Analysis of Current-Voltage Characteristics of Illuminated Cadmium

23 Analysis of Current-Voltage Characteristics of Illuminated Cadmium Selenide-Polysulfide Junctions Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 7, 2016 | http://pubs.acs.org Publication Date: March 2, 1981 | doi: 10.1021/bk-1981-0146.ch023

JOSEPH REICHMAN and MICHAEL A. RUSSAK Research Department A01/26, Grumman Aerospace Corporation, Bethpage, N Y 11714 Comparisons of experimental I-V characteristics with those predicted by theoretical models ( J J are commonly made to analyze the effects of illumination on semiconductor junction devices. These comparisons have not normally been made for semiconductorelectrolyte (S-E) junctions, most likely due to the lack of suitable theoretical models. In this paper the calculated I-V characteristics using a model that includes depletion region recombination (2) are com pared with experimental results for single-crystal CdSe electrode/polysulfide electrolyte junctions. In particular the predicted effects of redox ion concentration and light intensity on the I-V characteristics are analyzed and compared with exper imental data. Theoretical

Discussion

Models. The most commonly used model t o a n a l y z e t h e I-V p e r f o r m a n c e o f S-E j u n c t i o n s i s t h a t o f G a r t n e r (3) a s g i v e n by the f o l l o w i n g Ig= q F [ l - exp(-oW)/(l

+ oL)]

where F i s t h e a b s o r b e d m o n o c h r o m a t i c s o l a r f l u x , α i s t h e a b s o r p t i o n c o e f f i c i e n t , W i s t h e d e p l e t i o n w i d t h , and L i s t h e minority carrier diffusion length. T h i s e q u a t i o n shows a weak dependence o f c u r r e n t on v o l t a g e t h r o u g h t h e f u n c t i o n a l d e p e n dence o f d e p l e t i o n w i d t h on t h e s q u a r e r o o t o f p o t e n t i a l drop a c r o s s i t . T h i s e q u a t i o n o f t e n g i v e s a good f i t t o e x p e r i m e n t a l d a t a a t s h o r t c i r c u i t c o n d i t i o n s ( t h e r e d o x p o t e n t i a l ) and a t r e v e r s e b i a s ( a n o d i c p o l a r i z a t i o n f o r an η - t y p e s e m i c o n d u c t o r electrode). However, i n t h e f o r w a r d b i a s r a n g e ( c a t h o d i c p o l a r i z a t i o n ) , t h e r e g i o n of i n t e r e s t f o r p h o t o v o l t a i c performance a n a l y s i s , t h e G a r t n e r model p r e d i c t s a d e c r e a s e i n c u r r e n t c o n s i d e r a b l y smaller than i s observed e x p e r i m e n t a l l y . T h i s i s due t o t h e n e g l e c t o f t h e v a r i o u s r e c o m b i n a t i o n mechanisms t h a t c o n tribute to t h e decrease i n photocurrent with increasing

0097-6156/81 /0146-0359$05.00/0 © 1981 American Chemical Society Nozik; Photoeffects at Semiconductor-Electrolyte Interfaces ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 7, 2016 | http://pubs.acs.org Publication Date: March 2, 1981 | doi: 10.1021/bk-1981-0146.ch023

360

PHOTOEFFECTS AT SEMICONDUCTOR-ELECTROLYTE INTERFACES

p h o t o v o l t a g e ( o r d e c r e a s i n g band b e n d i n g ) . The G a r t n e r m o d e l , o r i g i n a l l y derived f o r a Schottky b a r r i e r i n reverse b i a s , only accounts f o r recombination o f c a r r i e r s generated i n the bulk o f the semiconductor. O t h e r mechanisms t h a t can c o n t r i b u t e t o photocurrent loss a r e : 1. D i f f u s i o n of d e p l e t i o n region generated m i n o r i t y c a r r i e r s t o t h e b u l k and s u b s e q u e n t r e c o m b i n a t i o n 2. Recombination i n the depletion region 3. Recombination a t the i n t e r f a c e 4. O p p o s i n g dark c u r r e n t . R e c o m b i n a t i o n i n t h e d e p l e t i o n l a y e r c a n become i m p o r t a n t when t h e c o n c e n t r a t i o n o f m i n o r i t y c a r r i e r s a t t h e i n t e r f a c e exceeds t h e m a j o r i t y c a r r i e r c o n c e n t r a t i o n . Under i l l u m i n a t i o n minority c a r r i e r buildup a t the semiconductor-electrolyte i n t e r f a c e c a n o c c u r due t o s l o w c h a r g e t r a n s f e r . Thus s u r f a c e i n v e r s i o n may o c c u r and r e c o m b i n a t i o n i n the depletion region can become t h e d o m i n a n t mechanism a c c o u n t i n g f o r l o s s i n photocurrent. Mechanisms 1 a n d 2 a r e i n c l u d e d i n t h e model t h a t i s used here f o r comparison w i t h experimental d a t a . Interface recombin ation and dark c u r r e n t e f f e c t s a r e n o t i n c l u d e d ; h o w e v e r , t h e e x p e r i m e n t a l d a t a have been a d j u s t e d t o e x c l u d e t h e e f f e c t s o f dark c u r r e n t . To i n c l u d e t h e a d d i t i o n a l b u l k and d e p l e t i o n l a y e r recombination l o s s e s , the d i f f u s i o n equation f o r minority c a r r i e r s i s s o l v e d u s i n g boundary c o n d i t i o n s r e l e v a n t t o t h e S-E j u n c t i o n ( i . e . , the photocurrent i s l i n e a r l y r e l a t e d to t h e con c e n t r a t i o n of minority c a r r i e r s a t the i n t e r f a c e ) . Using this boundary condition and a s s u m i n g q u a s i - e q u i l i b r i u m conditions ( f l a t q u a s i - F e r m i l e v e l s ) (4) i n t h e d e p l e t i o n r e g i o n , t h e f o l lowing current-voltage r e l a t i o n s h i p i s obtained. I = qvp

w

exp(q

Φι,/kT)

v/here ν i s t h e r a t e c o n s t a n t f o r c h a r g e t r a n s f e r , i s the p o t e n t i a l d r o p a c r o s s t h e d e p l e t i o n r e g i o n and p i s t h e h o l e c o n c e n t r a t i o n a t t h e d e p l e t i o n edge. To d e t e r m i n e p t h e f o l l o w i n g e q u a t i o n i s used w

w

K

w

L

κ + (K2 + 2A

ν 4Α0

2

2 Ί J

where A = q v e x p / k j ) + q L / τ , C = I + qvp exp /kT) and Κ = - n k l ( 2 e e / q / / T . In t h e a b o v e , L i s t h e h o l e d i f f u s i o n l e n g t h , τ i s t h e l i f e t i m e , p i s t h e e q u i l i b r i u m hole d e n s i t y , and Φ β i s t h e e q u i l i b r i u m band b e n d i n g v o l t a g e . These e q u a t i o n s a r e good a p p r o x i m a t i o n s when Φ i s n o t t o o s m a l l and a r e e q u i v a l e n t t o t h a t g i v e n i n [2) where t h e exchange c u r r e n t p a r a m e t e r i s u s e d i n s t e a d o f t h e charge t r a n s f e r r a t e c o n s t a n t . More a c c u r a t e b

a

0

b o

y

0

0

0

Nozik; Photoeffects at Semiconductor-Electrolyte Interfaces ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

23.

REiCHMAN

A N D RUSSAK

Illuminated CdSe-Polysulfide Junctions

361


e q u a t i o n s t h a t a p p l y t o t h e e x t i r e range o f p o t e n t i a l have been used i n t h e a n a l y s i s g i v e n h e r e ( 5 ) . The e q u a t i o n s however a r e somewhat complex and t h e r e f o r e a r e n o t p r e s e n t e d i n t h i s p a p e r . Predicted Results. The e f f e c t s o f c h a r g e t r a n s f e r r a t e c o n s t a n t , v , and i l l u m i n a t i o n i n t e n s i t y were s e l e c t e d f o r a n a l y s i s and c o m p a r i s o n w i t h e x p e r i m e n t . P r e d i c t e d r e s u l t s b a s e d on t h e model d e s c r i b e d above showing t h e e f f e c t s o f ν on t h e I-V c h a r a c t e r i s t i c s a r e g i v e n i n F i g u r e 1. Using the values o f the p a r a m e t e r s g i v e n i n t h e c a p t i o n , t h i s f i g u r e shows t h a t a s ν g e t s s m a l l e r , l o s s e s i n c u r r e n t due t o d e p l e t i o n r e g i o n r e c o m bination o c c u r a t h i g h e r v a l u e s o f band b e n d i n g . T h i s i s due to the higher c o n c e n t r a t i o n of m i n o r i t y c a r r i e r s a t the i n t e r face t h a t i s r q u i r e d to s u s t a i n a given p h o t o c u r r e n t as ν d e creases. This leads to higher recombination rates i n the d e p l e t i o n r e g i o n as t h e band b e n d i n g i s r e d u c e d . The e f f e c t o f v a r y i n g l i g h t i n t e n i t y on t h e I-V c h a r a c t e r i s t i c s a r e shown i n F i g u r e 2. Because t h e c u r v e s a r e n o r m a l i z e d t o t h e i n c i d e n t i n t e n s i t y , t h e y s h o u l d s u p e r p o s e each o t h e r i f t h e r e c o m b i n a t i o n l o s s e s were l i n e a r l y d e p e n d e n t on i n t e n s i t y . However, o u r model p r e d i c t s t h a t r e c o m b i n a t i o n l o s s e s i n t h e d e p l e t i o n region i s p r o p o r t i o n a l to t h e square r o o t of i n t e n sity. Thus l o s s e s due t o d e p l e t i o n r e g i o n r e c o m b i n a t i o n become r e l a t i v e l y l e s s s i g n i f i c a n t a t h i g h e r i n t e n s i t i e s and c o n s e q u e n t l y , f o r a g i v e n band b e n d i n g , h i g h e r c o l l e c t i o n e f f i c i e n cies result. F o r t h e p a r a m e t e r s used h e r e , t h e a d d i t i o n a l r e c o m b i n a t i o n due t o d i f f u s i o n from t h e d e p l e t i o n r e g i o n t o t h e b u l k do n o t become s i g n i f i c a n t u n t i l t h e band b e n d i n g becomes s m a l l . Discussion

o f Experiment

Experimental Procedure. E x p e r i m e n t a l I-V d a t a f o r a CdSe s i n g l e c r y s t a l e l e c t r o d e i n p o l y s u l f i d e e l e c t r o l y t e was used t o compare w i t h p r e d i c t i o n s o f t h e model t h a t i n c l u d e s d e p l e t i o n region recombinations. The c r y s t a l was o b t a i n e d f r o m C l e v e l a n d C r y s t a l C o r p . , C l e v e l a n d , O h i o , and p r e p a r e d f o r measurements a c c o r d i n g t o p r o c e d u r e s f o u n d i n t h e l i t e r a t u r e (6). Electrodes composed o f Na2S and s u l f u r i n 1M NaOH was used w i t h Argon gas bubbling through t h e c e l l d u r i n g measurements. Voltammetric measurements were made w i t h a PAR model 173 p o t e n t i o s t a t and Model 175 u n i v e r s a l programmer u s i n g a scan r a t e o f 10 MV/sec. S p e c t r a l measurements were made u s i n g t h e o u t p u t o f a t u n g s t e n h a l o g e n l a m p . M o n o c h r o m a t i c i n t e n s i t i e s were o b t a i n e d by u s i n g n a r r o w bandpass filters. I n t e n s i t i e s were measured u s i n g a Elppley thermopile detector. Electrode Character!zation. To m i n i m i z e t h e number o f a d j u s t a b l e p a r a m e t e r s o f t h e m o d e l , t h e o p t i c a l and e l e c t r o n i c p r o p e r t i e s o f t h e CdSe c r y s t a l e l e c t r o d e were meaured. Diffuse


362

PHOTOEFFECTS AT SEMICONDUCTOR-ELECTROLYTE

INTERFACES


1.0 r -

BAND BENDING, V O L T S

Figure 1. Calculated effect of rate constant on I-V characteristics (parameters: lifetime τ = 10' s; Ν = 1.5 Χ 10 cm' ; L = 1 μτη; a = 3 Χ 10 cm- ) ((A) 1000; (B)100; (C) 10; (D) 1 cm/s) 9

17

3

4

1

1.0 r -

0

O.2

O.4

O.6

O.8

BAND BENDING, V O L T S

Figure 2. Calculated effects of intensity on I-V characteristics (parameters as in Figure 1 with ν = 10 cm/s) ((A) 10 mA/cm ; (B) 1.0 mA/cm ; (C) O.1 mA/cm ) 2

2


2


23.

REiCHMAN A N D R U S S A K

Illuminated CdSe-Polysulfide Junctions

363

r e f l e c t a n c e measurements a s a f u n c t i o n o f w a v e l e n g t h from t h e e l e c t r o d e s u r f a c e immersed i n t h e e l e c t r o l y t e compartment were obtained. The a b s o r p t i o n c o e f f i c i e n t as a f u n c t i o n o f wavel e n g t h was o b t a i n e d from r e f l e c t a n c e and t r a n s m i t t a n c e m e a s u r e Tients o f CdSe t h i n f i l m s u s i n g conventional methods. The c a r r i e r d e n s i t y was o b t a i n e d from measurements o f r e s i s t i v i t y and H a l l v o l t a g e u s i n g t h e Van de Pauw method ( 7 J . The f l a t b a n d p o t e n t i a l was o b t a i n e d by d e t e r m i n i n g t h e p o t e n t i a l a t which a p h o t o r e s p o n s e i s o b s e r v e d u s i n g a h i g h i n t e n s i t y chopped l i g h t source. A d d i t i o n a l l y , M o t t - S c h o t t k y p l o t s were a l s o made f o r additional v e r i f i c a t i o n o f f l a t band p o t e n t i a l and c a r r i e r density. The r e s u l t s o f t h e s e measurements a r e summarized i n T a b l e I. Measurements o f p h o t o c u r r e n t a s a f u n c t i o n o f w a v e l e n g t h a t s h o r t c i r c u i t c o n d i t i o n s ( - O . 8 V r e l SCE) were made. The d a t a tfas r e d u c e d t o i n t e r n a l quantum e f f i c i e n c y by u s i n g t h e measured values of r e f l e c t a n c e , c o r r e c t i n g f o r e l e c t r o l y t e absorption, and m e a s u r i n g t h e i n c i d e n t i n t e n s i t y . The r e s u l t s a r e shown i n Figure 3 together with a best f i t to the data using the Gartner model ( E q u a t i o n 1 ) . The d e p l e t i o n w i d t h was c a l c u l a t e d u s i n g t h e measured v a l u e s o f c a r r i e r d e n s i t y and f l a t band p o t e n t i a l . F o r a d i f f u s i o n l e n g t h o f 1 ym and t h e measured v a l u e s o f t h e a b s o r p t i o n c o e f f i c i e n t s , a good f i t t o t h e d a t a was o b t a i n e d , a s seen f r o m F i g u r e 3 . The I-V c h a r a c t e r i s t i c s were o b t a i n e d a t v a r y i n g m o n o c h r o m a t i c i n t e n s i t i e s u s i n g a chopped beam a t a w a v e l e n g t h o f 6 5 0 nm. The i n t e r n a l quantum e f f i c i e n c y ( o r c o l l e c t i o n e f f i c i e n c y ) was t h e n d e t e r m i n e d , as a f u n c t i o n o f band b e n d i n g voltage, u s i n g t h e r e f l e c t a n c e and t r a n s m i t t a n c e d a t a . T h i s was done by f i r s t s u b t r a c t i n g t h e dark c u r r e n t from t h e p h o t o c u r r e n t as o b t a i n e d from t h e chopped l i g h t r e s p o n s e . Comparison o f Theory & Experiment To compare t h e e f f e c t s o f i n t e n s i t y , I-V c h a r a c t e r i s t i c s were o b t a i n e d f o r t h e C d S e / p o l y s u l f i d e j u n c t i o n a t i n t e n s i t i e s o f 3 . 7 and O.37 ma/cm a t a w a v e l e n g t h o f 6 5 0 nm. The r e s u l t s u s i n g t h e above d a t a r e d u c t i o n method, a r e shown i n F i g u r e 4 t o g e t h e r w i t h c a l c u l a t e d f i t s t o t h e d a t a u s i n g t h e model t h a t includes depletion layer recombination. The a d j u s t a b l e c o n s t a n t s were c a r r i e r l i f e t i m e and c h a r g e t r a n s f e r r a t e c o n s t a n t . O t h e r p a r a m e t e r s were o b t a i n e d from t h e p r e v i o u s meaurements. As c a n be seen from F i g u r e 4 r e a s o n a b l y good f i t s t o t h e d a t a a r e o b t a i n e d f o r v a l u e s o f band b e n d i n g >O.2 V. The p r e d i c t e d decreasing importance of d e p l e t i o n region recombination with i n c r e a s i n g i n t e n s i t y i s observed e x p e r i m e n t a l l y . At low values o f band b e n d i n g , e f f e c t s n o t i n c l u d e d i n t h e m o d e l , such a s interface recombination and changes i n p o t e n t i a l d r o p across t h e H e l m h o l t z l a y e r may become i m p o r t a n t and e x p l a i n t h e d i s crepancy. 2



364

PHOTOEFFECTS

Table I.

PARAMETER

AT SEMICONDUCTOR-ELECTROLYTE

INTERFACES

CdSe Single Crystal Electrode Characterization

MEASUREMENT

VALUES

ABSORPTION

TRANSMITTANCE

5x 1 0 c m "

COEFFICIENT (a)

& REFLECTANCE

TO 7 χ 1 0 c m "

REFLECTANCE

INTEGRATING SPHERE

O.10-O.12

CARRIER DENSITY

H A L L METHOD

1.5 χ 1 0

1 7

Analysis of Current-Voltage Characteristics of Illuminated Cadmium

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