, LS refersto the end where the two outer beams connect, and RS to the end where the two inner beamsconnect. For the rotator actuator, as seen in Figure 3-3, LS refers to the end with two beamsconnecting and RS to the end with the single beam connecting.

The data points marked as “on” refer to data taken when the voltage was applied – the absolutedisplacement from the initial zero reference. Data marked as “rest” refer to measurements takenafter the voltage had been removed, thus indicating permanent deformation. Finally, thosemarked as “diff” indicate the amount of relative motion – the difference between the absoluteand permanent displacements for a given actuation.

• on – absolute displacement with voltage applied• rest – permanent displacement after voltage removed• diff – relative motion per actuation (difference between “on” and “off”)

Notes

The plots of Deflection vs. Current are included for thoroughness, but may be misleading andappear unusable. This results from the experiment being voltage-controlled, not current-controlled. Thus, current is a dependent variable and does not always serve as an appropriatecomparison axis.

For graphs comparing measurement repeatability (Figures A-3, B-3, and C-3), the testingconditions varied slightly. While it is commonly accepted that the nearly neglictible heatcapacity of MEMS devices leads to nearly instant cooling times, the experimental observationsindicate a possible discrepancy. Testing done on Chip #2 was performed with very little pausebetween voltage increments. However, it was noted during the testing of Chip #5 that whengiven longer breaks, the unactuated (permanent) displacement continued to decrease towardzero. In one case, after 1 additional minute, the beam dropped 1.5µm, and one-half hour laterdropped another 3.5µm. This is an unexpected phenomenon with several possible explanations:continued cooling of the device, stiction effects, and/or slow elastic relaxation of the polysilicon.Therefore, to provide more consistent and accurate results, about 1 minute was counted betweensuccessive measurements during the testing of Chip #5.


Scissor-leg Table ActuatorsThick-flexure SLTA

Figure A-1 – Deflection vs. VoltageFigure A-2 – Deflection vs. CurrentFigure A-3 – Comparison of Repeat TestsFigure A-4 – Current vs. Voltage (with Comparion of Repeat Tests)

Note the nonlinearity of these curves. See comments in Section 3.3. Also, in thecomparison plot, both curves initially match. After 3 volts, they continue to matchin shape, but are offset. This variance in not yet explained.

Thin-flexure SLTAFigure B-1 – Deflection vs. Voltage

Note that there is now very little permanent deformation, and it remains fairlyconstant, especially compared to the previous tests, as seen in Figure B-3. Thisseems to correlate to the longer rest time between each voltage increase.

Figure B-2 – Deflection vs. CurrentFigure B-3 – Comparison of Repeat TestsFigure B-4 – Current vs. Voltage (with Comparion of Repeat Tests)

Here, the curve appears very smooth, as a result of more intermittent data pointsand the longer voltage rest time. Also note here the changing concavity of thecurve. The several inflections are unexplained and merit further investigation.Finally, the comparison curves match fairly closely here, indicating betterrepeatability.

ComparisonFigure AB-1 – Comparison of Absolute DisplacementsFigure AB-2 – Comparison of Relative DisplacementsFigure AB-3 – Comparison of Electrical Performance Curves

Neglecting the data point at 3 volts, these two curves are very similar in shape,with about a 1 mA offset starting at the 2 volt measurement. This agrees with thefact that the thicker beam should have lower resistance and thus higher currentfor a given voltage.


Rotator ActuatorThese graphs are the most erratic and unrepeatable. This is most likely due to theunique geometry employed, the contact of the thick beam and the single thinbeam, and the very large permanent deformations.

Figure C-1 – Deflection vs. VoltageNote that after 11 volts, further increases of voltage seem to have little effect onthe left side of the device. The measurements merely wander about an averagevalue. This could be explained by the contact that takes place at that side, thuspreventing any further motion. The data for the right-side seems more regularand is mostly monotonic.

Figure C-2 – Deflection vs. CurrentFigure C-3 – Comparison of Repeat Tests

The device on Chip #5 lasted longer than the one on Chip #2, surviving 4additional voltage increases. Several possible explanations exist: variedenvironmental conditions, the effect of pulsing vs. constant voltage, the differentcooling times employed, and external shocks experienced by the probe station.

Figure C-4 – Current vs. Voltage (with Comparion of Repeat Tests)The plot for Chip #5 is interesting in that it contains two linear segments, offset byabout 1 mA. The linear curves for each are shown; that data points used for thesecond line are circled. It is also interesting that the device on Chip #2 failedright as it reached the top of the first linear curve. Otherwise, the curves for bothchips are fairly consistent.

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Thermal Micromechanisms for Out-of-Plane Actuation