EE 245: Introduction to MEMS Lecture 13: Mechanics of Materials II CTN 10/6/09. Copyright 2009 Regents of the University of California
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![EE 45: Intrductn t MEMS Lecture 3: Mecancs Materals II CTN 0/6/09 Materal Prpertes r MEMS MEMS Materal Prpertes (E/ρ) s acustc velcty [Mark Spearng, MIT] EE C45: Intrductn t MEMS Desgn LecM 7 C.](/docs-images/89/100530458/images/1-2.jpg "Nguyen 9/8/07 EE C45: Intrductn t MEMS Desgn LecM 7 C.")
1 EE 45: Intrductn t MEMS Lecture 3: Mecancs Materals II CTN 0/6/09 Materal Prpertes r MEMS MEMS Materal Prpertes (E/ρ) s acustc velcty [Mark Spearng, MIT] EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 Yung s Mdulus Versus Densty Lnes cnstant acustc velcty Yeld Strengt Dentn: te stress at wc a materal experences sgncant plastc dermatn (dened at 0.% set pt.) Belw te yeld pnt: materal derms elastcally returns t ts rgnal sape wen te appled stress s remved Beynd te yeld pnt: sme ractn te dermatn s permanent and nn-reversble Yeld Strengt: dened at 0.% set pt. Elastc Lmt: stress at wc permanent dermatn begns [Asby, Mecancs Materals, Pergamn, 99] EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 3 Prprtnalty Lmt: pnt at wc curve ges nnlnear True Elastc Lmt: lwest stress at wc dslcatns mve EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 4 Cpyrgt 009 Regents te Unversty Calrna
2 EE 45: Intrductn t MEMS Lecture 3: Mecancs Materals II Yeld Strengt (cnt.) CTN 0/6/09 Yung s Mdulus and Useul Strengt Belw: typcal stress vs. stran curves r brttle (e.g., S) and ductle (e.g. steel) materals Stress Tensle Strengt T30 C) Brttle (S) Prprtnal Lmt Ductle (Mld Steel) Fracture (r T>900 C) Stran [Malu] EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 5 EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 6 Yung s Mdulus Versus Strengt Lnes cnstant maxmum stran ualty Factr (r ) [Asby, Mecancs Materals, Pergamn, 99] EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 7 EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 8 Cpyrgt 009 Regents te Unversty Calrna
3 EE 45: Intrductn t MEMS Lecture 3: Mecancs Materals II CTN 0/6/09 W r Frequency: Stness v π Mass Clamped-Clamped Beam μresnatr Resnatr Beam Electrde v kr m r L r Yung s Mdulus.03 Densty E ρ L r (e.g., m r r kg) kg) EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 9 V P V P C(t) ~0,000 ο V dc dt Smaller mass ger req. range and and lwer seres R x x P Nte: I I V P P 0V 0V devce Measure te requency selectvty a tuned crcut Dentn: ualty Factr (r ) Ttal Energy Per Cycle Energy Lst Per Cycle BW Example: seres LCR crcut Example: parallel LCR crcut EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/ dB Im Re Im Re ( Z ) L ( Z ) R CR ( Y ) C ( Y ) G LG BW -3dB Selectve Lw-Lss Flters: Need Oscllatr: Need r Hg Man Functn: prvde a stable utput requency Dculty: superpsed nse degrades requency stablty Sustanng Ampler A Ideal Snusd: v ( ) t Vsn π t In resnatr-based lters: g tank lw nsertn lss At rgt: a 0.% bandwdt, 3- res GHz (smulated) eavy nsertn lss r resnatr < 0, EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 3 Transmssn [db] Increasng Insertn Lss Tank 30,000 0,000 0,000 5,000 4, Frequency-Selectve Tank ο Hger Hger T O Real Snusd: v ( ) ( ) ( ) t V ε t sn π t t θ Zer-Crssng Pnt ο π/t O Tgter Tgter Spectrum Spectrum EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 3 ο Cpyrgt 009 Regents te Unversty Calrna 3
4 EE 45: Intrductn t MEMS Lecture 3: Mecancs Materals II Attanng Hg Prblem: IC s cannt aceve s n te tusands transstrs cnsume t muc pwer t get n-cp spral nductrs s n ger tan ~0 -cp nductrs s n te range 00 s Observatn: vbratng mecancal resnances >,000 Example: quartz crystal resnatrs (e.g., n wrstwatces) extremely g s ~ 0,000 r ger ( ~ 0 6 pssble) mecancally vbrates at a dstnct requency n a tckness-sear mde Energy Dsspatn and Resnatr Materal Deect Lsses Bendng CC-Beam deects Gas Gas Dampng vscus Termelastc Dampng () Tensn Cld Spt Cmpressn Ht Spt supprt CTN 0/6/09 Ancr Lsses At At g requency, ts ts s s ur ur bg bg prblem! Heat Flux ( Lss) Elastc Wave Radatn (Ancr Lss) EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 33 EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 34 Termelastc Dampng () Caracterstc Frequency Occurs wen eat mves rm cmpressed parts t tensned parts eat lux energy lss ς Γ( T ) Ω( ) α TE Γ( T ) 4ρ ( C p ) πk ρc Ω p Bendng CC-Beam Tensn Cld Spt Cmpressn Ht Spt Heat Flux ( Lss) ζ termelastc dampng actr α termal expansn cecent T beam temperature E elastc mdulus ρ materal densty C p eat capacty at cnst. pressure K termal cnductvty beam requency beam tckness caracterstc requency EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 35 πk ρc Gverned by Resnatr dmensns Materal prpertes p ρ materal densty C p eat capacty at cnst. pressure K termal cnductvty beam tckness caracterstc requency Crtcal Dampng Factr, ζ [rm Rszart, Hltn Head 990] Peak were s s mnmzed Relatve Frequency, / EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 36 Cpyrgt 009 Regents te Unversty Calrna 4
![cycle Alumnum Vbratng Resnatr ~500,000 at at 30K 30K [rm Bragnsky, Systems Wt Small Dsspatn] ~,50,000 at at 4K 4K Even Even alumnum aceves exceptnal s s at at crygenc temperatures EE C45: Intrductn](/docs-images/89/100530458/images/5-1.jpg "t MEMS Desgn LecM 7 C. Nguyen 9/8/07 37 Cmpund Mde (,) Ancr Output Input Wne Glass Dsk Resnatr Supprt Beams Input [Y.-W. Ln, Nguyen, JSSC Dec.")
![04] R 3 μm Ancr Output CTN 0/6/09 Plyslcn Wne-Glass Dsk Resnatr Resnatr Data R 3 3 μm, μm, 3 μm μm d 80 80 nm, nm, V p p 3 V EE C45: Intrductn t MEMS Desgn LecM 7 C.](/docs-images/89/100530458/images/5-2.jpg "Nguyen 9/8/07 38 Unmatced Transmssn [db] -40-60 -80-00 6.37 MHz 45,")
5 EE 45: Intrductn t MEMS Lecture 3: Mecancs Materals II uartz Crystal ~300,000,000 at at 4K 4K vs. Temperature ~5,000,000 at at 30K 30K Mecansm r r ncrease wt wt decreasng temperature tugt t t be be lnked lnked t t less less ysteretc mtn mtn materal deects less less energy lss lss per per cycle cycle Alumnum Vbratng Resnatr ~500,000 at at 30K 30K [rm Bragnsky, Systems Wt Small Dsspatn] ~,50,000 at at 4K 4K Even Even alumnum aceves exceptnal s s at at crygenc temperatures EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 37 Cmpund Mde (,) Ancr Output Input Wne Glass Dsk Resnatr Supprt Beams Input [Y.-W. Ln, Nguyen, JSSC Dec. 04] R 3 μm Ancr Output CTN 0/6/09 Plyslcn Wne-Glass Dsk Resnatr Resnatr Data R 3 3 μm, μm, 3 μm μm d nm, nm, V p p 3 V EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 38 Unmatced Transmssn [db] MHz 45, GHz,,555 Nancrystallne Damnd Dsk μmecancal Resnatr Impedance-msmatced stem r reduced ancr dsspatn Operated n te nd radal-cntur mde ~,555 (vacuum); ~0,00 (ar) Belw: 0 μm dameter dsk Plyslcn Stem (Impedance Msmatced -84 t Damnd Dsk) GHz,555 (vac) -88 0,00 (ar) -90 Plyslcn Electrde R -9 0,00 (ar) CVD Damnd μmecancal Dsk Grund Resnatr Plane EE C45: Intrductn t MEMS Desgn LecM 7 [Wang, C. Butler, Nguyen Nguyen 9/8/07 MEMS 04] 39 Mxed Ampltude [db] Desgn/Perrmance: R0μm, t.μm, d800å, V P 7V.5 GHz ( nd mde),,555 Dsk Resnatr Lss Mecansms (Nt Dmnant n Vacuum) Gas Gas Dampng Hysteretc Mtn Deect Deect (Dwared By Substrate Lss) Stran Energy Flw Dsk Stem Substrate Ndal Axs Electrnc Carrer (Dwared By Drt Drt Lss Lss Substrate Lss) N N mtn alng alng te te ndal ndal axs, axs, but but mtn alng alng e- te te nte nte wdt wdt te te stem stem Stem Hegt λ/4 λ/4 elps elps reduce lss, lss, but but nt nt perect Substrate Lss Lss Tru Tru Ancrs (Dmnates) EE C45: Intrductn t MEMS Desgn LecM 7 C. Nguyen 9/8/07 40 Cpyrgt 009 Regents te Unversty Calrna 5
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