[IEEE 1981 Ultrasonics Symposium - (1981.10.14-1981.10.16)] 1981 Ultrasonics Symposium - Power...

POWER DEPENDENCE OF A G I N G I N SAW RESONATORS

W.R. ShreveZ R.C. Bray$ S . E l l i o t t and Y . C . Chu+

*Hewlett-Packard Laborator ies, 1651 Page M i l l Rd., Palo A l t o , CA 94304

+Hewlett-Packard Santa Rosa Technology Center, Santa Rosa, CA 95404

Abs t rac t

The aging r a t e o f SAW resonators i n o s c i l l a t o r s has been found t o vary as the opera t i ng power i s va r ied . I nc reas ing the power can cause the aging r a t e t o va ry from a few p a r t s per m i l l i o n (ppm) per year t o more than a p a r t per thousand per year . Tests have been run p a s s i v e l y (no power d i s s i p a t e d i n the resona to r ) and a c t i v e l y a t l e v e l s from -10 dBm t o +20 dBm.

The major cause o f the power dependent aging i s a c o u s t i c a l l y induced m i g r a t i o n o f t he aluminum i n t h e coup l i ng transducers. The a d d i t i o n o f a small amount o f copper t o t h e f i l m was found t o reduce o r e l i m i n a t e these m i g r a t i o n e f f e c t s and a l l ow s t a b l e ope ra t i on a t h igh power l eve l s . I n t h i s study, d e t a i l e d t e s t r e s u l t s are described, t h e m i g r a t i o n phenomenon i s analyzed, and t h e s t ress i n t h e resonator i s q u a n t i t a t i v e l y r e l a t e d t o t h e power d i s s i p a t e d i n t h e resonator.

I n t r o d u c t i o n

I n the past, sur face acous t i c wave resonator (SAWR) aging s tud ies have been conducted w i t h l i t t l e regard f o r t he d r i v e l e v e l used. Many t e s t s ’ ” have been conducted p a s s i v e l y where t h e SAWRs are n o t dr iven. I n o the rs t h e d r i v e l e v e l i s as h igh as 0.1 t o 5.0 m i l l i w a t t s 3 9 4 . Tests have shown t h a t t he d r i v e l e v e l i n bu l k acous t i c wave resonato s BAWRs) a f f e c t s t h e c r y s t a l ’ s resonant frequency‘, (and a s t rong frequency dfpendence on d r i v e l e v e l has been repo r ted f o r SAWRs . A d d i t i o n a l l y h i g h d r i v e l e v e l has been i d e n t i f i e d as the cause o f m i g r a t i o n o f aluminum i n SAWR transducers7. These data suggest t h a t d r i v e l e v e l i s a key parameter a f f e c t i n g the s t a b i l i t y o f SAWR o s c i l l a t o r s .

I n t h i s work, t h e e f f e c t o f d r i v e l e v e l on aging r a t e i s examined w i t h spec ia l a t t e n t i o n t o t h e onset o f a c o u s t i c a l l y induced m i g r a t i o n o f aluminum f i l m s . The e f f e c t o f s t ress i n the f i l m and t h e e f f e c t o f doping the f i l m w i t h copper are both discussed.

Aging Tests

Our f i r s t t e s t s o f the e f f e c t o f d r i v e l e v e l were conducted a t 160 MHz w i t h one-port SAWRs. The dev ice des ign and f a b r i c a t i o n techniques used were descr ibed i n d e t a i l i n a prev ious paper8. I n t h i s t e s t , dev ices were made i n the same manner and the c i r c u i t was mod i f i ed t o change the d r i v e l e v e l

d u r i n g the t e s t . I n i t i a l l y t he devices were run a t a d i s s i p a t e d power l e v e l Pd = -7 * 1 dBm. (The power l e v e l was determined by probing the c i r c u i t w i t h a vec to r vo l tme te r and checking t h i s va lue by assuming c u r r e n t l i m i t i n g i n the t r a n s i s t o r amp1 i f i e r . )

I n the past7, d r i v e l e v e l has o f t e n been cha rac te r i zed by power a v a i l a b l e from a source. Th is power can be d i f f i c u l t t o determine i n an o s c i l l a t o r s ince i t depends on source impedance as w e l l as the source vo l tage o r cu r ren t . I n t h i s study, we use power d i s s i p a t e d i n the SAWR s ince t h i s can be determined from the SAWR equ iva len t c i r c u i t and the c u r r e n t through or vo l tage drop across the resonator independent o f the source and load.

As shown i n the appendix, t he power d i s s i p a t e d i n the resonator , Pd, i s r e l a t e d t o t h e peak s t r e s s by the express ion

when Jm i s a constant o f the m a t e r i a l , Q u i s the unloaded resonator Q, and L and W are t h e e f f e c t i v e c a v i t y l e n g t h and w i d t h respec t i ve l y . Th i s s t ress, t h e peak compressional s t ress i n the propagat ion d i r e c t i o n , can be used t o c h a r a c t e r i z e the s t ress f i e l d a t t he p i e z o e l e c t r i c surface, b u t i t i s accompanied by a s t ress perpendicu lar t o the propagat ion d i r e c t i o n T22 and shear s t resses T i 2 and T21. The r a t i o o f these s t resses i s determined by the c r y s t a l constants and c r y s t a l c u t as discussed i n the appendix. T h e i r r e l a t i v e importance t o aging i s n o t known.

For the 160 MHz resonators tes ted a t -7 dBm, t h i s peak s t r e s s was (2.1 ? .2) x lo7 N / d . The aging r e s u l t s obta ined on seven o s c i l l a t o r s r u n f o r 162 days are shown i n F i g u r e 1. A t t h a t t ime the t e s t was i n t e r r u p t e d and the c i r c u i t s were mod i f i ed t o increase t h e d i s s i p a t e d power by 6 dB. (The peak s t ress doubled.) The c i r c u i t changes a l so caused a s h i f t i n t he o s c i l l a t o r frequency. T o f a c i l i t a t e p l o t t i n g on a s i n g l e graph, the reference frequency was adjusted t o cancel t h i s s h i f t and the t e s t was r e s t a r t e d . The devices were aged f o r an a d d i t i o n a l 190 days a t t h i s new d r i v e l e v e l . The r e s u l t s are shown i n F igu re 1 t o the r i g h t o f the do t ted A c lose examination o f t he data shows t h a t 3 o s c i l l a t o r s remained e s s e n t i a l l y unchanged w h i l e the o the r 4 show a s i g n i f i c a n t decrease i n t h e i r aging

l i n e .

94 - 1981 ULTRASONICS SYMPOSIUM 0090-5607/81/oooO-0094 $00.75 0 1981 IEEE

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8.0 I 1

2 6.0 a a v

4.0 LL

0 +J

0 7 2.0

0. 0

I D -2. 0 ' J 0 50 100 150 200 250 3EO 353

T i m e (days)

Figure 1. Aging of 160 MH SAWRs. First 162 days

x 107nt/m . at a peakptress of 2 x 10 5 nt/m2; last 188 days at 4

rate which might indicate the initiation or acceleration of a significant aging process.

After the test was terminated, visual inspection of device C38 revealed aluminum migration of the type described in reference 7. The aluminum in the center of the cavity had.migrated and formed dendrites protruding from the film. None of the other devices showed any migration. The migration in C38 occurred at a relatively low stress and is clearly associated with a rapid downward shift in frequency.

SAWRs at frequencies between 700 and 800 MHz. These frequencies correspond to electrode and reflector widths of around 1 micrometer. The processing of these devices differed from that used to fabricate the 160 MHz SAWRs. Instead of fabricating the devices individually on crystal blanks the size of 5 MHz bulk wave resonators, these devices were fabricated on 50 mn diameter wafers and diced into 5 x 3 mn chips.

Four devices from wafer A were bonded into the same type of copper-ceramic header used for the 160 MHz devices and similarly were vacuum baked and cold-weld sealed. The devices were used in oscillators which were a justed so that the peak stress was 8.4 x 107 N/m . During the first 5 1 days two devices, C7 and F3, aged upwards rapidly as shown by the top two curves in Figure 2. The other two essentially identical devices, K8 and D5, also shifted up in frequency but at a much lower rate.

Four devices from wafer B were processed in an identical manner to those on the first wafer and mounted on a ceramic header. A nickel-plated steel lid was brazed to the base and a copper tube in the lid was used for vacuum bake-out and a final cold-weld seal. These devices had a slightly higher drjve le el corresponding to a peak stress of 10.7 x 10 N/m . All of these devices aged downward rapidly as shown in Figure 2.

A similar test was conducted on two-port

Devices from two wafers were tested.

9

!!

To see if the differences between these 8 devices was related to drive level, the dissipated power in devices C7, F3, K10, and 56 was reduced by 9 dB. The others were not modified. Three of the reduced power devices immediately began aging at a much lower rate as shown in Figure 3. Two of the unchanged devices continued aging with a logarithmic time dependence. The other two showed significant jumps to higher frequencies. Clearly reducing the drive level improved the aging.

is probably caused by a side-effect of acousto- migration of the aluminum metallization. The resonators are designed with apodized transducers to suppress higher order transverse modesg Migration in the film changes the electrode resistance and the effective excitation profile of the transducer. This causes higher order transverse modes to be excited and changes the amplitude and phase of the resonator frequency response. After the migration caused a 174 ppm shift downward in the frequency of the resonator, the oscillator could jump to the third order transverse mode. The size of this jump was 210.4 ppm which agrees well with the 211 ppm calculated mode separation.

The large jump taken by E7 on the 26th day

/ n 100

h i

------,E7 j -150 ' 0 10 20 30 40 50

T i m e (days) Figure 2. Aging of 795 MHz SAWRs at gigh sow;; level. Peak stress as follow 8.4 x 10 nt/m C7. F3, K8 and D5; 10.7 x 10': nt/m2 in 36, K10, H11, and E7.

\

c, I \ \ 1

0 50 100 150 200 250 300

Time (days) Figure 3. Further aging o f devices in Figure 2. The dissipated power was reduced by 9 dB in K10, 36, F3 and C7.

1981 ULTRASONICS SYMPOSIUM - 95

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-50 r\

E -100

U

-15E

,“ -203

-250

LL

3

m

-303 1 J 0 20 40 60 80

T i m e (days)

. Aging of SAWRs at a peak stress of 6.9 x :ds”lj”/,$. These data indicate that the onset of

acoustomigration manifests itself in a downward aging characteristic and that operation at powers just below this onset leads t o upward aging at a power dependent rate. The maximum stress corresponding t the nset o f migration appears to be 5 to 10 x 10’ N/I# and also appears to vary somewhat presumably due to processing differences between devices.

Another test was started to show that similar results are obtained when devices start aging at different power levels. Twelve devices from two wafers were divided into two groups. One groyp was aged at a peak stress level of 9 to 11 x 10 N/& and the ther group was aged at a level of 3.2 to

devices shifted dramatically. All six of these oscillators stopped oscillating in the first 30 days. Subsequent characterization of the devices showed the series resistance had increased, the Q had decreased, and the frequency response was distorted by transverse modes. The increased series resistance caused the oscillators to quit. The reduced-stress devices aged in a much more predictable fashion. Their frequencies increased by 5 to 10 ppm in 100 days.

Another test was conducted to accurately determine the migration threshold. Four devices we e ag d at peak stresses ranging from 6.7 to 7.1 x

initially aged downward rapidly. After 88 days they were aging at rates from -80 to -120 ppm/yenr.

3.5 x 10 s N/m2. The frequencies of the high stress

10 $ 5 N/W. As shown in Figure 4, all of the devices

Four more devices from She s me wafer were aged at a peak stress of 2.1 x 10 N/m . Like the other devices operated at lower stress levels, these devices aged upwards as shown in Figure 5. After 116 days the average rate was 6.3 ppmlyear. These data indicate the threshold for acoustically induced migrat‘on in2pure aluminum metalization on SAWRs is 6 x 10 nt/m with an uncertainity o f about +20%.

Another device was aged 3t a still lower power corresponding to 0.70 x 10 N/m2. It aged in essentially the same way as the other oscillators shown in Figure 5. This result suggests that below

h

’I

0 20 40 60 80 100

Fiyure 3. Aging of SAWRs at peak stfesse? o f 2.1 x 10 N/m (solid curves) and 0.7 x 10 N/m (dashed).

T i m e (doys)

the threshold for migration a mechanism that is independent of drive level is determining the aging rate.

To confirm this conclusion, a group of four devices was aged passively at 65°C. The SAWR frequency response can be accurately and repeatably measured on a network analyzer and the center frequency determined by averaging the 3 dB points. Still it is difficult to maintain this repeatability over a period of months. Small changes in contact resistance in fixtures or cables, cable reflections and temperature fluctuations can easily change the measured frequency by a few parts per million. Despite efforts to minimize these variations, our measurement accuracy was 52 ppm. The average shift in SAWR frequency was about 6 ppm in 6 months. This rate is comparable to those in the active tests, but the scatter in the data makes it impossible to draw meaningful conclusions at this time.

The rapid downward aging seen on devices operated at high stress correlates with visible migration of aluminum in the areas o f peak stress in the resonator. Figure 6a is a picture of a 33 ,um wide aluminum strip located in the center of the resonator cavity. It is grounded and acts as an rf shield. The migration at the peaks of the standing wave is clearly visible verifying that the migration is induced by the acoustic fields and not electric fields at electrode edges as has been previously reported”. A closer examination (Figure 6b) shows pits where material has been removed and hillocks have formed.

This acoustically induced migration (acoustomigration) bears a striking resemblance to electromigration induced by high currents in thin aluminum films”. In the case of electromigration, copper-doping the aluminum film has been found to increase film lifetime, defined as the time it takes for the film to change some physical property such as conductivity by an unacceptable amount. Film lifetime before failure was found to be an increasing function of copper content. Similar increases in aluminum film lifetime have been observed for films doped with small percentages o f Mg, Cr, and other metals. Mean failure time was

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Figure 6. Aluminum bar in center of SAWR cavity showing effects of migration. (a) Nomarski micrograph. (b) SEM of same device.

found to change from 6 hr (pure Al) to 400 hr (4% Cu in Al), a factor of 67 improvement, in one test13. In the case of SAW resonators fabricated with aluminum, similar improvements in device lifetime with copper doping have been reported7911, but little quantitative data i s available.

fabricated with pure aluminum and with copper-doped aluminum were compared in an accelerated aging system at high stress levels. Results are shown in Fig. 7. In all cases, the frequency shift is seen to be For devices with pure aluminum metalization, the magnitude of this downward shift is a rapidly increasing function of stress level. For aluminum-copper metalization this is not the case. Copper doping appears to increase the stress threshold for the onset of migration by at least a factor of 3. Thus doped films should be capable of handling at leat 10 times the power of undoped films.

In the present study SAW resonators

downward.

To verify this conclusion, a number of SAW resonators with aluminum-copper metal 1 ization (copper content between 2% and 8%) with center frequencies between 700 MHz and 800 MHz were aged actively in oscillators. The peak stress in the SAWRs ranged from 5 to 12 x lo7 N/m2. The oscillators ran continuously in individual ovens maintained at a temperature near 65°C with temperature drifts less than 0.2"C.

Active aging results for 4 representative aluminum-copper resonators are shown in Fig. 8. Ovens 1 and 4 contain SAWRs from the s me wafer operating at a peak stress of 10 x l o 7 N/m . Ovens 13 and 14 contain devices from a different wafer operating at 7.8 x l o 7 N/m2. After 60 days, devices 1,4 and 13 are aging upward at 3.5, 3.5, and 5.7 ppm/year respectively. All three are aging logarithmically with time. They demonstrate the value of copper doping to allow stable operation at higher stress levels.

Resonator 14 has aged linearly downward with time at about 25 ppm/year for the first 80 days. This difference in behavior may be caused by a different aging mechanism that is as yet unidentified.

h

D

E -25

Y

Y

2 E

-50

Figure 7. Frequency shift in SAWRs driven at high power levels with pure AL and A1-Cu metalizations.

20 40 60 8 0 100 120

TIME [DAYS)

Figure 8. Aging of SAWRs with 1 Cu metalization at stresses from 8 to 10 x 107 N/m $ - .

1981 ULTRASONICS SYMPOSIUM - 97

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Sumnary

D r i v e l e v e l has been shown t o be a dominant ag ing mechanism i f t h e peak s t r e s s i n resonators w i t h pure aluminum m e t a l i z a t i o n exceeds a l e v e l o f 6 x lo7 N/m2. The phys i ca l man i fes ta t i on o f ope ra t i ng a t t h i s l e v e l i s a c o u s t i c a l l y induced m i g r a t i o n of t he aluminum m e t a l i z a t i o n i n t h e r e g i o n o f peak s t ress. Th is acoustomigrat ion can be slowed o r e l i m i n a t e d by adding a small amount o f copper t o t h e m e t a l i z a t i o n . This doping increases the power hand l i ng c a p a b i l i t y by a t l e a s t 10 dB. Below t h e onset o f m ig ra t i on , no long term power dependent e f f e c t s were observed.

Appendix

C a l c u l a t i o n o f Peak Stress i n a SAW Resonator

I n t h i s sect ion, we f i r s t develop a s c a l a r model t o i l l u s t r a t e t h e c a l c u l a t i o n o f peak s t r e s s i n a SAW resonator. Th is model i s then used t o f i n d t h e peak tensor s t ress components f o r ST-quartz resonators f rom the numerical analyses o f Slobodnick, ,I.’’

L e t us represent the rms s t r e s s i n a SAW resonator by

where Tp i s t he rms value o f the s t r e s s a t t he s p a t i a l maximum, x, y, and z are orthogonal s p a t i a l coord inates, and Hx, Hy, and Hz are f u n c t i o n s rep resen t ing t h e s p a t i a l v a r i a t i o n s o f s t r e s s i n t h e resonant c a v i t y . I n the analys is , t h e subs t ra te su r face l i e s i n t h e x,z-plane w i t h waves t r a v e l i n g i n t h e x - d i r e c t i o n .

For s i m p l i c i t y , l e t us assume t h a t t h e m a t e r i a l s t i f f n e s s can be represented by an e f f e c t i v e s c a l a r va lue c. Then t h e s to red s t r a i n energy d e n s i t y Us and t h e k i n e t i c energy d e n s i t y Uv i n t h e s tanding wave can be represented by:

U = - = TS T2(xyy ’z ) cos2 (F) COS‘ ( u t ) (A2 ) 0

s 2 C

and

0

where v = p a r t i c l e v e l o c i t y , S = T/c i s t h e e l a s t i c s t r a i n , Vo i s t h e SAW phase v e l o c i t y i n t h e x - d i r e c t i o n , u i s t h e angular frequency o f t h e SAW, and P i s t he m a t e r i a l dens i t y . The t o t a l s to red acous t i c energy d e n s i t y U i s then ( n e g l e c t i n g p i e z o e l e c t r i c i t y )

From the d e f i n i t i o n o f device q u a l i t y f a c t o r Q, we have

Es Q, = - ‘d

where w r i s t h e angular frequency a t resonance, Es i s s to red energy and Pd i s power d i s s i p a t e d i n t h e SAWR.

The s to red energy can then be c a l c u l a t e d by i n t e g r a t i n g U over a l l space w i t h the assumption t h a t L >> w/vo.

T2 E, = LDW (A61

where

L = L H Z ( x ) dx

i s t he e f f e c t i v e c a v i t y length, and D and W are the e f f e c t i v e c a v i t y dep h and w id th ob ained by s i m i l a r

equat ion (A6) f o r pexk s t ress y i e l d s i n t e g r a t i o n over H $ ( y ) and H, 5 ( 2 ) . So lv ing

-

where the f a c t o r Jm i s a constant f o r a given subs t ra te m a t e r i a l and o r i e n t a t i o n . For SAWS on - c u t quar tz , D = .3 wave1 ngths c = 2.65 x 10 dT N/m: and J, = 2980 (kg/m 5 /sec)& .

Th is s c a l a r ana lys i s has y i e l d e d the f u n c t i o n a l dependence of s t r e s s on dev ice size, Q and d i s s i p a t e d power. The r e s u l t s can be app l i ed t o the more complicated tenso r s t resses bylllusing t h e numerical r e s u l t s o f Slobodnick, e t a l . They have tabu la ted s t r e s s components f o r SAW t r a v e l i n g wave Propagation on a v a r i e t y o f subs t ra tes i n va r ious o r i e n t a t i o n s . T h e i r r e s u l t s f o r ST-quartz s t a t e the f o l l o w i n g :

lTlll = 76.45 [PlMu1 ’ IT121 = 0.1097 I T l l [ (A81

IT221 = 0.3087 l T l l l

where P1M i s t he power f l o w per u n i t w idth i n the x - d i r e c t i o n , t h e s u b s c r i p t 1 corresponds t o t h e x - d i r e c t i o n and 2 corresponds t o the z - d i r e c t i o n (perpendicu lar t o x i n t h e p lane o f t he subs t ra te sur face) .

We can express the s tanding wave i n the resonator as t h e superpos i t i on o f two t r a v e l i n g waves w i t h opposi te d i r e c t i o n s o f propagation. Each o f these waves c a r r i e s h a l f o f t he t o t a l s to red energy. Therefore, f o r each t r a v e l i n g wave, the average power f l o w per u n i t area i s v U/2. Apply ing our d e f i n i t i o n s o f e f f e c t i v e length, e, w i d t h W and depth D, t he power per u n i t w id th i n each wave can be expressed ( f rom A5) as f o l l o w s :

Dvo - ‘0 Qu ‘d ‘1M = 2 - 2LWw,

The t o t a l s t r e s s ampli tude f o r t h e s tanding wave i s ( A 5 ) tw ice t h a t f o r t he t r a v e l i n g waves, so the peak

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spatial rms stress in the standing wave is (from A8 and A9)

and the other stress components are proportional indicated in Equation (A8).

The functional dependence of these components agrees with the scalar result in Equation ( A 7 ) . The scalar constant hcan be taken as a weighted average of the multipliers for the actual stress components.

The calculation of peak stress is completed by evaluating the effective cavity width and length. The width dependence of stress HZ(z) is determined by the profile of the fundamental waveguide mode and can be integrated to give the result

as

w 3 b/8

where b is the total grating width. The effective length is determined by the separation o f the reflector gratings d and the reflectivity per unit length K

L = d + 1 / ~

This distance is also the effective mirror spacingI5 that determines the mode separation in the resonator.

Acknowledgements

The authors thank Peter Cross, Sandy Gianotti, Catherine Johnsen, Don Johnson, George Nelson, Pete Planting, and Michael Symons for their help in fabricating devices, package design and packaging, testing and valuable discussions without which this work would not have been possible.

References

1.

2.

3.

4.

5.

6.

7.

8.

D.T. Bell, Jr., "Aging Processes in SAWR Resonators," 1977 Ultrasonics Symp. Proc.,

W.R. Shreve. "Aaina in Ouartz SAW Resonators," 851-856 (1978).

~. - Ibid. pp. 857-8il.- C.A. Adams and J.A. Kusters, "Improved Long-Term Aging in Deeply Etched SAW Resonators," Proc. 32nd AFCS*, 74-76 (1978). T.E. Parker, "Analysis o f Aging Data on SAW Oscillators," Proc. 34th AFCS*, 292-301 (1980). T.C. Anderson and F.G. Merrill, "Crystal Controlled Primary Frequency Standards: Latest Advances for Long Term Stability," IRE Trans. on Instrumentation, 136-140 (Sept. 1960). C.A. Adams and J.A. Kusters, "Deeply Etched SAW Resonators," Proc. 31st AFCS*, 246-250 (1977). J.I. Latham, W.R. Shreve, N.J. Tolar and P.B. Ghate. "Imoroved Metalization for Surface Acousiic Wave Devices," Thin Solid Films, 64, DD. 9-15 (1979). , , W.R. Shreve, 'J.A. Kusters and C.A. Adams,

9.

10.

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14.

15.

H.A. Haus, "Modes in SAW Grating Resonators,"

k.R. Shreve, "Surface Acoustic Wave Resonators J. Appl. Phys. 48, 4955-4961 (1977).

and Their Use in Narrowband Filters," 1976 Ultrasonics Symp. Proc., 857-861 (1977). W.J. Tanski, M. Block, A. Vulcan, "High performance SAW resonator filters for satellite use", 1980 Ultrasonics Symp. Proc. pp. 148-152, (1980). F.M. d'Heurle and R. Rosenberg, "Electromigration in thin films", Physics of Thin Films 7, pp. 257-310, (1973). I. Ames, F.M. d'Heurle, R. Horstmann, "Reduction of electromigration in aluminum films by copper doping", IBM J.Res.Develop. 14, 461 { 1970 1 .-- - - r

A.J. Slobodnick, Jr., E.D. Conway, R.T. Delmonico, Microwave Acoustics Handbook, Vol. l A . , Air Force Cambridge Research Laboratories m 7 3 \ - .--- - I - P.S. Cross, "Properties of Reflective Arrays for Surface Acoustic Resonators," IEEE Trans. Son. Ultrason. E, 255-262 (1976).

_ _ ~

*AFCS stands for Annual Frequency Control Symposium, U.S. Army Electronics Comnand, Ft. Monmouth, N.J., Copies available from Elec. Ind. Assn., 2001 Eye St., NW, Washington D.C., 20006.

"Fabrication of SAW Resonators for Improved Long Term Aging," 1978 Ultrasonics Symp. Proc. 573-579 (1978).

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