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DEFECTS IN AMORPHOUS CHALCOGENIDES AND SILICON
D. Adler
To cite this version:
D. Adler. DEFECTS IN AMORPHOUS CHALCOGENIDES AND SILICON. Journal de Physique
Colloques, 1981, 42 (C4), pp.C4-3-C4-14. �10.1051/jphyscol:1981401�. �jpa-00220705�
JOURNAL DE PHYSIQUE
Colloque C4, supplement ecu n°10, Tome 42, Oetobve 1981 page C4-3
DEFECTS IN AMORPHOUS CHALCOGENIDES AND SILICON
D. A d l e r
Department of Electrical Engineering and Computer Saienoe, and Center for Materials Soienoe and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02159, U.S.A.
Abstract.- Our comprehension of the physical properties of amorphous semicon- ductors has improved considerably over the past few years, but many puzzles remain. From our present perspective, the major features of chalcogenide glasses appear to be well understood, and some of the fine points which have arisen recently have been explained within the same general model. On the other hand, there are a great number of unresolved mysteries with regard to amorphous silicon-based alloys. In this paper, the valence-alternation model for chalcogenide glasses i& briefly reviewed. Two recent problems, the obser- vations of dispersive transport in arsenic selenide glasses and of large tran- sient field field effects in arsenic telluride glasses are analyzed in detail.
The present status of the analogous defect model for amorphous silicon alloys is discussed. Some of the major puzzles, the Staebler-Wronski effect, the Meyer-Neldel rule, and the mechanism for doping, are examined.
Introduction.- It has been clear for many years that the properties of chalcogenide glasses are sharply distinct from those of the tetrahedrally bonded amorphous semi- conductors (1,2). In general, the latter materials appear to be relatively conven- tional, in the sense that they can be prepared so that the Fermi energy is unpinned, and consequently the electrical conductivity can be modulated, e.g. by chemical doping or the field effect (3). In such films, the unpaired-spin density is very
small, variable-range hopping is not observed, and a relatively sharp optical edge is apparent. Alternatively, if low-quality films are prepared, large unpaired-spin density is found, variable-range hopping conduction predominates, the optical edge is diffuse, and no field effect or doping is observed (4). All of these features can be understood by postulating the existence of large densities of defects in the low-quality films. Careful preparation conditions, including the-judicious use of alloying, can drastically reduce the defect concentration, thereby allowing for the use of this class of materials in conventional semiconductor devices. In contrast, the gross features of chalcogenide glasses appear to be self-inconsistent. The Fermi energy is generally strongly pinned, and neither doping nor a field effect is observed under ordinary conditions. Nevertheless, variable-range hopping is sup- pressed and there is no evidence for any unpaired spins. The breakthrough in our understanding of this paradox came from an amalgam of two diverse approaches, the suggestion of a negative effective correlation energy (5) and its association with well-defined defect centers (6) on the one hand, and a chemical approach (7,8) which emphasized the unique electronic structure of chalcogen atoms, on the other. These pictures were merged by the valence alternation pair (VAP) model (9), which had great success in clarifying the experimental results. In brief, because of the lone-pair outer electrons on chalcogens, an extremely low-energy defect pair exists.
One example is a positively charged three-fold-coordinated ion (C^~). Since this VAP has the same total number of covalent bonds (four) as a pair of chalcogens in their ground state (C20), the creation energy is low and large densities are frozen in at the glass transition temperature, T„. Since the charged pair has lower total energy than a pair of neutral defects and the neutral defects are interconvertible by a bond breaking or formation, the effective correlation energy, Ueff, is nega- tive. Since a tathogen {Column IV) atom cannot overcoordinate using only s and p electrons, VAPs are impossible in amorphous silicon alloys. The relatively large value of |DeffI ^n chalcogenides ensures a strongly pinned Fermi energy, no measur- able unpaired-spin density, and the suppression of variable-range hopping conduction.
Chalcogenide Glasses.- Although the VAP model has had great success in understanding
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981401
C4-4 JOURNAL DE PHYSIQUE
t h e unique p r o p e r t i e s of most chalcogenide g l a s s e s , two r e c e n t experiments have proved t o be somewhat puzzling. The f i r s t concerns t h e o b s e r v a t i o n of d i s p e r s i v e t r a n s p o r t i n a wide c l a s s of chalcogenide g l a s s e s (10). The d i s p e r s i o n i n a-As2Seg has been shown t o r e s u l t from m u l t i p l e t r a p p i n g by an e x p o n e n t i a l d i s t r i b u t i o n of s t a t e s i n t h e gap ( l l ) , b r i n g i n g up t h e q u e s t i o n of how t h i s is compatible w i t h a model i n which t r a n s p o r t is c o n t r o l l e d by a s i n g l e t y p e of d e f e c t c e n t e r . A second problem i s t h e r o u t i n e o b s e r v a t i o n of f i e l d e f f e c t s i n a r s e n i c t e l l u r i d e g l a s s e s
1 2 3 Such a n e f f e c t would appear t o be i n c o n s i s t e n t w i t h a l a r g e n e g a t i v e Ueff (14).
D i s p e r s i v e Transport.- O r e n s t e i n and Kastner (11) have shown from t r a n s i e n t photo- c o n d u c t i v i t y measurements on a-As2Se3 t h a t t h e k i n e t i c s a r e c o n t r o l l e d by an expon- e n t i a l d i s t r i b u t i o n of t r a p s c h a r a c t e r i z e d by a decay temperature, To = 550K. This can be explained only i f t h e VAPs a r e c h a r a c t e r i z e d not by a s i n g l e well-defined energy, b u t r a t h e r by a spread of energ2es. The o r i g i n of such a spread was d i s - cussed i n t h e o r i g i n a l paper (91, i n which i t was noted t h a t an o p p o s i t e l y charged p a i r would have even lower c r e a t i o n energy i f t h e two c e n t e r s were i n t i m a t e (IVAPs) r a t h e r t h a n randomly spaced (NVAPs). I n f a c t , a quasi-continuous d i s t r i b u t i o n of e n e r g i e s would b e expected t o r e s u l t from t h e p o s s i b i l i t y of an a r r a y of separa- t i o n s , R, between t h e p a i r . We might expect t h a t t h e c o n c e n t r a t i o n of IVAPs sepa- r a t e d by a d i s t a n c e R is
[IVAPS(R)] = [iWfls] exp ( e 2 / 2 6 R k T ),
g (1)
a r e s u l t which would g i v e e x p o n e n t i a l t r a p d i s t r i b u t i o n s t a i l i n g away from b o t h t h e v a l e n c e and conducti'on bands, and c o n s i s t e n t w i t h t h e decay parameter given by Tg.
The e f f e c t i v e one-electron d e n s i t y of s t a t e s i n t h i s c a s e i s sketched i n Fig. 1.
E
Fig. 1: Sketch of t h e e f f e c t i v e one- e l e c t r o n d e n s i t y of s t a t e s r e s u l t i n g from a d i s t r i b u t i o n of IVAPs. M r e p r e - s e n t s t h e Coulomb a t t r a c t i o n between two
To
-
- -- -
- --
- o p p o s i t e l y charged c e n t e r s l o c a t e d onT~ -IUI nearest-neighboring s i t e s .
Support f o r t h i s model a l s o comes from t h e time-resolved photoluminescence (15), i n which t h e r e s u l t s can b e explained i n terms of c o n v e n t i o n a l donor-acceptor luminescence v i a o p p o s i t e l y charged c e n t e r s . The mean photoluminescence energy d e c r e a s e s monotonically w i t h i n c r e a s i n g time, j u s t a s would be expected from t h e model of a d i s t r i b u t i o n of IVAPs, a l t h o u g h t h e v a r i a t i o n i n t h i s c a s e a r i s e s from t h e lower t u n n e l i n g p r o b a b i l i t y of a t r a p p e d e l e c t r o n between more widely s e p a r a t e d c e n t e r s . The d i s p e r s i v e t r a n s p o r t r e s u l t s can perhaps a l s o be understood i n terms of m u l t i p l e t r a p p i n g i n a bnad t a i l ; however, t h i s cannot e x p l a i n t h e photolumin- escence, which r e q u i r e s t r a n s i t i o n s between c e n t e r s t h a t a r e charged i n t h e i r ground s t a t e s and n e u t r a l i n t h e i r e x c i t e d s t a t e s t o account f o r t h e d e c r e a s e i n energy w i t h i n c r e a s i n g time.
F i e l d Effect.- S i n c e NVAPs s t r o n g l y pi% t h e Fermi energy, and some a r e expected t o b e p r e s e n t even in g l a s s e s w l t h a r e l a t i v e l y low v a l u e of t h e d i e l e c t r i c c o n s t a n t , E, t h e f i e l d e f f e c t should be unmeasurable i n chalcogenides (16). I n g e n e r a l , t h i s i s t h e c a s e . However, a r s e n i c t e l l u r i d e g l a s s e s do r o u t i n e l y e x h i b i t f i e l d e f f e c t s (12,13), a l t h o u g h t h e r e h a s been a d i s c r e p a n c y w i t h r e g a r d t o t h e t e m p e r a t u r e depen- dence. The main problem i s t h a t t h e t r a p - l i m i t e d m o b i l i t y (observed i n t h e t r a n - s i e n t p h o t o c o n d u c t i v i t y experiments d e s c r i b e d i n t h e l a s t s e c t i o n ) should be r e - duced from t h e f r e e - h o l e m o b i l i t y by a f a c t o r of P ~ / N , where p, i s t h e e q u i l i b r i u m f r e e - h o l e c o n c e n t r a t i o n and N i s t h e d e n s i t y of tFAPs. Even f o r a r e l a t i v e l y narrow-gap g l a s s , po/N
"
The breakthrough i n understanding t h e p r e s e n c e of f i e l d e f f e c t s i n chalcogen- i d e g l a s s e s was t h e o b s e r v a t i o n t h a t t h e e f f e c t s a r e t r a n s i e n t (16,17). I n f a c t , the.decay is c h a r a c t e r i z e d by two time c o n s t a n t s , one of t h e o r d e r of minutes and t h e o t h e r of s e v e r a l hours a t room temperature (16). This r e s u l t focused a t t e n t i o n on t h e k i n e t i c s of e q u i l i b r a t i o n , i n p a r t i c u l a r t h e f a c t t h a t t h e e x i s t e n c e of a n e g a t i v e Ueff r e q u i r e s a d e f e c t i n t e r c o n v e r s i o n of t h e t y p e C 3 O S C1O. S i n c e i t might be expected that each n e u t r a l d e f e c t is a t a l o c a l ~ o t e n t i a l minimum, t h e n t h e b a r r i e r between t h e s e minima would r e t a r d t h e i n t e r c o n v e r s i o n and mask t h e e f f e c t s of t h e n e g a t i v e U e f f . I n f a c t , a b a r r i e r of about 0.7 eV is s u f f i c i e n t t o account f o r t h e l o n g t r a n s i e n t s observed.
I n d e t a i l , t h e e x i s t e n c e of a p o t e n t i a l b a r r i e r between n e u t r a l d e f e c t s essen- t i a l l y n u l l i f i e s t h e e f f e c t s of t h e n e g a t i v e Ueff a t s h o r t t i m e s (up t o s e v e r a l m i n - u t e s i n a r s e n i c t e l l u r i d e g l a s s e s a t room t e m p e r a t u r e ) . A t t i m e s s h o r t compared t o T ~ = T ~ exp (AV1/kT), where 'i0 i s t h e r e c i p r o c a l of a phonon frequency and AV1 i s t h e energy d i f f e r e n c e between t h e t o p of t h e b a r r i e r and t h e higher-energy n e u t r a l de- f e c t , a chalcogenide g l a s s resembles a compensated semiconductor. The Fermi energy i s n o t pinned, and a f i e l d e f f e c t is r e a d i l y observable. The e f f e c t i v e d e n s i t y of s t a t e s a t s h o r t t i m e s i s sketched i n Pig. 2(a). Note t h e s i m i l a r i t y between t h i s r e s u l t and t h e one f o r a-Se deduced by Abkowitz and Enck (18). However, a t t i m e s l o n g compared t o r2=-co exp (AV2/kT), where AV; i s t h e energy d i f f e r e n c e between t h e t o p of t h e b a r r i e r and t h e lower-energy n e u t r a l d e f e c t , t h e f u l l e f f e c t s of t h e n e g a t i v e Ueff become e v i d e n t . The Fermi energy i s s t r o n g l y pinned by two-electron s t a t e s , and t h e e f f e c t i v e d e n s i t y of s t a t e s i s a s sketched i n Fig. 2 ( b ) .
( a I ( b )
Fig. 2: E f f e c t i v e d e n s i t y of s t a t e s f o r i n t e r p r e t i n g f i e l d - e f f e c t experiments :
( a ) s h o r t t i m e s , t << TI;
I-;., I--.,
(b) l o n g t i m e s , t >> T2.The p h y s i c a l p r o c e s s e s i n a r e a l f i e l d - e f f e c t experiment a r e a c t u a l l y q u i t e complex (16). When a n e g a t i v e b i a s is a p p l i e d t o t h e g a t e , f r e e h o l e s i n i t i a l l y f l o o d t h e space c h a r g e r e g i o n . Although t h e v a s t m a j o r i t y a r e t r a p p e d by t h e n e g a t i v e l y charged c e n t e r s , t h e e x c e s s f r e e c h a r g e c o n t r i b u t e s t o an o b s e r v a b l e f i e l d e f f e c t . However, t h e t r a p p e d c h a r g e y i e l d s a n imbalance of n e u t r a l a c c e p t o r s
(e.g.
cLO
) compared t o n e u t r a l donors (e.g. C30), t h u s p r o v i d i n g a d r i v i n g f o r c e f o r t h e l r i n t e r c o n v e r s i o n . However, t h i s is r e t a r d e d by t h e e x i s t e n c e of t h e bar-.r i e r , and t h e k i n e t i c s a r e c h a r a c t e r i z e d by a time c o n s t a n t , ~ ~ 1 2 . Only a t t i m e s long compared w i t h T does t h e quasi-Fermi energy f o r h o l e s r e t u r n t o t h e p o s i t i o n of t h e e q u i l i b r i u m Fermi energy. On t h e o t h e r hand, a s t h e i n t e r c o n v e r s i o n i s tak- i n g p l a c e , t h e trapped c h a r g e d e n s i t y i n c r e a s e s , c a u s i n g a r e d u c t i o n i n t h e screen- i n g l e n g t h . I n t u r n , t h i s r e q u i r e s t h e emission of h o l e s i n t h e bulk, which t h e n move toward t h e g a t e . This p r o c e s s o c c u r s in s e v e r a l s t e p s . A s t h e p o t e n t i a l c o l - l a p s e s towards t h e g a t e , some of t h e donors emit t h e i r h o l e s . This l e a d s t o an imbalance of n e u t r a l donors, which c o n v e r t t o a c c e p t o r s w i t h a time c o n s t a n t of
~ ~ 1 2 . The r e s u l t i n g n e u t r a l a c c e p t o r s q u i c k l y emit a second h o l e and become posi- t i v e l y charged. The f r e e h o l e s a r e swept towards t h e g a t e , r e s t o r i n g e q u i l i b r i u m i n t h e bulk. The e x c e s s f r e e h o l e s n e a r t h e g a t e a r e a l s o q u i c k l y t r a p p e d , l e a d i n g t o an i n t e r c o n v e r s i o n of n e u t r a l a c c e p t o r s t o donors i n t h i s r e g i o n , a g a i n c h a r a c t e r - i z e d by t h e time c o n s t a n t , ~ ~ 1 2 . This model a l s o c l e a r s up t h e p r e v i o u s d i f f i c u l t y i n t h e t e m p e r a t u r e dependence of t h e f i e l d e f f e c t , s i n c e a t h i g h t e m p e r a t u r e s t h e i n i t i a l c u r r e n t s a r e h i g h e r , but t h e r a t e s of decay a r e a l s o f a s t e r . This r e s u l t s i n a c r o s s i n g of t h e A I ( t ) c u r v e s a t d i f f e r e n t temperatures.
It i s e v i d e n t t h a t t r a n s i e n t e f f e c t s can be of t h e utmost importance i n a l l nonequilibrium experiments, i n c l u d i n g t h e s t e a d y - s t a t e , p h o t o c o n d u c t i v i t y and photo- luminescence, Photoconductivity i s analogous t o t h e f i e l d e f f e c t , except f o r t h e
JOURNAL DE PHYSIQUE
a d d i t i o n a l requirement of charge n e u t r a l i t y (19). A key f a c t o r i s t h e r e l a t i v e en- e r g i e s of t h e two n e u t r a l d e f e c t s . I f t h e donor-like d e f e c t (e.g. C30) has lower energy t h a n t h e a c c e p t o r - l i k e d e f e c t (e.g. ClO), t h e n e l e c t r o n s a r e more s t r o n g l y t r a p p e d t h a n h o l e s . S i n c e t h e t r a p p i n g i s by charged c e n t e r s and i s t h u s f a s t , t h e short-term e f f e c t i s t o s u p p r e s s t h e n e t i n c r e a s e of f r e e e l e c t r o n s . Because t h e t r a p p e d c h a r g e i s predominantly n e g a t i v e , c h a r g e n e u t r a l i t y r e q u i r e s t h e concen- t r a t i o n of f r e e h o l e s t o r i s e f a s t e r t h a n t h a t of f r e e e l e c t r o n s , t h u s l e a d i n g t o an anomalously h i g h i n i t i a l p h o t o c o n d u c t i v i t y . The concomitant e x c e s s of t r a p p e d h o l e s d r i v e s acceptor-to-donor i n t e r c o n v e r s i o n s t o r e s t o r e thermal e q u i l i b r i u m . However, i f a b a r r i e r t o t h e i n t e r c o n v e r s i o n e x i s t s , t h i s could t a k e a v e r y long time. N e v e r t h e l e s s , t h e r e q u i s i t e d e n s i t y e v e n t u a l l y does transform, and most of t h e r e s u l t a n t n e u t r a l donors q u i c k l y c o n v e r t t o p o s i t i v e l y charged donors. This f i n a l component of p o s i t i v e t r a p p e d charge o f f s e t s t h e n e g a t i v e c h a r g e r e s u l t i n g from t h e e x c e s s t r a p p e d e l e c t r o n s , t h u s reducing t h e p h o t o c o n d u c t i v i t y . Among t h e i m p l i c a t i o n s of t h i s a n a l y s i s a r e t h e appearance of a maximum i n t h e time e v o l u t i o n of t h e p h o t o c o n d u c t i v i t y and a s t r o n g dependence of t h e p h o t o c o n d u c i t i v i t y on t h e chopping frequency. Both of t h e s e have r e c e n t l y been observed. Homma and Adler(20) found a p h o t o c u r r e n t maximum i n a-Seg9Te39Li2 about 45s a f t e r t u r n i n g on t h e l i g h t , w h i l e Onari e t a l . (21) observed s t r o n g v a r i a t i o n s i n t h e p h o t o c u r r e n t of a s e r i e s of As-Se g l a s s e s as t h e chopping frequency was v a r i e d . I n a l l c a s e s , a maximum i n photoresponse was found between 0.2 Hz and 400 Hz, j u s t a s p r e d i c t e d by t h e p r e v i - ous a n a l y s i s .
C l e a r l y , photoluminescence cannot occur a f t e r one of t h e two n e u t r a l c e n t e r s has converted i n t o t h e o t h e r , s i n c e b o t h d e f e c t s t h e n have t h e same energy. Thus, i n t e r c o n v e r s i o n r e p r e s e n t s a n o n r a d i a t i v e recombination branch which should be v e r y temperature-dependent. Indeed, t h e photoluminescence i s s t r o n g l y quenched by in- c r e a s i n g t h e t e m p e r a t u r e (22), t h e d e t a i l e d v a r i a t i o n n o t r e p r e s e n t i n g a simple a c t i v a t e d p r o c e s s but r a t h e r a more complex one s u g g e s t i n g a d i s t r i b u t i o n of IVAPs.
Even a t v e r y low t e m p e r a t u r e s , t h e photoluminescence f a t i g u e s w i t h t i m e (23). This f a t i g u e c o u l d r e p r e s e n t t h e f o r c e d i n t e r c o n v e r s i o n r e q u i r e d by t h e imbalance be- tween p o s i t i v e and n e g a t i v e t r a p p e d c h a r g e d i s c u s s e d p r e v i o u s l y . The f a t i g u e cor- r e l a t e s w i t h t h e growth of a s i g n i f i c a n t unpaired-spin c o n c e n t r a t i o n , presumably due t o t h e now m e t a s t a b l e n e u t r a l d e f e c t s .
Amorphous S i l i c o n . - Although a n enormous amount of work h a s been c a r r i e d o u t r e c e n t - l y on amorphous s i l i c o n - b a s e d a l l o y s , p a r t i c u l a r l y a-Si:H (24) and a-Si:F:H ( 2 5 ) , a g r e a t many m y s t e r i e s s t i l l remain, i n c l u d i n g some concerning fundamental i s s u e s . For example, we s t i l l a r e u n c e r t a i n about t h e microscopic s t r u c t u r e of t h e m a t e r i a l , t h e m o b i l i t y of f r e e c a r r i e r s , t h e predominant mode of t r a n s p o r t , t h e n a t u r e of t h e major t r a p p i n g c e n t e r s , t h e primary recombination mechanism, t h e e x t e n t of t h e band t a i l s , t h e e f f e c t s of hydrogen, f l u o r i n e , and oxygen, t h e o r i g i n and d e n s i t y of l o c a l i z e d s t a t e s i n t h e gap, and t h e mechanism f o r doping. There a r e a l s o some q u e s t i o n s about t h e s i z e of t h e m o b i l i t y gap, t h e e x t e n t of t h e l o c a l o r d e r , t h e o r i g i n s of t h e unpaired s p i n s and photoluminescence peaks, and t h e s i g n of t h e e f f e c t i v e c o r r e l a t i o n energy of t h e major d e f e c t c e n t e r s . F i n a l l y , t h e o r i g i n s of two important e x p e r i m e n t a l r e s u l t s , t h e Staebler-Wronski e f f e c t and t h e Meyer- Neldel r u l e a r e e s s e n t i a l l y a complete mystery. I n t h e remainder of t h i s paper, I s h a l l t r y t o a n a l y z e t h e s e problems from a d e f e c t - o r i e n t e d viewpoint.
S t r u c t u r e . - S e v e r a l i s s u e s w i t h r e g a r d t o t h e s t r u c t u r e of amorphous s i l i c o n a l l o y s have been c l a r i f i e d r e c e n t l y . It i s now c l e a r t h a t many i f n o t a l l f i l m s of a-Si:H a r e inhomogeneous (26), o r d i n a r i l y c o n t a i n i n g r e g i o n s r e l a t i v e l y r i c h i n hydrogen a l t e r n a t i n g w i t h r e g i o n s w i t h only about 3 % hydrogen. Some hydrogen c l u s t e r i n g e x i s t s even i n t h e d i l u t e phases. Furthermore, space-charge r e g i o n s e x i s t , espe- c i a l l y i n h i g h - q u a l i t y f i l m s w i t h low d e f e c t d e n s i t i e s (24). These can be p r e s e n t n e a r a n e l e c t r o d e , a s u b s t r a t e , o r even a f r e e s u r f a c e . Such r e g i o n s can l e a d t o very a n i s o t r o p i c behavior of t h e p h y s i c a l p r o p e r t i e s . F i n a l l y , t h e r e i s some e v i - dence f o r t h e p r e s e n c e of i n t e r m e d i a t e r a n g e o r d e r , e s p c i a l l y i n a-Si:F:H f i l m s
(27). It i s not y e t c l e a r i f t h i s t a k e s t h e form of j u s t a s h a r p e r d i s t r i b u t i o n of d i h e d r a l a n g l e s ( p r e s e r v i n g third-neighbor d i s t a n c e s ) o r of more e x t e n s i v e s t r u c - t u r a l o r d e r sucb a s t h e e x i s t e n c e of m i c r o c r y s t a l l i t e s . There is n o w a g r e a t d e a l of evidence that h e a v i l y doped, high-conductivity samples of both a-Si:H and a-S-l:
F:H a r e p o l y c r y s t a l l i n e (28).
Defects.- There i s no doubt about t h e e x i s t e n c e of well-defined d e f e c t s i n a-Si f i l m s (29). An immediate demonstration i s t h e success of s u b s t i t u t i o n a l doping ( 3 ) . I f phosphorus and boron e n t e r a-Si:H with t e t r a h e d r a l c o o r d i n a t i o n a s i s e s s e n t i a l t o a c h i e v e doping, such c e n t e r s r e p r e s e n t d e f e c t s . Even i n undoped samples, anneal- ing beyond 350°C r e s u l t s i n hydrogen e f f u s i o n and sharp i n c r e a s e s i n t h e unpaired- s p i n d e n s i t y . It is c l e a r t h a t tHe e f f u s i o n of hydrogen must l e a d t o t h e c r e a t i o n of d e f e c t s . The EPR s i g n a l r e s u l t i n g from unpaired s p i n s a f t e r hydrogen e f f u s e s i s t h e same a s that f o r s p i n s c r e a t e d by d e p o s i t i o n a t lower temperatures o r by i r r a d i - a t i o n (30). We can conclude t h a t some of t h e same d e f e c t s a r e p r e s e n t i n as-deposi- t e d f i l m s .
S i n c e t e t r a h e d r a l c o o r d i n a t i o n r e p r e s e n t s t h e maximum covalent-bond d e n s i t y p o s s i b l e u s i n g s and p o r b i t a l s o n l y , v a l e n c e a l t e r n a t i o n is impossible i n a-Si a l l o y s . Consequently, no low-energy d e f e c t s e x i s t i n such f i l m s , and r e l a t i v e l y d e f e c t - f r e e samples can be prepared i n p r i n c i p l e . However, s i g n i f i c a n t d e f e c t con- c e n t r a t i o n s a r e always p r e s e n t i n a l l r e a l samples, presumably due t o s t r a i n s d u r i n g t h e non-equilibrium p r e p a r a t i o n c o n d i t i o n s . A n important p o i n t i s t h a t t h e d e f e c t d e n s i t i e s a r e n o t c o n t r o l l e d by thermodynamics a s i n chalcogenide g l a s s e s , but r a t h e r a r e extremely dependent on t h e d e t a i l s of t h e growth procedure. Thus f a r , t h e lowest d e f e c t d e n s i t i e s appear t o c h a r a c t e r i z e f i l m s prepared by t h e plasma decomposition of SiH4 o r S ~ F , $ / H ~ m i x t u r e s , o r by t h e chemical vapor d e p o s i t i o n
(CVD) of SiH4 followed by a post-hydrogenation. T t is c l e a r t h a t r e l a t i v e l y small hydrogen i n c o r p o r a t i o n (3-20%) s e r v e s t o reduce t h e s t r a i n s c o n s i d e r a b l y by lowering t h e average c o o r d i n a t i o n number, while f l u o r i n e can accomplish t h e same end more e f f i c i e n t l y because of t h e g r e a t e r bond-angle freedom of t h e predominantly i o n i c Si-F bonds. Nevertheless, t h e extreme s e n s i t i v i t y of t h e d e f e c t d e n s i t y t o deposi- t i o n parameters has g r e a t l y r e t a r d e d our understanding of t h e p h y s i c a l p r o p e r t i e s of a-Si a l l o y s .
The lowest energy n e u t r a l d e f e c t s i n a-Si f i l m s a r e t h e dangling bond (T30) and t h e doubly coordinated S i c e n t e r (T20). It i s c l e a r t h a t t h e T;! c e n t e r s have a p o s i t i v e Ueff (31), but t h e s i g n of Ueff f o r Tj c e n t e r s i s s t i l l i n doubt. We s h a l l r e t u r n t o t h i s q u e s t i o n l a t e r . I n a d d i t i o n t o t h e p o s s i b i l i t y of T ~ + - T ~ - p a i r s , T ~ + - T ~ - p a i r s can a l s o form (29). E i t h e r t y p e of p a i r has been c a l l e d a charge t r a n s f e r d e f e c t (CTD), and they can be i n t i m a t e (ICTDs) o r more d i s t a n t l y s e p a r a t e d .
Amajor problem when two t y p e s of n o n - i n t e r c o n v e r t i b l e d e f e c t s a r e sirmultane- o u s l y p r e s e n t i s t h e i n v a l i d i t y of a n e f f e c t i v e one-electron d e n s i t y of s t a t e s d i a - gram (29). A q u a s i p a r t i c l e approach i s e s s e n t i a l f o r t h e c o r r e c t i n t e r p r e t a t i o n of t r a n s p o r t and o p t i c a l behavior. Other problems can r e s u l t from t h e p o s s i b i l i t y of complex d e f e c t i n t e r c o n v e r s i o n i n a-Si:H f i l m s v i a hydrogen t r a n s f e r (29).
Besides t h e well-defined d e f e c t s d i s c u s s e d above, c o n t i n u a of s t r e t c h e d bonds and d i s t o r t e d bond a n g l e s a r e p o s s i b l e . However, t h e r e is s t r u c t u r a l evidence only f o r t h e l a t t e r (32), which should be r e s p o n s i b l e f o r t h e v a l e n c e and conduction band t a i l s r a t h e r t h a n any s t a t e s deep in t h e gap. S t i l l another p o s s i b i l i t y i n hydro- genated f i l m s i s t h e presence of t h r e e - c e n t e r bonds with b r i d g i n g hydrogen atoms
(33). Recent c a l c u l a t i o n s (34) suggest t h a t such bonds can remove any l o c a l i z e d s t a t e r e s u l t i n g from a s t r e t c h e d bond from t h e energy gap. The e f f e c t i v e c o r r e l a - t i o n energy of such a complex i s p o s i t i v e , i n disagreement w i t h a p r e v i o u s sugges- t i o n (35). F i n a l l y , dopant atoms such a s P o r B o r i m p u r i t i e s such a s 0 can induce d i f f e r e n t t y p e s of d e f e c t c e n t e r s .
Density of Localized S t a t e s . - The d e n s i t y of l o c a l i z e d s t a t e s i n t h e gap of a-Si a l l o y s is one of t h e most important unresolved problems a t t h e p r e s e n t time. Clear- l y , it is very dependent on sample composition and q u a l i t y , and i s t h u s n o t a unique property. In a d d i t i o n , inhomogeneities and a n i s o t r o p i e s can a f f e c t t h e measurements enormously. N w e r t h e l e s s , t h e r e a r e s u f f i c i e n t s i m i l a r i t i e s i n t h e d e t a i l e d t r a n s - p o r t behavior among t h e h i g h e s t - q u a l i t y f i l m s prepared i n many d i f f e r e n t l a b o r a t o r - i e s t h a t we might expect t o be a b l e t o answer t h e following q u e s t i o n s w i t h regard t o such f i l m s : (1) Do s p i n l e s s d e f e c t s e x i s t i n a-Si:H? (2) Is t h e r e well-defined
C4-8 JOURNAL DE PHYSIQUE
s t r u c t u r e i n g ( E ) ? (3) Is t h e r e evidence f o r more t h a n one t y p e of d e f e c t ? (4) Does t h e i n t r i n s i c d e f e c t d e n s i t y change wich doping? (5) What is t h e minimum d e n s i t y of l o c a l i z e d s t a t e s i n t h e gap?
Unfortunately, we do n o t have unambiguous answers t o any of t h e s e q u e s t i o n s y e t . One of t h e problems i s t h e d i f f e r e n t r e s u l t s emerging from d i f f e r e n t e x p e r i - mental t e c h n i q u e s such as. f i e l d e f f e c t , c a p a c i t a n c e , and DLTS measurements. With t h e s e u n c e r t a i n t i e s i n mind, i t i s s t i l l u s e f u l t o s u m a r i z e t h e p r e s e n t weight of evidence.
The i s s u e of s p i n l e s s d e f e c t s i s of g r e a t importance t o s o r t i n g o u t t h e pro- p e r t i e s of a-Si:H. There is g e n e r a l agreement t h a t t h e minimum d e n s i t y of unpaired s p i n s i s of t h e o r d e r of 1016an-3 o r l e s s (24). F i e l d - e f f e c t and c a p a c i t a n c e measurements g e n e r a l l y tend t o i n d i c a t e t h a t t h e t o t a l d e n s i t y of deep gap s t a t e s i s s e v e r a l o r d e r s of a a g n i t u d e l a r g e r t h a n t h i s , a l t h o u g h t h e s e may r e s u l t from s u r f a c e o r i n t e r f a c e r a t h e r t h a n bulk s t a t e s . However, t h e r e i s a g r e a t d e a l of a d d i t i o n a l evidence on t h e q u e s t i o n . When atomic hydrogen is i n t r o d u c e d i n t o CVD a-Si f i l m s , t h e EPR s i g n a l i s quenched by H l e v e l s of t h e o r d e r of s p i n concentra- t i o n . However, about 100 times a s much H e n t e r s t h e f i l m b e f o r e h i g h - q u a l i t y a-Si:H r e s u l t s (36). S i m i l a r l y , about 100 t i m e s a s much H i s given o f f t h a n un- p a i r e d s p i n s a r e c r e a t e d ( 3 7 ) . Thus, it i s c l e a r that H compensates s p i n l e s s de- f e c t s . S i n c e we can conclude f r o m t h e work of Sol
e.
(36) t h a t H p r e f e r e n t i a l l y t i e s up dangling bonds and y e t some of t h o s e remain w e n i n t h e h i g h e s t - q u a l i t y f i l m s , i t i s extremely l i k e l y that s p i n l e s s d e f e c t s remain i n a l l samples. I n addi- t i o n , CVD a-Si:P c l e a r l y shows a d e c r e a s e i n 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 w i t h i n c r e a s i n g P c o n c e n t r a t i o n w h i l e t h e s p i n c o n c e n t r a t i o n remains c o n s t a n t (38,39).Thus, P i s a f f e c t i n g s p i n l e s s d e f e c t s i n t h i s range. These d e f e c t s a r e u n l i k e l y t o be s t r e t c h e d bonds, s i n c e t h e r e is no evidence f o r t h e s e i n p u r e a - S i (32).
They a r e probably n o t d i s t o r t e d bond a n g l e s , s i n c e H would n o t e a s i l y compensate such d e f e c t s . Most l i k e l y , t h e y a r e e i t h e r TZ0 c e n t e r s o r T3+-T3- p a i r s . (The l a t t e r would c h a r a c t e r i z e any i n t e r n a l s u r f a c e s t h a t may e x i s t due t o t h e growth k i n e t i c s (40) .)
The evidence t h a t t h e p r e s e n c e of well-defined d e f e c t s l e a d t o s t r u c t u r e i n g(E) comes from a wide a r r a y of o b s e r v a t i o n s i n c l u d i n g f i e l d e f f e c t , t u n n e l i n g , DLTS, and doping experiments (41). This s t r u c t u r e a p p e a r s t o e x i s t b o t h above and below t h e gap c e n t e r and i s q u i t e asymmetric. The l a t t e r i s a l s o evidence f o r t h e e x i s t e n c e of more t h a n one t y p e of d e f e c t .
EPR.- EPR measurements i n d i c a t e t h e presence of t h r e e d i f f e r e n t s p i n s i g n a l s , w i t h
-
g-values of 2.0055, 2.004, and 2.013 (42). Only t h e f i r s t of t h e s e i s p r e s e n t a t e q u i l i b r i u m in undoped f i l m s . T h i s can b e a s s o c i a t e d w i t h t h e n e u t r a l dangling bond, T30. The g=2.004 l i n e a p p e a r s i n P-doped f i l m s , w h i l e t h e gz2.013 l i n e char- a c t e r i z e s B-doped f i l m s . The c o n v e n t i o n a l i n t e r p r e t a t i o n i s t h a t t h e s e r e p r e s e n t e l e c t r o n s and h o l e s l o c a l i z e d i n t h e conduction and v a l e n c e band t a i l s , r e s p e c t i v e - l y . These band t a i l s a r e expected t o a r i s e from s t r a i n e d bonds i n t h e samples.However, t h e r e a r e d i f f i c u l t i e s w i t h t h i s i n t e r p r e t a t i o n . Both s p i n s i g n a l s main- t a i n t h e same p o s i t i o n and width, d e s p i t e t h e wide a r r a y of d i f f e r e n t t y p e s of s t r a i n e d bonds expected. I n a d d i t i o n a s t h e P c o n c e n t r a t i o n i n c r e a s e s , t h e g=2.004 s i g n a l goes through a maximum and begins t o d e c l i n e i n s t r e n g t h (42). A s i m i l a r maximum in d e n s i t y of t h e g=2.013 s p i n s o c c u r s w i t h i n c r e a s i n g B c o n c e n t r a t i o n (43).
These r e s u l t s a r e v e r y d i f f i c u l t t o understand i n terms of band t a i l s . Even i f such s t a t e s were c h a r a c t e r f z e d by a s m a l l c o r r e l a t i o n energy, a maximum i n s p i n d e n s i t y cannot occur u n l e s s phosphorus and boron begin t o reduce t h e d e n s i t y of s t r a i n e d bonds beyond a c r i t f c a l c o n c e n t r a t i o n . But, i n a d d i t i o n , a t a given P concentra- t i o n , t h e Fermi energy i n c r e a s e s w i t h i n c r e a s i n g temperature, w h i l e f o r a f i x e d B c o n c e n t r a t i o n , Ef d e c r e a s e s w i t h i n c r e a s i n g temperature (43). S i n c e Ef must move away from l a r g e d e n s i t i e s of s t a t e s a s t h e t e m p e r a t u r e i n c r e a s e s , both of t h e s e r e s u l t s a r e incompatible with a b a n d - t a i l i n t e r p r e t a t i o n .
Doubly c o o r d i n a t e d S i atoms a r e c h a r a c t e r i z e d by a p o s i t i v e Ueff and a r e spiv- l e s s when n e u t r a l . Five d i f f e r e n t charge c o n d i t i o n s a r e p o s s i b l e f o r such c e n t e r s , Tz2+, T ~ + , T20, T2-, and T~'-. A l l of t h e s e s t a t e s could appear i n t h e gap s i n c e
o n l y t h e T~~ and ~ 2 - s t a t e s are s i g n i f i c a n t l y s e p a r a t e d i n e n e r g y (44). Note t h a t TZ2+ and TZ2- c e n t e r s r e p r e s e n t t h e ground s t a t e s f o r t h e i r e l e c t r o n i c c o n f i g u r a - t i o n s . It a p p e a r s t o b e more l i k e l y t h a t t h e g=2.013 s p i n s a r e T + c e n t e r s , w h i l e t h e gx2.004 s p i n s a r e T2- e e n t e r s . The build-up of s p i n l e s s TZ2+'and T ~ e e n t e r s ~ - w i t h i n c r e a s e d doping c o n c e n t r a t i o n c a n t h e n e x p l a i n t h e maxima i n s p i n d e n s i t i e s i n a n a t u r a l way. Furthermore, i f t h e T + and T2- l e v e l s a r e s p l i t o f f from t h e v a l e n c e and c o n d u c t i o n bands by s e v e r a l ET, t h e o b s e r v e d t e m p e r a t u r e dependence o f Ef becomes u n d e r s t a n d a b l e .
Staebler-Wronski E f f e c t . - S t a e b l e r and Wronski (SW) observed t h a t a f i l m o f a-Si:H w i t h a n a c t i v a t i o n e n e r g y o f 0.57 eV f o r c o n d u c t i o n was m e t a s t a b l y changed upon pro- longed e x p o s u r e t o l i g h t (45). The a c t i v a t i o n e n e r g y i n c r e a s e d t o 0.87eV, t h e photo- c o n d u c t i v i t y d e c r e a s e d , and t h e r e c o m b i n a t i o n k i n e t i c s changed from b i m o l e c u l a r t o monomolecular. The o r i g i n a l s t a t e c o u l d be r e c o v e r e d by a t h e r m a l a n n e a l c o n t r o l l e d by a t i m e c o n s t a n t w i t h a n a c t i v a t i o n energy of a b o u t 1 . 5 eV f o r n-type samples. For p-type f i l m s , r e c o v e r y a p p e a r s t o b e more r a p i d (24). The m e t a s t a b l e s t a t e c o n t a i n s a b o u t d o u b l e t h e d e n s i t y o f g12.0055 s p i n s (46) and a n a s s o c i a t e d photoluminescence l i n e n e a r 0.8 eV i s a l s o r o u g h l y doubled a n i n t e n s i t y (47). DLTS e x p e r i m e n t s i n d i - c a t e that t h e photo-induced c h a n g e s are a b u l k r a t h e r t h a n j u s t a s u r f a c e e f f e c t
( 4 8 ) .
A v e r y i n t e r e s t i n g r e c e n t r e s u l t is that undoped f i l m s e x h i b i t a n i n v e r s e e f - f e c t , i n which t h e a c t i v a t i o n energy f o r c o n d u c t i o n d e c r e a s e s (49). Moderate P o r B doping b r i n g s about a l a r g e d i r e c t e f f e c t , w h i l e heavy (1%) doping quenches t h e e f f e c t c o m p l e t e l y . The r e s u l t s a r e shown i n Fig. 3.
"-1yPO
*
0-IVP*F i g . 3 : Doping dependence of t h e Stabler-Wronski e f f e c t . A r e f e r s t o t h e a n n e a l e d state and B t o t h e l i g h t soaked s t a t e ( 4 9 ) .
A E, ( F V ~
The c o n v e n t i o n a l i n t e r p r e t a t i o n o f t h e Staebler-Wronski e f f e c t i s simply a l i g h t - i n d u c e d c r e a t i o n of T30 s t a t e s . T h i s model has a major c o n c e p t u a l d i f f i c u l t y , however, s i n c e t h e e x c i t i n g l i g h t has energy o f l e s s t h a n 2 eV, much less t h a n t h e e x p e c t e d c r e a t i o n e n e r g y o f two d a n g l i n g bonds. (The c r e a t i o n o f a s i n g l e d a n g l i n g bond i s g e o m e t r i c a l l y i m p o s s i b l e . ) Furthermore, t h e l a c k of any exchange n a r r o w i n g of t h e phgto-induced EPR l i n e s i n d i c a t e s t h a t t h e new ~ 3 ' c e n t e r s must b e more t h a n a b o u t 1 0 A a p a r t (46). T h i s c o u l d be accomplished by t h e d i f f u s i o n o f p a i r s o f hydrogen atoms from w i d e l y s e p a r a t e d r e g i o n s t o a s p i n l e s s d e f e c t , b u t t h i s would a p p e a r t o b e r a t h e r u n l i k e l y and n o t e a s i l y r e v e r s i b l e . I n any e v e n t , s u c h a model has even more d i f f i c u l t y i n e x p l a i n i n g t h e r e s u l t s o f Fig. 3. I f t h e T30 c e n t e r s a r e c h a r a c t e r i z e d by a p o s i t i v e U e f f , two bumps i n t h e gap w i l l b e p r e s e n t , o n e a t To and t h e o t h e r a t To
+
U e f f . I f d a n g l i n g bonds a r e t h e predominant d e f e c t , t h e Ef s h o u l d b e l o c a t e d n e a r To+
Uepf/2 i n undoped samples, I n t h i s c a s e , any en- hancement of t h e T3O c e n t e r s by l i g h t w i l l n o t s i g n i f i c a n t l y a f f e c t Ef. As P i s added, Ef i n c r e a s e s , c o n v e r t i n g t h e c e n t e r s from T30 t o T3-. Any photo-induced c r e a t i o n of new c e n t e r s must t h e n d e c r e a s e Ef, s i n c e P atoms would n o t b e s o e f f e c - t i v e i n i n c r e a s i n g Ef i f t h e r e were more T3- s t a t e s t o f i l l . The magnitude o f t h e change i n Ef s h o u l d b e i n v e r s e l y p r o p o r t i o n a l t o g ( E f ) , s o t h a t AEf would become s m a l l o n l y a f t e r Ef r e a c h e s t h e P l e v e l s o r t h e conduction-band t a i l . S i m i l a r rea- s o n i n g s h o u l d p r e v a i l f o r B-doped samples. Thus, a n i n v e r s e SW e f f e c t i s d i f f i c u l t t o u n d e r s t a n d . I f o t h e r d e f e c t s a r e i m p o r t a n t and t h e T30 s t a t e s a r e n e a r t h e cen- t e r of t h e gap, i t i s p o s s i b l e t h a t Ef c o u l d l i e w i t h i n t h e s e states even i n undoped samples. I f t h i s is t h e c a s e , some of t h e c e n t e r s a r e T ~ + a t e q u i l i b r i u m and photo- induced d a n g l i n g bonds c o u l d i n c r e a s e Ef. However, t h e r e i s a g r e a t d e a l o f e v i -JOURNAL DE PHYSIQUE
dence a g a i n s t t h i s view. It p r e d i c t s t h a t t h e s p i n d e n s i t y should i n c r e a s e with P doping, i n disagreement w i t h o b s e r v a t i o n s (38,39,42). I f , a s i s commonly b e l i e v e d , t h e Tg- s t a t e s a r e c e n t e r e d 0.4 eV below Ec ( 3 ) , t h e r e should be a wide range of Ef
(more t h a n 0.6 eV) f o r which AEf
'
0. Not much should happen w i t h B doping u n t i l Ef-E,'
0.4 eV. I n f a c t , a s i s e v i d e n t from Fig. 3 , t h e r e v e r s e i s true--AEf r a p i d - l y v a n i s h e s a s Ef-E, approaches 0.4 eV. I n a d d i t i o n t o accounting f o r AEf, any model f o r t h e SW e f f e c t must a l s o e x p l a i n t h e concomitant p h o t o c o n d u c t i v i t y changes, t h e 1.5 eV a c t i v a t i o n energy f o r recovery, and t h e asymmetry between P and B doping.C l e a r l y , t h e s i t u a t i o n i s q u i t e complex.
T r a n s i e n t Photoconductivity.- Hvam and Brodsky (50) r e c e n t l y r e p o r t e d t h e observa- t i o n of d i s p e r s i v e t r a n s p o r t i n b o t h undoped and phosphorus-doped a-Si:H. The tem- p e r a t u r e dependence i n d i c a t e d t h e a p p l i c a b i l i t y of t h e m u l t i p l e - t r a p p i n g model d i s - cussed p r e v i o u s l y . Undoped samples e x h i b i t e d a decay temperature of To 3000K, but t h i s v a l u e i s s h a r p l y reduced upon doping. A d e t a i l e d a n a l y s i s of t h e d a t a ( 5 l ) s u g - g e s t s t h a t a broad e x p o n e n t i a l d i s t r i b u t i o n of i n t r i n s i c t r a p s e x i s t s i n undoped f i l m s , but t h a t i n t r o d u c t i o n of P l e a d s t o t h e formation of r e l a t i v e l y shallow t r a p s t o g e t h e r w i t h a concomitant r e d u c t i o n i n t h e i n t r i n s i c t r a p d e n s i t y . These shallow t r a p s b r i n g about a n i n c r e a s e i n recombtnation l i f e t i m e . I f t h e c o n v e n t i o n a l approach i s a c c e p t e d , t h e d i s p e r s i o n r e s u l t s from t r a p p i n g i n t h e conduction band t a i l . I n t h i s c a s e , t h e e x t e n t of t h e band t a i l and t h u s To should i n c r e a s e w i t h phosphorus doping due t o a d d i t i o n a l d i s o r d e r . I n f a c t , t h e r e v e r s e i s observed.
I n a d d i t i o n , t h e i n c r e a s e s i n i n i t i a l p h o t o c u r r e n t w i t h both phosphorus doping and t e m p e r a t u r e a r e d i f f i c u l t t o understand.
An A l t e r n a t i v e Model.- Many of t h e problems w i t h t h e c o n v e n t i o n a l approach can be overcome i f t h e p o s s i b i l i t y of n e g a t i v e l y c o r r e l a t e d s i t e s i s c o n s i d e r e d (52). The r e a c t i o n , 2T30 + T3+
+
T3- p r e s e r v e s t h e t o t a l number of bonds, but e l i m i n a t e s two nonbonding e l e c t r o n s . Note t h a t ~ 3 ' and T3- a r e both t h e lowest-energy configura- t i o n s f o r t h e i r e l e c t r o n i c s t r u c t u r e . However, a l t h o u g h t h e two c e n t e r s have t h e same c o o r d i n a t i o n number, t h e bond a n g l e s a r e v e r y d i f f e r e n t : T3+ most l i k e l y exhi- b i t s sp2 bonding w i t h a bond a n g l e n e a r 120°, w h i l e T3- would be expected t o e x h i b i t p r i m a r i l y p bonding w i t h a bond a n g l e i n t h e lo0-100° range. Thus, a l t h o u g h t h e two n e u t r a l c e n t e r s can i n t e r c o n v e r t by a l o c a l rearrangement, it i s extremely l i k e l y t h a t such a n i n t e r c o n v e r s i o n r e q u i r e s t h e overcoming of a p o t e n t i a l b a r r i e r ( r e c a l l t h e p r e v i o u s d i s c u s s i o n of t h e f i e l d e f f e c t and p h o t o c o n d u c t i v i t y i n c h a l c o g e n i d e s ) .It i s c l e a r t h a t unpaired s p i n s e x i s t i n a-Si:H. Although t h i s r e s u l t i s n o t incompatible w i t h a s m a l l n e g a t i v e U e f f , t h e r e l a t i v e l y s m a l l v a r i a t i o n s i n s p i n d e n s i t y w i t h t e m p e r a t u r e suggest t h a t some T30 c e n t e r s a r e s t a b l e . It i s p o s s i b l e t h a t Ueff i s p o s i t i v e f o r i s o l a t e d c e n t e r s , but t h a t t h e coulomb a t t r a c t i o n s t a b i l - i z e s i n t i m a t e p a i r s (53). The e f f e c t i v e d e n s i t y of s t a t e s f o r undoped f i l m s a t t i m e s t o o s h o r t t o a l l o w f o r any d e f e c t i n t e r c o n v e r s i o n s i s sketched i n Fig. 4 ( a ) . A s P i s i n t r o d u c e d , s e v e r a l e f f e c t s can occur. The most l i k e l y i n i t i a l consequence is a replacement of some of t h e T ~ + - T
-
a i r s by more s t a b l e P ~ + - T ~ - p a i r s . This3 .P
would keep t h e s p i n d e n s i t y c o n s t a n t w h l l e lowering t h e e f f e c t i v e g ( E f ) , i n accord- ance w i t h o b s e r v a t i o n s (38,39). F u r t h e r P doping would begin t o c o n v e r t i s o l a t e d 'T30 c e n t e r s i n t o Tg-, reducing t h e s p i n d e n s i t y and l e a d i n g t o a r a p i d i n c r e a s e i n E f . St211 more P would t h e n begin c o n v e r t i n g t h e l a r g e c o n c e n t r a t i o n s of T ~ + cen- t e r s t o Tg-, a s t h e i n c r e a s e i n Ef slows down. The e f f e c t i v e d e n s i t y of s t a t e s f o r moderate doping i s sketched i n Pig. 4 ( b ) .
F5g. 4: E f f e c t i v e d e n s i t y of s t a t e s f o r a-Si a l l o y s a t t i m e s t o o s h o r t f o r t h e i n t e r c o n v e r s i o n of T~~ c e n t e r s . T2 cen- t e r s a r e n o t shown. ( a ) Undoped f i l m . (b) P-doped f i l m .
The advantage of such a complex model i s t h a t i t p r o v i d e s a n a t u r a l explana- t i o n of b o t h t h e t r a n s i e n t photoconductivity and t h e SW e f f e c t . A s mentioned pre- v i o u s l y , t h e p h o t o c o n d u c t i v i t y r e s u l t s r e q u i r e a wide d i s t r i b u t i o n of i n t r i n s i c e l e c t r o n t r a p s which a r e g r a d u a l l y r e p l a c e d by shallower t r a p s a s P i s introduced.
This i s j u s t what would be expected from t h e g(E) of Fig. 4. I n a d d i t i o n , t h e model e a s i l y a c c o u n t s f o r t h e observed s t r u c t u r e i n t h e f i e l d e f f e c t and o t h e r measure- ments (41).
When i n t e n s e l i g h t i s i n c i d e n t on a sample f o r a long t i m e , o t h e r e f f e c t s e n t e r (19). F r e e e l e c t r o n s a r e p r e f e r e n t i a l l y t r a p p e d by T ~ + c e n t e r s , f r e e h o l e s by T3- c e n t e r s . The main f a c t o r c o n t r o l l i n g t h e subsequent behavior i n undoped sam- p l e s i s whether Ef i s c l o s e r t o t h e T ~ + o r t h e T3- s t a t e s . This i s l i k e l y t o be v e r y dependent on t h e e x a c t composition and p r e p a r a t i o n c o n d i t i o n s (e.g. it i s known t h a t H i n c r e a s e s t h e band gap, most l i k e l y by lowering t h e valence-band m o b i l i t y edge). I f Ef i s c l o s e r t o t h e donor s t a t e s , e l e c t r o n s a r e t r a p p e d more s t r o n g l y t h a n h o l e s , and t h e n e t i n c r e a s e i n f r e e - e l e c t r o n c o n c e n t r a t i o n i s suppressed during t h e i l l u m i n a t i o n . S i n c e t h e t r a p p e d charge d e n s i t y i s v e r y l a r g e compared t o t h e f r e e c a r r i e r d e n s i t y , c h a r g e n e u t r a l i t y r e q u i r e s t h e build-up of a n e x c e s s of both f r e e and trapped h o l e s . This e f f e c t s u p p r e s s e s t h e i n i t i a l p h o t o c o n d u c t i v i t y . But t h e e x c e s s trapped h o l e c o n c e n t r a t i o n p r o v i d e s a s t r o n g d r i v i n g f o r c e t o convert n e u t r a l a c c e p t o r s t o donors t o r e s t o r e thermal e q u i l i b r i u m . The r e s u l t i n g n e u t r a l donors t h e n q u i c k l y i o n i z e , i n c r e a s i n g t h e photoconductivity. When t h e l i g h t i s t u r n e d o f f , t h e donors and a c c e p t o r s r a p i d l y e q u i l i b r a t e w i t h t h e f r e e c a r r i e r s , but not w i t h each o t h e r (because of t h e p o t e n t i a l b a r r i e r ) . However, t h e g r e a t e r c o n c e n t r a t i o n of donors induces a n e t p o s i t i v e t r a p p e d charge, which i n t u r n l e a d s t o an i n c r e a s e of Ef t o r e s t o r e c h a r g e n e u t r a l i t y . Consequently, t h e a c t i v a t i o n energy f o r conduction i s reduced. Only a f t e r very long times o r a t e l e v a t e d temper- a t u r e does t h e reconversion of donors t o a c c e p t o r s r e s t o r e thermal e q u i l i b r i u m . This i s t h e i n v e r s e SW e f f e c t , e v i d e n t i n t h e undoped r a n g e of Fig. 3. On t h e o t h e r hand, a d i r e c t SW e f f e c t o c c u r s i n undoped m a t e r i a l when Ef i s c l o s e r t o t h e accep- t o r l e v e l s . Then t h e e x c e s s c o n c e n t r a t i o n of t r a p p e d e l e c t r o n s d u r i n g t h e illumina- t i o n d r i v e s a conversion of n e u t r a l donors t o a c c e p t o r s . T h e i r subsequent ioniza- t i o n c r e a t e s e x c e s s f r e e h o l e s which s u p p r e s s t h e p h o t o c o n d u c t i v i t y . A f t e r t h e l i g h t i s turned o f f , t h e g r e a t e r c o n c e n t r a t i o n of a c c e p t o r s produces a n e t n e g a t i v e trapped c h a r g e which i s reduced by a d e c r e a s e of Ef. The a c t i v a t i o n energy f o r conduction i s i n c r e a s e d u n t i l t h e slow recovery induced by overcoming t h e 1.5 eV p o t e n t i a l b a r r i e r e v e n t u a l l y r e s t o r e s e q u i l i b r i u m . I f recombination i s dominated by t h e r e l a t i v e l y s m a l l d e n s i t y of i s o l a t e d T30 c e n t e r s j u s t below E f , i t would t h e n be expected t o b e bimolecular i n t h e e q u i l i b r i u m s t a t e . However, a f t e r Ef d e c r e a s e s , t h e c e n t e r s a r e i o n i z e d t o T ~ + , changing t h e k i n e t i c s t o monomolecular, a s observed (45).
A s P i s added, many simultaneous e f f e c t s occur. The major one i s t h e r e p l a c e - ment of T ~ + - T ~ - p a i r s by P ~ + - T ~ - p a i r s . The d e n s i t y of charged a c c e p t o r s i n c r e a s e s and t h o s e of charged donors d e c r e a s e , w h i l e a c o n c e n t r a t i o n of shallow P donors b u i l d s up. Because of t h e shallow donors, Ef i n c r e a s e s . The a n a l y s i s is much more complex because of t h e two s e t s of donor l e v e l s , one i n t e r c o n v e r t i b l e w i t h t h e a c c e p t o r s , t h e o t h e r n o t . ( I s h a l l r e t u r n t o t h i s p o i n t l a t e r . ) I f it i s assumed t h a t t h e p4+ l e v e l s a r e j u s t below t h e conduction-band m o b i l i t y edge a s i n Fig. 4 ( b ) , a s i m i l a r a n a l y s i s i n d i c a t e s t h a t t h e SW e f f e c t remains d i r e c t u n t i l Ef p a s s e s t h e t o p of t h e ~ 3 ' band. A t t h i s p o i n t , a l l dangling bonds a r e n e g a t i v e l y charged, and a l l consequences of a n e g a t i v e Ueff i n c l u d i n g t h e SW e f f e c t must d i s a p p e a r . As B i s added, weight s h i f t s from t h e T3- band t o t h e T ~ + band a s Ef d e c r e a s e s . I f t h e Bq- l e v e l s a r e q u i t e shallow, a p o i n t w i l l b e reached i n which AEf becomes p o s i t i v e and t h e d a r k c o n d u c t i v i t y i n c r e a s e s . This should p e r s i s t u n t i l t h e sample be- comes p-type, a t which p o i n t t h e photo-induced i n c r e a s e i n Ef l e a d s t o a d e c r e a s e i n c o n d u c t i v i t y . This d i r e c t SW e f f e c t now p e r s i s t s u n t i l Ef f a l l s below t h e bot- tom of t h e T3- band, a t which p o i n t it d i s a p p e a r s . I n B-doped samples, t h e recovery c h a r a c t e r i s t i c s a r e governed by donor-to-acceptor c o n v e r s i o n s , which r e q u i r e t h e overcoming of a s m a l l e r p o t e n t i a l b a r r i e r ( s i n c e i n t h i s model t h e n e u t r a l a c c e p t o r h a s lower t o t a l energy t h a n t h e n e u t r a l donor). Consequently, r e c o v e r y should occur more r a p i d l y , i n accordance w i t h a p r e l i m i n a r y f i n d i n g (24).
JOURNAL DE PHYSIQUE
The appeal of t h i s model i s t h a t it e x p l a i n s a g r e a t d e a l of complex d a t a i n a c o n s r s t e n t way. S i n c e no new d e f e c t s a r e c r e a t e d by t h e l i g h t , t h e r e i s no need t o s e a r c h f o r d e f e c t s w i t h a l o w c r e a t i o n energy o r understand why t h e o r i g i n a l s t a t e i s r e s t o r e d completely by t h e a n n e a l i n g p r o c e s s . The model is a l s o c o n s i s t e n t w i t h t h e t r a n s i e n t p h o t o c o n d u c t i v i t y r e s u l t s , a s d e s c r i b e d p r e v i o u s l y .
Note t h a t t h e absence of an SW e f f e c t does not e n s u r e a d e f e c t - f r e e f i l m - - i t can simply be a conqequence of Ef f a l l i n g i n one of t h e two p o s i t i o n s i n which i t i s s t a b l e ( s e e Fig. 3 ) . S i m i l a r l y , i f an undoped f i l m c o n t a i n s an accumulation r e g i o n n e a r an i n t e r f a c e , a common s i t u a t i o n (24), t h e SW e f f e c t can be l a r g e n e a r t h e in- t e r f a c e and small i n t h e b u l k ( s e e Fig. 3 ) . I n such a c a s e , t h e e f f e c t is consider- a b l y s m a l l e r i n a sandwich s t r u c t u r e , and would e r r o n e o u s l y appear t o be a s u r f a c e r a t h e r t h a n a b u l k e f f e c t .
Mechanism f o r Dopin
.-
When P i s i n t r o d u c e d i n t o h i g h - q u a l i t y a-Si a l l o y s , Ef in- c r e a s e s . The mechangism f o r t h i s doping e f f e c t (assuming t h a t P i s a c t u a l l y doping a-Si, r a t h e r than c a t a l y z i n g t h e formation of doped m i c r o c r y s t a l l i t e s ) i s n o t en- t i r e l y obvious i n a n amorphous f i l m , s i n c e t h e lowest-energy c o n f i g u r a t i o n f o r P i s t r i g o n a l l y r a t h e r t h a n t e t r a h e d r a l l y c o o r d i n a t e d , and t r i g o n a l l y c o o r d i n a t e d P would not be e l e c t r i c a l l y a c t i v e . The f a c t t h a t many t r i g o n a l l y c o o r d i n a t e d s i l i c o n atoms appear i n p u r e a-Si f i l m s d e s p i t e t h e i r l a r g e c r e a t i o n e n e r g i e s i s s u f f i c i e n t evi- dence that such c o o r d i n a t i o n i s e a s i l y a t t a i n e d i n t h e amorphous network. However, t i g h t - b i n d i n g e s t i m a t e s show t h a t a P ~ + - T ~ - p a i r has a low c r e a t i o n energy (31).This comes about because such a p a i r p r e s e r v e s t h e optimal number of bonds, and would be a VAP except f o r s t e r i c c o n s t r a i n t s . (Although a P40 c e n t e r can, i n p r i n - c i p l e , convert i n t o a T30 c e n t e r by breaking a bond, t h e r e s u l t i n g r e l a x a t i o n would r e q u i r e b o t h t h e S i and t h e P t o m w e towards each o t h e r a f t e r t h e band b r e a k s , a h i g h l y e n e r g e t i c a l l y u n f a v o r a b l e motion.) For doping c o n c e n t r a t f o n below t h e den- s i t y of t r i g o n a l l y c o o r d i n a t e d S i atoms, most P atoms g i v e up an e l e c t r o n t o pre- v i o u s l y formed T ~ + o r T30 c e n t e r s and e n t e r t h e network a s p4+. This i s encouraged i n a plasma i n which t h e P atoms a r e a l r e a d y i o n i z e d . The formation of P ~ + - T ~ - p a i r s r e d u c e s t h e d e n s i t y of T~~ c e n t e r s , a s is observed (38,39). However, t h i s mechanism can e x p l a i n an i n c r e a s e of Ef o n l y t o a p o s i t i o n halfway between t h e t o p of t h e Tg- band and t h e p40 l e v e l s . Motion beyond t h i s p o i n t r e q u i r e s t h e p r e s e n c e of T2O c e n t e r s o r an e x t e n s i v e conduction-band t a i l . S i n c e T~~ c e n t e r s can accom- modate up t o two more e l e c t r o n s , t h e y p r o v i d e a simple mechanism f o r heavy doping.
Note t h a t H i s n o t e s s e n t i a l f o r doping, and i n f a c t might r e t a r d heavy doping by r e l i e v i n g s t r a i n s and t h u s r e d u c i n g t h e d e f e c t d e n s i t y . Indeed, CVD a-Si:P can b e prepared w i t h a c o n s i d e r a b l y h i g h e r c o n d u c t i v i t y t h a n doped a-Si:H ( 3 6 ) , presumably because of t h e l a r g e r d e f e c t c o n c e n t r a t i o n s .
Boron doping can e q u a l l y w e l l be explained by t h e c r e a t i o n of T ~ + - B ~ - and T ~ + - B ~ - p a i r s . However, t h e unique chemistry of B c o m p l i c a t e s t h e s i t u a t i o n con- s i d e r a b l y (33).
Meyer-Neldel Rule.- The e l e c t r i c a l c o n d u c t i v i t y of a-Si:H can g e n e r a l l y b e w r i t t e n ,
a
= ao0[exp (-EA/kT)l 1-a (2)where a = TITo, whether t h e a c t i v a t i o n energy i s changed by doping, t h e SW e f f e c t , o r s u r f a c e p o t e n t i a l s . Typical v a l u e s a r e Goo= l(%cm)'l and To = 700K. This amazing r u l e , i n which a l l o(T) c u r v e s c r o s s a t t h e same temperature, To, i s found i n a wide v a r i e t y of semiconductors (54). The s i m p l e s t o r i g i n of such an e f f e c t would be a c o n s t a n t l o g a r i t h m i c t e m p e r a t u r e d e r i v a t f v e of Ea, which r e q u i r e s t h e a c t i v a t i o n energy f o r conduction i n a l l samples t o v a n i s h a t t h e same temperature.
Although t h e r e i s no a p p a r e n t r e a s o n why t h i s should bccur i n t h e b u l k , i t could w e l l be a s u r f a c e e f f e c t . Solomon (55) has noted a l i n e a r i n c r e a s e i n band-bending a t t h e s u r f a c e w i t h i n c r e a s i n g temperature. If t h e r e is a common t e m p e r a t u r e To a t which t h e e x t r a p o l a t e d a c t i v a t i o n energy a t t h e s u r f a c e v a n i s h e s , t h e n t h e Meyer- Neldel r u l e follows. Other d e r i v a t i o n s of t h e r u l e a r e p o s s i b l e , but t h e y a r e ad hoc i n n a t u r e and depend on s m a l l e r v a r i a t i o n s of g(E) t h a n i s c o n s i s t e n t w i t h
--
t h e p r e s e n t interpretation of t h e experimental d a t a .Conclusion.- I n t h e p e r i o d 1970-75, amorphous-semiconductor t h e o r y was concerned p r i m a r i l y w i t h t h e u n i q u e a s p e c t s of t h e l a c k of long-range o r d e r , 3. l o c a l i z a - t i o n , band t a i l s , m o b i l i t y edges. Chemistry was g e n e r a l l y i g n o r e d w h i l e t h e over- a l l s t r u c t u r e o f t h e t h e o r y developed. The m a j o r a d v a n c e s i n t h e 1975-80 p e r i o d came a f t e r a r e a l i z a t i o n of t h e d i f f e r e n c e s i n p h y s i c a l p r o p e r t i e s between a-Si a l l o y s and c h a l c o g e n i d e g l a s s e s . Now, a s always, t h e pendulum i s swinging back.
Many s i m i l a r i t i e s between a-Si:H and t h e c h a l c o g e n i d e s a r e now e v i d e n t ,
e.
d i s - p e r s i v e t r a n s p o r t d u e t o m u l t i p l e t r a p p i n g , photo-induced changes, luminescence f a t i g u e , long-time t r a n s i e n t s ,s.
These e x p e r i m e n t s c o n t a i n a g r e a t d e a l of in- f o r m a t i o n and a r e d i f f i c u l t t o i n t e r p r e t , b u t p r o g r e s s w i l l come, e s p e c i a l l y i f t h e c h e m i s t r y is n o t f o r g o t t e n . A f t e r a l l , amorphous s e m i c o n d u c t o r s a r e s u b t l e b u t n o t d i a b o l i c a l .Acknowledgements.- I s h o u l d l i k e t o t h a n k B. C. F r y e , S. J. Hudgens, M. K a s t n e r , S. R. Ovshinsky, and M. S i l v e r f o r u s e f u l c o n v e r s a t i o n s . T h i s r e s e a r c h was s u p p o r t e d by t h e N a t i o n a l S c i e n c e Foundation Materials R e s e a r c h L a b o r a t o r y Grant No. DMR-78- 24185.
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