The Excitation and Detection of Surface-Generated Bulk ... - IEEE Xplore

IEEE TRANSACTIONS ON SONICS AND ULTKASONICS, VOL. SU-31, NO. 2 , M A R C H 1984

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The Excitation and Detection of Surface-Generated Bulk Waves MARK A. GOODBERLET, STUDENT MEMBER, IEEE, AND DONALD L. LEE, MEMBER, IEEE

Absrruct-The performance of a conventional pair of surface acoustic wave interdigital transducers (IDT’s) used to generate bulk acoustic waves is analyzed. An IDT located on the upper surface of a thick, rotated Ycut quartz crystal acts as the acoustic equivalent of an array antenna, launchingacollimated beam into the crystal bulk. The beam is reflected off the crystal bottom and redirected towards the upper crystal surface where it is intercepted by a second receiving IDT. Closed-form expressions are derived for the important electrical and acoustical delay line characteristics and comparison is made with experimental measurements. The analyzed characteristics of the reflected bulk wave (RBW)delay line are significantly different from either the SAW or SSBWand include a) a frequency bandwidth directly proportional t o transducer length, b) a center frequency determined not by finger-to-finger spacing but rather by the ratio of transducer separation t o crystal thickness, c) a nonresonant radiation resistance, d) the capability to synthesize filter designs in which the frequency response is proportional t o the correlation of the individual transducer finger weightings, and e) the capability t o modify temperature stability by change of transducer separation and crystal thickness.

I. INTRODUCTION ULK ACOUSTIC wave radiation generated by interdigital transducers has historically been considered as spurious, often degrading or interfering with the performance of devices based upon surface acoustic wave (SAW) excitation. Within the last several years, however, there has been increased interest in utilizing the bulk waves generated by IDT’s for practical microwave applications. Such surface-generated bulk waves make use of the IDT as an acoustic equivalent of a phasedarray antenna, with the electrode fingers constituting the array elements. The phasing between these elements is controlled by the applied signal frequency thereby allowing the direction of the acoustic beam radiated into the bulk to be scanned. The most well-known application of this principle is the surface skimming bulk wave (SSBW) which utilizes the IDT in an end-fire configuration [ 11 . With this geometry, transmission between a pair of IDT’s is via an acoustic beam which skims parallel but just below the crystal surface. Recently, several authors have reported on a new type geometry which is a higher frequency extension of the SSBW [2] , [ 3 ] . For this device, an acoustic beam is launched into the

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Manuscript received January 3, 1984,: revised March 19, 1984. This work was supported i n part by the National Science Foundation under Grant ITS-8 113429. 111. A. Goodberlet is with the Department of Flectrical Lngineering, University of Maine, Orono, ME: 04469. D. L. Lee was with the Department of 1:lectrical lhgineering and Laboratory for Surface Science and Technology, University of Maine, Orono, MI; 04469. He is presently with the Raytheon Research Division, 131 Spring St., Lesington, M A 02173.

crystal bulk at such an angle that the beam reflected off the crystal bottom is redirected to the surface and intercepted by a receiving IDT. In this paper, the electrical and acoustical characteristics of the reflected bulk wave (RBW) device are determined theoretically and experimentally for orientations on 9O0-propagating rotated Y-cut quartz. Closed-form expressions are obtained to describe the direction of power flow for the launched acoustic beam as it travels from input to output transducer. The analytical description of the path dependence upon frequency leads straight-forwardly to closed-form expressions for insertion loss and phase versus frequency as well as for temperature coefficient of delay. The analysis shows that the RBW exhibits a number of properties which are significantly different from SAW devices. These include a) an inherently higher frequency of operation, b) a frequency bandwidth which for uniformly weighted transducers is directly rather than inversely proportional to transducer length, c) a center frequency determined not only by the transducer finger-to-finger spacing but also dependent upon the ratio of transducer separation t o crystal thickness d) a nonlinear or chirped phase versus frequency characteristic from spatially unchirped transducers, e) a nonresonant radiation resistance. f ) the capability to synthesize filter designs in which the frequency response is proportional to the convolution of the individual transducer finger weightings, and g) the capability t o modify temperature stability by changing transducer separation of crystal thickness. 11. ACOUSTICWAVE SOLUTIONS

Fig. 1 shows the crystal and transducer geometry t o be analyzed. An identical pair of uniform interdigital transducers (IDT’s) having finger periodicity d and length L are separated by a center-to-center distance 1 on the surface of a rotated Y-cut quartz substrate. In Fig. 1 , the upper case letters X , Y , and Z refer t o the crystallographic coordinate system whereas the lower case coordinates x , y , and z are referenced t o the crystal plate as shown. The quantity O R represents the rotation angle of the Y-cut crystal orientation. Because propagation is assumed to be in a plane perpendicular t o X rather than along it as is the usual case for SAW orientations, the geometry above is referred t o as 9O0-propagating. The top and bottom crystal surfaces are assumed t o be parallel and separated by a distance h . When a time-harmonic voltage is applied to one of the transducers, the electrical signal is converted into a distributed surface stress along its length. giving rise t o an acoustic disturbance which propagates into the crystal. In analogy with optical or

0018-9537/84/0300-0067$01.OO 0 1984 IEEE

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IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-31, NO. 2 , MARCH 1984 Y

Fig. 1. Transducer and substrate geometry for excitation of reflected bulk waves.

Fig. 3. Radiation generated by an IDT on a crystal half-space.

The orientation of the major and minor axis of the ellipse relative to the substrate axis depends solely on the crystal rotation angle OR. It is important t o note from (1) that for fixed material parameters, the size of the ellipse expands or shrinks with increasing or decreasing frequency, respectively. 111. PHASE MATCHING AND POWER FLOW

Fig. 2. Graphical interpretation of phase-matching condition.

electromagnetic diffraction theory, this disturbance may in general be described in terms of a superposition of the outwardpropagating plane waves that are allowed in the given substrate medium. For a general piezoelectric substrate, it is possible in fact t o excite four distinct types of plane waves simultaneously: a quasi-electrostatic, quasi-longitudinal, and two quasi-shear waves [4].Fortunately, however, because of the crystal symmetry associated with the orientation shown in Fig. 1, only an ;-polarized shear wave is excited on Y-cut quartz [5] . Because of the weak piezoelectric nature of quartz, this wave can be treated to good approximation as unstiffened. The velocity of wave propagation is, therefore, nearly independent of the piezoelectric and dielectric constants of the material [5]. For plane wave propagation in the y-z plane of the assumed form $ ( y , z> (y e - i k , Y e-i’3 z the allowed shear wave solutions have been shown to satisfy the following dispersion relation [5] :

kzZC66 +k:C55 + 2 k 2 k 3 C . j 6 = p W 2 , (1) where the elastic constants cii referred to the plate coordinate system shown in Fig. 1 are given by Sykes [ 6 ] . Eq. (1) constrains the tip of the propagation wave vector =; k2 + z^ k3 to lie along the circumference of the ellipse shown in Fig. 2.

A . Infinitely Long Transducer In order to determine the actual propagation directions of acoustic waves excited by the IDT, standard phase-matching arguments can be used [3]. Let us first assume that the input IDT is infinitely long. With reference t o Fig. 3, each individual transducer electrode may be considered as the source of an infinite number of ;-polarized shear plane waves traveling radially outward in all directions. However, for an observer located in the far field at an angle 8, measured with respect t o the substrate surface, contributions from adjacent fingers will only add in phase provided that

Ill d cos e = 2pn,

p = ? i , + 3 , k 5 , . -,

or equivalently,

2 Pn k3 =-. d Eq. (2) is a mathematical statement of the requirement for phase matching and is shown diagrammatically in Fig. 2 . Note that associated with each integer value of p , there are generally two possible solutions having positive k , components, designated by k~ and kR . The two corresponding solutions having negative k 3 components are not of interest. For simplicity of analysis, it is assumed that the frequency of operation f i s sufficiently low so that only the solutions corresponding to p = 1 exist. B e c p e the substrate is anisotropic, the direction of power flow S is generally not in the same direction as k . Rather, for any given E, the direction for the corresponding s^ is obtained by constructing a normal to the wave surface at its point of intersection with k [4] . Fig. 2 indicates the directions of gL and & corresponding to and ER, respectively. With reference t o Fig. 4(a), the meaning of the subscripts 1, and R on k

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GOODBERLET A N D LEE: SUKI~ACI