Fundamental Aspects of Photoeffects at the n-Gallium Arsenide

22

Photoeffects at Semiconductor-Electrolyte Interfaces Downloaded from pubs.acs.org by NATL UNIV OF SINGAPORE on 05/05/18. For personal use only.

Fundamental Aspects of Photoeffects at the n-Gallium Arsenide-Molten-Salt Interphase R. J. G A L E , P. SMITH, P. SINGH, K. RAJESHWAR, and J. DUBOW Department of Electrical Engineering, Colorado State University, Fort Collins, CO 80523

Detailed studies of the semiconductor/electrolyte interphase boundary are necessary in order to understand fully the operation of photoelectrochemical cells. It is important to be able to establish the potential distribution throughout the interphasial regions because the surface potential barrier governs the separation of photogenerated electrons and holes and thus the energy conversion efficiency. Additionally, it is important to identify those factors that control or modify both the faradaic chargetransfer reactions occurring across the solid/liquid interface and the recombination processes within the semiconductor. For any particular system, a complete analysis in terms of the chemical identification of all the interposed molecules and their role would be an arduous, if not impossible task. Present knowledge of the catalytic and dielectric properties of the species existing in surface atomic layers and in the inner double layer region adjacent to semiconductor electrodes is particularly limited. We are restricted therefore to trying to identify the key factors affecting the output performance of cells and to devise experimental approaches that might ultimately provide a complete description of the photoelectrochemical processes in molecular detail. This work attempts to model a semiconductor/molten salt electrolyte interphase, in the absence of illumination, in terms of its basic circuit elements. Measurement of the equivalent electrical properties has been achieved using a newly developed technique of automated admittance measurements and some progress has been made toward identification of the frequency dependent device components (1). The system chosen for studying the semiconductor/ molten salt interphase has the configuration n-GaAs/AlCl : 1butylpyridinium chloride (BPC) melt/vitreous C., with the ferrocene/ ferricenium ion redox couple as the liquid phase charge carrier. Photoelectrochemical cell electrolytes can be divided broadly into two classes, aqueous and nonaqueous. If aqueous mixtures are included within the former classification, the non3

0097-6156/8 l/0146-0343$05.00/0 © 1981 American Chemical Society


344

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aqueous t y p e s can be s u b d i v i d e d f u r t h e r i n t o t h o s e based upon o r g a n i c o r i n o r g a n i c s o l v e n t s and m o l t e n s a l t e l e c t r o l y t e s , e a c h o f t h e s e r e q u i r i n g some means o f i o n i c c o n d u c t i o n a n d / o r a s u i t a b l e redox system. The r a t i o n a l e f o r s t u d y i n g t h e s e m i c o n d u c t o r / molten s a l t i n t e r p h a s e i s t h a t i n g e n e r a l , from c o r r o s i o n c o n s i d e r a t i o n s , nonaqueous e l e c t r o l y t e s a p p e a r t o be more a t t r a c t i v e t h a n t h e aqueous f o r use w i t h t h e t r a d i t i o n a l s e m i c o n d u c t o r m a t erials. Inherent advantages o f d e v e l o p i n g molten s a l t e l e c t r o l y t e s y s t e m s f o r c e l l s t o p r o d u c e e l e c t r i c i t y f r o m l i g h t have been d i s cussed elsewhere (2). Experimental Materials. S i n g l e c r y s t a l s o f S n - d o p e d n-GaAs o f o r i e n t a t i o n (100) were o b t a i n e d f r o m L a s e r Diode L a b , I n c . w i t h t h e f o l l o w i n g q u o t e d p r o p e r t i e s , N = 2.3 χ 1 0 c m " , ρ = O.0071 Ωαη, μ = 3900 cm V " s " . Ohmic c o n t a c t was a c h i e v e d w i t h t h e r m a l l y e v a p o r a t e d Ge-Au a l l o y a n n e a l e d i n N a t 400 C f o r 15 m i n u t e s . A Teflon c o a t e d Cu w i r e was a t t a c h e d w i t h s i l v e r epoxy cement and t h e s i n g l e c r y s t a l and t h e Ohmic c o n t a c t masked w i t h a n o n c o n d u c t i n g epoxy c e m e n t . S u r f a c e p r e p a r a t i o n o f t h e c r y s t a l s was s e q u e n t i a l l y a 30 sec e t c h i n 6M HC1, a d i s t i l l e d w a t e r r i n s e , a 1 m i n u t e immersion i n H S 0 : H 0 : H 0 (3:1:1 v o l . ) , a d i s t i l l e d water r i n s e , and a f i n a l r i n s e w i t h a b s o l u t e e t h a n o l . The wet a s s e m b l y was t h e n p l a c e d i m m e d i a t e l y i n t o t h e a n t e - c h a m b e r o f t h e d r y b o x t o be vacuum d r i e d . The c o u n t e r e l e c t r o d e c o m p r i s e d a p l a t e o f v i t r e o u s C ( A t o m e r g i c C h e m e t a l s , I n c . ) and t h e r e f e r e n c e e l e c t r o d e f o r a l l e x p e r i m e n t s c o n s i s t e d o f O.5 mm A l w i r e ( A l f a Y e n t r o n P u r a t r o n i c g r a d e , m4N8) immersed i n 2:1 m o l a r r a t i o A l C l : BPC m e l t , t h e p r e p a r a t i o n o f 1 - b u t y l p y r i d i n i u m c h l o r i d e and m e l t s have been d e s c r i b e d in e a r l i e r p u b l i c a t i o n s , e.g (3). 1 7

3

D

2

1

1

2

2

4

2

2

2

3

Apparatus

and

Technique

C i r c u i t r y used t o o b t a i n c a p a c i t a n c e - v o l t a g e d a t a f o r M o t t S c h o t t k y p l o t s was s i m i l a r t o t h a t u s e d p r e v i o u s l y ( 2 J . Linear v o l t a g e ramps ( 5 - 1 0 m V s " ) and 10 mV peak/peak ac s i g n a l s were added t o a PAR 173 P o t e n t i o s t a t / G a l v a n o s t a t f r o m a PAR 179 U n i v e r s i t y Programmer and I t h a c a D y n a t r a c 3 l o c k - i n a m p l i f i e r , r e spectively. The v o l t a g e o u t p u t f r o m t h e c u r r e n t f o l l o w e r o f a PAR 179 D i g i t a l C o u l o m e t e r was c o n n e c t e d t o t h e s i g n a l i n p u t o f t h e L I A and t h e c a p a c i t a n c e - v o l t a g e c u r v e s were d i s p l a y e d on a PAR RE 0074 X-Y r e c o r d e r . These measurements were made on c e l l s t h e r m o s t a t e d t o 40 + 1 C w i t h i n a d r y b o x . Most measurements were made in absolute darkness or i n c e l l s c a r e f u l l y screened w i t h Al f o i l to exclude l i g h t . A schematic o f the a u t o m a t i c network a n a l y s i s system used f o r p h o t o e l e c t r o c h e m i c a l c e l l measurements i s shown i n F i g u r e 1. The ac s i g n a l o f 20 mV p/p a m p l i t u d e i s a p p l i e d w i t h a H e w l e t t - P a c k a r d 3320B f r e q u e n c y s y n t h e s i z e r t o t h e c e l l and t o t h e r e f e r e n c e s i g 1

22.

GALE

345

n-GaAs-Molten-Salt Interphase

ET AL.

n a l i n p u t o f a HP 3570A a u t o m a t i c n e t w o r k a n a l y z e r . A h i g h speed c u r r e n t - v o l t a g e c o n v e r t e r ( T e l e d y n e P h i l b r i c k 1435) and c u r r e n t b o o s t e r w i t h a f l a t f r e q u e n c y r e s p o n s e f r o m d c * t o 1 MHz i s used t o buffer the analyzer. C e l l a d m i t t a n c e s c a n be c a l c u l a t e d f r o m t h e measured G ( s ) = (G.j + s C j ) / ( G + s C ) i n w h i c h G a n d G a r e t h e f

f

i

f

c o n d u c t a n c e s , C. and C t h e c a p a c i t a n c e s o f t h e c e l l and t h e f e e d back c o m p o n e n t s , r e s p e c t i v e l y , and s e q u a l s jo>. The d e s k t o p comp u t e r (HP 9825A) c o m m u n i c a t e s v i a t h e I E E E - 4 8 8 s t a n d a r d i n t e r f a c e bus w i t h t h e s y n t h e s i z e r a n d n e t w o r k a n a l y z e r t o sweep f r e q u e n c y , t o c o l l e c t g a i n and phase d a t a , t o c a l c u l a t e c a p a c i t a n c e and c o n d u c t a n c e v a l u e s and t h e n t o s t o r e t h i s i n f o r m a t i o n on f l e x i b l e discs. In t h e s e e x p e r i m e n t s , t h e b i a s was a d j u s t e d m a n u a l l y u s i n g a l o w n o i s e power s u p p l y u n t i l t h e r e q u i r e d p o t e n t i a l d r o p was o b t a i n e d between t h e r e f e r e n c e and w o r k i n g e l e c t r o d e s . Measurements were made i n two f r e q u e n c y r a n g e s f r o m 5-50 Hz and 5 0 - 1 0 0 KHz. D e t a i l s c o n c e r n i n g t h e c a l i b r a t i o n o f t h e s y s t e m and c o m p a r i s o n o f r e s u l t s o b t a i n a b l e t o t h e d a t a a c c e s s i b l e f r o m impedance b r i d g e t e c h n i q u e s have been o u t l i n e d a l r e a d y f o r m e t a l - i n s u l a t o r - s e m i conductor (MIS)/semiconductor-insulator-semiconductor (SIS) s o l a r c e l l s ( ] ) . Dummy c e l l c a l i b r a t i o n c u r v e s gave e r r o r s n o m i n a l l y < 3 p e r c e n t f o r g a i n and m o d e r a t e phase a n g l e s .


f

Results

and D i s c u s s i o n

Voltammetric Investigations. L i n e a r sweep v o l t a m m e t r y p r o v i d e s a s i m p l e , s e n s i t i v e a n d r a p i d means o f o b t a i n i n g a c u r r e n t voltage p r o f i l e of the semiconductor/electrolyte interphase. Figu r e 2 i l l u s t r a t e s t h e d a r k I-V c u r v e s a t a n-GaAs e l e c t r o d e i n b a s i c O.8:1 ( A 1 C 1 : BPC r e s p e c t i v e l y ) and a c i d i c 1.5:1 m o l a r ratio melts. In b a s i c m e l t s , a peak a t - O . 6 t o - O . 7 5 V i n c r e a s e s w i t h i l l u m i n a t i o n and by s c a n n i n g f u r t h e r i n t h e p o s i t i v e d i r e c i o n past t h e r e s t p o t e n t i a l a t -O.48 V ( F i g u r e 3 ) . T e n t a t i v e l y , t h i s r e d u c t i o n peak may be a s s i g n e d t o a homogeneous a r s e n i c c h l o r i d e s p e c i e s a t t h e e l e c t r o d e s u r f a c e b e c a u s e a s i m i l a r peak i s o b t a i n e d a t a C e l e c t r o d e by t h e a d d i t i o n o f A s C l t o t h e m e l t ( F i g u r e 4 ) . An a n o d i c peak i n F i g u r e 4 a t +O.47 V a p p e a r s o n l y a f t e r t h e c a t h o d i c r e a c t i o n a t -O.4 V b u t , p r o b a b l y due t o f i l m i n g , r e p e a t e d s c a n s c a u s e t h e waves t o d i s t o r t and d i m i n i s h . The e l e c t r o c h e m i s t r y o f g a l l i u m chloroaluminate species i n a high temperature Al C l : NaCl: KC1 e u t e c t i c has been s t u d i e d ( 4 ) . The s t a n d a r d e l e c t r o d e p o t e n t i a l s a r e r e p o r t e d t o be G a ( I I I ) / G a ( I ) = O.766 V , G a ( I I I ) / G a ( 0 ) = O.577 V and G a ( I ) / G a ( 0 ) = O.199 V v e r sus A l ( A l C I : NaCl: KC1 e u t . ) r e f e r e n c e . Extremely low e l e c t r o a c t i v i t y was i n d i c a t e d a t a C e l e c t r o d e a f t e r t h e a d d i t i o n o f G a C l t o t h e b a s i c room t e m p e r a t u r e m e l t b u t t h e p e a k s a t c i r c a +O.2 V and +O.8 V i n t h e voltammograms o f n-GaAs may be t e n t a t i v e l y a s s i g n e d t o compounds o f G a ( I ) and G a ( I I I ) , r e s p e c t i v e l y , e i t h e r homogeneous o r s u r f a c e bonded. 3

3

3

3

3

B o t h g a l l i u m and a r s e n i c compounds

exist

i n several

oxidation


346


Figure 1.

INTERFACES

Computer-controlled network analysis system for photoelectrochemical cell admittance measurements

Figure 2. Cyclic voltammograms of n-GaAs in O.8:1 (upper) and 1.5:1 (lower) melts at 50 mVs' and 20 mVs' , respectively, nonilluminated, 40°C 1

1

347



GALE E T A L .

Figure 4.

Cyclic voltammogram (initial scan) of AsCl (O.136 mL) added to O.95:1 melt (12.12 g), ν = 100 mVs , C electrode 3

1

American Chemical Society Library 1155 16th St., N.W. Washington, D.C. 20036

348


INTERFACES

s t a t e s and t h e p r o b a b i l i t y o f c o m p l e x e q u i l i b r i a w i t h h a l o - s p e c i e s and t h e d e g r e e o f i r r e v e r s i b i l i t y o f t h e e l e c t r o n - t r a n s f e r p r o c e s s e s makes a b s o l u t e c o r r e l a t i o n s o f p o t e n t i a l peaks w i t h d e f i n i t i v e species d i f f i c u l t . An e s s e n t i a l p r o b l e m t o o , i s t o d i s t i n g u i s h between t h e t r a c e amounts o f d i s s o l v e d p r o d u c t s f r o m c o r r o s i o n o f t h e s e m i c o n d u c t o r and c h e m i c a l s t a t e s t h a t may be p r e s e n t i n t h e surface atomic l a y e r .


E l e c t r o l y t e Composition

Effects

The m a j o r e q u i l i b r i u m p r o c e s s i s g i v e n by e q u a t i o n ( 1 } , 2 A i d /

c o n t r o l l i n g the solvent

A1 C1 " 2

7

acidity

+ Cl"

(1)

From a p o t e n t i o m e t r i c model f o r t h e c h l o r a l u m i n a t e s p e c i e s p r e s e n t i n t h e s e i o n i c m i x t u r e s , an e q u i l i b r i u m c o n s t a n t has been d e r i v e d u s i n g t h e mole f r a c t i o n s c a l e , Κ * 7.0 χ 1 0 " at 40° (3J. A pCl" can be d e f i n e d a n a l o g o u s t o pOH" i n aqueous m e d i a , pCl~= - l o g i o C l T M i x t u r e s w i t h an e x c e s s o f A l C l w i l l be L e w i s a c i d s c o n t a i n i n g t h e e l e c t r o n d e f i c i e n t A 1 C 1 " i o n w i t h some A 1 C 1 " i o n , w h e r e a s when t h e m o l a r r a t i o becomes < 1:1 A l C l : BPC, r e s p e c t i v e l y , t h e m e l t w i l l be t e r m e d b a s i c and c o n t a i n d o n o r C l " i o n s t o g e t h e r w i t h A l Cl 1+" i o n . S u r f a c e i n t e r a c t i o n s between t h e s u b s t r a t e m a t e r i a l and t h e e l e c t r o l y t e can a f f e c t s i g n i f i c a n t l y t h e p e r f o r m a n c e o f c e l l s ( 5 ) and t h e s e a r e o f two main t y p e s ( i ) s o l v e n t a c i d - b a s e i n d u c e d i o n i z a t i o n o f s u r f a c e compounds, and ( i i ) t h e a c c u m u l a t i o n o f s o l u t e species i n the inner double l a y e r region at the semi conductor surface ( s p e c i f i c or superequivalent ion adsorption, organic adsorbates, e t c . ) . Such a c l a s s i f i c a t i o n i s n o t c l e a r c u t because the phenomenological d e f i n i t i o n o f s p e c i f i c i o n a d s o r p t i o n a t m e t a l e l e c t r o d e s (6) does n o t d i s c u s s t h e c h e m i c a l s t a t e o f t h e s p e c i e s , t h e e s s e n t i a l c r i t e r i o n b e i n g t h a t an e x c e s s o f t h e s p e c i e s must be p r e s e n t a t t h e p o t e n t i a l o f z e r o c h a r g e . Different i a t i o n o f t h e s e p r o c e s s e s r e q u i r e s a knowledge o f t h e c h e m i c a l forces involved in the e q u i l i b r i a or the adsorption ( e l e c t r o s t a t i c plus chemical f o r i o n s ) , the extent of i o n i z a t i o n or the adsorp t i o n i s o t h e r m , and t h e s u r f a c e p o t e n t i a l p a r a m e t e r s a s s o c i a t e d with e i t h e r process. Q u a n t i t a t i v e expressions of these e f f e c t s a r e r e s t r i c t e d i n t h e l i t e r a t u r e . An e x p l a n a t i o n o f t h e f l a t - b a n d s h i f t f o u n d i n aqueous s o l u t i o n s a r i s e s f r o m a c o n s i d e r a t i o n o f surface e q u i l i b r i a of the t y p e , 1 3

3

2

7

4

3

-M0H + OH"

-MO" + H 0

An a d d i t i o n a l p o t e n t i a l d r o p o c c u r s a c r o s s ( 7 ) , given by, Δφ

η |

= const

(2)

2

the Helmholtz

- (2.3RT/F){[pH] + 1 o g ( f

M n

-

. X

layer,

M n

-)}

(3)

22.

GALE

ET

i n w h i c h A

DL

349

n-G aAs-Molten-Salt Interphase

AL.

i s t h e p o t e n t i a l drop a c r o s s

t h e d o u b l e l a y e r and

f j Q - and X Q - r e s p e c t i v e l y a r e t h e a c t i v i t y c o e f f i c i e n t and mole f r a c t i o n o f i o n i z e d groups i n the s u r f a c e . A l i n e a r r e l a t i o n be tween t h e f l a t b a n d p o t e n t i a l , Y . , and t h e pH s h o u l d be e x p e c t e d as l o n g as t h e c o n t r i b u t i o n f r o m t h e s e c o n d t e r m i s p a r e n t h e s i s i s m i n i m a l . G r y s e , Gomes, Cardon and V e n n i k (8) have d i s c u s s e d the e f f e c t o f the double l a y e r p o t e n t i a l drop. F i g u r e 5 c o n t a i n s a summary o f t h e M o t t - S c h o t t k y p l o t s o b t a i n e d a t 1 KHz and d i f f e r e n t e l e c t r o l y t e c o m p o s i t i o n s r a n g i n g f r o m O.8:1 t o 1.75:1 m o l a r r a t i o s . The i n t e r c e p t s were c a l c u l a t e d from the l e a s t squares g r a d i e n t s taken i n the v o l t a g e r e g i o n s where f a r a d a i c p r o c e s s e s a r e l e a s t s i g n i f i c a n t , namely 2 . 0 t o O.6 V f o r t h e a c i d i c and 1.0 t o -O.5 V f o r t h e b a s i c m e l t s . Faradaic p r o c e s s e s become a p p a r e n t as h y s t e r e s i s i n t h e C-V p l o t s and t h e s e e f f e c t s give r i s e to considerable s c a t t e r in data, p a r t i c u l a r l y n e a r t h e 1:1 m o l a r r a t i o c o m p o s i t i o n . Least squares analyses o f t h e s e d a t a g i v e a s h i f t o f t h e f l a t - b a n d w i t h p C l " o f O.066 V ( s t a n d a r d d e v i a t i o n , σ = O.009 V ) , o r a p p r o x i m a t e l y ( 2 . 3 RT/F) V a t 4 0 ° . T h i s A V . / p C l ~ v a l u e f o r t h e (100) o r i e n t a t i o n n-GaAs i s a p p r o x i m a t e l y o n e - h a l f t h a t o b t a i n e d w i t h (111) n-GaAs c r y s t a l s ( 2 ) , i n d i c a t i n g t h a t t h e c r y s t a l s u r f a c e atom d e n s i t y and t y p e can be a s i g n i f i c a n t f a c t o r i n t h e i n t e r a c t i o n s between s u b s t r a t e and electrolyte. F l a t - b a n d p o t e n t i a l v a l u e s f o r (100) and (111) n - G a A s / m o l t e n s a l t i n t e r p h a s e s and f o r t h e (111) n-GaAs/aqueous e l e c t r o l y t e i n t e r p h a s e a r e compared i n T a b l e I.


f

f

TABLE Xtal

n-GaAs

Orientation

aqueous

(TTT)face

n-GaAs ( l l l ) f a c e

pH

AlC1 :BPC 3

II

(100)face

V (NHE)

Ref.

-O.95V

(£)

f b

II

n-GaAs

I

A1C1 :BPC 3

II

2.1

pH 12

-1.50V

pCl "2

-1.25V

pCl "12

+O.1OV

pCl"2

-O.80V

This

work

pCl'l 2

-O.20V

This

work

(2)

T y p i c a l l y i n aqueous e l e c t r o l y t e s t h e f l a t - b a n d p o t e n t i a l v a r i a t i o n p e r pH u n i t i s ( 2 . 3 RT/F) V ( 7 , S M 5 ) b u t i n t h e h i g h t e m p e r a t u r e A l C l : N a C l m o l t e n e l e c t r o l y t e s , U c h i d a and c o w o r k e r s Q 6 > Π3 have r e p o r t e d f l a t - b a n d s h i f t s o f 2 ( 2 . 3 R T / F ) V p e r p C l " u n i t f o r Sb-doped S n 0 and n - T i 0 semiconductors. 3

2

2

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Figure 6.

Power curves for n-GaAsO.124Mferrocene cell, electrolyte unstirred, illumination ~ 100 mW cm' 2

22.

GALE

ET AL.


351

The c o n s e q u e n c e s o f q u i t e s m a l l c h a n g e s i n t h e s u r f a c e c h a r g e can be s i g n i f i c a n t t o d e v i c e p e r f o r m a n c e . Figure 6 i l l u s t r a t e s t h e i l l u m i n a t e d c u r r e n t - v o l t a g e b e h a v i o r o f a ( 1 0 0 ) n-GaAs e l e c trode i n a melt c o n t a i n i n g t h e f e r r o c e n e / f e r r i c e n i u m redox couple. At t h e exact n e u t r a l p o i n t , V . -O.91 V , o r 1.04 V n e g a t i v e o f t h e redox p o t e n t i a l o f t h e f e r r o c e n e c o u p l e . As t h e band gap o f n-GaAs i s a p p r o x i m a t e l y 1.44 V , a n e g a t i v e s h i f t o f t h e band edges o f O.4 Y w o u l d i m p r o v e t h e o v e r l a p between t h e r e d o x c o u p l e e n e r g y l e v e l s and t h e v a l e n c e band e d g e . T h u s , i t may be p o s s i b l e t o " t u n e " p h o t o e l e c t r o c h e m i c a l c e l l s f o r o p t i m a l p e r f o r m a n c e by d e l i b e r a t e l y v a r y i n g t h e extent o f t h e surface charge w i t h s u i t able adsorbates. These p h o t o e f f e c t s have been d i s c u s s e d i n g r e a t er d e t a i l elsewhere (18). The m a g n i t u d e o f t h e e r r o r s i n d e t e r m i n i n g t h e f l a t - b a n d p o t e n t i a l by c a p a c i t a n c e - v o l t a g e t e c h n i q u e s c a n be s i z a b l e b e c a u s e ( a ) t r a c e amounts o f c o r r o s i o n p r o d u c t s may be a d s o r b e d on t h e s u r f a c e , ( b ) i d e a l p o l a r i z a b i l i t y may n o t be a c h i e v e d w i t h r e g a r d to e l e c t r o l y t e decomposition processes, (c) surface states a r i s i n g f r o m c h e m i c a l i n t e r a c t i o n s between t h e e l e c t r o l y t e and s e m i c o n d u c t o r c a n d i s t o r t t h e C-V d a t a , and ( d ) c r y s t a l l i n e i n h o m o g e n e i t y , d e f e c t s , o r b u l k s u b s t r a t e e f f e c t s may be m a n i f e s t e d a t the s o l i d e l e c t r o d e causing frequency d i s p e r s i o n e f f e c t s . In t h e n e x t s e c t i o n , i t w i l l be shown t h a t t h e e q u i v a l e n t p a r a l l e l c o n d u c t a n c e t e c h n i q u e e n a b l e s more d i s c r i m i n a t o r y and p r e c i s e a n a l y ses o f t h e i n t e r p h a s i a l e l e c t r i c a l p r o p e r t i e s .


f

Automated A d m i t t a n c e Measurements Some o f t h e e x p e r i m e n t a l t e c h n i q u e s t h a t have been d e v e l o p e d f o r s t u d i e s o f MIS s o l a r c e l l s , f o r e x a m p l e , m i g h t be a p p l i e d s u c c e s s f u l l y to photoelectrochemical c e l l s . F e a t u r e s common t o e l e c t r o c h e m i c a l s o l a r c e l l s and m e t a l - o x i d e - s e m i c o n d u c t o r ( M 0 S ) , M I S , o r S I S d e v i c e s have been r e v i e w e d i n a t h e o r e t i c a l c o m p a r i s o n o f t h e i r u n d e r l y i n g modes o f o p e r a t i o n (19). An e s s e n t i a l s t a r t i n g p o i n t f o r d e v i c e a n a l y s i s i s t o be a b l e t o model e q u i v a l e n t c i r c u i t t h a t a c c u r a t e l y r e p r e s e n t and r e f l e c t t h e m a t e r i a l p r o p e r t i e s and c e l l b e h a v i o r i n b o t h t h e s t a t i c a n d , h o p e f u l l y , t h e o p e r a t i o n a l modes. T o m k i e w i c z ( 2 0 ) has a p p l i e d a r e l a x a t i o n s p e c t r u m analysis technique t o the n-Ti0 /aqueous e l e c t r o l y t e interphase and he c o u l d a s s i g n p a s s i v e e l e m e n t s t o two s p a c e c h a r g e l a y e r s w i t h d i f f e r e n t doping l e v e l s . In t h e l i g h t o f p r e v i o u s work w h i c h has d e m o n s t r a t e d ( 2 T j t h a t t h e e q u i v a l e n t p a r a l l e l c o n d u c t a n c e t e c h n i q u e i s more s e n s i t i v e t h a n c a p a c i t a n c e measurements f o r d e r i v i n g s u f a c e s t a t e i n f o r m a t i o n i n MIS d e v i c e s , we have made a s e r i e s o f t h e s e measurements on a p h o t o e l e c t r o c h e m i c a l c e l l . For o u r i n i t i a l e v a l u a t i o n s , t h e i n t e r f a c e was n o t i l l u m i n a t e d and no r e d o x c o u p l e was added t o t h e e l e c t r o l y t e . B o t h t h e c a p a c i t a n c e and c o n d u c t a n c e methods d e r i v e e q u i v a l e n t i n f o r m a t i o n as f u n c t i o n s o f t h e a p p l i e d v o l t a g e and f r e q u e n c y , however, t h e i n a c c u r a c i e s that a r i s e i n the treatment o f data g e n e r a l l y are l a r g e r using 2

352

PHOTOEFFECTS AT SEMICONDUCTOR-ELECTROLYTE INTERFACES

c a p a c i t a n c e measurements ( 2 1 ) . F i g u r e 6 i l l u s t r a t e s an e q u i v a l e n t c i r c u i t f o r the semiconductor/molten s a l t interphase. The c a p a c i t a n c e and r e s i s t i v e e l e m e n t s a s s o c i a t e d w i t h t h e l a r g e a r e a c o u n t e r e l e c t r o d e and t h e c e l l g e o m e t r y have been i g n o r e d i n t h i s analysis. Mathematical treatments f o r equivalent c i r c u i t o f t h i s type f o r a s i n g l e l e v e l and a c o n t i n u u m o f s u r f a c e s t a t e l e v e l s have been p r e s e n t e d e l s e w h e r e ( e . g . , 1 0 , 2Ό, 2 1 , 2 2 J . The a d m i t t a n c e o f the reduced c i r c u i t a f t e r removing the i n f l u e n c e o f R L , Photoeffects at Semiconductor-Electrolyte Interfaces Downloaded from pubs.acs.org by NATL UNIV OF SINGAPORE on 05/05/18. For personal use only.

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The unknown p a r a l l e l RC e l e m e n t s t h a t c o m p r i s e t h e impedance ζ i n F i g u r e 7 c a u s e a s e r i e s o f maxima i n t h e G/ω v s . ω d a t a a t ωτ = 1 , from which the m a j o r i t y c a r r i e r time c o n s t a n t τ o f a s i n g l e l e v e l i n t e r f a c e s t a t e , R C., o r any g e n e r a l RC t i m e c o n s t a n t may be o b tainable. Superposition o f curves occurs i f the i n d i v i d u a l time constants are c l o s e l y spaced. F i g u r e 8 i l l u s t r a t e s t h e d a t a p o i n t s and t h e o r e t i c a l c u r v e f i t s f o r t h e (100) n - G a A s / O . 8 : l m e l t i n t e r p h a s e . To i d e n t i f y t h e s p a c e c h a r g e c a p a c i t a n c e and t h e b u l k r e s i s t a n c e e l e m e n t s , t h e f r e q u e n c y i n d e p e n d e n t c a p a c i t a n c e s were d e r i v e d f r o m t h e maxima i n l o g (G/ω) v s . log(aj) p l o t s , e . g . , F i g u r e 8 , a s (G/œ)max s/ and c o n d u c t a n c e s f r o m t h e maxima i n log(a)C) v s . l o g ω p l o t s e . g . , F i g u r e 9 . The p r o c e d u r a l s t e p s f o r m o d e l i n g were ( a ) f i r s t l y , e s t a b l i s h t h e l i m i t i n g l o w f r e q u e n c y c o n d u c t a n c e G as d e s c r i b e d a b o v e , t h e R b u l k C c p a r a m e t e r s , ( b ) model a c u r v e f o r the c i r c u i t o b t a i n e d from the b a s i c elements, ( c ) s u b s t r a c t t h e o r e t i c a l curve from experimental data t o determine d i f f e r e n c e maxima a n d , f i n a l l y , ( d ) s u c e s s i v e t r i a l and e r r o r i n s e r t i o n o f RC v a l u e s c o n s t i t u t i n g ζ t o a t t a i n b e s t c u r v e f i t t o e x p e r i m e n t a l data. I n F i g u r e 8 , t h e c i r c u i t e l e m e n t R f a r O.83 ΜΩ d e t e r m i n e s t h e d e g r e e t o w h i c h i d e a l p o l a r i z a b i l i t y has been a c h i e v e d i . e . , t h e a b s e n c e o f c o r r o s i o n p r o c e s s e s and f a r a d a i c l o s s e s due t o e l e c t r o a c t i v e i m p u r i t i e s o r e l e c t r o l y t e decomposition (cf. n-Ti02/ aqueous i n t e r p h a s e ( 2 2 ) , R f = 10 ΚΩ). A d d i t i o n o f a l a r g e p s e u d o - c a p a c i t y o f Rfar d i d not a l t e r the s l o p e o f the low f r e quency s i m u l a t e d p o r t i o n o f t h e c u r v e . A v a l u e o f C f r - O.1 yF c a u s e s a peak a t l o w f r e q u e n c i e s (

Fundamental Aspects of Photoeffects at the n-Gallium Arsenide

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