atomic-scale precision motion control stage (the angstrom stage)

Atomic-Scale Precision Motion Control Stage (The Angstrom Stage)

Michael Holmesl, Dr. David Trumpet2, Dr. Robert Hocken' (1) Precision Engineering Group, University of Carolina, Charlotte

Mechanical Engineering Department, Massachusetts Institute of Technology Received on January 9,1995

Abstract

This paper describes a magnetically-suspended six-degree-of-freedom precision motion control stage with sub-nanomet.er positioning stability inside a 100 pm cube of travel. This stage utilizes multiple electromagnetic actuators and capacitance probes to provide control forces and position feedback, respectively. The suspended platen (3 kg mass) is floated in oil to enhance the Performance of tho magnetic bearings. Thc stage has been designed for use as a sample positioning stage for scanning- tunneling microscopy. We present images obtained by scanning-tunneling microscopy which show that the positioning noise of the stage is below 0.2 nm peak-to-peak over 5 seconds. These dat,a demonstrate the utility of this stage as a new concept for precision motion control.

Keywords: precision motion control

1. Introduct ion STM head mount ACTUATOR

As we entcr into the twenty-first century, the need for very high precision positioning stages with rela- tively large ranges of travel will grow. Consider the integrated circuit industry. Since the beginning of integrated circuits, there has been it steady increase in the number of devices manufactured per unit area on a semiconductor substrate or wafer. At the present time the number of devices per chip has grown into the millions. This increased number of devices per wafer is accompanied by a decreasing minimum feature size. As the minimum required feature size of a device shrinks, higher precision positioning stages will be needed to position the wafer during various processing steps. High-precision positioning stages are also needed in areas such as diamond turning and scanned probe microscopy. This research investigates a niagnetic-bearing motion control stage for achiev- ing very high positioning accuracies with an ultimate goal of 0.1 nm positioning resolution inside a 100 pm ciit)e of travel. This magnetic-bearing stage is here- after referred to as the Angstrom Stage [l].

2. Paper Overview

The body of this paper is organized as follows. Sec- tion 3 briefly describes the Angstrom Stage design and components. Section 4 develops the control laws for one of the degrees of freedom and presents a brief overview of the digital controller. Section 5 presents a 0.1 nm step and various STM images that characterize the stage's performance. Finally section 6 summarizes our research and conclusions.

3. The Angstrom Stage

The Angstrom Stage is a magnetically-snspended

cross section

sensor target SENSOR

, sensor 8'\

Figure 1: Angstrom Stage Exploded View

six-degree-of-freedom motion control stage with sub- nanometer positioning noise in a 100 p i cube of travel. The moving element (platen) is suspended by twelve electromagnetic actuators and floated in oil to support its weight and to provide mechanical damping and high frequency coupling between the machine frame and the suspended platen. The electroniag- netic actuators also provide the necessary forces to move the platen in all six-degrees-of-freedom. The six capacitive probe sensors track the position of the platen with sub-angstrorn resolution within the stage bandwidth of approximately 1 Hertz. The Angstrom Stage has been designed to serve as a sample po- sitioriirig stage for scanned probe microscopy. The machine frame supports a Scarinirig-Tunrielirig klilicro- scope (S'I'M) head while the samplo is supported by

Annals of the ClRP Vol. 44/1/1995 455

il ~ i i l l l ~ ) l t + holder iissrll1l)ly wl~icli is mounted 011 the iiioving plat,en. l'his configuratiori idlows samplc posit ioniiig as well its lateral scanning inotions during S'l1.I imaging t.o hc provided by the Angstrom Stage.

Fiyrrt. 1 shows a t.hrc!e-tiirnensional explotied view of t liv frimw. platen. act uator and sensor dcsigns. Eiich of t.he elect ro1liagllc:tic actuators is fi1hriciited with 230 turns of 22 gaug:ca copper wirr around 50-50 Ni-Fr E-core 1aminat.ions. The electromagnetic actu- iitors itr(1 potted directly into rectangular pock~ts in thc: frame. Each actuat.or acts on a corresponding I Ianiination target which is epoxied opposite the actuator in the platctn. 'I'he actuators operate with a nominal gap of 300 pm and are capable of producing in ox(:(w of 50 N at this gap, though normal operational forces are less than 5 N. An extra act,uator was potted ii1t.o a mounting (:artridge for the h g n e t i c Bcwing Calibration Fixture for forcc?-cnrrerit-gap characteri- zattion 121. Figure 2 shows ii gra.phica1 representation of t h c t cdibritt.ion fixture's output. The force-currcnt- gill> curves in Figure 2 show t8hat the core of t,hc

250 microns 90

80 / 1 80 70 I /, J 300 microns

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Current (A)

Figure 2: Force Versus Current for Target Separation Gaps of 250. 300. and 350 microns

it(t1litt,or is not seturatcd for c:urrents through 1.5 Amps and thus can be inodelletl by

where F is the electromagnetic force in Newtons, i is the coil current in Amps. x is the target separation gap in meters. arid C is a constant. [3]. From the data reprcsented in Figure 2. C = 2.45 x Nm2/A'. 'l'hc 12 c?lectromagnetit: actuators are driven by 12 linear power amplifiers which have a gain of 0.034 A/V. T h e linear power amplifiers are designed for low noise operat ion and a high negative current-slew-rate capability [2].

The capacitive sensors are comprised of three picxes, the sensor. guard: and housing. The sensor, guard, and housing are separated by an epoxy insula- tor which is used to bond the assembly together. The capacitance probes are fa.bricated from brass and designed for operation in the oil with a nominal standoff of 100 pin and a range of 150 p ~ n . The sensor/target, separation gap depcmdent. capacitance is converted to a voltage via ADE 3800 probe electronics modules (41. Each of the six capacitance probe circiiits are

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calibrated t,o +lo Volts correspondiug to f.50 p i i .

or cquivalent.ly 5 pm/V. This signal is then aniplified by 1000 resulting in a voltage-to-meters coefficient of 5 x lo-" m/V. The noise: level of the probes is less than 0.1 nni within the 1 Hz bant1widt.h of t.he stag(?

The frame is approximitt.ely 30x30~20 ~ 1 x 1 ~ and is fabricatcxl from 6061-TG aluminum. T h e platen is approximately 17x17~8 cm3 and is also fabricated from 6061-7'6 aluminum. The platen is light-weighted arid floated in oil to support its weight and to provide mechanical coupling of high frequency vibrations. The platen's mass is adjusted to approximately equal the mass of oil that it displaces. The platen and sample holder assembly have a combined mass of 3.09 kg.

15;.

ruby spheres , STM head sample holder support column ' sample holder , spring preload

capacitance probe damping film

actuator I

I actuator target

platen

frame 1. I, ,J

30 cm

Figure 3: Cross Section of the Angstrom Stage

Figure 3 shows a cross-section through the center of t.he stage. In this figure, a 30 cm line is included to indicate the scale. This view shows the platen inside the oil-filled chamber created by the frame. The samplc holder is mounted to t h e saniple holder support column which is bolted to the top of the platen. Three ruby spheres epoxied into pockets in the bot- tom of the sample holder fit into three corresponding grooves in the sample holder support column. This kinematic mount is pre-loaded with a permanent magnet. The STM head has three support columns. The foot of each support column is a steel sphere. The steel spheres fit into three grooves in the frame. Each groove is formed by two parallel cylinders which are pressed into pockets located in the frame. The position of the cylinders is such that the STM tip aligns over the center of the sample holder. This sec- ond kinematic mount is pre-loaded with three springs. With the platen inside the chamber and the top of the frame bolted in place, the chamber is filled with oil such that the oil level is approximately halfway up the sample holder support column. This ensures that all actuators and capacitance probes are operating in oil.

The oil used to float the platen is FS-1265 fluorosil- icone oil [6 ] . The choice of this fluid is dictated by the

following considerations. 1) FS-1265 hits a dielectric constant of 7.0 relative to vacui~ni. The high diclcc- tric constant increases the capacitance of the probes which reduces their noise level. 2) The density of the fluid is 1.27 g/cm3. This allows the light-weighted duniinum platen to achieve neutral buoyancy with rerrsonable size. The neutrally buoyant platen re- quires nea.r zero bias currents through the actuators for suspension thereby reducing t.he amount of heat entering the stage due to power dissipation by the actuators. 3) The oil-filled capacitance probe sensor gaps form squeeze film dampers which provide vis- cous damping in a system which would otherwise have none. Finally and perhaps rnost importantJy. 4) the oil provides high-frequency disturbance rejection. At high frequencies the platen is viscously locked to the franie via the oil. while at low frequencies the platen is free to move as driven by the actuators. Therefore, high-frequency disturbances are coupled to the SIIS-

pended platcm and do not result in relative inotiori betwwn the platen and frame.

4. Controller

The Arigst,rom Stage controller is developed by con- sidering two niodes of operation: lateral and vertical. This section starts by defining the lat.era1 and vertical modes of operation in terms of their corresponding degrees of freedom with rcspcct to act,uator and sensor assignments. Once the modes have been defined, 11 control loop for one of the lateral rnodc degrees of freedom is developed in detail. The lateral and vw- t.ical mode control loops as a whole are developed in a similar ~iianrier. but are not presented here due to space 1imitat.ions (see [I] for further details). Finally. the digital control system is described.

I n Figure 1. the (*apacitance probes. Cl-CG. and the ictuiitors, El-El2 (E8 is opposite E l l and riot. visible in this view), are contairied in the frame which is removed iii this figure. The three lat.cra1 degrees of freedom X: Y, and BZ are controllc!d by the latcral mode iictuators El-E6. Position in these degrees of freedom is measured by the lateral mode sensors C1- C3. The thrcx? vertical degrees of freedom are Z, B,? a.nd B y . The vertical mode actuators are E7-El2 and the vertical mode position sensors are C4-C6. Now that the t.wo modes of operation are defined. we de- velop a control loop for t,he X degrw of freedom as follows.

Figure 5 shows a schematic diagram, a free body diagram, and a control loop for the Angstrom Stage‘s X degree of freedom. The schematic and frcc body diagrams show the forces that, act on t,he suspended platen. This discussion assumes that the suspended platten is floated in oil and that? the mass of the platen equiils the mass of the oil that it, displaces, therefore gravity does not show up in these diagrams. Forces F3 and F 6 in the schematic diagram combine to forin force F in the free body diagram where F = F 3 - F6. ‘I’hc capacitance probe squeeze film dampers are r e p resented by the damping coefficient h. Only tnove- mcnt of the platen in X is considered here and rota-

..-&.!?

- ‘ E9

NOTE: Origin located at center of platen

Figure 4: Actuator iiild Serisor Orio~itations

SCHEMATIC DIAGRAM FREE BODY DIAGRAM

I6 actuator6 c_-

bx

F x

j ’ actuactor 3 -- -.. 13

CONTROL LOOP

digital controller actuators plant

t.ioris of the platen about the Z il.xis ;ir(l assun~vl t o be zero in this discussion.

The control loop is divideti into four scvt.ions. These are the digital controller. the actuators ( t o in- clude power amplifiers). the plaiit., a.ii(i thc positioii sensors. The inputs to t.he digital controllcr ilrr t,lic+ desired X positiori arid the actiial X position. The purpose of this block is to cornniand t,lie iippropriat.(a current so as to drive the X position (mmr to mrc). 1 he controller is purely proportioriii13 illitl its rrriits iire N/m. Since elcctromagnets can exert only attrnc:tive forces, only one of the actuators nec!d hc on ;it ;uiy given time. The decision iis to w1iic:h ac:tuat.or is on is based 011 the sign of the X posit,ion wror. If t,lw X position error is negative. theii i~ct.~iator 6 is ctrivcw with t8ho appropriate currctiit~. Likewise! for il posit,ivc* cr- ror. actiiator 3 is driven. The ac:tiiat.or sckt.or h1oc.k is responsible for dctcitling which actuator to t.urii on. ‘l‘hc input t,o t,his block is dcsirctd X-dirc?c:tctl forcr F.1:

and the output is either F3d = F:c i l l i d F6d = 0 for positivc F z : or F3d = 0 and FGrL = -. F x for nc’gii- tive F z . Consitlctring the case for a posit.ivc2 vrror. the?

T ,

457

tlcsircd force. is theii used to calculate thc necessary currmt for ictuator 3 using

t-L>

wlierc. :r:s is thc known actuator/target separation gap arid C is it constant (C is calculated from experimen- tal data as C = 2.45 x Nm'/A2). Substituting ( 2) into ( 1) r e suh in F ( z . i) = F3d if the model is accuratzto. T h e calculated current is t.hen used to drive ii(:tuator three which applies force F3 to the plant. If linctiirization is successful! the gain from F3d to F3 is unity and thc rc+sultirig force on the platen results in ii c:hangtb in X which is sensed by probes C2 and C3. ' I ' h c b output from the probes is avcraged to give the X position. The control laws for the remaining degrees of freetiom are devt:loped in a similar manner.

Figirrc G shows a system block diagram of the various c:oinpoiierit.s of the Angstrom Stage system which ilr(' now described. The Angstrom Stage frame contains six capacitanw probes which provide position feedback information to the controller. The six capac- ita.nce probc.8 arc connected to six electronics modules whose output. signal is a DC levd proportional to the (:;>pii(:itat>c:e ssnsor/target separation gap, specifically. 5 x 10-" rn/V. Keeping in mind our final objectivci of 0. I i i rn rt?soliition. we invert the (:onversion factor to

I

ANGSTROM STAGE

6 Capacitance 12 Actuators 1 :robes, (I

Z Piezo Volllage Capacitance

Electronics Amplifiers

11 Front-end Amplifiers

50 MHz 80486 PC

DIGITAL CONTROLLER I Figure 6: System Block Diagram

obtain 200,000 V/m and multiple by 0.1 nm to obtain a signal level of 20 pVI0.1 nm. The position feedback signal ultimately inputs to the digital controller via a data acquisition board. The data acquisition board has eight channels of 16-bit A/D, but experiences approximately 7-bits of peak-to-peak noise. With the A/D converter input range set to f 1 0 Volts, this corresponds to approximately 2 mV of noise peak-to-peak. The A/D converter noise is re- duced to 0.2 iriV peak-to-peak by oversampling acd

averaging the A/D converter channels [li. However! this is still a factor of ten too coarse to allow 0.1 nm resolution. Thus we have added front end amplifiers which amplify the position feedback signal from the capacitance probe electronics by 1000. This results in a voltage-to-meters coefficient of 5 x 1 0 - ~ m / v and thus reduces the inherent A/D noise to lo-" m. The problem here is that the input to the digital controller is limited to f 1 0 Volts and thus we have decreased our range of travel to about f 5 0 nm. To get our original range of travel ( f 5 0 pm) back, the stage operatcs about a coarse position setpoint which is adjustable throughout the f 5 0 pm range. The front end amplifiers also contain low-pass filters with a 1 Hz breakpoint to filter out high-frequency noise before the A/D converter.

The Angstrom Stage frame also contains 12 electromagnetic <actuators which provide the necessary forces to suspend and actuate the platen. The actuators are driven by 12 linear power amplifiers whose output current is proportional to the input voltage (0.034 A/V). The power amplifiers are commanded by the digital controller via. an analog output board. The 12-bit D/As are set to a total output range of 0-5 Volts thereby setting the actuator command current quanta level to approximately 42 p A with a full scale value of 170 mA.

Since the stage utilizes the STM to Characterize platen motions! the STM Z-piezo voltage is also read into the digital controller. This signal is not in the control loop, but is ,acquired in order to allow imaging of surfaces.

The final block is the digital controller. This block represents the 50 MHz 80486 PC which is used as the controller platform for the digital control system. The DT2838 data acquisition board, the PC422 analog output board, and a DSP board are all mapped into the PC's address space. The functions of the A/D and D/A boards have already been described. The Digital Signal Processing (DSP) board is utilized to perform the control loop floating-point calculations. The software architecture is multi-rasking in nature and has a state-machine structure. The DT2838 data acquisition board driver is a terminate-stay-resident (TSR) interrupt routine which takes advantage of the 80486's interrupt structure to gain processor execu- tion time and also uses the DMA controller to move the data. The control loop is implemented on the DSP board which can be thought of as an independent computer that shares memory with the 80486. The D/A is also driven by the TSR. The resulting controller runs in the background, stealing processor time when it needs to. The efficient nature of this controller allows for control loop sample rates of up to approximately 500 Hz.

5. Performance

In order to characterize what the capacitance probes are sensing while the Angstrom Stage is under closed- loop control, the measurement scheme illustrated in Figure 7 was used. A position feedback signal is fed

458

1 CAPACITANCE PROBE

P--J HF-300 - lOOHz

iioiw of the stage 'lhe (dihrittiori stiintlard uscd t o characterize the position noise of thc Ang.stron1 Stage is carbon atonis which are spac(~1 iipproxirnatcdy 0.3 iim apart on the surface of highly-oriented pyrolvtic graphitcx.

GAIN = 50

Figurck 7: Position Sensor Noise Jleasuremeiit Block Diagram

into il differ~titial amplifier with a gain of 50 arid bandwidth of 100Hz. The output of t h e tlifferential amplifier is fed to the input. of a digital scope which is connected to a printer. Figure 8 shows the output

V1 ?.OOV Trig +l.OV CH1

Figure 9: STM Image of a 2nm Square of Graphite

r

TIME (sec)

Figure 8: 0.1 nanometer Step Rmponse

voltage of oiie of t,lw vertical capacitance probes during a. 0.1 ntn vertical step. The potential differencc between the dotted lines in Figure 8 is shown in the upper left corner of the scope face ( A V l ) . To trans- late to ail equivalent position, this value is divided by 50, the gain of the differential amplifier! and multi- plied by the volta.ge-to-mcters coefficient (5 x m/V) of the front-end amplifiers and ciipacitance probe electronics to obtain the displacement. The pmk-to-peak noise, before and after the 0.1 nm step, is s w n to be approximately 0.04 ntn. According to the data presented by Figure 8, the Angstrom %age system described in this paper has sub-angstrom positioning noise inside a 100 pm range of travel. Note however that thermal changes result in drifts larger than 0.04 nrn. These drifts are now considered via scanning tunneling ~nicroscopy. The reader is referred to (71 for a discussion on STM.

ion 3 that therc is no mechanical contact between tlie machine frame/STM hetd and the platen/sample holder as- semblies. Thus STM images taken by the setup described will contain information about. the relative motions between the machine frame and the suspended platen. Further, if the sa.mples which we image contain features of known sizc and geomet,ry, then the Srkl provides an independent, means of calibrat- ing the Angstrom Stage. If the STM image is to be used as a calibration tool, then the sizc of the features on thc calibration sample must be on thct sanie order of magnitude as the level of the positioning

Note from the discussion in s

Figure 10: STM Image of a Singlr Strip of Atoms vs. Timt.

Figure 9 is a S'I'M imiige which was taken as dc- scribed above. The features of interost in Figure 9 are the carbon atoms which arc spaccd approximately 0.3 nm apart. While the carbon atoms are visible. rionuniformity throughout the image indicates that there is soine angstrom-sc& rclat,ivc! motion 1,etwrwn thr machino frame arid the susperitled platen. 111 order to brtt.er c:haractc?rizc: this noiso. the Y l t l t t d

piezn was disab1t:d on the STM head so t1ia.t the tip would scan repcatedly in X across ii single row of atonis while servoiiig in Z to maintain i i (:onstilnt. tunneling currcnt. If we plot Z versus X versus Time, we would expect the image to c:ontain vctrticid strips of high and low areas corresponding to the peaks arid vallctys that the tip goes through as it sweeps across that single row of at.oms. The vertical length of thr strips bhcn rcprescnts thc interval of timc. takcn in generating thc image. Any nonlinearity in thc st,rips result from the combination of positioning noise of the platon and thc S'I'M systcm noisct It!vt:l. Note thiit thc: lateral positioning noise of the platen is iri direct cor-

459

rrlation to t h v nonliiicwrity of tlw strips. Figure 10 rcprcwiits the height of the S T S I tip above the sain- ple by thv local gray v i l l l i (b . the. X position of the tip on the horizontal axis. a n r l Timc~ on tlw vwtical asis. Fioiii Figiirc 10. thc l;it(\rid positiolimg noise of t lw Angstroni Stage is IIO grcvittar thiLl1 0 2 nni pvlk-to- I)('iik ovor .5 scoxlds

'I lie ciiscwparic*y I)t.twtw tlic noise levels shown in Figurck 8 iirid i n Figure 10 inciicatc.s that wliih. the stiig" is capable of controlling the> relative position of the pliiterl to the machine frame to a sub-angstrom noisc. level. c.stcrna1 distirrbanccs on the svstern as a wtiolv indiice a niore significant level of noise in the S T l I iiti,igc.s These external tlistlirhances may br t l r w to t ~ ~ t ( ~ r 1 i i i l vibrat ions affwting the STSI licwl. tlyii,iniic s of t I I V t iiiin(4iiig process itself. or to trni- p r a t urv iilld prcwiiro conditions.

Figuro 11 : Sucwssive ST111 Images Demonstrathg Loiig RilIlgt' Capabilities

'I'lic. irriagcs in F1igiirc 9 iirld Figure 10 serve t,o cliarirctctriw the platen's motions as it is being held st i l l iintler closetl-loop control. All that remains is to t l~ !~~ lo~ i s t r i i t~~ the stage's ability to trawrsc rchtivcly long clistanccs and then rct.iirn to t h t t starting point. t 1 i e w l ) v d~illlollst.riiting the long-rangc capabiliticts of t l i e st;igti. Figure 11 shows t.liree sucwssivc. 6.8 i i n i

S(lllil.r(' S'l'kl inlii.gt.s. 'I'lic first imngc shows 3 p(1iiks t hi l t wi're' IIlil(1t.t 011 the grapliittb siiII1j)l(' by pulsing the t.ip with a 0.1 cis. -3.5 Volt pulse [Si. The next iniagc shows ill1 iireii some 40 pin away. The final iiiiagc? shows thc sanic 3 peaks that were visible in t tic. first image. il.ft.er retiirniiig from the point were iiiiagc! 2 was taken. Sote that, approxiitlately 1 nm of t1ierrn;il drift has taken plac:a diiring the a.pproxi- iiiat.(?ly ci minutes elapsed time het.ween t.he first, and lijst irna.gca.

6. Conclusions

It is the intent of t.his research to push thc pcrfor- 111ilnc~~ liniits of miignct.ic-bea.rings in the field of precision m o t h contml. 'The Arigstmiri Stage demon- stratcs the higlwst resolution performance of a rna.g- iictic bcaring stage which has yet beeii acliieved. T lwt best previorisly reported inagiic:tic bcaring position wise [9] is iihout. 3 11111 pctak-to-peak. il ful l orc1c.r of iiiiigIiit.udc~ higher than the rcsiilts we have achieved h c w . 'This also represents the first. tinit? that a- mag- riet ic: suspension stage has been used to provide scanning motions for a scanned-prohf, microscope. LL'c

11avt~ tlernonst.ratetl thv iitilitv of cwnbining magiittic siispension with neutrallv-luovaiit oil flotation in or- rler to ;ichicvc. cstrerriely high position resolution and tlisturbance rejection. 'This hvhrid system has c'xpw- iintLiit idlv rlcmonstratc4 ii novel approi1c.h to motioli control which provides resolution comprt itivc wit h pirzoelcctric actuators iis ~vcll i ~ s control of six degrees of freetlorri with only il single moving part. The tic- tuators also have the poteritial for rnuch longer travel t hari piezoelectric actuators. In conclusion. this work establishes proof-of-wncept for a new class of motion control stages with atomic resolution.

7. Acknowledgments

This work forins part of a thesis submitted for the cle- grw of 11a5ter of Science at the University of North Carolina at Ch;trlotte !I] . l'he research was carried out in the Prwision Engineering Laboratories and ivi\s fiiridecl by the. Niitioniil Scicwv Fouiidation 1111-

dttr grillit DDAI-9396305. 'The ADE Corporatioil provided design support for thv capiicitivc' gaging c 4 e c * - troiiics.

8. References

[l] Holuies. k1.L.. *.Analysis a i d Design of a. SIngnc.tically-Siispc.ndt?d Precision Motion Coiitrol Stage," Master's Thesis. Department of Electrical Engineering. UNCC. Ch;i.rlottc?. NC. 1994.

121 Poovey, T.. Holmes: M.L.. and Trurripcr: D.L.. *'A Kincmat,ically Coupled Magnetic: Beariiig Calibrii- tion Fixture." Precision Enginerring: Journal of thc Arnctrican So(5et.y for Precision Engineering. Vol. 16. No. 2. April 1994.

[3] Trnrtipert D.L.? Sanders. .J.C., Nguyeii: T.H.: ilnd Queen, M A . . .'Experinient.aI Results i n Nonlin- car Coinpensat,ion of i i Oric!-Dt:gree-of-Freecloiri 34ag- iietic Siispension.!' 1nt.c:rniltioriiil Symposium on Mag- netic Suspension Tcchiiology, NASA Langley Re- sc!arch Centrr: Haniptoil, Virginia, August 19-23. 1991.

[4] ADE 'Technologies, 77 Rowe Stxet , Newton. MA 02166. [S] Batchelder, D.! "Analysis and Design of High-

Rcsolution Capacitmce Probes for IJse in a. Preci- sion Motion Control Stage." h s t c r ' s Thesis, Depart- ment of Electrical Engineering. UNCC. Charlotte. YC. 1994.

161 Dow Corning Corporation: P.O. Box 997. Mid- land. MI 48686-0997.

171 Hansma, P.. and Tersoff, .J.: "Scanning tunneling microscopy," Journal of Applicd Physics 61 (2): 15 .January 1987. [8] Miller. J.A.. a.nd Hocken: R...J., "Scanning tan-

neling microscopy bit niakirig 011 highly orient.ed py- rolytic graphite," .J. Appl. Phys. 68, 905 (1990).

[9] Williains, h3.E.: 'I'rumpcir, D.L.: and Hocken. R.. ! *' hlil.glic:ti(: Beii.ring Stage for Pliotolitliographv." CIRP Annals 1993 hhiufacturing 'khnology, vol- urrie 42/1/1993? Pages 607-610.

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atomic-scale precision motion control stage (the angstrom stage)

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