Transactions of the VŠB Technical University of Ostrava, Mechanical Series. article No. 1932

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1 Transations of the VŠB Tehnial University of Ostrava, Mehanial Series No. 1, 213, vol. LIX artile No Vladimír KUTIŠ *, Gabriel GÁLIK **, Ivan RÝGER ***, Justín MURÍN ****, Juraj HRABOVSKÝ *****, Juraj PAULECH ******, Tibor LALINSKÝ ******* PIEZOELECTRIC ANALYSIS OF SAW SENSOR USING FINITE ELEMENT METHOD PIEZOELEKTRICKÁ ANALÝZA SAW SNÍMAČA POMOCOU METÓDY KONEČNÝCH PRVKOV Abstrat In this ontribution modeling and simulation of surfae aousti waves (SAW) sensor using finite element method will be presented. SAW sensor is made from piezoeletri GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequeny of SAW, whih is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM ode ANSYS. Abstrakt Príspevok sa zaoberá modelovaním a simuláiou SAW snímača, ktorý využíva šírenie povrhovýh vĺn, pričom na simulovanie sa využíva metóda konečnýh prvkov. SAW snímač je zložený z piezoelektrikej GaN vrstvy a z SiC substrátu. Vyšetrované sú dva typy analýz - modálna a prehodová. Cieľom modálnej analýzy je určiť vlastnú frekveniu SAW snímača, ktorá je následne využitá v prehodovej analýze. V prehodovej analýze sa vyšetruje šírenie sa povrhovej vlny v SAW snímači. Obe analýzy sú realizované v MKP programe ANSYS. Keywords SAW sensor, MEMS, piezoeletri material, FEM analysis, modal analysis, transient analysis 1 INTRODUCTION Surfae aousti wave (SAW) devie typially generate mehanial waves, whih propagate on surfae of piezoeletri layer. The waves are also alled Rayleigh waves [1]. The veloity of * do., ing., PhD., Department of Applied Mehanis and Mehatronis, IPAEE, Faulty of Eletrial Engineering and Information Engineering (FEI), STU Bratislava, Ilkoviova 3, Bratislava, Slovakia, tel. (+421) , vladimir.kutis@stuba.sk ** ing., Department of Applied Mehanis and Mehatronis, IPAEE, FEI STU Bratislava, Ilkoviova 3, Bratislava, Slovakia, tel. (+421) , xgalikg@is.stuba.sk *** ing., Institute of Eletrial Engineering, SAV, Dubravska esta 9, Bratislava, Slovakia, tel. (+421) , ivan.ryger@savba.sk **** prof., ing., DrS., Department of Applied Mehanis and Mehatronis, IPAEE, FEI STU Bratislava, Ilkoviova 3, Bratislava, Slovakia, tel. (+421) , justin.murin@stuba.sk ***** ing., Department of Applied Mehanis and Mehatronis, IPAEE, FEI STU Bratislava, Ilkoviova 3, Bratislava, Slovakia, tel. (+421) , juraj.hrabovsky@stuba.sk ****** ing., Department of Applied Mehanis and Mehatronis, IPAEE, FEI STU Bratislava, Ilkoviova 3, Bratislava, Slovakia, tel. (+421) , juraj.pauleh@stuba.sk ******* ing., DrS., Institute of Eletrial Engineering, SAV, Dubravska esta 9, Bratislava, Slovakia, tel. (+421) , eleklali@savba.sk 33

2 waves depends on density and elastiity material properties and are very sensitive on hange of surfae layer mehanial parameters (e.g. density). This sensitivity is the reason why SAW devies are so popular as sensor devies [2]. The SAW an be generated in piezoeletri material using interdigital transduer (IDT) [3]. It is basially omb-like struture with fingers onneted to eletri terminals (see Fig. 1). These eletrodes an be fabriated by lithographi proess, metal deposition and lift-off tehnique. The width and spaing of fingers affet the enter eigenfrequeny of IDT. The number of interdigital transduers affets the length of impulse harateristis and filter bandwidth [3,4]. The length of IDT fingers affets primarily the input admittane of IDT and defines the width of wave-beam, what is important when onsidering the diffration effets [4]. The basi IDT onepts uses uniform transduer with equal finger lengths. By weighting the length of IDT fingers we an adjust SAW filter passband harateristis. The paper is foused on modelling and simulation of SAW devie using finite element method [5], speially by ode ANSYS [6]. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequeny of SAW, whih is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Obtained numerial results an be used in the design of SAW sensor as well as in tehnology of manufaturing proess of SAW sensor. 2 GEOMETRY OF SAW SENSOR Fig. 1 shows geometry of SAW sensor made of piezoeletri GaN layer and SiC substrate. Interdigital transduers are loated on both sides of sensor - one as transmitter and one as reeiver. Both IDT are made from Gold. Fig. 1 Model of SAW sensor Position and shape of IDT are shown on Fig. 2. The distane between eah pair of IDT is half of wave length, the distane between input IDT and output IDT is denoted as d and the number of IDT pairs is n. Fig. 2 Main dimensions of SAW sensor In our simulation, we used following wave and geometry parameters: =4m, d=3 and n=5. Height of GaN piezoeletri layer was onsidered in range h GaN = m and the height of SiC substrate is h SiC =6. Beause we did not inlude wave absorber in the model, waves an reflet from 34

3 the left and right side of sensor and interfere with the waves. In order not to inlude interferene of waves in simulation, the extension of SAW sensor in longitudinal diretion and time of simulation has to be hosen adequately. 3 MATERIAL OF SAW SENSOR Material properties, whih have to be onsidered in piezoeletri analysis of SAW sensor, belong to three ategories: mehanial, eletrial and piezoeletrial. Mehanial properties have to be defined for all three materials, Gold (eletrodes), GaN (piezolayer) and SiC (substrate), but eletrial and piezoeletrial properties have to be defined only for GaN layer. Constitutive law for mehanial behaviour an be written in matrix form as C, (1) where is stress vetor, is strain vetor and C is elastiity matrix and for transversally isotropi material an have form C. (2) s 44 y 44 m 66 Elasti properties of GaN and SiC are summarized in Tab.1, density of GaN and SiC is 615 kg/m 3 and 2329kg/m 3, respetively. Tab. 1 Elasti properties of GaN and SiC Elasti onstants GaN [GPa] SiC [GPa] Elasti properties of Gold are defined as isotropi material properties with Young modulus 78GPa and Poisson's ratio.44, density is 193 kg/m 3. Constitutive law for piezoeletri behavior an be written in matrix form as E C ee, D e e E, where E is vetor of eletri intensity, D is vetor of eletri displaement, e p is permitivity matrix on ondition onstant strain, C E is elastiity matrix on ondition onstant eletri intensity E and e is matrix of piezoeletri properties. For polarization in z (number 3 in numerial labeling) diretion, elastiity matrix C E has form (2), permitivity matrix e p and matrix of piezoeletri properties e have form p (3)

4 e13 e e13 p e e 33 p ep, e. (4) e p e15 e15 Eletri and piezoeletri properties of GaN are summarized in Tab. 2. Tab. 2 Eletri and piezoeletri properties of GaN eletri properties - relative permitivity [-] piezoeletri properties [pc/m 2 ] e p =8.9 e 13 = e 33 = e 15 =.67 4 MODAL ANALYSIS OF SAW SENSOR Modal analysis an be used to determined the eigenfrequeny of SAW sensor, that an be used in transient analysis. Beause the geometry of SAW sensor under IDT is periodi, we an model only small part of SAW devie with length equal wave length. Only 2D model is onsidered. Boundary onditions have to enable periodi deformation of model. These onditions is satisfied by oupling of individual degree of freedom on left and right side of the model. Bottom of the model is fixed and the top is free - see Fig. 3 Left. Fig. 3 Left - boundary onditions of model for modal analysis, Right - Eigenmode of SAW sensor, whih auses surfae waves - GaN thikness is 1.5m To performed modal analysis, piezoeletri element PLANE223 of ode ANSYS is used. Blok Lanzos method is used to ompute eigenfrequenies and eigenmodes of the system. Obtained eigenmode and eigenfrequeny of Rayleigh wave for GaN thikness 1.5m are shown on Fig. 3. Right. Obtained eigenfrequenies for different thikness of GaN layer are summarized in Tab

5 Tab. 3 Obtained eigenfrequenies for different GaN thikness GaN thikness [m] Eigenfrequeny [GHz] TRANSIENT ANALYSIS OF SAW SENSOR Next step in simulation of SAW sensor is transient analysis that an be used to simulate real operation onditions of SAW devie. To redue omputational time, we model SAW sensor as 2D system. In transient analysis only GaN thikness 1.5m was investigated. Loading of the SAW sensor is harmoni eletri voltage on input IDT with amplitude 1V and with frequeny equal eigenfrequeny omputed in modal analysis, i.e. f=1.254ghz. SAW sensor is fixed at the bottom of substrate. The total time of simulation was set to 1.2x1-8 s. The goal of the simulation is to investigate wave propagation on the surfae of SAW sensor as well as indued voltage on output IDT. Fig. 4 Deformation of SAW sensor at the end of transient analysis Fig. 4. shows total deformation of system at the end time of simulation. As we an see from the figure, the waves propagate on the surfae of the sensor, but some of them propagate also into the substrate. Damping of waves in substrate an be observed also in Fig. 5 Left, where the derease of amplitude in transversal diretion is depited. Fig. 5 Right shows input and output voltage on IDT as a funtion of time. Input signal is harmoni from start of simulation, but output IDT needs some time to reeive Rayleigh waves. Fig. 5 Left - amplitude of waves in transversal diretion, Right - input and output voltage on IDT 37

6 6 CONCLUSIONS The paper deals with modelling and simulation of surfae aousti waves sensor using finite element method. In the modelling, FEM ode ANSYS is used, where modal and transient analysis are performed. Modal analysis is used to determined eigenfrequeny of the system and the frequeny is used as input in transient analysis as frequeny of exitation. In transient analysis with harmoni loading wave propagation is investigated. Our next researh in this area will be foused on modelling of sensitive layer on the top of the SAW sensor and investigation of influene of density hange on this sensitive layer aused by hemial reation with surroundings. ACKNOWLEDGEMENT This work was supported in part by the following projets: Slovak Researh and Development Ageny under the ontrats APVV-45-1, Grant Ageny KEGA - grant No. 15STU-4/212 and VEGA No. 1/534/12. REFERENCES [1] MAYERS, M. A. Dynami behavior of materials. Chihester : John Wiley & Sons. Ltd, pp. ISBN [2] FRADEN, J. Handbook of modern sensors: Physis, Designs, and Appliations. New York: Springer, pp. ISBN [3] DATTA, S. Surfae Aousti Wave Devies. Prentie-Hall, pp. ISBN [4] CAMPBELL, C. K. Surfae Aousti Wave Devies of Mobile and Wireless Communiations. Aademi Presss, pp. ISBN [5] BURNETT, D. S. Finite Element Analysis: From Conepts to Appliations. Addison Wesley Publishing Company, pp. ISBN [6] ANSYS, Version 14, Theory manual,