632 J'. E[ecfrochem. Soc.: E L E C T R O C t t E M I C A L SCIENCE A N D T E C H N O L O G Y March 1983
4.0
140
12.0
10.0
0
8.0 x
6.0 8
2.0
I 0 5O 10 20 30 40
T
/ /
CDioxane , %
Fig. 3. Plots of the amount of Ca 2+ (O) and $r 2+ (O ) deposit vs. the dioxane' concentration in solution. Solutions used contained 1.0 • 10-~M of Ca 2+ and 5.0 X !0-6M of Sr ~+, respectively.
the aqueous e lec t ro ly t ic solution. Deposit ions were run ga lvanos ta t ica l ly wi th a cur rent dens i ty of 1.0 A / c m 2 in vigorous s t i r r ing solution. F igure 3 shows the incre- ment of the amount of Ca 2+, Sr 2+ deposi t in accord- ance with the change of d ioxane concentra t ion in so- lution. The re la t ionships be tween the amount of Ca ~+, Sr 2+ deposi t and solut ion concentrat ion, e lectrolysis t ime in d ioxane solut ion were found to be s imi lar to those shown in Fig. 1 and 2. Thus, the deposi t ion p ro - cesses in mixed solvent sys tem fol low the same be- havior as that of aqueous. The deposi t ion efficiency in 40% (a rb i t r a r i l y selected) d ioxane solut ion was found to increase app rox ima te ly wi th an order of two in com- par i son wi th tha t of aqueous.
F r o m the results of this invest igat ion, deposi t ion of o ther e lect roinact ive species on appropr i a t e subs t ra te can be achieved easi ly if p roper reagent (by Eq. [1]) has been chosen. F u r t h e r exp lora t ion of this tech- nique might lead to some useful applications. For example , th in films (wi th known quan t i ty ) of rad io- active Sr 2+ or Ba ~+ (both are strong ~-emit t ing spe- cies) ion can be p repa red on sui table subs t ra te and thus serve as a ca l ibra ted s t andard for rad ioac t iv i ty measurement . The possible s imul taneous deposi t ion of a lka l ine ea r th meta l ion wi th o ther e lect roact ive species might induce some in teres t ing techniques for the deposi t ion of b ina ry meta l oxides (or hydrox ides ) , such as SrTiO3, BaTiOs which are solar energy con- vers ion re la ted compound (4, 5). Also, the quan t i t a - t ive deposi t ion of Ca 2+, Sr2+ on e lec t rode can be used as a p reconcent ra t ion step and, thus, might become a useful ana ly t ica l p rocedure for t race analysis of these species.
Acknowledgment The au thor wishes to thank UIRL in Hsinchu, Tai -
wan for the full suppor t of this work.
Manuscr ip t submi t ted March 18, 1982; revised manu- script received ca. Nov. 5, 1982.
A n y discussion of this paper wi l l appear in a Dis- cussion Section to be publ ished in the December 1983 JOURNAL. Al l discussions for the December 1983 Dis- cussion Section should be submi t ted by Aug. 1, 1983.
Publication costs of this article were assisted by National Sun Yat-Sen University.
REFERENCES 1. H. A. La i t inen and W. E. Harris , "Chemical Ana ly -
sis," 2nd ed., pp.142-149, McGraw-Hi l l Book Com- pany, New York (1975).
2. P. Delahay, "New Ins t rumenta l Methods in Elec t ro- chemistry ," p. 47, Interscience, New York (1954).
3. V. K. La Mer, Ind. Eng. Chem., 44, 1270 (1952). 4. M. S. Wrighton, A. B. Ellis, P. T. Wolczanski , D. L.
Morse, H. B. Abrahamson, and D. C. Ginley, J. Am. Chem. Soc., 98, 2774 (1976).
5. R. D. Nasby and R. K. Quinn, Mater. Res. Bull., 11, 985 (1976).
Mechanism of Hole Injection on Ferric Oxide Photoelectrodes
Tamds Pajkossy
Hungarian Academy of Sciences, Central Research Institute for Physics, Budapest, H-1525, Hungary
I t seems tha t ferr ic oxide is advantageous as a semi- conductor photoelec t rode for ut i l izing solar energy (1-10). Fer r ic oxide is an n - type semiconductor , its bandgap is reasonable for such purposes, i t can be m anufac tu r ed eas i ly and cheaply, and i t is r easonab ly stable. I t does, however , suffer f rom the d isadvantage of low quan tum efficiency. The efficiency can be in- creased if the surface processes are understood, and i t is known how to suppress surface recombinat ion.
Recently, analysis of photo t rans ien ts was used by Iwanski et al. to invest igate processes tak ing place on i l lumina ted fer r ic oxide electrodes (8). The resultw of s imi lar exper iments a re presented here. Our a{m was to de te rmine whe the r hole in ject ion at the in te r - face proceeds d i rec t ly from the valence band or via surface states. Wi th this in mind, the photocur ren t was measured on fer r ic oxide electrodes at constant e lec t rode poten t ia l and s l igh t ly modula ted i l lumina-
t ion as a funct ion of reducing agent concentrat ion. The average value of the pho tocur ren t was measured direct ly, and the cur ren t t ransients due to l ight modu- la t ion were recorded, using the s ignal averaging tech- nique.
Experimental Ferr ic oxide e lect rodes made b y the rma l oxida t ion
of i ron specimens were used. The detai ls of p r e p a r a - t ion and charac ter iza t ion of these electrodes a re re - por ted e lsewhere (10). The electrodes behave s imi- l a r ly to those repor ted in Ref. (4 and 7); f rom the convent ional ly de te rmined Mot t -Scho t tky plots a donor dens i ty of 101S/cm 3, and a f la tband potent ia l of a round --0.35V vs. sa tu ra t ed calomel e lec t rode (SCE) at pH 9.0 were evaluated. The long wave length edge of the spec t ra l response of the pho tocur ren t was found to be a round 610 rim, indica t ing that the bandgap of the semiconductor is about 2.1 eV. The overa l l oxide thickness was 0.15 ram.
VoZ. I30, No. 3 HOLE INJECTION 633
The solutions were 0.2M borate buffers of pH 9.0 With different concentrat ions of KI (0-22 mM). These solutions were carefully deaerated before and dur ing experiments by means of bubbl ing high pur i ty n i t ro- gen. The electrode potent ia l was main ta ined at 0.2V vs. SCE, since at this potential only KI is oxidized under i l luminat ion (10).
The measurements were made using a s tandard three-electrode cell, whose overall resistance is around 30~, de termined by extrapolat ion of high f requency impedance data. From the same impedance data the cell capacitance was also evaluated; it was found to be less than 1 ~F, thus, the cell response t ime is less than 30 ~sec. (The change in KI concentrat ion of the solution had only a minor effect on the cell t ime constant.)
A med ium speed potentiostat (AFKEL 415.5 ~sec rise t ime) and a current amplifier of 30 ~ e c rise t ime range (Keithley 427) were applied. The electrode was steadily i l luminated by a 150W tungsten lamp, fed from a d-c power supply, and by a smal ler lamp (50W), whose light was in ter rupted by a rotat ing sector. This sector gave rec tangular l ight pulses of 60 ~sec rise t ime and about 5 msec dura t ion every 30 msec. The light modulat ion depth was about 1%. (The use of white l ight may seem inexact in photoelectro- chemical measurements ; however, as our pre l iminary exper iments revealed, the measured t ransients were of the same shape at any wavelength, they differed from each other only in height.)
It is seen f rom the above data that the t ime con- stants of the cell, electronics, and shut ter are much smaller than 10 msec, this value being a characteristic decay t ime found in the experiments.
The cur ren t t ransients were recorded by means of an averaging t rans ient digitizer (KFKI, Hungary) . The number of the t ransients repeated and averaged was usual ly 21~ = 4096.
Theory As has been shown in detai l elsewhere (10) the
steady state photocurrent on ferric oxide at constant potential is highly influenced by the concentrat ion of the reducing substances, i.e., hole acceptors in the solution. The difference between the photocurrent and dark current , which we call excess photocurrent, j ', depends on the concentrat ion of reducing agent in the solut ion in steady state according to Eq. [1]
l / i s ' -- (1/jh) (1 + kz/k2Cred) [1]
where 3h is the hole flux to the surface, and kl and k2 are phenomenological rate coefficients for recombina- t ion and injection, respectively; is' is the steady-state excess photocurrent; and Cred is the concentrat ion of the reducing agent at the interface.
Equat ion [1] was obtained taking into account the following (10): Photogenerated charges in the semi- conductor space charge layer are separated by t rans- port processes, the details of which are beyond our present scope. A hole flux reaches the surface of the semiconductor, where holes are ei ther injected into the solution and react with a hole acceptor, or recom- b i n e with electrons in the semiconductor. At med ium electrode potentials, holes react only with s trongly re- ducing substances (e.g., [Fe(CN)6] 4-, I - ) , not with water molecules. At these electrode potentials there is competit ion between hole inject ion and recombina- tion; the competi t ion between the different hole ac- ceptors can be neglected. By means of Eq. [1], from the dependence of excess photocurrent on reducing agent concentrat ion the hole flux and the ratio of the rate constants can be obtained.
A n u m b e r of kinetic models can be formulated for steady state leading to Eq. [1] (11-14). The surface processes invclved in these models can be summarized as follows:
Hole inject ion proceeds either directly (model B) or via surface states (model A). Recombinat ion is as- sumed to proceed via surface states only (15). These two al ternat ive kinetic models are i l lustrated in Fig. 1. In order to be able to decide which of the two s im- plified models is more sui table for the i l luminated ferric oxide electrode, rate equations are established and compared with light modulat ion exper iments for both cases.
Let us suppose, for both cases, that hole current jh arr iving at the surface responds immediate ly to the change of i l luminat ion intensity, because the charge carrier t ransport in this semiconductor is considered to be very fast in comparison with surface processes. This can be supported by the results of photocurrent rise t ime calculations given in Ref. (13), being in the order of magni tude of 10-~-lO -~ sec. The charac- teristic decay t ime presented here, and ascribed to surface processes, is at least one order of magni tude longer.
On the other hand, the diffusion of hole acceptors in the l iquid phase can also be considered to be very fast. This was elsewhere demonstrated (10) as a con- sequence of the measurements being carried out, using an i l luminated rotat ing ferric oxide electrode.
Thus, the t ranspor t processes in both phases can be regarded as not to be rate de termining and may be ignored, allowing our a t tent ion to be centered on the surface processes. The role of surface states in our models is to act as intermediate states of charge. Their physical and /or chemical na tu re is not known, and from the present point of view their na ture is quite i rrelevant .
Let us suppose for both models that the part ial order for every reaction par tne r in the surface pro- cesses is one. A remark needs to be made concerning this assumption: The surface concentrat ion of the hole acceptor in the l iquid phase is considered to be pro- port ional to the bu lk concentration. In Ref. (10) it has been shown that the competit ion kinetics, ex- pressed in the form of Eq. [1], holds only if the sur- face and bulk concentrat ions of the reducing substance are proport ional to each other, i.e., weak adsorption O c c u r s .
In both models the measured excess photocurrent is the difference between the hole flux, ja, and the electron flux due to recombination, Jr
j ' = J h - Jr [2]
In the following the rate equations are presented. We calculate the current response of suddenly increasing i l luminat ion for both models.
Model A (Fig. 1A) Let the surface charge density of holes captured by
surface states be denoted by p, then
dp/dt -~ -~ 3h --. kiCred P - - krnep [3]
where kr is the rate coefficient of surface recombina- tion, ne the electron density at the interface, and ki
A B
MODEL A MODEL B
R~IECOMBINATIO N
t .1 RECOMBINATION CAPTURE BY HOLE FLUX HOLE FLUX URFACE STATES
I l
" ' - - " INJECTION
Fig. I. Two possible kinetic schemes of surface reactions. Surface states are denoted by "S".
634 J. E l e c t r o c h e m . Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y M a r c h I983
the ra te coefficient of hole in ject ion into the solution�9 Since both kr and ne are thought to be constant at con- s tant e lec t rode potent ia l , krne wil l be constant and de- noted by kr'. If, at t = 0, the l ight in tens i ty is in- creased ins tan taneous ly f rom I to I + AI, then the hole flux, 3h, increases f rom jh ~ to jh ~ + Ajh. The l a t t e r change wi l l be considered as an increase of s tep func- t ion form. In this case Eq. [3] has the form af te r r e a r r angemen t
alp~dr + (kiCred -~ kr ' )p = j h ~ + ~Jh " u ( t ) = 0 [4]
where u ( t ) is the uni t s tep funct ion (16). Since under s teady i l lumina t ion d p / d t _--_ 0, the
ini t ia l condi t ion is given as the s t eady- s t a t e solut ion of Eq. [4], i.e.
p ( t < 0 ) = "h~ 3 i red "~- kr ' ) [5]
Thus the solut ion to Eq. [4] equals
p ( t ) : (kiCred -~- kr ' ) - 1 . {jh o _}. Ajh �9 u ( t )
�9 [ 1 - - exp ( - - (k iCred+ kr') " t ) ]} [6]
The e lec t ron flux due to recombinat ion, Jr', is equal to kr'p, so for t > 0, JA', the excess pho tocur ren t f rom model A, using Eq. [2] and [6], is given as
3A" : [kicred/(kicred-~- k r ' ) ] {3h ~ -~ A3h(1 -~- (kr'/kiCred)
�9 e x p [ - - (kiCred "-~ kr ' ) " t ] ) } [7]
Model B (Fig. 1 B) For the analogous de r iva t ion we have to take i t
into account that only the ~ ---- kiCred/(kiCred -~ ka) f ract ion of the hole flux is in jected into the solution, the remain ing (1 -- ~) f ract ion is cap tu red b y surface states. The phenomenologica l ra te coefficient of cap ture is denoted by ka. Genera l ly the ra te of hole cap ture by surface states is p ropor t iona l to the occupancy of these s tates by electrons (15). In view of the smal l l ight pe r tu rba t ion applied, the occupancy can be re - garded as constant, and therefore in the express ion of ~, it is incorpora ted into the phenomenologica l ra te coefficient ka. In this case for the surface charge densi ty of holes, the fol lowing balance equat ion holds
d p / d t ~- Jh (1 - - ~) - - kr'p [8]
S imi l a r ly to the de r iva t ion appl ied for model A, using i l lumina t ion of the same s tep form, and tak ing ini t ia l condi t ion for t < 0
P ( t < 0) = ( jh /kr ' )
o n e gets for the excess pho tocur ren t f rom this model , i 'm for t > 0
J' = $" {Jh ~ + hJh [1 + (1/D (1 - - ~) �9 exp ( - - k r ' . t ) ]}
[9] If the i l lumina t ion of the e lect rode is modula ted by smal l r ec tangu la r pulses, the pho tocur ren t t rans ients can be compared wi th Eq. [7] and [9]. Right at the s ta r t of the l ight pulses an immedia te increase of pho tocur ren t is expected. The increase for both models is the same, and equals ~Jh. Jus t a f te r the pho tocur ren t j u m p a decay por t ion is expected�9 The ini t ia l s lope of t h e t rans ients for mode l A is
djA'/d$ ~ - - j h " kr' [ 1 0 ]
which is seen to be independen t of Cred. Fo r model B, however , one finds
djB' /d t ~ -- Jh " k / � 9 (1 - - ~) = - - jh" kr'
�9 ka/(kiCred + ]Ca) [11] In t roducing the nota t ion
= - - (1/Ajh) (d j ' /d t ) t-,o [12]
one finds for model A the expression
�9 A ---- 1/kr ' [13]
whereas the same t ime constant for model B is
�9 B -- (1 /kr ' ) (1 + kiCred/ka) [14]
If the modula t ion dep th is ve ry small , tha t is, hi < < I hence ~Ja < < Jh ~ then the average va lue of j ' under modula ted i l lumina t ion can be considered to be t h e
same as tha t under constant i l luminat ion, tha t is, j ; is' so the average excess pho tocur ren t for model A can be ca lcula ted as
1/jA' -= (1/jh ~ (1 + kr ' /k iCred)~ l / i s ' [15]
Both Eq. [15] and [16] a re of the same form as Eq. [1]; but the phys ica l meaning of the two fo rmer equations is more specified.
Results and Discussion The t rans ients in solutions conta ining different con-
centra t ions of KI can be seen in Fig. 2. The descending par t of the t rans ients depends on KI concentrat ion. Consequent ly model A must be inadequa te (cf. Eq. [ 1 0 ] ) .
The comparison be tween model B and exper imen t s was as follows: Since the r ise t ime of the t rans ients is about 1 msec (not zero as in our oversimplif ied model ) , the ini t ia l slope of the descending par t can be de te rmined wi th l imi ted accuracy only. However , the expe r imen ta l values, according to Eq. [14], de- pend l i nea r ly on Cred (Fig. 3). F r o m the Slope and in tercept of the T vs. Cred plot, ka/k i can be de termined. According to least squares fit ka/k i : 23 • 6 mM. As said above, ka/ki can be de te rmined independen t ly f rom the is' vs. Cred curve (Eq. [16]). F rom the s t eady- s ta te measurement , ka/ki = 36 • 1 mM (Fig. 4). Given the simplif icat ions of the model, these two values agree reasonab ly well.
Qual i ta t ively , the same tendency of ini t ia l slopes was observed in the solutions of two o ther reducing substances, K4[Fe(CN)s ] and Na2SO3; the charac te r - istic t ime of the decay of the t ransient , T, s ignif icant ly increased wi th the i r concentra t ion in the solution,
o
I i I I I 0 1 2 3 t-to(mS)
Fig. 2. Some representative current transients for different con- r of KI in 0.2M borate buffer of pH 9.0 (1-0 raM, 2-9.5 mM, 3-16.3 mM, 4-18.2 raM). [n each cose the base lines are made to coincide.
VoL 130, No. 3 HOLE INJECTION 635
~(ms)
20
I I
I I 10 20 Cred (mM)
Fig. 3. Dependence of 1; on CreW. The straight line is the least squares fit (cf. Eq. [14]).
indicating that model A is inappropriate also with these solutes.
Consequently, model B appears to be the more suit- able for describing hole injection from ferric oxide, i.e., holes are injected into the solution directly from the valence band, not via surface states.
This statement seems to be reasonable if we con- sider the energetics of the surface processes. The location of the valence bandedge of ferric oxide is 2.2 eV at pH 9.0 (17), the redox potential of the I - / I~ couple is 0.62 eV on the hydrogen scale. (The E~ values for the two other redox systems, [Fe(CN)6]4-/[Fe(CN)6] a- and SO82-/SO42- at pH 9.0, are 0.36 eV and --0.60 eV, respectively). Taking these data into consideration, hole injection from the valence band, since this process is highly exothermic, is energetically possible. It is not possible in view of there being insufficient data, however, to give any estimate of the phenomenological rate coefficients as they depend upon many factors: electrode potential, illumination intensity, nature of solute, etc. Our fur- ther work is aimed at the investigation of these de- pendences.
Acknowledgments The author is indebted to Dr. R. Schiller and to
Dr. L. Nyikos for stimulating discussions and help.
Manuscript submitted March 30, 1982; revised manu- script received Nov. 3, 1982.
Any discussion of this paper will appear in a Dis- cussion Section to be published in the December 1983 JOURNAL. All discussions for the December 1983 Dis- cussion Section should be submitted by Aug. I, 1983.
Publication costs of this article were assisted by the Central Research Institute for Physics.
I I |
-1 -3 ~ e (j',) .~
(A 4)
/Y ,o
I I I 40 80 120 Cred-l(M -1)
Fig. 4. Dependence of average excess photocurrent on crea. The straight line is the least squares fit (cf. Eq. [16]).
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