Outline. Batch fabrication from IC technologies. Introduction to MEMS. MEMS Electrostatic Vibration Energy Harvester (e-veh) 9/11/2014

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1 MEMS Elecrosaic Vibraion Energy Harveser (e-veh) P. Basse Universié Paris-Es ESYCOM lab - ESIEE Paris Ouline Inroducion o MEMS Inroducion o VEH Elecrosaic ransducer Elecrosaic energy conversion Eaple of a e-veh fro ESIEE Paris Conclusion NIPS Suer School 14, Perugia, Ialy Bach fabricaion fro IC echnologies Inroducion o MEMS 3 High cos for low volue / Low cos for high volue (> 1 MU) 4 1

2 UV source Phoolihography Thin fil MEMS lens ask Elecrical insulaor Fie srucural layer Mobile sruc. layer Sacrificial layer V resis srucural layer Use of (UV) ligh o ransfer a geoeric paern fro a phoo The silicon is ainly a handling layer The deposied layers are ypically in he µ range ask o a ligh-sensiive cheical "phoo resis on he subsrae 5 6 Bulk icroachining eaple on a SOI Subsrae on insulaor (SOI) Buried oide (BOX) Handel (HW) Inroducion o VEH The obile pars are in bulk silicon Thickness can be in he range (yp. ens o hundreds of µ) beer reliabiliy 7 8

3 Principle of a ypical VEH Principle of a yp. VEH + - ain seps: 1. Par of he vibraion energy is capured by he spring-ass syse Kineic energy (ass velociy) & poenial energy (spring copression) Deerine he aiu aoun of energy ha can be convered ino elecriciy. An elecroechanical ransducer convers soe of his energy ino elecrical for Energy ransduced Energy sored Vibraing body Energy conversion loss of kineic energy ( daping force) added elecrical power The loss of kineic energy coes fro he negaive work of an elecrical force inroduced by he elecroechanical ransducer Soe of his energy is also dissipaed ino hea 9 1 Energy dissipaed [Couresyof L. Gaaioni] k = spring siffness = ass β = daping coefficien A e = eernal acceleraion k β a e, = ransducer force and volage Y Dynaical odel nd Newon law: d ɺɺ = E + F _. + F + F d p ech dap e E p () = sored energy = k ²/ for a linear spring F ech_dap. = dissipaive force = -β.ẋ (, ) = force inroduced by he ransducer opposed o he oion during he energy conversion: < F e = -a e = vibraion force 11 Dynaical odel ɺ + β ɺ + k F (, V) = a V ɺ = ( ɺ f, V ) The ransducer force and he funcion f describing he dynaic of he ransducer oupu volage are deerined by: The ransducion echanis The geoery of he ransducer The condiioning circui of he ransducer The ransducer can no be sudied independenly of is condiioning circui e 1 3

4 The elecrosaic ransducer The elecrosaic ransducer MEMS capaciive ransducers are generally represened by wo parallel elecrodes I L S + +Q ε r -Q W h C Q S L W = = ε = ε εr V h h ε = periiviy of vacuu ε r = relaive periiviy of he dielecric S = (effecive) facing area of he elecrodes h = gap beween elecrodes 13 The capaciance is varying wih ie: dq d dv dc C = C( ) I = = ( CV ) = C + V d d d d elecrical echanic 14 Basic geoeries of a capaciive ransducer If he fringe elecric field can be negleced: C = ε + + C C C r S h ε S h ε r ε r1 r ε r anchored elecrode h S ε r anchored elecrode S = ε h Depending on he design, he capaciance variaion coes fro a change in he gap, he overlapping area or he periiviy C 15 C a e k The ransducer s force (1) V derives fro he poenial energy of C depends on he volage across C and on he obile ass posiion ɺɺ + β ɺ + k F (, V ) = a Cond. Circ. e is generaed by he condiioning circui (C.C.) The energy ransducer is a variable capacior C The ransducer force is an elecrosaic force d F = WC (, V ) d 16 4

5 C The ransducer s force () Cond. Circ. Force acing on he obile elecrode: Energy sored in he capaciance: C( ) V Q = = C ( ) d Q d( 1/ C ) Q dc V dc F = WC (, ) = = = V d d C d d W C for elecrode-overlap ransducers (@ cev) C () h l C () + w F ( ) V dc V εw = = d h w C ( ) = ε h ends o increase C is proporional o and o he gradien of C 17 () does no depend on he obile elecrode locaion 18 for gap-closing ransducers (@ ce ) C ceq C + h εwl C ( ) = h + C h +Q -Q Q d( 1/ C) Q 1 F = = = ce d εwl () -h -h F ( ) V C V εs = = h + ( ) () is srongly non linear wih 19 C () l h l w + Q h F = εw l ( + ) 5

6 Elecrosaic insabiliy: pull-in phenoena Elecrosaic spring sofening V F s F,W T [V²,1/(1-²)] -F s () k ( ) 1 1 C y NεS + h + y h y -k e h V pi pi h = 3 = 3 8kh 7εS sable posiion pull-in force energy V 1/3 unsable posiion 1 /h 1 k e V C NεSV NεSV εsv Fe, y = = N y y + h ( h y ) ( h y ) y<< 3 k + k k k = = = + V d C e e ω 1 dy k A gap-closing inerdigied-cob ransducer acs as negaive spring This elecrosaic spring is srongly non linear wih y volage dependence of he echanical resonance frequency Scaling The elecrosaic echanical elecrical energy conversion scales as L 3 X a scales as L Power scales as L 4 P = X A π a_ avail. a design driven e ω applicaion driven Power densiy falls drasically as size reduces In vibraion energy harvesing, size aer!!! 3 6

7 Sep 1 Principle of he elecrosaic energy conversion (e. of consan-charge operaion) A charge Q is applied on C when is value is aial (C a ) The energy sored in C is: Q = C a.v V W 1 Q = C a C = C a 5 Sep The volage source is disconneced The eernal vibraions bring C o isiniu value C in Vibraions Principle of he elecrosaic energy conversion (e. of consan-charge operaion) Q C C in The energy sored in C is now : Q = ce = C V = C V a in C V V = V W a _ a Cin 1 Q 1 = > W Cin 6 Principle of he elecrosaic energy conversion (e. of consan-charge operaion) Beween sep1 and sep, he difference of energy in he capaciance equals : C a W = W1 W = W 1 > C in The energy in C has increased by a facor (C a /C in -1) This increase of energy coes fro he echanical doain sep3 consiss in soring W 7 The QV diagra Ideally, he QV diagra of he conversion cycle is riangular Q a The area of he riangle corresponds o he harvesed energy [=W (C a /C in -1)for he ce Q cycle] This is he highes energy per cycle ha can be harvesed for a given ransducer using elecrosaic conversion and a given ass displaceen apliude However increasing W does no allow o harves beyond he aial power defined previously ( why?) Q charge injecion Q V-consrained cycle C a V V ce Q-consrained cycle C in Charge is colleced V a 8 7

8 The Condiioning circui The condiioning circui Two ain roles : Ensure he charge-discharge flow on he variable capacior, required by he echanical energy conversion principle Provide he inerface wih he load 9 3 The siples condiioning circui (C.C.) Basic C.C. V I C R L V = V + R I [ C ( ) V ( ) ] V can be a baery, an elecre, a recenna, a piezoelecric eleen Typically used o es he echanical ransducer d V = V + R d L L 31 V k ae R L Any C.C. ipacs he syse here is an opial value of R L Energy sored in he ransducer capaciance d β V ɺɺ + ɺ + k C ( ) = a d d RL [ C( ) V( ) ] + V ( ) = V d e 3 8

9 Predicion of he opial load (1) Predicion of he opial load () Q Q C I C I V ou C in V ou C in V R L C a V R L C a V V a V V a If R L is sall I av.r L << V ~ consan volage operaion wih low volage variaion across C during he cycle low harvesed power 33 If R L is high I av <<I av.r L << V ~ consan charge operaion wih low charge variaion in C during he cycle low harvesed power Frequency shif oward low frequencies 34 Predicion of he opial load (3) Q C I V R L V ou C a C in Eaple of MEMS e-veh V V a If I av.r L ~V Good elecroechanical coupling ipedance aching Frequency shif oward low frequencies region of ineres

10 Fabricaion process MEMS IPGC e-veh low-cos bach process o 3 asks In-Plane Gap-Closing (IPGC) e-veh 3 µ d = 46.5 µ «in-siu» vacuu package is possible d Volue of acive pars ~ 5 3 Toal volue of device (wih cap) ~ 35 3 Dynaic capaciance easureen Up/down frequency sweeps.5 g 1 g Theoreical a o = 3 V / 1 g / 15 Hz Triangular QU cycle: 7.5 µw Basic RC Cond. Circ.: 3. µw R L_op = 6 MΩ [Guillee e al., PowerMEMS 1] A 1 g, he cobinaion of he elecrosaic spring sofening and he sopper response leads o a bandwidh of 3%. µw of aiu power a ~ 15 Hz [Basse e al., JMM 14] 1

11 Elecrosaic conrol of he poeniel energy The poenial barriers are unable hrough he bias volage V Around V = he syse changes fro onosable o ulisable behavior For a given acceleraion, here is an opiu V aiizing he harvesed power under sochasic vibraions [Coone e al., Transducers 13] Sochasic noise eciaion.5 g over [-16Hz] 1 g over [-16Hz].5 & 1 g of inpu acceleraion disribued over he naural bandwidh of he ransducers (16 Hz) Very low acceleraion inpu PSD (~1-3 1 g) in he bandwidh only elecrosaic non-lineariies Conclusion MEMS e-veh are cople bu full of proises There are echanically reliable, low-cos if assproducion, sar elecronic can be ipleened Mechanical and elecrical non-lineariies can be cobined o eiher enlarge he bandwidh, creae a uli-sable syse or uned he resonan frequency 11