ACOUSTIC MODES IN Ga1-xAlxAs CRYSTALS AND RELATED SUPERLATTICES

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ACOUSTIC MODES IN Ga1-xAlxAs CRYSTALS AND RELATED SUPERLATTICES

J. Sapriel, J. Michel, J. Toledano, R. Vacher

To cite this version:

J. Sapriel, J. Michel, J. Toledano, R. Vacher. ACOUSTIC MODES IN Ga1-xAlxAs CRYSTALS AND RELATED SUPERLATTICES. Journal de Physique Colloques, 1984, 45 (C5), pp.C5-139-C5-143.

�10.1051/jphyscol:1984520�. �jpa-00224138�

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JOURNAL DE PHYSIQUE

Colloque C5, suppl6ment au n04, Tome 45, avril 1984 page C5-139

A C O U S T I C MODES I N G a l - x A l x A s C R Y S T A L S AND R E L A T E D S U P E R L A T T I C E S

J. Sapriel, J . C . Michel, J . C . Toledano and R. vacherr

Centre NationaZ dlEtudes des T&Z6cmmnication6, 196 rue de Paris, 9 2220 Bagneux, France

' ~ a b o r a t o i r e de Spectrom&trie RayZeigh BriZZouin, Universite' des Sciences e t Techniques du Lunguedoc, 39060 Montpezzier, France

Rksum6

-

Ceci e s t une 'etude cornbinge de diffusion Raman e t Brillouin. Les modes Raman suppl gmentaires dans 1 es super r6seaux peuvent t t r e interpr6t6s comme issus d'une interaction acoustooptique avec l e s phonons de vecteurs d'onde di ff6rents. La diffusion Brillouin a permis d'6tudier l e s variations des v i t e s s e s des ondes de Rayleigh dans des couches de Gal-xA1xAs en fonc- tion de

x

e t dans des superr6seaux de pas variable.

Abstract

-

This i s a parallel study of Brillouin and Raman scattering. The additional Raman modes in the superlattices can be interpreted as due t o an acousto-optical inter action with phonons of d i f f e r e n t wave-vectors.

Bril l o u i n scattering allowed the study of Rayleigh wave v e l o c i t i e s in Gal-x AIX As layers as a function of x and in superlattices of d i f f e r e n t period.

This study i s devoted to the observation and analysis of vibrational modes i n Ga As

-

^Ga

-,

Al, As superl a t t i c e s . The experimental techniques used are the Raman and Briliouin scattering and the measurements are focused on the phonons belonging to the bulk acoustic branch along the direction perpendicular to the l a y e r s , and to the surface acoustic branch associated to a propagation parallel to the free surface of the semi -infini t e superl a t t i c e (Ray1 eigh modes).

The i n v e s t i g a t e d superl a t t i c e s were made of a1 t e r n a t i n g GaAs and Ga,,, Al, As l a y e r s (0.25 <

x

^< 0.40) deposited on (001) oriented GaAs substrates. These layers were repeated a s u f f i c i e n t number of times to create c r y s t a l s of a few mic_ro- meters along the direction of-growth z. The point group of the s u p e r l a t t i c e i s 42 m though the layers belong to 43 m. The period of the s u p e r l a t t i c e s along

z

ranged between 45 A and 260 A. As a consequence of t h i s period43new phonon branches appear in the folded Brillouin zone as well as additional gaps for the vibrations propaga- t i n g along z. As the perturbation which a r i s e s from replacement of Ga atoms by A1 atomsis rather weak these gaps, for a f i r s t approximationyare so small t h a t they can be neglected. One thus obtains [ 4 ] for the expression of the lowest frequency branches :

where E means:integral part. The branch corresponding to

n=

1 i s associated with the f i r s t folded branch, n=2 with the second folded branch, etc.

..

^V i s the velocity of the superlattice considered as an hOm~geouS,medi~m :

d, and d2, vJ and v 2 are the t h i c k n e k e s aid the acoustic v e l o c i t i e s of the layers.

Z i s the r a t i o of the acoustic impedances.

As GaAs and Gal-, A1 As have an optical absorption c o e f f i c i e n t of the order of 107m-I, on1 y backscatter i ng experiments are a1 1 owed. The phonon involved has

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984520

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C5-140 30URNAL DE PHYSIQUE

a wavevector K = 4 r n / X

,

n being the r e f r a c t i v e index and 1 t h e wavelength o f the i n t e r a c t i n g 1 ig h t beam. The c i r c u l a r frequency fin o f the phonon i s o b t a i

-

ned by r e p l a c i n g k by K i n Equ. ( 1 )

.

t h e B r i l l o u i n s h i f t which corresponds t o n o i s o f the order o f 2.5 cm-l. ~ a n d e r c o & [ 5 ] has shown t h a t t h e B r i l l o u i n l i n e o f b u l k acoustic waves i n an absorbing m a t e r i a l underaoes a broadenin5

!yo

due t o c o n t r i b u t i o n o f wave vectors i n the range aKZ ^Ka

.

For a = 10

m ,

g i v i n g r i s e t o very imprecise determination o f t h e v e l o c i t i e s

%'%/ZRe

^et:sStic constants o f the m a t e r i a l s . It i s t h e r e f o r e more convenient t o mea- sure the frequencies Ql, "2,

. . . .

due t o t h e zone-folding which f a l l i n the ranqe o f frequencies which can e a s i l y be reached by means o f a Raman spectrometer(wz 6 an-l). Experimentaly we have observed the frequencies n l and a2 l y i n g on the f i r s t and second folded l o n g i t u d i n a l acoustic branches, i n a1 1 t h e i n v e s t i g a t e d samples. The experiments have been performed w i t h t h e 5145 A r a d i a t i o n o f an argon- .ion l a s e r , far from resonance, a t Brewster incidence and under vacum. The r e s u l t s a r e r e p o r t e d i n Table I. Only sample 5 e x h i b i t e d Raman l i n e s a t 0, and a, The i n t e n s i t y o f the l i n e s a t n, and a2 were near1 y the same and the i n t e n s i t y o f l i n e s a t Q 3 and Q b were approximately 6 % o f t h a t corresponding t o Ql and Q2 (Fig.1). The d i f f r a c t e d l i g h t was always p o l a r i z e d p a r a l l e l t o i n c i d e n t l i g h t p o l a r i z a t i o n and i t s i n t e n s i t y was independent o f t h i s p o l a r i z a t i o n . These s e l e c t i o n r u l e s can be w e l l understood by c o n s i d e r i n g the s u p e r l a t t i c e as a continuum o f t e t r a g o n a l symmetry whose e l a s t i c , d i e l e c t r i c and p h o t o e l a s t i c proper- t i e s are r e l a t e d t o t h e physical p r o p e r t i e s o f both k i n d o f a l t e r n a t e d l a y e r s . One can t h u s d e f i n e e f f e c t i v e p h o t o e l a s t i c constant P i j e f f and the a d d i t i o n a l l i n e s can be considered as issued from an acoustooptical [ 6 ] c o l l i n e a r i n t e r a c t i o n along [001 'Qftween 1 ig h t and the l o n g i t u d i n a l waves. The photoel a s t i c constant i n v o l v e d i s P1, From E q u ( 1 ) one can i n t e r p r e t the phenomenon as an i n t e r a c t i o n between t h e l i g h t and phonons o f t h e unfolded a c o u s t i c branch o f wavevectors Kn = (-I)"+

i 2a/? E(n+1/2). The c o u p l i n g o f transverse acoustic wave i n t h i s s c a t t e r i n g geome- t r y w i t h p h o t m s i s forbidden even a t resonance [ 7 ] f o r zinc-blende s t r u c t u r e [8].

TABLE I

-

Frequency of the Raman a c t i v e modes i n Ga As

-

Gal-xA1xAs s u p e r l a t t i c e s due t o the f o l d i n s of the l o n g i t u d i n a l acoustic branches ; Q I

,

^n2,n3, a4 c o r r e s - pond t o the f i r s t , second, t h i r d and f o u r t h branch ; as-a,= 8sV n/x for a l l samples ; A = 5145

#,

V i s given by Equ. ( 2 ) ; 0 3 = 18 cm-1 and = 22.7 for our sample 5. There i s a r a t h e r good agreement between t h e o r e t i c a l and experimental values

Sample dl(A) dp(A) x

1 ^{Q 2}

(cm- ) (cm-l)

1 24 24 0.3 32 37

O p t i c a l modes o f Gal,, A l x As mixed c r y s t a l have been i n v e s t i g a t e d by means o f Raman s c a t t e r i n g b u t n o t h i n g has y e t been published on a c o u s t i c a l p r o p e r t i e s o f these a l l o y s . We have per formed B r i l l o u i n s c a t t e r i n g measurements i n surface acoustic waves i n Gal-, Al, As e p i t a x i a l l a y e r o f several microns thickness deposited on a (001)

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Ga As substrate. The experimental s e t up i s described i n Ref. [ 4 ] Two d i r e c t i o n s have been i n v e s t i g a t e d [ I 0 0 1 and [ I 1 0 1 o f the f r e e surface. The wave-vector conser- v a t i o n requirement gives for the wave number [ 9 ] K o f the acoustic surface waves o f v e l o c i t y vs:

K =

ki s i n

e i

+ ^K s i n as ;

S ki and kS being the wave numbers

o f i n c i d e n t and s c a t t e r e d l i g h t , r e s p e c t i v e l y which make an angle eiand es w i t h the normal t o the surface.

I n F i g 2 are p l o t t e d two kinds o f curves. The f u l l l i n e s j o i n t h e experimental curves, the broken curves are obtained by keeping the same e l a s t i c constants as for GaAs i n the whole c o n c e n t r a t i o n range x. The v a r i a t i o n s o f t h e measured v e l o c i t i e s versus x can be approximated by the f o l l o w i n g l i n e a r laws :

vs= 2690

+

290 x m/s vs= 2817

+

315 x m/s

Comparisons between the f u l l l i n e s and the broken l i n e s o f F i g 2 i n d i c a t e a small s o f t e n i n g of the e l a s t i c constants w i t h i n c r e a s i n g values o f x. But for the moment we are n o t able t o separate the d i f f e r e n t c o n t r i b u t i o n s o f the e l a s t i c constants C l l C 1 2 _andC,

.

However, f o r the g a l l i u m r i c h samples ( x 0.41, t a k i n g the same cons- t a n t s s e t ?or the c y i n Ga,, A1,Ae as i n GaAs i s a r a t h e r good a p p r o x ~ m a t i o n .

The same B r i l l o u i n spectrometer w i t h s i m i l a r s c a t t e r i n g geometry was used t o i n v e s t i g a t e the acoustic p r o p e r t i e s o f s u p e r l a t f i c e s . Three samples o u t o f s i x have been selected for t h e i r good surface qua1 i t y . Their v e l o c i t i e s are given i n Table 11. The i n v e s t i g a t i o n s per formed on these super1 a t t i c e s have evidenced a s l i g h t increase i n the acoustic surface v e l o c i t i e s w i t h r e s p e c t t o the corresponding mean homogeneous medium where the A1 atoms are randomly d i s t r i b u t e d on the I 1 1 element s i t e s - w i t h a p r o b a b i l i t y

2

= xd /(d.a+d2 ) ( i .e. the a l l o y Ga -x -A1 As.) The surface velocities corresponding t o iT can be obtained w i t h the hellp o f h g . 2 . Possible stresses i n the s u p e r l a t t i c e due t o the l a t t i c e mismatch between adjacent l a y e r s c o u l d be a t the o r i g i n o f t h i s small increase i n the v e l o c i t i e s . I n e p i t a x i a l l a y e r s o f several micrometers th'ickness, t h e stresses, which are l o c a l i z e d i n t h e i n t e r face can r e l a x a t the f r e e boundary o f l a y e r s , g i v i n g t h e r e s u l t s o f F i g 2. It would be i n t e r e s t i n g t o apply the same measurements t o good s u p e r l a t t i c e s w i t h much more s e v e r e l y mismatched s e m i c o n d u c t o r s

[ l o ]

( i n GaAs

-

Gal-xAl As s u p e r l a t t i c e s the l a t t i c e constants o f the two m a t e r i a l d i f f e r by o n l y one p a r t i n a thousand).

Other Raman s c a t t e r i n g measurements performed i n the same k i n d o f s u p e r l a t t i c e s on the d i s p e r s i o n curves o f acoustic folded branches and the f o l d i n g o f o p t i c a l branches, are presented e l sewhere [ll]

.

TABLE I 1

-

Rayleigh wave v e l o c i t i e s i n s u p e r l a t t i c e s i n the two p r i n c i p a l d i r e c t i o n s

~ t h e 7 { 0 0 1 ) fr e e surface .(tn/s)

S u p e r l a t t i c e v s L100] vs

L1lO]

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J O U R N A L D E PHYSIQUE

C I

20 10 0

FREQUENCY SHIFT (cm-'1

Fig.1 : Raman s c a t t e r i n g i n a G ~ A S - G ~ ~ - ~ A ~ ~ A S s u p e r l a t t i t e ( s $ n p l ~ ~ 5 o f Table 1) showing several modes Q ~ , Q

, n,,

Q, belonging t o the lrS

, zn ,

4 folded

l o n g i d u t i n a l branch. The p o f a r i z a t i o n s o f i n c i d e n t and s c a t t e r e d are always p a r a l l e l and the s e l e c t i o n r u l e s are the same as for an acousto-optical i n t e r a c t i o n . The o r i g i n o f the frequency s h i f t i s given by the reduced Rayleigh l i n e R. The experimental r e s o l u t i o n i s 1 cm-l. The s e n s i t i v i t y o f the d e t e c t i o n for the upper spectrum i s increased w i t h r e s p e c t t o t h a t the lower.

Fig. 2 : Rayleigh-wave v e l o c i t i e s vs the concentration x i n Ga,,,Al As e p i t a x i a l l a y e r s . The broken l i n e s are c a l c u l a t e d curves obtained by k e e p ~ n g the same set o f e l a s t i c constants for a l l x values ( o n l y the d e n s i t y v a r i e s ) .

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REFERENCES :

[ I ] The e x c e l l e n t s u p e r l a t t i c e s have been grown by A. Regreny and X-ray c h a r a c t e r i z e d by J. Kervarec. I t i s a pleasure t o acknowledge both of them.

[ 2 ] Colvard C, Merlin R and Klein M.V, Phys. Rev. L e t t .

45

(1980)

[3] Sapriel ^{J . ,}~ j a f a r i - R o u h a n i B.and Dobrzynski L a i n t h e f i f t h European Conference on Surface S c i e ~ g ~ e , Ghent, 1982 Surf. Sci.

-

126 (1983) 197.

[4] Sapriel J., Michel J.C., Toledano J.C., Vacher R., Kervarec 3. and Regreny A., Phys. Rev B,

28

(1983) 2007.

[5] Sandercok R., Phys. Rev. L e t t . 28 (1972) 237 [6] Sapriel J . , Acousto-optics (Wiley, New York, 1979)

[7] Due t o non s t r i c t backscattering conditions (Brewster incidence). t r a n v e r s e modes have been observed by Colvard C., Merlin R., Klein M.V., J . Phys. ( P a r i s ) Coll oq.

42,

C6 (1981) 6 3 9 by resonnant Raman s c a t t e r i n g .

[ 8 ] Winterling G., Koteles E.S., Cardona M., Phys. Rev. L e t t .

-

39, (1977) 1286.

[9] Sandercock R., Sol id S t a t e Corn

26,

(1978) 547

[ l o ] Osborn G., Biefeld R., Gourley P. Appl. Phys. L e t t .

41,

(1982) 172.

[ l l ] Jusserand B, Paquet D , Kervarec J. and Regreniy A., i n t h e s e Proceedings.