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J . Phys. Chem. 1988, 92, 4676-4679
range of inert salt and surfactant concentration. It is noteworthy that the only parameters, besides the micellar rate constant which cannot be measured independently, are the ratios of the hydrophobic contributions to the transfer constants. Moreover, our generalized two-pseudophase approach reduces to the well-known equations of Berezin and of ionic-exchange models under limiting conditions and provides a very reasonable estimate of the degree of dissociation of the micelle from the fit of the kinetic data. Acknowledgment. We are grateful to CNR, MPI, and the European Research Standardization Group of the U S . Army under Contract No. DAJA 45-85-C-0023 for support of this work. We acknowledge pleasant discussion with Prof. L. Romsted during the Euchem Conference in Assisi, June 1987.
analytical concentration of the micellized surfactant (mol L-1)
analytical concentration of the J species (mol L-]) analytical concentration of the added salt; Csrefers to the analytical concentration of the inert ion as in its definition in eq 8 distribution coefficient defined in eq 9 ionic strength generic species J total transfer constant of the j species hydrophobic-transferconstant electrostatic-transfer constant for all kinds of K is the reciprocal of K, K' = 1 / K KLM = KL/KM KLN
=
KL/KN
K , = KLIKS
List of Symbols Boltzmann constant second-order rate constant on the micellar surface second-orderrate constant observed in the presence of surfactant value of k," in the aqueous pseudophase at the ionic strength calculated by using eq 15 normalized k,; k,' = k,/( 1 - cdu') observed second-order rate constant in homogeneous solution specific second-order rate constant at zero ionic strength specific second-order rate constant at infinite ionic strength number of molecules or moles radius specific micellar reaction volume (L mol-I) specific micellar volume (L mol-') mole fraction ionic charge constant in eq 2 constant in eq 14 Bjerrum length, BI = e2/4rtt,,kBT
"exchange constant" of U and V defined as the ratio Kv/Ku (also subscript) reactive counterion (Le., IrCI:-) (also subscript) reactive co-ion (i.e., Fez+) (also subscript) inert co-ion (Le., Na+) aggregation number of the micelle correlation coefficient (also subscript) inert counterion (Le., CI- or SO:-) =
aNaggr
bracketed quantity in the rhs term of eq 18 Ihs term in-eq 18 ionization degree of the micelle activity coefficient of the j species Debye-Hiickel reciprocal length proportionality constant in eq 6a potential subscript: bound or in the micellar pseudophase subscript: free or in the aqueous pseudophase standard state of nonelectrostatic (or hydrophobic) contributions, defined at infinite ionic strength subscript: refers to micellar phase or to micelle subscript: refers to aqueous phase
Surface Recombination Velocity Measurements of CdS Single Crystals Immersed in Electrolytes. A Picosecond Photoluminescence Study D. Benjamin and D. Huppert* Sackler Faculty of Exact Sciences, School of Chemistry, Ramat- Aviv, Tel- Auiu 69978, Israel (Received: June 8, 1987; In Final Form: January 19, 1988)
The effect of solution composition and concentration on the luminescence decay profile is measured for CdS single crystals immersed in various aqueous solutions. The surface recombination velocity is strongly dependent on the ionic solution composition and concentration. The experimental data are explained in terms of the chemisorption of ions on the CdS surface.
Introduction In previous studies, the photocurrent and photopotential transients of CdSe and CdS photoelectrochemical cells were measured with time resolution of a few nanoseconds.'V2 It has been noticed that significant photocharge recombination occurred within shorter time periods, probably of the order of the charge separation time. To increase the time resolution and observe ultrafast recombination processes, we measured on the picosecond time scale the timeresolved photoluminescence of CdS crystals immersed in aqueous electrolyte solution^.^^^ The luminescence time dependence is determined by bulk and surface recombination rates, the carriers ( 1 ) Harzion, Z.; Croitoru, N.; Gottesfeld, S. J . Electrochem. SOC.1981, 128. 551. (2) Harzion, Z.; Croitoru, N.; Huppert, D.; Gottesfeld, S . J . Efectroanal. Chem. 1983, 150, 511. (3) Evenor, M.; Gottesfeld, S.; Harzion, Z.; Huppert, D. J . Phys. Chem. 1984, 88, 6213. (4) Huppert, D.; Gottesfeld, S.; Harzion, Z.; Evenor, M. Ultrafast Phenomena; Auston, D., Eisenthal, K. B., Eds.; Springer-Verlag: Berlin, 1984; Vol. IV, p 181.
0022-3654/88/2092-4676!$01.50/0
diffusion constant, and the laser absorption cross section. The mathematical analysis assumes a semifinite uniform semiconductor that is irradiated by a picosecond laser pulse. Electron-hole pairs are generated at a rate g(x,t) and immediately thermalized to give free carriers. The concentration of the excess carriers is very high and therefore eliminates the space charge region by complete band flattening. Also, due to this high excess carrier concentration, the bulk recombination obeys pseudo-first-order kinetics with a characteristic lifetime Q,. The time-dependent carrier concentration, An(x,t) = Ap(x,t) can be described by the continuity equation5
where D*, the ambipolar diffusion coefficient: is 1.2 cm2/s (ref 7-9) for CdS. The instantaneous luminescence intensity, taking (5) Vaitkus, J. J . Phys. Status
Solidi 1976, 34A, 169.
(6) Van Roosbroeck, W. Phys. Rev. 1953, 282, 91.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 16, 1988 4677
CdS Single Crystals Immersed in Electrolytes into account self-absorption, is given by
I ( t ) = k,JmAn2(x,t) 0 exp(-x/d) d x
(2)
where d is the inverse of the absorption cross section at the absorption edges and k, is the second-order radiative rate constant. The boundary conditions are6 aAn(x=O,t) (3) where S is the surface recombination velocity (SRV). Our simulations for CdS show that large S values decrease the effective decay time. In the extreme case, when S is very small, i.e., S < 5 X lo3 cm/s, or very high, S > lo6 cm/s, the shape of the luminescence curve is not very sensitive to the exact value of S.3 The reason for that in case of small S values is that the SRV is too slow compared to the bulk recombination or to the diffusion of the carriers, and when S is very large the overall surface recombination is diffusion controlled. In our previous work3v4we found that very concentrated sulfide-polysulfide aqueous solutions decrease the luminescence quantum yield as well as the effective lifetime, corresponding to an increase of S by several orders of magnitude. Sulfide and polysulfide ions are used as redox couples in CdS and CdSe photoelectrochemical which are known to exhibit high solar to electric conversion efficiency. Sulfide ions are also known to adsorb at the surface of CdS ~ r y s t a 1 . l ~It is therefore assumed that the adsorbed sulfide ions enhance the surface reactivity by serving as a mediating center, in the photocharge transfer, to the acceptor in the solution. According to Wilson,14 the overall process of charge transfer from the semiconductor to the redox couple in solution includes two stages, which are for an n-type semiconductor
The second step, eq 4b, involves mass transport from the solution toward the surface. The rate of step 1 is very large, since we found that the surface recombination velocity is high. In such a case we expect step 2 to be slower than 1, and hence step 2 should be the rate-limiting step. In a recent study15we combined Wilson’s mechanism for charge transfer in CdS photoelectrochemical cell containing polysulfide solution with the picosecond study findings which showed that the interface exhibits high surface capture rate constants for both holes and electrons. Our simulation of current versus voltage curves, using S > lo5cm/s, showed significant conversion efficiencies under normal continuous illumination conditions. In this study we obtained quantitatively the surface recombination velocities of CdS immersed in several electrolyte-aqueous solutions. For each redox couple we varied the solution concentration from lo-’ to lo-’ M. By computer fits we estimated the SRV for each concentration and redox couple.
Experimental Section The schematics of the optical arrangement is described elsewhere.16 CdS single crystals were irradiated by a 352-nm, 25-ps (7) CRC Handbook of Chemistry and Physics, 62th ed.; CRC Press: Boca Raton, FL. (8) Wolf, M. J . Vac. Sci. Technol. 1975, 12, 984. (9) Wolf, H. F. Semiconductors; Wiley: New York, 1971; p 33. (10) Hodes, G.; Manassen, J.;Cahen, D. Nature (London) 1976,261,403. (11) Ellis, A. B.; Kaiser, S. W.; Bolts, J. M.; Wrighton, M. S.J . Am. Chem. SOC.1976, 98, 1635. (12) Miller, B.; Heller, A. Nature (London) 1976, 262, 680. (13) Inoue, T.; Watanabe, T.; Fujishima, A,; Honda, K.; Kohayakuwa, K. J . Electrochem. SOC.1977, 124, 719. (14) Wilson, R. H. In Photoeffects at Semiconductor-Electrolyte Interfaces; Nozik, A. J., Ed.; American Chemical Society: Washington DC, 1981; p 103. (15) Evenor, M.; Huppert, D.; Gottesfeld, S.J . Electrochem. SOC.1986, 133, 296. (16) Huppert, D.; Kolodney, E. J . Chem. Phys. 1981, 63, 401.
I
0
800
1600
T( sec 1
Figure 1. Experimental (dashed lines) and simulated (solid lines) photoluminescence decay curves for CdS single crystal obtained for an excitation wavelenght of 352 nm: (a) crystal immersed in distilled water, following chemical etching in 6 M HC1; (b) crystal immersed in 3 X lo-’ M of CuS04 solution; (c) 7 X lod M; (d) 2 X lo4 M.
1311-
0
800
1600
T(sec) Figure 2. Experimental and simulated photoluminescence decay curves for CdS single crystal immersed in 13-/1- aqueous solutions: (a) crystal immersed in distilled water, following chemical etching; (b) crystal immersed in 3 X 10” M of 13-/1-solution; (c) 7 X M. (d) 1 X lod M; (e) 3 X lo4 M. pulse (the third harmonic of a mode-locked Nd3+:YAG laser). The excitation level used in our experiments was of the order of lOI9 photons/cm3, based on the laser intensity and the absorption cross section. Photoluminescence was measured in the front surface mode. Colored glass filters (Schott GG 495) were placed before the streak camera (Hamamatsu Model C939) entrance slit to block the scattered light of the excitation beam. The output of the streak camera was imaged onto a silicon-intensified Vidicon connected to an optical multichannel analyzer (PAR 1205D). The streak records were averaged by a microcomputer. The hexagonal n-type CdS single crystals (Cleveland Crystals) were 1-2 mm thick, had a resistivity of 1-10 Cl cm-’ (donor concentration N D = 2 X 10l6 ~ m - ~and ) , had a surface perpendicular to the C axis. The surface was polished before the chemical etching by 0.015-pm alumina. Etching was carried out with 6 M HCl for 60-120 s, followed by rinsing with distilled water. All chemicals were of analytical grade. Solutions of 13-/I- were prepared by dissolving KI and I2 in water at a 1O:l ratio, respectively. Polysulfide solutions were prepared by dissolving Na2S and sulfur in water at a 1:2 ratio, respectively. The photoluminescence experiments
4678
The Journal of Physical Chemistry, Vol. 92, No. 16, 1988
Benjamin and Huppert I
1
I
" 3 I c
I
I
I
I
I
I
1
-18
i
T(sec)
' LOG ! 4 8
'
'
'
-32 -1'6 00 C 0N C E NT RAT I 0N Figure 5. Adsorption isotherm of 13-/I-. The solid curve is the calculated adsorption isotherm. The squares are the recombination velocities derived from Figure 2. - 3 4 4
Figure 3. Experimental and simulated photoluminescence decay curves for CdS single crystal immersed in Na2S solution: (a) crystal immersed in distilled water, following chemical etching; (b) crystal immersed in 3 X lo4 M of sulfide solution; (c) 7 X lo-) M; (d) 1 X lo-* M.
j
- 0.6
-2.4!
/
/
-30/64
'
'
-i2 -1'6 I LOG CONCENTRATION
-48
I'
0.0
Figure 4. Adsorption isotherm of Cu2+on CdS (sulfur face); the solid curve is the calculated adsorption isotherm (eq 7). The squares are the recombination velocities derived from Figure 1. The abscissa is the experimental concentration of the CuSO, solution.
were conducted on the "sulfur" face of the CdS crystal.
Results and Discussion Figures 1-3 show the experimental photoluminescence decay curves of chemically etched CdS single crystals immersed in aqueous solutions at various concentrations of Cu2+, 13-/1-, and sulfide ions, respectively. The presence of these ions in solution was found to decrease the CdS photoluminescence effective lifetime and quantum yield. For the computer fits of the luminescence curves we used the following crystal parameters: the ambipolar diffusion constant D* = 1.2 cm2/s, the bulk recombination time 7 b = 5 X lo-* s, and the penetration depth of the edge luminescence 6 = 7 X 10" cm. The surface recombination velocity, S, is the only variable parameter used to fit the computer simulation with experimental data. Since the luminescence decay curves are almost insensitive to surface recombination velocities, S < lo3 cm/s or S > lo6 cm/s, we are left with a reduced dynamic range of 3 orders of magnitude in determining the SRV. Therefore at very low ion concentrations, < M, we take the same SRV value as found for chemically etched CdS immersed in 10 M Q distilled water, So N lo3 cm/s. Figures 4-6 show on a logarithmic scale the plots of S - So as
-0,1841
/ '
'
'
-4L -3.2 -l!6 0.0 LOG. CON C E NTR ATlON Figure 6. Adsorption isotherm of Sz-; note the slow increase of 6 versus concentration compared to Figures 4 and 5.
-0'480L4
a function of the ion concentrations for Cu2+, 13-/1-, and Sz-, respectively. The plots of SRV for 13-/1- and Cu2+have a shape resembling an adsorption isotherm where at the low-concentration region the surface coverage is small and at the high concentration side the coverage is close to a unity. The SRV can be formally written as S = VthuNT,where V,, = lo7 cm/s is the thermal electron velocity, u is the electron or hole capture cross section by the surface state (the adsorbed ion), and NT is the reactive surface-state density. Thus the surface-state density can be related to the surface coverage, the parameter used to describe an adsorption isotherm. The adsorption isotherm most often employed in electrochemistry for electrodes immersed in electrolyte solution is that derived by Frumkin in 1925:17~18 [O/(l - O ) ] exp(f8) = KC exp(EF/RT)
(5)
where 0 is the surface coverage fraction, f is given by f = -r/RT, in which r is the rate of change of the apparent standard free energy of adsorption with coverage: r = dAGo/dO
(6)
K is the adsorption equilibrium constant, E is the electrical po(1 7) Frumkin, Z . Phys. Chem. 1925, l 16, 446.
(18) Gileadi, E. In Electrosorption; Gileadi, E., Ed.; Plenum: New York, 1976.
The Journal of Physical Chemistry, Vol. 92, No. 16, 1988 4679
CdS Single Crystals Immersed in Electrolytes TABLE I: Effect of Electrolytes on SRV
ionb
redox couples &-/I-
so/s20 s 2cu2+
:$+ncu
s20~-/so:-
CIcl2/cIPb2+ Pb2+/Pb K3Fe(CN)6/K4Fe(CN)6 CdZ+ Cd2+/Cd Zn2+
Zn2+/Zn
Na+ K+ cs+ Ca2+
Na+/Na K+/K cs+/cs Ca2+/Ca
standard potential,’ V +0.533 -0.58
SRV at lo-) M, cm/s >lo6
+0.337 + 1.98 + 1.36 -0.1262 -0.36 -0.403 -0.76 -2.71 -2.92 -2.92 -2.868
>io7
104 104
