EE 45: Intrductin t MEMS Lecture 3m: Capacitive Transducers Vltage-Cntrllable Center requency Micrresnatr Thermal Stability.7ppm/ C Gap Ply-Si μresnatr -7ppm/ C EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 6 Thermal stability f ply-si micrmechanical resnatr is 0X wrse than the wrst case f AT-cut quart crystal EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 7 Gemetric-Stress Cmpensatin Vltage-Cntrllable Center requency Use a temperature dependent mechanical stiffness t null frequency shifts due t Yung s mdulus thermal dep. [Hsu et al, IEDM 00] [W.-T. Hsu, et al., IEDM 00] Prblems: stress relaatin cmprmised design fleibility [Hsu et al IEDM 000] EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 8 Gap EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 9 Cpyright 0 Regents f the University f Califrnia
EE 45: Intrductin t MEMS Lecture 3m: Capacitive Transducers Tp Tp Electrde-t- Resnatr Gap Gap Elect. Elect. Stiffness: k e ~ e /d /d 3 3 requency: f f ~ (k (k m - -k e ) e ) 0.5 0.5 Cunteracts reductin in in frequency due due t t Yung s mdulus Ecellent Temperature Stability Resnatr.7ppm/ C Tp Metal Electrde Uncmpensated μresnatr [Hsu et al MEMS 0] Elect.-Stiffness Cmpensatin 0.4ppm/ C AT-cut Quart Crystal at Varius Cut Angles On On par par with with quart! temp. 00 temp. dependence [Ref: Hafner] EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 30 Measured Δf/f vs. T fr k e - Cmpensated μresnatrs Δf/f [ppm] 500 000 V P -V C 6V 4V 500 V 0V 9V 0 8V 7V -500 6V 4V Design/Perfrmance: V f =0MH, Q=4,000-000 0V V P =8V, h e =4μm 0.4ppm/ C CC d =000Å, h=μm -500 W r =8μm, L r =40μm 300 30 340 360 380 [Hsu et al MEMS 0] Temperature [K] Slits help t release the stress generated by lateral thermal epansin linear TC f curves 0.4ppm/ C!!! EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 3 Can One Cancel k e w/ Tw Electrdes? What if we dn t like the dependence f frequency n V P? Can we cancel k e via a differential input electrde cnfiguratin? If we d a similar analysis fr d at Electrde : d ω Subtracts frm the d term, as epected = V P C d C v csω t + V t v P sinω d V Adds t the quadrature term k e s add, n matter the electrde cnfiguratin! d d d d EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 3 Electrde V P m k m Electrde v V Prblems With Parallel-Plate C Drive Nnlinear vltage-t-frce transfer functin Resnance frequency becmes dependent n parameters (e.g., bias vltage V P ) Output current will als take n nnlinear characteristics as amplitude grws (i.e., as appraches d ) Nise can alias due t nnlinearity Range f mtin is small r larger mtin, need larger gap but larger gap weakens the electrstatic frce Large mtin is ften needed (e.g., by gyrscpes, vibrmtrs, ptical MEMS) EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 33 v V d d Electrde d d V P m k m Electrde v V Cpyright 0 Regents f the University f Califrnia
EE 45: Intrductin t MEMS Lecture 3m: Capacitive Transducers Electrstatic Cmb Drive Use f cmb-capacitive tranducers brings many benefits Linearies vltage-generated input frces (Ideally) eliminates dependence f frequency n dc-bias Allws a large range f mtin y Statr Rtr Electrstatic Cmb Drive Cmb-Driven lded Beam Actuatr EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 34 EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 35 y Typical Drive & Sense Cnfiguratin Cmb-Drive rce Equatin ( nd Pass) In ur st pass, we accunted fr Parallel-plate capacitance between statr and rtr but neglected: ringing fields Capacitance t the substrate All f these capacitrs must be included when evaluating the energy epressin! Statr Rtr EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 38 Grund Plane EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 39 Cpyright 0 Regents f the University f Califrnia 3
EE 45: Intrductin t MEMS Lecture 3m: Capacitive Transducers Cmb-Drive rce With Grund Plane Crrectin inger displacement changes nt nly the capacitance between statr and rtr, but als between these structures and the grund plane mdifies the capacitive energy Case: V r = V P = 0V C sp depends n whether r nt fingers are engaged Capacitance Epressins Capacitance per unit length Regin Regin 3 [Gary edder, Ph.D., UC Berkeley, 994] EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 40 [Gary edder, Ph.D., UC Berkeley, 994] EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 4 Cmb-Drive rce With Grund Plane Crrectin inger displacement changes nt nly the capacitance between statr and rtr, but als between these structures and the grund plane mdifies the capacitive energy Simulate t Get Capacitrs rce Belw: D finite element simulatin 0-40% reductin f e, [Gary edder, Ph.D., UC Berkeley, 994] EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 4 EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 43 Cpyright 0 Regents f the University f Califrnia 4
EE 45: Intrductin t MEMS Lecture 3m: Capacitive Transducers Vertical rce (Levitatin) Simulated Levitatin rce e, W = = dc d sp r V r = 0V (as shwn): V s + e, dcrp V d = N dcrs r + d d C + C ( V V ) ( sp, e rs ) EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 44 d s V s r Belw: simulated vertical frce vs. at different V P s [f/ Bill Tang Ph.D., UCB, 990] See that is rughly prprtinal t fr less than it s like an electrical stiffness that adds t the mechanical stiffness γ V ( ) = k ( ) EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 45 P e Electrical Stiffness Vertical Resnance requency Suppressing Levitatin ω /ω Vertical resnance frequency Vertical resnance frequency at V P = 0V k + k = γ ω e = where k e V ω k = Lateral resnance frequency Signs f electrical stiffnesses in MEMS: Cmb (-ais) k e = 0 Cmb (-ais) k e > 0 Parallel Plate k e < 0 EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 46 Pattern grund plane plysilicn int differentially ecited electrdes t minimie field lines terminating n tp f cmb Penalty: -ais frce is reduced EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 47 Cpyright 0 Regents f the University f Califrnia 5
EE 45: Intrductin t MEMS Lecture 3m: Capacitive Transducers rce f Cmb-Drive vs. Parallel-Plate Cmb drive (-directin) V = V = V S = V Differential Parallel-Plate (y-directin) V = 0V, V = V Parallel-plate generates a much larger frce; but at the cst f linearity EE C45: Intrductin t MEMS Design LecM C. Nguyen /8/08 48 Cpyright 0 Regents f the University f Califrnia 6