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PHONON DENSITIES OF STATES AND EIGENVECTORS IN HYDROGENATED AND
FLUORINATED AMORPHOUS SILICON
W. Pollard, G. Lucovsky
To cite this version:
W. Pollard, G. Lucovsky. PHONON DENSITIES OF STATES AND EIGENVECTORS IN HYDRO-
GENATED AND FLUORINATED AMORPHOUS SILICON. Journal de Physique Colloques, 1981,
42 (C4), pp.C4-353-C4-356. �10.1051/jphyscol:1981475�. �jpa-00220932�
JOURNAL DE PHYSIQUE
CoZZoque C4, suppZ6ment au nOIO, Tome 42, octobre 1981 page C4-353
PHONON DENSITIES OF STATES AND EIGENVECTORS IN HYDROGENATED AND FLUORINATED AMORPHOUS SILICON
W.B. P o l l a r d and G. Lucovsky
Department of Physics, North Carolina S t a t e University, Raleigh, NC 27650, U.S.A.
A b s t r a c t . - A s t u d y of t h e v i b r a t i o n a l p r o p e r t i e s o f amorphous s i l i c o n a l - l o y s i s p r e s e n t e d . Using t h e C l u s t e r - B e t h e - l a t t i c e method and i s o l a t e d c l q s t e r c a l c u l a t i o n s , l o c a l d e n s i t i e s of s t a t e s s p e c t r a and e i g e n v e c t o r s a r e c a l c u l a t e d . Our r e s u l t s i n d i c a t e t h a t a l l of t h e v i b r a t i o n a l m o d e s a s s o c i - a t e d w i t h H and F i n t h e a l l o y s e x h i b i t a l o c a l i z e d c h a r a c t e r : t h o s e above 500 cm-1 a r e l o c a l i z e d predominantly on t h e I! o r F s i t e s , w h i l e t h o s e below a r e in-band r e s o n a n c e s and l o c a l i z e d w i t h i n t h e f i r s t t h r e e l a y e r s of Si- atoms.
I n t r o d u c t i o n . - R e c e n t l y c o n s i d e r a b l e a t t e n t i o n h a s been p a i d t o t h e p r o p e r t i e s of amorphous s i l i c o n a l l o y s c o n t a i n i n g hydrogen o r f l u o r i n e . I n o r d e r t o c l a r i f y t h e chemical bonding s t r u c t u r e of t h e s e a l l o y s , t h e r e have been numerous i n f r a r e d ab- s o r p t i o n and Raman s c a t t e r i n g measurements (1-4). These s t u d i e s have emphasized t h e v a r i a t i o n of t h e v i b r a t i o n a l f r e q u e n c i e s w i t h t h e amount of i n c o r p o r a t e d H o r F, and have sought t o a s s o c i a t e t h e v a r i o u s observed s p e c t r a l f e a t u r e s w i t h d i f f e r e n t l o c a l bonding arrangements ( e . g . , S i s , X = F, H). There i s g e n e r a l agreement t h a t l o c a l - i z e d s t r e t c h i n g and bending modes o c c u r above 500 cm-' i n hydrogenated amorphous s i l i c o n a l l o y s (a-Si:H), w h i l e o n l y s t r e t c h i n g modes o c c u r i n t h i s r e g i o n f o r t h e f l u o r i n a t e d a l l o y s (a-Si:F). I n a d d i t i o n , i t i s found t h a t t h e i n c o r p o r a t i o n of b o t h H and F i n t o amorphous S i produce changes i n t h e a-Si network continuum below 500 cm-1. A t t h i s t i m e t h e r e i s some c o n t r o v e r s y c o n c e r n i n g t h e n a t u r e and o r i g i n of t h e s e changes ( 4 , 5 ) . I n t h i s work, we w i l l show t h a t t h e changes i n t h i s r e g i o n of t h e a l l o y s s p e c t r a a r e a s s o c i a t e d w i t h q u a s i - l o c a l i z e d in-band r e s o n a n c e s which i n v o l v e b o t h H ( o r F) and S i motion. F u r t h e r , we w i l l p r o v i d e i n s i g h t i n t o t h e p r e - c i s e n a t u r e of t h e h i g h f r e q u e n c y l o c a l i z e d v i b r a t i o n s by examining t h e phonon s t a t e d e n s i t i e s and e i g e n v e c t o r s f o r v a r i o u s l o c a l bonding c o n f i g u r a t i o n s t h a t a r e e x p e c t e d t o o c c u r i n a-Si:H, a-Si:F and a-Si:F:H a l l o y s . The approach t h a t we t a k e i n t h i s s t u d y i s b a s e d upon a combination of t h e i s o l a t e d c l u s t e r , and c l u s t e r - B e t h e l a t t i c e methods.
Method.- Two t h e o r e t i c a l t e c h n i q u e s have been employed t o s t u d y t h e v i b r a t i o n a l pro- p e r t i e s of hydrogenated and f l u o r i n a t e d a-Si a l l o y s . The f i r s t of t h e s e a r e i s o - l a t e d c l u s t e r c a l c u l a t i o n s ( 5 ) which a r e based upon c l u s t e r s c o n t a i n i n g t e n t o twenty atoms ( i n c l u d i n g t h e H o r F s i t e s ) , and have been v e r y u s e f u l i n d e s c r i b i n g t h e h i g h f r e q u e n c y l o c a l i z e d v i b r a t i o n a l modes of t h e a l l o y s . The major a d v a n t a g e o f t h i s t y p e of c a l c u l a t i o n i s t h a t t h e v i b r a t i o n a l s t a t e s o f t h e c l u s t e r c a n be d e t e r m i n e d u s i n g a r e a l i s t i c f o r c e c o n s t a n t models. The c l u s t e r c a l c u l a t i o n y i e l d s t h e f r e q u e n c i e s and t h e a s s o c i a t e d a t o m i c d i s p l a c e m e n t s f o r e a c h v i b r a t i o n a l mode.
U n f o r t u n a t e l y , t h e spectrum o b t a i n e d i s d i s c r e t e , making i t d i f f i c u l t t o d i s t i n g u i s h low f r e q u e n c y l o c a l i z e d s t a t e s from t h e continuum of t h e b u l k ; i n a d d i t i o n , t h e c a l - c u l a t e d f r e q u e n c i e s may be s e n s i t i v e t o t h e boundary c o n d i t i o n s imposed a t t h e s u r - f a c e of t h e c l u s t e r . The Cluster-Bethe l a t t i c e method (BLM) i s a n improvement upon t h i s t e c h n i q u e i n which a B e t h e - l a t t i c e i s used a s a boundary c o n d i t i o n on t h e c l u s t e r ( 6 ) . A Bethe l a t t i c e i s a n i d e a l i z a t i o n of t h e b u l k s t r u c t u r e , and t h e CBLM y i e l d s a d e n s i t y of b u l k s t a t e s which i s i n good agreement w i t h t h a t d e t e r m i n e d f o r t h e a c t u a l system. The major weaknesses of t h e CBLM h a s been t h a t i t r e s t r i c t s one t o t h e u s e of u n r e a l i s t i c f o r c e c o n s t a n t models which c a n n o t a c c u r a t e l y d e s c r i b e t h e low f r e q u e n c y bending o r wagging modes.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981475
C4-354 JOURNAL DE PHYSIOUE
FREQUENCY (m-') 0 460 800 1200 16002&
FREQUENCY (cm-1)
Fig. 1 LDOS for SiH. H-atom, and Si- Fig. 2 LDOS for SiH2. H-atom, and Si- atoms in three subsequent layers. atoms in three subsequent layers.
In this work, we have generalized the CBLM so that the Bethe lattice can be solved for a realistic valence force field representation of the near neighbor inter- actions which includes both two-body stretching and
3a
1
I 4 I,~;k
/\/Ah
I 1 I
O F
aSi
I
three-body stretching and bending forces (5, 7). In this way, it is possible to couple the CBLM results with the results of the isolated cluster calcula- tion. More importantly, this approach allows for a unique specification of both the fre- quency spectra and eigenvectors of hydrogenated and fluorinated Si alloys. We will not attempt a detailed analysis of the rather complicated experiment- al spectroscopic measurements on a-Si:H and a-Si:F which have been reported recently,
(1-4) but will instead concen- trate upon a few simple con- figurations which are important in understanding the vibration- al properties of these ma- terials. Specifically, we will focus upon the SiH and SiH2 units in a-Si:H, the SiF and SiF2 units in a-Si:F and a SiFH unit in a-Si:F:H.
i, 360 660
9bo I&FREQUENCY (cm-1)
Results.- In Fig. 1, we pre- Fig. 3 LDOS for SiF. F-atom and three Si-atoms. sent local densities of states(LDOS) s p e c t r a f o r an SiH u n i t i n a-Si. The LDOS of t h e H-atom and of a Si-atom i n each of t h e t h r e e subsequent l a y e r s of t h e b u l k S i s t r u c t u r e s a r e shown. Two l o c a l - i z e d modes a r e observed above 500 cm-1. A s c h e m a t i c r e p r e s e n t a t i o n of t h e H and S i d i s p l a c e m e n t s a s s o c i a t e d w i t h t h e s e modes i s a l s o shown i n F i g .
f
The mode c e n t e r e d a t 2000 cm-I i s t h e Si-H s t r e t c h i n g mode, and i s a s s o c i a t e d p r e d o i n a n t l y w i t h t h e motion of t h e H atom. The lower f r e q u e n c y mode c e n t e r e d a b o u t 630 cm-1 i s a Si-H bending mode which i n v o l v e s s u b s t a n t i a l S i motion, w i t h about 50% of'its weight d i s t r i b u t e d among t h e f i r s t t h r e e l a y e r s of S i atoms. By t h e t h i r d l a y e c , however, t h e e f f e c t s of t h e hydrogen motion a r e b a r e l y d i s c e r n i b l e ; t h a t i s , t h e LDOS of a Si-atom i n t h e t h i r d l a y e r i s e s s e n t i a l l y t h e Bethe l a t t i c e DOS!T h i s o b s e r v a t i o n i s a l s o t r u e f o r t h e SiH2 u n i t whose LDOS s p e c t r a a r e shown i n F i g . 2. Four d i s t i n c t f e a t u r e s a r e found above 500 cm-l: doubly d e g e n e r a t e s t r e t c h i n g modes n e a r 2100 cm-l, a H-Si-H s c i s s o r mode n e a r 880 cm-l, a wagging mode a t 642 cm-1 and a t w i s t i n g mode a t 609 cm-1. The h i g h e r f r e q u e n c y modes a r e l o c a l - i z e d w i t h i n t h e f i r s t a t o m i c l a y e r of S i atoms, w h i l e t h e wagging mode d e c a y s more s l o w l y i n t o b u l k . L a s t l y , i t i s i n t e r e s t i n g t o n o t e t h a t t h e in-band r e s o n a n c e s e e n a t 400 cm-1 which a r i s e s from Si-H "rocking1' motion. S i n c e t h i s v i b r a t i o n i n v o l v e s mainly H motion, i t i s a b s e n t i n t h e LDOS of t h e second l a y e r o f S i atoms. One might a r g u e t h a t t h e r a p i d decay of t h e hydrogen d e r i v e d f e a t u r e s i n t h e LDOS spec-
t r a s h o u l d be expected g i v e n t h e l a r g e S i t o H mass r a t i o (1.28). However, we f i n d s i m i l a r b e h a v i o r f o r f l u o r i n e i n a-Si. T h i s i s c l e a r l y e v i d e n t from F i g s . 3 and 4 where we show t h e LDOS f o r S i F and SiF2 u n i t s i n a - S i , r e s p e c t i v e l y .
I n t h e S i F s p e c t r a , t h r e e s i g n i f i c a n t f e a t u r e s a r e observed i n t h e r e g i o n o f t h e b u l k S i band. The f i r s t i s l o c a l i z e d m o s t l y on t h e f i r s t two S i l a y e r s and is found j u s t above t h e b u l k S i o p t i c band. The v i b r a t i o n which g i v e s r i s e t o t h i s mode c o r r e s p o n d s t o a Si-F s h e a r i n g mode i n which t h e S i and F move out-of-phase i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e Si-F bond. The second r e s o n a n c e i s c e n t e r e d n e a r 300 cm-I and a r i s e s from t h e Si-F bending mode. T h i s mode d e c a y s i n t o t h e b u l k a t a r a t e which i s slower t h a n t h a t of t h e 550 cm-I mode. The r e s o n a n c e a t t h e l o w e s t
c
0 300 600 900 1200
FREQUENCY (cm-1)
frequency i n F i g . 3 i s a s s o c i - a t e d w i t h in-phase motion of t h e F and S i atoms and h a s d i s - s i p a t e d by t h e t h i r d atomic l a y e r . S i m i l a r r e s o n a n c e s a r e observed i n t h e SiF2 s p e c t r a of F i g . 4. The broad f e a t u r e between 300 t o 400 cm-I i s a s - s o c i a t e d w i t h s c i s s o r s (391 cm-I), r o c k i n g (340 cm-I), and wagging (370 cm-1) motion.
More i m p o r t a n t l y t h e S i F s h e a r - i n g mode h a s been ushed up i n
P
f r e q u e n c y (620 cm- ) by t h e a d d i t i o n of a n o t h e r F atom.
A s one might e x p e c t , t h e r e s o n a n c e s decay l e s s r a p i d l y f o r t h e SiF2 u n i t s a s compared t o t h e S i F u n i t , s i n c e t h e b u l k s t a t e s a r e l e s s p e r t u r b e d by t h e l a t t e r u n i t . The s t r e t c h i n g and bending modes which o c c u r above 500 cm-I a r e l o c a l i z e d w i t h i n t h e f i r s t l a y e r of S i atoms f o r t h e SiF, u n i t s j u s t a s t h e y were f o r t h e SiHn u n i t s . However, s i n c e t h e S i t o F mass r a t i o i s s m a l l e r t h a n t h e S i t o H mass F i g . 4 LDOS f o r SiF2. F-atom, and Si-atoms i n r a t i o , more of t h e weight of t h r e e s u b s e q u e n t l a y e r s . t h e s e modes i s found on t h e
JOURNAL DE PHYSIQUE
Fig. 5 and Si-
underlying Si atoms.
Lastly, we turn our attention to the SiFH unit which is expected to occur in a-Si:F:H alloys. The results of our calculation for this unit are shown in Fig. 5, where we show the LDOS of the H atom, F atom and for atoms in each of the first three Si layers. There are two features which involve only H motion: the 2100 cm-I (Si-H stretch) and 630 cm-I (Si-H bend). The two modes at 900 cm-I and 800 cm-1 results from asymmetric and symmetric hydrogen scissors and fluorine stretching modes. Similarly, the reso- nances observed at 531 cm-1 and 350 cm-1 correspond to combinations of H and F motions. All of the H and F induced features are absent in the LDOS of Si atoms in the third layer.
In general, our results indicate that the higher frequency modes decay systematically faster into the bulk than the lower frequency modes which have frequency distributions which occur in the Si continuum. We find decay con- stants for the H and F induczd modes on the order of 0.3 i-1 to 0.5 A-1, hence after three to four layers of Si atoms all of the H and F derived features of
400 800 1200 18002000 2400
the DOS have healed. This establishes FREQUENCY(cm-1)
the credibility of isolated cluster cal-culations containing at least three layers LDOS for SiFH. F- and H-atoms, of Si atoms, since we find that the H -atoms in four subsequent layers. and/or F induced features require three
atomic layers to dissipate.
Acknowledgement.- This work is supported in part under SERI subcontract HZ-0-9238 under EG-77-C-01-4042.
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