AN X-RAY DIFFRACTION STUDY OF DISORDER IN GaAlAs-GaAs SUPERLATTICES

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AN X-RAY DIFFRACTION STUDY OF DISORDER IN GaAlAs-GaAs SUPERLATTICES

P. Auvray, M. Baudet, A. Regreny, A. Poudoulec, B. Guenais

To cite this version:

P. Auvray, M. Baudet, A. Regreny, A. Poudoulec, B. Guenais. AN X-RAY DIFFRACTION STUDY

OF DISORDER IN GaAlAs-GaAs SUPERLATTICES. Journal de Physique Colloques, 1987, 48 (C5),

pp.C5-105-C5-108. �10.1051/jphyscol:1987518�. �jpa-00226722�

A N X-RAY D I F F R A C T I O N STUDY OF D I S O R D E R I N G a A l A s - G a A s S U P E R L A T T I C E S

P . A W R A Y , M. BAUDET, A. R E G R E W , A. POUDOULEC a n d B. GUENAIS C e n t r e N a t i o n a l d ' E t u d e s d e s T ~ l e c o m m u n i c a t i o n s , R o u t e d e T r e g a s t e l , BP 4 0 , F-22301 L a m i o n C e d e x , F r a n c e

R B s m B

Un ddsordre a BtB introduit dans des superr6seaux GaAlAs-GaAs fabriquBs par E J M , en faisant varier intentionnellement, suivant une loi gaussienne, les Bpaisseurs des puits de GaAs. Les diagrammes de diffraction X donnss par ces structures presentent au voisinage des rBflexions satellites dlordre diffsrent de zdro, des effets inhabi- tuels (pics suppl6mentaires) qui croissent avec le dssordre. Un modele mathdmatique bass sur la thBorie cindmatique permet, connaissant la ssquence de croissance, d1ex- pliquer dans le detail les profils observBs.

Abstract

An intentional disorder has been introduced in MBE grown GaAlAs-GaAs superlattices by varying, following a gaussian law, the thicknesses of the GaAs wells. The experi- mental X-ray diffraction diagrams given by these structures show in the vicinity of non-zero order satellite reflections, unusual effects (extra-peaks) increasing with disorder. A mathematical model based on the kinematical theory was established : it allows the computing of the detailed shape of the diffraction profiles, provided the growh sequence is known.

1 - INTRODUCTION

X-ray diffraction experiments are at the present time in current use to determine the characteristic structural parameters of well-ordered artificial semiconductor based superlattices [l-51. They can also provide useful information in the case of non regular structures since the diffraction profiles are affected by random fluctuations in composition and in layer thicknesses [ 6 . 7 1.

A series of 6 intentionally disordered GaAlAs-GaAs superlattices was grown by MBE in order to study by photoluminescence the carrier localization and the inhibition of carrier transport along the growth axis as a function of an increasing disorder [ a ] . Their diffraction diagrams show subsidiary peaks (out of Bragg positions) which cannot be ex lained by statistical models based on the homogeneity of the disordered structures 111.10 ] : however as the growth sequence is known

the contribution of each layer to the scattered intensity can be taken separately into account, no attempt being made to separate the disorder term and the average structure term in the expression of the scattered amplitude.

2 - EXPERIMENTAL

The samples were grown by MBE on Si doped "laser quality"

Gaks wafers following a procedure described elsewhere [l1 1.

Their particular configuration is shown in fig.1 : SL1 and SL2 are identical and symmetrical with regard to We. Six samples were investigated : in the first one (reference sample) SL1 (and SL2) is strictly periodic with expected

4 9 p e r i o d s u p s r l a t l l c s SL2

Fig. 1 : Schematic diagram of the samples structure.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987518

CS-1 06 JOURNAL DE PHYSIQUE

v a l u e s of 0.3 f o r t h e A l c o n t e n t of 30 1 f o r t h e t h i c k n e s s e s of t h e GaAs o r GaAlAs s u b l a y e r s . I n t h e o t h e r s , t h e t h i c k n e s s of t h e GaAlAs b a r r i e r s i s c o n s t a n t whereas t h o s e of theoGaAs w e l l s v a r y randomly f o l l o w i n g a g a u s s i a n law w i t h a mean e x p e c t e d v a l u e of 30 A and a s t a n d a r d d e v i a t i o n S; S c h a r a c t e r i s e s t h e d i s o r d e r i n t e n t i o n a l l y i n t r o d u c e d and v a r i e s from 0 t o 11.76 A. The main o b s e r v e d c h a r a c t e r i s t i c s of t h e i n v e s t i g a t e d s a m p l e s a r e g a t h e r e d i n t a b l e 1.

T a b l e 1 : S, s t a n d a r d d e v i a t i o n o f t h e w e l l t h i c k n e s s e s . Te, t o t a l t h i c k n e s s of t h e e p i t a x y . We, e n l a r g e d w e l l t h i c k n e s s . C, mean v a l u e of t h e s u p e r p e r i o d . f , mean Al-content i n t h e e p i t a x y .

Al-content i n t h e b a r r i e r s . ng, number of molecu- l a r lanes i n t h e b a r r i e r s . % . a v e r a g e number of m o l e c u l a r lanes i n t h e w e l l s .

k c r o s s s e c t i o n a l d a r k f i e d TB4 image f i g . 2 ) o f t h e most d i s o r d e r e d sample l l u s t r a t e s one of t h e growth s e q u e n c e s . i g u r e 3a shows t h a t non-zero o r d e r s a t e l - i t e peaks which r e v e a l t h e SL m o d u l a t i o n , r e a f f e c t e d bv d i s o r d e r whereas t h e mean

Q I S p l i t i n t o s m a l l e r ~ e a k s and a s d i s o r d e r l b n c r e a s e s s o d o e s t h e a n g u l a r r a n g e cove-

ed by e a c h g r o u p of p e a k s around t h e a t e l l i t e p o s i t i o n s of t h e n o n - d i s o r d e r e d L. I t i s however p o s s i b l e t o d e f i n e , i n a c h s a t e l l i t e g r o u p , a mean peak p o s i t i o n t t h e c e n t e r of g r a v i t y o f t h e group.

F i g . 2 : ( 0 0 2 ) d a r k f i e l d TIN image of Thus t h e f 1 mean s i t e l l i t e peak p o s i t i o n s

sample S = 11.76 A. and t h e mean 001 SL peak were used

i n t h e u s u a l manner t o d e t e r m i n e t h e SL p e r i o d C, and t h e mean Al-content v a l u e Z i n each sample.

F i g . 3 :

X-ray d i f f r a c t i o n d i a g r a m s c l o s e t o

t h e 002 GaAs s u b s t r a t e r e f l e c t i o n

a ) o b s e r v e d b) c a l c u l a t e d . Only t h e

f i r s t o r d e r s a t e l l i t e peaks a r e

shown b e c a u s e t h e y a r e i n t e n s e and

a l w a y s v i s i b l e e v e n when d i s o r d e r

i s high.

l I

Fig.4 : T y p i c a l DDX p r o f i l e s c l o s e t o t h e 004 GaAs s u b s t r a t e r e f l e c t i o n showing t h e simi- l a r i t y o f t h e zero order sa- t e l l i t e peaks o f samgles S

0 and S

11.76 A.

S u b s t r a t e

Fig.5 : Model f o r t h e c a l c u l a t i o n o f 001 scat- t e r e d i n t e n s i t y .

- 0

Fig.6 : Magnified d i f f r a c t i o n p r o f i l e s corresponding t o t h e -1 order s a t e l l i t e o f t h e h i g h e s t disordered sample ( S

11.76 R ) .

The t h e o r e t i c a l p r o f i l e s were c a l c u l a t e d conside- r i n g t h a t t h e l a y e r t h i c k n e s s e s are proportional t o t h e opening t i m e s o f t h e ovens and t h a t t h e s t e p s a t t h e i n t e r f a c e s are o n l y one molecular plane h i g h [ 1 2 , 131. Figure 5 shows t h e model f o r t h e s c a t t e r e d i n t e n s i t y c a l c u l a t i o n s f o r t h i s t y p e o f s t r u c t u r e s . The e x p r e s s i o n f o r t h e s c a t t e r e d amplitude a t angle

was d i r e c t l y derived from t h e b a s i c kinematicalu e x p r e s s i o n :

(1) Fool (8)

2 f j exp ( i k z j ) where

k = 4ll s i n 8/?f1 M i s t h e number o f molecular planes i n t h e s t r u c t u r e , f j i s t h e complex s c a t t e r i n g f a c t o r o f t h e J-th molecular l a y e r and z j i t s z-coordinate.

I n t h e model o f f i g u r e 5 o n l y one s t e p o f one monolayer i s drawn a t each i n t e r f a c e s i n c e t h e r e a l s t e p s p o s i t i o n s do not m a t t e r when one views t h e r e c i p r o c a l space along t h e 001 d i r e c t i o n . Only t h e proportion pj o f each m a t e r i a l a t each i n t e r f a c e molecular plane i s important. A f u l l mathematical de-elopment o f e x p r e s s i o n ( 1 ) i s t o

be published [ 1 4 ] .

The

v a l u e i n GaAlAs l a y e r s was t a k e n t o be equal t o ,be ( 1 + ^{i i w / n b ) where $} and ng a r e t h e mean numbers o f molecular planes i n t h e w e l l s and i n t h e b a r r i e r s r e s p e c t i v e l y , c a l c u l a t e d assuming t h e i r r a t i o i s as i n t e n d e d . The r e s u l t s are shown i n f i g . 3 b f a c i n g t h e observed diagrams.

4 - DISCUSSION

As long as t h e d i s o r d e r i s low ( S ( 1;) t h e e x p e r i m e n t a l diagrams and t h e c a l c u l a t e d ones d i s p l a y a decrease of t h e maximum i n t e n s i t y o f t h e s a t e l l i t e peaks and a l s o an i n c r e a s s o f t h e i r w i d t h a t h a l f maximum. Above S

1.25A s a t e l l i t e peaks become sharper and a f i n e s t r u c t u r e begins t o a p p e a r on e a c h s i d e o f t h e i r b a s e . The corresponding c a l c u l a t e d diagrams a l l show a s p l i t t i n g o f t h e 5 1 order s a t e l l i t e peaks, t o g e t h e r w i t h an i n c r e a s i n g d i f f e r e n c e o f i n t e n s i t y o f t h e two components o f t h e main peak.

T h i s non-equilibrium i s r e f l e c t e d i n t h e observed d i a g r a m s and e x p l a i n s f o r i n s t a n c e why t h e obserzed -1 order peak i s narrower f o r sample S

1 . 2 5 A than f o r sample S=0. For higher v a l u e s o f S

(2 3.141)extra peaks become v i s i b l e o u t s i d e t h e

Bragg p o s i t i o n s p r a c t i c a l l y w i t h o u t i n t e r r u p t i o n

i n t h e i n v e s t i g a t e d angular range i n agreement

w i t h t h e t h e o r e t i c a l e x p e c t a t i o n s . Inhomogeneities

such as in-plane g r a d i e n t s o f period and Al

c o n t e n t were not t a k e n i n t o account i n t h e

c a l c u l a t i o n s . I n s p i t e o f t h i s , t h e r e i s a good

a g r e e m e n t b e t w e e n o b s e r v e d and c a l c u l a t e d

p a t t e r n s . T ) i s i s p a r t i c u l a r l y obvious f o r sample

S 11.76 A which has t h e h i g h e s t w e l l t h i c k n e s s

standard d e v i a t i o n ( f i g . 6 ) . B u t , although t h e

d i s t u r b a n c e due t o d i s o r d e r i n t h e observ5d

diagrams i s l e s s s t r i k i n g f o r v a l u e s o f S <3.14 A,

C5-108 JOURNAL DE PHYSIQUE

i t c a n s t i l l be d e t e c t e d ( w i t h t h e h e l p of t h e o r e t i c a l d i a g r a m s ) e v e n i n t h e l e a s t d i s o r d e r e d s a m p l e s . T h i s means t h a t t h e r e s i d u a l d i s o r d e r i n h e r e n t i n t h e MBE t e c h n i q u e i s less t h a n 0.57 1 i n s t a n d a r d d e v i a t i o n f o r t h e r e f e r e n c e sample.

5 - CONCLUSION

T h i s s t u d y of a s e r i e s of i n t e n t i o n a l l y d i s o r d e r e d s a m p l e s h a s e n a b l e d u s t o show e x p e r i m e n t a l l y t h e e f f e c t of d i s o r d e r on t h e d i f f r a c t i o n p a t t e r n s . A t h e o r e t i c a l m o d e l which t a k e s i n t o a c c o u n t e v e r y l a y e r of t h e s t a c k i n g was worked o u t and c a l c u - l a t i o n s b a s e d on t h i s model l e d t o a n e x c e l l e n t a g r e e m e n t between o b s e r v e d and c a l - c u l a t e d d i a g r a m s . When d i s o r d e r is low t h e e x p e r i m e n t a l d i a g r a m s a r e w e a k l y d i s t u r - bed and a n a n a l y t i c a l a v e r a g i n g e x p r e s s i o n o n l y d e p e n d i n g on t h e mean s t r u c t u r e and t h e s t a n d a r d d e v i a t i o n of t h e v a r y i n g p a r a m e t e r o u g h t t o be s a t i s f a c t o r y . On t h e c o n t r a r y i n t h e c a s e of v e r y d i s o r d e r e d s a m p l e s , t h e b a s i c s c a t t e r i n g e x p r e s s i o n ( 1 ) h a s t o be u s e d , a t l e a s t when t h e number of d e p o s i t e d l a y e r s i s low, a s i n t h i s s t u d y . A s a m a t t e r of f a c t , we v e r i f i e d t h a t when t h i s number i n c r e a s e s , k e e p i n g t h e s t a n d a r d d e v i a t i o n c o n s t a n t , t h e complex s a t e l l i t e peak s t r u c t u r e s smooth o u t t o b r o a d e n e d p e a k s .

ACKNW LEGDEM ENTS

T h e a u t h o r s a r e g r a t e f u l t o Ph. Cabon who made a f i r s t t h e o r e t i c a l s t u d y of d i s o r d e r d u r i n g h i s s t a y i n o u r l a b o r a t o r y i n 1 9 8 3 , t o

Chomette f o r h e l p f u l d i s c u s s i o n s on t h e m o d e l l i n g o f t h e i n t e r f a c e s and t o J. C a u l e t f o r t e c h n i c a l a s s i s t a n c e .

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