Abstract IJERTV2IS International Journal of Engineering Research & Technology (IJERT) ISSN: Vol. 2 Issue 12, December

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1 Modelling, Simulation and Caracterization ZnO Piezoelectric Tin Films for FBAR Roger Ondo Ndong,*, Honoré Gnanga, Jean Aubin Ondo and Alain Foucaran. Laboratoire pluridisciplinaire des Sciences, LAPLUS, Ecole Normale Supérieure, BP 7009 Libreville Gabon. Institut Electronique du Sud, IES-Unité mixte de Recerce du CNRS n 54, Université Montpellier II, Place E. Bataillon, Montpellier cedex 05- France. Abstract Caracteristics of Zinc oxide (ZnO) piezoelectric tin films ave been investigated for tin film bulk acoustic resonators (FBAR) wit relationsip to bottom electrodes. Several critical parameters of te RF magnetron sputtering process deposition pressure, RF power, substrate temperature, O concentration and te target to substrate distance were determined to clarify teir effects on te material caracteristics of te ZnO. Higly c-axis oriented tin films as tick as 5.7 μm were grown and analyzed. Compressive stresses were observed. Te FBAR devices wit te ZnO films exibited a pronounced resonance peak centred at 790 MHz wit a k coupling coefficient of 7 %. It found terefore tat te impedance matcing of te FBAR could be easily acieved simply by controlling te resonance te resonator. Introduction Bulk acoustic wave (BAW) resonators using piezoelectric tin film are valuable devices for ig frequency telecommunications []. Many studies of BAW devices ave been carried out in recent years [- 6]. ZnO tin film is a practical piezoelectric material for applications to BAW and surface acoustic wave (SAW) devices for its large electro-mecanical coupling coefficient. It is very important to improve te resonant caracteristics of BAW resonator to be adopted for telecommunication devices tat ave severe specifications for electrical caracteristics. We ave investigated ZnO piezoelectric tin films and teir microstructure for SAW and BAW devices [7-8]. Te most critical factor determining te resonance caracteristics of FBAR devices is piezoelectric properties of te ZnO films, wic is directly related to degree of te preferred orientation of te Zno crystal structure [9-0]. Considerable effort as been made to fabricate ig quality ZnO films wit a strongly preferred orientation. However, eac approac as sown its own limitations suc as te complexity of te fabrication metods and te ig cost of process equipment. In FBAR devices, te ZnO film sould exert a minimum stress on te underlying layer and also ave a ig piezoelectric constant. Tis paper presents te modeling; simulation and te analysis of ZnO based FBAR s tat are centred at frequencies ranging from 300 to GHz. Te texture of zno tin film was analyzed by X-ray diffraction and te electromecanical coupling coefficient k was measured wit Network analyzer. On te oter and te electrical properties of te resonators were measured and are discussed as function of materials parameters and processing conditions.. Zinc oxide tin films Zinc oxide films were deposited by r.f magnetron sputtering using a zinc target (99,99%) wit diameter of 5 mm and 6 mm tick. Substrate is p-type silicon wit (00) orientation. Te substrates were torougly cleaned wit organic. Magnetron sputtering was carried out in oxygen and argon mixed gas atmospere by supplying r.f power at a frequency of 3.56 MHz. Te RF power was about 50 W. Te flow rates of bot te argon and oxygen were controlled by using flow meter (ASM, AF 600). Te sputtering pressure was maintained at torr controlling by a Pirani gauge. Before deposition, te pressure of te sputtering system was under torr for more tan and were controlled by using an ion gauge controller (IGC 6 F). Tin films were deposited on silicon, substrate under conditions listed in Table []. Tese deposition conditions were fixed in order to obtain te well-orientation zinc oxide films. Te presputtering occurred for 30 min to clean te target 79

2 surface. Deposition rates covered te range from 0.35 to 0.53μm/. All films were annealed in elium ambient at 650 C for 5mn. In tis study Pt was cosen as a bottom electrode material for te FBAR fabrication. In order to investigate te crystallograpic properties of te ZnO films, we carried out an X-ray diffraction (XRD) analysis using CuKα (λ = 0,54054 nm) radiation. Te diffractogram of a 5.7 μm ZnO tin film deposited on a platinized substrate. No oter peak tan te (00) one could be detected, indicating a very good c-axis texture. Te dielectric properties of Zno films were measured wit an impedance analyzer. Typical values for te relative permittivity and te dielectric losses were 8.5 and 0.00 respectively. Table : ZnO sputtering conditions Sputtering pressure 3.35 x 0-3 Torr Mixture gas Ar + O = 80 0 % Power RF 50 W Sputtering time 6 Substrate temperature 00 C Target-substrate distance 7 cm 3. Teoretical consideration Trougout piezoelectric material, tere is interdependence between mecanical and electrical quantities. Tis implies a coupling between elastic waves and electromagnetic waves. From te two solutions of te wave equation, it is possible to write linear relationsips between te mecanical (strengt and speed) and electrical parameters (voltage U and current I injected).te presentation of tese relations in matrix form ten allows deducing te equivalent electromecanical scemes. 3.. Impedance matrix Consider a piezoelectric slice tickness and A section subjected to an electrical voltage U and te forces F and F (Figure ). Te forces F and F exerted on eac of te faces and te velocities v and v entering a play similar to tat of te voltage and te current roll. Te forces F and F are written: F AT x F AT x A represents te cross section and te constraint T Fig. : Slice of piezoelectric material section A Te constraint T for a piezoelectric material is written: u T c D () x Wit, te displacement u, c induction constant rigidity, D electrical induction and ratio of te piezoelectric coefficient of te dielectric constant: e Deriving te expression () wit respect to time, by considering te equation of conservation of carge D t J( t) I( t) A and indicating te speed of te particles v u t, it is found tat: T v D v c c It () t x t x A Moreover te propagation equation is of te form: v v c t x Te general solution of tis equation is te armonic sum of two waves propagating in opposite directions ikx ikx (te speedv c ): v ae be va v (3) b wit k w V Te constraint expression is derived from te expression () by plotting te expression (3) speed: ikx ikx T Z( a. e b. e ) i I Aw From te expression of te stress and remembering tat te mecanical impedance can be written Z = ZA (were Z is te caracteristic impedance and A section of te piezoelectric segment bounded by te planes x = x and x = x ), we deduce tat te forces F and F are ten written in te form: ikx ikx F AT x Zae be i I w ikx ikx F AT x Zae be i I w Te relation (3) can write tat ikx ikx v vx ae be ikx ikx v vx ae be Were one draws te expressions of coefficients: s 80

3 ikx ikx ikx ikx ve ve a, ve ve b i sin( kd) i sin( kd) By feeding back tese coefficients in (Syst.), we find expressions connecting v, v and I to F and F : v v F i I (4) i tan kd i sin kd w v v F i I (5) i sin kd i tan kd w Bot acoustic access being caracterized, it remains to find te expression tat defines te electrical access. U voltage appearing between te two sides of te section A is expressed U x x E. dx Te electric field is derived from one of te two states of te piezoelectric equations, namely u u D D see E x x s Introducing te speed v iwu( x ) and v iwu( x ) te voltage U becomes: Id U ( v v ) (6) w iwc 0 Writing in matrix form equations (4), (5) and (6), sows te electromagnetic impedance matrix [Z]. F tan kd sin kd w v (7) F i v sin kd tan kd w U I w w wc0 3.. Masson and Redwood model Wen te material is piezoelectric, tere is an additional force must be taken into account in terms of F and F. Te equivalent circuit diagram of a portion of piezoelectric solid is obtained by juxtaposing te equivalent of non-piezoelectric contrasts wit te electromecanical transformer sceme. Fig. : Equivalent Mason model for piezoelectric We consider for simulation, tat te vibrations of te piezoelectric material will generate only longitudinal waves or only transverse waves. Tis will provide a model tat is valid and consistent wit reality. Te electrical input impedance of te computed from te matrix (7) is [, 3] structure: K Z Z(cos ) i( ZZ)sin Ze ( (8) ic0w ( Z ZZ )sin iz( ZZ )cos Z p, Z, Z eac represents te acoustic impedances of te piezoelectric material, settings on te front and rear of te piezoelectric material. k represents te electromecanical coupling coefficient. Around te resonance tis resonator can be represented by te following equivalent circuit: Fig.3: Electrical equivalent circuit of a piezoelectric resonator. a) Model Mason, b) Piezoelectric free. C 0 is te ability of te dielectric ZnO, L represents te inertia of te circuit structure, friction losses R C and te stiffness of te system. Tis circuit is an ideal model to represent te pysical caracteristics of a free resonator. Frequencies parallel and series resonance circuit can be written: and (9) fs L C f p CC 0 L C C IEEE standard [3] sows tat te coupling coefficient k is given by 0 8

4 k wit f S (0) tan fp Tis formula can be written in a more explicit approximate sape and ten te error introduced by te approximation is less tan % in te case were k 0., eiter: fs f () S k 4 f p fp Tis means tat we can calculate te coupling coefficient k just under te maximum real part of te impedance and admittance. Indeed, one can simply raise te maximum values of resistance (impedance) and conductance (admittance) to te resonant frequency wen te imaginary parts are zero. Using equation (8), we plot te teoretical evolution of te real and imaginary parts of te electrical admittance of te open resonator of 5.7m tick, depending on te frequency (Figure 4) Fig.5: Studied structure In te general case of a piezoelectric solid, note tat te essential condition for validity based on tose Masson, given te fact tat tey are one-dimensional models, tere is generation of single mode propagation. Gold in te zinc oxide, so as to enance a longitudinal propagation mode, it is necessary tat te axis of symmetry of order 6 is parallel to te electric field. Various experimental studies [] ave to control te orientation of te deposited layers, playing on various deposition parameters. Based on te equivalent model of Masson we get te result in Figure 6 were te reflection coefficient is plotted against te frequency linear. We ave also sown in te Smit cart of Figure 7 Fig. 6: Variation of reflection coefficient as function of te frequency Fig.4: Frequency dependence of te admittance of free resonator 4. Results Te structure comprises a piezoelectric material aving two electrodes (silver and titanium / platinum) on eac side. Te electric field of te signal applied between te electrodes to vibrate te piezoelectric puts solid (ZnO). Te vibrations are propagated in a medium mecanically secured (silicon) of te faces of a piezoelectric solid. Fig.7: Polar representation of te real and imaginary parts of te reflection coefficient By plotting te admittance as a function of frequency and comparing te same conditions te graps 8

5 corresponding to te infinite and finite media spread, we see in te second case te appearance of ringing Figure 8. However, te major problem lies in te fact tat uses a near-perfect model is terefore very far from reality. Tis explains wy on-oscillations seem to ave infinite amplitude around te inflection point wic corresponds to te natural resonance of ZnO. Fig.8: Admittance function frequency infinite medium, finite medium We integrate te penomena of dispersion and attenuation of te ultrasonic waves. Tese penomena are mainly due eiter to absorption or diffraction of a medium. We used te imaginary propagation speeds to simulate penomena. Te velocity V, clean te material, an expression of te form replace V( ki), k corresponds someow to te attenuation parameter (0 <k <0.) Taking into account te viscoelastic penomena is primarily a means of refine te modeling and tus get closer to a real case in Figure 9 Fig.9: Admittance function frequency infinite medium, finite medium We plotted te frequency dependence of te admittance of te resonator for a fundamental longitudinal mode. We observe tat te evolution of te frequency dependence of te admittance differs markedly from te previous case. Tere is recombination of waves propagating in te two directions of te delay line, wic leads to significant variations in te acoustic impedance returned to te surface of te piezoelectric element. Also, by studying te variation of te reflection coefficient as a function of frequency in linear coordinates and polar coordinates, we obtain, respectively, te results of Figure 0 and Figure. For a tickness of 5.7μm ZnO and te silicon substrate 380μm, we observe te resonance at 790MHz. Tis confirms te good quality of zinc oxide produced for use or FBAR filters. 83

6 Tese impedance variations we observe are oscillations of frequency intervals f. Tey result in te occurrence of significant canges in te real and imaginary parts of te admittance measured in peak sape as sown in Figure. Tese fluctuations occur wit a periodicity f satisfying te expression tat gives te resonant frequency of a vibrating cavity tickness mode. We found experimentally tat te frequency of ringing for an MHz value. And tis result is confirmed by simulation. Tese canges affect te sape of te electrical admittance. But, te existence of losses te delay line and te transducer causing attenuation of amplitudes of peaks. Tese attenuations are due eiter to te diffraction of te mecanical wave in te substrate wic forms an energy reservoir or wit relaxation of te coefficient of stiffness of te atoms constituting te substrate. Fig.0: Reflection coefficient as a function of frequency. simulation, testing Fig.: Reflection coefficient as a function of frequency in polar coordinate. Simulation, testing Fig.: frequency of ringing. Simulation, testing 84

7 5. Conclusions After presenting te basic equations governing piezoelectricity, we described te caracteristics of a vibrating piezoelectric structure in compression mode. At first, we studied in detail te equivalent circuit diagram of a free resonator composed of a piezoelectric ZnO layer wic bot sides are metalized. We ave tus determined te relationsip between te electrical impedance at te frequency. From tis relationsip, we modelled our structure. Te teoretical results were compared wit experimental results and give a good agreement wit respect to te resonance frequency and te effective coupling coefficient of te structure. Te FBAR devices wit te ZnO films exibited a pronounced resonance peak centred at 790 MHz wit a k coupling coefficient of 7 %. Te above result demonstrates tat te fabricated FBAR wit excellent performance will be promising for ig frequency applications. Nov;49():49-6. [] R. Ondo-Ndong, F. Pascal-Delannoy, A. Boyer, A. Giani, A. Foucaran, (003). Structural properties of zinc oxide tin films prepared by r. f. magnetron sputtering, Mat. Sci. Eng. B97 P. 68. [] D. Royer, E. Dieulesaint, «Ondes élastiques dans les solides»,tome, ed. Masson (996). [3] IEEE standard on piezoelectric IEEE / ANSI std. 76 (987). 6. References [] R. Ruby, P. Bradley, J. D. Larson III and Y. Osmyansky, Electronics Letters, 35, 794 (999). [] T. R. Sliker and D. A. Roberts, J. Appl. Pys., 5, 350 (967). [3] K. M. Lakin and J. S. Wang, Appl. Pys. Letters, 38, 5 (980). [4] Y. Miyasaka, S. Hosino and S. Takaasi, Jpn. J. Appl. Pys. Suppl., 3, 9 (983). [5] K. Nakamura, Y. Oasi and H. Simizu, Jpn. J. Appl. Pys., 5, 37 (986). [6] J. Siokawa, Y. Makisima, K. Hasimoto and M. Yamaguci, Jpn. J. Appl. Pys., 3, 3 (993). [7] Y. Yosino, T. Makino, Y. Katayama and T. Hata in te 5t international Symposium of Sputtering and Plasma Processes (Proc., Kanazawa, Japan, 999), [8] Y. Yosino in Microelectromecanical Structures for Materials Researc, edited by S. Brown, J. Gilbert, H. Guckel, R. Howe, G. Jonson, P. Krulevitc and C. Mulstein (Mater. Res. Soc. Proc. 58, Pittsburg, PA, 998), 9-4. [9] S. Fujisima, T. Kasanami, T. Nakamura, (983). Piezoelectric tin films and teir applications for electronics Jpn. J. Appl. Pys. p. 50. [0] Pinkett SL, Hunt WD, Barber BP, Gammel PL, (00). Determination of ZnO temperature coefficients using tin film bulk acoustic wave resonators,ieee Trans Ultrason Ferroelectr Freq Control. 85