ELECTRONIC AND STRUCTURAL PROPERTIES OF GRAIN BOUNDARIES IN Cz-GROWN SILICON BICRYSTALS

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ELECTRONIC AND STRUCTURAL PROPERTIES OF GRAIN BOUNDARIES IN Cz-GROWN SILICON

BICRYSTALS

J. Werner, H. Strunk

To cite this version:

J. Werner, H. Strunk. ELECTRONIC AND STRUCTURAL PROPERTIES OF GRAIN BOUND-

ARIES IN Cz-GROWN SILICON BICRYSTALS. Journal de Physique Colloques, 1982, 43 (C1),

pp.C1-89-C1-94. �10.1051/jphyscol:1982113�. �jpa-00221769�

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JOURNAL DE PHYSIQUE

CoLZoque C1, supp26rnent uu n o 10, Tome 4 5 , octobre 1982 page Ci-89

ELECTRONIC A N D S T R U C T U R A L PROPERTIES OF GRAIN B O U N D A R I E S IN Cz-GROWN SILICON

BI

CRYSTALS

J . Werner* and H . Strunk*'

*Ma~PLanck-ins tit-ut fur Festkiirperforsckung, Heisenbergstr. 1 , 7000 S t u t t g a r t 80, F.R. C.

**Max-PZanck-Institut fiir WetaLlforsckung, i n s t i t u t fiir Pkysik, Heisenbergsbr. 1 , 7000 S t u t t g a r t 80, F. R. C.

Rhsum6.- Les p r o p r i h t k s k l e c t r o n i q u e s d ' u n j o i n t de g r a i n s d p e t i t angle dans m r i s t a l de s i l i c i u m sont Gtudihes par l a technique de conductance de N i c o l -

l i a n e t Goetzberger. On trouve une d e n s i t e d ' k t a t s continue. La s t r u c t u r e c r i s t a l l o g r a p h i q u e de ce j o i n t de g r a i n s e s t c a r a c t e r i s k e avec un microscope h l e c t r o n i q u e ii transmission. Une comparison des r g s u l t a t s obtenus par ces deux mkthodes ind6pendantes i n d i q u e que l a charge dans l e j o i n t de g r a i n s e s t due aux d i s l o c a t i o n s extrins6ques.

A b s t r a c t .

-

The e l e c t r o n i c p r o p e r t i e s o f a low a n g l e g r a i n boundary i n a s i l i - con b i c r y s t a l a r e i n v e s t i g a t e d by the conductance technique o f N i c o l l i a n and Goetzberger. A continuous d e n s i t y o f s t a t e s i s found. The c r y s t a l l o g r a p h i c s t r u c t u r e o f t h i s g r a i n boundary i s c h a r a c t e r i z e d by transmission e l e c t r o n m i - croscopy. A comparison o f r e s u l t s obtained by these two independent methods i n - d i c a t e s t h a t the charge i n the boundary i s caused by e x t r i n s i c d i s l o c a t i o n s .

1. I n t r o d u c t i o n . A g r e a t number o f experimental techniques was used i n t h e l a s t years f o r the c h a r a c t e r i z a t i o n o f p o l y c r y s t a l l i n e semiconductors. However the c u r - r e n t understanding o f g r a i n boundaries (GB) i n semiconductors s t i l l s u f f e r s from a t l e a s t two f a c t s :

a ) There a r e o n l y very few methods t o evaluate t h e e l e c t r o n i c parameters o f t h e t r a p s t a t e s l o c a t e d a t the GB.

b ) Nearly no attempts have been made so f a r t o c o r r e l a t e t h e c r y s t a l l o g r a p h i c and e l e c t r o n i c s t r u c t u r e o f GB's.

I n t h i s c o n t r i b u t i o n we want t o show t h a t t h e conductance method o f N i c o l l i a n and Goetzberger [I] o r i g i n a l l y develloped f o r the S i / S i 0 2 i n t e r f a c e , can be t r a n s f e r r e d t o d e s c r i b e t h e behaviour o f a s i n n l e s i l i c o n GB. The e l e c t r i c a l l y a c t i v e GB i s ana- l y z e d by e l e c t r o n microscopy. I t w i l l be shown t h a t t h i s combination o f experimental techniques y i e l d s i n s t r u c t i v e i n s i g h t i n t o t h e r o l e o f t h e GB m i c r o s t r u c t u r e .

15 -3

2. Sample p r e a r a t i o n . Boron doped (NA=l'10 cm ) b i c r y s t a l s ar? grown by a double seed Czochra-l!ki techniaue. The two seeds a r e t i 1 ted around I-1101

.

For t h e e l e c t r i c a l c h a r a c t e r i z a t i o n , samples o f 12x3x0.4mm3 a r e c u t , the GB b i - s e c t i n g t h e l o n g edge [2,3]. Sections o f t h e b i c r y s t a l adjacent t o those f o r the e l e c t r i c a l c h a r a c t e r i z a t i o n a r e prepared f o r t h e e l e c t r o n microscope a n a l y s i s . A f t e r g r i n d i n g t o -50 Hm the specimens a r e i o n - m i l l e d u n t i l a h o l e appears t h a t i n t e r s e c t s t h e GB. High v o l t a g e e l e c t r o n microscopy (650 kV) permits i n s p e c t i o n

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982113

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C 1-90 JOURUAL DE PHYSIQUE

o f t h e GB o v e r a r e l a t i v e l y l o n g d i s t a n c e . A Siemens 102 (125 kV) i s used f o r h i g h e r r e s o l u t i o n . Due t o t h e s p e c i a l o r i e n t a t i o n o f t h e s e c t i o n s , t h e f o i l s a r e e x p e c t e d t o have t h e i r normal c o i n c i d i n g w i t h t h e t i l t a x i s o f t h e GP and t o c o n t a i n t h e GH p e r p e n d i c u l a r t o t h e s u r f a c e .

3. S t r u c t u r a l o b s e r v a t i o n s . The e x a c t p o s i t i o n o f t h e r o t a t i o n a l a x i s can be d e t e r - mined b y t h e K i k u c h i r n s o f b o t h g r a i n s . The a x i s i s found t o be l o c a t e d i n t h e m i d d l e o f t h e s t e r e o g r a p h i c t r i a n g l e a b o u t 16' o f f C1101 towards 4 1 3 1 1 , i . e . a l m o s t [29,45,101. The boundary p l a n e i s asymmetrical l y s i t u a t e d between t h e two g r a i n s and s h i f t e d t o n e a r [ I 2 1 1 i n one g r a i n . The a n g l e o f r o t a t i o n i s 7.8+0.3'.

F i g . 1 H i g h r e s o l u t i o n m i c r o g r a p h o f t h e i n v e f t i g a t e d GB. Upper g r a i n imaged i n m u l t i b e a m t e c h n i q u e , b r i g h t f i e l d .

F i g u r e 1 shows a h i g h r e s o l u t i o n micrograph. .The up e r g r a i n i s o r i e n t e d such t h a t t h e e l e c t r o n beam i s i n c i d e n t e x a c t l y a l o n g 11101. Decond g r a i n i s imaged v e r y k i n e - m a t i c a l l y . A p a r t f r o m h o r i z o n t a l t h i c k n e s s f r i n g e s a f i n e s t r u c t u r e w i t h a r e p e t i - t i o n d i s t a n c e o f 1.8 nm i s v i s i b l e a l o n g t h e GB. T h i s s t r u c t u r e can be , a t t r i b u t e d t o t h e d i s l o c a t i o n network making up t h i s GB. A c r u d e model f o r a [ I 1 0 1 t i l t boundary f o m d by two s e t s o f d i s l o c a t i o n s w i t h B u r g e r s v e c t o r s o f t y p e 1/2 <011> y i e l d s a d i s t a n c e o f -2.5 nm.

Another f e a t u r e o f t h e boundary i s documented by t h e f a i n t ' s e m i c i r c u l a r ' c o n t r a s t s v i s i b l e e s p e c i a l l y i n t h e k i n e m a t i c a l l y imaged g r a i n . These c o n t r a s t s and t h e p e r - t a i n i n g s t r u c t u r e i n t h e boundary a r e more pronounced i n F i 9 . 2 where b o t h g r a i n s a r e s e t f o r simultaneous e x c i t a t i o n o f t h e c o r r e s p o n d i n g {2201 d i f f r a c t i o n v e c t o r s .

F i g . 2 E x t r i n s i c d i s l o c a t i o n s i n t h e g r a i n boundary. B o t h g r a i n s f o r s i - multaneous e x c i t a t i o n . g = d i f f r a c t i o n v e c t o r

The observed s t r u c t u r e s a r e t y p i c a l f o r ' e x t r i n s i c ' GB d i s l o c a t i o n s [41 which i n t h i s case a r e c o n s i d e r a b l y 'smeared-out'

.

The U U W ~ Q ~ d i s t a n c e between t h e s e d i s l o - c a t i o n s ( t h a t a c t u a l l y r e p r e s e n t a r r a y s o f d i s t u r b a n c e s i n t h e small s c a l e d i s l o c a - t i o n network o f F i g . l ) i s - 2 5 nm. I t w i l l be shown i n t h e e l e c t r i c a l measurements t h a t f r o m t h e s t a t i s t i c a l model o f charge f l u c t u a t i o n s a t t h e GB, a minimum d i s t a n c e o f charges can be e v a l u a t e d . I f t h e GB charge would be s i t u a t e d i n t h e c l o s e l y spaced d i s l o c a t i o n s , t h i s d i s t a n c e s h o u l d b e comparable t o o r even s m a l l e r t h a n 1,8 nm.

F i g u r e 3 shows t h e GB a t a s m a l l e r m a g n i f i c a t i o n and i n d i c a t e s a quasihomogeneous d i s t r i b u t i o n o f t h e e x t r i n s i c d i s l o c a t i o n s , a t l e a s t o v e r d i s t a n c e s c o r r e s p o n d i n g t o t h e f i e l d o f view, i . e . a few 10 um. I t s h o u l d be n o t e d t h a t no i n d i c a t i o n i s

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Mg.3

Quasihomogeneous d i s t r i b u t i o n o f e x t r i n s i c d i s l o c a t i o n s . Upper g r a i n two beam case, l o w e r g r a i n v e r y k i n e m a t i c a l l y .

found f o r GB p r e c i p i t a t i o n i n t h e range lnm o r l a r g e r . A l s o no l a t t i c e d i s l o c a t i o n s a r e observed.

4. E l e c t r i c a l measurements. R e c e n t l y we have shown [2,3] t h a t t h e z e r o b i a s dc conductance and t h e h i g h frequency b e h a v i o r o f a s i n g l e GB can be q u a n t i t a t i w d y e x - p l a i n e d by t h e r m i o n i c emission o f m a j o r i t y c a r r i e r s o v e r a GB p o t e n t i a l b a r r i e r c r e - a t e d by charged t r a p s t a t e s . The response o f t h i s charge t o sub-bandgap l i g h t a l l o w s us t o d e r i v e a d e n s i t y o f s t a t e s . The e l e c t r i c a l measurements r e p o r t e d h e r e a n a l y z e t h e response o f t h e charge on an a p p l i e d ac s i g n a l .

F i g u r e 4 shows c a p a c i t a n c e C and conductance G o f t h e GB f o r v a r i o u s dc b i a s a t 260K (ac o s c i l l a t o r l e v e l 10 mV). F o r f r e q u e n c i e s v < l o 6 ~ z t h e b e h a v i o r o f C cannot be ex- p l a i n e d bv t h e small s i g n a l response o f t h e d e p l e t i o n l a y e r w i d t h s ( F i g . 5 ) . W i t h t h i s model t h e huge c a p a c i t a n c e would l e a d o de l e t i o n l a y e r w i d t h s o f - 1 n m , incom- p a t i b l e w i t h known t r a p p e d charge of -1 -10' fe/rm

k

( f r o m h i g h frequency c a p a c i t a n c e ) . The behaviour o f C and

C

w i l l be b r i e f l y discussed here, d e t a i l s w i l l be p u b l i s h e d e l sewhere.

Error bar valid tor all curves from 30 lo 300 Hz

Fig.4. Capacitance C and conductance G f o r v a r i o u s b i a s values a t 260 K.

-

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CI-92 JOURNAL DE PHYSIQUE

The n e t t h e r m i o n i c c u r r e n t o f h o l e s from l e f t t o r i g h t i n F i g . 5 i s :

F o r U=U +6UaC; ~ = @ ~ ~ - 6 @ ; eUdc>ikT; 6 ~ ~ ~ = ~ e j ~ ~ ; 6 @ ~ & j ( ~ ~ + f l = A1+jAZ, t h e measured dc

a d m i t t a n c e Yth=ajth/a6uac, w i t h y=e/k A*T exp(-eg/kT) e ~ p ( - e @ ~ ~ / k T ) can be shown t o be:

E q u a t i o n ( 2 ) shows t h a t t h e c u r r e n t

j t h

i s n o t determined by t h e ac v o l t a g e d i r e c t - l y , b u t by t h e response o f t h e b a r r i e r t o t h e v o l t a g e . A phase l a g between 6+ and 6Uac causes a c a p a c i t i v e t h e r m i o n i c c u r r e n t . The r e a l and i m a g i n a r y p a r t s A1 ,A2 o f t h e b a r r i e r can be c a l c u l a t e d from charge Q and t r a p p i n g c u r r e n t jSs:

w:

Band scheme a t t h e GB

GS and BSS a r e t h e conductance and susceptance of t h e t r a p p i n g process a t t h e GB w ~ t h r e s p e c t t o 6@. From ( 3 ) and ( 4 ) we g e t f i n a l l y :

B =wC BZ=w(C +C ) ; CL and C a r e t h e h i g h frequency c a p a c i t a n c i e s o f t h e l e f t aRd r & h t spa& caarge. The d a s u r e d a d m i t t a n c e can be w r i t t e n :

Yth = G ^tj B = G ^tjwC = y ( a , t j a 2 ) ( 6 ) The conductance G,, can be e x t r a c t e d from ( 5 ) and ( 6 ) w i t h t h e f i n a l r e s u l t :

E q u a t i o n ( 7 ) shows t h a t Gss can be c a l c u l a t e d f r o m conductance and susceptance o f t h e t h e r m i o n i c c u r r e n t . Gss may t h e n be a n a l y l e d u s i n g t h e w e l l known methods o f ad- mi t t a n c e spectroscopy f r o m s i n g l e c r y s t a l s o r MOS s t r u c t u r e s [ I ] .

I n F i g . 6 v a l u e s f o r Gs,/w e v a l u a t e d w i t h ( 7 ) from t h e d a t a o f Fig.4 a r e shown i n comparison t o t h e o r e t i c a l G,Jw c h a r a c t e r i s t i c s f o r t h r e e d i f f e r e n t d i s t r i b u t i ns

2

8

o f GB t r a p s t a t e s o v e r energy and space. Curve a ) repres_en_ts G,,/~=C,w~/(ltw T ) Z Z - -

f o r a s i n g l e l e v e l , c u r v e b ) G S S / w = ( e N S s / 2 ~ ~ ) I n ( l + w T ~ ) f o r a d e n s i t y o f s t a t e s (51. I n b o t h cases, t i m e c o n s t a n t % and d e n s i t y o f s t a t e s NSS c o u l d be determined f r o m t h e maximum o f t h e curve.

I t can be seen t h a t b o t h curves do n o t f i t t h e measured c u r v e even c l o s e l y . Time c o n s t a n t d i s p e r s i o n i s f a r broader. The t i m e c o n s t a n t -im i s r e l a t e d t o thermal ve- l o c i t y < v t h > , c a p t u r e c r o s s s e c t i o n ~ t h , g r a i n c a r r i e r c o n c e n t r a t i o n pG and t h e b a r r i e r h e i g h t @B by:

T~ = e ~ p ( e @ ~ / k T ) / < v > t h O t h

hi

^{( 8 )}

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F i g . 6

-

Gss/w evaluated from the data o f F i g . 4.

Comparison t o t h r e e d i f - f e r e n t models f o r t h e d i s t r i b u t i o n o f t r a p s t a t e s i n energy and over space.

x

lo-'

6

Equation ( 8 ) shows t h a t small f l u c t u a t i o n s o f @ due t o s p a t i a l f l u c t u a t i o n s o f charge l e a d t o a d i s p e r s i o n o f time constants and t h e r e f o r e broaden GSS/w. This was taken i n t o account by N i c o l l i a n and Goetzberger i n t h e i r paper about the Si/Si02 i n - t e r f a c e by a s t a t i s t i c a l model o f the f l u c t u a t i o n s [ l l . For t h e p r o b a b i l i t y o f po- t e n t i a l s a Gaussian d i s t r i b u t i o n p ( @ ) was used.

-

^---f r a n measured &lo l a 3 5 V )

I n t h e framework o f t h i s we1 1 i n t r o d u c e d model Nss, o t h and the standard d e v i a t i o n as o f the p o t e n t i a l can be evaluated from exact s o l u t i o n s o f the i n t e g r a l ( 9 ) 1 6 , 7 J . We use t h e procedure given by Simonne [ 7 ] which r e q u i r e s the values o f t h e measured Gss/w a t the maximum o f the curve and a t t h e frequency 5umax.

0) single level

b l continuum 01 states [51 c t statistical model [ I ]

h r m i 1sr.l El 0518 .Y N,

.

13- 10"/crn'.v

loZ

m3 m4 m5 m6

To t e s t the a p p l i c a b i l i t y o f the model the i n t e g r a l i s then n u m e r i c a l l y c a l c u l a t e d f o r t h e whole frequency range. The agreement over the wide frequency range ( F i g . 6 )

proves t h a t the charge i n the GB i s d i s t r i b u t e d ~ ~o v a n p c e 5and c o v r t i - ~ ~ y

~ 1 ~ 1 o u ~ l . y i n energy.

6. Minimum d i s t a n c e o f charges a t the GB. Analyzing t h e model o f charge f l u c t u a t i o n s i n a general way, Brews 181 found the standard d e v i a t i o n as t o be r e l a t e d t o the minimum distance o f charges. This d i s t a n c e

x

can be c a l c u l a t e d f o r a GB by:

x

= (ea-I)-'/* b, (10)

We c a l c u l a t e from our data a bias-independent minimum distance o f

X

= 752 nm.

7. Density o f s t a t e s , capture cross s e c t i o n and standard d e v i a t i o n . For the energy range o v+

.

^{e t o} ^e cgbresgon i n g t e {QS j a ues o f F i g . l ) , t h e den- s i t y 0 f ~ s : a t ~ s ~ : ~ c ~ e a s e ~ ~ ; \ : ~ 6 1 . ~ . ! D /cm eYdto 1.: 1:

/cm

e:. The capture cross s e c t i o n i s (2.5+0.5) 1014cm

.

The standard d e v i a t i o n f o r a l l b i a s values i s ( 1 . 8 3 . 5 ) kTfe St the temperature o f 260 K.

Conclusions. The dec,Cticd p r o p e r t i e s o f the i n v e s t i g a t e d GB can be analyzed i n t h e framework o f the model o f p o t e n t i a l f l u c t u a t i o n s o r i g i n a l l y devel opped by N i c o l l i a n and Goetzberger [I] f o r the Si/SiOz i n t e r f a c e . I t provides a d e s c r i p t i o n o f t h ob-

%

served behavior o f the conductance and capacitance i n the frequency range 5-10 Hz.

E s p e c i a l l y the observed broad d i s p e r s i o n o f the time constants o f t r a p p i n g processes a t t h e GB can be explained by a colztinuoub d e n s i t y o f s t a t e s caused by charges d i s - t r i b u t e d b 2 a X h f i c & y i n space. The a t t r i b u t i o n o f a ningte l e v e l t o t h e GB i s no-t

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C 1-94 JOURNAL DE PHYSIQUE

a p p l i c a h l e . As i n t h e case o f t h e S i / S i 0 2 i n t e r f a c e t h e p o t e n t i a l f l u c t u a t i o n model y i e l d s t h e d e n s i t y o f s t a t e s , NSS, t h e c a p t u r e c r o s s section,oth, and t h e s t a n d a r d

d e v i a t i o n o f p o t e n t i a l s , u s .

T h i s a n a l y s i s p e r m i t s t h e c o r r e l a t i o n o f e l e c t r o n i c p r o p e r t i e s w i t h t h e c h y n ~ o - g&uSic s t r u c t u r e o f t h e GB:

The s t a n d a r d d e v i a t i o n o

,

as o b t a i n e d from t h e p o t e n t i a l f l u c t u a t i o n model, y i e l d s a

m W w n

d i s t a n c e betwaen t h e s t a t i s t i c a l l y d i s t r i b u t e d charges o f 7+2 nm. The ob- s e r v a t i o n s on t h e e x t r i n s i c d i s l o c a t i o n s a r e c o m p a t i b l e w i t h t h i s anaTysis. They have an a v u a g e d i s t a n c e o f -25 nm and are,, c o n t r a r y t o t h e r e g u l a r a r r a y o f t h e n a r r o w l y spaced d i s l o c a t i o n s , &egu.eahey d i s t r i b u t e d i n t h e GB. T h i s comparison thus l e a d s t o t h e c o n c l u s i o n t h a t t h e charges a r e caused by and l o c a t e d a t t h e ex- t r i n s i c d i s l o c a t i o n s i n t h e i n v e s t i g a t e d g r a i n boundary.

Acknowledgments. The a u t h o r s a r e g r a t e f u l t o P r o f . H.J. Q u e i s s e r f o r h i s c o n t i n u o u s s u p p o r t e s p e c i a l l y by h e l p f u l d i s c u s s i o n s and s u g g e s t i o n s d u r i n g t h e course o f t h e work. They a l s o acknowledge f r u i t f u l d i s c u s s i o n s w i t h R. B a r t o n and M. P e i s l ( S i e - mens AG). Thanks a r e due t o E. Schonherr und E. K i s e l a and t h e i r groups f o r t h e growth and p r e p a r a t i o n o f t h e b i c r y s t a l s . U. Heinz, S. S a u t e r , and A. Vierhaus were o f i n d i s p e n s a b l e h e l p d u r i n g t h e p r e p a r a t i o n o f t h e m a n u s c r i p t .

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