Design of capacitive MEMS transverse-comb accelerometers with test hardware

Transcription

1 Suprficis y Vacío 6(1 4-1, marzo d 01 Socidad Mxicana d Cincia y Tcnología d Suprficis y Matrials Dsign of capacitiv MEMS transvrs-comb acclromtrs with tst hardwar Ibarra-Villgas F. J., Ortga-Cisnros S., Sandoval-Ibarra F. Cntro d Invstigación y Estudios Avanzados (CINVESTAV dl Instituto Politécnico Nacional Av. dl Bosqu #1145, Col. l Bajío, C.P , Zapopan, Jalisco, México Raygoza-Panduro J. J., Rivra-Domínguz J. Cntro Univrsitario d Cincias Exactas Ingnirías (CUCEI d la Univrsidad d Guadalajara Blvd. Marclino García Barragán #141, Col. Olímpica, C.P. 4440, Guadalajara, Jalisco, México (Rcibido: 7 d sptimbr d 01; Acptado: 18 d nro d 01 This papr proposs th dsign of MEMS acclromtrs, which includ hardwar to prform tsting in a rlativly simpl way, with diffrnt manufacturing procsss, PolyMUMPs and SUMMiT V of MEMSCAP and Sandia Labs rspctivly, using a mthodology that allows thm to b adaptd to any of ths tchnologis. This mthod was cratd to provid th basis to th dsigning of micro lctromchanical dvics, optimizing th larning tim. Th snsors ar onaxis transvrsal comb acclromtrs which us an intrdigital capacitors array to masur th capacitanc chang among thr indpndnt comb arrays whn th systm is xposd to positiv or ngativ G forcs. In addition, it includs anothr st of combs which intract as tst dvics, du to th fact that a voltag can b applid, which will crat an lctric fild in th lctrods of ths combs, producing an attraction forc that will shift th mobil mass of th snsor, mulating an acclration to which th dvic is xposd. Som physical paramtrs and dimnsions proposd for this acclromtr ar prsntd to show th dsign mthodology of such dvics. Th acclromtrs wr dsignd undr constraints st by th manufacturing rgulations of PolyMUMPS and SUMMiT V Th acclromtr layouts wr dsignd using MEMS PRO v4.0 and AutoCAD and both wr simulatd with ANSYS Workbnch. Kywords: Micro-lctromchanical systms (MEMS, acclromtr, capacitiv, transvrs comb. 1. Introduction Th us and inclusion of inrtial snsors, such as acclromtrs and gyroscops, has xpandd significantly in rcnt yars in automotiv applications, mobil dvics, computrs, global positioning systms (GPS, vido gams, arospac quipmnt, and biomdical snsors, among many othr applications. In th automotiv ara, th bst xampl of th us of ths dvics is th snsor that dtcts a dclration causd by a crash, which activats th jction systm of air bags in ordr to sav th livs of passngrs [1]. In smart phons (Smart Phons and GPS, th us of ths snsors has bcom vry popular for dtcting th rotation of th dvic, adjusting th scrn for bttr viwing, and also to turn th dvic off whn it is droppd, protcting th intrnal componnts []. For vido gams, ths dvics ar usd as proximity or motion snsors such as in th cas of th Wii consol rmot control. In th biomdical fild, acclromtrs and gyroscops hav bn usd to masur th ability of motion or rotation of a joint [], among othr important applications [4]. Th contribution of this projct is th proposal of a mthodology for MEMS acclromtr dsign adaptabl to any manufacturing procss and th inclusion of tst hardwar to prform th vrification of th snsor [5].. Dscription Th transvrs comb acclromtr with tst systm consists of a st of lctrods, which function as capacitors (snsor lctrods, and anothr st that oprats as actuators to mulat th acclration (tsting lctrods [6]. A common pattrn is to put thr sts of combs, vn for th snsor part and th tsting part. On of thos combs is mobil and th othr two ar fixd so that th capacitors ar placd in an intrdigital array [7]. In addition, th movabl mass has two springs on ach sid to allow flxibility and stability to th systm (Figur 1. If thr is acclration in th axis to masur, th movabl mass will mov and th movabl comb lctrods will b clos to th lctrods of on of th fixd combs, whil rmovd from th othr fixd comb. This causs th capacitanc to incras btwn th movabl comb and th first fixd comb whil dcrasing with th scond on [8]. This chang in capacitanc can b masurd and convrtd into an lctrical signal, rprsntativ of th acclration to which th systm is xposd. Th acclration can b mulatd through th tsting combs that actuat, moving th cntral plat and th movabl lctrods in on dirction as if th acclromtr wr undr acclration. Th tsting combs will allow us to prform th charactrization of th acclromtr with much lss sophisticatd quipmnt than if thy wr not availabl. 4

2 Suprficis y Vacío 6(1 4-1, marzo d 01 Socidadd Mxicana d Cincia y Tcnología d Suprficis y Matrials. Dsign Mthodology Figur 1. Transvrs comb acclromtr. Figur. Intrdigital capacitors array. This dsign mthod can b usd with any manufacturing tchnology, taking into account th constraints that ach prsnts [9]. Th mthod bgins by proposing th dsird capacitanc for ach pair of lctrods and th sparation btwn thm (Figur. This is in ordr to calculat th lngth of th lctrods (l from th quation of th capacitanc (Equation 1, whr th ara (A is dirctly proportional to th product of th lngth by th hight (h of th lctrods. Th hight dpnds on th layr width with which th lctrods ar constructd, according to th manufacturing procss. Th sparation btwn th lctrods (d must also b proposd, following th constraints dictatd by th slctd MEMS tchnology. Th vacuumm prmittivity is usd as an absolut, as th dilctric matrial btwn th lctrods is air and its absolut prmittivity is practically th sam as its vacuum prmittivity (ε=8.85x10-1 F/m. C1 A ( l ( h = ε = ε d d l ( C = ( 1 d ( ε ( h (1 Figur. Total lngth of th cntral plat. Th capacitanc btwn a movabl lctrod and two of th fixd lctrods is th sam whn th systm is at rstingg stat. Thn th total systm capacitanc btwn th movabl comb and ach of th fixd combs arrays is calculatd by multiplying th capacitanc of on capacitor by th numbr of lctrods hld by ach comb (N (Equation. C = ( C ( N T 1 ( Figur 4. Total width of acclromtr vs. total opning of springs. Whn th acclromtr is dsignd, it is usful to indicat at th bginning what is th maximumm distanc that th movabl mass will mov. Whn th mass movs ovr th axis to b masurd, on of th capacitors incrass its capacitanc whil th othr on dcrass. This chang in capacitanc is what should b masurd by som mthod to gt a signal which is proportional to th acclration to whichh th systm is xposd. Th diffrnc btwn ths capacitancs ( C T can b dtrmind from Equation, whr d is th displacmnt of th movabl mass. Figur 5. Volums of th movabl mass. ΔC T 1 1 = N εa d Δd d + Δd ( Figur 6. Springs Modl. Th nxt stp is to calculat th proportions of th cntral plat of th movabl mass. Th lngth of this cntral plat ( can b calculatd with Equation 4, which was obtaind spcifically for this acclromtr modl, whr w is th width of th lctrods and must b proposd by th dsignr, taking into account th dsign ruls of th manufacturing procss and N t is th numbr of tsting lctrods. Th sparation btwn th snsorss and tst combs ( s must b proposd. 5

3 Suprficis y Vacío 6(1 4-1, marzo d 01 Socidadd Mxicana d Cincia y Tcnología d Suprficis y Matrials MATLAB cod: Figur 7. Graph: width of cntral plat vs. th magnitud of th springs (PolyMUMPS. %Lngth of th cntral plat: Lp=* *((N+Np/*(W+d-*d+(0-6; Hp=..5-6; %Thicknss of th cntral plat HpGold=0.5-6; %Thicknss of gold layr g1=9..81; %1 G forc = m/s^ a=0* *g1; %Acclration to b masurd V=(N+Np*W*L*H; %Volum of th lctrods %Volum of th junctions: Vu=(100-6*(0-6 *(-6*; plat Figur 8. Anchors of fixd lctrods (PolyMUMPS. % Elctrods charactristics: N=60; %Snsor lctrods Np=0; %Tsting lctrods W=-6; %Elctrods width L= ; %Elctrods lngth + gap H=-6; %Elctrods Thicknss d=-6; %Distanc btwn lctrods E=1699; %Young s Modulus Wr=-6; % of th springs Hr=-6; %Thicknss of th springs x=1.85-6; %Maximum displacmnt dnsity=0; %Polysilicon dnsity dnsityg=1900; %Gold dnsity Wp=1-06:1-6:600-6; % of th cntral %Lngth of ach part of th springs Lr=(( (((pi^4/96*(*x*e*hr*(wr^./... ((dnsitysilicon*a*(v+vu+lp*hp.*wp+... dnsityg*a*(lp* *HpGold.*Wp.^(1/; La=Lr.*+104-6; %Total opning of th springss %Total width of th acclromtr: Wa=Wp+(L+40-6*; plot( (Wp,Wa,'--',Wp,La,':',Wp,Lr,'linwidth',1.5,... xlabl({'cntral plat width';'(m'},... ylabl({'dimnsions';'(m'},... lgnd('total acclromtr width',... 'Total magnitud of th springs',... 'Lngth of ach part of th springs' = ( (( N N + t / ( w + d d + ( Δs (4 Figur 9. Total Dformation simulation of th PolyMUMPs MEMS acclromtr. Figur 10. Strss simulation of th PolyMUMPs MEMS acclromtr. In th last quation th numbr of lctrods (N +N t must b multiplid by thr, bcaus thr ar thr combs pr sid with th sam numbr of lctrods. Furthrmor, th total numbr of lctrods must b dividd by two bcaus ths ar qually distributd on both sids of th cntral plat. Th total numbr of lctrods pr sid is multiplid by its width (w and by th sparation btwn thm (d. To this magnitud is subtractd two tims th sparation btwn lctrods (d bcaus th last lctrods of th snsing and tsting combs ar not sparatd from anothr on. Finally, th sparation btwn snsing combs and tst combs ( s is addd to obtain th total lngth of th cntral plat ( (Figur. Th width of th cntral plat (W p p must also b proposd by th dsignr. Howvr, this variabl affcts th final magnituds of th springs and th total width of th acclromtr (Figur 4. Th largr th width of th cntral plat th largr th total width of th acclromtr and th smallr th magnitud of th springs. 6

4 Suprficis y Vacío 6(1 4-1, marzo d 01 Socidadd Mxicana d Cincia y Tcnología d Suprficis y Matrials Tabl 1. Summary of th acclromtr dimnsionss (PolyMUMPS. Charactristic Siz (µm Lngth 11 Elctrods Thicknss Lngth 496 Cntral plat Thicknss 7 4 Lngth of ach part 9.5 Springs Thicknss Anchors Lngth Lngth 0 Junctions 100 Thicknss Total width of th acclromtr Total lngth of th acclromtr Total opning of th springs Figur 11. Layout of th PolyMUMPs MEMS aclromtr. Aftr that, th spring constant (k of th systm must b calculatd (Equation 5, so that according to a givn acclration (a, a proportional movmnt on th mass xists, which will rsult in a diffrnc in capacitanc. Th acclration that ths dvics can masur is givn in G- forcs. F m a V k = = M a = δ x x x a ( V k = δ + Vu + Vp x a ( V k = δ + Vu + Lp Wp H p x (5 Figur 1. PolyMUMPs MEMS acclromtr built. whr F is th forc that th movabl mass (m rcivs du to acclration (a. Th constant δ is th dnsity of th matrial from which th acclromtrr will b built (0kg/m for polysilicon and 1900 kg/m for gold. Th variabl x is th maximum displacmnt of th movabl mass. V M is th volum of th movabl mass, which is composd of th volum of th lctrods (V, th volum of th junctions btwn th springs and th movabl mass (V u, and th volum of th cntral plat (VV p (Figur 5., W p and H p ar th dimnsions (lngth, width and thicknss, rspctivly of th cntral plat. Th spring constant has to b dividd by th two springs that contain th modl of th transvrs comb acclromtr (Equation 6. Figur 1. Graph: width of cntral plat vs. th magnitud of th springs (SUMMiT V k δ a ( V + Vu + Lp Wp H p k r = = x (6 Th modl of th springs usd in this acclromtr consists of four parts for ach on, L r1, L r, L r and L r4 (Figur 6 [10]. Figur 14. Anchors of fixd lctrods (SUMMiT V 7

5 Suprficis y Vacío 6(1 4-1, marzo d 01 Socidadd Mxicana d Cincia y Tcnología d Suprficis y Matrials Tabl. Modal analysis of th PolyMUMPs MEMS acclromtr. Mod Frquncy (khz If th four sids of ach spring wr dsignd so that thy had th sam lngth (L r1 = Lr = L r = L r4 = L r, th lngths of th four parts of th spring ar calculatd using th following quation [10]: L r = 4 π EH 96 rw kr r (7 Figur 15. Total Dformation simulation of th SUMMiT V MEMS acclromtr. By obtaining th lngths of ach of th four parts of both springs, th physical dsign of th acclromtr concluds. Othr dimnsionss ndd for th acclromtr will b basd on th constraints st by th dsign guids of th manufacturing procsss PolyMUMPs [11] and SUMMiT V [1], according to th rquirmnts of th dsignr. Anothr important aspct of th snsor is its rsonanc frquncy and snsitivity. Th rsonanc frquncy (f r is a function that dpnds on th movabl mass (m and th spring constant of th systm (k r (Equation 8 [1]. f r 1 = π k m Th snsitivity of th acclromtr (S is dfind as th ratio btwn th displacmnt of mass and acclration that th systm can masur (Equation 9 [14]. (8 Figur 16. Strss simulation of th SUMMiT V MEMS acclromtr. x m 1 S = = = a k 4π f r (9 4. Dsign of a transvrs comb acclromtr with PolyMUMPS This acclromtr is dsignd as xplaind abov and following th dsign ruls. Th combs, and th springs will b built from a µm-thicknss polysilicon layr (Poly1 and th movabl mass from thr layrs that will hav an ovrall thicknss of 4µm (Poly1, Poly and Mtal [15]. Th main dsign spcifications ar: Acclration to b masurd: 0-0G (1G= =9.81m/s Rquird capacitanc for ach pair of lctrods: 1fF Distanc btwn lctrods: µm Numbr of lctrods pr snsor comb: 60 (0 pr sid Numbr of lctrods pr tst comb: 0 (10 pr sid Figur 17. Layout of th SUMMiT V MEMS aclromtr. 8

6 Suprficis y Vacío 6(1 4-1, marzo d 01 Maximum displacmnt of th movabl mass (x: 1.85µm Th lngth of th lctrods ncssary to obtain a capacitanc of 1fF is calculatd from Equation 1: l C d (1 ff (μm = ( 1 = = μm 11μm ( εh (8.85 pf / m(μm If vry pair of lctrods has a capacitanc of 1fF, thn ach complt fixd comb has a capacitanc of 60fF (Equation with rspct to th movabl comb whn th systm is rsting, bcaus thy hav 60 lctrods ach. Whn th systm is xposd to th maximum acclration to b masurd, th movabl mass will mov th maximum distanc, producing a diffrnc in capacitanc of 80fF (Equation. Th width of th lctrods is proposd to b µm and th sparation btwn th snsors and tst combs is 0 µm. Th lngth of th cntral plat is calculatd from Equation 4: L p = (( N + N / ( w + d d + ( Δs t = (( / (μ m + μm (μm + (0μm = 496μm To obtain th width of th cntral plat and th lngth of ach part of th springs, a program mad in MATLAB from quations 4, 5, 6 and 7 was dsignd to calculat and graph ths dimnsions (Figur 7. According to th graph in Figur 7, which was gnratd from th MATLAB cod abov, th smallr siz of th acclromtr can b obtaind if th width of th cntral plat is proposd to b 7µm. This would nsur that th total width of th acclromtr and total opning of th springs is 58µm. Each part of th springs will b 9.5 µm. Taking into account th lngth of th cntral plat, th springs and th anchors ncssary to support th moving mass, th final dvic will hav a lngth of 64µm. Th total width of th acclromtr (58µm considrs th anchors to support th fixd lctrods and th gap btwn thm that is 40µm pr sid (Figur 8, th width of th cntral plat and th lngth of th movabl lctrods (115µm including a gap of µm. Tabl 1 shows a summary of calculations and proposd dimnsions of ach part of th acclromtr, so that it may achiv th spcifications listd at th bginning of this sction. Th lastic constant of th spring systm (k, which was obtaind using Equation 5, is 98.74x10 - kg/s. Th total mass of th movabl mass (m is.506x10-9 kg and it was calculatd taking into account th volum of th polysilicon parts, th volum of th mtal layr in th cntral plat and th dnsity of polisylicon and gold. Th rsonanc frquncy and th snsitivity of this acclromtr can b calculatd from quations 8 and 9 rspctivly. Socidad Mxicana d Cincia y Tcnología d Suprficis y Matrials kg / s f r =. 007kHz 9 π kg 1.85μm S = = 61.66nm / G 0G 4.1. Simulation of th PolyMUMPs acclromtr Th acclromtr dsignd abov was modld and simulatd using ANSYS Workbnch softwar. Th first simulation shows th total dformation whn an acclration of 0G is applid along th axis to b masurd (Figur 9. Th simulation shows that th maximum movmnt of th acclromtr is 1.964µm, which is a valid rsult within th rang of movmnt that can mak th dvic, as th distanc btwn lctrods is µm. In th nxt simulation (Figur 10, th locations whr th maximum strss is prsnt whn an acclration is applid to th dvic, can b clarly idntifid. Th maximum strss, according to th simulation, is MPa, which is undr th fractur strngth of polysilicon with which th systm will b built. That is approximatly 1.1 ±0.8 to 1.65 ±0.8GPa according to th PolyMUMPs dsign handbook [11]. Th highst strss occurs at th junctions of th springs with th anchors and th moving mass and th ndpoints of both springs. Th last simulation prformd to this acclromtr is a modal analysis. This simulation valuats th rspons of th structur whn it is subjctd to vibrations on diffrnt dirctions. Th modal analysis simulation provids th rsonant frquncis dpnding on th dirction of vibration. Rsults of th modal analysis ar shown in Tabl. Th lowst rsonant frquncy, according to th rsults of this simulation, is 1.855kHz. This rsonant frquncy is approximatly qual to th prviously calculatd (.007kHz. 4.. Layout Figur 11 shows th layout of th acclromtr, which will b built from a top mtal layr of 0.5µm thick, two polysilicon layrs, POLY1 and POLY, with µmthicknss and 1.5µm-thicknss rspctivly, on anothr polysilicon layr (POLY 0 which srvs as ground plan as wll as to intrconnct th fixd lctrods and for transmitting lctrical signals. This layout was drawn using MEMS PRO v4.0 softwar. This acclromtr was snt to b built by with th company MEMSCAP. Figur 1 shows th final vrsion of th acclromtr. Pads to connct th acclromtr to a packag and to prform tsts at th acclromtr ar found around th dvic. 9

7 Suprficis y Vacío 6(1 4-1, marzo d 01 Tabl I. Summary of th acclromtr dimnsions (SUMMiT V. Charactristic Siz (µm Lngth 45. Elctrods 1 Thicknss.5 Lngth 58 Cntral plat 115 Thicknss 7 Lngth of ach part 10.5 Springs 1 Thicknss 1 Anchors Lngth 0 50 Lngth 10 Junctions 50 Thicknss.5 Total width of th acclromtr 57 Total lngth of th acclromtr 4 Total opning of th springs Dsign of a transvrs comb acclromtr with SUMMiT V This acclromtr was also dsignd lik th prvious on, but according to th dsign ruls of SUMMiT V manufacturing procss. Th combs will b built from two polysilicon layrs with a total thicknss of.5µm (MMPOLY1 and MMPOLY and th movabl mass from four polysilicon layrs that will hav an ovrall thicknss of 7µm (MMPOLY1, MMPOLY, MMPOLY and MMPOLY4. Th main dsign spcifications ar almost th sam as th last acclromtr, xcpt for th distanc btwn lctrods and th maximum displacmnt of th movabl mass: Acclration to b masurd: 0-0G (1G=9.81m/s Rquird capacitanc for ach pair of lctrods: 1fF Distanc btwn lctrods: 1µm Numbr of lctrods pr snsor comb: 60 (0 pr sid Numbr of lctrods pr tst comb: 0 (10 pr sid Maximum displacmnt of th movabl mass (x: 0.5µm Equation 1 is usd to gt th lngth of th lctrods ncssary to obtain a capacitanc of 1fF: C d ff m l ( (1 (1μ = 1 = = μm 45.μm ( εh (8.85 pf / m(.5μm Tabl 4. Modal analysis of th SUMMiT V MEMS acclromtr Mod Frquncy (khz Socidad Mxicana d Cincia y Tcnología d Suprficis y Matrials Th complt fixd combs hav a capacitanc of 60fF with rspct to th movabl comb whn th systm is at rsting stat, bcaus ach has 0 lctrods pr sid (Equation. Whn th systm is xposd to an acclration and th movabl mass movs 0.5µm, th diffrnc in capacitanc is 80fF (Equation. For this acclromtr, th width of th lctrods is proposd to b 1µm, that is bcaus th manufacturing procss allows it, and th sparation btwn th snsors and tst combs is also 0µm. Equation 4 is usd to calculat th lngth of th cntral plat: L p = (( N + N / ( w + d d + ( Δs t = (( / (1μ m + 1μm (1μm + (0μm = 58μm Th program in MATLAB is also usd to gt th width of th cntral plat and th lngth of ach part of th springs. Figur 1 shows that th width of th cntral plat should b 115µm in ordr to obtain th smallr siz of th acclromtr. With this valu, th total width of th acclromtr and total opning of th springs is 57µm and ach part of th springs will b 10.5µm. Th total lngth of th dvic is 54µm, which includs th lngth of th cntral plat, th springs and th anchors ncssary to support th moving mass. Th anchors to support th fixd lctrods and th gap btwn thm hav a width of 4µm (Figur 14. A summary of all dimnsions of ach part of th acclromtr is shown in Tabl. Th mass of th movabl bodis was obtaind by multiplying th dnsity of th polysilicon by th volum of th movabl mass: m = δ V = δ ( V + V + V p M m = (0 kg / m (9.44 fm +.5 fm fm m = u 1 Th lastic constant of th spring systm can b calculatd from Equation 5, using th mass multiplid by th acclration and dividd by th maximum displacmnt of th movabl mass, as shown as follow: m a k = x kg 1 ( kg (94.m / s k = 0.5μm k = kg / s Equation 8 can b usd to calculat th rsonanc frquncy of th acclromtr and its snsitivity from Equation kg / s f r =. 861kHz 1 π kg 10

8 Suprficis y Vacío 6(1 4-1, marzo d 01 Socidad Mxicana d Cincia y Tcnología d Suprficis y Matrials MATLAB cod: 1 m S = μ =.nm/ G 0G 1 and, and th springs only with polysilicon layr 1, allowing thm to hav mor flxibility. 6. Conclusions % Elctrods charactristics: N=60; %Snsor lctrods Np=0; %Tsting lctrods W=1-6; %Elctrods width L= ; %Elctrods lngth H=.5-6; %Elctrods Thicknss d=1-6; %Distanc btwn lctrods E=1609; %Young s Modulus Wr=1-6; % of th springs Hr=1-6; %Thicknss of th springs x=0.5-6; %Maximum displacmnt dnsity=0; %Polysilicon dnsity %Lngth of th cntral plat Lp=*((N+Np/*(W+d-*d+(0-6; Hp=7-6; %Thicknss of th cntral plat g1=9.81; %1 G forc = 9.81 m/s^ a=0*g1; %Acclration to b masurd V=(N+Np*W*L*H; %Volum of th lctrods %Volum of th junctions Vu=(50-6*(10-6*(.5-6*; Wp=1-06:1-6:00-6; % of th cntral plat %Lngth of ach part of th springs Lr=((((pi^4/96*(*x*E*Hr*(Wr^./... (dnsity*a*(v+vu+lp*hp.*wp.^(1/; La=Lr.*+5-6; %Total opning of th springs %Total width of th acclromtr Wa=Wp+(L+4-6*; plot(wp,wa,'--',wp,la,':',wp,lr,'linwidth',1.5,... xlabl({'cntral plat width';'(m'},... ylabl({'dimnsions';'(m'},... lgnd('total acclromtr width',... 'Total magnitud of th springs',... 'Lngth of ach part of th springs' 5.1. Simulation of th SUMMiT V acclromtr Similar to th prvious acclromtr, th SUMMiT V acclromtr was also modld and simulatd using ANSYS Workbnch softwar. Whn an acclration of 0G is applid along th axis to b masurd, th total dformation of th dvic is µm (Figur 15. This dformation rprsnts th maximum movmnt of th acclromtr at that acclration. Th rsult is valid bcaus it is in th rang that th dvic can mov bcaus th distanc btwn lctrods is 1µm. Th strss simulation shows that th maximum strss to which th dvic is subjctd is 1.0MPa, which is undr th fractur strngth of polysilicon (Figur 16. Finally, th rsults of th modal analysis, which ar prsntd in Tabl 4, show that th lowst rsonant frquncy is about.496khz and it is vry similar to th frquncy calculatd for this dvic (.861kHz. 5.. Layout Th layout of th acclromtr is shown in Figur 17. This layout was drawn in AutoCAD. Th cntral plat will b built with polysilicon layrs 1,, and 4 with a thicknss of 1µm, 1.5 µm,.5µm and.5µm rspctivly. Elctrods will b built with polisilicon layrs Th acclromtrs dsignd in this papr wr simulatd in ANSYS Workbnch softwar. Th rsults of ths simulations hav bn vry satisfactory according to mathmatical calculations, so it is considrd that th dsign mthodology proposd in sction 0 is fasibl to dvlop this typ of MEMS dvics, simplifying thir dsign. Th manufacturing procsss usd in this work hav thir own advantags and disadvantags in th dsign of MEMS dvics. PolyMUMPs is a µm, -lvl, surfac micromachining tchnology. This procss turns out to b of th chapst compard to othr tchnologis sinc it is focusd on th ara of rsarch in univrsitis, industry and govrnmnt. A major disadvantag of this tchnology is that it rlis on th rstrictions to add or implmnt diffrnt layrs or fabrication stps along th construction of th acclromtr structur, so diffrnt rsults can b obtaind in th charactristics of th matrial usd in th fabrication lin. SUMMiT V procss is a 1µm, 5-lvl, surfac micromachining tchnology. This procss has a bttr rsolution and mor mchanical layrs than PolyMUMPs, which allows on to obtain smallr dvics. Morovr, this numbr of mchanical layrs allows build mor complx structurs. On disadvantag of this tchnology is that it is slightly mor xpnsiv than that prviously dscribd. Howvr, its rsolution and construction quality nsur that dvics hav bttr prformanc. Rfrncs [1] D. S. Eddy, D. R. Sparks, Intrnational Symposium on Micromchatronics and Human Scinc, Nagoya, Japan, [] T. Sthuramalingam, A. Vimalajulit, nd Intrnational Confrnc on Mchanical and Elctrical Tchnology, 010. [] M. Mottaghi, F. Ghalichi, H. B. Ghavifkr, Intrnational Confrnc on Microlctronics, Niš, Srbia, 008. [4] S. Grvais Ducourt, Snsors Applications Symposium, San Antonio, TX, USA, 011. [5] B. Li, D. Lu, W. Wang, Snsors and Actuators, 79, 19 (000. [6] B. D. Pant, L. Dhakar, P. J. Gorg, S. Ahmad, Snsors & Transducrs, 109, 9 (009. [7] F. A. Hassani, A. F. Payam, M. Fathipour, Smart Structurs and Systms, Thran, Iran, 010. [8] J. G. Korvink y O. Paul, MEMS: A Practical Guid to Dsign, Analysis, and Applications, Friburg, Grmany: William Andrw, Inc, 006. [9] F. J. Ibarra V., Mastr Thsis: Guadalajara, Jal., México, 011. [10] S. D. Snturia, Microsystm Dsign, Kluwr Acadmic Publishrs, (Nw York, USA, 00. [11] MEMSCAP, PolyMUMPs Dsign Handbook, [1] Sandia National Laboratoris, SUMMiT V Dsign Manual, Albuqurqu, Nw Mxico, USA,

9 Suprficis y Vacío 6(1 4-1, marzo d 01 [1] J. J. Alln, Micro lctro mchanical systm dsign, (Boca Raton, FL: CRC Prss, Taylor & Francis Group, 005. [14] S. Baglio, S. Castorina y N. Savalli, Scaling Issus and Dsign of MEMS, Chichstr, John Wily & Sons Ltd, (Wst Sussx, England, 007. Socidad Mxicana d Cincia y Tcnología d Suprficis y Matrials [15] R. Rincón Jara, R. Ambrosio Lázaro, J. Mirls y A. Jiménz Pérz, V Smana Nacional d Ingniría Elctrónica (SENIE 09, Ocotlan, Jal. México,