Unformatted text preview: MECH 466 Microelectromechanical Systems
University of Victoria Dept. of Mechanical Engineering Lecture 19: Polymer MEMS Stiction in MEMS July 16th, 2007
Mech 466, N. Dechev, UVic
Polymer Materials for MEMS fabrication Introduction to Stiction Causes of Stiction Stiction Modeling Stiction Reduction Methods Mech 466, N. Dechev, UVic 2 Polymer Materials
Polymer materials are created by a long repeating series of smaller molecules (chains of smaller molecules). Image of polyethylene polymer chain [Image from University of Florida] Image of ‘cross-linked’ polymer chains [Center for Polymer Studies] The smaller molecules have a ‘natural tendency’ to link together with each other, when subjected to a ‘driving force’ to form long chains, that cross-link with other chains, again and again, to form a ‘solid material’.
Mech 466, N. Dechev, UVic
3 Polymer Categories
Polymers can be categorized into three major classes: Fibers Natural Fibres -Hair, Cotton, Cellulose, Silk, etc... Synthetic Fibres - Polyester, Polyamide Nylon, etc... Plastics Polyethylene, Polypropylene, Polyvinyl Chloride (PVC) Polymethyl methacrylate (Acrylic), etc... Elastomers Rubber, etc... See Table 12.1 in textbook for the properties of these three classes of polymers. Mech 466, N. Dechev, UVic 4 Polymer Categories
Polymers can also be categorized in terms of temperature response: Thermal Plastic Polymers (Thermalplasts) -Can be re-melted and re-shaped repeatedly (e.g. acrylic, and PVC) Thermal Setting Polymers (Thermalsets) -Take on a permanent shape once polymerized/processed (e.g. epoxy, and phenolic) Mech 466, N. Dechev, UVic 5 Polymers in Microelectronics
The use of Polymers in microelectronics and MEMS is a growing area. In microelectronics, polymer technology is being developed for applications such as: -Plastic transistors, -Organic thin-film displays -Plastic Memory The motivation for the use of plastics is: -Unique properties: Flexibility, Bio-compatibility, etc... -Lower cost of materials -Lower cost of fabrication: Injection molding, screen printing of layers, thermal embossing, etc....
Mech 466, N. Dechev, UVic
6 Polymers in MEMS
The advantages that apply to microelectronics, apply similarly to MEMS. Especially the unique aspects of plastic material properties. Typical Polymers that are used in MEMS include: - Polyimide - SU-8 - Liquid Crystal Polymer - PDMS (poly dimethylsioxane) - PMMA (poly methyl methacrylate, ‘acrylic’) - Parylene - Teflon Mech 466, N. Dechev, UVic 7 Example of Polymer Pressure Sensor
We have previously reviewed a pressure sensor made with bulk micromachining. Here is a Case Study (12.3) of a pressure sensors made with surface micromachining, using polymer MEMS: Polymer Pressure Sensor, [Image from F.of.MEMS, Chang Liu] Mech 466, N. Dechev, UVic
8 Example of Polymer Pressure Sensor
Consider the Schematic of the Top View and Cross-Sectional View:
resistor O A A etch channel cavity resistor A-O substrate O-A Polymer Pressure Sensor, [Image from F.of.MEMS, Chang Liu] Mech 466, N. Dechev, UVic
9 Polymer MEMS
For Homework, Review Case Studies: 12.2, 12.3 and 12.4 Mech 466, N. Dechev, UVic 10 What is Stiction?
Stiction is a combination of one or more ‘adhesion forces’ or ‘adhesion phenomena’ between two objects in contact. Stiction occurs at all scales, and has a finite effect, based on effective contact area (true points of contact between two rough surfaces), and other parameters. Consider the example below of two typical surfaces in contact, each with some amount of surface roughness:
A physical model to predict stiction in MEMS A physical model to predict stiction in MEMS A physical model to predict stiction in MEMS A physical model to predict stiction in MEMS surfaces, we are interested in the distanceaces, abe are deterested in the distanceaces, abe are deterested in the distanceaces, abe are deterested in the distance probability density surf prob w ility innsity surf prob w ility innsity surf prob w ility innsity function of the surfaces, because this function iofgtoie g to aces, because this function iofgtoie g to aces, because this function iofgtoie g to aces, because this function is going to give function s h n surf give function s h n surf give function s h n surf give us the amount of surface at a speciﬁc thetance,untnd fhsurfe ce at a speciﬁc thetance,untnd fhsurfe ce at a speciﬁc thetance,untnd fhsurfe ce at a speciﬁc distance, and hence us dis amo a o enc a us dis amo a o enc a us dis amo a o enc a its inﬂuence on the total energy. With inﬂuconﬁgonation total energy. With inﬂuconﬁgonation total energy. With inﬂuconﬁgonation total energy. With the conﬁguration of its the ence ur the f its the ence ur the of its the ence ur the f ﬁgure 9, we obtain, from the heightﬁdisrteibutiwn ounainonfr,om the heightﬁdisrteibutiwn ounainonfr,om the heightﬁdisrteibutiwn ounainonfr,om the height distribution functions, gu r 9, o e f bt cti , s gu r 9, o e f bt cti , s gu r 9, o e f bt cti , s za zoausbilany function, hab (z). For the zaaussian this distance probability function, habhzs .diFtanceepG ba s it t ( i ) s or th ra this distance pG bability function, habhzs .diFtanceepGausbilany function, hab (z). For the Gaussian ro t ( i ) s or th roba s it is as a dists. ti an, g s calculat is as a dists. ti an, g s calculat Surface a distribution, the calculation SurfacefollowribuHovinthe urfaces ion SurfacefollowribuHovinthe urfaces ion is as followribuHovinthe urfaces ion is as follows. Having surfaces dists. ti an, g s calculat with distributions ha (z) and hb (z) givenith distributions ha (z) and hb (z) givenith distributions ha (z) and hb (z) givenith distributions ha (z) and hb (z) given by w by w by w by (z − za )2 ¯ 1 1 (z − za )2 ¯ (z − za )2 ¯ ha (z,n¯d ) = √ exp − a za and 2σa2 2σa2 σa 2π a (7) (7) (7) 2 1 1 (z − zb ) ¯ (z − zb ) ¯ 1 1 (z − zb )2 ¯ (z − zb )2 ¯ ,¯ ,¯ ¯ hb (z, zb ) = √ exp − hb (z, zb ) = √ exp − ,¯ , hb (z, zb ) = √ exp − hb (z, zb ) = √ exp − 2 2 2 2 2σb 2σb σb 2π σb 2π 2σb 2σb σb 2π σb 2π 1 1
2 Roughness of Surface B ¯ h (z, z ) = √ exp − h (z,n¯d ) = √ exp − az and Figure 8. Gaussian distribution of surfaceFieigre s.. Gaussian distribuaion ofasurfaceFie2πe s.. Gaussian σi2 tribuaion ofasurfaceFie2πe s.. Gaussian σi2 tribhai(z,o¯ asu=ace heights.xp − h gu ht 8 t gh 2 das 2 das ut on z ) rf σ √2π e t gh f σa hgiur t 8 σa hgiur t 8 (z − za )2 ¯ (7) Surface b Surface b Surface b th the surf utio a f h d Surface b th the surf utio a f h d the distribution of the distance between e distribacesnhob (tz)eis istance between e distribacesnhob (tz)eis istance between e distribacesnhob (tz)eis istance between the surfaces hab (z) is th the surf utio a f h d Object B zb
0 za ¯¯ hab (z, za + zb ) =
Surf ace a zb 1
2 2π σa2 + σb 0 Roughness of Surface A Surf ace a Mech 466, N. Dechev, UVic At the micro-scale, the forces associated with the stiction effect are often greater than other micro-forces.
707 707 = N =1 N =1 N =1 together, the ﬁrst contact points will tyigedhpr, stieaﬁlrstdcontoct points will tyigedhpr, stieaﬁlrstdcontoct points will tyigedhpr, stieaﬁlrstdcontoct points will yieldNpl1 stically due to o el t e la thc l y ue a o el t e la thc l y ue ta o el t e la thc l y ue a a or a givethe l are sforcese that it erea. can an wh ecalcuare sforcese that it erea. can an wh ecalculate thn se + z , we can giv n separatio e ¯ n sep ge o clo ¯ + ¯ , or giv the l late o ce ¯ + ¯ , n sep ge th lo p n the large force per unit area. Only when weargesforceseer unitharea.FOnly when weararation zaer uzbthawe FOnly ow en weararation zaer uzbthawe FOnly ow en we are so ce za thatbthe For anow ecalculate thn za + zb , we can now calculate the the l are o clo p that t e ¯ ¯ or giv n separatio lo ¯ pn force can be fully counteracted by thefmate rian ofetfullsurfounteraseedgbvinhefthetescan ooftfuhleurfougherasee, gbvbnhefthevesluantooo fuhleurfougherasee, gbvbnhe qheveslualtooo hte eurfeiceht sses, gSvbngeqhevalum oo the height sets, Sab , equivalent to orc e c l b he y c ace, ct t i y t g ma erual bfe htel s c eicntt sctsd Syi t gequate ri m bfefthtel s c eicntt sctsd Syi t ge t uat ari m f ft hs h a g , et t i a i , t ui s ent t f orc i m y h a e, et t i a , m i ace n t orc l y h a e, et t i a , m i en t equilibrium is reached, but by then the uilibestm isereached, buttheypreviothsly ilibestmistance ded, buttheypfuenothslyhgbhestmistance ded, buttheypfuenothslyhgbhest fdistance distributhenpfuncouslyhgbvz) fdistance distribution function hab (z) for eq highriu asp rities are b then uequ igihriu d isereach istribution th nctioe uilibriu fd risereach istribution th nctioe higivz) asperities are tio revi tion a i( en or e h g ven asp rities are n a ( en o b revi ueq higivz) asp rities are b revi u n a ( en or not the only ones governing the surnace thnternlyion eenergy rnithg Gaussian ce thnternistion eenergy rnithg Gaussian ce thnternistion eenergy rnithg Gaussian ce interaistion energy the Gaussian case. It is f ot i e o act on s gove n e the surna case. Italy on s gove n e the surna case. Italy on s gove n e the surfa case. It c f ot i e o c f ot i e o c of the system. We get the situationof fthﬁgsyetem.in We icht the situationof fthﬁgsyetem.in We icht the situationof fthﬁgsyetem.in We icht the situation of ﬁgure 9, in which o e ur s 9, wh ge o e ur s 9, wh ge o e ur s 9, wh ge ¯ ¯ ¯ ¯ ¯ ¯ ¯ there is a certain distance za + zb between ths a certain siitstance zaa+ :zb zb1 t− een +hs zb1 eanzb ),s(itstance azaa+ :zb zb1 t− een +hs zb1 eanzb ),s(itstance azaa+ :zb zb1 t− een +h(zb1 eanzb ),s(ziaons za ) ab : (za1 − za ) + (zb1 − zb ), (za2 − za ) ¯ there i e mean po d ions ¯S b ¯ ( a e w zeret i ( a certain diziaons z ¯) b ¯ ( a e w zeret i ( a certain diziaons z ¯) b ¯ ( a e w za ) t e m − ¯ po it 2 − ¯ S th a ) e m − ¯ po 2 − ¯ S th a ) e m − ¯ po 2 − ¯ S to e f ott z ¯ Tc ¯ to¯ e , t ¯ ¯ a + b of the bottom surface za and the of pthsurbaceomb . surfahe za and (tzbe − zbhsur.b.ot(omb−uraf) he(zzan − zb )t.he − zbhsur.b.ot() mb−uraf) he(zzan − zb )t.he − zb )sur.f(ace) azb− zaThe(zb n − zb ). b2 − zb ), . . (12) an − za ) + (zb n − zb ). ¯ + h 2 of pt ), . facezaz . s z T ce ¯ and (zb2 of pt ), . f(aceoaz . s z T c ¯ and (zb2 top , . .12 z ¯ . ¯ ) + + ¯ ,t n ¯ to¯ e 12 z ¯ ¯ a + b n + + ¯ ,( n ¯ (z ¯ . , (z ¯ ¯ (12) standard deviations of the surface heaghtard rdevia tions σ b, the surface heaghtard rdevia tions σ b, the surface heaghtard rdevia tions σ b, the surface heights are σ a and σ b, sti nd s a e σ a and of sti nd s a e σ a and of sti nd s a e σ a and of In the samerway wie deﬁne Sd0 to be Sab nohe saimerza ay¯ wie ddy..ne Sd0 to be Sab nohe saime za ay¯ w=dd0 .ne Sd0 to be Sab nohe saime za ay¯ w=dd0 .ne Sd0 to be Sab for which za + zb = d0 . I f t r wh ch ¯ +ect =el 0 w p zb v eﬁ I f t r wh ch ¯ + zb e eﬁ w I f t r wh ch ¯ + zb e eﬁ w ¯¯ respectively. respectively. espect vely. es t at ue t us r oighh v n e t t z , t at ue t us h hg , l c t nt r ue t i us r ha he The origin of the z-axis is at the meanThegortigialue ohe he axiInis he trhe mieanThef ortie ialaof ohwhewxlInis heinee monanThhf oztie ialaof ohwhewxlInis heinee monan e eif (tzt)valapeofwhewilIn oheinemaondee of (tz), paper we will continue to use ha (z), hei h v n of t f t z- s t at ema nder eighh g p uper f e e -a i il cont trh maie dee eea (tr )g p uper f e e -a i il cont trh maie der o a hhe p ue r t e ho t v n e t t z s h s hb ( t , n ml ) eys nudr(z) w owa lower surface (the plane where the comlowterisuefaace thoulld ne where zhe hob (zowterishefaac,(khoulldnbe where ehcahob (zoaanriuheftfhe ,(khoulldnbe where ehcahob (z)laanduhe 0tfhe , knouldnbe that we )cahab (z)aanduhe 0t(ze , knowing that we can always use the ple nt r rf ce ( we p a be hb ( t ), c a ml )le ednud0 f z)e t ne p i nge that w z)e c a alwlwte dss e0 aace t ne p i nge that w z)e c a alw eye ins er(ace w owi g p an t r r(ce w owa hb ( t , n mp t s t d z) hb (z , n alw ys s d h ) p t r ce measu h e tu t u f s S sets o reali measur he ih t u f s d in case the surfaces were not rough). Wecassutme shafasurs acere not rough). Wecassutme shafasoers twerae not rough)d Wecanstemd sf afasoers twerae not rough)d We anstemd if atpoirftsces , Sb , Sab fand Smeasueement points Sa , Sb , Sab and Sd0 instead if in ase h tur t ce f w s sets of realin ase remenr tpc in aces , Sb , Sab fan . Sn0 iassutemenr tpc in ac Ss , Sb , Sab fan . Smeasurement su n a Sa sets o real d0 inst r ad if sets o real d0 i ssu a e th se a t u approaching each other will halt at an prouilibrium distance wreqharedat aneequilibsriutme distance directlyredat aneeqeachiintgtme distance directlyredat aneeqem usriutme distance directlyred.ttinge them useothe sets by directly putting them into ap eq aching each other ill ui lt . W proaching h sets ther wreqhalt u.tting proum usriu h sets ther wreqhalt u.tting th uilibneo h sets by requi pu W can int ap can u e each o by ill ui p W th ilibneo each o by ill ui p W can i t ap can a numericaza calz ulatid0n, ‘binning’ tha m u(ms riin aa ahaszogaaid0n, ‘binning’ tha m u(ms riin aa hastogaaion, ‘binning’ tha m u(ms riin aa hastogaaion, ‘binning’ them (as in a histogram) l + ¯ = o. c e n a e c z ci l¯ ulr t m). l +t = o c e n a e c l ci lculr t m) za + zb = d0 . ¯¯ za + zb = d0 . ¯¯ e n a e c l ci lculr t m) ¯ ¯ b b at eigh i h o e t c ain f n Therfpo h i h o e at eig t c ain f n at r po The height distribution functions of the surhaces tarestribz)tiontouobttions ewer edsuahaces tarestribz)tiontouobtemnifewerudsuahcalintarestribz)tiontouobtemnifewerudsuaicalintare efa (rz) usito obtem ifewerudaeaicalints before using them in a numerical The f eigh di ha ( u f nc ain f of thTherfpointsdbefa (ru usinfg nhtio snoa themeri aces tsdbefa (ru usinfg nhtio snoa themer faces s b h o e ng th ain n a n m t r po calculatio zand ﬁttin )h n inner h tio funcalculatio(nandiﬁtting.ag inner h tio funcalculatio(n mriﬁttingh g ntalytical r hb g t ction t t emr n ng )h n talytical ction t t e n n u an ) d hb g t h i we h t i o talytical and hb (z). If we have a function e(zangivin(z). eIf nteracavena function e(n,)ogivin(zg.aeIfawe acavena functiono ehz,)ogavid (ustineIfawe acavena functiono ehz,)ogavid g stine ianeractionfuncalculation,mraﬁttinsing analytical function to them and using ction to the o nd ug an hb z energy per unit area, varying with theenistanceer unit area,theryingis functheenistancee.r unit area,theryingis functheenistancee.r unit area,theryingis functhen istance .z between the this function directly. d ergy p z between va th with tion directlyz between va th with tion directlyz between va th with tio ddirectly d ergy p d ergy p For the special case in which za + zbF= the the equilibrium which za + zbF= the the equilibrium which za + zbF= the the equilibrium which za + zb = d0 , the equilibrium ¯ ¯ ¯ or d0 , special case in ¯ or d0 , special case in ¯ ¯ ¯ or d0 , special case in ¯ distance, we will call the distance distribsttioce, unction hd0 (zh.e distance distribsttioce, unction hd0 (zh.e distance distribsttioce, unction hd0 (zh.e distance distribution function hd0 (z). di uan n f we will call t) di uan n f we will call t) di uan n f we will call t) Figure 9. Modeling of surface roughnessesiand e quiMbrduling of surface roughncosesientreeqGiaibrduainapprsurimatrougihncosesrentreeeGiMbrduainapprsurimatrougihncosesrentheeGiandsuan approximationOf rathese,rtheeGandsian approximation is rather crude, and F gur e 9. li o i em Of es uFs a,udhe 9u Mo si l n g of oxface ionOfres hFs a,udhdq,. ano si l n g of oxface ionOfres hes a,rd dq, a ibsri i m rg s atue ig ru e 9u li d i em rc us s atur c u e u lu . lus i em is cour r c ud , us distance. distance. distasefe. l when the forces beeween s hedsstrfncfe.s when the forces beeween s hessuufacus when the forces beeween s hessuufacus when the forces between the surfaces are nc u i uusacul are ae e becomes less u b tcome t l ss b tcome t le s rsefe l are b tcome t l s rsefe l are very weak, because of the deviations from tweak, bdistributiothe deviations from tweak, bdistributiothe deviations from tweak, bdistributiothe deviations from the real distribution very he real ecause of n very he real ecause of n very he real ecause of n distances. If we know this distributiodi,stanccan calculateothethisin itsteibuil of,sthnccanusf iwe.lateothethwiedmteasuile of,sehsurfsaces iwe.lateothethwedmteasutionhe surfaces late the n we es. If we kn w d hr ta tiodi we Gsa calcu kWhen is n its eiba tiodi tanccanusf an kWhen is is rib re t , we can calcu n a e e . I s an n w hr t r nh we Ga. calcu n w t e e Is in the tail of the Gaussian. When wie measaile of ehsurfaces ian. When we measure the surfaces n the tur th t e Gauss surface interaction energy. This principleace interactionpoiergy. with anincipleace inget mainepoierdescripis an.inciplethis inget mainepoierdescripis pr.inciplethis case main point surf was the main en nt This pr AFM, was the a bn tterntgy. with pr AFM, wascase a bn tterntgy. Th tion In was the surf we teractio en Th tion surface the teractio en In we with an AFM, we get a better description. AFM, is case a better description. In this case with an In th we get of the previously referred to paper of of nhSperngeouet y l efer]. d twe agetr of dianhStprngeouet yolfefer].hd itwe agamplfedianhStp’ngoouet yolfefer].hd ito t asamplfevan iSps’ngon et al . va t e p evi n sl a r [22 re o p pe a ofst repe evitnSsl a r [22 re e ght s etr o ofpt reps revenSsl a r [22 re e ghp per o po nt e fer v c e e se n ‘ o p pe a v soin e sf it r a n‘ ce e e a gt d we s et a sc ie s et The next part covers the quest to Thed ntexs part cce ers the quest to Thed ntexs part cce ers the quest to Thed ntexs part cce erswe e equa st iscrete dsett iSa dof n c‘height gampledipornte’ sfor Sa of n ‘height sample points’ for ﬁn hi t distan ov ﬁn hi t distan ov ﬁn hi t distan ov th e to ﬁn h s istan e surface a, surface a, a su distribution function. The model aldostrsbusion functuon. ul The model aldostrsbusion functuon. ul The model aldostrsbusion functuon. ul The rface l ,allows us to ﬁnd useful surface a, l i w i t to ﬁnd i sef l i w i ut to ﬁnd i sef l i w i t to ﬁnd i sef mode trends, and be able to understand bettetrrenhat, happbe s blctuoluy derstand bettetrrenhat, hS ppbe s,bzetuol.ly,dz rs.tand bettetrrenhat, hS p9be s,bzetuol.ly,dz rs.tand better what hap9) ns actually w ds and en a a e t a l n w ds aa d: en a alc t a u.n e na za1 a2 , . w ds aaadp) n1 alc 2t a u.n ean n(: e a a a , . z an S (pe a1 , za , . . . , z . Sa(9) a1 , za2 , . . . , zan . :z :z (9) in a situation in which stiction is occua situation in ewhich stiction is occua situation in ewhich stiction is occua situation in ewhich stiction is occurring, awhich e2fects an in rring, which ffects in rring, which ffects in rring, which ffects f are important and which conditions dare omhaveanuch d whgch con dhteons dareaiy, haereaetuaah ea wbhgch tcon ohteesnsmdfacaiy, haereaetuaah ea wbhgch tcon ohteesnsmdfacay, hae e etua h ea S rgor thIe oheesamrfacay, we get a set S for the other surface, o n i t port s t an a lar i e I n t i i sameow omwovt nt c s dt S r for hIendthior a uraree,mwovt nt c s dt S r for hIendthior a ur owe,t w v g s c s t la f e n t p g s n la i e ti eow ot p g s n la i e n ti e no n tth r su e we, b b inﬂuence. Finally, we can deﬁne winrﬂuence. situations we can deﬁne winrﬂuence. situations we can deﬁne winrﬂuence. situations we can deﬁne worst-case situations for o st-case Finally, for o st-case Finally, for o st-case Finally, for different environmental conditions andferenftaces, irond enve conditions andferenftaces, irozbmenv.e, zcn .nditions andferenftaces, irozbmenv.e, zcn .nditions and surSaces, 1 , zb2 ,gi.v.e, zbn . dif sur env a nm gi tal : zb a n 2 . ( en)b a n 2 . : (: ) dif surSb env 1 , nd ,gi.tal b o dif surSb 10zv 1 , nd ,gi.tal b o f b 10zb and . Sb 10zb1 , zb2 , . . . , zbn . (: ) (10) suggestions for engineering solutionssuggvsaitong the etigtion ring solutionssuggvsaitong the etigtion ring solutionssuggvsaitong the etigtion ring solutions alleviating the stiction allee i t i ns for sn cinee allee i t i ns for sn cinee allee i t i ns for sn cinee Now we neprd bleeferin ceEMSht for both sureanepr,owlhiefh rwnceEMSht for both sureanee, whiefh rwnce height for both sureanee, whiefh rwnce height for both surfaces, which we e o a r ms enM heig . Now w f c ed b eme ineM heig . s a rcs e problems in MEMS. problems in MEMS. Now w f cesd a r c e e e Now w f c sd a r c e e e ag u n t hoos oT criptamean hoi gh i eu nnchoos e oT criptamean hei gh i eu nnchoos o s e ipt m of r ei gh ag n bc ag n t e s rt of r i g The starting point is a quantitative desheiptioning pounthis a qaiancitative tdebhetheioning pounthti,sgavqaiabyitative tdebhetheioning pounthti,sgavqaiabyitative tdebcrtheionean hought, giveain yhoose to be the mean height, given by T cr s art of r i g s e st rt of r ei g ag n t s surfaces in contact. We deﬁne a MEMS dein coinact. ich e deﬁne a MEMS n ein coinact. ich e deﬁne a MEMS n ein coinact. ich e deﬁne a MEMS device in which surfaces vice nt wh W d surfaces vice nt wh W surfaces vice nt wh W d n n n n n n 1 1 two surfaces a and b coming together arerfpossiblyand ne coming together 1arerfpossiblyand ne coming together 1arerfpossiblyand ne coming together 1are possibly prone 1 two su aces a pro b pro 1 1 aces pz zaN z ¯ z za.two su (zaN aand ro bb = 11) ¯ z¯. (zaN 11) za two su aces aand bb = ¯= ¯= N N zb ¯ zbza. = (zaN and zb = 11) ¯ zbN . (11) ¯ N to stiction. When we bring the surfaces cloner andenloser bring the surfaces cloner andenloser bring the b rfaces cloner andenloser bring the bzarf= n closer anandloser = n to stictios . Wh c we n n n n to stictios . Wh c we su to stictios . Wh c we su aces dc n n Object A Surf ace a (z − (za + zb ))2 zb 1 ¯¯ (z − (za + zb ))2 zb 1 ¯¯ 1 (z − (za + zb ))2 ¯¯ (z − (za + zb ))2 ¯¯ . . exp hab (z, za +2zb ) = −¯¯2 exp hab (z, za +2zb ) = −¯¯2 . . exp hab (z, za +2zb ) = −¯¯2 exp − 0 0 2 2 σa + σb 2 σa + σb 2 2 σa + σb 2 σa2 + σb 2 2π σa2 + σb 2π σ 2 + σ 2 2π σa2 + σb za za a b (8) (8) (8) (8)
Surf ace a 11 N =1 N =1 N =1 N =1 What is Stiction? As a result, if stiction is present in a micro-system, it can dominate the system. This usually has negative effects, such as microobjects sticking together with no way to separate them, or high amounts of dissipative loss between two objects in sliding contact. 707 707 Mech 466, N. Dechev, UVic 12 Stiction vs. Friction
Friction occurs between two objects in contact with each other, with a normal force Fn, between them, the coefficient of friction, and is independent of contact area, as shown: Fn
Ff Fn In this sense, if the normal force is removed, the force of friction will be gone. Stiction is an adhesion force that will occur ‘upon contact’ between objects, and will keep the two objects in contact indefinitely, even if the initial force that brought the two objects together is gone. Stiction is directly proportional to surface area of contact. Mech 466, N. Dechev, UVic 13 The Causes of Stiction for MEMS
Stiction will occur upon contact between micro-objects, so a good question may be, “Why did that contact occur in the first place”? Contact can occur due to: Electrostatic Forces Drying Process after the HF release of sacrificial layers Shock loading or rapid acceleration that can bring two surfaces together Inadequate stiffness of supporting micro-beams against gravity or normal operation Desired contact by design Mech 466, N. Dechev, UVic 14 The Causes of Stiction for MEMS
Once contact has occurred, there are four major phenomena that individually contribute to the ‘overall effect’ of stiction. These are: Capillary Forces Hydrogen Bridging Electrostatic Forces Van der Waals forces Mech 466, N. Dechev, UVic 15 Stiction due to Capillary Forces
Capillary forces occur when there is a liquid-solid interface.
N Tas et al Consider the following example of two parallel plates with a liquid between them: d Figure 2. Liquid drop (L) on a solid (S), in air (A). θC contact angle between liquid and solid in air. Surface Tension Between Plates [Image from N. Tas, et al.]
between two plates. θ is the than 90˚, then a If the angle of the contact angleair, g isis lesscontact angle between is the force F !c the liquid layer thickness, and A liquid and solid in wetted area. A will exist between the two plates.force F is applied to maintain equilibrium.
C Figure 1. A thin layer of liquid working as an adhesive Mech 466, N. Dechev, UVic where γl a is the surface tension of the liquid–air interface, and r is the radius of curvature of the meniscus (negative if concave). In ﬁgure 1, the liquid is between the plates and the liquid contacts the solid at the ﬁxed contact angle. From simple geometry it follows that r = −g /2 cos θC . In equilibrium, an external force F separating the plates must be applied to counterbalance the capillary pressure forces: F = − pl a A = 2Aγl a cos θC g (2) Figure 3. Liquid bridging two solids. The liquid is non-spreading. The solid is only covered in the bridg area Ab . At is the total facing area. 16 Stiction due to Capillary Forces
The pressure difference between the liquid-air interface is given by the equation: where: "pla = pressure difference at liquid-air interface #la = surface tension of the liquid-air interface r = radius of curvature of the meniscus of liquid Based on the above expression, the force between the two plates can be expressed as: where: A = Area between the two plates !c = contact angle between liquid and solid d = separation distance between plates Mech 466, N. Dechev, UVic 17 Stiction due to Hydrogen Bridging
Some materials absorb water to a small depth just below their surface layer, and are said to have ‘hydrated surfaces’. For example, hydrophilic (favorable to water) silicon surfaces, under atmospheric conditions and temperatures well below 200 ! C, contain adsorbed water layers. When two of these hydrated surfaces are brought into close contact, hydrogen bonds may form between oxygen and the hydrogen atoms of the adsorbed water layers in each of the surfaces. This is a chemical bond that will remain, as long as the surfaces remain hydrated. Mech 466, N. Dechev, UVic 18 Stiction due to Electrostatic Attraction
Electrostatic force can serve two functions in stiction: Firstly, it can act over a distance to bring two micro-objects into contact. Secondly, if there is a dielectric layer of material present between the two bodies in contact, such as silicon dioxide, or other material, the charge between the two bodies may remain for some time. After the contact occurs, the electrostatic charges will dissipate or equalize, based on the material properties, resulting in no net force. Mech 466, N. Dechev, UVic 19 Stiction due to van der Waals Force
The van der Waals forces between two bodies are caused by mutual electric interaction of the induced dipoles in the two bodies. These bodies can be considered as molecules or for the case of MEMS, grains within a polycrystalline material. The effect of van der Waals force depends on a material’s properties, and it is usually noteworthy when strongly polar molecules or elements within materials are in contact. Mech 466, N. Dechev, UVic 20 The Effective Contact Area Between Two Surfaces A rough surface is generally modeled as a rough plane with a mean height and a standard deviation using a Gaussian A physical model to predict stiction in ME surfaces, we are interested in the distance probability den distribution of heights, as shown below:
Surface a za Figure 8 Gaace Modeling of the equilibrium.Surfussiaan distribubetweenhetwo surfaces in distance tion of surface ights. contact. Determination of equilibrium distance is not trivial,b(and= √ exp −− ()z − z2b ) , a 1 (z z ¯ ¯ h z, zb ) 1 ¯ 2σ b and ¯ p h (z, z ) = √ σb ex2π − good reference is W. Merlijn.SvansiaSpengen,f etrfal.heights. Figure 8 Gaus n distribution o su ace 2σ σ 2π urface b
a a a a 2 a 2 ﬁgure 9, we obtain, from the height distribution functions, 1 za )2 ¯ this distance probability function, hab ((z .−For the Gaussian ¯ ha (z, za ) = √ exp − z) and distribution, the calculation πs as follows2σa2 aving surfaces .H σa 2 i with distributions ha (z) and hb (z) given by 2 function of the surfaces, because this function is going to g us the amount of surface at a speciﬁc distance, and he A t h t si l mode redict ic i c in ﬁgu S its inﬂuence on the poyalcaenerglyt.o pWith stthteon onMEMration ﬁgu w 9a win obtain, fr the t istance ht bab ribu i e fu surfaces,re e , re e terested inom dhe heigprodistility tdonsitynctio this d tt e ce aces, bility f this o n han z . F g t e G function ofishansurfprobabecauseunctifun,ctiob (is)goinortohgive aus [Image from us theisaributnon,f tsurfcalculation eiciﬁc disltlance, and vience urfa d t mou i t o he ace at a sp s as fo ows. Ha h ng s Merlijn-van-Spengen,et-al] its inﬂuendistoibutionotala (z) and hb (ith givecoby guration of with ce rn the t s h energy. W z) the n nﬁ the distribution of the distance between the surfaces 7)ab (z (h
¯ hb (z, zb ) = zb
Surface b 0 [Image special π σ 2 + σ For the from 2case ain wbhich za + zb = d0 , the equilibr ¯ ¯ M tance, we will call the distan diserlijn-van-Spengen,et-al] ce distribution function hd0 (8) S l rf a o f s Figure 9. Modeuing ce aurface roughnesses and equilibrium Of course, the Gaussian approximation is rather crude, distance. For tbecopecialecasesin ul hich n athe zborces 0 ,ettheeequtilibriurfaces he s mes l ss u ef w whe z + ¯f = d b w en he su m ¯ distavery we willbecause dif thece eviatioution fm the n hd0distribu nce, weak, call the o stan d 21 distrib ns fro unctioreal (z). Mech 466, N. Dechev, UVic di u anc s. I e ing k surf t e o disn ib es a n, we ibri m Figstre 9.eModf lwe ofnowachirs ughtressutiond equilcanucalculate the Of che rtai,lthe Ghe sGan ssiproximation is eather crude, he d urfa in t ou se of t au siau ap an. When w r measure t an s dsurface interaction energy. This principle was the main pointecomes less useful when the forces between the surfaces are istance. b with an AFM, we get a better description. In this c of the previously referred to paper of van Spengen et al .ery we g, becausecof tee setviatioof from the ht sampleutionnts’ v weak t d s eth de S ns n ei real distrib p distanThs. nfexte partwctovs rsistribution,stwe can calcuis dthe cin the tail eof ahe iGarussian. Wahen we ‘heagure the surfacoi ce e I w kno hi e d the que to ﬁnd th late istan e ms es surface at , suisace utiteraction teonrgy.TThis prdel allows ths mainnpoiuseful d rftrib in on func i ne . he moinciple was u e to ﬁ d nt with an AFM, we get a better description. In this case otf ehe s,raviously ble erred dersaper ofevter Speatghapeteals[act]ually get a discrete set S of n ‘height sample points’ for r tnd p end be a ref to unto p tand b t an wh n en p n 22 . we Saa : za1 , za2 , . . . , zan . The next part covers the quest to ﬁnd this distance su in a situation in which stiction is occurring, which effects rface a, distribution function. The model allows us to ﬁnd useful are important and which conditions do not have such a large In the same way, we get a set Sb for the other surface, trends, and be able to understand better what happens actually Sa : za1 , za2 , . . . , zan . (9) inﬂuence. Finally, we can deﬁne worst-case situations for in a situation in which stiction is occurring, which effects deffmportaenvironwhich cocontdons ns not havefsuch a aargegive i ierent nt and mental ndi i itio do and sur aces, l nd Sb : zb1 , zb2 , . . . , zbn . ( ar In the same way, we get a set Sb for the other surface, s ﬂuensti s f ally w n eri g ﬁn u ion st-case situg the for inuggece.onFinor e,ngie ecanndesole twors alleviatinations stiction Now we need a reference height for both surfaces, which Stiction dpfferenms nnironmental conditions and surfaces, and give i roble t e i v MEMS. Sb : zb1 , zb2 , . . . , zbn . (10) suggeTthonstaoting ginenrins a olutintisaaiveviaeing ipteostiotion ugh again choose to be the mean height, given by s i e s f r r en poi et i g s qua on t t ll e d t scr thi n c f ro N c psurflaces iinMEMact. We deﬁne a MEMS device in which ow we need a referenn e height for both surfaces, which we rob ems n cont S. water n height, Stengl n h twoTsurfacesng pannt bs coquingitaoigether cription ssibly gpronagain choose to be t1 e mealayers.given by 1 et al  h he starti a oid i a mant t t v des are po of rou h e zb = ¯ . ( za = ¯ to stiction When We d ing a surfaces clos i wh clo ener=1 zaN ofandabout n100zbNmJ m− n N gy surfaces in .contact. we breﬁne theMEMS device ern andich ser n n N =1 1 1 two esurfr, the aﬁrstdconcact inoinos ethll yaredpplastilcalpy de e to tog the aces an b t om p g tt g wi er iel ossib y l ronu zaN an zb = ¯ z N. (11) za = ¯ model. d ¯ From wafer bonding to e large forcehen unit bring Only when we are so cd se that the For a given separation za + zbn we can now calculate n N =1 ¯ , N =1 b th stiction. W per we area. the surfaces closer an locloser toorchec, nhbeﬁrullyontuctteroicttedwiyl tyie lmatlersitacalfy he sutrface, set giving tstiction f experiments [4, 20],valen gete ra t e f st c coa n p a n s b l h e d p a il o l t due o he sum o the height sets, Sab , equi adh f ¯ ¯ the uargeriurceiser unit ed, but by when we are sheclose that the areor the iprevisepsly givena distancwe istribnow ncalculaten theb (z) eq l ilib fo m p reach area. Only then the hig o st asperities F a g ven ou aration270 zb , em−2 havefunctio repor and z + mJ d can utio been ha fnrce tcan onlfuloy es ugoerernengbyhte esmaterealintetrhe tsiurface,ergyet givingauhe sum of It e height sets, Sab , equivalent to oot he be y l n co nt v acti d t h urfac i of ac on en s the G t ssian case. th is ◦ eqf ilibrium is reached, but by then the n igheﬁ asperities are the previously given d< 200 C). n function hab (z) for (T istance distributio o u the Between Two Contacting io h of st Capillary Condensationsystem. We get the situatSurfacesgure 9, in which nthtere e soa lcertain dioverning t+ezbetweenhaction n nersiyionthe Gaussian 1case.aIt + (zb1 − zb ), (za2 − za ) o th i n y condensation ¯ sureaweenter e mea contacting ab : (za − z ) is ones g stance z h b f t ce i n t two e po g t s S Figure 5. N. Tas, et al.] Capillary ¯ ¯ ¯ a [Image from of t e system. W get the ¯situatbi surfaces. Thehtmeniscusecurvaturesotn eoftop use r9acen zbhich ThSab : (za1 + (zab) + (zb1),− .z. ,,((za2 − z¯aa) + (zb n − zb ). are equal ¯ the Kelvin − z 2 − zb . ¯ ) zan − ¯z ) e of he bottom surface za and h ﬁg ru f , itow . ¯ ¯ ¯ ( ¯ b ¯ there is a certain distance z + z between the mean positions ¯ standard ev t s h s fa radius; the contacttdomiasiuornaceofzata e dburYecetoheisghts are¯ bσ a and σ b, + (zb2 − z ), 2.3.zaElectrostatic . forces betwe p ur equation. of the bo tangles satisfy thoung’s face z . The f ¯ an ¯ be w.a.y, wend− zae Sd(ztbo be zb ) for which z(1+ ) = . ( ¯ )+ ¯ 2z n − Sab In the sam eﬁn ¯a ¯b 0 respectively. standard deviations of the surface heights are σ a and σ b, nder of the paper f r ill ch z z to u The y. e In the remaiElectrostatic weowwhicontainue = d0s.e ha ¯ ¯b b respectivelorigin of the z-axis is at the mean height value of thIn the same way we deﬁne Sd0 to be Saattractive+forces ac lowTr suorigie (ohehelana where the complhtegnteralue of ohed ben thhbrem,ahadez)oanhehpa(z), wnowil gotntanueeto an e lha az), use e h rfac n t p z e s e (z) in b (r f td d0 per ke wiln c h i t w c us a w( ys he mean ee i v face w t ul I from a p ference S ys s d n a general form,seewhichfctisnw-erxeieniesttartetcombothntisesrhftacespreadingb(andabo(fz)realdmeasu)r,emendifoitntast wae, cabn, inwawork0thifunc i wer h c s ( h a l s valid for p W the that d b f s sets an hd0 (z knowting h S S alab anduSe e stea lon cas urtfae e utrfe pea e wh r o h ough).leteei a ume woulsureaceh z), h ap ase the condition t o r can so t sets , S b and S insteg h the non-spreading inurfaces wetrheenowrillugh). Weansseque that smrfacstance of real measucharginghseof, Sopposedd0psurfaces in cproach s g each o r : halt at a um ilibriu u di es sets required. Weementupe int Sa bby adirectly uttinadtifem a n . We cancusc lheion, by directly puttina ie a ih totogr ale at sets z roachin d . ¯¯ apap+ zb = g 0each other will halt at an equilibrium distance requiredumerical the utwork ‘binning’ them (gsthnmtoisthe function leads n ) m r c ain cu at dat p n n n ’ them ( si n h his og a n ) za + zThe d0 . ht distribution functions of the surfaces are ha (za nutoeoibtal caflewlerion, a‘bioinitsgbefore uasnig ta em tin ramumer ¯ ¯ b = heig double ean e u by a net n th eri l calcu z) t we − n nγi a of th iC andThb (E.s hf distributioa Abctionscos egsvrnaces e inhe(action (4tc) flation, atraﬁttings ablayertical themtionatransferdof h e heig I= Chave 2 fun ctlon e(z) θuif g th are t a rz) to ob ain ewer do point n foraly sing func in toumemcan us andergyzp.erIf nit area, vafunctiowithzthgiving the iz tbeaween thcalculation,nor ﬁtting an an.aother. nContactm and using directly en hb ( ) u we have a rying n e( ) e distance n er t ction e this fu ctionto the lytical fu ction to the potentials Surf ace a zb
0 za 2 2 the distribution of the distance σetween the surfaces2haσ(z+ iσb ba ) s 2π b 2 + σ 2 a b ¯¯ hab (z, za + zb ) = σb 2π 1 √ exp − (z − zb )2 ¯ , 2 1 2σb exp − (z − (za + zb ))2 ¯¯ za ¯¯ hab (z, za + zb ) = 1
2 exp − (z − (za + zb ))2 ¯¯ . 2 2 σa2 + σb The Effective Contact Area Between Two Surfaces Example of capillary action between two rough surfaces: Note that the contact area A, and distance between the two surfaces d, are now a function of the surface roughness. account the constant terms in (4a , b). The importance of liquid mediated adhesion is supported by both stiction and Mech 466, N. Dechev, UVic friction experiments. Stiction of released structures can show a large dependence on the relative humidity of air . Friction measurements of silicon and silicon compounds  show a strong dependence of the static For example, for polysilicon surfaces, the surface roughness typically has a value of 1 to 3 nm RMS. This is considered to be highly smooth, and hence the high degree of stiction when contact ener y p u t area, varying with the distanc z bet een the th into is made. where γla cos gθCerisnithe adhesion tension,e andwC takes is function directly. the resulting surface charge and 707 1013 elementary charges per s small separations the electrost surfaces is 22 generally lower than . Temporary charging ca  or operation. Examples o Example of Beam Stiction
Consider the following simple case of a cantilever beam stuck dN Tas et al substrate: own to the The critical length of the beam (the length at which stiction will hold the beam down) can be found using the expression: surfaces,the adhesion of hydrophobic surfaces might be more sensitive to surface roughness because smoothing by condensed water is absent.
where: Figure 6. [Image from N. Tas, et al.] of length l and thickness t , A cantilever beam anchored at a initial gap spacing g . The beam attaches the substrate at distance x from the anchor. Cantilever Stuck Down on Substrate Mech 466, N. Dechev, UVic 3. Critical dimensions of beams and membranes E = young’s modulus of material t = beam thickness d = seperation distance at anchor (shown as ‘g’ in diagram above) #s = adhesion energy per unit area As soon as a structure touches the substrate, the total surface energy is lowered. The structure will permanently stick to the substrate if during peel-off the total energy of the system reaches a minimum. The total energy of the system consists Example of Beam Stiction of the elastic deformation energy and the surface energy, Ifwhich is a is submerged inthe adhesion energy. This enerdried. the beam constant minus a liquid, it must eventually be gy balance is easily made for a cantilever beam . Figure 6 In the process of being ‘dried’lengtha lwet micromachining shows a cantilever beam of after , thickness t and width pw , anchored as oxide removal, the beam will tend to be pulled rocess, such at a initial gap spacing g . downThe beam attaches toby capillary action, as shown:from toward the substrate the substrate at diatance x the anchor. The elastic energy stored in the cantilever is given by Et 3g2w . (7) Em = 2x 3 The surface energy as a function of the attachment length l − x is given by Es = C − γs (l − x )w (8) dependence on t , g , E in (11) should be cha doubly clamped beam a critical radius of cir times larger than the c obtain an idea of the st the critical length of ca assuming an adhesion Young’s modulus of 1 of the beams that are j function of beam thickn The dotted line in ﬁgu doubly clamped beam the beam is taken into that are four times the 23 g = 4 µm), the critical this effect. The ﬁgure shows with a large gap spaci of only 310 µm (880 It is clear that stiction many devices. (11) sh less than proportionall adhesion energy. A re energy only yields an factor of two. 4. Contact during fa After wet sacriﬁcial l is immersed in liquid structures are pinned forces. A theoretical given in the next parag 4.1. Capillary forces where γs is the adhesion energy per unit area. In equilibrium, the total energy Em + Es is minimal. An equilibrium detachment length xeq can be found, where the decrease of Mech 466, N. Dechev, UVic the elastic energy is equal to the increase of the surface energy, by increasing the detachment length x : Consider a beam with 24 width. In the ﬁnal sta volume approaches ze Example of Beam Stiction
The critical beam length (beyond which it will be pulled down by capillary action), can be expressed as: where: E = young’s modulus of material t = beam thickness d = separation distance at anchor (shown as ‘g’ in diagram above) #la = surface tension of the liquid-air interface !c = contact angle between liquid and solid Mech 466, N. Dechev, UVic 25 Stiction Reduction Methods
Organic Pillar Method: Use organic pillar to support the structure during the liquid removal. The organic pillar is removed by oxygen plasma etching. Process to Create Organic Pillars [Image from C. Liu] Mech 466, N. Dechev, UVic 26 Stiction Reduction Methods
Anti-Stiction by Supercritical CO2 Point Drying: Avoid surface tension by relaying on phase change with less surface tension than watervapor. Supercritical state: temp > 31.1 oC and pressure > 72.8 atm. Step 1: change water with methanol Step 2: change methanol with liquid carbon dioxide (room temperature and 1200 psi) Step 3: content heated to 35 oC and the carbon dioxide is vented. Free-standing cantilever beams up to 850 um can stay released.
PT Diagram for Supercritical CO2 Drying [Image from C. Liu] Mech 466, N. Dechev, UVic 27 Stiction Reduction Methods
Anti-Stiction by Self Assembled Monolayer Forming low stiction, chemically stable surface coating using selfassembly monolayer (SAM) SAM file is comprised of close packed array of alkyl chains which spontaneously form on oxidized silicon surface, and can remain stable after 18 months in air. OTS: octadecyltrichlorosilane (forming C18H37SiCl3)
Self-Assembled Monolayers [Image from C. Liu] Mech 466, N. Dechev, UVic 28 Selected Stiction References
N. Tas, T. Sonnenberg, H. Jansen, R. Legtenberg, and M. Elwenspoek, “Stiction in Surface Micromachining”, Journal of Micromechanics and Microengineering, vol. 6, 1996, pp. 385-397 C. H. Mastrangelo, and C. H. Hsu, “Mechanical stability and adhesion of microstructures under capillary forces—part I: basic theory”, Journal of Microelectromechanical Systems, vol. 2, 1993, pp. 33-43 W. Merlijn van Spengen, R. Puers, and I. De Wolf, “A Physical Model to Predict Stiction in MEMS”, Journal of Micromechanics and Microengineering, vol. 12, 2002, pp. 702-713 29 ...
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This note was uploaded on 02/02/2010 for the course MECH 466 taught by Professor Dechev during the Summer '07 term at University of Victoria.
- Summer '07
- Mechanical Engineering