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MINORITY CARRIER TRANSPORT IN DEPLETION LAYERS OF n-i-p a-Si : H SOLAR CELLS
V. Dalal, F. Alvarez
To cite this version:
V. Dalal, F. Alvarez. MINORITY CARRIER TRANSPORT IN DEPLETION LAYERS OF n- i-p a-Si : H SOLAR CELLS. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-491-C4-494.
�10.1051/jphyscol:19814104�. �jpa-00220719�
JOURNAL DE PHYSIQUE
CoZZoque C4, suppZ6ment au nO1O, Tome 42, octobre 1981 page C4-491
M I N O R I T Y C A R R I E R TRANSPORT I N D E P L E T I O N LAYERS OF n-.i-p a - S i : H SOLAR C E L L S
V. Dalal and F. Alvarez
I n s t i t u t e of Energy Conversion, University o f DeZaware, Newark, Delaware 19712, U.S.A.
A b s t r a c t , 7. Transport p r o p e r t i e s o f e l e c t r o n s and h o l e s i n i l a y e r s of p i n a-Si s o l a r c e l l s a r e important i n determining t h e c u r r e n t c o l l e c t i o n e f f i c i e n c y o f t h e s e c e l l s . I n t h i s p a p e r , we d e s c r i b e a new technique f o r measuring t h e
(v-r) p r o d u c t of m i n o r i t y c a r r i e r s i n t h e undoped l a y e r of an a-Si:H c e l l . I t i s shown t h a t t h e t r a n s p o r t p r o p e r t i e s i n d e p l e t i o n l a y e r s o f s o l a r c e l l s can be very d i f f e r e n t from t h e t r a n s p o r t i n v i r g i n i l a y e r s , and t h a t under c e r t a i n circumstances, e l e c t r o n s can become t h e m i n o r i t y c a r r i e r s , i n s t r o n g c o n t r a s t t o v i r g i n i l a y e r s , where h o l e s a r e t h e m i n o r i t y c a r r i e r s ,
I n t r o d u c t i o n . - The c u r r e n t c o l l e c t i o n e f f i c i e n c y of a-Si:H s o l a r c e l l s i s l i m i t e d by t h e t r a n s p o r t p r o p e r t i e s , p a r t i c u l a r l y (PT) p r o d u c t s and d i f f u s i o n l e n g t h s L, and of e l e c t r o n s and h o l e s . Generally speaking, i t i s assumed t h a t t h e ( y ~ ) product o
' 2
h o l e s i s much smaller than t h a t of e l e c t r o n s (1-3), and hence, h o l e s a r e t h e l i m i t i n g o r m i n o r i t y c a r r i e r s (4,5)_, However, no r e l i a b l e evidence e x i s t s t h a t such i s indeed t h e case i n t h e i l a y e r of a p i n c e l l . I n t h i s p a p e r , we d i s c u s s a new technique f o r i d e n t i f y i n g t h e l i m i t i n g c a r r i e r and f o r e s t i m a t i n g t h e (PT) product and d e p l e t i o n width o f t h e j u n c t i o n i n p i n c e l l s . We s h a l l show t h a t under c e r t a i n circumstances, t h e e l e c t r o n s may have a lower ( y ~ ) product t h a n h o l e s and may s e r v e a s m i n o r i t y c a r r i e r s . I t i s p o s t u l a t e d t h a t such a c o n d i t i o n can a r i s e because of cross-contamination between t h e p+ and i l a y e r s d u r i n g th'e growth of t h e c e l l . Basic Model.
-
The b a s i c model f o r analyzing t h e c u r r e n t c o l l e c t i o n e f f i c i e n c y of p i n c k l l s ' i s shown i n F i g u r e 1 (5). The model s t a t e s t h a t t h e r e a r e two j u n c t i o n s i n a n+ip* a-Si:H s o l a r c e l l , t h e f r o n t n + i j u n c t i o n and t h e back i p + T n c t i o n . Thus, t h e r e a r e two d e p l e t i o n r e g i o n s , s e p a r a t e d by a n e u t r a l r e g i o n o f low f i e l d . The s p a t i a l e x t e n t of t h e f i e l d r e g i o n s depends upon t h e d e n s i t y of s t a t e s ( 5 ) . I f t h e d e n s i t y of s t a t e s i n t h e mid-gap r e g i o n i s high, t h e d e p l e t i o n t h i c k n e s s e st l and t g a r e small, and n e u t r a l region t h i c k n e s s t a i s l a r g e . I f t h e mid-gap d e n s i t y i s low, t h e d e p l e t i o n t h i c k n e s s e s overlap and t h e r e i s no n e u t r a l r e g i o n . In t h i s c a s e , t h e p o t e n t i a l i n t h e i l a y e r can be approximated by a l l o t t
b a r r i e r ( 6 ) , b u t with s h a r p p o t e n t i a l p r o f i l e s a t t h e edges.
Using t h e b a s i c model of F i g u r e 1, we can p r e d i c t t h e behavior of t h e c o l l e c t i o n e f f i c i e n c y of a-Si s o l a r c e l l s with a p p l i e d v o l t a g e . A s t h e a p p l i e d v o l t a g e i n t h e forward d i r e c t i o n i n c r e a s e s , t h e d e p l e t i o n r e g i o n s w i l l s h r i n k , and t h e n e u t r a l r e g i o n w i l l i n c r e a s e . Consequently, i f t h e d i f f u s i o n l e n g t h of c a r r i e r s i s small, t h e c a r r i e r c o l l e c t i o n e f f i c i e n c y w i l l d e c l i n e . Conversely, f o r r e v e r s e a p p l i e d v o l t a g e , t h e c o l l e c t i o n e f f i c i e n c y w i l l i n c r e a s e . S i m i l a r c o n s i d e r a t i o n s hold f o r t h e M o t t - b a r r i e r c a s e , where a forward v o l t a g e reduces t h e f i e l d , and a r e v e r s e v o l t a g e i n c r e a s e s t h e f i e l d . S i n c e t h e c a r r i e r s r e l y on f i e l d a s s i s t e d t r a n s p o r t , i f t h e range of c a r r i e r s (p-rE) is comparable t o t h e f i l m t h i c k n e s s , t h e c a r r i e r c o l l e c t i o n q f f i c i e n c y w i l l i n c r e a s e w i t h r e v e r s e v o l t a g e and d e c r e a s e with forward v o l t a g e . Therefore, a measurement of c o l l e c t i o n e f f i c i e n c y w i t h b i a s v o l t a g e p r o v i d e s a t o o l f o r measuring ( W ) p r o d u c t s .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814104
C4-492 JOURNAL DE PHYSIQUE
Analysis. - E l e c t r i c F i e l d P r o f i l e : The e l e c t r i c f i e l d and p o t e n t i a l p r o f i l e s i n t h e i l a y e r depend upon t h e d e n s i t y of s t a t e s i n t h e mid;.gap ( 7 ) . Recent r e s u l t s on t h e measurement of d e n s i t y of s t a t e s i n a-Si:H by DLTS (8,9) and by m o b i l i t y t r a n s p o r t (10) show t h a t t h e d e n s i t y of s t a t e s i n a-SizH i s w e l l r e p r e s e n t e d by Figure 2 , w i t h s h a r p t a i l s n e a r t h e band edges and a f l a t d e n s i t y 'L 1 0 ' ~ / c m ~ - e v i n t h e middle. I n such a c a s e , f o r a t h i n i l a y e r (?. 0.4 pm), t h e e l e c t r i c f i e l d extends over t h e e n t i r e i l a y e r ; i . e . , a Mott b a r r i e r e x i s t s .
For s i m p l i c i t y , we can assume t h a t t h e f i e l d i s uniform, given by E:(v~ + V ) / t i , where V i s a p p l i e d v o l t a g e , VD t h e d i f f u s i o n v o l t a g e , and t i t h e t h i c k n e s s of i
l a y e r . VD i s given by: VD = Eg - A Ef,,
-
A Ef,b where Eg is t h e bandgap, A Ef,n = (Ec - Ef,n) on t h e n - s ~ d e A Ef,p = (Ev-
hf,P) on t h e p - s i d e . T y p i c a l l y , we measure A Ef,, = 0.25V, A E f , p = 0:4V and Eg = 1.7V. T h u s , V ~ = 1.05V and E6
2 . 5 X 104v/cm i n our sample a t zero b i a s .For s i m p l i c i t y , we can a l s o assume t h a t oniy one kind of c a r r i e r i s important;
i . e . , (UT) product f o r one c a r r i e r << t h a t of t h e o t h e r . Then, t h e following equation h o l d s f o r quantum e f f i c i e n c y (IE(X), of photogenerated c a r r i e r s , assuming a n i p / m e t a l c e l l ( l i g h t i n c i d e n t from n s i d e ) and e l e c t r o n s t h e m i n o r i t y c a r r i e r s i n t h e i l a y e r .
where a i s a b s o r p t i o n c o e f f i c i e n t
and S, = ( ~ T ) , . E i s t h e range o f e l e c t r o n s . T h e r e f o r e , from t h e dependence of QE(X) on V , we should b e a b l e t o o b t a i n ( P T ) ~ .
E eriment. - The experiment c o n s i s t e d o f measuring t h e quantum e f f i c i e n c y QE(X) h a 1 a - S i s o l a r c e l l s . A t y p i c a l c e l l was made by d e p o s i t i n g s u c c e s s i v e l y p , i and n l a y e r s on a Ti/7059 s u b s t r a t e . The t h i c k n e s s of n l a y e r was 2002 and i
l a y e r , 42002. A s e m i - t r a n s p a r e n t 75.8 t h i c k T i d o t of 0.20cm2 a c t i v e a r e a was d e p o s i t e d on t h e n l a y e r and monochromatic l i g h t was i n c i d e n t on t h e Ti d o t . The a b s o r p t i o n of t h e Ti. d o t wasmea$ured a t 'L 10% and t h e r e f l e c t i o n from t h e T i / a - S i combination was 45%, allowing a 45% l i g h t t ~ a n s m i s s i o n , The monochromatic beam was chopped and QE(A) measured a s a f u n c t i o n of v o l t a g e i n t h e presence o+ a w h i t e - l i g h t b i a s a t M.ll i l l u m i n a t i o n l e v e l s o a s t o approximate t h e c o n d i t i o n s faced by t h e s o l a r c e l l i n a c t u a l o p e r a t i o n ( 1 1 ) .
I n F i g u r e 3 we show t h e i n t e r n a l QE(X) of t h e c e l l under t h r e e v o l t a g e c o n d i t i o n s , zero b i a s and
+
0.4V. I t i s immediately obvious t h a t t h e range of c a r r i e r s i s comparable t o t h i c k n e s s , s o t h a t a r e d u c t i o n i n f i e l d causes a r e d u c t i o n i n QE. Much more i n f o r m a t i o n can be o b t a i n e d 6y p l o t t i n g t h e r a t i o QE(V)QE(V = 0 ) v s . wavelength, which is done i n Figure 4. A s t r i k i n g f e a t u r e of Figure 4 i s t h a t t h e c a r r i e r s g e n e r a t e d deeper i n t h e i l a y e r (long X photons) s u f f e r much g r e a t e r r e d u c t i o n i n QE t h a n c a r r i e r s g e n e r a t e d n e a r e r t h e n+ l a y e r( s h o r t 1 p h o t o n s ) . This can Be t r u e only i f t h e m i n o r i t y c a r r i e r i s of t h e t y p e which h a s t o t r a v e r s e towards t h e n+ l a y e r t o b e c o l l e c t e d ; i . e . , i f t h e m i n o r i t y c a r r i e r i s an e l e c t r o n . Thus, t h e shape o f QE(V)QE(V = 0 ) curve g i v e s us t h e of c a r r i e r with t h e s m a l l e r PT p r o d u c t .
Q u a n t i t a t i v e i n f o r m a t i o n i s obtained by measuring QE(X) v s . v o l t a g e f o r s e v e r a l wavelengths, and t h e n f i t t i n g t o Eqn. 1 t o determine S,, knowing a. This i s done i n Figure S , where we p l o t a n a l y t i c a l curves from Eqn. 1 f o r t h r e e wave- l e n g t h s , 0.5, 0 . 6 , and 0 . 7 ym. The r e l a t i o n between QE(X) and S, i s computed from t h e experimental QE(A) v s . v o l t a g e d a t a using an i t e r a t i v e p r o c e s s with (PT) a s a f i t t i n g parameter. The f i t between t h e a n a l y t i c a l e x p r e s s i o n and t h e d a t a
p o i n t s (+ + +) i s seen i n Figure 5. We o b t a i n an e s t i m a t e of Sn
2
0.25ym a t V = 0 , g i v i n g (PT) f o r e l e c t r o n s2
1 0 - ~ c m ~ / ~ . Note t h a t t h e f i t between experimental and a n a l y t i c a l curves d e t e r i o r a t e s a t extreme v o l t a g e s because t h e model i s no longer v a l i d a t t h o s e v o l t a g e s . This v a l u e of (PT) can now be used t o f i t F i g u r e 4( s o l i d l i n e s ) and i t i s seen t h a t t h e f i t i s q u i t e good. Thus, our simple model
fits the experimental QE curves quite well. Due to the ~implTcitr of the model, the value of (WT) is accurate only to approximately 25%.
Conclusion. - In conclusion, we have described a new technique for determining the (WT) product of minority carriers in i layers of nip a-Si:H solar cells. A surprising conclusion is that the electrons are the minority carriers, a probable consequence of the severe p-type contamination that exists in i layers made immediately after depositing the p-layer. Clearly, for making high quality cells, this cross-contamination problem will have to be addressed and solved.
This work was partially supported by Solar Energy Research Institute under subcontract XG-9-9195.
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1. DEBNEY, B. Solid-State Electron Devices
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S p e c i d qxsue; (1978) 515.2. STAEBLER, D. J. Noncryst. Solids,
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(1980) 387. ' - '3. WRONSKI, C. IEEE Trans. Electron Devices
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(1977) 351.4. CRANDALL, R., WILLIAMS, R., and TOMPKINS, B. E. J . Appl. Phys.
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(1970) 5506.5. DALAL, V. L. Solar Cells
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(1980) 936.7. SPEAR, W., LE COMBER, P., and SNELL, A. J. Phil. Nag. B38, (1978) 303.
8. COHEN, J. D., LANG, D., and HARBISON, J. P. Phys. ~ev.tktt. 45, (1980) 197.
9. JOHNSON, N. To be published in Proc. AIP Conf. on ~etrahedral~orphous Semiconductors. (Carefree, Arizona, 1981).
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Fig. 1
B a n d D i a g r a m f o r a - S i : H n i p j u n c t i o n
Ev Ec
ENERGY
'Fig. 2
Approximate D e n s i t y of S t a t e s i n a - S i 4 H
JOURNAL DE PHYSIQUE
Figure 3
Quantum Efficiency of nip cell for short-circuit, forward
(-) and reverse (+) voltage. Figure 4
Ratio of Quantum Efficiencies vs.
wavelength.
Figure 5
Experimental and analytical curves of r)E vs. Range Sn
