Effects of Bonding and Electrode Layers on the Transmission Parameters of Piezoelectric Transducers

Used in Ultrasonic Digital Delay Lines

Absfracf-In ultrasonic delay lines with thickness-driven piezo- electric transducers, it is necessary to have electrode and, possibly, bonding layers in the sound transmission path. If these layers have characteristic impedances that are substantially different from those of the piezoelectric transducer and the delay medium, they act as mismatched transmission line sections between the trans- ducer and its load, and transform the normally real load impedance into a complex one.

The resulting shifted and deformed response curves are com- puted for a large number of layer parameters by means of Mason's equivalent circuit. From these plots, information as to permissible layer thickness, etc., may be obtained and used in the design procedure of ultrasonic delay lines.

In digital delay lines, where linear phase response is a design requirement, any intermediate layers should be as thin as possible or be closely matched to the delay medium in order to avoid fast ripples in the frequency response, which would give rise to side lobes far away from the main signal in the time domain.

I. IKTRODUCTION

LARGE NUl113ER of ultr:isonic delay lines use thickness-driven ~)iczoelectric tr:lnsducers, in which the electrode platings are part of the sound

transmission path. At frequencies above, say, 100 MHz the piezoelectric layer:: n ~ y coneist of nmterials like CdS or ZnO, which can be depo.sited on the substrate delay medium without having to interpose additional layers other than electrodes. However, up to now, no high-coupling f&or tr;tnscluccrs have been made by such techniques, P O tllut nlaterials, be they crystalline, like quartz or l i thium niohte, or ceramic, like sodium- potassium niobatr, nwd to be hondccl to the substrate by means of a suitable adhesive layer, n-hich also is in the sound transmission path.

At higher frtquencics these layers cannot he assumed to be ncyJigi1)ly thin conlpared vith the round wave- length and act, tlmcfore, as transmission line sections that modify the overall transfer function of the ultra- sonic device. Many authors, [ l ] through [ 7 ] may serve as a sample, have dealt with various aspects of this fact, and ha re suggested its exploitation to increase t h e band- pass of a delay line by using a wave filter rcprcsentation to determine t h e proper clin~ensiona of an intennediate layer. However, tllese treatment,s tendccl to diFregard the

%,, = pc' (1)

The ilnpedance of Z h prem1ted to the hack face of tlle piezoelectric layer eitller equals Zob (= 0 if missing) or is ol)tninetl, if intermediate layers are present, as follows.

- J Z o / S I N y 7 / \ ' Z o T A N ( Y ' 2 '

SITTIG: EFFECTS OE' nomIs ( ; ASD ELECTRODE IAYERS OF PIEZOELECTRIC TRASSDUCERS 3

PIEZOELECTRIC LAYER

( : l )

l Z O n T A N ( y n l 2 l

INTERMEDIATE LAYER

(11)

I.

t a TRANSDUCER I N P U T ,TR:::?:oN[ Z a t TRANSDUCER OUTPUT

T"

In the sanle manner, one postmultiplies the right-hand side of ( 7 ) with all matriccs clescrihing the intcrmedi:ltt~ layers between the piezoelectric one and the t ~ ~ n n s m i s ~ i o n nwdium of impetlance Zot. In terms of the new l u n t r i s with components A , L', C. and D, one c a n now ohtain tlle voltage transfer ratio E,/E,? of tlle arrangement show~l

4 IEEE TRASSACTIOK'S O S SOSICS A S D CLTRASONICS, JANDARY 1969

SITTIG: EFFECTS OF BONDING AXD ELECTRODE LAYERS OF PIEZOELECTRIC TRANSDUCERS 6

0.2 0.4 0.6 0.8 1.0 1.2 L4 I 6 1.8 f Ifg

Fig. 3. Input conductance ratio of an unhacked transducer with k = 0.2 attached to a transmision medium of impedance z as shown.

-400

W VI 2 -600 n

+ l

P

f / fo

Fig. 4.

0 5 0 2

Figs. 4-5. Insertion gain and phasc through transducers, as in

X , = XI = 0, in the arrangement of Fig. l ( c ) . The t ransmis Fig. 3, hctwecn untuned terminations I?, = R I = I/W~C,, and

sion medium is assumed to he lossless.

replacement of y by (v + 6) as long a s 6 << 1, Since in this case

6 Pbllb*O/ZO, (24)

the frequency of maximum response f,,z is simply lowered in proportion to the mass loading of the back face.

As tbl is permitted to increase, an additional effect

0 -

-10-

m

z z 9 -30-

k? -40- 0

g

0

-20-

z

U) W

-50-

f/f,

Fig. 6.

/

I \

f If,

Fig. 7.

-400

VI W

9 -600

l- .' ,

2 -800

? 2 -1000

3 0.5 , 0.2 /'

0 I /' a I

-1200 -. ,I/_ ---L. - 0 2 0.4 0.6 08 1.0 1.2 1.4 1.6 1.8

f I f o

Fig. 8.

Figs. &S. Same as Figs. 3 through 5, for transducers with 1; = 0.6.

realizing t.lmt. l ) t'he stress a t tllc far end of the backing layer must vanish and 2 ) that the piezoelcctric layer will produce a maximum output voltage if it straddles t,he stress maximum symmetrically. Since the presence of the backing layer causes the stress maximum to be shifted towards t.he back of the piezoelcctric layer for a given frequency, the response maximum will be attained at a frequency sufficiently lower to restore the stress max-

takes place, which may most easily be visualized by imum to the center plane of t.he piezoelectric layer.

6 IEEE TRAXSACTIONS o s SONICS ASD VLTRASONICS, JANUARY 1969

The effect of the electrode layer of impedance Zofl = ptlctl and normalized thickness t t l hetween t,he piezo- electric layer and the transmission nlcdium of impedance Zot = ptc, is more complicatctl. Its transmission line ac- tion rnakes the t,ransclucer tee a transmission n~ctiiunl of impedance

2, = ZorL(zof + jzorl t an rtl)l(zofl + j z o t tan rtd. (25) Ol)viously, if t,he layer n ~ t c l l c s t h e impedance of the transmission medium, it simply forms an extcmsion of t h e latter and does not, cause any shift. of f,.. Howcver, in t.he rxngc t f l < 1, the imaginary telmw in (25) cause f,,, to increase if Zotl/Zot < 1 ancl to (Iecrrase if Z,,,,/Z,,, > 1.

It is convenient to introduce :it, this point a shorthand notation to describe an arrangement of layers. In the order depicted in Fig. I , one 1ist.s ( z , t ) for each layer as tlefinctl hy (18) and i19). For layers assumed to have infinite extension, such :IS an absorptive hacking layer or tfhr transmission nlediunl, thc corrrspontling entry t = m is omittetl. The piczocllcctrir layer nerds only to he de- scrihcd by an ent,ry for the coupling factor h. and dcsig- natcd as ruch by the Ictter P. Thus the notation i0..5, 0.1) - P(0.2) - (0.2, 0.1) - i1.01 n-odd dcscrit)c a trans- tlurer consikting of an unbackcd electrode l a y r of imped- ancc rat'io 0.5 and normalized thickness 0.1, the piczo- clcctric layer of coupling factor 0.2, ancl another electrode of impedance rnt,io 0.2 and normalized thickness 0.1, a l l attached to a transmission medium of unity impcrlanrc ratio.

An overview of the effects due to elcct,rode platings may be obtained from Figs. 9 t.hrough 16, wl~icll show tl1c: insertion gain and pllnre response of transducers with identical electrode platings on eithcr face, spCcifica11y the arrangement ( 2 , t ) - P(0.2) - ( 2 , t ) - (1.0) for 0.1 5 z 5 5 and 0.05 5 t 5 0.3, which covers most caws of t,echniral interest. The curves for z = 1 illustrate the aforementioned fact that the hacking layer, e w n if matched, will lower f,,i, but will not cause phase distor- t ion. In all other cases even a moderately nlismatchcd or very thin electrode layer will curtail the handwic1t.h and pause discernible phase distortion. This point ncrds to be c*onsidcred for the evaluation of deposited thin-film trmsducers a t frequencies exceeding 100 MHz, sincr it is rawly possible to match the elcct.rotle layers to either suhdrate or piezoelectric layer, or makc them thin cmough not to matter.

V. TIIE IKFLUESCE OF B o s n ~ s o L A Y E R S

At frequencies helow 100 MHz the transducr>rs of :I

dchlay line arc usually bonded t o the material constitut- ing t,he (Jrlay path. Essentially, two hontling tecl~niquc~s are in use: I ) thermo-conlpression hontling with indium or lead, and 2 ) adhesive bonding using epoxy or a sinlilar polymer adhesive.

Typically, the n1et:tllic bonds resulting from the first technique involve layers with characteristic impednncc ratios in the range o..j 5 z 5 1. Plastic polymers, on the other hand, typically fall in the range 0.1 5 z 5 0.2, eo

SITTIG EFFECTS OF BONDIXG AND ELECTRODE LAYERS OF PIEZOELECTRIC TRANSDUCERS 7

m -10 0 - 1

- 5 0 ~

0 . 2 0.4 0.6 0 8 l 0 I 2 I 4 1.6 1.8 f / f o

Fig. 9.

f / f o

Fig. 10.

04 06 08 I O I 2 1.4 1.6 f / fo

Fig. 11.

-12001 I 0.2 0.4 0 6 0 8 1.0 I 2 14 1.6 1.E

f / f o

Fig. 12.

111 0

Fig. 13.

-1 U) W W 6 -200 W n

z -1200

0 2

0-

m - IO -

0

E L

- 2 0 ~

0 - 3 0 -

0 k- 5 - 4 0 - m E

-50 -

-60 0.2 -

I

f / f o

Fig. 14.

0.4 0.6 0 8 1.0 I 2 1.4 1.6

f / f o

Fig. 15.

-m -

-400 -

-600 -

-800-

-1000

-1200 t 0 2 04 0.6 0 8 1.0 1.2 1.4 1.6 1.8

f / f o

Fig. 16.

with R , = R Z I/w,C,, with electrode laycrs of the normalized thicknrss t and impedance ratio z as indicated. Figs. S1-16. Insertion gain and phase of a pair of piezoelectric lnycrs with k = 0.2 in the arrangement of Fig. l((;)

8 IEER TRANSACTIONS OK S O N I C 8 AND ULTRASONICS, JANUARY 1969

0 2 0.4 0.6 0 8 1.0 I 2 1.4 1.6 f / f o

Fig. 17.

n c -500- 3

-600- 3

l- 3

-700-

2 -800- - -9001 ' 1 I I

0.2 0 4 0 6 0.8 I O 12 14 1.6 f / f o

Fig. 18.

-U"- P(0 21-107, t ) - ( l 1

-20- m

z V

-30- - d z 2 - 4 0 - K W v) z -50 -

-60 'l I l

0.2 0 4 0.6 08 I O 1.2 14 1.6 f/fo

Fig. 19.

n

5 -600 - a l- 3 0

c' -800- L

.lOOOl ' I ! 1 1 1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

f / f o

Fig. 2 0 .

Figs. 17-20. Insertion gain and phase of a pair of piezoelectric layers, affixed to the lossless transmission medium bp a bond of impedance ratio z and normalized thickness t as indicated.

-10 -

m V

- 2 0 -

5 * -30- 0 k -40-

z

z

W v)

-50 -

-60-

f / l o

Fig. 21.

I 1

0.2 0.4 06 0 8 I O 1.2 1.4 1.6 f / l o

Fig. 22.

f/f,

Fig. 23.

v)

0

5 -800-

$ - l O O O -

p' -1200

a l- . l-

- z -

-1400 ' 0.2 0.4 0.6 0.8 I O 1 . 2 1.4 1.6

f /lo

Fig. 2 4 .

SITTIG: EFFECTS OF BONDIKG AKD ELECTRODE LAYERS OF PIEZOELECTRIC TRANSDUCERS 9

Figs. 25-26. Insertion gain and phase if the transducrrs are

three quarter-wave layers of the impedance ,ratios indicated. affixed to the transmission medium with bonds consistmg of

The curves for P(02)-(1) having no intermcdlate layers what- ever are shown for comparison.

quired is det,ermined by the permissible ripple in the passband and by the minimum thickness achievable for ench layer. As the frequency of operation approaches 100 &ZHz, any such scheme hccomcs impract,ical, since it be- comes progrcssirely hardc3r to olhkin adequate dimen- sional cont,rol.

-60” 1 _ L _ ’ 05 06 07 08 09 1.0 I I 1.2 13 1.4

f / fo

Fig. 25.

f / fo

Fig. 26.

quency. If the layer is made a multiple of h / 4 , the paes- band again is symmetric.

Thus the following stratagem suggests itself, i f st,rongly mismatched layers such as adhesive bonds are unavoid- able and cannot be made thin enough. First, one may make this layer a quarter wave to accomplish symmetry of the passband. One then uses a series of quarter-wave layers with suitably stepped characterist,ic impedances on either side to match to the offending layer within a given ripple specification. For a three-layer bond in the combi- nation P ( 0 . 2 ) - (2, 0.5) - (0.1, 0.5) - (Z, 0.5) - ( l ) , this is shown in Figs. 25 and 26. B u t even if one could find materials with z about 0.25, the amplitude ripple would be about 8 dB over the usable passband, so t h a t more layers would be needed to reduce the ripple in the passband to acceptable values. This scheme appears prac- tical only as a three-layer bond with 0.5 5 zot2 5 2.

Various other stratagems are possible, since, concep- tually, a layer of intermediate impedance can be made up by stacking alternately thin high- and low-impedance layers, so that a small number of such layers will consti- tute an approximation. Again, the number of layers re-

VII. CONCLUSIOXS The conclusions to be drawn from the preceding sec-

t,ions depend lnrgclg on the technical constraints imposed on the problem at hand. For a device with minimal loss and a short, transient response, one needs [S] phase linearity ancl an amplitude response rolling off from the frequency of maximum response f,,2 not faster than sin4 (sf/fn,\). As one realizes t,llat thc effects of bandpass vari- ations duct to the presence of intermediate layers are caused hy their transforming tllc, load impedance seen by the piezoelectric layer, one may reduce most of these effects by provitling an nhsorpt,ive backing, which consti- tutes a constant load. Rou-ewr, hy t l x s:trnC: token, this backing ahsorbs encrgy, thus increasing the inscbrtion loss, and it may create spurious signals if its far cnd returns residual reflections. Moreover, if the backing has to be att,aclled by means of another intermediate layer, the problem may even be furtllcr complicated.

If one ckqigns thr transducers of an 11ltrasonic device with all thcir layers on the basis of loss-free transmission line sections, oncl, in essence, minimizes distortions by breaking them up into smaller but faster varying terms. In the time domain, this means that time side lobes far from t h e main response may be generated, which cause int,ersymhol interference among many channels in a time- multiplexetl transmission system, rather than among nearest neighbors only. Whether this is acceptable de- pends on the circumstances. Thus it appears best to keep the number of intermediate layers low. Response distor- tions can t,hen be only minimized if bhe layers are as closely matched to the transmission medium and made as thin as possible. The discussion in Section 111 indicates that polymer adhesive bonds cease to be useful a t fre- quencies above 100 MHz, unless the bonds can be made substantially thinner t,hm tho 0.1 pm achievable a t pres- ent [17]. However, indium or lead bonds, which are better matched to the transmission media of technical interest, extend the posibility of making bonded high- coupling-factor transducers with their inherently lower insertion loss up to several hundred megahertz.

REFERENCES [l1 H. J. McSkimin, “Transducrr design for ultrasonic delay

[21 D B. Dianov, “Ultrasonic radiation through plane-parallel

131 K . S Aleksandrov, L S. Gurevits, and E. I. Kamenskii, “Ef- feet of an intermediate layer on the frequency characteristics

170-177, 1960. of ultrasonic delay lines,” Sov. Phys. Acous., vol. 6, pp.

141 W . F. Konig, L. B. Lambert, and D. L. Schilling, “The bandwidth, insertion loss, and reflection coefficient of ultra- sonic delay lines for backing materials and finite thickness

linrs,” J . Acous. Soc. Am., vol. 27, pp. 302-309, 1955.

lavers,” Sou. Phys. Acous., vol. 5, pp. 30-35, 1959.

10 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-16, NO. 1, JANUARY 1969

bonds,” IRE Internat’l Conv. Rer . , vol. 9, pt . 6, pp. 285- 295, 1961.

151 L. G. Merkulov and L. M. Yablonik, “Operation of a

intcxrmtrdiat,e layers,” Sou. Phy.s. r i c o ~ . , vol. 9, pp. 365-372, damped piezoelectric transducer contaming a nuxnhrr of

1964. 161 G. Kossoff, “The efferts of backing and matching on the

performance of piezoclcctric ceramic t,ranstlwers.” ZEEE

1966. I‘rcms. Sonics and Ultrmsonics, vol. SU-13, pp. 20-30. March

171 C. F. Brockelsby. J. S. P:~lfreeman, ant1 It. JV. Gil)son, U l - trusonic Delay Lines. London: Iliffe, 1963.

L81 1 4 1 . K. Sittig, “High speed digital delay linc design: a re- statcmcnt of somc basic considerations,” Proc. I E E E , vol.

(91 J. R. Klauder. A. C. Price, S. Darlington, and W . J. Alhcr- shcim, “The theory and design of chirp radar,” BrU Sus. Tech. J . , vol. 39. pp. 74.5808, 1960.

C101 Sec, for cxample, C. E. Cook and M . Brrnfeld, R a d a r Sig- nals. N c : w York: Aratiemlc, 1967, p. 46.5.

1111 E . K. Sit t ig, “Transmision parametcm of thirkncss-driven pic.zor.lc~tric t r : ~ n s d ~ ~ w r s arranged in multilayer configura-

56, pp. 1194-1202, July 196s.

tions.” I E E E Trans. Sonics and Ultrasonics. vol. $U-14. pp.-167-174, October 1967.

1123 D. A. Berlincourt, D. R. Curran, and H. Jaffe, Physical Acomfics , W . P. Mason. Ed. h-ew York: Academic, 1964,

[l31 M. Onoe. “Relationships hctwvcen input admittmce and v01 1, pt; h . pp. 233-242.

transmission chnractrristirs of an ultrasonic delay line,” I R E Trans. Ultraso,& Engi?zre~ing, vol. UE-9, p p , 42-46,

141

1151

1 161

December 1962. H. J. Riblet, “General synthrsis of quartcr-wave impedance

niques, .col. MTT-5, pp. 3643, January 1957. Also B. K. transformers,” I R E Tmns., Jfirroumve Theor21 and I‘ech-

Kinarirvala, “Thcory of casratlrtl struc.tures: 1osslc.ss trxns-

L. Young, “Synthesis of multiple antireflection films ovcr a mission lines,’! Bell Sus. T e d . J., vol. 45, pp. 631450, 1966.

prescribed frcquenc,p 11:lntl,” J . O p t . Soc. Am. , vol. 51, pp.

J. T. Cox, G. Hass, :~nd R. F. Rownt.rr,r, “Two-layer anti- reflection coatings for lass in the ncnr in f rmd ,” Vacztum,

967-974, 1961.

[l71 J. S. Joncs, “PHF ticlay line bonding,” prcsentcd a t the vol. 4, pp. 445455, 1954:

1966 Ultrawnirs Symp., Clevelnud. Ohio. paper N-8.

High-Isolation Single-Crystal Magnetoelastic Delay Lines

Abstract-The two-port operation of a magnetoelastic delay line employing a single rod of yttrium iron garnet (YIG) and a LLroller coaster” axial magnetic field configuration is described. It is shown that efficient coupling near the edges of the rod face is possible by using thin sheets of magnetic material to properly shape the static magnetic field near the RF coupling loops. It is also shown that the leakage of the undelayed signal may be significantly reduced by properly reducing the axial static magnetic field near the center of the YIG rod. An insertion loss to the desired delayed signal smaller than 35 dB and an isolation to the undelayed signal larger than 72 dB, with the delay lime operating near 2 GHz, are reported.

W 14: HAVE ACHIEVED two-port operation of a magnetoelastic delay line hy employing a single rod of yttrium iron garnet (YIG) and a roller

coaster axial magnetic field configuration, such as tha t proposed by Strauss [l] and operated hy Collins e t al. [2]. However, we have used different means to achiere the necessary field shaping and, morc important, have achieved lower insert.ion loss of the desired delayed pulse and reduced leakage of the undelayed pulse. These im- provements are obtained 1 ) by using thin sheets of mag- netic material to properly shape the static magnetic field, so tha t efficient coupling of the RF magnetic field into the spin waves can occur near the erlgw of the rod face where

The author mas with the Acrospacc Group, T h e Boeing Com- Manuscript receivcd July 19, 1968; rrvistd Septen~lwr 6, 1968.

pany, Seattle, Wash. 98124. Ho is now with the Department of

Tex. 77843. Electrical Engineering, Tcxas A&M Vniversity, College Station,

the R F coul)ling 1001)s arc placcd, and 2) by properly re- ducing the axial static magnetic field near t,he center of the rod, so that the direct mzlgnetostatic coupling hetween input and output port is practically eliminated.

Beforr describing our dcvirc in tletnil, we shall review briefly the considerations on which t,hc design of surh devices are based.

Excitation and detection of magnetoelastic waves in fcrrimagnet,ic nmterials by direct, photon-magnon con- version, of crucial irnport,ance for the operation of prac- tical magnet,oc>lastic delay lines, has been carefully studied in the past fern ye:lrs. It has bcen found that, the energy conversion from electromagnetic to magnetoelastic waves in ferrimagnetic crystals with R nonzero magnetic field gradient is much more complex than t.he direct energy conversion process at, the turning points of the rnngnetoclastic waves, as described by Strauss [3]. It is presently beliewd t,hat t,he coupling from rlcctrornagnetic waves to exchange-cloIninated spin waves is not a direct process. The electromagnet,ic W ~ V C S are first coupled to the nlagnet.ost,atic waves 141, which are then converted into exchange-dominat’ed spin n-nves, and finally into clastic waves, when a proper field gradient exists within the ferrimagnetic medium [.5]-[7]. Two of the, .e conver- sion processes are of particular importance: one is the electrornagnetic -+ magnetostatic and the other the spin + elastic. For the spin -+ elastic process, st,ablc trajec- tories along a ferrimagnetic roc1 may exist only when the