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McCorquodale, James L. McCann, and Richard B. Brown Lecturer: Michael S. McCorquodale, Ph.D. Mobius Microsystems, Inc. ASP-DAC 2006, Yokohama.ZJ)2s,+dOutlineIntroduction to MEMS simulation and synthesis approaches Finite element analysis Nodal analysis Automated design synthesis Library-based analytical synthesis (Newton) Example analytical expression and computational algorithm CCB resonator design overview Euler-Bernoulli method Tool framework Graphical user interface Synthesis engine A synthesis example and experimental results Conclusion9ZnZ:Z5ZZ*Z8Z9f:5*85h8Introduction to MEMS simulation and synthesis approaches} IntroductionChallenges with MEMS design automation Devices are similar to analog circuits Myriad of devices Fabrication processes not standardized and vary Current MEMS DA approaches Simulation SynthesisL'i'ipMEMS simulation approachesFinite element analysis Application: arbitrary device-level design Approach: develop solid model for device, decompose into finite elements (mesh), set mechanical boundary conditions, perform simulation or analysis Pros/cons: accurate and versatile, but requires substantial design effort Nodal analysis Application: arbitrary device-level design Approach: construct devices from parameterized geometric building blocks (e.g. beams, gaps, anchors) and simulate using nodal approach Pros/cons: faster than FEA, though design iteration required    @  ~ 3qMEMS synthesis approaches;Automated design synthesis Application: arbitrary device-level design Approach: evolutionary using multi-objective genetic algorithms Pros/cons: enables rapid design space exploration though requires design iteration Library-based analytical synthesis Application: direct synthesis of specific devices from performance objective Approach: use parameterized analytical formulations to directly synthesize physical design and equivalent electrical model Pros/cons: very fast though accuracy limited to model quality and synthesis limited to specifically supported devices ZZZ#Z?Z  7 I# A r m1Newton: A library-based analytical synthesis tool,2+iMotivation for and overview of Newton Only a finite number of MEMS devices have utility MEMS process technologies slowly consolidating Library-based approach is fastest and draws closest analogy to circuit design automation and synthesis Need to develop highly accurate analytical models Need to develop extensible software framework to support multiple devices0&DDi9Example analytical expression and computational algorithm|CCB resonator design overviewClamped-clamped beam RF-MEMS resonator Mechanical beam clamped at each end and suspended over an electrode Beam designed to resonate at a distinct frequency Applications in frequency/clock synthesis and RF filtering Device fabricated with a surface micromachining process Process technology defines subset of variables Primary design objective is accurate prediction of resonant frequency&'^'^oCCB resonator design overviewrCCB resonator design overviewResonant modes Device can resonant in one of many modes (first and third shown) Resonant mode will be parameterized in analytical model&yy{CCB resonator design overviewAt resonance, CCB resonator can be modeled by a series RLC circuit Use electromechanical analogy to determine device model parameters Synthesize netlist for SPICE co-simulation with transistor devices2sEuler-Bernoulli methodBegin with simple physics-based analytical formulation Account for  spring softening due to subtractive electrical spring constant Spring softening is nonuniform across beam Use equivalent mass technique to derive accurate analytical expressionsZ W~Synthesis engine variablesSynthesis engine variables,CCB resonator constant and derived variablesjTool frameworkyFramework overviewnGraphical user interfacezGraphical user interfacefPhysical design viewpoint Modify performance-independent parameters Export to CIF and generate netlist.ZMZM_tSynthesis engineImplemented in Mathematica Pros: useful for symbolic integrals in derived analytical expressions, fast, extensible, supports plotting Cons: requires license Future work: integrate analytical expressions using a math and plotting package Pros: self-contained Cons: substantial effortP. gP k,A synthesis example and experimental resultsSynthesis exampleuExperimental resultsElectron micrograph of fabricated CCB resonator Surface micromachined poly-Si process at U. of Michigan Resonant frequency tested under vacuum with spectrum analyzer&0v0v,8 YxExperimental resultsXFEA with Coventorware >10hrs. design/mesh + 15min. sim. 2.70% error in fo comp. to meas.nPCP  1 >  ^Meas. results from Newton design <1min. design and synthesis 0.70% error in fo comp. to targetz!P>P+ Ll ConclusionvConclusion and future workAchievements Demonstrated the first complete and extensible analytical CAD tool for the direct synthesis of MEMS devices Demonstrated rapid synthesis with high performance accuracy verified through measurement of fabricated devices (0.70% error) Future work Verify accuracy of analytical formulations for larger sample sets Develop analytical formulations for 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"0 ^Resonant frequency [ T  Hdf8c?"  0 W Performance   [ T  H<f8c?" b0 fo4 [ T  Hf8c?"  " [Electrode width [ T  H4f8c?"   W Performance   [  T  Hf8c?" b  fWe4 [  T  H8f8c?"  "  V Beam width   [  T  Hf8c?"   W Performance   [  T  Hf8c?" b   Wr4 [  T  Hf8c?"  "  X Bias voltage   [ T  Hf8c?"   W Performance   [ T  H#f8c?" b   fVP4 [ T  H,f8c?"  "  ]Determine by mode [ T  H6f8c?"   W Performance   [ T  H@f8c?" b   kn4 [ T  H|0f8c?"  "  ^Beam-electrode gap [ T  HKf8c?"   SProcess [ T  H[f8c?" b   fdo4 [ T  H8ef8c?"  r"  W Beam height   [ T  H@nf8c?" r  SProcess [ T  Hwf8c?" br  xhrF [ T  HЁf8c?"  X"r jYoung s Modulus [ T  Hf8c?" X r SProcess [ T  H@f8c?" bXr QE  [ T  Hf8c?"  <"X SDensity [ T  HDf8c?" < X SProcess [ T  Hf8c?" b<X Or [ T  H 8c?"  !"< W Description   [  T  H8c?" ! < PType [ !T  H8c?" b!< [Design variable [`B "T  0o ?b!"!ZB #T  s *1 ?b<"<ZB $T  s *1 ?bX"XZB %T  s *1 ?br"rZB &T  s *1 ?b " ZB 'T  s *1 ?b " ZB (T  s *1 ?b " ZB )T  s *1 ?b " ZB *T  s *1 ?b " ZB +T  s *1 ?b"`B ,T  0o ?b0"0`B -T  0o ?b!b0ZB .T  s *1 ?!0ZB /T  s *1 ? ! 0`B 0T  0o ?"!"0 5T 6 "`b"! C/CCB resonator process and performance variables2 7T 68c"`D^ ,$D  02 8T 68c"` ^0,$D  0H T 0޽h ? 3380___PPT10.@+`D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7T %(D' =-s6Bwipe(left)*<3<*7T D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8T %(D' =-s6Bwipe(left)*<3<*8T + 4 0L0 LD."g\ (  \ x \ c $M`@    r ,\ S @b"!   b"0 -\  #"*!b"0  \  H8c?"  x"0 W Beam length   [ \  H\8c?"  x 0 W Synthesized   [ \  H8c?" bx 0 eL4 [ \  H\ 8c?"  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[ Cd  H8c ?" + $   e 2330kg/m3,  [ Dd  Ht88c ?" b$ +   f Density, r,  [ Ed  HpA8c ?" + - $  QValue [ Fd  HdK8c ?" b- + $  ]Process-Dependent [fB Gd  6o ?b- - `B Hd  01 ?b$ $ `B Id  01 ?b  `B Jd  01 ?b `B Kd  01 ?b fB Md  6o ?b fB Nd  6o ?b- b`B Od  01 ?+ - + fB Pd  6o ? - 2 Xd 638c"`w,$D  0H d 0޽h ? 33}___PPT10].@+NoD1' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Xd %(D' =-s6Bwipe(left)*<3<*Xd D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Zd %(+{& ) 0L0 `, (   x  c $PfM`@    ~  s *fb"    3 A 28c clampedbeamcroppededited"`@.:0 l 4:   4: ,$D 0   B$i8c" :  Wr = 6mmR  fB  6D8c4z  l `     ` ,$D 0   B8q8c" `   vhr = 2mmR  fB  6D8c l l 6  4    6 4 ,$D  0   BXy8c" @  49  w We = 20mmR  fB  6D8c6  l >v    v > ,$D  0   BH8c" h F  fL = 40mmB fB  6D8c>v B ol   R^    R^ ,$D 0   B8c" s R  ; Electrode (    BCDEFA8c2e6yJy@  "`  V^ l v ,   v , ,$D 0   B8c"  m k Gap do = 500B (    BCDEFA8c=?G3R@  "`4v , pl b F 0Z   F b 0Z ,$D 0   Hx8c" : 0Z  6Beam(    BC DEFA8c 5y]M.&@  "`b F P H  0޽h ? 33 ___PPT10.@+D' = @B Dq' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(DI' =4@BBB*B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B)barn(outHorizontal)*<3<* D' =%(D' =%(DI' =4@BBB*B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B)barn(outHorizontal)*<3<* D' =%(D' =%(DE' =4@BBB%B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B%barn(outVertical)*<3<* D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(DE' =4@BBB%B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B%barn(outVertical)*<3<* D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+: , 0L0 e&]&,;I %(   x  c $M`@     D S Z b <$ 0   E S Z r "<$ 0  ol A \  I A \ ,$D 0b    c $8c"` \ \    S 8c"` \      BCvDE F8cv@"`       BCvDE F8cv@"`      BCvDE F8cv@"`./     BCvDE F8cv@"`     BCvDE F8cv@"`     BCDE F8c@"` \     BCDE F8c@"` \    BCDE F8c@"` \    BCDE F8c@"` O\PHB   C 8c \    BCvDE F8cvv@"` \ HB  C 8c  HB  C 8c  HB   C 8c     < KX  L9.91,F DHB   C 8c   <\- X  L9.92,F DHB    C 8c./ !  < X  L9.93,F DHB #  C 8c $  < LX  L9.94,F DHB &  C 8c '  <. 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Pictures-Current User\SummaryInformation(0UPowerPoint Document(gDocumentSummaryInformation8,Microsoft Equation 3.0 Equation Equation.30,Microsoft Equation 3.0D/ 0|DArialew RomanTTzܖ 0ܖDWingdingsRomanTTzܖ 0ܖ DTrebuchet MSanTTzܖ 0ܖ"0DTimes New RomanTTzܖ 0ܖ@DSymbolew RomanTTzܖ 0ܖ@ .  @n?" dd@  @@`` XP 79+M!@e%+F";q  0 -, )& Y !} c Dsq  6 HHHNQQQ1 g    S\[[     #  D  Q[ZZ Q "   Xr>WgXeipr8L #-7 ;  L 3 L :: 6 0r>WgXeipr8L b    C~ >WBgge"ivzv:Q   _ +  h     R g< wQ :' '  456=B*      1&vk`J' GA29h[   b$@3 6?-)b$6u,ztb$~7He隳Vb$pT-g (pYb$>pu`-qsh$b$[r,ЪB/?2$,@hPq& b$x Tr<3PLX $$$$$2$!i|'*^Y AA8c"  f>3333[YZ@8*a/ ʚ;s8ʚ;g4DdDd  0"ppp@ <4dddd k 0Ty <4BdBd l 0Tg4bdbd 0Dp p <4!d!d k 0Ty80___PPT10 ``? -O  =m$TMHNewton: A Library-Based Analytical Synthesis Tool for RF-MEMS ResonatorsAuthors: Michael S. McCorquodale, James L. McCann, and Richard B. Brown Lecturer: Michael S. McCorquodale, Ph.D. Mobius Microsystems, Inc. ASP-DAC 2006, Yokohama.ZJ)2s,+dOutlineIntroduction to MEMS simulation and synthesis approaches Finite element analysis Nodal analysis Automated design synthesis Library-based analytical synthesis (Newton) Example analytical expression and computational algorithm CCB resonator design overview Euler-Bernoulli method Tool framework Graphical user interface Synthesis engine A synthesis example and experimental results Conclusion9ZnZ:Z5ZZ*Z8Z9f:5*85h8Introduction to MEMS simulation and synthesis approaches} IntroductionChallenges with MEMS design automation Devices are similar to analog circuits Myriad of devices Fabrication processes not standardized and vary Current MEMS DA approaches Simulation SynthesisL'i'ipMEMS simulation approachesFinite element analysis Application: arbitrary device-level design Approach: develop solid model for device, decompose into finite elements (mesh), set mechanical boundary conditions, perform simulation or analysis Pros/cons: accurate and versatile, but requires substantial design effort Nodal analysis Application: arbitrary device-level design Approach: construct devices from parameterized geometric building blocks (e.g. beams, gaps, anchors) and simulate using nodal approach Pros/cons: faster than FEA, though design iteration required    @  ~ 3qMEMS synthesis approaches;Automated design synthesis Application: arbitrary device-level design Approach: evolutionary using multi-objective genetic algorithms Pros/cons: enables rapid design space exploration though requires design iteration Library-based analytical synthesis Application: direct synthesis of specific devices from performance objective Approach: use parameterized analytical formulations to directly synthesize physical design and equivalent electrical model Pros/cons: very fast though accuracy limited to model quality and synthesis limited to specifically supported devices ZZZ#Z?Z  7 I# A r m1Newton: A library-based analytical synthesis tool,2+iMotivation for and overview of Newton Only a finite number of MEMS devices have utility MEMS process technologies slowly consolidating Library-based approach is fastest and draws closest analogy to circuit design automation and synthesis Need to develop highly accurate analytical models Need to develop extensible software framework to support multiple devices0&DDi9Example analytical expression and computational algorithm|CCB resonator design overviewClamped-clamped beam RF-MEMS resonator Mechanical beam clamped at each end and suspended over an electrode Beam designed to resonate at a distinct frequency Applications in frequency/clock synthesis and RF filtering Device fabricated with a surface micromachining process Process technology defines subset of variables Primary design objective is accurate prediction of resonant frequency&'^'^oCCB resonator design overviewrCCB resonator design overviewResonant modes Device can resonant in one of many modes (first and third shown) Resonant mode will be parameterized in analytical model&yy{CCB resonator design overviewAt resonance, CCB resonator can be modeled by a series RLC circuit Use electromechanical analogy to determine device model parameters Synthesize netlist for SPICE co-simulation with transistor devices2sEuler-Bernoulli methodBegin with simple physics-based analytical formulation Account for  spring softening due to subtractive electrical spring constant Spring softening is nonuniform across beam Use equivalent mass technique to derive accurate analytical expressionsZ W~Synthesis engine variablesSynthesis engine variables,CCB resonator constant and derived variablesjTool frameworkyFramework overviewnGraphical user interfacezGraphical user interfacefPhysical design viewpoint Modify performance-independent parameters Export to CIF and generate netlist.ZMZM_tSynthesis engineImplemented in Mathematica Pros: useful for symbolic integrals in derived analytical expressions, fast, extensible, supports plotting Cons: requires license Future work: integrate analytical expressions using a math and plotting package Pros: self-contained Cons: substantial effortP. gP k,A synthesis example and experimental resultsSynthesis exampleuExperimental resultsElectron micrograph of fabricated CCB resonator Surface micromachined poly-Si process at U. of Michigan Resonant frequency tested under vacuum with spectrum analyzer&0v0v,8 YxExperimental resultsXFEA with Coventorware >10hrs. design/mesh + 15min. sim. 2.70% error in fo comp. to meas.nPCP  1 >  ^Meas. results from Newton design <1min. design and synthesis 0.70% error in fo comp. to targetz!P>P+ Ll ConclusionvConclusion and future workAchievements Demonstrated the first complete and extensible analytical CAD tool for the direct synthesis of MEMS devices Demonstrated rapid synthesis with high performance accuracy verified through measurement of fabricated devices (0.70% error) Future work Verify accuracy of analytical formulations for larger sample sets Develop analytical formulations for 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