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APPLICATIONS OF THERMAL-WAVE PHYSICS TOSEMICONDUCTOR MATERIALS ANALYSIS

A. Rosencwaig

To cite this version:A. Rosencwaig. APPLICATIONS OF THERMAL-WAVE PHYSICS TO SEMICONDUCTORMATERIALS ANALYSIS. Journal de Physique Colloques, 1983, 44 (C6), pp.C6-437-C6-452.<10.1051/jphyscol:1983671>. <jpa-00223230>

J O U R N A L DE P H Y S I Q U E

Co l loque C6, supplement a u nO1O, T o m e 44, o c t o b r e 1983 page C6- 437

A P P L I C A T I O N S OF THERMAL-WAVE P H Y S I C S TO SEMICONDUCTOR M A T E R I A L S

ANALYS I S

A. Rosencwaig

Therma-Wave, Inc., Fremont, CA 94539, U.S.A.

RGsum6 - On d 4 c r i t l e s a p p l i c a t i o n s d e s ondes thermiques 2 l ' i m a g e r i e e t aux mesures q u a n t i t a t i v e s d ' 4pa i s seu r de f i l m s minces pa r d e s mat4riaux semiconducteurs e t d e s composants.

Abs t r ac t - Nonspectroscopic a p p l i c a t i o n s of thermal-wave phys i c s , i n p a r t i c u l a r t h o s e i nvo lv ing m a t e r i a l s a n a l y s i s through t h e r - mal-wave imaging, and q u a n t i t a t i v e t h i n - f i l m th ickness measure- ments, a r e desc r ibed f o r t h e s tudy of semiconductor m a t e r i a l s and dev ices .

I - INTRODUCTION

Thermal-wave phys i c s i s p l ay ing an eve r - inc reas ing r o l e i n t h e s tudy

of m a t e r i a l parameters . I t has been employed i n o p t i c a l i n v e s t i g a -

t i o n s of s o l i d s , l i q u i d s and gases w i th photoacoust ic1 and thermal-

l e n s 2 spectroscopy. Thermal waves have a l s o been used t o s tudy the

thermal and thermodynamic p rope r t i e s1 f3 o f m a t e r i a l s , and f o r imaging

thermal and m a t e r i a l f e a t u r e s w i t h i n a s o l i d sample. 4

Thermal waves a r e p r e s e n t whenever t h e r e i s p e r i o d i c hea t gene ra t ion

and hea t flow i n a medium. There a r e , t h e r e f o r e , a mul t i tude of

mechanisms by which t h e s e waves can be produced, wi th t he two most

common invo lv ing t h e abso rp t ion by t h e sample o f energy from e i t h e r

an in tens i ty-modula ted o p t i c a l beam,' o r from an intensi ty-modulated

e l e c t r o n S e v e r a l mechanisms a r e a l s o a v a i l a b l e f o r d e t e c t i n g ,

d i r e c t l y , o r i n d i r e c t l y , t h e r e s u l t i n g thermal waves. These inc lude ;

gas-microphone pho toacous t i c d e t e c t i o n of h e a t flow from t h e sample

t o t h e surrounding gas i n which p re s su re changes a r e mon i to red ; l r5 photothermal measurements of i n f r a r e d r a d i a t i o n emi t ted from t h e heat-

ed sample su r f ace ; 6-80p t i ca l beam d e f l e c t i o n of a l a s e r beam t r a v e r s i n g

t h e p e r i o d i c a l l y hea t ed gaseous o r l i q u i d l a y e r j u s t above t h e sample

s u r f ace ; 9-11 . l n t e r f e r o m e t r i c d e t e c t i o n of t h e t he rmoe la s t i c d i sp l ace -

ments of t h e s u r f a c e ; 12'13 o p t i c a l d e t e c t i o n of t h e t he rmoe la s t i c

deformations of t h e s u r f a c e ; 13-16 and p i e z o e l e c t r i c d e t e c t i o n of

thermoacoust ic s i g n a l s genera ted i n t h e sample. 1 ,17,18

To d a t e , on ly t h i s l a s t t echnique invo lv ing thermoacoust ic d e t e c t i o n

has been used r o u t i n e l y f o r d e t e c t i n g high-frequency ( i . e . MHz regime)

thermal waves. The thermoacous t ic d e t e c t i o n methodology has. t he re -

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983671

C6-438 JOURNAL DE PHYSIQUE

14,19,20 at f o r e found important a p p l i c a t i o n s i n thermal-wave imaging

high s p a t i a l r e s o l u t i o n where micron-sized thermal waves a r e needed,

a s i n t h e s tudy of semiconductor m a t e r i a l s and devices .

I s h a l l he re d i s c u s s some nonspectroscopic app l i ca t i ons of high f r e -

quency thermal waves f o r imaging and th in- f i lm th ickness measurements

i n semiconductor m a t e r i a l s ana lys i s .

11. THERMAL-WAVE IMAGING

Thermal-wave imaging i s a new technique whereby microscopic thermal

f e a t u r e s on o r beneath t h e sur face of a sample can be de t ec t ed and

imaged. Thermal f e a t u r e s a r e those reg ions of an otherwise homogen-

eous m a t e r i a l t h a t e x h i b i t v a r i a t i o n s , r e l a t i v e t o t h e i r surroundings,

i n e i t h e r t h e d e n s i t y t h e s p e c i f i c hea t , o r , most impor tan t ly , t h e

thermal conduct iv i ty of t h e sample. Va r i a t i ons i n t he se thermal para-

meters can a r i s e from changes i n b a s i c m a t e r i a l composition, from the

presence of mechanical d e f e c t s such a s microcracks, vo ids and delam-

i n a t i o n ~ , from changes i n c r y s t a l l i n e o rde r o r s t r u c t u r e , and evenfrom

t h e presence of smal l concent ra t ions of fo re ign ions o r l a t t i c e d e f e c t s

i n an otherwise p e r f e c t c r y s t a l .

In thermal-wave microscopy a l a s e r 2 1 o r e l e c t r o n beam 22123 i s i n t e n s i -

ty-modulated i n t h e 100 kHz-10 MHz range, focused, and scanned over

t h e su r f ace of a sample. The p e r i o d i c su r f ace hea t ing t h a t r e s u l t s

from the absorp t ion of t h e i n c i d e n t beam genera tes thermal waves t h a t

propagate from t h e i n i t i a l l y heated reg ions . These d i f f u s i v e thermal

waves a r e c r i t i c a l l y damped and propagate only one t o two wavelengths

before t h e i r i n t e n s i t y becomes n e g l i g i b l y small . Nevertheless , w i th in

t h e i r propagat ion range, t h e thermal waves w i l l s c a t t e r and r e f l e c t

from thermal f e a t u r e s much l i k e conventional propagat ing waves do from

o p t i c a l o r a c o u s t i c f ea tu re s . Imaging of t h e thermal f e a t u r e s t hus r e -

q u i r e s d e t e c t i o n of t h e s c a t t e r e d and r e f l e c t e d thermal-waves. A

Therma-Wave , 1nc. 2 4 thermal-wave microscope uses t h e e l e c t r o n beam i n a

scanning e l e c t r o n mircoscope t o genera te t he thermal waves and d e t e c t s

t h e s c a t t e r e d and r e f l e c t e d thermal waves through t h e i r e f f e c t on t h e

thermoacoustic s i g n a l s generated i n t h e bulk of t h e sample. The thermo-

acous t i c s i g n a l s a r e de t ec t ed i n t u r n wi th a s u i t a b l e p i e z o e l e c t r i c

t ransducer i n a c o u s t i c con tac t wi th t h e sample. The magnitude and phase

of , the thermoacoustic s i g n a l s a r e d i r e c t l y a f f e c t e d by t h e presence of

sca ' t tered and r e f l e c t e d thermal waves. 25 Thus by measuring t h e magnitude

and/or phase of t h e thermoacoustic s i g n a l a s a func t ion of e l e c t r o n beam

p o s i t i o n on t h e su r f ace of t h e sample, an image i s genera ted t h a t d e p i c t s

t h e va r ious thermal-wave s c a t t e r i n g and r e f l e c t i o n events t h a t occur a t

each p o i n t on t h e sample.

SUBSURFACE DEFECTS

Subsurface mechanical de fec t s such a s voids , c racks and delaminations

r ep re sen t s u b s t a n t i a l thermal f e a t u r e s and t h u s a r e r e a d i l y de tec ted

wi th a thermal-wave microscope. 4 ' 2 0 One i l l u s t r a t i o n of t h i s appl ica-

t i o n is shown i n Figure 1. Figure l a i s t h e e l e c t r o n image of a GaAs

device , where t he only v i s i b l e d e f e c t s a r e two seemingly i n s i g n i f i c a n t

chip-outs a t t h e edge of the device , one along the right-hand edge,

and t h e o t h e r along t h e bottom. The thermal-wave image i n Figure l b

shows, however, t h a t t h e small chip-out along t h e right-hand s i d e is

a much l a r g e r subsurface delaminat ion which extends i n t o t he lower

g a t e of t h e device where it r e s u l t s i n a " loop-l ike" subsurface flaw.

The small chip-out along t h e bottom i s a l s o seen t o be t h e o r i g i n of

a long subsurface c rack . Therefore, where o p t i c a l and e l e c t r o n images

show only two i n s i g n i f i c a n t d e f e c t s , t h e thermal-wave image shows t h e

presence of s e r i o u s subsurface de fec t s .

Fig. 1 - Examples of subsurface d e f e c t s i n a GaAs device. The e l ec - t r o n micrograph ( a ) shows only 2 small edge chip-outs , one along the r ight-hand s i d e , t h e o t h e r a t t h e bottom. The thermal-wave image (b) shows more s e r ious d e f e c t s - t he chip-out along t h e r ight-hand s i d e is seen a s a s u b s t a n t i a l delaminat ion extending i n t o t h e lower ga t e re - g ion where a " loop-l ike" d e f e c t i s v i s i b l e ; t h e chip-out a t t h e bottom i s t h e o r i g i n of a long subsurface microcrack running up i n t o t he device. (Magnigication 220x)

C6-440 JOURNAL DE PHYSIQUE

CRYSTALLINE VARIATIONS

When a c r y s t a l l a t t i c e i s h ighly ordered , minor changes i n l a t t i c e s t r u c t u r e can produce measurable changes i n t h e l o c a l thermal conduc- t i v i t y of t e m a t e r i a l and thus can be imaged wi th a thermal-wave microscope. This c a p a b i l i t y i s i l l u s t r a t e d i n Figures 2 and 3 which show GaAs devices . The o p t i c a l and e l e c t r o n micrographs image t h e v i s i b l e f e a t u r e s of t h e ga t e s t r u c t u r e s i n t h e devices . The the r - mal-wave images show, i n add i t i on , t h e Si-doped reg ions of t h e G a A s , s i nce t hese reg ions have a d i f f e r e n t thermal conduct iv i ty t h a t t he un- doped regions. Such images permit a r ap id and nondes t ruc t ive a n a l y s i s of t h e e f f e c t s of l a t e r a l d i f f u s i o n s of dopants i n semiconducting c r y s t a l s .

Fig. 2 - Images of GaAs device. The o p t i c a l ( a ) and e l e c t r o n micro- graphs (b) show t h e v i s i b l e f e a t u r e s . The thermal-wave image ( c ) shows i n add i t i on t h e Si-doped reg ions of t h e GaAs. (Magnif icat ion 4 0 0 x 1 .

Fig. 3 - Images of a ga t e region i n a GaAs device. The o p t i c a l ( a ) and e l e c t r o n micrographs (b) show t h e v i s i b l e f e a t u r e s . The thermal- wave image ( c ) shows i n add i t i on t h e l a t e r a l l y d i f f u s e d S i doped region around t h e ga t e s t r u c t u r e . (Magnif icat ion 500x).

C6-442 JOURNAL DE PHYSIQUE

Another i n t e r e s t i n g example o f thermal-wave d e t e c t i o n of l a t t i c e per-

t u r b a t i o n s is shown i n F igu re 4 . A sample of GaAs was f i r s t masked i n

a p a t t e r n and then bombarded wi th e n e r g e t i c p ro tons (40KeV) a t a f l u x 15 2

of 10 /cm . These p ro tons produced a c o n t r o l l e d d e f e c t zone of va-

canc i e s and i n t e r s t i t i a l s about 0.5pm benea th t h e s u r f a c e wherever t h e

GaAs was not p ro t ec t ed by t h e mask. The e l e c t r o n micrograph of t h e

GaAs shows, a f t e r removal of t h e mask, no v i s i b l e p a t t e r n s (Fig. 4 a ) .

However, t h e thermal-wave image of t h e same a r e a (F ig . 4b) c l e a r l y shows

t h e masking p a t t e r n (whi te r e g i o n s ) . The image c o n t r a s t a r i s e s from

t h e f a c t t h a t t h e proton-bombarded GaAs (dark r eg ions ) now has a

lower thermal conduc t iv i t y t h a t t h e unper turbed GaAs (whi te r e g i o n s ) .

F ig . 4 - Images of a proton-bombarded GaAs wafer ; (a) e l e c t r o n micro- graph of t h e GaAs sample a f t e r removal o f t h e mask, showing no e v i - dence of t h e masking p a t t e r n : (b) thermal-wave r eg ion of same re- g i o n s showing proton-bombarded (da rk ) r eg ions and unperturbed (wh i t e ) r eg ions . (Magnif icat ion 100x) .

The imaging of c r y s t a l l i n e v a r i a t i o n s can a l s o be useful. i n metal lo-

graphy , 4118f27 s ince d i f f e r e n t m e t a l l i c phases o r g r a i n s can be read- i l y imaged wi th no s p e c i a l sample p r e p a r a t i o n . We i l l u s t r a t e t h i s i n

Figure 5 where the columnar g r a i n s and t r a n s i t i o n zone i n a weld r eg ion ,o f an aluninum a l l o y a r e c l e a r l y v i s i b l e i n the thermal-wave

image.

F ig . 5 - Thermal-wave image of a weld region i n an aluminom a l l o y . The columar g r a i n s i n t h i s region a r e c l e a r l y v i s i b l e . (Magnif icat ion 30x).

C6-444 JOURNAL DE PHYSIQUE

Another example, Figure 6, shows t h e e l e c t r o n and thermal-wave images

of an Al-Zn a l l o y . The e lec t ron image ( a ) shows only topographical.

f e a t u r e s , while the thermal-wave image (b ) c l e a r l y shows both the q r a i n

s t r u c t u r e and, a t high magnification, t h e presence of Fe or Sn pre-

c i p i t a t e s . Other s t u d i e s with meta ls ind ica te appl ica t ions i n inves t -

i g a t i o n s of mechanical deformation2' and g ra in boundaries. 19

Fig. 6 - Electron ( a ) and thermal-wave (b) micrographs a t 50x of an Al-Zn a l l o y . The thermal-wave micrqgraph shows t h e Al-Zn g r a i n s , and the presence of Fe o r Sn p r e c i p i t a t e s .

BONDING INTEGRITY

Microscopic d e t a i l s i n a thermal-wave image a r e due t o r e f l e c t i o n and

s c a t t e r i n g of thermal waves from su r f ace and subsur face thermal fea-

t u r e s . I n add i t i on , thermal-wave images o f t e n e x h i b i t l a rge b r i q h t

and dark a r e a s which r ep re sen t t h e acous t i c modes o f t h e sample. 19

The inc iden t e l e c t r o n beam i s very e f f e c t i v e i n e x c i t i n g t h e p l a t e

modes of v i b r a t i o n s i n t h i n samples such a s I C ch ips and wafers. Thus,

a t c e r t a i n resonant f requencies , v i b r a t i o n p a t t e r n s a r e s e t up on t h e

sample cha rac t e r i zed by r egu la r ly spaced nodes and ant inodes. When

t h e e l e c t r o n beam i s a t a p l a t e node on t h e sample su r f ace , t h e r e is

no enhancement of t h e thermoacoustic s i g n a l . However, a t t he a n t i -

nodes t h e r e is a cons iderable enhancement, wi th t h e enhancement being 0 180 out-of-phase between a p o s i t i v e and negat ive ant inode. Thus t h e

p l a t e mode v i b r a t i o n i s seen a s a p a t t e r n of b r i g h t and dark reg ions

i n t h e thermal-wave image, corresponding t o t h e p o s i t i v e and negat ive

ant inode reg ions on t h e sample su r f ace . I f t h e sample is a w i r e ,

then the thermal-wave image d i s p l a y s the r a d i a l a c o u s t i c modes i n t he

wire.

Because of t h e i r s h o r t wavelength (gene ra l ly <20pm), high frequency

thermal waves a r e unable t o p e n e t r a t e through an I C d i e t o probe t h e

bonding between the d i e and i t s support s t r u c t u r e . However, I C d i e s

a r e t h i n p l a t e s and thus w i l l e x h i b i t p l a t e mode v i b r a t i o n p a t t e r n s

i n t h e i r thermal-wave images. The i n t e n s i t y of these v i b r a t i o n s is a

s e n s i t i v e func t ion of t h e th ickness of t h e sample, decreas ing a s t he

t h i ckness i nc reases . The same e f f e c t occurs when t h e sample i s

bonded t o a t h i c k e r s u b s t r a t e . The combination of t he two s t r u c t u r e s

now c o n s t i t u t e s a much t h i c k e r sample and the v i b r a t i o n i n t e n s i t i e s

w i l l now decrease. How s t rong t h i s e f f e c t w i l l be is dependent on the

i n t e g r i t y and uniformity of t h e bond between t h e d i e and i t s support-

i ng s t r u c t u r e . The p l a t e mode p a t t e r n s seen i n t he thermal-wave image

can thus be used f o r comparative eva lua t ion of d i e a t t a c h .

Figures 7a and 7b show t h e thermal-wave images of two l a r g e s i l i c o n

I C d i e s mounted i n l a r g e ceramic DIP packages. The d i e i n Figure 7a

is known t o have a "poor" d i e - a t t ach , while t h a t i n Figure 7b is a

"good" d ie -a t tach . I n agreement with t h i s , t h e d i e i n Figure 7a

shows a s t r o n g p l a t e mode p a t t e r n i n d i c a t i v e of a " th in -p l a t e " sample,

t h a t i s , of a d i e t h a t is poorly a t tached . On t h e o t h e r hand, t h e

d i e i n F igure 7b shows l i t t l e evidence of a p l a t e mode p a t t e r n thereby

i n d i c a t i n g a " th ick-p la te" sample, t h a t i s , a d i e f i rmly and uniformly

bonded t o i t s suppor t s t r u c t u r e .

C6-446 JOURNAL DE PHYSIQUE

Fig. 7 - Examples o f a bonding i n t e g r i t y s tudy . Thermal,-wave image of l a r g e IC d i e i n D I P package wi th ( a ) poor d i e - a t t a c h and ex- h i b i t i n g s t rong p l a t e mode p a t t e r n ; and (b)bgood d i e - a t t a c h exhi- b i t i n g no p l a t e mode p a t t e r n (Magni f ica t ion '40x1.

Although s t i l l i n i t s formative s t age , thermal-wave imaging has a l -

ready demonstrated severa l i n t e r e s t i n g and use fu l app l i ca t ions f o r a

v a r i e t y of material s t u d i e s .

111. LASER BEAM DEFLECTION

The examples above were obtained with an e lec t ron beam t o generate

the thermal waves. Clear ly the same images could have been obtain-

ed with a l a s e r beam a s However i n both cases the use of a

thermoacoustic probe t o d e t e c t the r e f l e c t i o n and s c a t t e r i n g of the

thermal waves from the thermal f e a t u r e s s u f f e r s from the major draw-

back of requiring acous t i c ~ 0 u p l i n q between the sample and an u l t r a -

sonic transducer. In the ana lys i s of semiconductor ma te r i a l s and

devices, one would l i k e t o opera te i n an open environment, employ

completely contact less methods f o r thermal-wave generation and de-

t e c t i o n , and be able t o make measurements o r obta in images a t high

s p a t i a l resolution. This l a s t requirement n e c e s s i t a t e s the use of a

highly focused beam f o r thermal-wave generation and the c a p a b i l i t y

f o r detect ing high-frequency (>100kHz) thermal waves.

To s a t i s f y a l l of the above condi t ions one needs t o u t i l i z e l a s e r s

f o r both generating and de tec t ing the thermal waves. The genera-,

t i o n i s , of course, s t ra ightforward. The de tec t ion i s performed

e i t h e r by l a s e r in te r fe romet r i c de tec t ipn of the thermoelas t ic d i s -

placements of the sample surf ace , 12114*15 o r by l a s e r de tec t ion of

the l o c a l thermoelast ic deformations of the surf ace. 13-16 Both

techniques a r e analogous t o the o p t i c a l methods used f o r de tec t ing 29 , 30

su r f ace acoust ic waves, although here the surface displacements

and deformations a r e due t o the thermal waves. A l l of the o t h e r

methods f o r thermal-wave de tec t ion s u f f e r from e i t h e r being l imi ted

t o low modulation frequencies o r from requ i r ing contact t o t h e sample.

There have been some i n i t a l s t u d i e s of thermal-wave de tec t ion using

the l a s e r techniques described above. Ameri e t a 1 have performed a

rudimentary imaging experiment with t h e l a s e r in te r fe romet r i c techni-

que,12 while Arner and h i s col leagues have used both the l a s e r def lec-

t i o n (surface deformation de tec t ion) technique and the l a s e r i n t e r -

ferometr ic technique f o r spect roscopic ~ t u d i e s . ' ~ - ~ ~ These i n v e s t i -

ga t ions have a l l been performed a t low t o moderate modulation frequen-

c i e s (<100kHz) only. We have employed t h e l a s e r de f l ec t ion technique i n

a somewhat d i f f e r e n t experimental conf igurat ion a t high thermal-wave

frequencies (up t o 10MHz) f o r q u a n t i t a t i v e measurements of th in-f i lm

th icknesses . 1 6

JOURNAL DE PHYSIQUE

I V . DEPTH-PROFILING AND THIN-FILM THICKNESS MEASUREMENTS

Semiconductor dev ices a r e composed o f a complicated three-dimensjonal

a r r a y of t h i n f i l m s . Thermal-wave phys i c s p rov ides an i d e a l t o o l t o

s tudy such systems because o f i t s unique dep th -p ro f i l i ng c a p a b i l i t y . 3 1

We have employed t h e l a s e r d e f l e c t i o n method a t f r equenc ie s a s h igh

a s lOMHz t o measure t h e t h i c k n e s s of opaque and t r a n s p a r e n t f i lms

used i n semiconductor process ing .16 Using an i n c i d e n t hea t ing l a s e r

beam of approximately 30mW a t lMHz, we a r e a b l e t o d e t e c t l o c a l su r -

face deformations t h a t correspond t o s u r f a c e displacements of approx-

imate ly 10-*2/&, a s e n s i t i v i t y t h a t i s cons ide rab ly b e t t e r than t h a t

r epo r t ed p rev ious ly . 12,13-15

To make q u a n t i t a t i v e t h i n f i l m th i ckness measurements wi th t h e l a s e r

probe technique we extended t h e Opsal-Rosencwaig thermal-wave depth-

p r o f i l i n g t o t h r e e dimensions, and inc luded the rmoe la s t i c

su r f ace deformat ions , thermal l e n s e f f e c t s , o p t i c a l e f f e c t s and non-

l i n e a r e f f e c t s a r i s i n g from t h e tempera ture dependence of t h e var ious

m a t e r i a l parameters . When a l l o f t h e s e e f f e c t s a r e proper ly inc luded

i n t h e model, q u a n t i t a t i v e measurements on s i n g l e and mul t i p l e f i lms

a r e t hen p o s s i b l e . This i s i l l u s t r a t e d i n F igu re 8 w h e ~ e we show

t h e o r e t i c a l cu rves and d a t a ob t a ined f o r s i n g l e f i l m s of A 1 on S i

and f o r f i l m s o f A 1 on S i02 on S i . We have used t h e magnitude of

t h e thermal-wave s i g n a l r a t h e r t h a t t h e phase i n t h e s e measure-

ments s i n c e t h e magnitude has a g r e a t e r range and can be measured more

p r e c i s e l y . The d a t a i n F igu re 8 i s an e x c e l l e n t agreement wi th t h e

theory both f o r t h e s i n g l e and t h e double fi.lms. The p r e c i s i o n of

t he readings ob ta ined wi th a 1-sec averaging t ime over t h e t h i ckness

range of 5002 - 15,0008 i s 22% f o r t h e s e A 1 f i lms.

In F igu re 9 , we show t h e t h e o r e t i c a l curves and t h e d a t a f o r a s e r i e s of t r a n s p a r e n t Si02 f i l m s on S i . Although only a s i n g l e f i l m problem, t h e t heo ry i n t h i s ca se must i n c l u d e the rmoe la s t i c deformations a t bo th t h e Si-SiO2 and t h e S i 0 2 - a i r i n t e r f a c e s , thermal l e n s e s i n bo th t h e Si02 and t h e a i r , and o p t i c a l i n t e r - f e r ences e f f e c t s i n t h e Si02 ( s e e Reference 1 6 ) . The f i t be- tween theo ry and experiment i s s t i l l , w i th a l l t h i s complexity, q u i t e good, i n d i c a t i n g t h a t t r a n s p a r e n t a s w e l l as opaque f i l m s can be measured wi th thermal-wave technolosv . The th i ckness -- s e n s i t i v i t y f o r Si02 f i l m s on S i appears t o be 52% over t h e range 500g - 15,OOOg.

0 .5 1 .O 1.5 2.0 2.5

THICKNESS (microns)

Fig . 8 - Rela t ive ampli tude a t 1 MHz o f l a s e r beam d e f l e c t i o n s i g n a l a s a func t ion of A 1 f i l m t h i c k n e s s f o r a s e r i e s of Al-on-Si and A l - on-Si02-on S i f i lms . C i r c l e s a r e experimented d a t a and curves a r e from t h e extended Opsal-Rosencwaig model.

JOURNAL DE PHYSIQUE

THICKNESS (microns)

Fig. 9 - Relat ive amplitude a t 1 MHz of l a s e r beam def lec t ion s igna l a s a funct ion of Si02 f i lm th ickness f o r a s e r i e s of Si02-on-Si f i lms. C i rc les a r e experimental da ta and curves a r e from the extended Opsal- Rosencwaig model.

V. CONCLUSIONS

Thermal-wave p h y s i c s h a s been a p p l i e d , f o r s e v e r a l y e a r s , t o t h e

s t u d y of many m a t e r i a l s i n c l u d i n q semiconductor m a t e r i a l s . U n t i l

r e c e n t l y , t h e s e s t u d i e s have been c o n f i n e d p r i m a r i l y t o s p e c t r o -

s c o p i c i n v e s t i g a t i o n s . The examples p r e s e n t e d above i l l u s t r a t e

t h a t thermal-wave p h y s i c s can a l s o p l a y a major r o l e i n o t h e r i m -

p o r t a n t a p p l i c a t i o n s r e l a t e d t o semiconductor m a t e r i a l s , such a s

imaging and q u a n t i t a t i v e t h i n - f i l m measurements.

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