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PHONON DENSITIES OF STATES ANDEIGENVECTORS IN HYDROGENATED AND

FLUORINATED AMORPHOUS SILICONW. 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>

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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. Po l l a rd and G. Lucovsky

Department of Physics, North Carolina State University, Raleigh, NC 27650, U.S.A.

Abstract . - A s tudy 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 of amorphous s i l i c o n a l - l o y s i s presented. Using t h e C lus te r -Be the - l a t t i ce 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 igenvec to r s a r e ca lcu la ted . 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 soc i - a t e d wi th 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 hose 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 , whi le those below a r e in-band resonances 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.

Int roduct ion.- Recently cons ide rab le a t t e n t i o n has been paid 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 con ta in ing hydrogen o r f l u o r i n e . I n o rde 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 requencies wi th t h e amount of incorporated H o r F, and have sought t o a s s o c i a t e t h e va r ious observed s p e c t r a l f e a t u r e s wi th 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 genera l agreement t h a t loca l - i z e d s t r e t c h i n g and bending modes occur above 500 cm-' i n hydrogenated amorphous s i l i c o n a l l o y s (a-Si:H), wh i l e only s t r e t c h i n g modes occur i n t h i s region 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 incorpora t ion of both 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 ime t h e r e i s some controversy concerning t h e n a t u r e and o r i g i n of these 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 region of t h e a l l o y s s p e c t r a a r e a s soc ia ted wi th quas i - loca l i zed in-band resonances which involve both H (o r F) and S i motion. Fur the r , we w i l l provide i n s i g h t i n t o t h e pre- c i s e n a t u r e of t h e high frequency 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 igenvec to r s f o r va r ious l o c a l bonding conf igura t ions t h a t a r e expected t o occur 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 ake i n t h i s s tudy i s based upon a combination of t h e i s o l a t e d c l u s t e r , and c lus ter-Bethe l a t t i c e methods.

Method.- Two t h e o r e t i c a l techniques have been employed t o s tudy 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 so - 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 con ta in ing t e n t o twenty atoms ( inc lud ing t h e H o r F s i t e s ) , and have been ve ry u s e f u l i n desc r ib ing t h e high frequency 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 advantage of t h i s type of c a l c u l a t i o n is t h a t t h e v i b r a t i o n a l s t a t e s of t h e c l u s t e r can be determined us ing a r e a l i s t i c f o r c e constant 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 equenc ies and t h e a s soc ia ted atomic displacements f o r each v i b r a t i o n a l mode. Unfor tunate ly , t h e spectrum obtained 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 frequency l o c a l i z e d s t a t e s from t h e continuum of t h e bulk; i n a d d i t i o n , t h e ca l - cu la t ed f requencies may be s e n s i t i v e t o t h e boundary cond i t ions imposed a t t h e sur- 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 an improvement upon t h i s technique i n which a Be the - l a t t i ce i s used a s a boundary cond i t ion on t h e c l u s t e r (6 ) . A Bethe l a t t i c e is an i d e a l i z a t i o n of t h e bulk 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 bulk s t a t e s which is i n good agreement wi th t h a t determined f o r t h e a c t u a l system. The major weaknesses of t h e CBLM has been t h a t i t r e s t r i c t s one t o t h e use of u n r e a l i s t i c f o r c e cons tan t models which can no t accura te ly d e s c r i b e t h e low frequency 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

,~;k 1 4

I I

/\/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 bulk 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 schematic r e p r e s e n t a t i o n of t h e H and S i d isplacements a s soc ia ted wi th these modes i s a l s o shown i n Fig. f The mode centered a t 2000 cm-I is t h e Si-H s t r e t c h i n g mode, and i s assoc ia ted predo i n a n t l y wi th t h e motion of t h e H atom. The lower frequency mode cen te red about 630 cm-1 i s a Si-H bending mode which involves s u b s t a n t i a l S i motion, wi th 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 layec, however, t h e e f f e c t s of t h e hydrogen motion a r e ba re ly d i s c e r n i b l e ; t h a t is, t h e LDOS of a Si-atom i n the t h i r d l a y e r is e s s e n t i a l l y t h e Bethe l a t t i c e DOS!

This observat ion 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 Fig. 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 degenerate s t r e t c h i n g modes near 2100 cm-l, a H-Si-H s c i s s o r mode near 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 igher frequency modes a r e l o c a l - i zed w i t h i n t h e f i r s t atomic l a y e r of S i atoms, whi le t h e wagging mode decays more slowly i n t o bulk . 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 resonance seen a t 400 cm-1 which a r i s e s from Si-H "rocking1' motion. Since t h i s v i b r a t i o n involves mainly H motion, i t is absent i n t h e LDOS of t h e second l a y e r of S i atoms. One might argue t h a t t h e r a p i d decay of t h e hydrogen der ived f e a t u r e s i n t h e LDOS spec- t r a should be expected given 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 behavior f o r f l u o r i n e i n a-Si. This i s c l e a r l y evident from Figs . 3 and 4 where we show t h e LDOS f o r SiF and SiF2 u n i t s i n a-Si, r e spec t ive ly .

I n t h e S iF 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 region of t h e bulk S i band. The f i r s t i s l o c a l i z e d mostly 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 bulk S i o p t i c band. The v i b r a t i o n which g ives r i s e t o t h i s mode corresponds t o a Si-F shea r ing 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 perpendicular t o t h e Si-F bond. The second resonance i s cen te red near 300 cm-I and a r i s e s from t h e Si-F bending mode. This mode decays i n t o t h e bulk a t a r a t e which is slower than t h a t of t h e 550 cm-I mode. The resonance a t t h e lowest

c 0 300 600 900 1200

FREQUENCY (cm-1)

frequency i n Fig . 3 i s assoc i - a t e d wi th in-phase motion of t h e F and S i atoms and has 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 imi la r resonances a r e observed i n t h e SiF2 s p e c t r a of Fig . 4. The broad f e a t u r e between 300 t o 400 cm-I i s as- soc ia t ed wi th s c i s s o r s (391 cm-I), rocking (340 cm-I), and wagging (370 cm-1) motion. More important ly t h e SiF shear- ing mode h a s been ushed up i n P frequency (620 cm- ) by t h e a d d i t i o n of another F atom. A s one might expect , t h e resonances 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 iF u n i t , s i n c e t h e bulk s t a t e s a r e l e s s per turbed 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 occur 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 they 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 is smal l e r than t h e S i t o H mass

Fig . 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 subsequent l a y e r s . t hese modes is found on t h e

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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.

References. (1) mlIGHTS J.C., LUCOVSKY G., and NEMANICH R.J., Philos. Mag. B E (1978) 467; and

LUCOVSKY G., NEMANICH R.J., and KNIGHTS J.C., Phys. Rev. B g (1979) 2068. (2) BRODSKY M.H., CARDONA M., CUOMO J.J., Phys. Rev. B E (1977) 3556. (3) SHIMADA H., KATAYAMA Y., HORIGONE S., Jap. J. Appl. Phys. 19 (1980) 265. (4) LEY L., SHANKS H.R., FANG C.J., GRUNT2 K.L., CARDONA M., J. Phys. Soc. Jap. 49

(Suppl. A) (1980) 1241. (5) LUCOVSKY G., Springer Series in Solid State Sciences 25 (1981) 87; and in

these proceedings. (6) POLLARD W.B., JOANNOPOULOS J.D., Phys. Rev. B g (1981) 5263. (7) KEATINGS P.N., Phys. Rev. (1966) 637.