SURFACE WAVE GENERATION BY INTERDIGITAL TRANSDUCER

where C is the local surface reflectivity of the sub-

considered, it is seen that the diffracted light con- sists of two spectral components as shown in Fig. 2.

proportional to the acoustlc energy flow in the +z direction; the other component arises from sound waves propagating in the -z direction and is at frequency (wo - n). In actual experiments a stray light contribu- tion at the laser frequency, wo is also present.

' strate, see Fig. 1. Thus, if only the +1 direction is

One is at the frequency (U + Q) and its intensity is

1:

P.J. Vella, W.S. Goruk and G.I.A. Stegeman Department of Physics, University of Toronto

Toronto, Ontario H5S l A 7 , Canada

- - l-l - - * - - . a I

I

A ) I \

ABSTRACT. High resolution optical spectroscopy was employed to study 1) the growth of a con- tinuously generated surface acoustic wave (SAW) under interdigital transducers; 2) the generating mechanical displacement field (WF) of the transducer; 3) the basic interaction of a surface wave with a free-metallized surface interface. The observed SAW growth on, and away from, the surface wave resonance for 15- and 25- finger-pair aluminum grids agreed with a simple theoretical analysis which assumed the SAW and the generating ?lDF are actively coupled at the transducer. From a fit of the experimental results to the theory, a value for the effective electromechanical coupling coefficient, K2 of 0.03 ? 0.003 for yz LiNb03 was measured. time at 1 % and, as expected was found to be a uniform standing wave field which did not propagate beyond the transducer region. metallized and unmetallized surface revealed a transition region of -6 acoustic wavelengths where a redistribution in the SAW energy occurred, a reflected SAW was created, and bulk waves were generated.

The MDF of the transducer was observed for the first

Experimental studies of a SAW interacting with an interface between a

I. Introduction

Most theories dealing with the operation of

elements and acoustic these interdigital then, theories wave in assuming parallel. transducers (SAW) do not linear growth predict Although analyse coupling, with the generally propagation a observed single cascade pair successful, surface multiple distance element '+I 14 under the transducer for high coupling materials such as yz LINb03. Furthermore, the insensitivity of elec- trical measurements to the SAW generation mechanism limits the value of such techniques to the determination

ance. In this paper, High Resolution Spectroscopy is used to investigate on yz LiNb03 1) the growth of con-

operating at, and away from, their synchronous frequency: 2) the generating mechanical displacement fields (MDF) , i.e. the 1 kT spatial harmonic of the transducer; and 3) the basic interaction of a SAW with a free-metallized surface interface.

of transducer lump parameters such as electrical irfped-

tinuously generated SAW under interdigital transducers

z

LiNbO,

Fig. 1 Crystal geometry and acousto-optic interaction.

11. Acousto-optic Interaction and Experimental Set-up

If light at frequency, wo Interacts with a SAW of the form SAW makes it possible to distinguish between oppositely

directed sound waves. Furthennore, the inherent stray light rejection (contrast) of the Fabry-Perot can prove particularly useful in the optical probing of regions such as the transducer where stray light contributions are 3 orders of magnitude more intense than the signal of interest.

S(t,z) yin(nt - KZ) + R2sin(Qt 4- K Z ) , (1)

then, the spectrum ofllight reflected in the +1 and -1 direction is given by

1 , c w I

SPATIAL FA8111 - P E R 0 1 I N T E R F f R O Y E T E R

DISTANCE (mm.) Fig. 3 Experimental arrangement f o r observing spec t ra

of l i g h t d i f f r a c t e d by acous t ic dis turbances.

Details of our experimental arrangement are shown i n Fig. 3. Opt ica l r a d i a t i o n from a s i n g l e f r e - quency Ar' laser was focussed a t n o m 1 incidence by a c y l i n d r i c a l l e n s onto the A1-Lm03 i n t e r d i g i t a l s t ruc- ture . The l i g h t d i f f r a c t e d by t h e SAW was passed through a high reso lu t ion Fabry-Perot interferometer and detected by a RCA 931 phototube. The interferome- ter used w a s of t h e confocal type, had a l i n e r i d t h of 1.5 MHz and a f i n e s s e c l o s e t o 100. The s p a t i a l pro- f i l e of the o p t i c a l beam inc ident on t h e c r y s t a l sur- f a c e w a s uniform i n t h e d i r e c t i o n of t h e f ingers and approximately a Gaussian of fu l lwid th a t half i n t e n s i t y of 34~1, measured along t h e d i r e c t i o n of acous t ic propa- gation. f i l e , d i s c o n t i n u i t i e s i n the o p t i c a l sur face r e f l e c t i v - i t y inherent t o the i n t e r d i g i t a l s t r u c t u r e were reduced without introducing excessive s p a t i a l spreading of the d i f f r a c t e d o p t i c a l s igna l . to t r a n s l a t e t h e c r y s t a l r e l a t i v e t o t h e l i g h t beam i n s t e p s of l O u , measured along the d i r e c t i o n of propaga- t i o n . measured with t h i s technique.

With such a width f o r the inc ident beam pro-

A s tepping motor vas used

Acoustic displacements as small as 10-2 61 were

111. Charac ter i s t ics of SAW Growth

SAW growth curves corresponding t o excita- t i o n by 15- and 25- f inger-pair aluminum transducers , operat ing a t t h e i r resonance frequency on yz LiNbO3, are s h a m i n Fig. 4. The gross peaks a t the boundaries of the t ransducers arise from t h e abrupt change i n t h e o p t i c a l r e f l e c t i v i t y , C between the unmetalljzed f r e e sur face and t h e transducer region. Hurlburt has pre- d i c t e d t h a t , f o r materials wi th weak coupling, t h e growth of the acoust ic i n t e n s i t y would be quadra t ic with d is tance along the propagation path. It is evident from Fig. 4 (b) that a t h e o r e t i c a l quadrat ic dependence does not agree with t h e experimental r e s u l t s . A new theory t h a t i s i n very good agreement with the experimental observations on resonance, and which is a b l e t o pred ic t the SAW growth away from t h e synchron- ous frequency of the transducer ( see Fig. 5) w i l l be out l ined i n t h e next sec t ion .

There are two other gross f e a t u r e s i n the growth curves of Pig. 4 t h a t m e r i t d iscussion. The secondary m a x i m a a t the boundary of the transducer a r i s e from an o p t i c a l phenomena pecul ia r t o the type of experiment done, and do not convey any information about t h e SAW. The l i g h t inc ident on t h e i n t e r d i g i t a l t ransducer is r e f l e c t e d of f t h e per iodic metal l ized

- M

L t a i a W

L

L

DISTANCE Imm.1

Fig. 4 Experimental growth curves f o r SAW generated by (a) 15- and (b) 25-finger-pair I D T ' s operat ing a t t h e SAW resonance on yz LiNb03. The I D T boundaries are designated by the peaked l i n e s . d a t a poin ts f o r SAW'S propagating t o the r i g h t . and t o t h e l e f t hand s i d e s , respec t ive ly . The s o l i d l i n e represents our t h e o r e t i c a l f i t and t h e dot ted l i n e shows the quadra t ic f i t .

A and o represent experimental

region i n t o d i f f r a c t i o n orders , the i n t e n s i t y of which depends on the s i z e of t h e ' i n c i d e n t beam p r o f i l e . Thus, the SAW i n t h e transducer region i n t e r a c t s with mul t ip le o p t i c a l sources and, on resonance, the +1 d i f f r a c t i o n order contains an a d d i t i o n a l cont r ibu t ion a r i s i n g from t h e f i r s t order g r i d d i f f r a c t e d s i g n a l i n t e r a c t i n g with t h e SAW. This a d d i t i o n a l contribu- t i o n gives rise t o the secondary peaks observed i n Fig. 4. The o s c i l l a t o r y behaviour of the SAW j u s t ou ts ide t h e transducer boundary o r i g i n a t e s from changes i n the boundary condi t ions between the trans- ducer region and the f r e e surface. This explanation is confirmed by the experiments described i n sec t ion VI.

'

IV. Theoret ical Considerations

Consider an i n t e r d i g i t a l i ransducer of p e r i o d i c i t y L = 2 n / k ~ on yz l i thium niobate . When an

108

I

the d i e l e c t r i c constant, p i e z o e l e c t r i c constant , densi ty and second order e l a s t i c cons tan ts , res- pec t ive ly of l i thium niobate . When l i g h t is inc ident normally on the two t r a v e l l i n g wave f i e l d s , l i g h t is d i f f r a c t e d i n t o t l orders a t an angle e = kT/ko which is independent of t h e e x c i t a t i o n frequency. ( S p a t i a l harmonies of wavevector nkT would produce d i f f r a c t i o n a t angles en = n%/k,,.) Therefore, t h e technique out l ined i n Section I1 can be used t o study the v j f i e l d s .

Near resonance t h e displacement and e l e c t r i c p o t e n t i a l associated with a sur face wave must be in- cluded i n the t o t a l p o t e n t i a l + and displacement v j under t h e transducer. We w i l l restrict t h e discussion to the sur face wave' (and transducer f i e l d ) t r a v e l l i n g i n the +z d i r e c t i o n and write the SAW i n t h e form

The transducer displacement f i e l d is modified by t h e presence of the sur face wave t o w - v w j a F(z) . Subs t i tu t ing i n t o eqni!. (53 and (61, assuming t h a t t h e sur face wave s a t i s f i e s t h e wave equation i n t h e f i r s t approximation, and that D ' ( L ) K << D(z), we ob ta in

- u j , where

Fig. 5 Evolution of SAW a t the f i r s t zero of t h e transducer response function.

where

o s c i l l a t i n g vol tage is applied t o t h e transducer, a p o t e n t i a l is crea ted3 i n the medium which has Fourier components a t odd mult ip les of JLT. The f i r s t s p a t i a l harmonic (1% component) of t h e p o t e n t i a l , + where

induces (v ia t h e material p i e z o e l e c t r i c i t y ) a mechan- ical displacement f i e l d v of the form J

v, - B(z)Gj(y){ei(nt - + C.C.

+ e i(nt + SZ) + C.C.I . (4)

This s tanding wave displacement f i e l d can be consider- ed as the superposi t ion of two t r a v e l l i n g wave f i e l d s which then can ind iv idua l ly couple t o sur face waves propagating i n the appropriate d i r e c t i o n . This coupling occurs only under the transducer which def ines t h e boundaries of the s tanding wave f i e l d . For convenience, we now consider t ransducer e x c i t a t i o n i n two l i m i t s , f a r o f f resonance and near resonance.

Far of f resonance w e can assume that t h e coupling t o , and the presence o f , sur face waves under the t ransducer can be neglected. The p o t e n t i a l , 4 and displacement, v j must s a t i s f y Maxwell's Equations and the mechanical wave equation a t every poin t , subjec t of course t o t h e electrical and stress boundary condi t ions a t the surface. Thus,

?

'ik"ki - eikmVk,mi = o ( 5 )

and "j CijkEvk,Li - eki j ' ,k i ' ( 6 )

2 and I( is the e f f e c t i v e electromechanical coupling constant. assumed to be a c t i v e l y coupled, then, from t h e con- serva t ion of energy p r i n c i p l e , w e can write

I f the two modes a,(z) and a2(z) are

da2 i- * k a2 - alll'. (12) dz T

The s o l u t i o n t o t h e coupled mode eqs. ( 8 ) and (12) are w e l l known, and f o r a SAW or ig ina t ing a t z = 0 , t h e energy of the generated SAW propagating i n the +z d i r e c t i o n i s given by

(13) 2 P - (const.)shin z / r ,

It is i n t e r e s t i n g t o note t h a t t h i s formula reduces t o a quadra t ic dependence on z when r i s l a r g e ( i .e . , I 'K /ZUN >> 1, where N is the number of f inger -pa i rs ) . Moreover, awas from t h e IT(K - %)I21 reduces t o a (sin x ) / x -1) and K is t h e wave vec tor of t h e SAW.

synchronous frequency >>21, q d the transducer response

dependence, where x * nN(K/$

V. Generating F ie lds and SAW Growth Curves

The mechanical s tanding wave f i e l d of a 25-finger-pair aluminum transducer on yz LiNbO3 w a s s tudied by l i g h t s c a t t e r i n g , and the r e s u l t s are shown i n Fig. 6 . The o p t i c a l probe w a s l O O u wide ('3 f inger -pa i rs wide) and the transducer w a s exc i ted a t 58 MHz, f a r below t h e resonance frequency of 105 MHz. The magnitudes of oppomitely propagating dis- placement f i e l d s were equal a t every point and, as

t t t

DISTANCE Imm)

X

t

Fig. 6 Experimental p l o t of t h e MDF a t 1%.

Typical r e s u l t s f o r SAW growth on resonance are shown i n Fig. 4. The exce l len t agreement between experiment and ca lcu la t ions v indica tes the theory out- l ined i n t h e previous sec t ion , and from these growth curves a va lue of r - 350 t 30p (-11 acous t ic wave- lengths) w a s found. electromechanical coupling cons tan t , K2 of 0.030 f 0.003 is i n good agreement with Williamson's Av/v measurements4 f o r open c i r c u i t e d metal s t r i p s on yz LlNbO3.

The derived value f o r the

From the t h e o r e t i c a l treatment of sec t ion I V , i t can be shown that t h e response funct ion of a 25-finger-pair i n t e r d i g i t a l t ransducer on yz LiNbO3 is zero when IK/kT-1J - 0.04. occurs a t approximately 101.1 MHz, where the r e s u l t s shown i n Fig. 5 were obtained. Since the two opposite- l y d i rec ted SAW were of equal i n t e n s i t i e s a t each point along the propagation path, only one wave has been p l o t t e d i n Fig. 5.

The f i r s t zero thus

V I . I n t e r a c t i o n of SAW with Metallic Edge

It was observed i n s e c t i o n 111 t h a t the normal component of t h e SAW undergoes per iodic o s c i l l a t i o n s on leaving the t ransducer region. W e had s t a t e d then t h a t these energy f l u c t u a t i o n s could be in te rpre ted as a r e d i s t r i b u t i o n i n the SAW energy as t h e wave ad- jus ted t o new boundary condi t ions outs ide t h e m e t a l - l i z e d region. This problem ( i n a somewhat s implif ied form) w a s pursued f u r t h e r , and the i n t e r a c t i o n of a SAW with t h e edge of an aluminum pad, 1200 R th ick , deposited on t h e propagating sur face of a pz L m O 3 c r y s t a l w a s invest igated. The sample configurat ion is shown i n Fig. 7. A 1311 o p t i c a l beam (< 1 acous t ic

t

O L O D

OISTANCE(mm)

Fig. 8 I n t e n s i t y of l i g h t d i f f r a c t e d by a SAW t r a v e l l i n g from l e f t t o r i g h t through aluminum pad with edges a t 3.118 mm and 0.118 rum.

wavelength) was used t o probe the free-metallized boundary i n s t e p s of 1 O u . Experimental r e s u l t s are shown i n Fig. 8. The l a r g e changes i n o p t i c a l s i g n a l a t 3.118 mm and 0.118 mm a r e due to the d i f fe rence i n o p t i c a l r e f l e c t i v i t y between t h e pad and t h e f r e e sur face . The o s c i l l a t o r y behaviour observed a t the pad boundaries is i n d i c a t i v e of the r e d i s t r i b u t i o n of SAW energy due t o the change i n electrical boundary condi t ions encountered a t the in te r faces . This t r a n s i t i o n region extended -3h on e i t h e r s i d e of t h e i n t e r f a c e . The magnitude of t h e o p i t c a l s i g n a l measured on and of f t h e pad i n d i c a t e s t h a t the SAW l o s e s less then 2% of i t s i n i t i a l energy a t the two i n t e r f a c e s . The re f lec ted SAW was found to con- s t i t u t e less than 0.03% of the incident SAW and, therefore , t h i s 2% l o s s i n energy is mostly due t o bulk wave generation. Bergmann-Schaeff er5 type experiment i n which a wide o p t i c a l beam was used t o probe the c r y s t a l d i r e c t l y under t h e pad.

This w a s confirmed by a

V I I . summary

High r e s o l u t i o n o p t i c a l spectroscopy has proved t o be a h igh ly v e r s a t i l e t o o l i n t h e s tudy of SAW devices . SAW growth measurements have been done a t , and away from, t h e t ransducer synchronous f r e - quency on yz LiNbO3 and were found t o be i n e x c e l l e n t agreement w i t h a theory t h a t p r e d i c t s exponent ia l type of coupling a t the SAW resonance. From the theoret- i c a l f i t t o t hese measurements, t he e f f e c t i v e e l e c t r o - mechanical coupling c o e f f i c i e n t ( fo r yz LiNbO3) , K2 was found t o be 0.030 i 0.003. The gene ra t ing f i e l d s of t h e t ransducer a t 1 % were inves t iga t ed and t h e method was employed t o d e t e c t l oca l i zed mechanical f lows in t h e i n t e r d i g i t a l g r i d s t r u c t u r e . i n t e r a c t i o n of a SAW wi th a me ta l l i zed boundary on y z LiNb03 w a s i nves t iga t ed . -6 a c o u s t i c wavelengths w a s observed i n which t h e SAW underwent a r e d i s t r i b u t i o n of energy, a r e f l e c t e d SAW occurred and bulk waves were generated.

The b a s i c

A t r a n s i t i o n region of

1.

2 .

3.

4.

5 .

References

P i J . Vella, G.I.A. Stegeman, H. Zul i an i , and V.M. Ristic, J. Appl. Phys. 9, 1 (1973).

D.H. Hurlburt , 1972 Ul t r a son ic Symposium Proceedings ( I n s t i t u t e of E l e c t r i c a l and E lec t ron ic s Engineers, New York, 19721, p. 417.

H. Engan, IEEE Trans. E lec t ron Devices ED-16, 1014 (1969).

R.C. Williamson, 1972 Ul t r a son ic Symposium Proceedings ( I n s t i t u t e of E l e c t r i c a l and E l e c t r o n i c s Engineers, N e w York, 1972). p. 323.

L. Bergmann, U l t r a son ic s (G. B e l l and Sons Ltd. , London 1938) pp. 164-184.