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DISLOCATIONS IN SEMICONDUCTORS AS STUDIED BY WEAK-BEAM ELECTRON
MICROSCOPY
D. Cockayne, A. Hons
To cite this version:
D. Cockayne, A. Hons. DISLOCATIONS IN SEMICONDUCTORS AS STUDIED BY WEAK- BEAM ELECTRON MICROSCOPY. Journal de Physique Colloques, 1979, 40 (C6), pp.C6-11-C6-18.
�10.1051/jphyscol:1979603�. �jpa-00219019�
JOURNAL DE PHYSIQUE CoZZoque C6, suppZ6ment LA n06, tcme 4 0 , juin 1979, page C6-11
DISLOCATIONS
I NSEMICONDUCTORS AS STUDIED B Y WEAK-BEAM ELECTRON MICROSCOPY
D.J.H. Cockayne and A. Hons
Electron Microscope Unit, U n i v e r s i t y of Sydney, N.S. W. 2006, Australia
Resum@.- On d i s c u t e l a c o n f i g u r a t i o n des d i s l o c a t i o n s observees dans l e s semiconducteurs
a
l ' a i d e de l a t e c h n i q u e du f a i s c e a u f a i b l e en m i c r o s c o p i e e l e c t r o n i q u e . La d i s s o c i a t i o n de ces d i s l o c a t i o n s e s t b i e n aver@e. P l u s i e u r s problemes r e l a t i f sa
l a geometric de ces d i s l o c a t i o n s s o n t b i e n r e s o l u s . Par c o n t r e l e s o b s e r v a t i o n s r e v e l e n t l ' e x i s t e n c e de nouveaux problernes g@om@triques non encorer e -
s o l u s .
A b s t r a c t . - The c o n f i g u r a t i o n o f d i s l o c a t i o n s i n semiconductors as r e v e a l e d by t h e weak-beam method o f e l e c t r o n microscopy i s d i s c u s s e d . The d i s s o c i a t i o n o f t h e s e d i s l o c a t i o n s has been c l e a r l y e s t a - b l i s h e d , b u t w h i l e many e a r l i e r q u e s t i o n s c o n c e r n i n g t h e d i s l o c a t i o n geometries have been r e s o l v e d , new d i s l o c a t i o n geometries have been r e v e a l e d w h i c h a r e as y e t unexplained.
1. I n t r o d u c t i o n . - While t h e weak-beam method o f e l e c t r o n microscopy
/ I /
has been a p p l i e d t o t h e s t u d y o f many t y p e s o f d e f e c t i n many d i f f e r e n t ma- t e r i a l s , i t s a p p l i c a t i o n t o d i s l o c a t i o n s i n semi- conductors has been one o f t h e most f r u i t f u l areas.B u t a l t h o u g h i t has p r o v i d e d answers t o many l o n g - s t a n d i n g q u e s t i o n s about d i s l o c a t i o n geometries, o t h e r s remain u n r e s o l v e d , and new q u e s t i o n s have a r i s e n . F o r example t h e d i s s o c i a t i o n o f d i s l o c a t i o n s i n s i l i c o n and germanium i s no l o n g e r i n d i s p u t e (which means t h a t many t h e o r e t i c a l analyses based upon u n d i s s o c i a t e d d i s l o c a t i o n s must now be recon- s i d e r e d ) , b u t whether o r n o t these d i s l o c a t i o n s a r e o f t h e g e s e t o r t h e s h u f f l e s e t remains unre- s o l v e d . A t t h e same t i m e d e t a i l e d weak-beam s t u d i e s o f these d i s l o c a t i o n s have r e v e a l e d many p r o p e r t i e s which a r e y e t t o be understood.
I n t h i s paper, t h e p r o p e r t i e s o f d i s l o c a t i o n s i n semiconductors r e v e a l e d by weak-beam e l e c t r o n microscopy a r e reviewed, and r e c e n t r e s u l t s presen- t e d . The d a t a f r o m t h e s e s t u d i e s a r e compared w i t h d a t a f r o m o t h e r e l e c t r o n microscope t e c h n i q u e s , and i n p a r t i c u l a r t h a t a v a i l a b l e f r o m t h e l a t t i c e f r i n g e t e c h n i q u e . D e f i c i e n c i e s i n t h e p r e s e n t e l e c t r o n m i - croscope t e c h n i q u e s f o r p r o v i d i n g i n f o r m a t i o n a b o u t t h e geometry o f d i s l o c a t i o n s below 2nm a r e d i s c u s - sed, and a t t e m p t s t o overcome t h e s e d e f i c i e n c i e s a r e o u t 1 in e d .
2. P r i n c i p l e s o f t h e weak-beam method.- The p r i n c i - p l e s o f t h e weak-beam method and i t s p r a c t i c e a r e now we31 e s t a b l i s h e d f o r d e f e c t d e t a i l g r e a t e r t h a n 2nm ( f o r a d i s c u s s i o n o f s t u d i e s o f d e f e c t d e t a i l below 2nm see
5
6 ) . D e t a i l e d d e s c r i p t i o n s o f t h e method had been g i v e n f r o m t h e o r e t i c a l /2,3,4/ ande x p e r i m e n t a l /5,6/ p o i n t s o f view. The l a s t o f t h e s e r e f e r e n c e s / 6 / can be c o n s i d e r e d as a companion t o t h i s paper. The i n f l u e n c e o f beam d i v e r g e n c e upon t h e images has been i n v e s t i g a t e d /7,8/, as has t h e e f f e c t o f n o n - s y s t e m a t i c r e f l e c t i o n s
191.
Several a p p l i c a t i o n s o f t h e weak-beam method a t h i g h v o l t a - ges have been r e p o r t e d , and some a t t e n t i o n has been g i v e n t o t h e t h e o r y o f i t s use a t such v o l t a g e s/ l o / ;
however i t would seem t h a t f u r t h e r t h e o r e t i c a l s t u - d i e s would be u s e f u l t o e s t a b l i s h t h e optimum c o n d i - t i o n s f o r h i g h v o l t a g e a p p l i c a t i o n s .
Because o f t h e s e pub1 is h e d t r e a t m e n t s , i t wi 11 s u f f i c e t o g i v e h e r e an o u t l i n e o f t h e t e c h n i q u e as a b a s i s f o r f u r t h e r d i s c u s s i o n ( f o r a more d e t a i l e d d e s c r i p t i o n o f t h e method, r e f e r t o /5/ and
161).
The p r i n c i p l e o f t h e method i s as f o l l o w s : a Bragg r e - f l e c t i o n g i s chosen, and t h e p e r f e c t c r y s t a l i s-
o r i e n t e d t o be f a r f r o m s a t i s f y i n g t h e Bragg c o n d i - t i o n f o r t h i s r e f l e c t i o n . Under t h e s e c o n d i t o n s , a d a r k - f i e l d image of t h e p e r f e c t c r y s t a l formed w i t h t h e r e f l e c t i o n g shows o n l y weak i n t e n s i t y because,
-
i n t h i s o r i e n t a t i o n , t h e p e r f e c t c r y s t a l s c a t t e r s o n l y weakly i n t o t h e r e f l e c t i o n g. However
-
i f t h e r e i s some s m a l l volume i n t h e c r y s t a l where t h e l a t t i - ce i s o r i e n t e d (e.g. by l a t t i c e s t r a i n ) i n t o o r near t o t h e Bragg a n g l e f o r t h e r e f l e c t i o n g, t h e n t h i s-
r e g i o n w i l l produce i n c r e a s e d s c a t t e r i n g r e s u l t i n g i n \ n c r e a s e d i n t e n s i t y i n t h e image. C o n f i r m a t i o n o f t h i s i d e a i s g i v e n by images c a l c u l a t e d f o r a v a r i e t y o f d e f e c t geometries, and an example i s shown i n f i g u r e 1 f o r t h e case o f an u n d i s s o c i a t e d d i s l o c a t i o n .
I t i s e v i d e n t from f i g u r e 1 t h a t t h e image l i e s t o one s i d e o f t h e d i s l o c a t i o n c o r e . I f t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979603
C 6 - 1 2 JOURNAL DE PHYSIQUE
m i s o r i e n t a t i o n o f t h e l a t t i c e i s made s u f f i c i e n t l y l a r g e ( a s i n f i g u r e l ) , t h e n t h e d i s p l a c e m e n t o f t h e image peak from t h e c o r e can be made l e s s t h a n 2nm.
Furthermore i f a model o f t h e d i s l o c a t i o n s t r a i n f i e l d i s assumed (e.g. f o r i s o t r o p i c e l a s t i c i t y t h e o r y ) t h e n t h e d i s t a n c e o f t h e c o r e f r o m t h e image peak can be determined a n a l y t i c a l l y /2,5/, i f neces- s a r y t a k i n g i n t o account image displacements due t o non-column e f f e c t s /11/. From computed images, i t has been e s t a b l i s h e d t h a t t h e image peak can be used t o d e f i n e t h e p o s i t i o n o f t h e d i s l o c a t i o n c o r e t o an accuracy o f lnm.
F i g . 1 : a ) Geometry o f an edge d i s l o c a t i o n . b ) C a l c u l a t e d 220 weak-beam image o f t h e
edge d i s l o c a t i o n i n ( a ) f o r s 2 7 0 = 2x10-' . D i s l o c a t i o n a t d e p t h 5 i n f o i l o f t h i c k n e s s ESg ; e l e c t r o n 'ener- gy = 100 key; 6 beam c a l c u l a t i o n . As w e l l as a c c u r a t e l y d e f i n i n g p o s i t i o n s i n t h e l a t t i c e where l a r g e s t r a i n e x i s t s , t h e weak-beam method can a l s o be used t o r e v e a l small r e g i o n s o f s t a c k i n g f a u l t . Thus i n f i g u r e 2, a d i s l o c a t i o n l i n e which i s d i s s o c i a t e d f o r c e r t a i n segments can be imaged ( u s i n g t h e a p p r o p r i a t e weak r e f 1 e c t i o n g) t o show o n l y those p a r t s o f t h e d i s l o c a t i o n l i n e where a s t a c k i n g f a u l t e x i s t s .
The advantages o f t h e t e c h n i q u e compared t o t h e normal strong-beam t e c h n i q u e o f f o r m i n g images a r e c l e a r l y seen i n f i g u r e 2. F o r d i s l o c a t i o n s , t h e power o f t h e t e c h n i q u e l i e s i n i t s a b i l i t y t o g i v e a d i r e c t l y i n t e r p r e t a b l e " p r o j e c t i o n " o f t h e p o s i - t i o n o f t h e d i s l o c a t i o n c o r e f o r d e f e c t d e t a i l s down t o 2nm.
F i g . 2 : A c o n s t r i c t e d d i s l o c a t i o n i n s i l i c o n imaged under v a r i o u s d i f f r a c t i n g c o n d i t i o n s : a ) A s t r o n g heam 220 d a r k - f i e l d image, i n w h i c h t h e c o n s t r i c t e d segments and node e x t e n s i o n a r e masked. b ) A weak- beam 220 d a r k - f i e l d image showing b o t h p a r t i a l d i s - l o c a t i o n s . ~ ) A weak-beam 111 d a r k - f i e l d image, g i v i n g g.b = 0 f o r t h e t o t a l Burgers v e c t o r , showing t h e S t Z c k i n g f a u l t imaged a t t h e extended node and a t t h e "bowed" d i s l o c a t i o n segments. (From Ray and Cockayne /16/ b y c o u r t e s y of t h e Royal S o c i e t y ) . 3. D i s l o c a t i o n d i s s o c i a t i o n . - 3.1. h r l y - g l e c t r o n y i c r o s c g p e - ~ t u j - j e s . - The e a r l i e s t a t t e m p t t o observe t h e s t r u c t u r e o f d i s l o c a t i o n s i n semiconductors was made b y A e r t s , D e l a v i g n e t t e , Siems and Amelinckx /12/, who examined d i s l o c a t i o n networks produced b y t w i s t i n g a < I l l > b a r o f s i l i c o n about i t s a x i s . Using c o n v e n t i o n a l b r i g h t - f i e l d images, t h e y found t h a t many o f t h e e l e c t r o n microscope images o f s i n g l e d i s - l o c a t i o n s showed two peaks, which t h e y i n t e r p r e t e d as d i s s o c i a t i o n i n t o p a r t i a l d i s l o c a t i o n s w i t h a d i s s o c i a t i o n w i d t h o f about 8.5nm. U n c e r t a i n t i e s i n t h e r e l a t i o n s h i p between t h e s e image peaks and t h e d i s l o c a t i o n geometry r e s u l t e d i n l a r g e u n c e r t a i n t i e s i n t h e d e t e r m i n a t i o n o f t h e s t a c k i n g f a u l t energy y, g i v e n as y = 45 -c 30
mJ
m-'a I n t h e same study, o b s e r v a t i o n s o f d i s l o c a t i o n nodes were i n t e r p r e t e d as showing an e x t e n s i o n c o r r e s p o n d i n g t o a v a l u e o f y = 50 mJ m-2.However t h e s e r e s u l t s were c r i t i c i z e d /13,14/
D. J . H . Cockayne and A. Hons C6-13
on t h e basis of image c a l c u l a t i o n s which showed t h a t , f o r t h e imaging conditions used, unextended nodes i n s i l i c o n appear t o be extended with a geometry c o r r e s - ponding t o
y =60 mJ m-'. As a consequence i t was concluded t h a t no deductions could be made a s t o d i s l o c a t i o n d i s s o c i a t i o n and node extension i n s i l i - con from images taken under s t r o n g two-beam o r many- beam conditions.
3.2. Wgakbbegm-ntud j g ~ - g f ~ d j s ~ _ o ~ j g t j o n _ - i n _ - ~ j 1 j ~ g c mi-gepnnjym.- Proof t h a t d i s l o c a t i o n s i n s i l i c o n
a r e g e n e r a l l y d i s s o c i a t e d came from weak-beam stu- d i e s of material deformed i n a number of ways /15,16/.
Samples from material s t r a i n e d 10% i n tension a t 850°C i n an argon atmosphere, and from material t w i s t e d 3"mm-' about a < I l l > a x i s a t 1200°C i n an argon a t - mosphere, showed long d i s s o c i a t e d d i s l o c a t i o n s , t h e d i s s o c i a t i o n width being 7.5nm f o r d i s l o c a t i o n s clo- s e t o t h e edge o r i e n t a t i o n . An example i s shown i n f i g u r e 3.
Fig. 3
:A weak-beam 220 d a r k - f i e l d image of a 30"
d i s l o c a t i o n i n s i l i c o n . The separation of t h e peaks i n t h e image is 4.8nm, corresponding t o a p a r t i a l d i s l o c a t i o n separation of 4.5nm.
The s e p a r a t i o n of t h e p a r t i a l s a s a function of l i n e o r i e n t a t i o n i s shown i n f i g u r e 4, and no s i g n i f i c a n t d i f f e r e n c e s were observed f o r t h e two d i f f e r e n t tem- p e r a t u r e s of deformation. From t h e s e measurements, a value of y
=51 + 5 mJ m-2 was determined /16/, and subsequent determinations using t h e same method /17/ have confirmed this value w i t h minor v a r i a t i o n s and w i t h no apparent dependence upon deformation
temperature from 1200°C t o 850°C /16/.
Fig. 4
:Measured p a r t i a l d i s l o c a t i o n s e p a r a t i o n s f o r i s o l a t e d d i s l o c a t i o n s i n s i l i c o n p l o t t e d a s a function of 1 in e o r i e n t a t i o n . The curves give theo- r e t i c a l values f o r
y=46 mJ m-2(curke a ) , and
y =56 mJ m-2 (curve b), computed using a n i s o t r o p i c e l a s t i c theory. (From Ray and Cockayne /16/ by cour- t e s y of t h e Royal Socitety).
S i m i l a r s t u d i e s have been made of d i s l o c a t i o n s i n germanium deformed a t temperatures between 500°C and 800°C /17, 19, 201. Long d i s l o c a t i o n s w i t h d i s s o - c i a t i o n s c o n s i s t e n t with a value of
y =60 + 8 mJ were observed i n a l l c a s e s .
3.3. D j s z o c j g t j g n z - j n - o t _ h ~ r - ~ e m j c o ~ d ~ c t g r ~ .
-The weak-beam method has been used t o measure d i s s o c i a - t i o n s i n many o t h e r semiconductor m a t e r i a l s . Gott- schalk, P a t z e r and Alexander /21/ measured the d i s s o - c i a t i o n width f o r edge d i s l o c a t i o n s i n GaAs, Gap, GaSb, InAs, InP and InSb, from which they s t u d i e d t h e c o r r e l a t i o n of the stacking f a u l t energy with bond i o n i c i t y . Dissociation of d i s l o c a t i o n s i n GaAso.7Po.s /22/, and Gap /23/ have a l s o been observed, and a new d i s s o c i a t i o n mode in s i l i c o n reported /24/.
3.4. Afigmalgus-dlsSgcjgtjgn-cl,jdt_hs.- The observation t h a t d i s l o c a t i o n s i n s i l i c o n and germanium a r e exten- ded "seems t o be incompatible with t h e work of Schaumberg /25/ and George ( s e e /20/), who observed c r o s s s l i p of s i n g l e screw d i s l o c a t i o n s i n germanium and s i l i c o n " (Hausserman and Schaumburg / 2 0 / ) . For t h i s reason Gomez e t a1 . /17/ s t u d i e d i n d e t a i l d i s - l o c a t i o n s near screw o r i e n t a t i o n i n germanium and s i
1icon. Specimens were prepared by bending < I l l >
s l i c e s of material a t a high temperature (600°C and
800°C f o r germanium, 880°C f o r s i l i c o n ) . A f t e r de-
formation t h e s l i c e s were annealed a t t h e deforma-
t i o n temperature f o r approximately 10 min. and then
slowly cooled. Dislocations near screw o r i e n t a t i o n
were found t o be d i s s o c i a t e d , and t h e r e s u l t s f o r
germanium (together with those from e a r l i e r experi-
ments of Ray and Cockayne /19/) a r e shown in f i g u r e
5. I t i s evident t h a t while some d i s s o c i a t i o n s
C6-14 JOURNAL DE PHYSIQUE
f o l l o w t h e dependence on l i n e o r i e n t a t i o n expected from a n i s o t r o p i c e l a s t i c i t y f o r y = 60
+
8 mJ m-', a l a r g e p r o p o r t i o n w i t h l i n e o r i e n t a t i o n between 60"and screw do n o t . Standard imaging techniques were used t o i d e n t i f y a number o f the w i d e l y d i s s o c i a t e d d i s l o c a t i o n s near screw o r i e n t a t i o n as bounding ex- t r i n s i c f a u l t s , w h i l e some w i t h the narrow d i s s o c i a - t i o n were found t o bound i n t r i n s i c f a u l t s . I d e n t i f i - c a t i o n o f the t y p e o f f a u l t was n o t p o s s i b l e i n a l l cases. I n s i l i c o n two d i s s o c i a t i o n widths f o r d i s l o - c a t i o n s near screw o r i e n t a t i o n were found also, and t h e n a t u r e o f t h e f a u l t f o l l o w e d the same p a t t e r n as f o r germanium.
d i s l o c a t i o n s move i n a d i s s o c i a t e d c o n f i g u r a t i o n bounding i n t r i n s i c f a u l t s , t r a n s f o r m i n g t o a c o n f i - g u r a t i o n bounding e x t r i n s i c f a u l t s when t h e d i s l o c a - t i o n s become s t a t i o n a r y . This model assumes t h a t yeXt= 0.5 yint, and t h a t t h e n u c l e a t i o n s i t e f o r t h e t r a n s f o r m a t i o n i s a c o n s t r i c t i o n on the d i s l o c a t i o n l i n e . The model i s supported by t h e observation t h a t d i s s o c i a t e d d i p o l e s i n h e a v i l y deformed s i l i c o n are o n l y present i n the Z
-
vacancy, and n o t the S-
vacancy, form /26/ (see
5
5 ) .A 600' C 8 0 0 ' C
RAY & COC KAY N E
L I N E O R I E N T A T I O N ( DEG )
Fig. 5 : The measured d i s s o c i a t i o n o f d i s l o c a t i o n s i n germanium, t h e symbols
A
and r e f e r r i n g t o two tem- Reratures o f deformation /17/, and the symbol r e f e r r i n g t o e a r l i e r measurements /16/. T h e o r e t i c a l curves based on a n i s o t r o p i c e l a s t i c i t y f o r y = 52 and 68 mJ m-'(-) and y = 23 and 28 mJIn-'(---)
are shown.(From Gomez e t a1. /17/, by courtesy o f t h e P h i l o s o p h i c a l Vagazine).
Attempts t o e x p l a i n these observations i n H i r s c h /27/ has proposed t h a t t h e anomalously terms o f e l e c t r o s t a t i c forces between p a r t i a l s due l a r g e d i s s o c i a t i o n widths r e p o r t e d by Gomez e t a l . t o d a n g l i n g bonds were unsuccessful because t h e /17/ can be explained by e l e c t r o s t a t i c charges asso- charge d e n s i t y due t o such bonds appeared t o be t o o c i a t e d w i t h t h e p a r t i a l d i s l o c a t i o n s , these charges low (Cockayne and Hirsch, unpublished). Gomez e t a l . being c a r r i e d by p o i n t d e f e c t s concentrated a t t h e /17/ o f f e r e d an explanation based on a model i n which d i s l o c a t i o n l i n e s .
D . J . H . Cockayne and A . Hons C6-15
Several o t h e r observations o f anomalous par- t i a l separations i n s i l i c o n and germanium have been obtained. During an i n v e s t i g a t i o n o f t h e frequency of c o n s t r i c t i o n s on d i s l o c a t i o n l i n e s , Packeiser and Haasen /28/ r e p o r t e d anomalous p a r t i a l separations o f screw d i s l o c a t i o n s i n germanium which had been deformed i n two stages, a t 600°C and 400°C, and then annealed f o r 2 hours a t 450°C. As w e l l as screw d i s - l o c a t i o n s having d i s s o c i a t i o n s o f w i d t h 3.6nm ( i . e . near t o the "normal" (narrow) values r e p o r t e d by Gomez e t a l . /17/) they found many screw d i s l o c a t i o n s w i t h d i s s o c i a t i o n s o f approximately 2nm f o r uncons- t r i c t e d segments o f d i s l o c a t i o n 1 in e exceeding 200nm i n length. They were n o t able t o i d e n t i f y the n a t u r e o f the f a u l t s between t h e p a r t i a l d i s l o c a t i o n s i n t h e two cases.
I n a r e c e n t s e t o f experiments (Cockayne and Hons t o be published), h i g h p u r i t y (10.000 ncm) s i l i - con wafers were deformed a t l.OOO°C between s i l i c o n chucks and s l o w l y cooled. Long lengths o f dissociated d i s l o c a t i o n s , w i t h o r i e n t a t i o n s between screw and 30°, were observed ( t o be published) a l l having d i s s o c i a - t i o n widths approximately equal t o those r e p o r t e d by Ray and Cockayne /16/ and Gomez e t a l . /17/, and corresponding t o a s t a c k i n g f a u l t energy o f y = 50 c 12 mJ m-'. This i s p a r t o f a study i n t o t h e r o l e o f i m p u r i t i e s i n determining d i s s o c i a t i o n widths.
It i s p e r t i n e n t t o r e f e r here t o observations o f d i s l o c a t i o n s i n semiconductors i n t h i n f o i l s u s i n g the l a t t i c e f r i n g e method. While many h i g h r e - s o l u t i o n l a t t i c e - f r i n g e images from r e g i o n s o f crys- t a l c o n t a i n i n g d e f e c t s have been obtained showing f e a t u r e s (e.g. f r i n g e bending, t e r m i n a t i n g f r i n g e s ) which appear easy t o i n t e r p r e t i n terms o f d e f e c t s t r u c t u r e , t h e c o n d i t i o n s f o r such a s t r a i g h t f o r w a r d i n t e r p r e t a t i o n have r a r e l y been s a t i s f i e d /29/. One o f the main problems has been a l a c k o f experimental c o n t r o l over t h e o r i e n t a t i o n o f the d i s l o c a t i o n l i n e . I n a s e r i e s o f experiments, Bourret and coworkers /30, 31/ have overcome these problems t o some e x t e n t by t h e use o f d i s l o c a t i o n s p h y s i c a l l y constrained i n g r a i n boundaries. I n t h i s way they haLfe observed an undissociated s e s s i l e d i s l o c a t i o n , and a d i s s o c i a t e d 60" d i s l o c a t i o n , both i n germanium f o i l s o f approxi- mately lOnm thickness. For t h e 60" d i s l o c a t i o n , t h e f a u l t between the p a r t i a l s was i d e n t i f i e d as i n t r i n - s i c , and t h e p a r t i a l s separation was determined a t 3.1 2 0.3nm corresponding t o a s t a c k i n g f a u l t energy o f y = 100
+
10 mJ m-2.
This separation i s t o be compared w i t h t h e value o f 4.9 ? 0.7nm r e p o r t e d by Gomez e t a l . /17/ f o r 60' d i s l o c a t i o n s i n germanium.Spence and K o l a r /32/ have used the l a t t i c e f r i n g e method t o observe f a u l t e d d i p o l e s i n s i l i c o n . From measurements o f t h e d i p o l e geometry bhey have determined a s t a c k i n g f a u l t energy o f 76
+
12 mJ m-'.From the above summary i t i s apparent t h a t , w h i l e t h e d i s s o c i a t i o n o f d i s l o c a t i o n s i n s i l i c o n and germani um has been c l e a r l y e s t a b l i s h e d by e x p e r i - ments u s i n g the weak-beam method, a v a r i e t y o f disso- c i a t i o n widths have been obtained. I n many o f t h e s t u d i e s t h e m a t e r i a l used i s h i g h i n i m p u r i t i e s /17/, b u t t h e u n i f o r m i t y o f t h e d i s s o c i a t i o n w i d t h f o r long l e n g t h s o f d i s l o c a t i o n l i n e f o r many o f t h e anomalous cases,and t h e f a c t t h a t more than one s e t o f disso- c i a t i o n widths are o f t e n observed i n the same mate- r i a l , appear t o suggest t h a t i m p u r i t y p i n n i n q as i t i s n o r m a l l y understood i s n o t the cause.
I t seems more l i k e l y t h a t f o r any given l i n e o r i e n t a t i o n t h e r e e x i s t a number o f s t a b l e d i s s o c i a - t i o n c o n f i g u r a t i o n s , each g i v i n g r i s e t o a d i f f e r e n t p a r t i a l separation. Whether these c o n f i g u r a t i o n s r e - l a t e t o t h e mode o f d i s s o c i a t i o n , o r whether they a r i s e from i n t e r a c t i o n w i t h d i f f e r e n t i n t e r s t i t i a l and vacancy d e f e c t s created a t d i f f e r e n t temperatu- r e s (e.g. /33/) i s f a r from c l e a r . I f t h e r o l e o f charges on d i s l o c a t i o n cores i s important i n d e t e r - mining d i s s o c i a t i o n widths, as suggested by H i r s c h /27/, then i t i s p o s s i b l e t h a t i m p u r i t i e s could i n - fluence t h e d e n s i t y o f these charges.
4. S t r u c t u r e along d i s l o c a t i o n 1 ines.- D i s l o c a t i o n s i n s i l i c o n and germanium formed by deformation a t h i g h temperatures f o l l o w e d by slow c o o l i n g a r e gene- r a l l y d i s s o c i a t e d w i t h occasional c o n s t r i c t i o n s o r c o n s t r i c t e d segments. Such r e s u l t s i n s i l i c o n have been r e p o r t e d f o r deformation temperatures o f 85OUC and 1200°C /16/ and i n germanium f o r deformation temperatures o f 520°C /20/ and 800°C /17/.
Packeiser and Haasen /28/ have r e p o r t e d t h a t i n germanium deformed i n two stages ( a t 600°C and 400°C) and annealed f o r 2 hours a t 450°C a f t e r un- loading, t h e average s e p a r a t i o n o f c o n s t r i c t i o n s i s 9501, and t h a t f o r s h o r t d i s s o c i a t i o n segments t h e c o n s t r i c t i o n s considerably reduce the w i d t h o f the f a u l t between t h e p a r t i a l s . Alexander /34/ suggested t h a t t h e d e n s i t y o f c o n s t r i c t e d segments was h i g h e r w i t h h i g h e r deformation temperature.
The d e n s i t y o f c o n s t r i c t i o n s has been examined as a f u n c t i o n o f deformation temperature and c o o l i n g r a t e . I d e n t i c a l < I l l > s l i c e s o f s i l i c o n have been deformed by bending a t 1250°C, 1000°C and 850°C between s i l i c o n chucks i n an argon atmosphere. Sam- p l e s cooled slowly, by removing the heat source,
C6-16 JOURNAL DE PHYSIQUE
show long d i s s o c i a t e d d i s l o c a t i o n s with few c o n s t r i c - t i o n s o r c o n s t r i c t e d segments, a s described above.
However samples deformed a t 1000°C and quenched i n t o water show a high d e n s i t y of c o n s t r i c t i o n s , and c o n s t r i c t e d segments of various lengths. In many cases t h e s e c o n s t r i c t i o n s appear t o be very s i m i l a r t o those studied i n copper a l l o y s by Carter and Ray /35/, which were deduced t o be jogs. Many of the d i s l o c a t i o n s i n s i l i c o n were c l o s e t o screw o r i e n t a - t i o n , and f o r t h e s e t h e s h o r t c o n s t r i c t e d segments appeared t o r o t a t e towards screw o r i e n t a t i o n ( F i g . 6 ) , p o s s i b l y brought about due t o c r o s s s l i p /38/.
3. Annealing produces long c o n s t r i c t e d segments, which f o r l i n e d i r e c t i o n s near edge a r e o r i e n t e d in ( o r near) edge o r i e n t a t i o n .
These observations suggest t h a t jogs, formed a t high temperature, coalesce upon annealing, and t h a t t h e r e s u l t a n t configuration produces segments of d i s l o c a t i o n which have no d i s s o c i a t i o n , o r a d i s - s o c i a t i o n l e s s than 2nm, and f o r which t h e r e i s a p r e f e r e n t i a l o r i e n t a t i o n along, or near t o , a <110>
d i r e c t i o n .
5 . Geometry of d i s l o c a t i o n s under s t r e s s . - S i g n i f i - c a n t information about d i s l o c a t i o n motion and bar- r i e r s t o motion has been obtained by studying t h e configuration of d i s l o c a t i o n geometries under condi- t i o n s of local s t r e s s . The weak-beam method has enabled t h e s e c o n f i g u r a t i o n s t o be studied i n consi- derable d e t a i l . The i n f l u e n c e of s t r e s s e s from i n t e r - a c t i n g d i s l o c a t i o n s has been studied f o r d i s l o c a t i o n nodes /16/ and f o r d i p o l e s /26/, while t h e geometry of d i s l o c a t i o n s during motion has been decuced both by cooling deformed c r y s t a l s under load /34/ and by t h e use of a hot s t a g e i n t h e e l e c t r o n microscope / 38/.
Dislocation nodes i n s i l i c o n a r e found t o be extended with a l t e r n a t e i n t r i n s i c and e x t r i n s i c s t a c k i n g f a u l t s /16/. From a study of t h e f a u l t geo- metry, a stacking f a u l t energy f o r t h e i n t r i n s i c f a u l t of
y =50 + 15 mJ m m 2 was determined, and t h e e x t r i n s i c f a u l t energy was considered t o be of t h e same o r d e r of magnitude. This observation i s i n F i q .
:Weak-beam image of dislocations i n s i l i c o n agreement with the model of Gomez e t a l . /17/ d i s - which has been quenched i n t o water. g
=220. Seg- cussed i n 5 3.4. f o r t h e formation of d i s s o c i a ~ e d ments of t h e d i s l o c a t i o n a r e aligned c l o s e t o screw
o r i e n t a t i o n , probably due t o c r o s s s l i p . d i s l o c a t i o n s with e x t r i n s i c f a u l t s .
In a study of d i s l o c a t i o n s i n heavily deformed a t high tempera-
s i l i c o n , Winter, Mahajan and Brasen /26/ observed t u r e s produces an appreciable i n c r e a s e i n t h e densi-
both unfaul t e d and f a u l t e d d i p o l e s . While f a u l t e d t y and length of c o n s t r i c t e d segments. Ray and
d i p o l e s were a l l of vacancy type i n t h e
Zconfigura- Cockayne /16/ showed d i s l o c a t i o n s with c o n s t r i c t i o n s
t i o n , t h e unfaulted d i p o l e s were e q u a l l y divided occupying approximately 50% of the. l i n e i n s i l i c o n
between i n t e r s t i t i a l and vacancy i n c h a r a c t e r . They deformed a t 1200°C and annealed f o r 10h. a t 1350°C.
suggested t h a t , i f the f a u l t i n g reaction occurs by In t h e s e experiments t h e deformation procedure fa-
t h e passage of a Shockley p a r t i a l along t h e f a u l t i n g voured t h e formation of d i s l o c a t i o n s near edge orien-
plane, then t h i s p a r t i a l has a lower c o r e energy f o r t a t i o n , and on t h e s e d i s l o c a t i o n s t h e c o n s t r i c t e d
the formation of the i n t r i n s i c f a u l t (vacancy dipo- segments aligned themselves i n t h e edge o r i e n t a t i o n
l e ) . The model of a Shockley p a r t i a l sweeping across ( F i g . 2 ) .
t h e f a u l t plane is supported by the observation of From t h e s e observations i t i s concluded t h a t
:p a r t i a l l y f a u l t e d d i p o l e s i n s i l i c o n ( F i g . 7 ) , simi- 1. The d e n s i t y of c o n s t r i c t i o n s i s dependent more on
l a r to those observed i n copper /36/. I n f i g u r e cooling r a t e than on deformation temperature.
t h e d i s l o c a t i o n s forming the d i p o l e a r e apparently 2. Quenching from a high temperature produces p o i n t s
held up a t t h e b a r r i e r s , with t h e reswlting d i p o l e of c o n s t r i c t i o n on d i s l o c a t i o n 1 in e s , but few
a1 igning i t s e l f along two <110> d i r e c t i o n s (a1 though c o n s t r i c t e d segments.
with some misalignement ( c . f . /36/). Weak-beam images
D .J.H. Cockayne and A. Hons C6-17
such as i n f i g u r e 7b show t h a t a l l segments p a r a l l e l t o one o f these two <110> d i r e c t i o n s are f a u l t e d , w h i l e a l l segments p a r a l l e l t o t h e o t h e r <1102 d i r e c - t i o n are not. This suggests t h a t , i f the f a u l t i s formed by the sweeping o f p a r t i a l s , then these par- t i a l s a r e h e l d up a t t h e corner o f t h e d i p o l e , p o s s i b l y because o f t h e h i g h energy d i s l o c a t i o n con- f i g u r a t i o n which must be overcome a t t h i s p o i n t /36/.
have d i f f e r e n t formation energies f o r t h e two par- t i a l s ) , o r ( 2 ) a d i f f e r e n c e i n t h e core s t r u c t u r e o f the two p a r t i a l s .
Gomez and H i r s c h /38/ have s t u d i e d t h e motion o f d i s s o c i a t e d d i s l o c a t i o n s i n germanium and s i l i c o n , u s i n g t h e weak-beam technique w i t h a h e a t i n g stage.
T h e i r observations l e d t o t h e conclusion " t h a t the d i s l o c a t i o n s g l i d e i n the d i s s o c i a t e d c o n f i g u r a t i o n , and t h a t , t h e r e f o r e , t h e o r i e s o f t h e m o b i l i t y o f d i s l o c a t i o n s i n s i l i c o n and germanium would have t o take t h i s i n t o account".
6. Studies o f d i s l o c a t i o n s a t r e s o l u t i o n below 2nm.- I t i s e v i d e n t from the foregoing discussion t h a t more d e t a i l e d s t u d i e s o f d i s l o c a t i o n s t r u c t u r e s i n semi- conductors a r e required, w i t h c o n t r o l 1 ed c o n d i t i o n s o f deformation temperature, annealing temperature, and i m p u r i t y l e v e l s . For d e f e c t d e t a i l above 2nm, the weak-beam method as i t i s c u r r e n t l y p r a c t i s e d i s q u i t e adequate, although b r i g h t e r e l e c t r o n guns and more s t a b l e h i g h temperature stages w i l l be an advan- F i g . 7a : Weak-beam 223 image o f a p a r t i a l l y f a u l t e d
d i p o l e i n s i l i c o n . Segments are c l o s e l y a1 igned tage.
along <110> d i r e c t i o n s . However many mechanisms p o s t u l a t e d f o r c o n t r o l - l i n q d i s l o c a t i o n p r o p e r t i e s i n v o l v e geometrical fea-
F i g . 7b : Weak-beam 202 image o f (a), showing disap- pearance o f f a u l t e d segments. Other segments c o u l d n o t be made t o vanish i n <220> images.
I n a d e t a i l e d weak-beam study o f d i s l o c a t i o n s i n s i l i c o n deformed under h i g h s t r e s s and cooled under-load, Wessel and Alexander /37/ found t h a t p r a c t i c a l l y a l l d i s l o c a t i o n s were dissociated, w i t h i n t r i n s i c s t a c k i n g f a u l t ribbons. N e a r l y a l l d i s l o - c a t i o n s were " e x a c t l y s t r a i g h t and p a r a l l e l t o one o f the t h r e e <110> d i r e c t i o n s " , and o f t e n the disso- c i a t i o n was extremly wide, w i t h d i s s o c i a t i o n widths exceeding 100nm. I n these cases t h e t r a i l i n g p a r t i a l f o l l o w e d a <110> d i r e c t i o n . Wessel and Alexander i n t e r p r e t e d these observations as r e s u l t i n g from a d i f f e r e n c e i n m o b i l i t i e s o f t h e two p a r t i a l s . They o f f e r e d as explanations o f t h i s d i f f e r e n c e (1) a n e c e s s i t y t o form double kinks as t h e fundamental step o f d i s l o c a t i o n motion ( a mechanism which m i g h t
t u r e s i n t h e 2nm t o 0.3nm range, As y e t t h e r e are no imaging methods s u i t a b l e f o r studying most o f these
1
f e a t u r e s . For example present techniques do n o t ena- b l e j o g s and k i n k s below 2nm i n s i z e t o be imaged, t h e d i s s o c i a t i o n o f d i s l o c a t i o n s l e s s than 2nm i n width cannot be s t u d i e d w i t h any l a t i t u d e over geo- m e t r i c a l parameters, and n e i t h e r can t h e s t r u c t u r e o f d i s l o c a t i o n cores. While the l a t t i c e f r i n g e methods o f f e r s some promise i n these areas, t o date i t s r e - quirements t h a t the d i s l o c a t i o n be viewed along i t s l i n e , and t h a t t h e geometry along t h e l i n e be inva- r i a n t , p l a c e severe r e s t r i c t i o n s on i t s usefulness.
Studies t o extend the weak-beam method so t h a t i t can be used t o i n v e s t i g a t e d e t a i l s o f d e f e c t geometry below 2nm a r e i n progress. The f i r s t r e q u i - rement, t h a t t o be u s e f u l i n t h i s range o r r e s o l u - t i o n t h e weak-beam method must produce image d e t a i l o f approximately lnm, has been demonstrated f o r se- v e r a l d e f e c t s /39, 40/. The second requirement, t h a t t h e image d e t a i l must be s e n s i t i v e t o v a r i a t i o n s i n d e f e c t geometry a t t h e l e v e l o f r e s o l u t i o n o f i n t e - r e s t , has a l s o been v e r i f i e d f o r the case o f d i s l o - c a t i o n cores /41, 18/. I t remains t o e s t a b l i s h t h a t t h e image d e t a i l can be i n t e r p r e t e d unambiguously i n terms o f a p a r t i c u l a r geometrical model. To do t h i s , d e t a i l e d image c a l c u l a t i o n s , accurate a t t h e l e v e l o f r e s o l u t i o n o f i n t e r e s t , are necessary. The method o f p e r i o d i c c o n t i n u a t i o n /42/ has provided t h e key
C6-18 JOURNAL DE PHYSIQUE
f o r t h e s e c a l c u l a t i o n s .
Acknowledgment
.
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