The development of modern integrated wireless communication
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1 IEEE Tansacions on Ulasonics, Feoelecics, and Fequency Conol, vol. 57, no. 9, Sepembe Tansducion of High-Oveone Conou- Mode Resonaos Hengky Chandahalim, Membe, IEEE, Sunil. Bhave, Senio Membe, IEEE, Ronald G. Polcawich, Membe, IEEE, Jeffey S. Pulskamp, and Roge Kaul, Senio Life Membe, IEEE bsac This pape pesens he Buewoh-van Dyke model and quaniaive compaison ha exploe he design space of lead ziconae ianae-only () and on 3-, 5-, and 10-μm single-cysal silicon (SCS) high-oveone widhexensional mode (WEM) esonaos wih idenical laeal dimensions fo incopoaion ino adio fequency micoelecomechanical sysems (RF MEMS) files and oscillaos. novel fabicaion echnique was developed o fabicae he esonaos wih and wihou a silicon caie laye using he same mask se on he same wafe. The ai-bidge meal ouings wee implemened o cay elecical signals while avoiding lage capaciances fom he bond-pads. We heoeically deived and expeimenally measued he coelaion of moional impedance (R X ), qualiy faco (Q), and esonance fequency (f) wih he esonaos silicon laye hickness ( Si ) up o fequencies of opeaion above 1 GHz. I. Inoducion The developmen of moden inegaed wieless communicaion sysems has pushed he invesigaion of efficien elecomechanical ansduce maeials fo micoelecomechanical esonaos and files. Feoelecic maeials such as lead ziconae ianae () ae favoable ansduces fo devices ha opeae a high fequencies up o he UHF ange because hey avoid hick film equiemens and educe he aea equied fo he esonaos and files. Fuhemoe, exhibis a lage elecomechanical coupling coefficien, enabling he design of lage pecenage bandwidh files [1]. is also an aacive elecomechanical ansduce because i possesses a dc bias-dependen elasic modulus. This popey has been uilized o design ansduced lengh-exensional mode (LEM) esonaos wih up o 5% fequency uning []. Howeve, -only esonaos ae well known o have low Q. To ovecome he low Q of only esonaos, we have developed a new fabicaion echnology o inegae ansducion wih single-cysal silicon (SCS) esonaos. This fabicaion echnology allows us o fabicae -only and -on-silicon esonaos using he same mask se on he same wafe. Manuscip eceived Januay 5, 010; acceped June 18, 010. H. Chandahalim was wih he School of Elecical and Compue Engineeing, Conell Univesiy, Ihaca, NY. He is now wih he Mico and Nanosysems Laboaoy, Swiss Fedeal Insiue of Technology, Zuich, Swizeland ( hengky.chandahalim@mico.mav.ehz.ch). S.. Bhave is wih he School of Elecical and Compue Engineeing, Conell Univesiy, Ihaca, NY. R. G. Polcawich, J. S. Pulskamp, and R. Kaul ae wih he US my Reseach Laboaoy, delphi, MD. Digial Objec Idenifie /TUFFC The maeial popeies and piezoelecic coefficien of solely dominae he Buewoh-van Dyke (BVD) model in -only esonaos. Howeve, he effecive mass, M, effecive siffness, K, and he damping faco, ζ, of -on-silicon esonaos ae scaled by he aio of he hickness of he laye,, o ha of he silicon laye, Si. Seveal eseach goups have peviously demonsaed aluminum niide (ln) and zinc oxide (ZnO) ansducion of MEMS esonaos wih and wihou a silicon caie laye and deived he coesponding BVD models [3] [5]. Howeve, he hicknesses of piezoelecic films in many applicaions ae usually much smalle han he hickness of he silicon caie laye. Thus, he mass of he hin film ansduce can be negleced wihou affecing he accuacy of he equivalen elecical model vey much. In his pape we deive, simulae, and expeimenally jusify a model ha will hold ue fo any hickness aio of he piezoelecic ansduce and silicon caie laye. The model conveges o models pesened in efeences [3] [5] fo he specific hickness cases. II. High-Oveone WEM Resonao -ansduced LEM esonaos have been successfully demonsaed. By vaying he silicon hickness, Si, (heeby he pecen mass of cysalline silicon in he esonao) and dc bias volage, we can define he desied Q and fequency uning ange of he esonaos []. Howeve, vaious applicaions in wieless communicaion sysems demand highe fequency of opeaion. To each f above 100 MHz using he lengh-exensional mode of vibaion, he lengh of -on-silicon esonaos mus be scaled down o less han 40 μm. The lengh of -only esonaos mus be shunk even moe because of he lowe acousic velociy compaed wih -on-silicon esonaos. ggessive scaling in laeal dimensions of he esonao educes he ansducion aea, esuling in poo moional impedances. To enable -ansduced esonaos wih a high fequency of opeaion while mainaining low moional impedance, design and fabicaion of ansduced high-oveone widh-exensional mode (WEM) esonaos will be pesened.. Design of a High-Oveone WEM Resonao high-oveone widh-exensional mode of vibaion can be excied o achieve a high esonance fequency while uilizing a lage ansducion aea [6]. The schemaic of /$ IEEE
2 036 IEEE Tansacions on Ulasonics, Feoelecics, and Fequency Conol, vol. 57, no. 9, Sepembe 010 Fig. 1. Schemaic of (a) -only esonao and (b) -on-silicon esonao. Fig. 3. The coss-secional view of a widh-exensional mode esonao. a one-dimensional model. The esonao vibaes in he diecion nomal o aea (no shown in he picue). Fom Newon s law of moion, he sum of foces ha ac on he esonao can be expessed as (1) ux (,) ( s(,) x + ds( x,) ) -s(,) x dx, whee u and σ ae he displacemen of cene mass and he disibued sess acoss he hickness of he composie esonao, especively. Eq. (1) can be simplified as Fig.. NSYS mode shape of a high-oveone widh-exensional mode esonao. -only and -on-silicon esonaos ae illusaed in Figs. 1(a) and 1(b), especively. By selecively paening he inedigiaed elecodes on op of he esonaos, he highe oveone of widh-exensional mode is excied as demonsaed in NSYS modal analysis (nsys, Inc., Canonsbug, P) in Fig.. B. ecive Mass, Damping Raio, and ecive Sping Consan The coss-secional view of a WEM esonao wih widh W and hickness + Si is shown in Fig. 3. We assume in ou analysis and deivaion houghou his pape ha he sucue of ou devices is eihe dominaed by laye (, fo -only esonaos) o and silicon composie sucue ( + Si, fo -on-silicon esonaos). Though he sain is assumed o be unifom in he x-, y-, and z-diecions, we designed all suspensions of he esonaos o songly excie he widh-exensional mode of vibaions. Because he displacemen nomal o he x-diecion is pesumed o be negligibly small, he hee-dimensional equaion of moion can be educed ino s(,) x ux (,) x E x () ux (,) x ux (,) (3) E ux (,) ux (,), (4) x whee E and ρ ae he effecive wo-dimensional elasic modulus and densiy of he composie esonao, especively. The wave equaion fo a one-dimensional vibaing widh-exensional mode esonao including he damping faco, b and exenal foces, f(x, ) is u u x b x E u f (,)- (,)- (,) x (,). x x x x (5) By he mehod of sepaaion of vaiables, we assume (5) has soluions of he fom æn ux (,) g()sin p, (6) whee g() is he vibaion ampliude as a funcion of ime. Subsiuing (6) ino (5) gives
3 chandahalim e al.: ansducion of high-oveone conou-mode esonaos 037 sin ænp p p g b n n () + æ è ç ö W sin æ g () + E æ ö n p W æ np ö ø W x g f sin () ( x,). x (7) Muliply (7) by sin(((nπ)/w)x) and inegae ove he widh o yield whee W/ ò -W / é ê ë æ np W x g sin æ è ç öö () æ p + b n ö æ æn W g p ö () sin æ + E n è p ö æ æ ö ç W np ö ù sin () û ú (), W x g d x F F() W / ò -W / f æ np x sin d x is he ime dependen exciaion foce. Eq. (8) can be simplified as W g () bw ænpö g () + W EW ænp ö + W g () F. () Fom (9), we can ecognize ha he effecive mass, damping aio, and effecive sping consan of a widh-exensional mode esonao wih widh W ae given by K M W (8) (9) (10) bw ænpö p z nb W (11) W EW ænpö ne p W. (1) W C. ecive Elasic Modulus and Densiy The piezoelecic foce induced by he laye is disibued along he hickness of he composie esonao ( Si + ). The unifom displacemen along he hickness of he composie esonao leads ino he aveage sain, ε. e DW W, (13) whee ΔW is he amoun of change in saic widh caused by ime-dependen exciaion foce F(). Because of he elasic popeies of and silicon layes, he sess componens of and silicon ae and s s Si E e (14) E e, (15) Si whee E and E Si ae he wo-dimensional elasic moduli of and silicon, especively. The aveage sess, σ acs on he coss-secional aea,, of he composie esonao which is ohogonal o he diecion of moion. This aveage sess yields an effecive foce, F, on he composie esonao F s s + s. (16) Si Si By subsiuing (16) wih (14) and (15), we obain s E e + E e. (17) Si Si The effecive wo-dimensional elasic modulus, E is obained by dividing σ in (17) by ε : E E + E + Si Si Si. (18) We assume he lengh of he ansduce, L, in ou device is appoximaely he same as he lengh of he silicon caie laye, L Si. By using he same line of deivaion, he effecive densiy, ρ, of he composie esonao is given by + + Si Si D. Elecomechanical Tansducion iciency Si. (19) The laeal sess, σ in he film is given by s e 31 v C, (0) whee e 31 and ae he ansvese piezoelecic sess consan and hickness of laye, especively, and v C is he ime-dependen acuaion volage. By subsiuing e 31 wih d 31 E, (0) can be wien as C s d 31 E v, (1) whee d 31 and E ae he ansvese piezoelecic coefficien and wo-dimensional elasic modulus of, especively. The geneaed piezoelecic foce, F W/ caused by ansducion a W/ can be obained by muli-
4 038 IEEE Tansacions on Ulasonics, Feoelecics, and Fequency Conol, vol. 57, no. 9, Sepembe 010 plying he geneaed sess wih he coss-secional aea of he film which is ohogonal o diecion of moion: F s d E Lv. () W/ 31 C We assume he lengh of he ansduce, L, in ou device is appoximaely he same as he lengh of he silicon caie laye, L Si, and is denoed by L in (). Because of he widh-exensional bounday condiion ha was imposed o excie he esonao, he same piezoelecic foce, F W/ wih opposie diecion exiss a W/. The efficiency of elecomechanical ansducion by is indicaed by he elecomechanical ansducion efficiency, η; η is he aio of he oal geneaed piezoelecic foce, F, o he applied ime vaying volage, v C : F h d 31 E L. (3) v C E. Small-Signal Elecical Equivalen Cicui The effecive mass, damping aio, and effecive sping consan can be elaed o he elecical cicui paamees. In he pocess of elecomechanical ansducion, he ime-dependen volage v C geneaes a laeal foce, F, hough he ansvese piezoelecic sess consan, e 31. The dynamic foce F excies acousic vibaions wih ampliude g(). The chage modulaion in he laye due o vibaion velociy g()/ induces a moional cuen oupu, i(). The elaion beween ime-dependen inpu simulus v C and i() can be expessed mahemaically as g i () () h. (4) By subsiuing g()/ in (9) by i()/η, we obain o M M h h i () z K i i d F + () h + h ò () () (5) i () z K i () i () d vc() + h + h ò. (6) Fom (6), we can define he moional esisance, capaciance, and inducance of he -po -on-silicon composie esonao. They ae nomally epesened in paallel wih he feedhough capaciance C f, as shown in Fig. 4. Fo a given ansducion efficiency η, R X ζ/η, C X η / K, and L X M /η. The feedhough capaciance in a wo-po esonao oiginaes fom elecic field coupling fom he inpu elecode o he oupu elecode and is a funcion of elecode geomey. The nominal capaciance, C 0, is he saic capaciance beween he elecode and he esonao s body. high-oveone widh-exensional mode esonao can be eaed as an aay of smalle widhexensional mode esonaos conneced in paallel. Thus, Fig. 4. Elecical equivalen cicui of a -ansduced high-oveone WEM esonao, including he saic capaciance beween he elecode and esonao s body, C 0, he feedhough capaciance beween inpu and oupu pos, C f, and he eminaion impedance, R L. he small signal elecical equivalen impedances of a esonao consis of j numbe of WEM esonaos wih widh W vibaing in fundamenal mode (n 1) conneced in paallel ae 1 1 / p E / Si + 1 RX jq 4 E L d LW E C X 4 jp ( Si + ) E ( ) j W L X ( Si + ) 1 4 E L d d 31 31, 31 (7) (8) (9) whee Q is he mechanical qualiy faco of he esonao. Using he idenical line of deivaion, he moional esisance, capaciance, and inducance of he -po only ansduced esonao ae given by 1 / R X p 1 jqe 4 3L d L C X 4 jp / 31 (30) W E d31 (31) j W L X 1 4 E L d 31, (3) which ae he small-signal elecical equivalen impedances of piezo-only esonaos pesened in [3]. The esonan fequency f is given by f 1 p 1 C X L X III. Fabicaion Pocess. (33) The device fabicaion is lagely based on he fabicaion sequence oulined in [] wih addiional impovemens in he pocess o eliminae he pad capaciances. is well known o have a lage pemiiviy ha can lead o lage pad capaciances. Theefoe, in his efined fabicaion pocess, ai-bidge meal ouings wee implemened o cay elecical signals while avoiding lage capaciances fom he bond-pads. In addiion, a novel fabicaion
5 chandahalim e al.: ansducion of high-oveone conou-mode esonaos 039 Fig. 5. i-bidge pocess coss-secion of -only and -on-silicon high-oveone widh-exensional mode esonaos fabicaed on he same wafe. echnique was developed o fabicae he esonaos wih and wihou silicon laye using he same mask se on he same wafe. sysemaic sudy is essenial o invesigae he effec of silicon on Q, f, and R X of -ansduced esonaos a adio fequency. In his eseach effo, we fabicaed -only and on 3-, 5-, and 10-μm SCS high-oveone widh-exensional mode esonaos wih idenical laeal dimensions. ansduce compised of Ti/P//P wee deposied on SOI wafes wih 3-, 5-, and 10-μm hick device laye. The 0.5-μm hick films wee deposied using a chemical soluion deposiion mehod wih a cysallizaion empeaue of 700 C o achieve full densificaion and high cysalliniy. The inpu and oupu eminals of he esonaos ae lihogaphically defined by paening he op P elecode on op of he acuao. The cuen configuaion of he esonao uses a common boom P elecode undeneah he fo boh he inpu and oupu pos. The pocess coss-secion of eleased on-silicon and -only esonaos is shown in Fig. 5. To ensue suvival of he single-cysal silicon componen of he esonaos, an oganic phoo-definable laye was developed o povide poecion of he esonao while allowing undecuing of he handle silicon wafe using a XeF ech. he end of device fabicaion, he film aleady possesses some degee of poling as a esul of he plasma pocessing. To impove he degee of poling, he esonaos wee subjeced o elecic fields of 00 kv/cm fo 10 min befoe esing. n SEM image of he fabicaed high-oveone widh-exensional mode esonao is shown in Fig. 6. IV. Chaaceizaion of High-Oveone WEM Resonaos The esonaos wee chaaceized in an RF pobe saion in a -po configuaion using GSG pobes. Paasiics up o he pobe ips wee fis calibaed wih SOLT measuemens on a sandad calibaion subsae. ll measuemens wee pefomed in ai, a oom empeaue and pessue. The measuemen seup is pesened in Fig. Fig. 6. SEM image of he fabicaed high-oveone widh-exensional mode esonao. The close-up picue shows he ai-bidge ouing ha isolaes he esonao fom he bonding-pads. 7. The ade-offs in Q, f, and R X of esonaos wih diffeen silicon hicknesses wee ecoded. Resonaos wih hicke silicon laye exhibi highe Q, highe f, and lowe R X fo fequency up o abou 900 MHz as shown in Fig. 8. The measued chaaceisics of he second-oveone WEM esonaos wih diffeen silicon hicknesses ae summaized in Table I. Table II compaes he analyically esimaed moional inducance and capaciance of second-oveone WEM esonaos wih he expeimenally exaced daa. The maximum vaiaion beween heoeical and measued daa is less han 9%. The measued esonance fequency of he esonaos wih diffeen silicon hicknesses ae in ageemen wih he heoeically analyzed and simulaed daa. Fig. 9 ploed
6 040 IEEE Tansacions on Ulasonics, Feoelecics, and Fequency Conol, vol. 57, no. 9, Sepembe 010 TBLE I. The Measued Chaaceisics of High-Oveone WEM Resonaos Wih Diffeen Silicon Thicknesses. Si (μm) Q Loaded f (MHz) R X (Ω) R L (Ω) f Q TBLE II. LC Tank of High-Oveone WEM Resonaos: Design and Measuemen Summay. Si (μm) Designed Measued L X (μh) C X (ff) f (MHz) L X (μh) C X (ff) f (MHz) Fig. 7. Tesing configuaion fo a -ansduced high-oveone widhexensional mode esonao. he calculaed, simulaed, and measued esonance fequency of ansduced second-oveone WEM esonaos wih diffeen silicon hicknesses ( Si ). By inegaing ansducion wih single-cysal silicon, he figue of mei, f Q, is impoved by one ode of magniude. V. Conclusion In conclusion, we have fabicaed ansduced high-oveone WEM esonaos wih and wihou a silicon device laye using he same mask on he same wafe. novel fabicaion echnique has been developed o allow cancelaion of lage pad capaciances. The BVD models fo -only and -on-silicon high-oveone WEM esonaos have been deived and used o design esonaos wih fequency above 1 GHz. The pefomances of ansduced high-oveone WEM esonaos wih vaious silicon hicknesses wee invesigaed. Inegaing Fig. 8. Measued ansmission esponse of -only and on 3-, 5-, and 10-μm silicon WEM second-oveone esonaos wih he exac same laeal dimensions in ai a oom empeaue and pessue. ll measuemens wee pefomed using eminaion impedances (R L ) of 50 Ω. ansducion wih silicon impoves he f Q by one ode of magniude. Fequency of opeaion is dominaed by he silicon laye fo silicon hickness lage han 3 μm. By vaying he silicon hickness, we can define he desied Q and cene fequency of he esonaos fom high fequency up o he ula high fequency ange. This echnology will enable -ansduced esonaos, files, and oscillaos ha cove he ange up o low-band GSM fequencies. cknowledgmen The auhos would like o hank B. Powe, J. Main, and R. Piekaz of he my Reseach Laboaoy fo hei assisance in fabicaing he esonaos.
7 chandahalim e al.: ansducion of high-oveone conou-mode esonaos 041 Hengky Chandahalim (S 04 M 09) compleed his undegaduae educaion wih he B.S. degee in elecical and compue engineeing fom he Ohio Sae Univesiy. He eceived his Ph.D. degee in elecical and compue engineeing fom Conell Univesiy in 009 wih eseach focus in volage unable adio fequency mico-elecomechanical esonaos and files. D. Chandahalim woked as an inegaed cicui design enginee a Inegaed Cicui Sysems, Inc. in San Jose, C, fom 000 o 003. Soon afe his gaduaion fom Conell Univesiy, D. Chandahalim joined he Mico and Nanosysems laboaoy a ETH Zuich as a posdocoal eseach associae. His cuen eseach focus is in cabon-nanoubes-based nano-elecomechanical signal pocessos. D. Chandahalim was he ecipien of he IEEE Ulasonics, Feoelecics, and Fequency Conol Sociey 009 Suden Bes Pape wad. Sunil. Bhave (S 99 M 04 SM 10) eceived he B.S. and Ph.D. degees in elecical engineeing and compue sciences fom he Univesiy of Califonia, Bekeley in 1998 and 004, especively. In 004, he joined he faculy of Conell Univesiy, whee he is cuenly an ssisan Pofesso in he School of Elecical and Compue Engineeing. His eseach ineess include MEMS esonaos fo adios, meged CMOS-NEMS, ineial and acousic sensos, and hybid phoonic-nems and magneic-nems fo low-phase-noise micowave oscillaos. Pofesso Bhave is a ecipien of he NSF Ealy CREER Developmen wad in 007 and he DRP Young Faculy wad in 008. Togehe wih his sudens, he has eceived he Bes Pape awads a IEDM 007 and Ulasonics 009. Fig. 9. plo of silicon hickness ( Si ) vesus he calculaed, simulaed, and measued esonance fequency (f). Refeences [1] J. D. Lason, III, S. R. Gilbe, and B. Xu, maeial popeies a UHF and micowave fequencies deived fom FBR measuemens, in Poc. IEEE Ulasonics Symp., Moneal, Canada, 004, vol. 1, pp [] H. Chandahalim, S.. Bhave, R. Polcawich, J. Pulskamp, D. Judy, R. Kaul, and M. Dubey, Pefomance compaison of Pb(Z 0.5 Ti 0.48 ) O 3 -only and Pb(Z 0.5 Ti 0.48 )O 3 -on-silicon esonaos, ppl. Phys. Le., vol. 93, no. 3, a. no , 008. [3] G. Piazza, P. J. Sephanou, and. P. Pisano, Piezoelecic aluminum niide vibaing conou-mode MEMS esonaos, J. Micoelecomech. Sys., vol. 15, no. 6, pp , 006. [4] G. K. Ho, R. bdolvand,. Sivapuapu, S. Humad, and F. yazi, Piezoelecic-on-silicon laeal bulk acousic wave micomechanical esonaos, J. Micoelecomech. Sys., vol. 17, no., pp , 008. [5]. Jaakkola, P. Rosenbeg,. Numela, T. Pensala, T. Riekkinen, J. Dekke, T. Maila, and. lasalo, Piezoansduced singlecysal silicon BW esonaos, in Poc. IEEE Ulasonics Symp., New Yok, NY, 007, pp [6] G. K. Ho, R. bdolvand, and F. yazi, High-ode composie bulk acousic esonaos, in Poc. IEEE In. Conf. Mico Eleco Mechanical Sysems (MEMS), Kobe, Japan, 007, pp Ronald G. Polcawich (M 07) eceived he B.S. in maeials science and engineeing fom Canegie-Mellon Univesiy, Pisbugh, P, in 1997, and he M.S. and Ph.D. degees in maeials fom The Pennsylvania Sae Univesiy, Univesiy Pak, in 1999 and 007, especively. He is a saff eseache in he Mico & Nano Maeials & Devices Banch of he US my Reseach Laboaoy (RL), delphi, MD. He is cuenly he eam lead fo he RF MEMS and Millimee-Scale Roboics pogams a RL. His eseach aciviies include maeials pocessing of hin films, MEMS fabicaion, piezoelecic MEMS, RF componens, MEMS acuaos, and millimeescale oboics. D. Polcawich is a membe of he Maeials Reseach Sociey and IEEE. Jeffey S. Pulskamp eceived he B.S. degee in mechanical engineeing fom he Univesiy of Mayland a College Pak, in 000. He is cuenly a Mechanical Enginee wih he dvanced MicoDevices Banch, delphi Laboaoy Cene, U.S. my Reseach Laboaoy, delphi, MD. His cuen eseach focuses on RF MEMS devices, eleconic scanning anenna, mechanical modeling of MEMS, and micooboics. Roge Kaul (S 60 M 6 SM 88 SLM 06) eceived he Ph.D. degee in elecical engineeing and applied sciences fom Case Wesen Reseve Univesiy, Cleveland, OH, in Unil 1974, he eseached Gunn insabiliies a he Unied icaf Reseach Laboaoies. He hen joined ORI Inc. and pefomed space sysem sudies fo he Naional eonauics and Space dminisaion (NS). Fom 1981 o 1987, he conduced sudies elaed o eleconic wafae and millimee-wave communicaion sysems wih he mecom Division, Lion. Unil 001, he was involved wih he developmen of micowave hadening echnology echniques and evaluaing micowave devices and cicuis fo my applicaions a he my Reseach Laboaoy (RL). He coninues o assis he RL in he developmen and evaluaion of micoelecomechanical sysems (MEMS) echnology as a membe of he RL Emeius Cops. He is a Pa-Time Insuco wih he Whiing School of Engineeing, Johns Hopkins Univesiy, Balimoe, MD. D. Kaul is pas chai of he MTT-16 Micowave Sysems Technical Commiee and emains acive in he Washingon DC/Nohen Viginia Chape of he IEEE Micowave Theoy and Techniques Sociey (IEEE MTT-S).
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