Design, Prototyping, Modeling and Control of a MEMS Nanopositioning Stage

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1 Amercan Cntrl Cnference n O'Farrell Street, San Francsc, CA, USA June 9 - July, Desgn, Prttypng, Mdelng and Cntrl f a MEMS Nanpstnng Stage Y. Zhu, Member, IEEE, A. Bazae, S. O. R. Mheman, Fellw, IEEE, and M. R. Yuce, Senr Member, IEEE Abstract In ths paper, real-tme feedback cntrl f a nvel mcr-machned -degree-f-freedm (-DF) thermal nanpstner wth n-chp electrthermal pstnng sensrs s presented. The actuatn wrks based n thermal expansn f slcn beams. The sensng mechansm wrks based n the dfference between the electrcal resstances f tw electrcally based dentcal Slcn beams. The dfference ncreases wth dsplacement as the heat cnductance f the sensr beams vary ppstely wth pstn, resultng n dfferent beam temperatures and resstances. The sensr par s perated n a dfferental way t reduce lw-frequency drft. The nanpstner has a nnlnear statc nput-utput characterstc. An pen-lp cntrl system s frst desgned usng plynmals that apprxmately cmpensate the nnlnear characterstcs. It s expermentally shwn that plant uncertantes and sensr drft result n unacceptable perfrmance fr pen-lp cntrl f the thermal nanpstner. Hence, feedback cntrl methds are necessary fr accurate nanpstnng. A clsed-lp feedback cntrl system was then desgned usng a prprtnal-ntegral (PI) cntrller and the nnlnear cmpensatr used fr the pen-lp cntrl system. The clsed-lp system prvdes acceptable and rbust trackng perfrmance fr a wde range f set pnt values. Fr trangular reference trackng, whch s needed n raster-scanned SPM, the trackng perfrmance f the clsed-lp system s further mprved by ncrpratng a sutable pre-flter. Index Terms-Thermal actuatn, thermal pstn sensng, mcrelectrmechancal system (MEMS), nanpstnng, feedback cntrl. H I. INTRODUCTION gh precsn nanpstners have been used extensvely n many applcatns such as scannng prbe mcrscpy (SPM) [], atmc frce mcrscpy (AFM) [], and emergng ultrahgh densty prbe strage system [3, 4]. Althugh macr-scale nanpstners can acheve nanmeter-scale pstnng reslutn and accuracy, they are relatvely large and expensve [, 6]. Mcrelectrmechancal System (MEMS) nanpstners have attracted ncreasng research nterest recently due t ther small sze, lw cst, Manuscrpt receved September 8,. Ths research was funded by Australan Research Cuncl (ARC) dscvery grant- DP Y.Zhu s wth the Schl f Engneerng, Grffth Unversty, Australa (emal: y.zhu@grffth.edu.au). A.Bazae, S.O.R.Mheman, and M.R.Yuce are wth the Schl f Electrcal Engneerng and Cmputer Scence, the Unversty f Newcastle, Australa (emal: {al.bazae, reza.mheman, and hghly parallel nanscale manpulatn and assembly strateges [7]. Clsed-lp feedback cntrl f the pstners s hghly desrable f a hgh degree f dsplacement precsn s requred, and such a cntrl system needs an accurate surce f pstn nfrmatn [8]. Hwever, many f the MEMS nanpstners reprted n the lterature have n n-chp sensrs due t the restrctns asscated wth mcr-fabrcatn prcesses [9]. Thus, the n-plane mvements are ften measured by laser reflectance mcrscpes [, ] r ptcal mcrscpes [], makng the ftprnt f the whle system farly large. There are several exceptns n the lterature, fr example, an embedded n-chp capactve dsplacement sensr was ntegrated n a thermally actuated pstner n [3]. Nevertheless, nly pen-lp results were btaned, and a cmplex fabrcatn prcess was requred fr electrcal nsulatn between electrcal heatng and sensng crcuts. Recently, a thermal sensng scheme was used n a prbe-based strage devce [4]. Mcr-heaters were used t measure the mtn f a MEMS mcr-scanner wth reslutn f less than nm. Cmpared t a cmb capactve sensr, a thermal sensr s mre cmpact and can be easly ntegrated wth actuatrs n a MEMS devce. In [, 6], ff-chp electrmagnetc cl actuatrs were adpted fr scanner actuatn, and a cmplex mass-balanced structure was desgned fr vbratn resstance purpses. In ths paper, a nvel electrthermal pstn sensr s ntegrated wth a thermal actuatr n the same MEMS chp wthut the need fr nclusn f extra electrcal nsulatn fabrcatn prcess as reprted n [3], r assemblng tw chps as reprted n []. Cmpared t ther MEMS actuatn mechansms, the thermal actuatrs have advantages f lw vltage peratn, large frces, and a hgh vbratn resstance due t ther stff structures [7]. A MEMS devce wth ntegrated electrthermal actuatn and sensng has been mcr-fabrcated n a bulk slcn prcess. T reduce the lw frequency thermal drft, the sensrs are perated n a par and measured by a dfferental crcutry. The n-chp dsplacement sensng enables a feedback cntrl capablty. A mdel f the pstner s derved and a prprtnalntegral (PI) feedback cntrller s mplemented dgtally n a dspace rapd prttypng system t nvestgate the clsed-lp perfrmance f the pstner. Open-lp and clsed-lp step dsplacement trackng were nvestgated. The clsed-lp step respnse results shw a pstnng reslutn f 7.9 nm and a tme cnstant f.6 ms, whle the //$6. AACC 78

2 pen-lp seek peratn resulted n a maxmum pstnng errr f 6 nm. Gd trackng perfrmance was als btaned fr a Hz trangular reference by usng a -DF feedback cntrl system cnsstng f a PI cntrller and a pre-flter. Fg.. Schematc dagram f the thermal pstn sensr wth a dfferental amplfer crcut. Befre applyng a vltage acrss the actuatr, the pstner stage s at the ntal rest pstn (dashed bx n Fg.), where the tw edges f the snk plate are exactly algned wth the mddle f the tw thermal resstve sensrs R and R. The sensrs are based by a dc vltage surce dc, and the heat generated n the resstve heater s cnducted thrugh the ar t the heat snk plate (pstner stage). As the plate s centered between the tw thermal sensrs, the heat fluxes ut f the sensrs are dentcal, thereby equalng the temperature and resstance f the sensrs. After applyng a vltage n the actuatr beams, the pstner stage s dsplaced twards left. The heat fluxes asscated wth the sensrs n the left and n the rght are becmng dfferent, resultng n a crrespndng dfference n the resstance f the left sensr (R ), and the rght sensr (R ). Thus, the dsplacement nfrmatn f the pstner stage can be detected by measurng the resstance dfference between the tw sensrs. The dfferental changes f the resstance result n current varatns n the beam resstrs, and the currents are cnverted t an utput vltage usng a par f transmpedance amplfers and an nstrumentatn amplfer. T suppress the cmmn-mde nse, the gans f these tw trans-mpedance amplfers must be well matched by adjustng the feedback resstance f the trans-mpedance amplfers. Emplyng the dfferental tplgy allws the sensr utput t be mmune frm undesrable drft effects due t changes n ambent temperature r agng effects. II. DESIGN The cnceptual schematc vew f the nanpstner s presented n Fg.. The devce s mcr-fabrcated frm sngle-crystal slcn usng a cmmercal bulk slcn mcrmachnng technlgy-soimump n MEMSCAP. Ths prcess has a µm thck slcn devce layer and a mnmum feature/gap f µm. The Scannng Electrn Mcrscpe (SEM) mage f the whle devce and a sectn f t are prvded n Fg.. The pstn sensrs are tw beam-shaped resstve heaters made frm dped slcn. Applcatn f a fxed dc vltage acrss the heaters results n a current passng thrugh them, thereby heatng the beams. As a heat snk, a rectangular plate s placed besde the beam heaters wth a µm ar gap. The pstner stage s actuated by a thermal actuatr, as llustrated n Fg.. Fg.. SEM mages f the mcrmachned nanpstner The pstner stage s actuated by a chevrn thermal actuatr, as llustrated n Fg.. Cmpared t ther actuatn methds, the thermal actuatrs are smple t mplement, perate at lw vltage, and prvde large frces. Due t the stffness f the structures, n cmplex mass-balanced structures are needed fr vbratn resstance purpses, as prpsed n [6]. The chevrn thermal actuatr has tw pars f thn ht arms at a small angle wth respect t each ther as shwn n Fg., and the dmensns are lsted n Table I. The chevrn actuatr s peratng vltage range s typcally t, dependng n the gemetry. The dsplacement s prprtnal t, and the maxmum dsplacement s lmted by bucklng f the ht arms at hgh temperatures (>7 ºC) []. T reduce the thermal cuplng effects frm the thermal actuatrs t thermal sensrs, a number f hles were made n the centre shuttle between actuatrs and the heat snk plate. The hles are expected t mprve the thermal cnvectn, thereby thermally nsulatng the heat snk plate frm actuatrs. The suspensn beams help the thermal nsulatn as well, due t the heat can transfer t the substrate thrugh the suspensn beams and ts anchrs. III. MODELING In ths sectn, we predct the sensr temperature and resstance as a functn f sensr bas and actuatr dsplacement. T smplfy the analyss, lumped parameter apprach and statc cndtns are cnsdered here. Ths means we assume a unfrm temperature dstrbutn n each sensng resstr. The fllwng dscussn shws hw lumped parameter analyss can predct the temperature n terms f the appled vltage. Let the electrc resstance f a resstr at rm temperature T be R (Ω) and ts varatn wth temperature s descrbed by a cnstant temperature ceffcent α (/ C). The verall thermal cnductance between the resstr and the utsde wrld, ncludng ts cnnectn t a vltage surce, s K (W/ C). Assumng a unfrm temperature dstrbutn T acrss the resstr, we can equate the electrc pwer generat- 79

3 Temperature (Centgrade) ed n the resstr wth the thermal pwer flw frm the resstr t the utsde wrld as: K ( T T ) R [ ( T T )] () where s the cnstant vltage acrss the resstr. Snce the cnstant α des nt depend n temperature, the resstance value and ts temperature can be frmulated n the fllwng frm: R R T T R K R K Fg. 3. Schematc dagram f the based thermal sensrs. Referrng t Fg. 3, let us defne K and K as the verall thermal cnductance frm electrc resstrs R and R f the sensr t the area arund the sensr, respectvely. As the plate n Fg. 3 mves t the left sde, K ncreases whle K decreases. Let us assume a smple dependency between the thermal cnductance and the plate pstn x, defned n Fg. 3, n the fllwng frms: K ( x ) K K K x m n m ax m n, K ( x ) K m n K K m ax m n ( x ) (4) where x x / L s the nrmalzed pstn, L s the length f each resstr, and K mn and K max refer t mnmum and maxmum thermal cnductance f each resstr. In ths way, Equatns () and (3) can be used t predct the steady-state values f resstrs and ther temperatures n the fllwng frm: R ( x, ) R T ( x, ) T R K ( x ) R K ( x ) {, }, () where R s each resstance value at zer bas vltage. At zer actuatn, where x. and K K, () (3) ( K K ) /, we assume that the sensr resstrs m ax m n match. Hence, the sensr utput vltage s prprtnal t R R. We emply ths dfference between electrc cnductances t measure the dsplacement as llustrated n the fllwng smulatn (a) T T x / L (b) Resstances x / L (c) Sensr utput.6 R / R R (R - -R - ) R / R x / L Fg.4. Steady-state values versus dsplacement fr (a) resstr temperatures, (b) resstr values, and (c) nrmalzed sensr utput. Assumng the parameter values n Table I and usng Equatns (4) and (), the steady-state values f temperatures, resstances, and sensr utput fr dfferent pstn values are btaned as shwn n Fg. 4(a)-(c), respectvely. Althugh the resstance values depend nnlnearly n dsplacement, the sensr utput exhbts an almst lnear dependency n dsplacement. TABLE I. PARAMETER ALUES FOR SIMULATION Parameter alue α (K - ) R (Ω) 39 T ( C) 7 K mn (W/K) 8 - K max (W/K) 6 - () 6 I. CONTROL In ths sectn, pen-lp and clsed-lp pstn cntrl strateges are nvestgated fr the pstner. A dspace- 3 rapd prttypng system was used fr real tme mplementatn f the cntrllers and data acqustn. A. Open-lp cntrl Wth a sensr bas vltage f 7, an pen-lp test was perfrmed where a slwly varyng trapezdal vltage n the range f -9 was appled t the actuatr (usng dspace). Fg. shws the wavefrms. The sensr has a small ffset at zer actuatn. After cancellng the sensr ffset, the bserved sensr utput respnse t actuatn nput can be descrbed by the utput-nput statnary characterstc shwn n Fg.6. 8

4 (-) Sensr utput () Actuatn vltage () Actuatn vltage () (-) Sensr Output () Dsplacement ( m) Tme (sec) Fg.. Open-lp respnse f thermal pstner t a slwly varyng trapezdal actuatn Experment Ftted Plynmal lne. Havng btaned the dsplacement data, a statc dsplacement characterstc can be generated fr the sensr as shwn n Fg. 9 (the rsng prtn f the data n Fg. was used wth the sensr ffset cancelled). As shwn n Fg. 9, anther nnlnear mappng s btaned by fttng a seventh rder plynmal t the expermental sensr characterstcs. Ths mappng, whch s used fr nlne apprxmatn f the dsplacement usng the sensr sgnal, s descrbed as: d P ( y ). 3 y. 7 7 y y y y. 4 y. y. 4 8 where d s the dsplacement n μm and y s the sensr sgnal n vlts multpled by (-) after ffset cancellatn. Experment Ftted Plynmal 3 4 (-) Sensr utput () Fg.6. Output-nput statnary characterstc ( P () ). T generate ths characterstc, we used the rsng prtn f the expermental trapezdal data. A nnlnear mappng was btaned by fttng a nnth rder plynmal t the expermental utput-nput characterstc, shwn n Fg.6. As shwn n Fg. 7, mappng P ( ) s used n seres wth the actuatn fr cmpensatn f the nnlnearty n the statc nput-utput characterstc. 3 4 (-) Sensr utput () Fg.9. Statc dsplacement-sensr characterstc ( P () ). 4 3 Experment Ftted Plynmal Fg.7. Blck dagram f the pen-lp cntrller. Calbratn Data pnts Ftted plynmal y =.x -.x x x +.6x Actuatn vltage () Fg.8. Nnlnear mappng frm actuatn t dsplacement usng calbratn data. T cnvert the sensr utput vltage t dsplacement, a ffth rder plynmal was ftted t the calbratn data btaned by PMA. The plynmal alng wth the calbratn data pnts are shwn n Fg. 8. Usng ths plynmal, a dsplacement data crrespndng t the trapezdal actuatn vltage s btaned and dsplayed n Fg. wth the dashed y = d d d 3 -.3d +.d+.4 Fg.. Statc sensr-dsplacement characterstc ( P () ). ( ) In rder t map a desred dsplacement t ts crrespndng sensr sgnal value, a ffth rder plynmal, dented by P r n Fg. 7, was ftted t the expermental sensrdsplacement characterstc, as shwn n Fg.. Fr penlp cntrl we use the nnlnear mappngs P () and P (), as shwn n Fg. 7, t cmpensate fr system nnlneartes. Usng a sample and hld blck, the sensr ffset s autmatcally cancelled befre applyng the actuatn vltage. As shwn n Fg. wth a star case reference sgnal, the pen-lp cntrl methd cannt prvde an acceptable trackng perfrmance fr dsplacement. Ths s due t plant uncertantes and sensr drft. Hence feedback cntrl s 8

5 Trackng errr ( m ) Phase (degree) Magntude (db) Trackng errr ( m ) necessary fr accurate pstnng. (a) Reference Open lp Clsed lp (b) feedback. The pre-flter wth the frequency respnse shwn n Fg. 4, s used t speed up the respnse and reduce the trackng errr wthut affectng the stablty margns and unty lw-frequency gan f the clsed-lp system. The trackng perfrmance fr a Hz trangular reference s shwn n Fg.. It s seen that dsplacement utput clsely fllws a desred trangular reference wthn a wde range f μm wth a standard devatn f.8 μm. - Open-lp Clsed-lp Tme (sec) Fg.. Clsed-lp and pen-lp expermental results fr,.,, 7. and µm seek peratns. (a) Dsplacements, (b) Trackng errrs. B. Clsed-lp cntrl Fr clsed-lp cntrl, we ncrprated a PI cntrller n addtn t the nnlnear mappngs, as shwn n Fg.. The ntegratn part n PI cntrller prvdes a clsed-lp unty lw frequency gan frm reference t dsplacement fr setpnt trackng and rbustness t uncertantes and dsturbances. The prprtnal part n the PI cntrller s used t reduce versht n step respnse. Wth an ntegral gan f k= and a prprtnal gan f kp=., the pstnng perfrmance s sgnfcantly mprved as shwn n Fg.. Based n ths cntrl scheme, a cntrllable desred respnse f. µm steps ver a µm range was btaned wth a tme cnstant f.6 ms, as llustrated n Fg.. As a cmparsn, a smlar pen-lp seek peratn resulted n a maxmum pstnng errr f.6 µm. Fg.3. Tw-degree-f-freedm feedback cntrl structure Frequency (Hz) Fg.4. Bde dagram f pre-flter n -DF cntrl system. Dsplacement Reference (a) (b) Fg.. Blck dagram f the clsed-lp PI cntrller. Fr trangular reference trackng, we used a -degree-ffreedm cntrl system as shwn n Fg. 3. The DF cntrl system cnssts f a PI cntrller and a pre-flter (the nnlnear mappngs are as befre). T prvde mre stablty margns we used lwer gans f k=3 and kp=.6 fr the PI cntrller. Ths s als useful t reduce effect f measurement nse n the cntrlled dsplacement utput due t Tme (sec) Fg.. Trangular reference trackng by -DF feedback cntrl system. 8

6 . CONCLUSION A nvel mcrmachned slcn nanpstner wth nchp thermal actuatr and sensr has been presented wth nanmeter reslutn and lw sensr drft. The MEMS pstner was embedded n a feedback lp t realze a precse pstn cntrl. Due t the nnlnear nature f the thermal actuatr, a nnlnear nversn blck was added t the feedback lp t lnearze the plant. The expermental results shwed that the pstner wth the PI cntrller acheved a hgh degree f pstnng accuracy wth very gd rbustness. Due t the lmtatn f the SOIMUMPs fabrcatn prcess, t s nt pssble t desgn a tw-dmensnal thermal based pstner n a sngle devce layer. Hwever, the thermal sensrs and actuatrs can be placed n dfferent layers, whch can be fabrcated n METALMUMPs prcess thrugh MEMSCAP. A DOF thermal based nanpstner s under nvestgatn by the authrs fr magnng applcatns. [4] M.A.Lantz, G.K.Bnnng, M.Despnt, and U.Drechsler, A mcrmechancal thermal dsplacement sensr wth nanmetre reslutn, Nantechnlgy, 6 (), pp [] A.Sebastan, A.Pantaz, S.O.R. Mheman, H.Pzds, and E.Eleftheru, Achevng subnanmeter precsn n a MEMS-based strage devce durng self-serv wrte prcess, IEEE Tran. n nantechnlgy, vl.7, n., 8, pp.86-9 [6] M.A.Lantz,, H.E.Rthuzen, U.Drechsler, W.Haberle, and M.Despnt, A vbratn resstant nanpstner fr mble parallel-prbe strage applcatns, J. mcrelectrmechancal systems, vl.6, n, 7, pp [7].Kaajakar, Practcal MEMS. Las egas, N: Small Gear Publshng, 9. REFERENCES [] G.Bnnng, and H.Rhrer, The scannng tunnelng mcrscpe, Sc.Am., vl.3, pp.-6, 986. [] G.Bnnng, C.Quate, and C.Gerber, Atmc frce mcrscpe, Phys. Rev. Lett., vl.6, n.9, pp , 986. [3] N.B.Hubbard, M.L.Culpepper, and L.L.Hwell, Actuatrs fr mcrpstners and nanpstners, Transactns f the ASME, l.9 Nvember 6, pp [4] A.Pantaz, M.A.Lantz, G.Cherubn, and H.Pzds, and E.Eleftheru, A servmechansm fr a mcr-electr-mechancal-system-based scannng-prbe data strage devce, Nantechnlgy,, pp.s6- S6, 4 [] Y.K.Yng, S.S.Aphale, and S.O.R.Mheman, Desgn, Identfcatn, and Cntrl f a Flexure-Based XY Stage fr Fast Nanscale Pstnng, IEEE Trans. n Nantechnlgy, l.8, N., pp.46-4, 9. [6] Y.K.Yng, S.S.Aphale, and S.O.R.Mheman, Atmc frce mcrscpy wth a -electrde pezelectrc tube scanner, Revew f Scentfc Instruments, l.8, N.3, pp337,. [7] C.H.Km, and Y.K.Km, Mcr XY-stage usng slcn n a glass substrate, J.Mcrmech. Mcreng., l., pp.3-7,. [8] S.Devasa, E.Eleftheru, and S.O.R.Mheman, A survey f cntrl ssues n nanpstnng, IEEE Trans. n cntrl systems technlgy, vl., n., 7, pp.8-83 [9] K.Gum, X.X.L, H.Ba, B.Lu, Y.Wang, M.Lu, Z.Yang, and B.Cheng, Sngle wafer prcessed nanpstnng XY-stage wth trench-sdewall mcrmachng technlgy, J.Mcrmech.Mcreng., l.6, pp , 6. [] J.J. Grman, Y-S. Km, and N.G. Dagalaks, Cntrl f MEMS nanpstners wth nan-scale reslutn, Prceedng f IMECE6, Chcag, IIIns USA, Nvember -, 6. [] R.Hchey, D.Samet, T.Hubbard, and M.Kujath, Tme and frequency respnse f tw-arm mcrmachned thermal actuatrs, J.Mcrmech.Mcreng., 3, (3), pp [] Y.Sun, M.A.Gremnger, D.P.Ptasek, and B.J.Nelsn, A sually Served MEMS Manpulatr, Expermental Rbtcs III, Sprnger Berln/Hedelberg, 3, pp.-64. [3] L.L. Chu, and Y.B. Ganchandan, A mcrmachned D pstner wth electrthermal actuatn and sub-nanmeter capactve sensng, J. Mcrmech. Mcreng., 3 (3), pp