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A NO-STOKES SHIFT MODEL FOR THE PHOTOLUMINESCENCE OF a-Si:H
D. Dunstan, F. Boulitrop
To cite this version:
D. Dunstan, F. Boulitrop. A NO-STOKES SHIFT MODEL FOR THE PHOTOLUMINESCENCE OF a-Si:H. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-331-C4-334. �10.1051/jphyscol:1981470�.
�jpa-00220927�
A NO-STOKES SHIFT MODEL FOR THE PHOTOLUMINESCENCE OF a - S i : H
D. J. Dunstan and F. Boulitrop*
D.R.F. Resonance Magngtique, Centre drEtudes NucZlaire de GrenobZe, 85X, 38041 GrenobZe Cedex, France
* L . E. T . I .
Nouveaux Composants EZectroniques, Centre dtEtudes NucZgaire de
GrenobZe, 85X, 38041 GrenobZe Cedex, France
A b s t r a c t From t h e c l o s e s i m i l a r i t y of t h e a b s o r p t i o n and e x c i t a t i o n s p e c t r a below t h e gap, we deduce t h a t t h e r e i s no s i g n i f i c a n t Stokes s h i f t i n t h e luminescence of a-Si:H. We propose a model f o r t h e zero-phonon s t a t e s which accounts f o r t h e luminescence and t h e a b s o r p t i o n spectrum i n terms of d i s o r d e r r e l a t e d f l u c t u a t i o n s of t h e band-gap.
The photoZuminescence of a-Si:H shows t h r e e p r i n c i p a l emission bands, a t -0.8eV, -1.25eV and a t -1.4eV, depending on sample p r e p a r a t i o n . The low energy bands a r e thought t o be d e f e c t - r e l a t e d and w i l l n o t b e considered h e r e , w h i l e t h e 1.4eV band i s u s u a l l y considered t o be i n t r i n s i c , due t o recombination between b a n d - t a i l s t a t e s . The mechanism i s n o t y e t d e f i n i t e l y e s t a b l i s h e d ; both d i s t a n t - p a i r (1,2,3) and c o r r e l a t e d p a i r (geminate) (4,5,6) models have been proposed. Evidence f o r a d i s t a n t - p a i r model i s given by ODMR ( 3 ) , i n which t h e t r a n s i e n t response of t h e resonance t o t h e microwave f i e l d i s d i f f e r e n t f o r t h e two models; while t h e temper- a t u r e dependence of t h e luminescence decay h a s been i n t e r p r e t e d i n terms of a gemin- a t e model ( 6 ) . The decay i t s e l f , measured by time-resolved s p e c t r o s c o p y , h a s been i n t e r p r e t e d by both models, d i s t a n t - p a i r (1,2) and geminate ( 5 , 6 ) . I n e i t h e r c a s e , however, i t i s u s u a l l y assumed t h a t t h e depth of t h e emission below t h e gap (-0.5eV) and t h e a c t i v a t i o n energy of thermal quenching (-l3OmeV) r e q u i r e a Stokes s h i f t of t h e o r d e r of 0.4-0.5eV, and S t r e e t ( 7 ) h a s shown t h a t such a Stokes s h i f t i s s u f f i c i e n t t o account f o r t h e width of t h e emission band. However, both t h e
a b s o r p t i o n and e x c i t a t i o n s p e c t r a show e x p o n e n t i a l t a i l s below t h e band-gap, and t h e s i m i l a r i t y of t h e s e t a i l s and t h e i r independence of temperature l e a d s us t o propose a no-Stokes s h i f t model f o r t h e 1.4eV emission band.
The e x p o n e n t i a l t a i l s may be d e s c r i b e d by cxaexp(ghv) where 8 i s about 2 0 e ~ - I , a s i n most amorphous m a t e r i a l s (8). However, t h e v a l u e of $ v a r i e s somewhat from
sample t o sample, s o we have measured t h e a b s o r p t i o n spectrum a(hv) and t h e e x c i t a t i o n
c m - j
- 5 Although we were unable t o c a r r y t h e spectrum a,(hv) i n t h e same sample (Fig I ) . measurements f a r below t h e gap because of 1000 s c a t t e r e d l i g h t , we s e e t h a t t h e two s p e c t r a
V1 C c a r e e x p o n e n t i a l with t h e same s l o p e , 16eTt,
100
2
t o w i t h i n experimental e r r o r . Cody e t a 1(F
9
(9) show t h a t t h e a b s o r p t i o n t a i l remains$
e x p o n e n t i a l t o below 1.4eV and S t r e e t (7) 104
g i v e s an e x c i t a t i o n spectrum e x p o n e n t i a l t o 1.7 1-8 1.9 2.0 eV 1.4eV, s o we conclude t h a t from t h e gap a t - - F i g 1: Logarithmic p l o t of t h e - 1 . 9 e ~ t o t h e emission a t -1.4eV t h e absorp-absorption (a) and the excitation t i o n and e x c i t a t i o n s p e c t r a a r e i d e n t i c a l .
( a 3
s p e c t r a f o r a 1 . 8 ~ sample ofhydrogenated s p u t t e r e d amorphous When t h e r e i s a Stokes s h i f t , a b s o r p t i o n s i l i c o n . cx i s i n cm-', a, i s i n of photons of l e s s than t h e zero-phonon a r b i t r a r y u n i t s . energy may take p l a c e by simultaneous
a b s o r p t i o n of a phonon (phonon-assisted
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981470
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a b s o r p t i ~ . ~ ) . However, t h i s i s a temperature-dependent p r o c e s s , and t h e r e f o r e cannot account f o r t h e b u l k of t h e a b s o r p t i o n below t h e p o s t u l a t e d zero-phonon energy -1.8eV, s i n c e t h e a b s o r p t i o n i s temperature-independent up t o -400K (10). On t h e o t h e r hand, t h e photoluminescence can have a quantum e f f i c i e n c y of n e a r l y one f o r e x c i t a t i o n above t h e gap (11); i n t h e absence of a l a r g e change i n quantum e f f i c i - ency around 1.8eV (and t h i s i s r u l e d o u t by t h e s i m i l a r i t y of t h e a b s o r p t i o n and e x c i t a t i o n s p e c t r a ) , t h e mechanism of a b s o r p t i o n below t h e gap must be t h e same a s t h a t above t h e gap and ( i n high quantum e f f i c i e n c y samples) t h e same a s t h e mechan- i s m of t h e a b s o r p t i o n t h a t g i v e s luminescence ( a ~ ) . Thus a Stokes s h i f t r e q u i r e s t h a t t h e a b s o r p t i o n below t h e gap should b e temperature-dependent; i t i s n o t , and we conclude t h a t t h e r e i s no s i g n i f i c a n t Stokes s h i f t . The decrease i n B above 400K may be due t o a small Stokes s h i f t , b u t w i t h o u t a g e n e r a l l y accepted model f o r t h e a b s o r p t i o n below t h e gap, o r h i g h r e s o l u t i o n e x c i t a t i o n s p e c t r a around 1.4eV, any e s t i m a t e would be s p e c u l a t i v e .
Temperature
3 0 0 150 1 0 0 K The temperature-quenching of t h e luminescence i s g e n e r a l l y considered t o be due t o thermal a c t i v a t i o n of t h e c a r r i e r s t o t h e bands, followed by d i f f - u s i o n t o n o n - r a d i a t i v e recombination c e n t r e s . I n t h e absence of a Stokes s h i f t , we might expect t h e a c t i v a t i o n energy of t h i s p r o c e s s t o be 200-300meV, r a t h e r t h a n t h e 13OmeV observed (12).
The observed v a l u e may be understood, however, i n terms of t h e v e r y wide range of decay times, from lOns t o t e n s of ms
( 5 ) . The p o s i t i o n of t h e elbow of t h e
0 5 1 0 quenching curve depends on decay time,
1 0 0 0 / T and t h e s u p e r i m p o s i t i o n of curves w i t h d i f f e r e n t decay times, and hence with F i g 2: The family of curves B a r e t h e
t h e o r e t i c a l quenching curves f o r decay t h e i r elbows a t d i f f e r e n t t e m p e r a t u r e s , l e a d s , f o r t h e d i s t r i b u t i o n of l i f e t i m e s times from 1011s t o Ions, weighted f o r given by Tsang and Street (5), and f o r a i n t e n s i t y according t o t h e d i s t r i b u t i o n
given i n Ref. 5. Curve A i s t h e sum r e a l a c t i v a t i o n energy of 250meV, t o a of curves B; we see between points curve d i s p l a y i n g an a p p a r e n t a c t i v a t i o n and ii an a p p a r e n t a c t i v a t i o n energy energy of 130meV ( F i g 2) up t o about of 13OmeV. Below p o i n t i t h e t r u e 250K.
a c t i v a t i o n energy of 250meV a p p e a r s .
The d o t t e d l i n e s show t h e s l o p e s c o r r - Absorption measurements by Cody e t esponding t o a c t i v a t i o n e n e r g i e s of a 1 (9) and Pankove e t a 1 (13) show
13OmeV and 250meV. evidence of a peak, o r a t l e a s t a
p l a t e a u , i n t h e spectrum of about 1Ocm"
around 1.3eV. This peak may correspond t o t h e i n v e r s e of t h e luminescence t r a n s i t i o n s , and t h e n c o n s i d e r a t i o n s of d e t a i l e d balance (14) g i v e a v a l u e of N / T - 1 0 ~ ~ c m - ~ s - ' where N i s t h e d e n s i t y of e m i t t i n g
" c e n t r e s " and T i s a mean l i f e t i m e . O p t i c a l s a t u r a t i o n would t h e n be expected a t - 1 0 ~ ~ ~ h o t o n s ~ r n - ~ s - ' , compared with s t r e e t ' s measured v a l u e more than one o r d e r of magnitude h i g h e r ( 7 ) . This d i s c r e p a n c y i s a r e a l d i f f i c u l t y f o r a no-Stokes s h i f t model, and n e c e s s i t a t e s f u r t h e r work. Meanwhile, we r e c a l l t h a t t h e a n a l y s i s of Fowler and Dexter (15) shows t h a t d e t a i l e d b a l a n c e should h o l d s t r i c t l y only f o r r e s o n a n t systems i n high symmetry. The i n c r e a s e of 6 above 400K shows a small phonon i n t e r a c t i o n , t h e symmetry of amorphous s i l i c o n i s c e r t a i n l y not h i g h , and furthermore t h e system does not c o n s i s t of s e p a r a t e c e n t r e s . N e v e r t h e l e s s , i t i s d i f f i c u l t t o s e e how t h e s e c o n s i d e r a t i o n s can account f o r a breakdown of d e t a i l e d b a l a n c e by more t h a n one o r d e r of magnitude.
The a b s o r p t i o n t a i l s of amorphous semiconductors a r e r e m i n i s c e n t of t h e Urbach t a i l s seen i n many c r y s t a l l i n e semiconductors, w i t h t h e d i f f e r e n c e t h a t t h e l a t t e r a r e temperature-dependent with B-(l/kT). U n f o r t u n a t e l y , t h e r e i s no s i n g l e accepted e x p l a n a t i o n of t h e Urbach t a i l (16). However, t h e i n t e n s i t y of t h e Urbach t a i l i s s u c c e s s f u l l y p r e d i c t e d by assuming 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 l o c a l v a l u e s of
f i t t o t h e experimental s p e c t r a ( t a k e n from Ref. 8) i s e x c e l l e n t . I n c r y s t a l l i n e semiconductors, S k e t t r u p (17) shows t h a t t h e e x p o n e n t i a l d i s t r i b u t i o n of band-gap
a r i s e s from t h e Poisson d i s t r i b u -
200
--
t i o n of phonon p o p u l a t i o n d e n s i t yand i s thus r e l a t e d t o t h e r m a l l y induced d i s o r d e r . That t h e same
-
mechanism a p p l i e s i n amorphous m a t e r i a l s i s suggested by t h e c l o s e f i t of F i g 3, and s o we-
propose t h a t t h e t a i l i n amorphous.-
m a t e r i a l s i s due t o s i m i l a rd i s o r d e r , w i t h t h e d i f f e r e n c e t h a t i n t h i s c a s e t h e d i s o r d e r i s f r o z e n i n , a t an e f f e c t i v e temp- e r a t u r e e v i d e n t l y r e l a t e d t o t h e r e c r y s t a l l i s a t i o n temperature.
1.6 2.0 eV Tauc (18) s i m i l a r l y suggested
t h a t t h e t a i l i s due t o f r o z e n - i n F i g 3: The curves a r e t h e experimental absorp-
t i o n s p e c t r a of a-As Se ( d a t a of JT Edmond, phonons, b u t accounted f o r t h e t a k e n from Ref 8) and a-Si:H (same sample a s by the Franz-Keldysh
e f f e c t of t h e e l e c t r i c f i e l d s due i n F i g 1 ) . The p o i n t s show t h e o r e t i c a l f i t s t o t h e phonons. Brodsky (19) u s i n g e x p o n e n t i a l d i s t r i b u t i o n s of band-gap. suggested t h a t band-gap f l u c t u - The t h r e e f i t t i n g parameters a r e a. and
Eo,
determined by t h e p a r a b o l i c p a r t of t h e curve, a t i o n s (quantum w e l l s ) due t o compositional d i s o r d e r c o u l d and i a l t a i l ) .
B
(determined by t h e s l o p e of t h e exponent- We s e e t h a t t h e i n t e n s i t y of t h e account f o r the absorption taili n a-Si:H. However, an explan- t a i l i s c o r r e c t l y p r e d i c t e d .
a t i o n i n terms of band-gar, -
-
f l u c t u a t i o n s due t o t h e amorphous n a t u r e of t h e m a t e r i a l i s g e n e r a l l y a p p l i c a b l e t o a l l amorphous m a t e r i a l s , and a s we s e e i n F i g 3 accounts f o r t h e i n t e n s i t i e s of t h e t a i l s .
s h i f t i s expected i n t h i s model, s i n c e t h e Valence Band
c a r r i e r s a r e l o c a l i s e d by a slowly changing F i g 4: Schematic band diagram p o t e n t i a l ( t h e s l o p e of t h e f l u c t u a t i o n s of band
gap and chemical p o t e n t i a l ) and s o t h e l o c a l i s e d f o r a-Si:H, showing t h e proposed
partly correlated fluctuations s t a t e s a r e l i t t l e p e r t u r b e d from t h o s e of t h e of t h e bands. Absorption (A) bands a t kzO.
Now, i f t h e band-gap f l u c t u a t e s , e x c i t e d c a r r i e r s w i l l t e n d t o l o c a l i s e a t t h e s p a t i a l minima ( i n energy) of t h e bands. I f , a s i s probable, t h e chemical p o t e n t i a l f l u c t u a t e s with a s i m i l a r coherence l e n g t h , t h e minima of t h e conduction band w i l l n o t always b e s p a t i a l l y c o i n c i d e n t w i t h t h e maxima of t h e valence band, and t h e
and luminescence (L) t r a n s i t i o n s F i n a l l y , we c o n s i d e r t h e s p a t i a l d i s t r i b u - a r e shown, w i t h t h e t h e r m a l i s - t i o n of l o c a l i s e d c a r r i e r s i n r e l a t i o n t o a t i o n i n t o band extrema. geminate recombination and recombination k i n -
Conduction Band
e t i c s . A t low temperature, w i t h no thermal r e - e x c i t a t i o n t o t h e bands, t h e s e p a r a t i o n of a c a r r i e r s w i l l g e n e r a l l y n o t be t r a p p e d a t t h e same p l a c e ( F i g 4 ) . Recombination can t a k e p l a c e by t u n n e l l i n g w i t h t h e t r a n s i t i o n probab- ility depending on t h e s e p a r a t i o n . Thus t h e main f e a t u r e s of t h e time-resolved s p e c t r a a r e accounted f o r . E l e c t r i c f i e l d s o r thermal e x c i t a t i o n permit de-trapping and d i f f u s i o n t o n o n - r a d i a t i v e c e n t r e s such a s dangling bonds.
Furthermore, t h e shallower c a r r i e r s w i l l de-trap more e a s i l y t h a n t h e deeper ones, c o n s i s t e n t with t h e s h i f t of t h e luminescence t o lower energy with temperature. No s i g n i f i c a n t Stokes
JOURNAL DE PHYSIQUE
geminate pair of excited carriers will have a distribution independent of excitation density. Consequently, at low excitation powers the average pair separation d may be much less than the average separation between pairs, A, and recombination will be geminate. As the excitation density increases, recombination ceases to be geminate when A-d. However, recombination remains monomolecular until A decreases to less than or of the order of the diameter a of the wave-function of a localised carrier (20). Depending on the relative magnitudes of a and d there may be a regime where the recombination is monomolecular but not geminate (a<A<d) and is termed distant- pair. Given the long lifetimes of most of the 1.4eV band, the range of excitation power in which this is the case is large. Clearly, it is not correct to take, as has been done in the literature, the excitation power density at the onset of bimolecular recombination as indicative of the diffusion distance d; rather, this measures the wave-function size a. Thus, although the recombination will be geminate at sufficiently low excitation density, much lower than that at which it will be monomolecular, this is not an essential feature of the 1.4eV band.
Acknowledgements: We are grateful to Mr P Bouchut for providing the absorption data of Fig 1 and to Dr A Chenevas-Paule, Dr R Cox and Dr A HervC for helpful discussions.
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