HAL Id: jpa-00220902
https://hal.archives-ouvertes.fr/jpa-00220902
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
STRUCTURAL ORDERING RELATED TO CHEMICAL BONDS IN RANDOM NETWORKS
A. Revesz, S. Wemple, G. Gibbs
To cite this version:
A. Revesz, S. Wemple, G. Gibbs. STRUCTURAL ORDERING RELATED TO CHEMICAL BONDS IN RANDOM NETWORKS. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-217-C4-219.
�10.1051/jphyscol:1981445�. �jpa-00220902�
JOURNAL DE P H Y S I Q U E
CoZZoque C4, suppZ6ment au nOIO, Tome 42, octobre 1981 page c4-217
STRUCTURAL ORDERING RELATED TO CHEMICAL BONDS I N RANDOM NETWORKS
A . G . Revesz, S . H . wemplen and G.V. ~ i b b s * *
COMSAT Labs, CZarksburg, MD, U. S. A.
*
Be22 Labs, Murray H i l l , NJ, U.S.A.x n VPI, BZacksburg, VA, U.S.A.
SYNOPSIS
The s t r u c t u r e o f many n o n c r y s t a l l i n e ( N C ) s o l i d s ( S i , S i 0 2 , e t c . ) is u s u a l l y d e s c r i b e d by c o n t i n u o u s random network
(CRN) models r e s u l t i n g i n r a d i a l d i s t r i b u t i o n f u n c t i o n s (RDF) t o i n t e r p r e t t h e e x p e r i m e n t a l d i f f r a c t i o n d a t a . These models g i v e mean v a l u e s o f t h e i n t e r a t o m i c d i s t a n c e s w i t h a g i v e n s c a t t e r up t o a b o u t t h e f o u r t h neighbor b u t do n o t p r o v i d e i n f o r m a t i o n on bonding between atoms a s , f o r i n s t a n c e , t h e e x t e n t o f bond d e l o c a l i z a t i o n ; a l s o , t h e y do n o t c o n s i d e r pos- s i b l e c o r r e l a t i o n s between bond a n g l e s and l e n g t h s s i n c e t h e s e p a r a m e t e r s a r e t r e a t e d a s random v a r i a b l e s . Furthermore, t h e CRN models do n o t g i v e any i n s i g h t i n t o t h e n a t u r e o f l o c a l o r d e r e d r e g i o n s which may b e hidden i n t h e s t r u c t u r e which, from t h e viewpoint of d i f f r a c t i o n a n a l y s i s , may a p p e a r a s random. These t h r e e a s p e c t s o f NC s o l i d s , i . e . , bonding, c o r r e l a t i o n s , and l o c a l i z e d o r d e r , a r e d i s c u s s e d i n t h i s paper.
The inadequacy of t h e RDFs t o d e s c r i b e
all
f e a t u r e s o f NC s o l i d s i s i l l u s t r a t e d by t h e o p t i c a l p r o p e r t i e s o f NC S i 0 2 and S i : f o r S i 0 2 t h e r e i s a l m o s t no d i f f e r e n c e between t h e c r y s - t a l l i n e ( C ) and NC forms, whereas t h e d i f f e r e n c e i s g r e a t i n t h e c a s e o f S i , even though t h e RDFs o f b o t h amorphous ( a ) S i and v i t r e o u s ( v ) S i 0 2 c l o s e l y resemble t h e c o r r e s p o n d i n g c r y s t a l s ( t r i d y m i t e and f c c S i , r e s p e c t i v e l y ) . The d i f f e r e n c e between v-Si02 and a - S i i s shown by t h e v a l u e s o f t h e s h o r t - range-order (SRO) parameter, F; 1 f o r v-SiO? ( h i g h l y d e l o c a l - i z e d bonding, d a n g l i n g bonds < 1 0 l ~ c m - ~ ) a n d 0.6-0.8 f o r a - S i(reduced d e l o c a l i z a t i o n o f bonding e l e c t r o n s , d a n g l i n g bonds:
-1019-1021cm-3). The parameter F i s d e f i n e d a s F z f ( N C ) / f ( C ) where f i s t h e normalized o s c i l l a t o r s t r e n g t h used i n t h e a n a l y s i s of o p t i c a l d i e l e c t r i c p r o p e r t i e s o f s o l i d s . Another i m p o r t a n t parameter i n t h i s a n a l y s i s i s t h e s i n g l e a v e r a g e e x c i t a t i o n energy Eo; b o t h f and Eo can be d e r i v e d from t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981445
C4-218 JOURNAL DE PHYSIQUE
frequency dependence o f t h e imaginary component of t h e o p t i c a l d i e l e c t r i c c o n s t a n t . Those NC s o l i d s whose F v a l u e i s c l o s e t o 1 a r e l a b e l e d v i t r e o u s , (e.9. S i 0 2 , Ta205, As2S3) and t h o s e w i t h F v a l u e s s i g n i f i c a n t l y l e s s t h a n 1, amorphous (e.g. S i , Ge, A s ) ; t h e b o r d e r i s n o t s h a r p l y d e f i n e d . Hydrogenated a - S i , o r r a t h e r , Sil-xHx, r e p r e s e n t s an i n t e r e s t i n g c a s e a s t h e i n - c o r p o r a t i o n o f H a f f e c t s b o t h t h e f and Eo v a l u e s o f t h e S i network ( t h e c o n t r i b u t i o n o f Si-H bonds i s r a t h e r s m a l l a s t h e f r a c t i o n o f Si-H bonds i s u s u a l l y l e s s t h a n -0.15 and t h e e x c i t a t i o n energy of t h e Si-H bond, 1 1 . 4 eV, i s much h i g h e r t h a n t h a t of S i - S i bonds, 4.3 eV). With i n c r e a s i n g d e p o s i t i o n t e m p e r a t u r e and/or i n c r e a s i n g H-content F may r e a c h even u n i t y , i n d i c a t i n g i n c r e a s e d d e l o c a l i z a t i o n of bonding e l e c t r o n s ; f o r t h i s r e a s o n t h i s m a t e r i a l i s c o n s i d e r e d a s q u a s i - v i t r e o u s . The v a l u e of Eo c h a r a c t e r i z i n g t h e S i network i n c r e a s e s from 3.4 eV a t 0% H t o - 4 . 2 eV f o r -30 a t . % H ; t h e former v a l u e i s p r a c t i c a l l y i d e n t i c a l w i t h E o f CVD a - S i and w i t h t h e e s t i -
0
mated v a l u e o f t h e bcc polymorph o f S i . T h i s s i m i l a r i t y sug- g e s t s t h a t some l o c a l c o n f i g u r a t i o n s i n CVD a-Si and Sil-xHx may resemble bcc-Si i n which t h e chemical bonding of S i atoms c a n n o t b e d e s c r i b e d by s p 3 h y b r i d i z a t i o n a s i n t h e f c c - S i , r a t h e r , d - o r b i t a l s a r e involved.
I f t h e d e n s i t y o f broken ( d a n g l i n g ) bonds i s r e a s o n a b l y s m a l l , t h e n t h e bonds may n o t o n l y b e l a r g e l y d e l o c a l i z e d b u t t h e y may a f f e c t t h e bond l e n g t h s and a n g l e s a s w e l l s i n c e t h e i r v a l u e s a r e determined by t h e a c t u a l l o c a l h y b r i d i z a t i o n s t a t e . A s a r e s u l t , t h e bond a n g l e s and l e n g t h s a r e c o r r e - l a t e d r a t h e r t h a n random. T h i s p o i n t i s i l l u s t r a t e d by v-Si02 where t h e Si-0-Si bond a n g l e , $, and Si-0 bond l e n g t h , r ( S i - O ) , a r e c o r r e l a t e d : a s $ v a r i e s from 120° t o 180° ( t h e r a n g e i n v-Si02) r ( S i - 0 ) v a r i e s from 0.156 t o 0.165 nm. I n c o n t r a s t , t h e r a n g e i n t h e CRN model i s 0.145-0.175 nm. Another a s p e c t o f non-randomness i s t h e d i s t r i b u t i o n of t o r s i o n a l a n g l e , 8 , by which two S i O 4 l 2 t e t r a h e d r a a r e r o t a t e d ( a t $ = c o n s t . ) w i t h r e s p e c t t o each o t h e r . T h i s a n g l e i s c o n s i d e r e d t o be r a n - domly d i s t r i b u t e d i n t h e CRN model. However, i f t h e
+
d i s -t r i b u t i o n i s c a l c u l a t e d on t h i s b a s i s , t h e d i s t r i b u t i o n i s u n r e a l i s t i c a s t h e s i g $ t e r m i n t h e i n t e g r a l used i n t h e c a l - c u l a t i o n f ( $ ) = / E ( $ ) s i n $ d $ overemphasizes t h e r a n g e $ < - 1 5 0 ° . A r e a l i s t i c d i s t r i b u t i o n i s o b t a i n e d i f t h i s term is o m i t t e d , i . e . , t h e d i s t r i b u t i o n i s c o n s i d e r e d a s non-random and d e t e r - mined s o l e l y by t h e energy term. The dependence of energy on
$ has been determined by MO c a l c u l a t i o n s on p y r o s i l i c i c a c i d ,
(HO) 3SiOSi (OH) 3 ; t h e energy v a r i e s o n l y
-
2 k c a l mole-l above and below t h e minimum a t $=140° a s $ v a r i e s from 120' t o 180°.The s m a l l v a r i a t i o n i n energy w i t h $ and t h e c o r r e l a t e d n a t u r e of r ( S i - 0 ) and $ make i t p o s s i b l e t h a t o r d e r e d r e g i o n s may o c c u r l o c a l l y i n v-Si02. T r a n s p o r t p r o p e r t i e s , r a t h e r t h a n X-ray o r e l e c t r o n d i f f r a c t i o n , a r e s e n s i t i v e i n d i c a t o r s of such r e g i o n s . For example, t h e s e p a r a t i o n of s o l u b i l i t y s i t e s f o r O2 molecules i n v-Si02 i s - 2 . 2 nm, i f t h i s d i s t a n c e i s covered by a s i n g l e jump d u r i n g t h e d i f f u s i o n o f 0 2 , t h e n t h e d i f f u s i o n probably o c c u r s a l o n g c h a n n e l s whose s t r u c t u r e c o r r e s p o n d s t o t h e atomic arrangement a l o n g t h e C-axis i n t r i d y m i t e c r y s t a l . The f o r m a t i o n o f v-Si02 f i l m on S i sub- s t r a t e d u r i n g t h e r m a l o x i d a t i o n o c c u r s v i a O 2 d i f f u s i o n , and t h e growth p r o c e s s can b e a n a l y z e d i n terms o f o r d e r i n g and d i s o r d e r i n g e f f e c t s t a k i n g p l a c e i n t h e o x i d e f i l m and a t t h e S i / S i 0 2 i n t e r f a c e . The o r d e r i n g e f f e c t i n t h e v-Si02 f i l m i s t h e growth and/or i n c r e a s e d alignment ( p e r p e n d i c u l a r l y t o t h e S i s u b s t r a t e ) o f c h a n n e l s a s t h e growth r a t e d e c r e a s e s w i t h i n c r e a s i n g o x i d e t h i c k n e s s ) , r e s u l t i n g i n i n c r e a s e d 02 d i f - f u s i v i t y . D i s o r d e r i n g i s due t o t h e l i m i t e d b u t n o n - n e g l i g i b l e i n t e r a c t i o n between 02 and S i 0 2 which scrambles t h e s t r u c t u r e and, hence, d e c r e a s e s t h e 02 d i f f u s i v i t y ; t h i s p r o c e s s o c c u r s when new o x i d e grows on t h e t o p of a w e l l - o r d e r e d f i l m . Thus, t h e s t r u c t u r e o f v-Si02 on S i and 02 d i f f u s i o n a r e i n t i m a t e l y i n t e r - r e l a t e d and 02 d i f f u s i o n i n v-Si02 f i l m s c a n n o t be d i s - c u s s e d i n terms of a r i g i d r e f e r e n c e framework a s i t i s u s u a l l y done i n t h e c a s e o f c r y s t a l l i n e s o l i d s .
