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DISORDER AND THE OPTICAL ABSORPTION EDGE OF HYDROGENATED AMORPHOUS
SILICON
G. Cody, T. Tiedje, B. Abeles, T. Moustakas, B. Brooks, Y. Goldstein
To cite this version:
G. Cody, T. Tiedje, B. Abeles, T. Moustakas, B. Brooks, et al.. DISORDER AND THE OPTI-
CAL ABSORPTION EDGE OF HYDROGENATED AMORPHOUS SILICON. Journal de Physique
Colloques, 1981, 42 (C4), pp.C4-301-C4-304. �10.1051/jphyscol:1981463�. �jpa-00220920�
CoZloque C4, suppZ6ment au nOIO, Tome 42, octobre 1981 page 10 C4-301
D I S O R D E R AND T H E O P T I C A L A B S O R P T I O N EDGE O F HYDROGENATED AMORPHOUS S I L I C O N
G.D. Cody, T. T i e d j e , B. Abeles, T.D. Moustakas, B. Brooks and Y. G o l d s t e i n
Corporate Research, E n o n Research and Engineering Co., P. 0. BOX 45, Linden, NJ 07036, U.S.A.
Abstract.- Lie i n v e s t i g a t e the e f f e c t of thermal and s t r u c t u r a l d i s o r d e r on t h e e l e c t r o n i c s t r u c t u r e of hydrogenated amorphous s i l i c o n , by measuring t h e shape o f t h e o p t i c a l a b s o r p t i o n edge as a f u n c t i o n o f temperature and hydrogen content. The data i s c o n s i s t e n t w i t h t h e idea t h a t t h e thermal and s t r u c t u r a l d i s o r d e r are a d d i t i v e , and suggests t h a t d i s o r d e r i s t h e fundamental determining f a c t o r o f t h e o p t i c a l bandgap.
he have measured the o p t i c a l a b s o r p t i o n edge as a f u n c t i o n o f temperature on h i g h d e n s i t y 1 a-SiHx f i l m s . k!e f i n d t h a t our data i s c o n s i s t e n t w i t h t h e i n t e r y e - t a t i o n t h a t both the w i d t h o f t h e exponential edge2
4
t h e o p t i c a l band pap are c o n t r o l l e d by t h e amount o f d i s o r d e r , s t r u c t u r a l and thermal, i n t h e network, and t h a t hydrogen e f f e c t s t h e band gap i n d i r e c t 1,
through i t s e f f e c t on d i s o r d e r . This r e l a t i o n s h i p between t h e o p t i c a l gap and t h i sharpness o f t h e a b s o r p t i o n edge suggests t h a t t h e r e i s a fundamental t r a d e o f f i n a-Sit!, s o l a r c e l l s between o p t i c a l absorption and e l e c t r o n - h o l e p a i r e x t r a c t i o n e f f i c i e n c y .C e t a i l s o f f i l m p r e p a r a t i o n and t h e o p t i c a l measurements have been given p r e - v i o u s l y . 3 I n order t o compare t h e e f f e c t s o f s t r u c t u r a l an3 thermal d i s o r d e r on t h e a b s o r p t i o n edge we have a l s o induced s t r u c t u r a l d i s o r d e r i n t e n t i o n a l l y i n t h e f i l m s by i n t r o d u c i n g d a n g l i n g bonds through thermal e v o l u t i o n o f hydrogen. I n Fig. 1 are shown o p t i c a l measurements as a f u n c t i o n o f photon energy, E, a t T = 12.7K, 151K and 293K on an "as prepared" f i l m o f composition SiHg.13. 1,Je a l s o show data obtained a t T = 293K on a s i m i l a r f i l m , from which hydrogen was evolved i n a step-wise manner through isochronal h e a t i n g i n a vacuum a t 25C i n t e r v a l s from 400-600C (TH) f o r 30 minutes a t a time. We note t h a t t h e a b s o r p t i o n edge broadens and s h i f t s t o lower energy w i t h e i t h e r i n c r e a s i n g thermal d i s o r d e r o r w i t h s t r u c t u r a l d i s o r d e r due t o t h e isochronal h e a t i n The exponential depen- dence o f a on E, f o r 2 x 102 cm-1 < a < 5 x 103 cm-7; (See Fig. 1 ) has been shovin i n a previous paper t o extend f o r about t h r e e and h a l f orders o f magnitude i n a 2 . The departure from an exponential shown i n Fig. 1 a t low a i s due t o the i n s e n s i t i v i t y o f the o p t i c a l transmission measurement technique. From Fig. 1 we draw t h e conclusion t h a t u(E,T) can be expressed by t h e Urbach form4,5
where Eo(T,X) i s the w i d t h o f the exponential t a i l , X i s an as y e t t o be d e f i n e d
?arameter d e s c r i b i n g s t r u c t u r a l d i s o r d e r , and a, = (1.3
+
0.4) x 106 cm-l and El = 2.17*
3.02 eV, as determined b a l e a s t square f i t o f Eq. (1) t o t h e datar
f o r 2 x 102 cm-1 < a < 5 x 103 cm-
.
To deduce t h e temperature dependence o f the o p t i c a l energy gap Eg, we f i t t e d a(E,T) o u t s i d e t h e exponential r e g i o n ( a > 104 cm-I), by t h e expression
[ ~ ( E , T ) E ] ' / ~ = C(E-EG(T)) ( 2 )
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981463
C4-302 JOURNAL DE PHYSIQUE
where t h e c o n s t a n t C = 6.9 F 0.2 ( ~ V W ) - " ~ was f o u n d t o be independent o f tempera- t u r e . Eq. (2) i s w i d e l y used t o d e f i n e t h e band gap i n amorphous semiconductors f r o m o p t i c a l a b s o r p t i o n data.6 The s t r i k i n g s i m i l a r i t y between t h e t e m p e r a t u r e dependences o f EG and Eo i s i l l u s t r a t e d i n F i g . 2 where EG(T) i s p l o t t e d a g a i n s t Eo(T), w i t h temperature as a paramet&. The l i n e a r r e l a t i o n s h i p between EG and Eo c o n f i r m s t h a t t h e i r t e m p e r a t u r e dependences have t h e same f u n c t i o n a l form. I n a d d i t i o n , i n F i g . 2, we show t h a t t h e same r e l a t i o n s h i p between EG and Eo c o n t i n u e s t o h o l d when t h e p l o t i s extended t o i n c l u d e t h e (EG, Eo) v a l u e s f o r a f i l m
measured a t room t e m p e r a t u r e a f t e r a p r o g r e s s i v e s e r i e s o f h e a t t r e a t m e n t s i n which H i s evolved, d i s o r d e r i n g t h e l a t t i c e .
Pholon Energy E (eV)
F i g . 1. O p t i c a l a b s o r p t i o n c o e f f i c i e n t , a, F i g . 2. O p t i c a l gap EG(T,X) as a as a f u n c t i o n o f photon energy. The s o l i d f u n c t i o n o f Eo(T,X) f o r t h e measure- symbols r e f e r t o d a t a o b t a i n e d a t d i f f e r e n t ments a t v a r i a b l e T and c o n s t a n t X measurement temperature, Tm. The open sym- ( s o l i d c i r c l e s ) (H = 12 a t %) and b o l s r e f e r t o a f i l m t h a t has been i s o c h r o n - f o r measurements a t c o n s t a n t T and a l l y h e a t e d a t temperature, TH, as d e s c r i b e d v a r i a b l e X (open c i r c l e s ) (H =
i n t h e t e x t . 12-1 - a t %). The square i s d e r i v e d
f o r CVD a-Si f r o m Ref. ( 1 1 ) a t T = 300K. The crosses a r e o b t a i n e d f r o m measurements on r e a c t i v e l y s p u t t e r e d films,9,10 ( H = 22% a t %.
H = 8 a t % ) .
Standard t r e a t m e n t s o f t h e Urbach edge i n c r y s t a l l i n e semiconductors4,5 conclude t h a t t h e w i d t h o f t h e a b s o r p t i o n edge Eo, i s p r o p o r t i o n a l to.<U2>
j,
a thermal average, l i k e t h e Debye-Waller f a c t o r , o f t h e square o f t h e d i s p l a c e m e n t U of t h e atoms f r o m t h e i r e q u i l i b r u m p o s i t i o n s . To i n c l u d e t h e e f f e c t o f s t r u c t u r a l d i s - o r d e r on Eo, we make t h e p l a u s i b l e g e n e r a l i z a t i o n t h a t ,where < u ~ > ~ i s - t h e c o n t r i b u t i o n o f s t r u c t u r a l ( t o p o l o g i c a l ) d i s o r d e r t o t h e mean square d e v i a t i o n o f t h e a t o m i c p o s i t i o n s f r o m a p e r f e c t l y o r d e r e d c o n f i g u r a t i o n . As a j u s t i f i c a t i o n o f t h i s c e n t r a l h y p o t h e s i s t h e dynamic phonon d i s o r d e r and s t a t i c s t r u c t u r a l d i s o r d e r , i n t h e a d i a b a t i c a p p r o x i m a t i o n , s h o u l d have s i m i l a r e f f e c t s on t h e e l e c t r o n i c energy l e v e l s . I n o r d e r t o e s t i m a t e t h e t e m p e r a t u r e
E i n s t e i n o s c i l l a t o r w i t h c h a r a c t e r i s t i c t e m p e r a t u r e o ( t h e E i n s t e i n model i s a good a p p r o x i m a t i o n t o a Debye phonon spectrum w i t h a Debye t e m p e r a t u r e OD equal t o 40/3). I n t h i s model, Eq. ( 3 ) can be expressed as,
where we have e l i m i n a t e d K i n Eq. ( 3 ) b y imposing t h e c o n d i t i o n t h a t Eo(T,X)+T/a0 as T -t a, w i t h ao an Urbach edge parameter o f o r d e r u n i t y . I n Eq. ( 4 ) ,
X = < ~ 2 > ~ / < ~ 2 > ~ i s a measure o f t h e s t r u c t u r a l d i s o r d e r n o r m a l i z e d t o <uZ>,, t h e z e r o p o i n t u n c e r t a i n t y i n t h e a t o m i c p o s i t i o n s .
The " e x p l i c i t " temperature dependence o f t h e bandgap i n c r y s t a l l i n e semiconductors can be w r i t t e n , 8
EG(T) = EG(0)
-
D ( < u ~ > ~ - < u ~ > ~ ) ( 5 ) where EG(0) i s t h e z e r o t e m p e r a t u r e o p t i c a l gap and D i s a second o r d e r d e f o r - m a t i o n p o t e n t i a l . The d i s t i n c t i o n between t h e " i m p l i c i t " and " e x p l i c i t " tempera- t u r e dependence o f EG i s d i s c u s s e d i n Ref. ( 8 ) . For a - S i , i t i s e a s i l y shown t h a tthe
" i m p l i c i t " t e m p e r a t u r e dependence can be n e g l e c t e d . I f Eq. ( 5 ) i s g e n e r a l i z e d a n a l o g o u s l y t o Eq. ( 3 ) t o i n c l u d e t h e e f f e c t s o f s t r u c t u r a l d i s o r d e r , t h e n t h e mean square l a t t i c e displacements i n Eq. ( 5 ) can be expressed i n terms o f t h e e x p e r i m e n t a l l y measured q u a n t i t y Eo(T,X) and Eq. ( 5 ) r e w r i t t e n as f o l l o w s :EG(T,X) = E ~ ( o . o ) - < u ~ > ~ D{(EO(T,X)/EO(O,O))-11 ( 6 )
T h i s l i n e a r r e l a t i o n s h i p between t h e bandgap and t h e w i d t h o f t h e a b s o r p t i o n t a i l i s i n good agreement w i t h t h e e x p e r i m e n t a l d a t a , as shown i n F i g . 2 . Furthermore, t h e parameters o f Eq. ( 6 ) and Eq. ( 4 ) a r e p h y s i c a l l y r e a s o n a b l e . From t h e tem- p e r a t u r e dependence o f Eo(T,X) we o b t a i n f r o m Eq. ( 4 ) (ao = 1 ) X = 2.2, and a = 400K. T h i s v a l u e f o r o corresponds t o a Debye t e m p e r a t u r e o f 540K i n reason- a b l e agreement w i t h t h e Debye-temperature o f X-Si. The s t r u c t u r a l d i s o r d e r parameter, X = 2.2, i s somewhat l a r g e r t h a n t h e room t e m p e r a t u r e t h e r m a l d i s o r d e r term, 2/[exp(o/T)-1] = 0.7, as expected. Based on E 0 ) = 062, t h e l i n e a r f i t shown i n F i g . 2 and t h e z e r o p o i n t u n c e r t a i n t y *U2>o'jq'= 0.06A ( a p p r o p r i a t e t o an o s c i l l a t o r w i t h f r e q u e n c y ko/h), t h e d e f o r m a t i o n p o t e n t i a l D, i n Eq. ( 6 ) , i s 3 0 e ~ / ~ 2 .
T h i s v a l u e i s o f t h e same o r d e r as s i m i l a r d e f o r m a t i o n p o t e n t i a l s i n x - G ~ . ~ The r e m a i n i n g undetermined parameter o f t h e model EG(O,O) i s determined f r o m F i g . 2, and i s 2.0eV f o r Eo(O,O) = 17.8 meV i n f a i r agreement w i t h t h e f o c u s energy o f F i g . 1.
The above e x p e r i m e n t a l d a t a on a-SiHx o b t a i n e d f r o m glow d i s c h a r g e decomposition o f p u r e SiH4 suggests t h a t t h e o p t i c a l bandgap EG(T,X) i s determined b y t h e degree o f d i s o r d e r i n t h e l a t t i c e , r a t h e r t h a n by t h e H c o n t e n t , as i s commonly assumed i n t h e l i t e r a t u r e . I n o u r model, t h e H a f f e c t s t h e bandgap o n l y i n d i r e c t l y t h m u g h l i t s a b i l i t y t o r e l i e v e s t r a i n i n t h e n e t w o r k .
We a l s o i n c l u d e i n F i g . 2, t h e v a l u e s o f EG and Eo o b t a i n e d f o r two r e a c t i v e l y s p u t t e r e d f i l m s ( H = 8 and 22 a t %) whose p r e p a r a t i o n has been d e s c r i b e d
p r e v i o u s l y . 9 For t h e h i g h band gap m a t e r i a l t h e band edge parameter, Eo, d e t e r - mined by t r a n s m i s s i o n measurements was 63 x I C - ~ eV. The p l o t t e d p o i n t o f 45 x
10-3eV was o b t a i n e d by s u b t r a c t i n g f r o m t h e measured t r a n s m i s s i o n f o r t h i s 1 0 ~ specimen r e s i d u a l s c a t t e r i n g l o s s e s o f 60 cm-1.10 These f i l m s have d e n s i t i e s a b o u t 10% l e s s t h a n t h e glow d i s c h a r g e m a t e r i a l .l F i n a l l y we show t h e bandgap and w i d t h o f t h e e x p o n e n t i a l t a i l i n f e r r e d f r o m t h e d a t a on CVD f i l m s o f J a n a i and
~ a r l s o n . 1 1 The agreement w i t h Eq. ( 7 ) i s remarkable, f o r a l l t h e s e f i l m s o f a-SiHx p r e p a r e d i n r a d i c a l l y d i f f e r e n t ways. The e x p e r i m e n t a l d a t a suggests t h a t t h e o p t i c a l gap o b t a i n e d f r o m Eq. 2 i s a l i n e a r f u n c t i o n o f Eo, and t h r o u g h i t ,
C4-304 JOURNAL DE PHYSIQUE
o f temperature and s t r u c t u r a l d i s o r d e r . A l t h o u g h t h e hydrogen c o n t e n t v a r i e s f o r f i l m s shown i n F i g . 2, f r o m l e s s t h a n one p e r c e n t t o 20%, t h e bonded H c o n t e n t i t - s e l f i s n o t t h e fundamental c o n t r o l l i n g f a c t o r i n t h e o p t i c a l bandgap. Rather i t i s t h e s t r u c t u r a l d i s o r d e r , w h i c h i s i n f l u e n c e d i n d i r e c t l y by t h e H c o n t e n t . These r e s u l t s a r e i m p o r t a n t f o r o p t i m i z a t i o n o f s o l a r c e l l s . The c o u p l i n g o f EG t o Eo suggests an u n a n t i c i p a t e d t r a d e o f f between t h e e l e c t r i c a l " q u a l i t y " o f a-Si:H and i t s o p t i c a l a b s o r p t i o n . Sharpening o f t h e band t a i l s i s d e s i r a b l e f r o m t h e v i e w p o i n t o f t r a n s p o r t s i n c e i t l o w e r s t r a p d e n s i t i e s as w e l l as deep recom- b i n a t i o n c e n t e r s . However, such e l e c t r i c a l improvement i n t h e m a t e r i a l r e s u l t s i n an i n c r e a s e i n EG and s i g n i f i c a n t l y p o o r e r o p t i c a l a b s o r p t i o n ! I f l o w e r bandgaps a r e u n a t t a i n a b l e i n t h e a-Si:H system, s u b s t a n t i a l improvements i n e f f i c i e n c y can o n l y come f r o m an i n c r e a s e i n open c i r c u i t v o l t a q e and f i l l f a c t o r s i n c e t h e s h o r t c i r c u i t currg:fI a r e a l r e a d y w i t h i n 15% o f t h e maximum expected f o r m a t e r i a l s w i t h EG = 1 .72eV.
We a r e g r a t e f u l t o C. R. Wronski f o r h e l p f u l d i s c u s s i o n s and t o C. M i k e s e l l and H. S t a s i e w s k i f o r t e c h n i c a l a s s i s t a n c e .
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