TIMA Lab. Research Reports

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1 ISSN 9-86 NS INPG UJF TIMA ab. sarch prts TIMA abratry, 46 avnu Féli Viallt, 38 Grnbl Franc

2 Dynaic siulatin f an lctrstatic pwr icr-gnratr Wi Ma., Man Wng 3, ibr ufr TIMA abratry, 46 Av. Féli Viallt, 38 3 Grnbl, Franc Dpt f Mch. Engg., 3 Dpt f EE Engg., th Hng Kng Univrsity f Scinc and Tchnlgy, lar Watr Bay, Kwln, Hng Kng Abstract Micr-fabricatd lctric gnratrs, scavnging abint chanical nrgy, ar th ptntial pwr surcs fr autnus systs. Th analysis f such a icr-gnratr including an nrgy cupling fild shws a high dgr f cplity. Nnlinar bhavir f th syst as th analysis vn r difficult. In this papr, w prsnt th dling f an intgratd flating gat lctrstatic pwr icr-gnratr. Nnlinar stat quatins dscribing its dynaic bhavir ar intgratd nurically using SIMUINK. A linar quivalnt circuit ntwr basd n an lctr-chanical analgy was als built. Bth dls shw th cnsistncy in th sall-signal rgi. Pwr gnratin up t µw is prdictd, at a driving frquncy arund 4 Hz and assuing an input displacnt f 5µ. Kywrds: Enrgy scavnging, lctrstatic MEMS dvic, transducr dling.. Intrductin Vibratin-t-lctricity cnvrsin ffrs th ptntial fr autnus systs t b slf-sustaining in any nvirnnts. cnt advancs in MEMS tchnlgy nabl th cratin f a slf-pwrd syst with a MEMS dvic acting as an lctrchanical transducr. Thr ar thr physical principls typically usd t gnrat lctrical pwr fr chanical tin: lctragntic [], lctrstatic [] and pizlctric [3]. Elctrstatic ffct was shwn as a prising slutin fr th st significant advantag f its ptntial fr intgratin with icrlctrnics. A singl-wafr intgratd flating-gat lctrstatic pwr icr-gnratr has bn iplntd in ur rcnt wr. paring with th structur assbling a chanical rsnatr t anthr substrat cntaining an lctrt, dscribd in [4, 5], ur gnratr uss an insulatd flating gat ad f plycrystallin silicn (ply-si) t prvid a bias vltag ncssary fr its pratin [6]. Such a slutin liinats th nn-trivial alignnt f th substrats that hindrs ptial pratin and scaling f th gnratrs. Th dynaic bhavir f th gnratr can b dscribd using a st f diffrntial lctr-dynaical quatins. lsd-fr analytical slutin t th cplt syst

3 is difficult t btain, du t its nnlinarity. Fr sall-signals whr th syst can b cnsidrd as linar, a linarizd dl, basd n th quivalnt circuit ntwr, can b usd. Such a linar quivalnt circuit ntwr was built. Whn th input displacnt attains larg variatins, it is ncssary t us th diffrntial quatins in thir gnral fr. W hav als built a syst dl basd n th stat quatins that can b usd fr th siulatin f bth linar and nnlinar bhavir. Th rsults btaind fr ths tw dls ar prsntd and discussd. Th papr is structurd as fllws. In Sctin, th wring principl f th flating gat lctrstatic pwr icr-gnratr is discussd. In Sctin 3, th bacgrund f th dvic dling is prvidd. In Sctin 4, th siulatin rsults ar shwn and in Sctin 5, th iplntatin f th dvic is dscribd. Finally, Sctin 6 is th cnclusin.. Wring principl Th prsnt pwr gnratr (Figur ) includs a chanical rsnatr and an insulatd flating gat ad f ply-si. hargd by lctrn tunnling, th flating gat wrs li n in a nn-vlatil ry dvic. Pwr is gnratd using a variabl capacitr ( cf ), frd btwn a vabl lctrd (als th prf ass f th rsnatr) and a fid cuntr lctrd (als th flating gat). Mchanical ε a tin in -dirctin inducs changs in cf ( y) ( b y ), hnc als a h currnt thrugh th trnal lad ( ). is th lctric prittivity, h is th gap btwn th lctrds, a is th width f th capacitr lctrds nral t th dirctin f tin and b is th lngth f th lctrds alng th dirctin f tin. Th rsnatr is ralizd using a phtrsist ldd lw tpratur lctrplating prcss [7] that is cpatibl with th flating gat prcss. Th vabl lctrd with its suspnsin lnts ar ad f gld, thus bringing an additinal advantag f rducd intrnal pwr lss. M ß i (t) Arbitrary rfrnc y(t) cf (-y) Flating gat with nt charg f Figur. upd lctrchanical dl f th flating-gat pwr gnratr.

4 3. Dynaic dl and linarizatin Th pwr gnratr is an lctrchanical syst, including a purly lctrical part, a purly chanical part, and a cupling chanis lining th tw parts. An lctrstatic cupling fild btwn th lctrds f th dvic prvids nrgy chang f th pwr gnratr. Suppsing thr is n lss in th cupling fild, th nrgy put int th fild by th lctrical and chanical surc is strd and can b rcvrd cpltly du t its cnsrvatin. Enrgy chang in th cupling fild can b dscribd by th trinal pairs f vltag V and currnt i in th lctrical part and frc F and vlcity ẋ in th chanical part. Bth vltag V and frc F can b drivd fr th ttal diffrntial f th nrgy W strd in th fild: cf V W ε a h ( b y ) () F W cf aε sgn( y) sgn( y) () y y cf cf whr sgn ( y) if y and if < y. Th bhavir f th lctrstatic pwr gnratr can b dscribd by a st f diffrntial quatins. Th diffrntial quatin f th chanical part f th syst is btaind by th applicatin f Nwtn s nd law: M β ( y) F, (3) whr M is th ass, ß is th daping cfficint, is th spring cnstant and F is th lctrical frc acting n M by th cupling fild. Th valus and y ar th displacnts f th uppr and lwr (fra) lctrds f cf, as shwn in Figur. Th diffrntial quatin f th lctrical part f th syst is basd n Kirchff s vltag law, taing int accunt vltag drps n th cpnnts, cf, and, als shwn in Figur. Th iprtant part f all lctrstatic transducrs is a bias vltag supplying th nrgy t th syst. Unli traditinal slutins using lctrts with fid chargs, a ply-si flating gat is prsntly usd. Th diffrntial quatin gvrning th lctrical part f th gnratr is givn by d dt cf cf f, (4)

5 whr is th flating gat t grund capacitanc, is th charg ving thrugh th lp. f is th nt charg strd in th flating gat and ffctiv bias vltag V f st up by f. dnts th It is clar that th frc F displays a quadratic dpndnc n th charg, which as th syst nnlinar. f 3. Gnral dl Th dynaic bhavir f th lctrstatic pwr gnratr in its gnral fr can b dscribd by th st f diffrntial stat quatins [8]. Such a dscriptin can b usd fr th siulatin f bth linar and nnlinar bhavir f th syst. Stat quatins can b slvd ithr nurically r using a syst diagra that rprsnts by blcs ach part f a athatical dscriptin. W hav built a syst dl basd n th stat quatins using SIMUINK, a sftwar pacag fr ulti-dain dling and dsign f dynaic systs. Th dl is basd n fllwing stat quatins f th syst ( X y) f cf X cf ( X y) (5) X X X 3 (6) a X X ε ( ) sgn( ) 3 βx 3 X y X y (7) M hcf ( X y) whr X, X and X 3 ar th stat variabls. Thy dnt th charg, displacnt and vlcity ẋ, rspctivly, and ar dtrind by th prsnt stat and th instantanus valus f all inputs. cf is a functin f diagra usd fr th analysis is shwn in Figur. X y. Th cplt blc Th charg is btaind n th utput f th intgratin unit shwn in th uppr part f th blc diagra, th chanical cpnnts, vlcity ẋ and displacnt ar valuatd in th lwr part f th sa diagra. In th diagra is als dfind th lctrstatic frc aing th cupling btwn th chanical and lctrical parts.

6 u Elctrical part urrnt s Vltag 7 harg h//ps/a/n u Frc 3 Acclratin 4 Vlcity 5 Displacnt 6 / s s Elctrd Width b B u Abs ps*a*n/h Input Displacnt X Balanc Pint Mchanical part Figur. Dynaic dl f th pwr gnratr built in SIMUINK. 3. inarizd dl A linar dl has a grat practical iprtanc in th cass whn a sall-signal pratin nar an quilibriu pint can b suppsd. Th syst can b thus dscribd in a sipl way by ans f a linarizd lupd-paratr dl basd n an lctrchanical analgy. inar bhavir is achivd fr incrntal variatins arund an quilibriu stat. Th linarizd vltag V l and frc F l can b btaind thrugh Taylr sris pansin abut a static quilibriu pint, th stat with zr displacnt y in ur dsign, as V F l l V V V, ( y) ( y) (8) b [ ( y) ] [ ( y) ] ( y) V ( y) ( y) F F, (9) ( y) b b whr is th capacitanc f cf at th quilibriu pint, th linarizd quatins can b writtn as f. Thn

7 ( ) [ ] Γ Γ ) ( ) ( d d d d d d V b V t t M t in in β () whr b V F Γ. It is bvius that scnd it f F l in quatin (9) acts li a psitiv spring in th chanical part b V. Figur 3 shws th linarizd quivalnt circuit ntwr that has bn st up basd n th quatin () fr th cas f lctrstatic pwr gnratr. Th ntwrs f lctrical and chanical parts ar lind by an idal transfrr with a transductin factr Γ. cf ß M ẋ ẋ in ( ) in F V Γ - ( ) in i iγ V - : Γ * Figur 3. Equivalnt circuit f th linar dl. Th linarizd quivalnt ntwr can b asily analyzd using th aplac transfr and ipdanc thd. Th rsulting utput currnt i and utput pwr P dissipatd n th lad ar givn by fllwing prssins Γ j j Y j i ζ ζ ζ ) ( () ( ) 4 4 ) 4 ( Γ Y P ζ ζ ζ () In ths prssins M *, is th natural chanical angular frquncy,

8 is th natural lctrical angular frquncy, and ζ β M is th daping rati f th syst. 4. Siulatin rsults Siulatin was first dn using th linar dl shwn in Figur 3. Th valus f lnts usd in this dl wr dfind basd n th tchnlgy paratrs and dvic dinsins. W hav thus cnsidrd ass f vabl lctrd M -7 g, spring cnstant was valuatd basd n FEA as 38 g s-², and th daping cfficint was stiatd as β. g s-. Th capacitanc.9 pf and pf. Th transductin factr was Γ.4-6 NV-. Analysis was undrtan by an input displacnt ranging fr µ t 5µ. Th rsults f pwr and currnt utput shw bviusly psitiv dpndnc n th incrasing f th input. Figur 4 shws th 3D plt f th utput pwr P dpnding n th lad and vibrating frquncy f fr th input displacnt f y 5µ. Th utput pwr P clarly shws th aiu rspns at th natural vibrating frquncy 4.3 Hz and th ptiu valu f th lad rsistanc 58 MO. Whn th input displacnt is µ, th frquncy rspns f th utput currnt fr th ptial lad rsistanc is shwn in Figur 5. Output Pwr P f(f,) Output Pwr [µw] [MOh] 4 Frquncy [Hz] Figur 4. Pwr utput fr th linar dl dpndnt n th vibratin frquncy and rsistanc lad (input displacnt y5µ).

9 3 Output urrnt I f(f), 58MOh 5 Output urrnt [na] Frquncy [Hz] Figur 5. Frquncy rspns f th utput currnt btaind fr th linar dl (input displacnt yµ). Using th sa cpnnt valus as fr th linar dl and ptiu cnditins btaind fr th linar analysis, w hav prfrd th siulatin basd n th SIMUINK dl. Analysis was dn at th rsnant frquncy f r 4.3 Hz, with th input displacnt ranging fr µ t 5 µ. In th dvic dscribd hr, thr is an ffct causing a strng nnlinarity f th scnd rdr that is basd n th gtrical dispsitin f th structur. t us supps that bth lctrds ar in th quilibriu placd s that thir plans f sytry prpndicular t th ain surfacs ar idntical. If th vabl lctrd is undr th sinusidal vnt prpndicular t th plan f sytry, bth th psitiv and th ngativ halvs f th displacnt prid lad t a dcrasing f th capacity cf. Th abslut valu f th displacnt ust b thus cnsidrd which shws a strng prsnc f th scnd harnic frquncy in th utput signal. This ffct is illustratd in Figur 6 whr th ain frquncy cpnnt has a valu qual t th f r.

10 6 Output urrnt I f(t), Displacnt 5µ 3 Frquncy ntnt f Output urrnt, Displacnt 5µ 4 5 Output urrnt [na] Pwr Spctral Dnsity [na²]/ ti [s] -3 (a) Frquncy [Hz] (b) Figur 6. Wavfr and spctru f th utput currnt fr th input displacnt f y 5 µ. In rdr t liinat th nnlinarity du t th dvic sytry, a nn-zr chanical bias was intrducd t th dl. This bias is rprsntd by a balanc pint X in Figur. In th fllwing, a chanically biasd dvic will b suppsd. Such a cnditin will b prvidd by stting th chanical bias t a valu at last qual t th pa lctrd displacnt. Whn th input displacnt f µ is cnsidrd, th utput currnt wavfr prsnts prfct linarity aftr th first scillatin (Figur 7a). This is cnfird by th pwr spctral dnsity f th currnt signal that cntains principally n cpnnt crrspnding t th frquncy f th input signal (Figur 7b). Th stady currnt valu fr this cas crrspnds t th utput fr th linar analysis that is shwn in Figur 5. 4 Output urrnt I f(t), Displacnt µ 4 Frquncy ntnt f Output urrnt, Displacnt µ 3 35 Output urrnt [na] - - Pwr Spctral Dnsity [na²]/ ti [s] -3 (a) Frquncy [Hz] (b) Figur 7. Wavfr and spctru f currnt rspns in linar rang (input displacnt y µ). Nnlinarity appars gradually whn th input displacnt incrass. Whn th input rachs 3 µ, thr is an bvius distrtin in th wavfr f th currnt

11 utput (Figur 8a); harnic distrtin ffcts du t th nnlinaritis ar visibl in th frquncy spctru (Figur 8b) as ultipls f th frquncy f th input signal. Output urrnt I f(t), Displacnt 3µ 6 Frquncy ntnt f Output urrnt, Displacnt 3µ 5 5 Output urrnt [na] Pwr Spctral Dnsity [na²]/ ti [s] -3 (a) Frquncy [Hz] (b) Figur 8. Wavfr and spctru f th utput currnt fr th input displacnt f y 3 µ. 5. Dvic iplntatin Th icr pwr gnratr was dsignd with th dinsin basd n th dscribd analysis and iplntd using a MOS frnt-nd lctrnic dvic fabricatin and th pst-mos bac-nd MEMS dvic prcss. Th havily dpd ply-si flating gat was sandwichd btwn tw layrs f lw-strss silicn-rich nitrid. Using aluinu as th sacrificial layr, th rsnatr was frd by lctrplatd gld. Th rsnatr structurs wr ttally suspndd aftr rving th sacrificial layr. A icrgraph f a fabricatd gnratr with a 54 rsnatr array is shwn in Figur 9. Dvic tsting is undrtaing nw. Figur 9. Micrgraph f th iplntd 54 array icr pwr gnratr.

12 6. nclusins A gnral dl that dscribs th dynaic bhavir f th iplntd flating-gat lctrstatic icr pwr gnratr was prsntd basd n th nnlinar stat quatins that gvrn th lctrical, chanical and th cupling fild rspctivly. Nurical siulatin dn in SIMUINK disclss th syst rspns clarly and rapidly cparing th tdius analytical slutins. A linarizd quivalnt circuit ntwr basd n th lctr-chanical analgy was als built t a th sall signal analysis straightfrward. Bth dls shw th cnsistncy in th btaind rsults at linar rang and prdict th pwr f µw gnratd by th dvic arund 4Hz assuing an input displacnt f 5µ. Tsting n th dvics is undrtaing and furthr analysis will b dn by cparing th tsting and siulatin rsults. 7. frncs. H. Kulah and K. Najafi, An lctragntic icr pwr gnratr fr lw-frquncy nvirnntal vibratins, MEMS 4, pp S. Mningr, J. O. Mur-Miranda,. Airtharajah, A. P. handraasan and J. ang, Vibratin-t-lctric cnvrsin, IEEE Trans. VSI Syst., Vl. 9, N.,, pp P. Gynn-Jns, S. P. Bby, N. W. Whit, Tward a pizlctric vibratin-pwrd icrgnratr, IEEE prc. Sci. Mas. Tchnlgy, Vl. 48, N.,, pp J. Bland, Y. H. ha, Y. Suzui and Y.. Tai, Micr lctrt pwr gnratr, MEMS 3, Kyt, 9-3, Jan., 3, pp T. Strn, P. Firini, K. Bart,. Purs and G. Brghs, An lctrt-basd lctrstatic µ-gnratr, Transducr 3, 8- Jun, 3, pp T. Ma, T. Y. Man, Y.. han, Y. Zhar and M. Wng, Dsign and fabricatin f an intgratd prgraabl flating-gat icrphn, MEMS, pp W. Ma, G. i, Y. Zhar and M. Wng, Fabricatin and pacaging f inrtia icr-switch using lw-tpratur pht-rsist ldd tal-lctrplating tchnlgy, Snsrs & Actuatrs A, vl., pp. 63-7, S. D. Snturia, Micrsyst dsign, Kluwr Acadic Publishrs, Bstn,.