EE 247B/ME 218: Introduction to MEMS Design Lecture 12m1: Mechanics of Materials CTN 2/25/16. Copyright 2016 Regents of the University of California

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1 v lamped-lamped Beam Resnatr ualty Factr (r ) EE 45: Intrductn t MEMS Desgn 9/8/7 8 W r Frequency: Stness Resnatr Beam Electrde Mass v kr m r L r Yung s Mdulus.3 Densty E L r (e.g., m r = r -3-3 kg) kg) EE 45: Intrductn t MEMS Desgn 9/8/7 9 V P V P (t) v ~, V d dt Smaller mass ger req. req. range and and lwer seres R x x P Nte: I I V P = P V V devce Measure te requency selectvty a tuned crcut Dentn: Example: seres LR crcut Example: parallel LR crcut ualty Factr (r ) Ttal Energy Per ycle Energy Lst Per ycle BW EE 45: Intrductn t MEMS Desgn 9/8/7 3 3dB Im Re Im Re Z L Z R R Y Y G LG BW -3dB Selectve Lw-Lss Flters: Need In resnatr-based lters: g tank lw nsertn lss At rgt: a.% bandwdt, 3- res GHz (smulated) eavy nsertn lss r EE 45: Intrductn t MEMS Desgn 9/8/7 3 Transmssn [db] resnatr <, Increasng Insertn Lss Tank 3,,, 5, 4, pyrgt 6 Regents te Unversty alrna

2 Man Functn: prvde a stable utput requency Dculty: superpsed nse degrades requency stablty v Sustanng Ampler A Frequency-Selectve Tank Oscllatr: Need r Hg Hger Hger v Ideal Snusd: v t Vsn t T O =/T O Real Snusd: v t V t sn t t Zer-rssng Pnt Tgter Tgter Spectrum Spectrum EE 45: Intrductn t MEMS Desgn 9/8/7 3 Attanng Hg Prblem: I s cannt aceve s n te tusands transstrs cnsume t muc pwer t get n-cp spral nductrs s n ger tan ~ -cp nductrs s n te range s Observatn: vbratng mecancal resnances >, Example: quartz crystal resnatrs (e.g., n wrstwatces) extremely g s ~, r ger ( ~ 6 pssble) mecancally vbrates at a dstnct requency n a tckness-sear mde EE 45: Intrductn t MEMS Desgn 9/8/7 33 Energy Dsspatn and Resnatr Termelastc Dampng (TED) Materal Deect Lsses Bendng -Beam deects TED Gas Gas Dampng vscus Termelastc Dampng (TED) Tensn ld Spt mpressn Ht Spt Heat Flux (TED Lss) supprt Ancr Lsses At At g g requency, ts ts s s ur ur bg bg prblem! Elastc Wave Radatn (Ancr Lss) EE 45: Intrductn t MEMS Desgn 9/8/7 34 Occurs wen eat mves rm cmpressed parts t tensned parts eat lux = energy lss ( T ) ( ) TE ( T ) 4 p ) K TED ( TED TED p Bendng -Beam Tensn ld Spt mpressn Ht Spt Heat Flux (TED Lss) = termelastc dampng actr = termal expansn cecent T = beam temperature E = elastc mdulus = materal densty p = eat capacty at cnst. pressure K = termal cnductvty = beam requency = beam tckness TED = caracterstc TED requency EE 45: Intrductn t MEMS Desgn 9/8/7 35 pyrgt 6 Regents te Unversty alrna

3 TED aracterstc Frequency uartz rystal = materal densty p = eat capacty at cnst. pressure K = termal cnductvty = beam tckness TED = caracterstc TED requency K p Gverned by ~5, ~5, at at3k 3K Peak Peak were were ss mnmzed mnmzed rtcal Dampng Factr, Resnatr dmensns Materal prpertes ~5,, ~5,, at at3k 3K ~3,, ~3,,at at4k 4K 9/8/7 36 Unmatced Transmssn [db] mpund Mde (,) Ancr Wne Glass Dsk Resnatr Supprt Beams R = 3 m EE 45: Intrductn t MEMS Desgn 9/8/7 37 Impedance-msmatced stem r = 6.37 MHz = 45,78 reduced ancr dsspatn Operated n te nd radal-cntur mde ~,555 (vacuum); ~, (ar) Desgn/Perrmance: Belw: m dameter dsk R= m, t=. m, d=8å, V =7V -6 P =.5 GHz (nd mde), =,555 Plyslcn Stem (Impedance Msmatced t Damnd Dsk) Resnatr ResnatrData Data RR==3 3 m, m,==33 m m dd==8 8nm, nm,vvp ==33VV p Ancr Plyslcn Electrde R [Y.-W. Ln, Nguyen, JSS Dec. 4] EE 45: Intrductn t MEMS Desgn Even Even alumnum alumnum aceves aceves exceptnal exceptnal s s at at crygenc crygenc temperatures temperatures.5-ghz, =,555 Nancrystallne Damnd Dsk Mecancal Resnatr Plyslcn Wne-Glass Dsk Resnatr -4 ~,5, ~,5,at at4k 4K Mecansm Mecansm r r ncrease ncrease wt wt decreasng decreasng temperature temperature tugt tugt t t be be lnked lnked t t less less ysteretc ysteretc mtn mtn materal materal deects deects less less energy energy lss lss per per cycle cycle [rm Rszart, Hltn Head 99] [rm Bragnsky, Systems Wt Small Dsspatn] Relatve Frequency, /TED EE 45: Intrductn t MEMS Desgn Alumnum Vbratng Resnatr Mxed Ampltude [db] TED vs. Temperature 9/8/7 38 pyrgt 6 Regents te Unversty alrna VD Damnd Mecancal Dsk Resnatr EE 45: Intrductn t MEMS Desgn Grund Plane =.5 GHz =,555 (vac) =, (ar) =, (ar) [Wang,. Butler, MEMS 4] Nguyen Nguyen 9/8/7 39 3

4 Dsk Resnatr Lss Mecansms (Nt Dmnant n Vacuum) Gas Gas Dampng Hysteretc Mtn Mtn Deect Deect (Dwared By Substrate Lss) Stran Energy Flw Dsk Stem Substrate Ndal Axs Electrnc arrer arrer Drt Drt Lss Lss e- Stem Hegt (Dwared By Substrate Lss) N N mtn mtn alng alng te te ndal ndal axs, axs, but but mtn mtn alng alng te te nte nte wdt wdt te te stem stem /4 /4 elps elps reduce reduce lss, lss, but but nt nt perect perect Substrate Lss Lss Tru Tru Ancrs (Dmnates) MEMS Materal Prperty Test Structures EE 45: Intrductn t MEMS Desgn 9/8/7 4 EE 45: Intrductn t MEMS Desgn 9/8/7 4 Stress Measurement Va Waer urvature mpressvely stressed lm bends a waer nt a cnvex sape Tensle stressed lm bends a waer nt a cncave sape an ptcally measure te delectn te waer bere and ater te lm s depsted Determne te radus curvature R, ten apply: E 6Rt Laser Scan te mrrr S-substrate Detectr Mrrr = lm stress [Pa] R E = E/(-) = baxal elastc mdulus [Pa] = substrate tckness [m] t = lm tckness R = substrate radus curvature [m] EE 45: Intrductn t MEMS Desgn 9/8/7 4 Slpe = /R x x t MEMS Stress Test Structure Smple Apprac: use a clampedclamped beam mpressve stress causes bucklng Arrays wt ncreasng lengt are used t determne te crtcal bucklng lad, were crtcal Lmtatn: Only cmpressve stress s measurable E 3 L E = Yung s mdulus [Pa] I = (/)W 3 = mment nerta L, W, ndcated n te gure = tckness EE 45: Intrductn t MEMS Desgn 9/8/7 43 L W pyrgt 6 Regents te Unversty alrna 4

5 Mre Eectve Stress Dagnstc Measurement Usng Resnatrs cmpressve and tensle stress Expansn r cntractn test beam delectn pnter Verner mvement ndcates type and magntude stress Unmatced Transmssn [db] Sngle structure measures bt mpund Mde (,) Ancr Wne Glass Dsk Resnatr Expansn mpressn R = 3 m EE 45: Intrductn t MEMS Desgn 9/8/7 44 Flded-Beam mb-drve Resnatr EE 45: Intrductn t MEMS Desgn Resnatr ResnatrData Data RR==3 3 m, m,==33 m m dd==8 8nm, nm,vvp ==33VV [Y.-W. Ln, Nguyen, JSS Dec. 4] 6.35 ntractn Tensle Supprt Beams = 6.37 MHz = 45,78-4 p Ancr 9/8/7 45 mb-drve Resnatr n Actn Issue w/ Wne-Glass Resnatr: nn-standard ab prcess Slutn: use a lded-beam cmb-drve resnatr Belw: ully ntegrated mcrmecancal resnatr scllatr usng a MEMS-last ntegratn apprac =34.5kHz =4, 34, Hz EE 45: Intrductn t MEMS Desgn 9/8/7 46 pyrgt 6 Regents te Unversty alrna EE 45: Intrductn t MEMS Desgn 9/8/7 47 5

6 Flded-Beam mb-drve Resnatr Measurement Yung s Mdulus Issue w/ Wne-Glass Resnatr: nn-standard ab prcess Slutn: use a lded-beam cmb-drve resnatr =34.5kHz =4, 34, Hz EE 45: Intrductn t MEMS Desgn 9/8/7 48 Use mcrmecancal resnatrs Yung s mdulus Resnance requency depends n E Fr a lded-beam resnatr: 3 W Resnance Frequency = = tckness L 4E( W M L) EE 45: Intrductn t MEMS Desgn 9/8/7 49 eq Equvalent mass Extract E rm measured requency Measure r several resnatrs wt varyng dmensns Use multple data pnts t remve uncertanty n sme parameters Elastc nstants n rystallne Materals Anstrpc Materals Get derent elastc cnstants n derent crystallgrapc drectns 8 tem n all ubc symmetres make 6 tese terms zer, leavng tem remanng tat need be accunted r Tus, descrbe stress-stran relatns usng a 6x6 matrx x y z yz zx xy x y z yz zx xy Stresses Stness ecents Strans EE 45: Intrductn t MEMS Desgn 9/8/7 5 EE 45: Intrductn t MEMS Desgn 9/8/7 5 pyrgt 6 Regents te Unversty alrna 6

7 Stness ecents Slcn Yung s Mdulus n te () Plane Due t symmetry, nly a ew te cecents are nn-zer Wt cubc symmetry, slcn as nly 3 ndependent cmpnents, and ts stness matrx can be wrtten as: x y z yz zx xy 3 were x y z yz zx 66 xy EE 45: Intrductn t MEMS Desgn 9/8/ = 65.7 GPa = 63.9 GPa 44 = 79.6 GPa [unts = GPa] [unts = GPa] EE 45: Intrductn t MEMS Desgn 9/8/7 53 Pssn Rat n () Plane Anstrpc Desgn Implcatns EE 45: Intrductn t MEMS Desgn 9/8/7 54 Yung s mdulus and Pssn rat varatns n anstrpc materals can pse prblems n te desgn certan structures E.g., dsk r rng resnatrs, wc rely n strpc prpertes n te radal drectns Okay t gnre varatn n RF resnatrs, altug sme t s prbably beng taken E.g., rng vbratry rate gyrscpes Mde matcng s requred, were requences alng derent axes a rng must be te same Nt kay t gnre anstrpc varatns, ere Drve Axs Rng Gyrscpe Wne-Glass Mde Dsk Sense Axs EE 45: Intrductn t MEMS Desgn 9/8/7 55 pyrgt 6 Regents te Unversty alrna 7