C o m p o s i t i o n a n d S t r a i n o f S e m i c o n d u c t o r Q u a n t u m D o t s C o m p o s i t i o n a n d S t r a i n o f S e m i c o n d u c t o r Q u a n t u m D o t s Fig. 1 F i g . 1 . A s c h e m a t i c o f t h e g r a z i n g i n c i d e n c e s c a t t e r i n g g e o m e t r y e m p l o y e d i n t h e R e c i p r o c a l S p a c e M a p p i n g m e t h o d . Fig. 2(a) Fig. 2(b) Quantum dots exhibit confinements of electronic carriers and have been a major focus of research i n t e r e s t i n t h e l a s t d e c a d e . T h e c o n f i n e m e n t resulted from the dot dimension , which is typically i n t h e r a n g e o f 1 0 n m t o 5 0 n m . A l t h o u g h n e w fabrication techniques for various dots have greatly advanced, our fundamental knowledge of quantum dots in terms of equilibrium and kinetic properties of f o r m a t i o n r e m a i n s l i m i t e d . C o m p a r e d t o b u l k cr ys ta ls or ep it ax ia l fi lm s, th e co nc ep ts of eq ui li br iu m c r y s t a l s h a p e , s u r f a c e s e g r e g a t i o n , a n d p h a s e d i a g r a m a l l n e e d t o b e d e v e l o p e d f o r d i f f e r e n t qu an tu m do t sy st em s. T o be ab le to ex pe ri me nt al ly deter mine the exact atomi c posit ions of the dot is one of the critical steps in this research. T h e m e t h o d w e h a v e e m p l o y e d t o s t u d y t h e s t r u c t u r e o f q u a n t u m d o t s i s a n e x t e n s i o n o f t h e c o n v e n t i o n a l g r a z i n g i n c i d e n c e s u r f a c e X - r a y d i f f r a c t i o n t e c h n i q u e . T h e b a s i c i d e a i s t h a t t h e dots can be divided into iso-strain slab s , which are region s with constant lateral lattice parameter s [1]. X - r a y s s c a t t e r e d b y d i f f e r e n t i s o - s t r a i n s l a b s a t dif fer ent hei ght s wil l dis tri but e to dif fer ent par t s of the reciprocal space ( ). Therefore, from the d e t a i l e d p r o f i l e o f t h e X - r a y i n t e n s i t y d i s t r i b u t i o n a r o u n d s u r f a c e B r a g g p e a k s , w e a r e a b l e t o reconstruct the shape and the strain field within the dots. The methodology is called Reciprocal Space Mapping ( RSM ) [1]. In this work, we further explore the resonant X-ray effect in RSM to study quantum dot s. F o r s e m i c o n d u c t o r s y s t e m s , t h e f a b r i c a t i o n t e c h n i q u e s o f d i f f e r e n t q u a n t u m d o t s h a v e b e e n w e l l d e v e l o p e d t o t h e e x t e n t t h a t o p t o - e l e c t r o n i c d e v i c e s c a n b e c o m m e r c i a l i z e d . N o w a d a y s , t h e m o s t e f f e c t i v e w a y t o f a b r i c a t e s e m i c o n d u c t o r q u a n t u m d o t s i s b y t h e s e l f - a s s e m b l e d g r o w t h m o d e , w h i c h r e l i e s o n s t r a i n - i n d u c e d i s l a n d f o r m a t i o n v i a a S t r a n s k i - K r a s t a n o w e p i t a x i a l g r o w t h . I n t e r e s t i n g l y , s u c h q u a n t u m d o t s a r e dislocation free and often exhibit a preferred shape with narrow size distribution [2]. We applied RSM t o u n c a p p e d I n G a A s q u a n t u m d o t s g r o w n o n a G a A s ( 0 0 1 ) s u b s t r a t e . T h e s u r f a c e t o p o l o g y o f a typical sample studied is shown in . T h e X - r a y s c a t t e r i n g m e a s u r e m e n t s w e r e c o n d u c t e d a t b o t h t h e b e n d i n g m a g n e t b e a m l i n e B L 1 2 B 2 a t S P r i n g - 8 a n d t h e w i g g l e r b e a m l i n e BL 17 B o f Ta iw an L ig ht S ou rc e. Th e gr az in g in ci de nt scattering geometry was set with α i < α c of GaAs. W i t h t h i s s c a t t e r i n g g e o m e t r y , w e e x p l o r e d a n i l l u m i n a t e d a r e a o f a f e w m m 2 c o n t a i n i n g ~ 1 0 6 q u a n t u m d o t s . T h e r e s u l t s o b t a i n e d b y n o n - r e s o n a n t R S M o f t h e s t r a i n a n d c o m p o s i t i o n a l distributions of the InGaAs dots are shown in [3]. T h e r e s o n a n t R S M m e t h o d i n c o r p o r a t e s t h e anomalous X-ray effect near the absorption edges [ 4 ] , w h e r e t h e d i s p e r s i o n c o r r e c t i o n s ƒ ’ a n d ƒ ” m a k e a r a t h e r l a r g e c o n t r i b u t i o n t o t h e a t o m i c s c a t t e r i n g f a c t o r s a n d v a r y d r a s t i c a l l y w i t h t h e e n e r g y o f t h e i n c i d e n t X - r a y s . T h i s v a r i a t i o n i s further enhanced for weak reflections and provides a h i g h l y s e n s i t i v e m e a n s t o d e t e r m i n e t h e com pos iti on ( x ) of eac h iso -st rai n sla b. One can better understand the sensitivity of the method by 34 q r q z q a k f k i α f α i Figure 3( a) Fig. 3(b) References [1] I. Kegel et al. , Phys. Rev. B 63 (2001) 35318. [2] L.G. Wang et al. , Phys. Rev. B 62 (2000) 1897. [3] C.H. Hsu et al. , 7th Int’l Conf. on Surface X-ray a n d N e u t r o n S c a t t e r i n g , S e p . 2 0 0 2 , t o a p p e a r i n Physica B (2003). [4] Y. Stestko et al. , to be published. examining the structure factor of even reflections of In x Ga 1- x As, whic h has the zinc -ble nd stru ctur e, as given by F InGaAs = [ x F InAs + ( 1- x ) F GaAs ] = 4 [ x ( f In f As ) + ( 1- x ) ( f Ga f As )] , where F ’s and ƒ ’s are the structure factors and the atomic scattering factors and the plus (minus) sign is for strong (weak) reflection, respectively. il lu st ra te s th e en er gy d ep en de nc e of n or ma li ze d s c a t t e r e d i n t e n s i t i e s f o r t h e I n x G a 1- x A s ( 2 0 0 ) a n d (4 00 ) re fl ec ti on s wi th In co mp os it io n x of 0. 1 an d 0.4. These calculated profiles agree qualitatively to the experimental ones as shown in . The o b t a i n e d h e i g h t - s t r a i n a n d c o m p o s i t i o n - s t r a i n d e p e n d e n c e c l e a r l y i n d i c a t e t h a t t h e I n c o n c e n t r a t i o n i s m u c h l o w e r t h a n t h e n o m i n a l c o m p o s i t i o n 0 . 5 ne ar th e do t/ su bs tr at e in te rf ac e re gi on an d gr ow s wi th in cr ea si ng la tt ic e mi sm at ch . De ta il ed re su lt s will be published [4]. Keng S. Liang National Synchrotron Radiation Research Center, Taiwan E-mail: ksliang @ srrc.gov.tw Fig. 2. (a) An AFM image of uncapped In x Ga 1-x As quantum dots formed on GaAs (001) surface with a nominal x = 0.5. (b) The variations of radius and I n c o n t e n t o f I n G a A s q u a n t u m d o t s o b t a i n e d b y non-resonant RSM method. Fig. 3. (a) The energy dependence of normalized scattered in te ns it ie s fo r th e In x Ga 1-x As (2 00 ) an d (4 00 ) re fl ec ti on s wi th In co mp os it io n x of 0. 1 an d 0. 4. In se t: th e en er gy dispersion corrections ƒ’ and ƒ” near Ga K-edge. (b) The e x p e r i m e n t a l e n e r g y - s c a n n e d p r o f i l e s a t d i f f e r e n t q r p o s i t i o n s a s i n d i c a t e d i n t h e i n s e t . D i f f e r e n t p r o f i l e s c o r r e s p o n d t o q u a n t u m d o t l a y e r s w i t h d i f f e r e n t I n concentration. The curves are offset vertically for clarity. 35 1 0 - 3 I - 0 . 0 4 - 0 . 0 2 0 . 0 0 q r ( r l u ) E ( k e V ) I ( a r b . u n i t ) 1 0 0 1 0 1 1 0 . 1 1 0 . 2 1 0 . 3 1 0 . 4 1 0 . 5 1 0 . 1 1 0 . 2 1 0 . 3 1 0 . 4 1 0 . 5 G a K - e d g e 4 0 - 4 - 8 E l e c t r o n s E ( k e V ) 1 0 . 2 1 0 . 4 f ’ f ” N o r m a l i z e d I n t e n s i t y E ( k e V ) 1 0 0 1 0 1 ( 2 0 0 ) , x = 0 . 1 ( 4 0 0 ) , x = 0 . 4 ( 2 0 0 ) , x = 0 . 4 ( 4 0 0 ) , x = 0 . 1 ( b ) ( a ) 0 . 0 0 8 6 μ m / d i v 0 0 . 2 0 μ m / d i v 0 . 2 0 μ m / d i v 0 4 8 1 2 1 6 2 0 2 4 2 8 R ( n m ) 0 1 2 3 4 5 6 7 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 0 1 2 3 4 5 6 7 I n ( % ) Z ( n m ) Z ( n m ) ( b ) ( a )
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