Aville online t www.sciencedirect.com ScienceDirect Procedi Engineering 64 ( 013 ) 9 301 Interntionl Conference On DESIGN AND MANUFACTURING, IConDM 013 A PSpice Model for the study of Therml effects in Cpcitive MEMS Accelerometers C. Kvith * nd M. Gnesh Mdhn Deprtment of Electronics Engineering, Ann University, M.I.T Cmpus, Chenni, 600 044, Indi Astrct An electricl equivlent circuit model is developed to study the therml effects in cpcitive MEMS ccelerometer. The mechnicl system of the MEMS is implemented s n nlogous electricl system nd nlyzed under different temperture conditions in the rnge of 100K to 400K. The vrition in elongtion, spring constnt, dmping coefficient of the MEMS cntilever re incorported in the model. The entire nlysis is crried t constnt pressure of 30P. The trnsient nd frequency response is determined y simulting the equivlent circuit using PSpice circuit simultor. 013 The Authors. Pulished y Elsevier td. Open ccess under CC BY-NC-ND license. 013 The Authors. Pulished y Elsevier td. Open ccess under CC BY-NC-ND license. Selection nd peer-review under responsiility of the orgnizing nd review committee of IConDM 013. Selection nd peer-review under responsiility of the orgnizing nd review committee of IConDM 013 Keywords:Therml effect; cpcitive ccelerometer; MEMS; PSpice; circuit model. 1. Introduction MEMS (Micro Electro Mechnicl System) comprises of micro sensors, micro ctutors, microelectronics nd microstructures. MEMS ccelerometer is one of the most populr MEMS devices for ccelertion sensing. This signl to e detected my e sttic or dynmic due to grvity or motion respectively. These re used to detect seismic ctivity, ngles of inclintion, dynmic distnce s well s speed, nd rte of virtion. Accelerometer pplictions include medicl, nvigtion, trnsporttion, consumer electronics, nd structurl integrity. The cpcitive type is preferred mong piezoelectric, piezoresistive, hot ir ules, nd light sed devices, due to high sensitivity, low noise nd power sving fetures. Other chrcteristics include high resolution, ccurcy nd reliility. Accelerometers refer specificlly to mss-displcer [1] tht cn trnslte externl forces such s * Corresponding uthor. Tel.: 978605893; fx: +91-44-3403. E-mil ddress:kviphd011@yhoo.co.in 1877-7058 013 The Authors. Pulished y Elsevier td. Open ccess under CC BY-NC-ND license. Selection nd peer-review under responsiility of the orgnizing nd review committee of IConDM 013 doi: 10.1016/j.proeng.013.09.101
C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 93 grvity into kinetic motion. The sensing prt of the ccelerometer usully consists of some type of spring force in order to lnce the externl pressure nd displce its mss, thus leding to the motion. Since the structure consist of proof mss, s well s cntilever em, residul gs is seled inside the device, which cn cuse dmping. Timo Veijol et. l. [-4] hs developed circuit model tht involves dmping nd spring forces creted y squeezed film in MEMS ccelerometer. They hve determined the response of the device using liner nd nonliner frequency dependent components, under different pressures. They hve used self developed circuit simultion progrm APAC [5] for their nlysis. We report n equivlent circuit model sed on Timo Veijol s pproch, to study the effect of temperture [6-9] on cpcitive MEMS ccelerometer. As equivlent circuits re developed for MEMS structure, single domin pproch to study the mechnicl nd electricl effects is possile. Incorporting therml effects nd implementing in electricl equivlent circuit model will help to provide n integrted pproch to evlute the MEMS performnce under electricl, mechnicl nd therml domins. In our pproch, the prllel resontor circuit model is replced y vrile inductor nd resistor implemented s controlled current sources [10]. This scheme lso includes pressure dependent squeezed film nd thermo elstic dmping models. Bsed on this model, the trnsient nd frequency response nlysis re crried out t different tempertures, using commercil circuit simultor PSpice.. MEMS cpcitive ccelerometer.1. MEMS structure Fig. 1. Structure of Micromechnicl Accelerometer [1]. A micromechnicl ccelerometer consists of mss suspended with two cntilever ems [1, 3]. The structure is implemented y three wfers in which top nd ottom wfers re thick nd developed s fixed electrodes nd the middle one is thin nd movle. The structure is shown in Fig. 1. The electrode is deposited y metl film which is formed on top surfce of insulting glss lyer. The seled cvity is filled with the gs for dmping of the system. At one side the contct pds re deposited in chip... MEMS Accelerometer Modeling The mechnicl model developed s mss spring dshpot is shown in Fig. (). According to Hooke's w, extension is directly proportionl to lod. However, this proportionlity holds up to certin limit clled the elstic limit. If the mss displced y distnce of x from its rest position, spring cuses the restoring force s F r kx. Where k is the spring constnt. Assuming tht dmping is purely viscous, nd then the mss moves with the velocity v dx dt, the force creted y the dmper is FD Dv. Where D is the dmping coefficient. As n externl ccelertion is pplied, proof mss tends to move in opposite direction of the ccelertion, due to Newton s lw of motion. The force y the ccelertion is F M. Where M is the mss, is the ccelertion. The dynmics of simple ccelerometer is chrcterized y the following eqution
94 C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 Fig.. () schemtic digrm of single xis ccelerometer []; () electricl equivlent circuit of simple ccelerometer [3]. dx dx M D kx F dt dt EXT (1) The force F is the sum of n externl mechnicl force FEXT nd n internl electricl ttrctive force F el. The electricl ttrctive force on the mss is cused y the potentil difference cross the cpcitor pltes. Assuming the motion is perpendiculr to the plte surfces, the electrosttic force is given y F el ε AU d () Where ε is the dielectric constnt of the gs, nd d is the gp width. The sensing element typiclly consists of seismic mss which cn move freely etween two fixed electrodes, ech forming cpcitor with the seismic mss used s the common centre electrode. The differentil chnge in cpcitnce etween the electrodes is proportionl to the deflection of the seismic mss from the centre position. The mechnicl ccelerometer model is relized y the equivlent electricl model of prllel resontor. The mss is considered s cpcitnce, cntilever or spring nd dshpot re equted to inductnce nd resistnce [3-5] respectively. The system is given y the differentil eqution s d ϕ C 1 dϕ 1 ϕ dt R dt I EXT (3) Where ϕ is the flux in inductnce is, C is the cpcitnce, R is the resistnce nd I EXT is the externl current. The displcement x equls I, where I is the current through the inductor. The electricl equivlent circuit of mss spring dmper system with displcement is shown in Fig. (). The ccelerometer physicl prmeters used in this work re listed in Tle 1. Tle 1. Specifictions of the MEMS ccelerometer Prmeters Mss M Width of the moving mss w ength of the moving l ength of the cntilever em Gp widths d A nd d B Men free pth λ t 1 tm Viscosity coefficient η Temperture T Vlues 4.9 μg.96 mm 1.78 mm 50 μm 3.95 0.05 μm 70.0 0.7 nm.6 0. μn.. sm 100-400 K
C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 95.3. Therml modeling It is well known tht s temperture increses, the therml expnsion coefficient lso increses [6-9] nd Young s modulus decreses, s shown in Fig. 3. This ffects the length nd spring constnt of the cntilever. The chnge in cntilever length is given y the following reltion (1 α ( T T)) o 1 (4) Where is the finl length of cntilever em o is the initil length of the cntilever, α is the therml expnsion coefficient of silicon mteril, T1 nd T re the initil nd finl tempertures respectively. µ µ Fig. 3. Therml effect on ccelerometer prmeters () length, therml expnsion coefficient; () young s modulus, spring constnt. The length of cntilever increses due to therml expnsion. The originl length of cntilever em is otined s 519.6μm t 0 C. The totl expnsion of cntilever em is clculted y δ α T. Therml strin nd stress cn e estimted s εt α ndσ T Eε T. Where T is the chnge in temperture, εt is the Strin, σ T is the stress, E is the Young s Modulus of silicon mteril. Moment of inerti of em is given y I h 3 1.Where is the width of the cntilever em nd h is the thickness of the cntilever em. As temperture increses mss of cntilever em lso increses y hlρ [1, 13]. Where ρ is the density of silicon for the em. The temperture dependent prmeters of liner type ccelerometer in the mechnicl domin nd its equivlent in electricl domin re given in Tle. Tle. Temperture dependent prmeters Mechnicl Element Electricl Element Temperture Dmping Coefficient Spring constnt Proof Mss Conductnce Inductnce Cpcitnce Dependent Dependent Independent The dmping coefficient is dependent on the dynmic viscosity nd length, which depends on temperture nd therml expnsion coefficient. It is incorported s n inverse of resistnce. The spring constnt tht depends on young s modulus, length nd inerti is implemented s n inverse of inductnce. This implementtion is shown in Fig. 4. The effect of temperture on mechnicl nd electricl prmeters of n MEMS ccelerometer is shown in Fig. 5.
96 C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 Fig.4. Electricl implementtion of therml effects () resistnce; () inductnce. µ Fig. 5. Therml effect on ccelerometer () mechnicl prmeters; () electricl prmeters. The increse in cntilever length ffects the spring constnt s per the following eqution K 3EI 3 (5) nd in turn ffects the resonnt frequency of the MEMS ccelerometer s per the eqution (6) f r 1 π K M (6) Viscosity of the gs is ffected y temperture s follows η η o 0.555T0 C T 0.555T C T 0 3/ (7) Where η is dynmic viscosity t input temperturet, ηo is reference viscosity t reference temperture T o, C is the Sutherlnd constnt for rgon gs (133). The men free pth eqution for the gs medium is given y λ RT π d P (8)
C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 97 1 1 3 1 Where R is gs lw constnt 8.314510JK mole, is the Avogdro s numer 6.01367*10 mole, 10 T is the temperture in Kelvin, d is the collisionl cross section 3.57*10 m, P is the Pressure. As temperture increses the viscosity increses s per the Sutherlnds formul. The effective viscosity depends on the solute viscosity. The dmping coefficient is determined y D η d (9).4. Electricl Equivlent Circuit Model In the proposed model, inputs re temperture, force nd the is voltge pplied to the prllel pltes. The resultnt displcement is the output otined from the system. The generl lock digrm is shown in Fig. 6(). Fig. 6. () Proposed model; () equivlent electricl circuit for cpcitive ccelerometer with therml effects. The electricl equivlent circuit incorporting therml effects is normlly developed from the prllel RC circuit with two ir gp sections implemented in the form of prllel R sections (squeezed film dmping effects) [-4]. The completed equivlent circuit is shown in Fig. 6(). The temperture is modeled s voltge source VTE in PSpice which hs shown in Fig. 7(). The pressure of the rgon gs, considered s the dmping medium, is lso fixed s 30 P. The pressure prmeter ffects the Knudsen numer, dynmic viscosity nd effective viscosity. Fig. 7. () Temperture s independent voltge source; () VCVS for therml expnsion coefficient nd young s modulus. Temperture is vried in the rnge of 100K to 400K for the device nd the performnce is studied. The therml expnsion coefficient ETEC nd young s modulus EYM vlues re evluted y second order polynomil, using curve fitting technique y the constnt nd. They re implemented s Voltge controlled voltge source (VCVS) nd is shown in Fig. 7(). R TE, R TEC, RYM represent the resistnce used for enling the clcultion. Resistnce nd inductnce in the nlogous prllel resontor re implemented s nonliner voltge controlled current sources (VCCS) nd re shown in Fig. 8. By considering Tle 1 specifictions, the electricl prmeters re clculted under different tempertures. The inductnce nd resistnce vlues re found to vry in the rnge of 3.43mH to 3.49mH nd 3.06MΩ to 5.43MΩ respectively, for temperture rnge of 100K to 400K. The eqution is formed y second order polynomil curve fitting method for the vlues of dmping coefficient nd spring
98 C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 constnt. These equtions re implemented s voltge controlled voltge source (VCVS) in the simultor to get s voltge in prticulr node. To implement temperture controlled resistnce model, the ove sid node voltge of dmping coefficient EG is considered with one independent voltge source VINR for developing Voltge controlled current source G INR, which replces the resistnce element in prllel resontor model reported in the literture [1]. An input voltge ( E ) is pplied with n inductnce, for determining the vlue of current in inductnce. These re connected in series with smll vlue of resistnce R which is used to void the convergence prolem. This current is tken out using current controlled current source [11] in the other node. The previously evluted spring constnt vlue s voltge nd CCCS node voltge F re used for further clcultions. They re considered s inputs for the second order polynomil element of Voltge controlled current source G IN. R INR, R G, R INR1, R, RIN re the resistnce required to fix the sources. Fig. 8. Voltge controlled () resistnce model; () inductnce model. The voltge controlled current source model of resistnce nd inductnce is used to replce the simple resistnce nd inductnce elements of the erlier model. The complete equivlent circuit is shown in Fig. 9. The developed model cn e used to determine the system performnce t ny temperture in the rnge of 100 400K. 3. Simultion results 3.1. Trnsient Anlysis Fig. 9. Temperture controlled equivlent circuit. A step input current equivlent to n ccelertion of 0.5g is pplied to the movle mss nd the plte moves from the centre position. The gp increses in one side nd decreses in the other. It reflects in the cpcitnce chnge in oth ir gps. Cpcitnce vritions due to two different tempertures 100K nd 400K t 30P pressure
C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 99 re shown in Fig. 10. At lower pressures, the displcement exhiits lrge oscilltions. These results re in ccordnce with the results of Timo Veijol [1] nd thus vlidte our model. Fig.10. Trnsient response on cpcitnce t the temperture of () 100K; () 400K. The ir gp (da) cpcitnce voltge in one side is reduced nd the other side is incresed. Further, the settling time of oth cpcitnces is reduced s the temperture increses. This phenomenon is shown in Fig. 11. Fig.11. Temperture vrition on cpcitnce () voltge; () settling time. The trnsient response of displcement is shown in Fig. 1. As the temperture increses, the corresponding displcement nd settling time decreses, which is evident from the simultion crried out t 100K nd 400K.
300 C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 Fig.1. Trnsient response on displcement t the temperture of () 100K; () 400K. The displcement nd settling time found to e 10nm, 30ms nd 114nm, 17ms respectively, t 30P. The pek vlue nd settling time vrition with temperture is shown in Fig. 13. 3.. Frequency Anlysis Fig.13. Temperture vrition on pek vlue nd settling time of displcement. An externl ±3g force is pplied to the mss of ccelerometer nd the displcement t ech frequency is evluted. 100 K 400 K Fig.14. Frequency response on displcement t the temperture of () 100K nd () 400K. Fig.15. Temperture vrition on normlized displcement.
C. Kvith nd M. Gnesh Mdhn / Procedi Engineering 64 ( 013 ) 9 301 301 The nlysis is repeted for different tempertures t constnt pressure of 30P. The response is plotted in Fig. 14. From the response, the normlized displcement vlue of 17.81 db, 1.975 db t the resonnce frequency of 1.589 KHz, for the temperture of 100K nd 400K re otined. It is oserved tht, s the temperture increses, the normlized displcement decreses s shown in Fig. 15. However, elow the resonnt frequency, the impct of temperture is not significnt. 4. Conclusion A nonliner electricl equivlent circuit model is developed for the nlysis of therml effects on the dmping coefficient nd spring constnt of MEMS ccelerometer. The nlysis is crried out in the rnge of 100K to 400K, t constnt pressure of 30P. It is found tht, s temperture increses the normlized pek displcement, t resonnce decreses. In the cses of trnsient nlysis, the settling time for displcement nd cpcitnce re found to reduce with increse in temperture. The model is comptile with ny electronic circuit implemented in PSpice simultor. Acknowledgements The uthors grtefully cknowledge Ann University, Chenni for providing finncil support to crry out this reserch work under Ann Centenry Reserch Fellowship (ACRF) scheme. One of the uthors, C. Kvith is thnkful to Ann University, Chenni for the wrd of Ann Centenry Reserch Fellowship. References [1] Timo Veijol., Heikki Kuism., Juh hdenper., Tpni Ryhnen., 1995. Equivlent circuit model of the squeezed gs film in silicon ccelerometer, Sensor Actutor A-Physics 48, p. 39. [] Timo Veijol., Heikki Kuism., Juh hdenper., 1998. Dynmic modeling nd simultion of microelectromechnicl devices with circuit simultion progrm, Modeling nd Simultion of Microsystems - Proceedings of the 1998 Interntionl Conference on Modeling nd Simultion of Microsystems, pp. 45-50. [3] Timo Veijol., Tpni Ryhnen., 1995. Model of cpcitive micro mechnicl ccelerometer including effect of squeezed gs film, IEEE Interntionl Symposium on Circuits nd Systems, pp. 664-667. [4] Bourgeois, C., Porret, F., Hoogerwerf, A., 1997. Anlyticl modeling of squeeze-film dmping in ccelerometers, Interntionl Conference on Solid- stte Sensors nd Actutors, pp. 1117-110. [5] Accelerometer model in APAC: Report CT-18 1994, Circuit Theory ortory, Fe. 1994. [6] Edwrds, M J., Bowen, C R., Allsopp, D W E., Dent, A C E., 010. Modeling wfer ow in silicon-polycrystlline CVD dimond sustrtes for GN-sed devices, Journl of Physics D: Applied Physics 43, p. 1. [7] Gng Di., Mei i., Xioping He., 011. Therml drift nlysis using multiphysics model of ulk silicon MEMS cpcitive ccelerometer, Sensors nd Actutors A Physics 17, p. 369. [8] Jeong., Jeung-hyun., Sung-hoon Chung., Se-Ho-ee., Dongil Kwon., 003. Evlution of elstic properties nd temperture effects in Si thin films using n electrosttic microresontor, Journl of Microelectromechnicl Systems 1, p. 54. [9] Jing Wng., Qing-An Hung., Hong Yu., 008. Size nd temperture dependence of Young s modulus of silicon nno-plte, Journl of Physics D: Applied Physics 41, p. 1. [10] Kvith, C., Gnesh Mdhn, M., 013. An improved SPICE model for MEMS sed Cpcitive Accelerometers, Semiconductor Mterils nd Devices - Proceedings of the nd Interntionl Symposium, Semiconductor Mterils nd Devices, pp. 116-1. [11] Muhmmd H Rshid., 004. Introduction to PSpice Using OrCAD for Circuits nd Electronics, Prentice Hll, Upper Sddle River, NJ. [1] Ti Rn Hsu., 00. MEMS nd Microsystems Design nd Mnufcture, Tt McGrw Hill. td. [13] Rudolph, H., 1993. Simultion of therml effects in integrted circuits with SPICE ehviorl model pproch, Microelectronics Journl 4, p. 849-861.