EFFICIENCY OF SURFACE GENERATED BULK ACOUSTIC WAVES IN ROTATED Y-CUTS OF LiNbO3

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EFFICIENCY OF SURFACE GENERATED BULK ACOUSTIC WAVES IN ROTATED Y-CUTS OF

LiNbO3

Y. Zhang

To cite this version:

Y. Zhang. EFFICIENCY OF SURFACE GENERATED BULK ACOUSTIC WAVES IN RO- TATED Y-CUTS OF LiNbO3. Journal de Physique Colloques, 1990, 51 (C2), pp.C2-21-C2-24.

�10.1051/jphyscol:1990205�. �jpa-00230373�

COLLOQUE DE PHYSIQUE

Colloque C2, supplement au n°2. Tome 51, Fevrier 1990 C2-21 ler Congres Frangais d'Rcoustlque 1990

EFFICIENCY OF SURFACE GENERATED BULK ACOUSTIC WAVES IN ROTATED Y-CUTS OF LiNb03

Y.W. ZHANG

Laboratoire de Physique et Metrologie des Oscillateurs du CNRS associe a 1'VniversitS de Franche-Comte-Besangon, 32, Avenue de 1'Observatoire, F-25000 Besangon, France

Résumé - Nous étudions les ondes acoustiques rayonnées par un transducteur interdigité dans le volume d'un substrat piézoélectrique. Des diagrammes de rayonnement dans des coupes de LiNbÛ3 sont présentés ainsi que leurs vitesses de propagation et angles du flux d'énergie. L'effet d'anisotropie sur le diagramme et le couplage entre ondes de volume et ondes de surface avec fuite sont analysés. Le critère de sélection d'une coupe selon une application particulière de ces ondes est proposé.

Abstract - The paper presents our calculated radiation diagrams, propagation velocities and power flow angles of deep bulk acoustic waves radiated by an interdigital transducer in several LiNbC»3 substrates. Anisotropy effect on the radiation patterns and the coupling between bulk waves and leaky surface waves are analyzed.

Optimum cuts for designing a specified device are proposed and general criteria of selecting transducer- material configurations are discussed.

1 - INTRODUCTION

It is well known that the interdigitally electroded transducers (IDT) are efficient for exciting surface acoustic waves (SAW) in piezoelectric substrates. Since then are developed a large number of acousto-electronic devices consisting of IDT for signal processing. But in the same devices, a simultaneous excitation of other acoustic modes, in particular the bulk acoustic waves (BAW) is frequently observed. These diverse waves were initially considered as parasite signals and excluded in the analysis of SAW devices and IDT performance because of their complex nature.

However, it has been found later that [1,2] the study of BAW radiated by an IDT may be of interest in the design of surface skimming bulk wave (SSBW) devices, where the SSBW excited and detected by IDT is utilized as the main propagating mode. Furthermore, studies of BAW radiation patterns also have practical importance in designing certain acousto-optic devices such as Bragg cell acousto-optic spectrum analyser, channeliser and acousto-optic deflector [3-5], where eigher broad-band SAW transducers are required or the knowledge of deep BAW radiation patterns are necessary for achieving the most efficient interactions between the radiated bulk acoustic waves and the light beam. The potential possibility of utilising these Bragg cells to construct broad-band acousto-optic modulators is particularly attractive for us to put on a theoretical study of BAW radiation by DDT in SAW devices.

Based on the previous works [6,7], we apply our analysis to calculating radiation patterns in other highly piezoelectric cuts of LiNbC>3. As demonstrated earlier, the bulk wave radiation pattern obtained in far-field depends on two factors, one is the material factor corresponding to the pattern radiated by a line source, and the other is determined by the geometry of the IDT and operating frequency. In section 2, new results concerning the material factor will be given and analysed in some details, taking account of full piezoelectricity. Characteristics of the waves so radiated, such as velocity, power flow angle are given in section 3. The coupling between bulk waves and leaky waves as well as caustics which occur in certain cases will be analyzed through numerical examples given for several cuts of LiNb03.

2 - MATERLA.L EFFICffiNCY - LINE-SOURCE RADIATION PATTERNS

The efficiency of BAW radiation in a given substrate depends on the radiation direction in the substrate because of the material anisotropy. The power density of a progressive wave in the volume of the substrate may be represented by the associated Poynting vector. We have shown [7] that, in the far-field, the Poyinting vector expressed in polar coordinates can be put into the following form

where P0("' represents a normalized amplitude of the nth bulk mode (longitudinal, fast shear or slow shear) ; Km.p.e^n' correspond, with the corresponding index, the "mechanical, piezoelectrical and

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990205

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electrical" part of the power, Kp(d is the electromechanical coupling coefficient of the correspondin wave in a n unbounded medium of the same material ; ro is the distance from the source. We c a 8

"material factor" the product of P,(d by the sum of K(d, because i t gives the radiation pattern of a line-source, which models an ideal infinite band-pass transducer and does not favour any frequency.

In contrast, the factor Af does depend on the IDT geometry and the operating frequency. To study the material efficiency, we put Af = 1. Then the plot of P,(n) versus radiation angle 8, with r, fixed gives power distribution diagram i n the substrate due to a line-source excitation.

Numerical calculations were carried out for a number of rotated Y-cuts of LiNbOs. In Fig. 1 are shown radiation diagrams in these cuts calculated by the above formula. Fig. l(a) represents the diagram i n the sagittal plane of a Y-cut Z-propagation substrate, and l ( b ) i n a Z-cut Y-propagation substrate, we see that the radiation patterns are not symmetrical about the vertical direction, this i s due to the anisotropy of the material. By contrast, in these configurations, the wave movement i s confined i n the sagittal plane, so only present a r e the longitudinally and vertically polarized bulk modes. The latter is more strongly excited than the former i n both configurations, b u t t h e longitudinal mode is favoured in 121" and 29" directions in YZ-cut, and lobes of this mode i s less obvious in ZY-cut; the vertical shear mode radiates in some privileged directions, which include 120"

in ZY-cut and 124", 78", 65" in YZ-cut. The diagrams were computed assuming that the substrate surface is unmetallized. When the surface is metallized, the overall appearance of the pattern remains almost the same, only the magnitude becomes a little larger. Fig. l(d) and l(e) show the diagrams for X-cut Z-propagation and Z-cut X-propagation configurations. Because these cuts are symmetrical with respect to the vertical direction, only the half of the diagrams has been given i n Fig. l(e). Now all three bulk waves are present. We note that in ZX-cut it is the longitudinal mode t h a t radiates more strongly in vertical direction, but in XZ-cut what radiates more strongly i n the same direction i s the fast shear mode. Moreover, we note the existence of some isolated directions i n which the radiation of the slow shear mode is important. This is due to the interaction of this bulk mode with the leaky surface wave which exists in these cuts.

The radiation pattern in 41" YX-cut is given in Fig. l(c), here we find a new phenomenon t h a t the fast shear mode with a quasi-horizontal polarization is very well coupled and radiated near the substrate surface. The longitudinal mode in vertical direction and the leaky nature of the slow shear (vertical polarisation) mode are similar to ZX-cut. Com arison of the figure l(c) and l(e) suggests that, for the intermediate cuts (0=90° to 415, the lobe o f t h e fast shear mode progressively changes from 60"

direction (in ZX-cut) to 5" direction (in 41" YX-cut). We have demonstrated t h a t 171 the magnitude of the radiation diagram i n 41" YX-LiNb03 cut is about three times larger than that in 36" YX-LiTa03 cut, so this cut h a s a better electromechanical coupling for SSBW device.

3

-

What is presented i n the Fig. 1 is the module of the Poynting vector projected in the sagittal plane. I n fact, this vector i n general does not lie i.n the sagittal plane because of the anisotropy, instead, i t lies i n a direction 8,with respect to the sasttal-plane projection. Moreover, the projection i n the sagittal plane of the Poynting vector and the wave vector forms an angle Oe, called power flow angle, these two angles together with the module completely describe the power distribution in the bulk. In Fig. 2 are shown the curves of these a n les and the corresponding phase velocities. Greater is the value of 0,, more important will be the diffraction losses.

4

-

Radiation patterns in far-field of the bulk waves are obtained by evaluating the integrals of the field quanties with the method of steepest descent path, together with all relevant parameters determined : magnitude and angles of the power flow density, propagation velocity as a function of the radiation direction. These data allow us to determine the optimum operating frequency which favours a particular mode i n a given direction.The radiation diagrams presented in Fig. 1 show the existence of privileged directions intrinsic to the material configurations. The radiation of the fast shear wave i n YZ-cut is reinforced in 78" and 124" directions because of the caustic in these positions; the same thing is true i n XZ-cut alon 88" and 92" directions. Two points are to be remarked. First, the SH- mode in 41' YX-cut is not r a s a t e d a t the surface when this latter is metallized ; second, the SV-mode can leak some energies i n a small angular interval because i t couples the leaky surface wave i n these directions.

Knowing the radiation patterns we may select ap ro riate modes for specific applications, for instance, the SH-mode i n 41" YX-cut would be use& For SSBW devices such a s broad-bandwidth bandpass filters involving multistrip couplers and high frequency oscillators [1,21. On the other hand the longitudinal mode i n ZX-cut and in 41" YX-cut as well a s the fast shear mode in XZ -cut may be suitable for designing gigahertz acousto-optic modulators andripectrum analysers [3-51.

REFERENCES

111 M.F. Lewis, "Surface skimming bulk waves. SSBW". Proc. 1977 Ultrasonics Symp., IEEE cat # 77CH2641SU, p.

744.

/W K.H. Yen, K.F. Lau and R.S. Kagiwada, "Recent advances in shallow bulk acoustic wave devicese', Proc. 1979 Ultrasonics Symp.. IEEE cat # 79CH1482-9, p. 776.

131 K. Hashimoto, M. Toyoda, M. Yamaguehi and H. Kogo, "Acoushptic Bragg diffraction by deep bulk aeoustic waves for use in optic spectrum analyser", Japanese J. Appl. Phys. 25,220 (1986).

141 F. SabebPeyman and I.C. Chang, "High dynamic range bulk acoustic wave channeliser", Proc. 1985 Ultrasonics Symp., IEEE cat # 85CH2209-5, p. 335.

/51 L. Palmieri, G. Soeino and E. Verona, "Acoustic beam steering by an interdigital transducer for wide band bulk wave a c o u s h p t i c deflectors", Proc. 1985 Ultrasonics Symp., IEEE cat # 85CH2209-5, p.358.

/6/ Y.W. Zhang and M. Planat, "Anisotropy dependence of the focused field radiated into a piezoelectric half-space by a n interdigital transducer". Appl. Phys. Lett. 52 (6), 458 (1988).

17/ Y.W. Zhang, "Surface generated bulk acoustic waves by interdigital transducers in strongly coupling materials", Proc. 1989 URSI International Symp. on Signals, Systems, and Electronics, p. 456, Erlangen, Fed. Rep. of Germany, sept. 1&20,1989.

Fig. 1.

Radiation patterns

bulk waves

some cuts

LiNbOs

substrate excited

a line-source.

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