Charge Transfer at Illuminated Semiconductor-Electrolyte Interfaces

9 Charge Transfer at Illuminated Semiconductor-Electrolyte Interfaces 1

Downloaded by CORNELL UNIV on September 2, 2016 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1980-0184.ch009

A. J. NOZIK , D. S. BOUDREAUX,

and R. R. CHANCE

Corporate Research Center, Allied Chemical Corporation, Morristown, NJ 07960 FERD WILLIAMS Department of Physics, University of Delaware, Newark, D E 19711

A new heterojunction model for the semiconductor-electro lyte interface is presented that considers the electrolyte as a doped semiconductor and that predicts that hot photogen erated minority carriers can be infected into the electrolyte. Preliminary calculations are presented in support of the hot carrier injection hypothesis. Recent experimental results on the photoenhanced reduction of N on p-GaP cathodes are discussed and they appear to provide experimental evidence for hot electron injection. The importance of hot carrier injection for photoelectrochemical cells is also discussed. 2

In

r e c e n t years a great d e a l o f interest h a s d e v e l o p e d i n t h e field o f photoelectrochemistry

based

o n photoactive

semiconducting

trodes, e s p e c i a l l y i n t h e a p p l i c a t i o n o f these systems t o solar c o n v e r s i o n a n d c h e m i c a l synthesis ( 1 - 9 ) .

elec energy

I n F i g u r e 1, a c l a s s i f i c a t i o n

scheme i s p r e s e n t e d f o r t h e v a r i o u s types o f p h o t o e l e c t r o c h e m i c a l cells. T h e first d i v i s i o n is i n t o : ( a ) cells w h e r e i n t h e free e n e r g y c h a n g e i n t h e e l e c t r o l y t e i s zero

( e l e c t r o c h e m i c a l p h o t o v o l t a i c c e l l s ) , a n d ( b ) cells

w h e r e i n t h e free e n e r g y i n the e l e c t r o l y t e i s n o n z e r o

(photoelectrosyn-

t h e t i c c e l l s ) . I n t h e f o r m e r c e l l , o n l y one effective r e d o x c o u p l e i s p r e s e n t i n t h e e l e c t r o l y t e — t h e o x i d a t i o n a n d r e d u c t i o n reactions a t t h e a n o d e a n d c a t h o d e a r e i n v e r s e t o e a c h other. T h e n e t photoeffect 1

is thus t h e

Present address: Solar Energy Research Institute, Golden, CO 80401. 0-8412-0474-8/80/33-184-155$05.00/0 © 1980 American Chemical Society Wrighton; Interfacial Photoprocesses: Energy Conversion and Synthesis Advances in Chemistry; American Chemical Society: Washington, DC, 1980.

156

INTERFACIAL

PHOTOPROCESSES

ELECTROCHEMICAL PHOTOVOLTAIC CELLS ' (LIQUID JUNCTION SOLAR CELLS)

/

AG=0

/ \

PHOTOELECTROCHEMICAL CELLS \

PHOTOELECTROLYSIS CELLS (ENERGY STORING)

/

AG#0

r(t*.H 0-H +tC^) 1 I

8

[CC^+HgO-CHgO+OgJ

PHOTOELECTROSYNTHETIC CELLS

PHOTOCATALYTIC CELLS (e.g.,N +3H —2NH )


2

Figure 1.

Classification scheme for photoelectrochemical

2

3

cells

c i r c u l a t i o n o f c h a r g e e x t e r n a l to t h e c e l l , p r o d u c i n g a n e x t e r n a l p h o t o voltage a n d photocurrent

( a l i q u i d j u n c t i o n solar c e l l ) ; n o c h e m i c a l

change occurs i n the electrolyte. I n t h e p h o t o e l e c t r o s y n t h e t i c c e l l , t w o effective r e d o x c o u p l e s a r e p r e s e n t i n t h e e l e c t r o l y t e a n d a net c h e m i c a l c h a n g e o c c u r s u p o n i l l u m i n a t i o n . I f t h e free e n e r g y c h a n g e o f t h e n e t e l e c t r o l y t e r e a c t i o n is p o s i t i v e , optical energy

is c o n v e r t e d i n t o c h e m i c a l e n e r g y

labeled photoelectrolysis.

a n d t h e process i s

O n t h e other h a n d , i f t h e net electrolyte

r e a c t i o n has a n e g a t i v e free e n e r g y c h a n g e , o p t i c a l e n e r g y p r o v i d e s t h e a c t i v a t i o n e n e r g y f o r t h e r e a c t i o n , a n d t h e process

is labeled

photo-

catalysis. E n e r g y l e v e l d i a g r a m s f o r these three t y p e s o f cells a r e s h o w n i n F i g u r e s 2 a n d 3. T h e m o s t i m p o r t a n t aspects o f a l l p h o t o e l e c t r o c h e m i c a l cells a r e the nature of the semiconductor-electrolyte

junction a n d the photo

i n d u c e d c h a r g e t r a n s f e r process across t h e j u n c t i o n . A n e w m o d e l f o r

ANODE

e

C +h

+

C

+

CATHODE

C++ e~—•C

AG = 0

Figure 2. Energy level diagram for electrochemical photovoltaic cells. C / C is a redox couple in the electrolyte that produces the indicated anodic and cathodic reactions such that no net chemical change occurs. +

Wrighton; Interfacial Photoprocesses: Energy Conversion and Synthesis Advances in Chemistry; American Chemical Society: Washington, DC, 1980.

Wrighton; Interfacial Photoprocesses: Energy Conversion and Synthesis Advances in Chemistry; American Chemical Society: Washington, DC, 1980. T

AG

C"+2A

NET:

+

B"+ A — • B + A >0

PHOTOELECTROLYSIS

AG

+

A +e~-*A

A +e"-*A +

CATHODE

0*+ 2A T

d

T

H> TT,

, TgE, T . A s c h e m a t i c r e p r e s e n t a t i o n o f these c o m p e t i n g r

processes is d e p i c t e d i n F i g u r e 6 for n - t y p e s e m i c o n d u c t o r s . »-Ti0 .

H O L E TUNNELING TIMES.

2

Quantum mechanical tunneling

times w e r e c a l c u l a t e d f r o m t h e q u a s i c l a s s i c a l f r e q u e n c y f a c t o r o f t h e q u a n t i z e d states i n t h e d e p l e t i o n l a y e r a n d t h e i r t u n n e l i n g p r o b a b i l i t i e s (13). and

T h e c a l c u l a t i o n s d e p e n d u p o n t h e m i n o r i t y c a r r i e r effective mass the b a r r i e r t h i c k n e s s . D e t a i l e d c a l c u l a t i o n s h a v e b e e n m a d e f o r t h e

case o f n - T i 0

2

i n w h i c h d is t a k e n as 10 A , a n d v a l u e s o f 0.01 a n d 0.1

are u s e d f o r t h e h o l e effective mass ( r a * ) . h

A d o f 10 A represents a n u p p e r l i m i t t h a t y i e l d s v e r y c o n s e r v a t i v e estimates o f the t u n n e l i n g t i m e ; m o r e p r o b a b l e values o f d are f r o m 2 - 4 A.

T h e c o r r e c t v a l u e o f m * for T i 0 h

2

is not k n o w n , b u t i t is e x p e c t e d t o

b e l o w because the v a l e n c e b a n d o f T i 0 a v a l u e o f m * = 10" for T i 0 h

2

2

2

is a v e r y w i d e 2 p o x y g e n b a n d ;

has b e e n p u b l i s h e d (14). P r e s e n t c a l c u -


162

INTERFACIAL

PHOTOPROCESSES

lations u s e v a l u e s of 0.1 a n d 0.01 f o r ra * to test t h e s e n s i t i v i t y o f t h e h

results to m * . T h e d i m e n s i o n s o f t h e p o t e n t i a l w e l l f o r t h e case of n - T i 0 h

i n a q u e o u s e l e c t r o l y t e are U = 3 e V (10), V The

results of c a l c u l a t i o n s f o r n - T i 0

2

— 1 e V , w = 200 A (10).

B

that were made b y s i m p l y

2

m u l t i p y l i n g t h e f r e q u e n c y f a c t o r of t h e q u a n t i z e d state i n t h e d e p l e t i o n l a y e r b y t h e t r a n s m i s s i o n coefficient f o r t h e p o t e n t i a l b a r r i e r s h o w t h a t f o r t h e case w h e r e m * — 0.1, q u a n t i z e d states n e a r t h e b o t t o m o f t h e h

w e l l h a v e a t u n n e l i n g t i m e of a b o u t 5 X 10"

13

sec; t h e s p a c i n g b e t w e e n

levels is a b o u t 0.04 e V . Q u a n t i z e d states n e a r t h e t o p of t h e w e l l s h o w t u n n e l i n g times of a b o u t 1 X

10"

12

sec, a n d are s p a c e d a b o u t 0.01 e V

apart. W h e n t h e v a l u e of m * is r e d u c e d to 0.01, o n l y o n e state appears Downloaded by CORNELL UNIV on September 2, 2016 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1980-0184.ch009

h

i n t h e w e l l w i t h a n energy l e v e l 0.56 e V f r o m t h e w e l l b o t t o m ; f o r t h i s state r — 1 X 10" T

14

sec.

C a l c u l a t i o n s b a s e d o n resonance t u n n e l i n g b e t w e e n t h e s e m i c o n d u c t o r a n d e l e c t r o l y t e p o t e n t i a l w e l l s s h o w t h a t f o r m * — 0.1 T h

X

10'

13

t

=

2

sec at t h e b o t t o m of t h e s e m i c o n d u c t o r w e l l ; f o r a state of 0.5 e V

f r o m t h e b o t t o m of t h e s e m i c o n d u c t o r w e l l T — 3 X 10" T

13

sec. R e d u c t i o n

of t h e h o l e effective mass to 0.05 reduces t h e t u n n e l i n g t i m e f o r t h e state n e a r t h e b o t t o m of t h e s e m i c o n d u c t o r w e l l t o 1 X 10"

13

sec.

T h u s , i f i t is a s s u m e d t h a t m * lies b e t w e e n 0.1 a n d 0.05, t h e n o n e h

w o u l d e x p e c t T T ' S t o b e of t h e o r d e r of 5 X 10"

sec f o r cTs of 10 A , a n d

13

e n e r g y l e v e l spacings to b e o f t h e o r d e r of 0.1 e V . V a l u e s of d less t h a n 10 A decrease t h e T ' S a c c o r d i n g l y . F o r a d of T

3 A and with m * = h

T

T

= 3 X 10"

13

0.1, T

T

— 3 X 10'

sec f o r s i m p l e t u n n e l i n g , a n d

14

sec f o r resonance t u n n e l i n g f o r states n e a r t h e t o p of t h e

semiconductor well.

I f m * is r e d u c e d to 0.01, t h e n t h e r e s p e c t i v e T ' S h

T

f o r t h e 3 - A b a r r i e r a r e r e d u c e d t o 3 X 10"

sec a n d 4 X 10"

15

14

sec f o r t h e

s i n g l e state i n t h e s e m i c o n d u c t o r w e l l . T h u s , i f m * lies b e t w e e n 0.1 a n d h

0.01, t h e n one w o u l d expect T ' S to b e of t h e o r d e r of a b o u t 5 X T

10"

14

sec f o r a d of 3 A . HOLE

DIFFUSION

TIMES.

The

time

for

photogenerated

minority

carriers to diffuse across t h e d e p l e t i o n l a y e r u n d e r t h e i n f l u e n c e o f t h e i n t e r n a l e l e c t r i c field ( T ) , a n d b e t r a n s f e r r e d to t h e e l e c t r o l y t e across d

the semiconductor electrolyte interface ( T E ) c a n be estimated u s i n g a S

classical m o d e l a n d compared w i t h the q u a n t u m m e c h a n i c a l t u n n e l i n g t i m e . T h e d r i f t v e l o c i t y ( V ) i n t h e d e p l e t i o n l a y e r is V D

— fiE, w h e r e

D

E is t h e e l e c t r i c field ( E = V / u ; ) i n t h e d e p l e t i o n l a y e r , a n d p is m i n o r i t y B

carrier mobility. Hence, T

D

— w/V

D

— u; //i,V . 2

cross t h e s e m i c o n d u c t o r - e l e c t r o l y t e i n t e r f a c e ( T

B

s e

T h e time required to ) is d/V , T

where V

T

is

t h e t h e r m a l v e l o c i t y of t h e c a r r i e r . I f i t is a s s u m e d t h a t t h e h o l e m o b i l i t y , / i , for T i 0 h

2

is at least 100 c m / V sec (14), a n d t h a t V 2

10 A , a n d w — 200 A , t h e n t h e results y i e l d T

D

B

— 4 X

— 1 eV, d — 10"

14


sec, a n d

NOZIK E T A L .

9.

TSE =

3 X 10"

1 5

Charge

Transfer

163

at Interfaces

sec. T h u s , t h e c l a s s i c a l d i f f u s i o n t i m e s a r e o f t h e s a m e

o r d e r o f m a g n i t u d e as t h e t u n n e l i n g times f o r b a r r i e r thicknesses o f t h e o r d e r o f 3 - 5 A , a n d effective h o l e masses b e t w e e n 0.01 a n d 0.1. HOLE THERMALIZATION TIMES.

I f i t is a s s u m e d t h a t t h e r m a l i z a t i o n

of m i n o r i t y carriers i n t h e d e p l e t i o n l a y e r o c c u r s v i a c o n s e c u t i v e

single

p h o n o n - c a r r i e r c o l l i s i o n s , t h e n T H w i l l b e e q u a l to t h e n u m b e r of s u c h T

collisions r e q u i r e d to dissipate the b a n d b e n d i n g potential energy m u l t i p l i e d b y the characteristic time between c a r r i e r - p h o n o n collisions. T h e latter t i m e is c a l l e d t h e s c a t t e r i n g t i m e ( T m *fi/e. h


to b e 0.06 e V ( 1 5 ) , t h e n T V m V/0.06e. B

8 c a

t ) a n d b y definition, T

8 c a

t

=

I f t h e e n e r g y loss p e r s i n g l e p h o n o n - c a r r i e r c o l l i s i o n i s t a k e n For n-Ti0

h

c m / V sec, this y i e l d s T 2

T

H

2

T

H v i a single p h o n o n interactions is T T H

with V

B

— 1 e V , m * — 0.1, a n d ^ h

— 1 X 10"

13

=

h

—

100

sec.

C o n s i d e r a t i o n o f t h e q u a n t i z a t i o n of e n e r g y levels i n t h e d e p l e t i o n l a y e r leads to l o n g e r T tized

levels

T H

is greater

S.

T h i s occurs w h e n the spacing between

than the phonon

energy,

such

quan

that multiple

p h o n o n - c a r r i e r interactions are r e q u i r e d to dissipate energy.

T h e prob

a b i l i t y o f m u l t i p l e p h o n o n - c a r r i e r c o l l i s i o n s is m u c h s m a l l e r t h a n t h a t o f single p h o n o n - c a r r i e r

collisions, a n d the corresponding

t i m e constants a r e l o n g e r .

s p a c i n g s of a b o u t 0.1 e V p r o d u c e T Thus, for n - T i 0

2

characteristic

I n i t i a l estimates i n d i c a t e t h a t q u a n t i z e d l e v e l T H

' S o f t h e o r d e r o f 1 0 " 1 1 sec.

i n aqueous electrolyte, the

T H'S T

i n the semicon

ductor, i n v o l v i n g either single p h o n o n - c a r r i e r collisions ( T T H ~ 1 0 " or m u l t i p l e p h o n o n - c a r r i e r collisions ( T H ~ T

10"

11

be longer than either the expected tunneling time ( T T ^ c l a s s i c a l d i f f u s i o n t i m e across t h e d e p l e t i o n l a y e r ( T ^ d

T h i s means t h a t h o t p h o t o g e n e r a t e d Ti0

2

surface.

r

b e i n g faster t h a n

T

T

sec)

10" ) or the 14

4 X 10"

14

sec).

holes c a n b e e x p e c t e d to r e a c h t h e

T h e i r i n j e c t i o n i n t o t h e e l e c t r o l y t e as h o t holes w i l l

depend upon T

1 3

s e c ) , are e x p e c t e d t o

finally

H «

RELAXATION TIMES INELECTROLYTE.

F o r complete dipolar relaxation

i n a q u e o u s e l e c t r o l y t e , t h e c h a r a c t e r i s t i c t i m e constant i s 1 0 " sec ( 1 6 , 1 7 ) ; this is t h e t i m e r e q u i r e d f o r H

2

11

to 1 0 "

1 2

0 molecules to reorient t h e m

selves i n t o a n e w e q u i l i b r i u m s o l v a t i o n s t r u c t u r e a r o u n d a d o n o r o r a c c e p t o r species after t h e species h a s p a r t i c i p a t e d i n a c h a r g e

transfer

process. H o w e v e r , c o m p l e t e r e l a x a t i o n is n o t r e q u i r e d t o p r e v e n t reverse c h a r g e transfer f r o m t h e e l e c t r o l y t e t o t h e s e m i c o n d u c t o r . need

o n l y b e sufficient t o p r o d u c e

T h e relaxation

misalignment w i t h the quantized

e n e r g y levels i n t h e d e p l e t i o n l a y e r , o r at m o s t t o b r i n g t h e e l e c t r o l y t e energy level outside the energy range of the depletion layer. F o r t h e case of n - T i 0

2

w i t h large separation between the q u a n t i z e d

levels i n the depletion layer ( T T H ~ t o b e faster (13)

1 0 " s e c ) , t h e effective T 11

r

is e x p e c t e d

t h a n T T H , SO h o t c a r r i e r i n j e c t i o n is f e a s i b l e .


F o r the

164

INTERFACIAL

case w h e r e t h e r m a l i z a t i o n occurs ( T T H ~ 10"

13

PHOTOPROCESSES

v i a single p h o n o n - c a r r i e r

s e c ) , i t has n o t y e t b e e n e s t a b l i s h e d i f T

r

collisions

is faster t h a n T T H ;

c a l c u l a t i o n s o n t h i s p r o b l e m a r e i n progress ( 1 3 ) . H o t h o l e i n j e c t i o n f r o m m e t a l electrodes i n t o l i q u i d e l e c t r o l y t e h a s b e e n e x p e r i m e n t a l l y o b s e r v e d ( 1 8 ) . T h i s s u p p o r t s t h e i d e a t h a t effective r e l a x a t i o n processes i n l i q u i d e l e c t r o l y t e c a n b e fast c o m p a r e d t o elec t r o n i c r e l a x a t i o n processes i n solids. £-GaP.

T h e o c c u r r e n c e of h o t e l e c t r o n i n j e c t i o n f r o m p - G a P p h o t o -

cathodes i n t o v a c u u m is w e l l k n o w n i n s o l i d state p h y s i c s

(19,20,21).

T h i s effect is p r o d u c e d i n s e m i c o n d u c t o r s t h a t h a v e a s u r f a c e l a y e r w i t h a s m a l l w o r k f u n c t i o n (e.g., C s o r C s 0 ) s u c h t h a t a l a r g e d e g r e e of b a n d


2

b e n d i n g is i n d u c e d i n t h e s e m i c o n d u c t o r ; s u c h systems a r e l a b e l e d " n e g a t i v e e l e c t r o n affinity p h o t o c a t h o d e s "

I n F i g u r e 7, a n e n e r g y

(19,20,21).

l e v e l d i a g r a m is s h o w n f o r a p - G a P p h o t o c a t h o d e layer.

with a C s 0

surface

2

T h e large b a n d b e n d i n g p r o d u c e d b y the C s 0 layer places t h e 2

e n e r g y of t h e c o n d u c t i o n b a n d ( E ) of b u l k p - G a P a b o v e t h e v a c u u m c

l e v e l ( t h i s creates a c o n d i t i o n of n e g a t i v e e l e c t r o n a f f i n i t y ) .

Photogen

e r a t e d electrons s u b s e q u e n t l y i n j e c t e d i n t o v a c u u m suffer o n l y a f e w e l e c t r o n - p h o n o n c o l l i s i o n s a n d are e m i t t e d w i t h a h o t e n e r g y d i s t r i b u t i o n as s h o w n i n F i g u r e 7. I n t h e n e x t section, e x p e r i m e n t a l results a r e r e p o r t e d f o r a p - G a P electrode

that provide qualitative support

h o t e l e c t r o n i n j e c t i o n process. t h e p - G a P is 5 X 1 0

1 7

cm

- 3

for a

photoelectrochemical

I n this e x p e r i m e n t , t h e c a r r i e r d e n s i t y o f

and V

B

= 2.5 e V . T h e r e f o r e , t h e f o l l o w i n g

c a l c u l a t i o n s o n d i f f u s i o n a n d t h e r m a l i z a t i o n times a r e b a s e d o n these p a r a m e t e r s . T u n n e l i n g times h a v e n o t y e t b e e n c a l c u l a t e d f o r t h e p - G a P case. ELECTRON DIFFUSION TIMES.

For p-GaP,

c m / V sec ( 2 2 ) ; w i t h N — 5 X 1 0 2

Hence, T

D

— w /fxV 2

B

= 2 X IO

- 1 8

1 7

ra * e

cm" and V 3

sec. A l s o , T

S

E

B

=

0.5 a n d /* —

100

= 2.5 e V , w — 7 0 0 A .

— d/V

T

= 7 X 10"

15

sec

f o r d = 10 A . ELECTRON THERMALIZATION TIMES.

F o r consecutive single p h o n o n -

e l e c t r o n c o l l i s i o n s , t h e e n e r g y loss p e r c o l l i s i o n is 0.05 e V (20). —

T T H

IO"

14

(VB/0.05)

T e a t S

—

V *m */0.05e — 2 X IO" B /

12

e

sec; w

Hence, —

3 X

sec. T h u s , f o r t h e p - G a P case, T H is l o n g e r t h a n t h e T , a n d h o t electrons d

T

arrive at the semiconductor-electrolyte

interface.

F o r t h i s case, t h e

actual n u m b e r of single phonon-electron collisions resulting f r o m diffusion across t h e d e p l e t i o n l a y e r is e q u a l to

T

D

/ T

8

C

a t

=

7 collisions; hence only

a b o u t 0.35 e V of t h e 2.5 e V a v a i l a b l e f r o m t h e b a n d - b e n d i n g p o t e n t i a l is d i s s i p a t e d .



9.

NOZIK E T A L .

Charge

Transfer

at Interfaces

165

CSgO LAYER Figure 7.

Hot electron injection from a negative electron affinity cathode (Cs 0 on p-GaP) (19)

photo-

2

T h e T T H f o r single phonon-electron

collisions ( 2 X

10"

1 2

sec) is

s l o w e r t h a n that f o r the n - T i 0 case, a n d q u a n t i z a t i o n effects c o u l d s l o w 2

i t d o w n e v e n f u r t h e r as p r e v i o u s l y discussed. T h e r e f o r e , T

r

i n t h e elec

t r o l y t e c a n b e faster t h a n t h e T H i n t h e s e m i c o n d u c t o r f o r t h e reasons T

d i s c u s s e d earlier. T h i s means t h a t h o t e l e c t r o n i n j e c t i o n f r o m p - G a P electrodes i n t o l i q u i d electrolyte s h o u l d b e p o s s i b l e . Photoenhanced Reduction

of N

2

on p - G a P Cathodes

R e c e n t e x p e r i m e n t s (23) o n t h e p h o t o e n h a n c e d r e d u c t i o n o f N

2

in

a photoelectrochemical cell appear to provide qualitative evidence for a h o t e l e c t r o n i n j e c t i o n process.

T h e system s t u d i e d i s a p h o t o e l e c t r o

c h e m i c a l cell w h i c h contains a p - G a P cathode a n d a n A l - m e t a l

anode

i m m e r s e d i n a n o n a q u e o u s electrolyte of t i t a n i u m t e t r a i s o p r o p o x i d e a n d


166

INTERFACIAL

AICI3 d i s s o l v e d i n g l y m e

(1,2-dimethoxyethane).

When N

t h r o u g h t h e e l e c t r o l y t e a n d t h e p - G a P electrode band

g a p l i g h t , the N

2

is p a s s e d

is i l l u m i n a t e d

is r e d u c e d a n d is r e c o v e r e d

2

PHOTOPROCESSES

with

as N H ; A l is 3

c o n s u m e d i n t h e process a n d acts as t h e r e d u c i n g agent. A l t h o u g h t h e r e d u c t i o n of N

to N H w i t h A l is t h e r m o d y n a m i c a l l y f a v o r e d ( A G

Charge Transfer at Illuminated Semiconductor-Electrolyte Interfaces

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