S t r u c t u r a l S t u d y o f / / ( 0 0 1 ) C r y s t a l b y a H o l o g r a p h i c M e t h o d u s i n g X - r a y D i f f r a c t i o n S t r u c t u r a l S t u d y o f Si / Ge / Si ( 0 0 1 ) C r y s t a l b y a H o l o g r a p h i c M e t h o d u s i n g X - r a y D i f f r a c t i o n Holography is a well-known technique to d irectly r econstruct an image of objects. In this technique, a detecting plate called a hologram is first created by using an interference effect between two waves: one is a reference wave c oming d irectly from a light so ur ce to th e de te ct in g pl at e , wh il e an ot he r is an o b j e c t w a v e c o m i n g a f t e r o n c e s c a t t e r e d b y ob je ct s. In th e se co nd st ep , on e ca n re co ns tr uc t th e ob je ct s by il lu mi na ti ng th e re fe re nc e wa ve on t h e h o l o g r a m . I n t h e p r e s e n t w o r k , w e s h o w a similar holographic method to reconstruct images of s u r f a c e a n d i n t e r f a c e a t o m s w i t h a n a t o m i c r e s o l u t i o n . H e r e w e t r e a t t w o - d i m e n s i o n a l l y o r d e r e d a t o m s o n a s u b s t r a t e c r y s t a l . H i t h e r t o s i m i l a r a t t e m p t s h a v e b e e n m a d e a s t o t w o - dimensional structures projected on the surface [1]. In t hi s wo rk , ho we ve r, w e sh ow th e f ir st e xp er im en ta l res ult s of thr ee- dim ens ion al rec ons tru ct ed ima ges of surface atoms. To analyze the structure of surface atoms on crystals, we usually measure integrated intensities for a number of diffraction spots. Then we compare t h e o b s e r v e d i n t e n s i t i e s w i t h t h o s e c a l c u l a t e d f o r p o s s i b l e m o d e l s u n t i l w e f i n d a g o o d m o d e l t h a t a t t a i n s a g o o d a g r e e m e n t b e t w e e n t h o s e t w o substrate crystal, and can calculate the phase and modul us of the ampli tude by cryst al-tr uncat ion- rod s c a t t e r i n g [ 2 ] b a s e d o n t h e k i n e m a t i c a l t h e o r y o f X - r a y d i f f r a c t i o n . T h u s w e c a n r e g a r d t h e w a v e scattered from the substrate crystal as a reference wave. In this situation, we can reconstruct unknown sur fac e ato ms by a Fou rie r tra nsf orm aft er pro per n o r m a l i z a t i o n o f t h e e x p e r i m e n t a l d a t a i n s t e a d o f i l l u m i n a t i n g a r e f e r e n c e w a v e a s i n o p t i c a l holography. Figure 2 shows images of Ge atoms on Si(001) s u b s t r a t e c r y s t a l r e c o n s t r u c t e d f r o m o b s e r v e d i n t e n s i t i e s . H e r e w e u s e d a s a m p l e i n w h i c h a monolayer of Ge atoms are epitaxially grown on a clean Si(001) surface at 775 K. A few nanometers of an amorphous Si layer was further deposited on th e sa mp le at 29 5 K to wi th st an d in th e at mo sp he re . T o r e c o n s t r u c t t h e i m a g e s , w e h a v e o b t a i n e d in te ns it ie s ab ou t at 25 0 po in ts , mo st of wh ic h ar e m e a s u r e d a t p o i n t s o n t h e r o d c l o s e t o B r a g g points. Figure 3 shows a schematic illustration of the i n t e r f a c e . F i g u r e 2 c o r r e s p o n d s t o t h e h a t c h e d are as in Fig . 3 . The res ult cle arl y sho ws tha t Ge a t o m s l o c a t e p o s i t i o n s t h a t S i a t o m s w o u l d i n t e n s i t i e s . I n t h e p r e s e n t w o r k , however, we could directly determine t h e s t r u c t u r e o f s u r f a c e a t o m s f r o m experimentally obtained intensities. Figure 1 illustrates the principle of the present method. In this case the diffraction amplitude is divide d i n two; on e is a co nt ri bu ti on fr om a su rf ac e layer to be determined, and the o ther i s a c o n t r i b u t i o n f r o m a s u b s t r a t e cr ys ta l gi ve n by the sum of am pl it ud es f r o m s e m i - i n f i n i t e l a y e r s . I n m o s t cases one knows the structure of the Surface layers Substrate Object wave Interference Reference wave Fig. 1. Principle of the present method to reconstruct images of surface atoms using an interference effect. 36 Toshio Takahashi and Kazushi Sumitani The University of Tokyo E-mail: ttaka @ issp.u-tokyo.ac.jp o t h e r w i s e o c c u p y . T h e p o s i t i o n o f G e a t o m s i s s l i g h t l y r e l a x e d t o w a r d t h e s u r f a c e , r e f l e c t i n g t h e d i f f e r e n c e i n b o n d l e n g t h s b e t w e e n G e a n d S i i n crystals. In regard to structur al analysis of surfaces and i n te r fa c e s , c o n s tr u c t i n g a n i n i ti a l m o d e l i s a m o s t intricate task . However, once the initial structure is directly obtained from experimental data, one could easily refine the structure, with for instance, t he use of conventional fitting procedures. References [1] L.D . Ma rks et al. , S urf . R ev. Le tt. 5 (1 998 ) 1 087 . [2] I.K. Robinson, Phys. Rev. B 33 (1986) 3830. [ 3 ] K . S u m i t a n i , T . T a k a h a s h i , S . N a k a t a n i , A . N o j i m a , O . S a k a t a , Y . Y o d a , S . K o h , T . I r i s a w a , and Y. Shi rak i, Jpn . J. App l. Phy s. 42 (2 003 ) L18 9. 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 X Y 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 X Z F i g . 2 . C o n t o u r m a p s o f G e a t o m s o n S i ( 0 0 1 ) sub str ate cry sta l at pla nes par all el (up per ) and perpendicular (lower) to the surface. Rectangular regions correspond to the hatched areas in Fig. 3. Fig. 3. Schematic illustration of reconstructed Ge atoms with respect to the Si(001) substrate crystal. 37 Z S i d e V i e w Y X T o p V i e w G e S i
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