MEASUREMENT OF AN ATOMIC POSITION COHERENCE LENGTH IN a-Ge

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MEASUREMENT OF AN ATOMIC POSITION

COHERENCE LENGTH IN a-Ge

J. Rodenburg

To cite this version:

MEASUREMENT O F AN A T O M I C P O S I T I O N C O H E R E N C E LENGTH I N a - G e J.M. Rodenburg

Cavendish Laboratory, MadingZey Road, Cambridge, CE3 OHE,

U.

Abstract - A scanning transmission electron microscope (STEM) has been used to obtain microdiffraction patterns from small volumes (3 - 650 nm3) of a-Ge. These are recorded on new high-resolution, high-efficiency instrumentation. It appears as if the reciprocal space of even comparatively large volumes (30 thousand atoms) contains statistically significant, spherically anisotropic fluctuations.

1

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Diffraction experiments generally involve the study of samples which are extremely large relative to the characteristic inter-atomic spacings. Though in perfect crystals this only serves to clarify the reciprocal space lattice, in amorphous materials it can be regarded as averaging-out and destroying useful information pertaining to medium-range order. By being able to control the amount of material contributing to the diffraction pattern, at a scale within an order of magnitude of the atomic spacing, it should be possible to extract more information than merely the one-dimensional radial distribution function.

A scanning transmission electron microscope (STEM) provides a means of obtaining a very fine focussed probe of high energy electrons. The beam cross-over is the plane of the specimen and under good conditions can be less than 0.5 nm in diameter. Appreciable numbers of electrons are scattered into the diffraction plane, even from very thin specimens (5 nm thick), because they interact so strongly with matter. From amorphous materials, the resulting 'microdiffraction' patterns appear spotty as the smooth diffraction rings break up into discontinuous patches. This is presumably due to the existence of preferential scattering directions within such a small group of atoms. Such patterns have been observed before /1-3/, however, because of a combination of various instrumental limitations / & / , it has been impossible to record them at both high angular resolution and near-unity quantum efficiency, thus inhibiting a detailed study of their structure.

This paper presents some initial observations of microdiffraction patterns from amorphous germanium obtained on new instrumentation which overcomes the previous difficulties of specimen contamination and drift. By defocussing the probe, an approximate measurement is made of the maximum volume beyond which spottiness is no

C9-64 JOURNAL

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longer observed. It is t e n t a t i v e l y suggested t h a t t h i s may correspond t o a

coherence l e n g t h i n atomic p o s i t i o n and bonding-angle o r i e n t a t i o n .

II - EXPERIMENTAL

Germanium was evaporated i n vacuum ( - 1 0 - ~ mbar) and deposited on

a

s u b s t r a t e of NaCl, and f l o a t e d o f f i n d i s t i l l e d water ont0 copper g r i d s p e r f o r a t e d by 10 Pm diameter holes. Such f i l m s were found t o be s e l f - s u p p o r t i n g down t o a t h i n n e s s of about 5-6 nm'.

Figure 1 shows a schematic r a y diagram of t h e VG S c i e n t i f i c HB501 STEM on which t h e

experiments were performed. Electrons emanating from a cold, f i e l d emission source

( e f f e c t i v e s i z e -5 nm) a r e a c c e l e r a t e d t o 100 keV and focussed ont0 t h e specimen by

demagnifying magnetic l e n s e s with a f i n a l semi-angle of convergence of 8 mrad.

Focus and s t i g m a t i o n of t h e o p t i c s a r e achieved by observing t h e scanned, high

r e s o l u t i o n image of t h e specimen /5/. The e l e c t r o n d i s t r i b u t i o n i n t h e

m i c r o d i f f r a c t i o n plane is recorded d i r e c t l y ont0 photographic f i l m which is s h i e l d e d from t h e u l t r a - h i g h vacuum of t h e specimen chamber by a t h i n s e p a r a t i o n f o i 1 /6/.

Typical exposure times, which a r e c o n t r o l l e d by a beam-blanking f a c i l i t y , a r e

between 8 and 16 m s , depending on t h e beam c u r r e n t and specimen thickness. This is

s h o r t enough t o avoid t h e e f f e c t s of contamination and d r i f t i n g of t h e probe r e l a t i v e t o t h e specimen.

CONDENSER OBJECTIVE

LENS (ES) LENS MICRODIFFRACTION PLANE

Fig. 1

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The specimen t h i c k n e s s was measured by examining t h e energy-loss spectrum of t h e i n e l a s t i c a l l y s c a t t e r e d e l e c t r o n s using a magnetic-prism spectrometer ( r e s o l u t i o n

-1 eV) mounted beyond t h e m i c r o d i f f r a c t i o n plane. The r a t i o of t h e a r e a s under t h e

zero-loss Peak and t h e f i r s t c o l l e c t i v e e x c i t a t i o n (plasmon) Peak g i v e s a d i r e c t

measure of t h e t h i c k n e s s because t h e mean-free path l e n g t h of t h e i n t e r a c t i o n is a

measurable constant /7/. To avoid beam spreading, dynamical s c a t t e r i n g events and

o v e r l a p phenomena i n t h e two-dimensional p r o j e c t i o n p o t e n t i a l of t h e Specimen

f u n c t i o n , t h e very t h i n n e s t specimens a v a i l a b l e were used.

The volume of specimen c o n t r i b u t i n g t o t h e p a t t e r n was varied by a d j u s t i n g t h e e x c i t a t i o n of t h e o b j e c t i v e (probe-forming) l e n s by a known amount away from focus. t h u s i n c r e a s i n g t h e diameter of t h e d i s c of i l l u m i n a t i o n on t h e specimen. P a t t e r n s

obtained i n t h i s way t h e r e f o r e have t h e same average d e n s i t y

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being t h e defocus.

III - RESULTS AND INTERPRETATION

p r o b e ) , which would r e d u c e e r r a n t r a y s , i n c r e a s e s d i f f r a c t i o n - s p r e a d i n g ( t h e probe b e i n g an a b e r r a t e d Airy d i s c ) . I t is w e l l e s t a b l i s h e d /8/ t h a t t h e r e t h e r e f o r e e x i s t s an optimum a n g l e o f convergence g i v e n by

where A is t h e wavelength (0.0037 nm f o r 100 keV e l e c t r o n s ) , and Cs is t h e s p h e r i c a l

a b e r r a t i o n c o n s t a n t ( i n t h i s c a s e , nominally 3.1 m m ) . For t h e 8 mrad a p e r t u r e used,

which f u l f i l l s t h i s c r i t e r i o n , t h e c o r r e s p o n d i n g probe diameter is 0.5 nm. However,

because of t e c h n i c a l r e s t r i c t i o n s , t h e microscope was n o t run under optimum

c o n d i t i o n s f o r maximum d e m a g n i f i c a t i o n o f t h e s o u r c e , t h e image of which is

convoluted w i t h t h e A i r y d i s c . I n t h e s e experiments, t h e minimum probe was p e r h a p s

a s l a r g e a s 0.8 nm i n diameter.

F i g u r e 2 shows a t y p i c a l minimal probe m i c r o d i f f r a c t i o n p a t t e r n . For t h e purposes o f p u b l i c a t i o n , t h e s e have been p r i n t e d on h a r d p h o t o g r a p h i c paper t o enhance c o n t r a s t . I t is observed t h a t t h e a p p a r e n t s p o t ( o r ' b l o t c h ' ) s i z e is c o n s t a n t i r r e s p e c t i v e o f its d i s t a n c e o u t i n t o r e c i p r o c a l space. The volume i r r a d i a t e d is a b o u t 3 nm3, o r fewer t h a n 200 atoms.

F i g . 2 - A s i n g l e minimal volume m i c r o d i f f r a c t i o n p a t t e r n from 6 nm t h i c k a-Ge. The t h r e e p r i n t s a r e a t i n c r e a s i n g exposure t o i l l u s t r a t e t h e a p p a r e n t l y c o n s t a n t ' b l o t c h ' s i z e o u t i n t o r e c i p r o c a l space. The d i a m e t e r o f t h e o b j e c t i v e a p e r t u r e is 1 6 mrad.

A s would b e expected, t h e p a t t e r n s do n o t d i s p l a y any e v i d e n c e o f c r y s t a l l i t e s t r u c t u r e . There is no c l e a r r e p l i c a t i o n of an o b j e c t i v e a p e r t u r e d i s c a s can be a c h i e v e d from, Say, p a r t i a l l y g r a p h i t i z e d carbon ( s e e f i g . 3 ) where t h e domains a r e l a r g e (up t o 4 nm).

Upon d e f o c u s s i n g t h e probe ( f i g . 4 ) . t h e d i f f r a c t e d b l o t c h e s a r e s e e n t o p r o g r e s s i v e l y s h r i n k , g r a d u a l l y t e n d i n g towards t h e l i m i t of a t o t a l l y defocussed

p r o b e

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C9-66 JOURNAL DE PHYSIQUE Fig. 3 - M i c r o d i f f r a c t i o n p a t t e r n from p a r t i a l l y g r a p h i t i z e d carbon i l l u s t r a t i n g d i f f r a c t e d c i r c u l a r o b j e c t i v e a p e r t u r e f u n c t i o n s . I n t h i s case, l o c a l regions of t h e specimen have c l e a r l y defined peaks i n r e c i p r o c a l space, with which t h e a p e r t u r e f u n c t i o n is convoluted.

I t should be emphasised t h a t i n m i c r o f i f f r a c t i o n , every point i n r e c i p r o c a l space is

convoluted i n amplitude with t h e o b j e c t i v e a p e r t u r e function. Furthermore, t h e

f i e l d emission source is a t l e a s t p a r t i a l l y qoherent over t h e range of angles encountered i n t h e o b j e c t i v e a p e r t u r e / 9 / . This implies t h a t t h e b l o t c h s i z e and amplitude does not n e c e s s a r i l y bear a d i r e c t r e l a t i o n s h i p t o t h e sharpness and

d e f i n i t i o n of t h e r e c i p r o c a l space of t h e o b j e c t . I t is, i n s t e a d , a complex

i n t e r f e r e n c e phenomenon. However. i t is reasonable t o suggest t h a t t h e defocus

s e t t i n g a t which r i n g speckle disappears corresponds t o t h e volume of m a t e r i a l r e q u i r e d a t which r e c i p r o c a l space becomes s p h e r i c a l l y i s o t r o p i c .

Defining t h e limits of i s o t r o p y is n e c e s s a r i l y a r b i t a r y but may e v e n t u a l l y be

compared with t h e o r e t i c a l models. I t is noted t h a t blotches on a s c a l e of 2 mrad

a r e observable on a through-focal s e r i e s up t o 700 nm of defocus. A t such l a r g e

v a l u e s , modifications t o t h e diameter of i l l u m i n a t i o n caused by a b e r r a t i o n and d i f f r a c t i o n ( o t h e r than a c o n s t a n t term of 0 . 5 nm), a r e n e g l i g i b l e . Ray o p t i c s implies an i l l u m i n a t i o n d i s c of diameter 11.7 nm, corresponding t o a volume ( i n a 6 nm t h i c k sample) of 650 nm3, or about 30 thousand atoms i n a sphere of r a d i u s 5.4 m.

I n t e r p r e t a t i o n of t h e s e r e s u l t s is not straightfoward. Alben e t a l / I O / have

performed c a l c u l a t i o n s t o e s t i m a t e f l u c t u a t i o n s i n r e c i p r o c a l space i n t e n s i t y f o r

v a r i o u s small dense random packing models. These r e p r e s e n t t h e l e a s t ordered

systems l i k e l y t o occur i n p r a c t i c e , y e t a p p r e c i a b l e v a r i a t i o n s i n i n t e n s i t y a r e

shown t o e x i s t i n c l u s t e r s exceeding 800 atoms. This number of atoms corresponds

c l o s e l y t o t h e focussed probe c o n d i t i o n , i n which broad v a r i a t i o n s of i n t e n s i t y a r e c e r t a i n l y observable. Further a n a l y s i s would r e q u i r e t h e t h e o r e t i c a l mode1 t o t a k e

i n t o account t h e angular range of coherent i l l u m i n a t i o n i n STEM. I t is conceivable

t h a t i n models with g r e a t e r o r d e r , t h e r e c i p r o c a l space has small s c a l e v a r i a t i o n s

even from comparatively l a r g e c l u s t e r s of atoms. Experimentally, i t would appear

t h a t t h e s t a t i s t i c a l coherence l e n g t h i n a-Ge, i . e . t h e d i s t a n c e over which t h e r e i S s t i l l s t a t i s t i c a l c o r r e l a t i o n s i n t h e atomic p o s i t i o n s or bonding-angles, is a s l a r g e a s 5

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I V

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M i c r o d i f f r a c t i o n p a t t e r n s obtained from small, v a r i a b l e volumes of a-Ge have been presented. The d i f f r a c t i o n r i n g s appear t o show s i g n i f i c a n t i n t e n s i t y f l u c t u a t i o n s

of various d i f f r a c t e d amplitudes, t h i s i n t e r p r e t a t i o n i s , perhaps, r a t h e r naive. I t

is t h e s i m p l e s t measurement t h a t can be made from a d i f f r a c t i o n experiment t h a t , a t

l e a s t t h e o r e t i c a l l y . should contain much more information than t h e r a d i a l

d i s t r i b u t i o n function.

The author would l i k e t o thank D r . A . Howie and D r . L.M. Brown f o r many h e l p f u l

d i s c u s s i o n s , and acknowledges f i n a n c i a l support from t h e SERC and VG S c i e n t i f i c Ltd.

Fig. &

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a-Ge. Top l e f t , i n focus; top r i g h t ,

220 nm defocus; r i g h t , 700 nm defocus.

Specimen t h i c k n e s s , 6 nm. The blotch

JOURNAL DE PHYSIQUE

REFERENCES

/1/ Geiss, R.H., Proc. 33rd EMSA Meeting, Claitor's Publishing, Barton Rouge (19753 218.

/2/ Brown, L.M., Craven, A.J., Jones, L.G.P., Griffith, A., Stobbs, W.M. and Wilson, C.J., Scanning Electron Microscopy, Ed. O. Johari, (SEM Inc., AMF O'Hare, Chicago) II (1976) 353.

/3/ Cowley, J.M., 'Diffraction Studies in Non-Crystalline Substances', Eds. 1. Hargittan and W.J. Orville Thomas, (Publishing House of the Hungarian Academy of Sciences, Budapest, 1981 ) 849.

/4/ Rodenburg, J.M. and McMullan, D., Inst. Phys. Conf. Ser. No. 68 (1984) 511. /5/ Brown, L.M., J. Phys. F (GB) No. 1 (1981) 1.

/6/ Rodenburg, J.M. and McMullan, D., 'The Recording of Microdiffraction Patterns in STEM', J. Phys. E (Sci. Instrum.), in press.

/7/ Raether, H., Springer Tracts in Modern Physics, (Springer-Verlag Berlin, Heidelberg, N.Y., 1980) 23.

/8/ Crewe, A.V., Rep. Prog. Phys.,

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