BOND ORDERING IN NONCRYSTALLINE SOLIDS

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BOND ORDERING IN NONCRYSTALLINE SOLIDS

A. Revesz

To cite this version:

A. Revesz. BOND ORDERING IN NONCRYSTALLINE SOLIDS. Journal de Physique Colloques,

1982, 43 (C9), pp.C9-307-C9-310. �10.1051/jphyscol:1982956�. �jpa-00222485�

JOURNAL DE PHYSIQUE

Colloque C9, supplement au n°12, Tome 43, decembre 1982 page C9-307

BOND ORDERING IN NONCRYSTALLINE SOLIDS

A. G. Revesz

COMSAT Laboratories, Clarksburg, MD 20871, U.S.A.

Résumé - A partir de l'analyse des propriétés optiques des solides non cristallins (ne) et des solides cristallins correspondant avec des liaisons à caractère covalen- tiel prédominant, on obtient un paramètre d'ordre F. Ce paramètre détecte les dif- férences entre les solides ne caractérisés par un ordre à courte distance semblable p. ex. Si amorphe (F < 0,8) et silice vitreuse, S1O2 (F - I). Les propriétés optiques et électroniques indiquent que, contrairement aux solides amorphes, dans les solides vitreux, les états électroniques peuvent demeurer délocalisés même s'il n'y a pas d'ordre à longue distance.

Abstract—From the analysis of optical properties of noncrystalline (nc) and the corresponding crystalline solids with predominantly covalent bonds a bonding order parameter, F, is derived. This parameter reveals differences between nc solids which are characterized by similar degree of short-range- order as, e.g., amorphous Si (F < 0.8) and vitreous Si02 (F - 1). Both the optical and electrical properties indicate that, in contrast to amorphous solids, the electronic states in vitreous solids may remain delocalized even though there is no long-range-order.

1. Introduction—The structure of noncrystalline (nc) solids, as derived from dif- fraction experiments is usually described in terms of a radial distribution function

(RDF).1 The RDF's are often characterized by a few (up to about four) peaks corre- sponding to the first, second, etc. neighbor interatomic distances whose mean values generally correspond to those in the crystalline Co) solid, indicating that short- range-order (SRO) is largely preserved in nc solids even though lphg-range-order

(LRO) is absent. Because the nc structure is not uniquely defined, it is necessary to use a model which approximates both the experimental RDF and the experimental density;1 these models are usually based on a continuous random network (CRN) of the constituent atoms.

These CRN models do not consider local disruptions of the structure (i.e., bond breaking). Broken bonds in a nc solid do not necessarily affect the average inter- atomic distances and, hence, the RDF, but they can have a very significant effect on some other (e.g., optical, electrical) properties. Thus, the SRO, as derived from the RDF of a CRN model is inadequate to describe all short range features of nc solids. This shortcoming of CRN models is especially manifested in predominantly covalent nc solids in which the local atomic configurations are closely tied to local bonding. When the parameters characterizing a local configuration exceed some limiting values, the bond is broken or a new bonding associated with a new config- uration arises.

2. Optical Properties as Indicators of Bond Ordering—The above mentioned inadequacy of CRN models is illustrated by the example of vitreous (v) Si02 and vacuum depos- ited (Or sputtered) amorphous (a) Si. In both cases interatomic distances deter- mined by the RDFs closely resemble those of the corresponding crystals2'3 so that one would expect the relationship between various properties of these nc solids to those of the corresponding crystals to be rather similar. This would be partic- ularly true for properties which are determined by the valence band (e.g., optical properties) since the density of valence states is supposed to be primarily deter- mined by SRO.1*

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982956

C9-308 JOURNAL DE PHYSIQUE

Contrary t o t h i s e x p e c t a t i o n , t h e o p t i c a l p r o p e r t i e s of a-Si a r e r a t h e r d i f f e r e n t from t h o s e of f c c c-Si b u t t h e d i f f e r e n c e between v-Si02 and q u a r t z c r y s t a l i s simply due t o t h e d i f f e r e n c e i n t h e i r density.' This i s t h e reason t h a t , i n c o n t r a s t t o a-Si, v-Si02 h a s been l a b e l l e d a s an o p t i c a l l y ordered s o l i d . 9 The degree of o r d e r a s r e l a t e d t o o p t i c a l p r o p e r t i e s can be q u a n t i t i v e l y expressed by t h e normal- i z e d o s c i l l a t o r s t r e n g t h , f , d e r i v e d from t h e frequency dependence 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 , E = €1

-

where d i s t h e n e a r e s t neighbor d i s t a n c e i n Angstroms, N i s t h e d e n s i t y of valence e l e c t r o n s p e r A 3 , and Z i s t h e formal chemical valency. Ckl t h e b a s i s of t h e be- h a v i o r of f , nc s o l i d s have been c l a s s i f i e d a s ( 1 ) v i t r e o u s and ( 2 ) amorphous. The f values i n group ( 1 ) a r e almost t h e same a s i n t h e corresponding c r y s t a l while i n group ( 2 ) t h e y a r e l e s s . 'Ihis behavior has been a t t r i b u t e d t o a d e c r e a s e i n delo- c a l i z a t i o n ( i n c r e a s e d l o c a l i z a t i o n ) of t h e bonding e l e c t r o n s i n amorphous s o l i d s which a p p a r e n t l y does n o t occur i n v i t r e o u s s o l i d s .

I t i s suggested h e r e t h a t bond o r d e r i n g (BO) i n a nc s o l i d can be d e r i v e d from op- t i c a l p r o p e r - t i e s by using t h e parameter F d e f i n e d a s

F E f ( n c ) / f ( c ) ( 2 )

The f v a l u e s f o r S i 0 2 a r e 5.1 and 5.0 eV f o r q u a r t z c r y s t a l and v l t r e o u s s l l l c a , r e s p e ~ t i v e l y , ~ s o t h a t F = 0.98 ( " 1 ) . In c o n t r a s t , t h e f v a l u e s of s p u t t e r e d a-Si

( 2.3 eV) and vacuum d e p o s i t e d a-Si (3.6 eV) a r e l e s s than t h o s e of f c c c-Si (4.4 eV) o r c o v a l e n t c r y s t a l s i n g e n e r a l ( 4 . 4 6 f 4 5.1 eV) , 6 t e s u l t i n g i n F = 0.52 and F = 0.82, r e s p e c t i v e l y . Accordingly, -0.5 < [ F ( a - S i ) / F ( v - S i 0 2 ) ] 6 4 . 8 , i n d i c a t i n g t h a t t h e BO i n a-Si i s s i g n i f i c a n t l y reduced r e l a t i v e t o v-Si, even though t h e SRO i s about t h e same. Another example of v i t r e o u s nc s o l i d i s As2S3, whereas Ge and Te a r e examples of amorphous s o l i d s .

The discrepancy r e g a r d i n g BO and SRO i n a-Si and v-Si02 i s r e l a t e d t o t h e f a c t t h a t t h e wide range of Si-0-Si bond a n g l e s (--120°

-

-

According t o t h e s e c o n s i d e r a t i o n s , t h e

local

The r e l a t i o n s h i p between BO and s t r u c t u r e i s a g a i n i l l u s t r a t e d by t h e examples of a-Si and v-Si02. The d e n s i t y of EPR-active d e f e c t s , i.e., broken ( " d a n g l i n g " ) bonds i s of t h e o r d e r of "lo2' cm-3 i n s p u t t e r e d o r vacuum d e p o s i t e d a-Si and d e c r e a s e s d u r i n g annealing t o "1018 cm-3 a s a-Si c r y s t a l l i z e s and t h e o p t i c a l p r o p e r t i e s approach t h o s e of fcc-Si.1° From t h e d e n s i t y of EPR-active d e f e c t s t h e i r average s e p a r a t i o n i n a-Si i s estimated a s being of t h e o r d e r cm. Assuming t h a t a 3-coordinated Si atom, i . e . with a broken bond, r e p r e s e n t s t h e end of bonding e l e c - t r o n d e l o c a l i z a t i o n a l o n g a l l t h r e e c h a i n s of S i atoms ending a t such an atom, t h e e x t e n t of BO i s of t h e o r d e r of lo-' cm i n a-Si. In c o n t r a s t t o a-Si, t h e d e n s i t y of EPR-active d e f e c t s i n v-Si02 i s e s t i m a t e d a s l e s s than - 1 0 ~ 3 l 1 s o t h a t t h e e x t e n t of BO i s about 5 x cm.

3. Comparison Between Bonding Orders Derived From O p t i c a l and Other Properties--In a d d i t i o n t o the o p t i c a l p r o p e r t i e s and d e n s i t y of EPR-active d e f e c t s , a-Si and v-Si02 e x h i b i t some o t h e r d i f f e r e n c e s . For i n s t a n c e , t h e d e n s i t y of l o c a l i z e d s t a t e s r e s p o n s i b l e f o r hopping conduction i s -1019 cm-3 (ev)"' i n a-Si. l 2 I n con- t r a s t , t h e m o b i l i t y of photo-injected e l e c t r o n s i n v-Si02 i s -20 cm2 ~-'s-','~ i n d i - c a t i n g t h a t t h e range of l o c a l i z e d s t a t e s a t t h e conduction band edge i s n e g l i g i b l y s m a l l , being l e s s than "0.025 eV.I4 These o b s e r v a t i o n s i n d i c a t e t h a t , v-Si02 i s more p e r f e c t than a-Si which i s i n accordance with a conclusion reached above from o p t i c a l p r o p e r t i e s .

The e x t e n t of band t a i l i n g , AE, i s a l s o considered a s a measure of d i s o r d e r :

AE a E2 where E i s a measure of d e v i a t i o n from SRO i n t h e sense t h a t t h e i n t e r a t o m i c d i s t a n c e , a , i n t h e one dimensional l a t t i c e becomes a ( 1

+

r e s u l t i n g i n €(a-Si)/E(v-Si02) > -3. In o t h e r words, v-Si02 appears t o be a t l e a s t 3 times more ordered than a-Si. As a comparison, t h e F v a l u e s i n d i c a t e a f a c t o r i n t h e range of 1.2

-

Along s i m i l a r l i n e s t o t h e above c o n s i d e r a t i o n s , t h e c a l c u l a t e d bandgap was sug- g e s t e d a s a measure of d i s o r d e r i n CFUi models of a-Si; f o r a s e r i e s of f o u r modeis c h a r a c t e r i z e d by 3 . 8 % , 2.5%, 1.2%, and 1.1 ^% r e l a t i v e s t a n d a r d d e v i a t i o n s i n t h e bond l e n g t h d i s t r i b u t i o n s a s w e l l a s by 12.3O, 13', 1 1 . 5 O , and 7.1° s t a n d a r d d e v i a t i o n s i n t h e bond a n g l e d i s t r i b u t i o n s , t h e bandgap v a l u e s were found t o be 0, 0.67, 1.26, and 2.19 eV i n t h e above order. l 6 Note t h a t , d e s p i t e t h e s i g n i f i c a n t v a r i a t i o n i n t h e spread of t h e parameters, a l l t h e s e models reproduce reasonably w e l l t h e e x p e r i - mental RDF. Also note t h a t t h e l a r g e v a r i a t i o n i n t h e c a l c u l a t e d bandgap does n o t r e s u l t from t h e e f f e c t s of broken bonds s i n c e c o n t i n u i t y i s assumed i n t h e models.

5. Concluding Remarks--&om a comparison of t h e o p t i c a l p r o p e r t i e s of c o v a l e n t l y bonded n o n c r y s t a l l i n e ( n c ) and c r y s t a l l i n e ( c ) s o l i d s a bond o r d e r i n g parameter h a s been defined; i t s value i s about one f o r v i t r e o u s nc s o l i d and l e s s than one f o r amorphous s o l i d s . Bond o r d e r i n g r e f e r s t o s t r u c t u r e a s s o c i a t e d with t h e c o v a l e n t bonds, whereas t h e d i s o r d e r parameter, ^{E ,} used above r e f e r s t o l a t t i c e ( f o r t h e c r y s t a l ) o r network ( f o r t h e nc s o l i d ) . e e absence of long-range-order (LRO) i n t h e nc s o l i d is thought t o a r i s e from t h e cumulative e f f e c t s of d e v i a t i o n s i n s h o r t - range-order (SRO): The d e v i a t i o n from t h e c o r r e c t p o s i t i o n i n c r e a s e s with n a s t h e d i s t a n c e between t h e n t h and (n

+

''

=

c a s e with v-Si02.

The f a i l u r e of v a r i o u s d i s o r d e r parameters t o d e s c r i b e t h e p r o p e r t i e s of v i t r e o u s s o l i d s r e s u l t s from two f a c t o r s . One i s t h a t t h e f r e q u e n t l y implied one-to-one cor- respondence between network and s t r u c t u r e i s n o t v a l i d when t h e network p o i n t s a r e a s s o c i a t e d with a s t r u c t u r a l u n i t comprising more than one atom. The second f a c t o r i s t h a t t h e n a t u r e of l o c a l i z e d bonds i s n o t considered a s t h e d i s o r d e r parameters r e f e r t o p o s i t i o n a l d i s o r d e r alone.

The key f e a t u r e of bond o r d e r i n g i s bond f l e x i b i l i t y r e s u l t i n g i n s t r u c t u r a l f l e x i - b i l i t y . I f t h e r e i s only one kind of predominantly c o v a l e n t bond which i s i n h e r -

C9-310 JOURNAL DE PHYSIQUE

e n t l y f l e x i b l e (i.e., t h e bond energy changes very l i t t l e w i t h t h e bond a n g l e by which t h e q u a s i - i n v a r i a n t s t r u c t u r a l u n i t s a r e l i n k e d a s e.g., i n v-Si02), then t h e n c s o l i d i s v i t r e o u s . I n q u a s i - v i t r e o u s s o l i d s t h e f l e x i b i l i t y can a r i s e from mix- i n g two o r more k i n d s o f bonds. These bonds may be between i d e n t i c a l atoms b u t a r e c h a r a c t e r i z e d by more than one kind of h y b r i d i z a t i o n s t a t e and, hence, by d i f f e r e n t l o c a l c o n f i g u r a t i o n s a s , f o r i n s t a n c e , i n nc-Se.18 It i s a l s o p o s s i b l e t h a t two o r more d i f f e r e n t k i n d s of atoms a r e involved a s i n nc-Sil,H, and nc-SixNyHz f i l m s .

5 v i t r e o u s and q u a s i - v i t r e o u s s o l i d s a r e l a t i v e l y high degree of BO can be main- t a i n e d even though t h e r e is no LRO. In c o n t r a s t , those s o l i d s , i n which t h e bond f l e x i b i l i t y i s reduced (e.g. S i where t h e s p 3 h y b r i d bonds a r e r a t h e r r i g i d ) , a r e u s u a l l y amorphous when they a r e i n t h e n c s t a t e . Here, t h e l a c k of LRO i s a s s o - c i a t e d with reduced BO a s may bonds a r e broken o r s e v e r e l y s t r a i n e d .

Bond o r d e r i n g p l a y s a key r o l e i n t h e c o r r e l a t i o n between bond parameters, such a s , bond l e n g t h s and a n g l e s a s , f o r i n s t a n c e , i n v-SiO2. The c o r r e l a t i o n i s , i n t u r n , r e s p o n s i b l e f o r l o c a l i z e d o r d e r i n g i n v i t r e o u s s o l i d s a s manifested by s t r u c t u r a l l y o r d e r e d t r i d y m i t e - l i k e regions1' and "pre-ordered" domains20 i n v-Si02 as w e l l a s by

" s t r u c t u r a l c h a n n e l s n 2 1 , p a r t i c u l a r l y , i n S i 0 2 f i l m s o b t a i n e d by thermal o x i d a t i o n o f s i l i c o n .

In conclusion, t h e s e arguments demonstrate t h a t bond o r d e r i n g a s s o c i a t e d with bond and s t r u c t u r a l f l e x i b i l i t y p l a y s a more fundamental r o l e i n determining t h e proper- t i e s of nc s o l i d s with predominantly c o v a l e n t bonds t h a n short-range-order d e r i v e d from continuous random network models.

6. Acknowledgments--This paper i s based on work performed a t COMSAT L a b o r a t o r i e s under t h e s p o n s o r s h i p o f Communications S a t e l l i t e Corporation. B e a u t h o r i s g r e a t l y indebted t o S. H. Wemple f o r many v a l u a b l e d i s c u s s i o n s . Thanks a r e a l s o due t o F. Galeener, N. F. Mott, and A. C. Wright f o r h e l p f u l comments on t h e manuscript.

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