J . Phys. Chem. 1984, 88, 6213-6218
6213
Time-Resolved Photoluminescence in the Picosecond Time Domain from CdS Crystals Immersed in Electrolytes Moshe Evenor, Shimshon Gottesfeld,* Zvi Harzion, Dan Huppert, Department of Chemistry, Tel Aviv University, 69978 Ramat Aviv, Tel-Aviv, Israel
and Stephen W. Feldberg Division of Chemical Sciences, Department of Energy and Environment, Brookhaven National Laboratory, Upton, New York 1 1 973 (Received: May 14, 1984)
The effect of the solution composition on the luminescence decay time following picosecond laser pulses is examined for CdS single crystals immersed in various aqueous solutions. A digital simulation technique is demonstrated as an efficient tool for the quantitative analysis of luminescencedecay curves in the picosecond time domain, using the exact generation function in the simulation. Such analysis yields numerical values for the bulk lifetime, q,,and for the surface recombination velocity, S . A typical value of T~ = 2.5 X lo4 s was found for the CdS crystals employed. The surface recombination velocity evaluated for an etched crystal immersed in distilled water was S d 5 X lo3 cm/s. Immersing the etched CdS crystal in a basic sulfide-polysulfide solution increased the surface recombination velocity to a level of lo6 cm/s. This indicates a photohole surface capture velocity of S 2 lo6 cm/s at a sulfide-covered CdS surface.
Introduction The origin of this study is in an attempt to obtain information on the kinetics of elementary processes in illuminated semiconductor-aqueous electrolyte interfaces, from measurements of the transient response to perturbations induced by short light pulses. In previous contributions we described measurements of photocurrent transients under closed-circuit conditions and of photopotential transients under open-circuit conditions, both taken following light pulses of nanosecond width.’I2 Both modes of the electrical signal transient response reflect processes which can be described from an electrical point of view as the discharge of a photoacceptor, which takes place following the termination of the “charging” illumination pulse. The decay of both the photocurrent and the photopotential signals is controlled by the rate of recombination of the separated photocarriers, which have been generated by the pulse and subsequently immediately separated by the field near the semiconductor Both modes of electrical measurements revealed strong effects of the state of the semiconductor surface, especially when comparing mechanically polished and chemically etched surfaces.’g2 The time window available for the electrical signal transient measurements ( t > 20 ns) enabled only a study of recombination processes which occur subsequent to the very fast photocarrier generation and charge separation steps. It has been noticed, however, that significant recombination occurred in these semiconductor crystals within shorter time periods, of the order of the charge separation time or l e s ~ . ~The . ~ fast recombination modes were apparent by their effect on the maximum amplitude of the electrical transient signaL2 In order to perform time-resolved measurements of such recombination processes, which occur in the nano- and picosecond time domains, a shorter light pulse and a faster detection system were required. Such measurements were subsequently performed by employing a 25-ps laser flash and by following the decay of the resulting photoluminescence. Preliminary results of our time-resolved photoluminescence experiments have been described b e f ~ r e . * , ~It, ~has been demonstrated that (1) Harzion, Z.; Croitoru, N.; Gottesfeld, S . J. Electrochem. SOC.1981, 128, 551.
(2) Harzion, Z.; Gottesfeld, S.; Huppert, D.; Croitoru, N. J . Electroanal. Chem. Interfacial Electrochem. 1983, 150, 57 1. (3) Gottesfeld, S.; Feldberg, S . W. J . Electroanal. Chem. Interfacial Electrochem. 1983, 146, 41. (4) Huppert, D.; Harzion, Z.; Croitoru, N.; Gottesfeld, S . In “Picosecond
Phenomena 111”; Eisenthal, K. B.; Hochstrasser, R. M.; Kaiser, W.; Laubereau, A., Eds.; Springer-Verlag; New York, 1982; p 360.
0022-3654/84/2088-6213$01.50/0
ultrafast decay (T < 100 ps) could be measured in samples with mechanically damaged surfaces, while much longer photoluminescence decay times (T > 1 ns) were recorded following chemical etching. It was also demonstrated that emission of photons of subband-gap energies could serve as a potential source of information on the population of mid-gap states associated with trapping and recombination activitiese2 To make the photoluminescence decay a quantitative source of information on bulk and surface recombination rates, a mathematical solution is required for the problem at hand, which involves coupling of transport processes with bulk and surface kinetics. Digital simulation of the photoluminescence response was employed in this work for this purpose. Analytical solutions for this problem have been presented before,6 but such solutions are less flexible when attempting to modify the problem, eg., by including a general form of the generation function or, especially, when second-order kinetics or additional processes may be involved. We show in this work that by fitting simulated and experimental photoluminescencedecay curves, measured for bulk semiconductor samples immersed in an electrolyte solution, the effect of electrolyte composition on the surface recombination velocity can be quantitatively evaluated. Experimental Section Photoluminescence. The schematics of the optical arrangement is described elsewhere.’ CdS single crystals were irradiated by a 352-nm 25-ps pulse (this is the third harmonic of a mode-locked Nd3’/YAG laser) or a 450-nm 65-ps pulse (from a cumarin 440 dye laser pumped by the third harmonic pulse). The excitation levels used in our experiments were of the order of lozo photons/cm3 pulse-’, based on the known laser intensity and the penetration depth of the light in the semiconductor phase. Photoluminescencewas collected from the front face of the crystal. Colored glass filters were placed before the streak camera (Hamamatsu Model C939) entrance slit to block scattered light of the excitation beam wavelength. 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 Delta microcomputer. The impulse ( 5 ) Harzion, Z.; Croitoru, N.; Huppert, D.; Gottesfeld, S. In ‘4th International Conference on Photoelectrochemical Conversion and Storage of Solar Energy, Aug. 1982, Jerusalem, Israel”; Weizmann Science Press: Jerusalem, Israd; 1982-1983; p 82. ( 6 ) Vatikus, J. Phys. Status Solidi A 1976, 34, 769. (7) Huppert, D.; Kolodney, E. Chem. Phys. 1981,63,401.
0 1984 American Chemical Society
6214
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
Evenor et al.
response of the detection system, for the time window of these experiments, is a Gaussian with fwhm of 50 ps. Materials and Solutions. The hexagonal n-type CdS single crystals (Cleveland Crystals) were 1-2 mm thick, had a resistivity ), of 1-10 ohm cm (donor concentration, N D = 2 X 10l6~ m - ~and a surface perpendicular to the C axis. Polishing of the surface crystal was performed before the first etch by 0.05-pm alumina. Etching was carried out with concentrated HCl, followed by rinsing with distilled water. Etching was repeated before each set of experiments. All chemicals were of analytical grade.
Analysis A semiinfinite uniform semiconductor sample is assumed. The semiconductor surface is irradiated with a laser pulse which creates electron-hole (e-h) pairs a t a rate g(x,t) in the semiconductor phase. In all the experiments performed, conditions corresponding to a high injection level prevailed within the time window of the measurement, Le., the concentration of the excess of carriers is much higher than their equilibrium values. Thus, according to the Hall-Schockley-Read theory for recombination decay via recombination centers,*vgit can be expected that the excess e-h pairs recombine in the bulk by first-order kinetics, with a lifetime T+,. The time-dependent equation for the local excess of carrier concentration, Ac(x,t),can be written as6
0 0.475
I650 l
I
1
l
l
i
I
I
l
b
0.380
0.285
a ’
g(x,t) is the generation function given by
0. I90
where go(t) is the time dependence of the excitation pulse. We define x = 0 as the coordinate of the front surface, 61 is the penetration depth of the laser pulse in the semiconductor, and D’ is the ambipolar diffusion coefficient10which for the case of equal concentrations of holes and electrons is given by
(3) De and Dh are the diffusion coefficients of electrons and holes, respectively. The instantaneous luminescence intensity, taking into account self-absorption, is given in terms of the local excess carrier concentration as
Z(t) = k , ~ m A c 2 ( x ,exp(-x/$) t) 0
dx
(4)
where 62 is the penetration depth of the edge emission and k, is the second-order radiative rate constant. As the form of the decay curve was not found to depend upon the intensity of the excitation, it can be assumed that the rate of radiative decay is negligible compared to the nonradiative modes of bulk (eq 1) and surface (eq 5) recombinations. The photoluminescence intensity thus serves only as a probe of the instantaneous photocarrier population, which decays via nonradiative modes. Implicit in these equations is the assumption that electroneutrality is maintained. The validity of this presumption has been examined in detail elsewhere (ref 11). In our system the deviation from electroneutrality and the attendant error in the calculated fluorescence will be acceptably small if Ac0 > 10’’ ~ m - ~ An. upper limit of Aco < lozocm-3 is dictated by our desire to minimize the temperature increase. This concentration range had been maintained throughout the whole measured decay in our experiments (8) Hall, R. N. Phys. Rev. 1952, 87, 387. (9) Shockley, W.; Read, Jr., W. T. Phys. Rev. 1952,87, 835. (10) Van Roosbroeck, W. Phys. Rev. 1953, 91, 282. (1 1) Feldberg, S. W.; Evenor, M.; Huppert, D.; Gottesfeld, S. J . Electroanal. Interfacial Electrochem., submitted for publication.
0.095
0
1650 t (PSI Figure 1. Simulated luminescence decay curves from a semiconductor crystal for excitation by a 6 ( t ) laser pulse, and assuming the detection system has an impulse response of 6 ( t ) as well. D* = 0.8 cmz/s, 62 = 7.3 X cm, ib = 2.5 X s and the values for S are 0, 5 X lo3, 2 X lo4, 5 X lo4, 1 X lo5, 2 X lo5, 1 X lo6, 1 X lo7 cm/s. In Figure l a Pa = 0.39, and in Figure l b Pa = 0.105.
by controlling the laser pulse intensity. It has been further shown” that the use of the ambipolar diffusion equation for this concentration range results in an error in the calculated instantaneous photoluminescence which does not exceed a few percent compared with the rigorous (but much more complex) calculation based on a separate evaluation of instantaneous profiles of electrons and holes. For the geometry employed, the boundary conditions are dAc(x=O,t) = -Ac(x=O,t) S ax xso D*
(5)
where 3 is the surface recombination velocity. In practice, the laser pulse can be of arbitrary shape and width. When the response of the physical system is linear, and the solution for a 6(t) pulse is known: the more general solution for excitation by a pulse of finite width can be found by convoluting the solution for a 6 ( t ) function with the actual shape of the exciting pulse. However, recalling that luminescence is not a linear process (see eq 2), we preferred to solve the time-dependent equation numerically, including a numerical simulation of the generation function. This solution was subsequently convoluted with the response function of the detection system (streak camera).
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 6215 -0.701
a
0
1
7
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1
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I
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I
1
I
1
I
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1
0.380 0.285
a" 0.190
0.095
1650
0
Figure 3. Simulated plots of In PI vs. time when the crystal is excited by a s ( t ) laser pulse and the detection system has an impulse response of s ( t ) a.s well. D* = 0.8 cm2/s, h2 = 7.3 X 10 cm, rb = 2.5 X s, and S = 0 cm/s. Solid line is for Pa = 0.39 and dashed line is for Pa = 0.105.
1
0.380
0.285
a0.190
0.095
1650 t(ps) Figure 2. Simulated luminescence decay curves from a semiconductor crystal for excitation by a laser pulse which has a Gaussian shape with a fwhm of 25 ps, and assuming the impulse response of the detection system is also a Gaussian with a fwhm of 50 ps. All other parameters are as in Figure 1. In Figure 2a Pa = 0.39, and in Figure 2b Pa = 0.105.
0
Figure 1 shows the simulated time dependence of the normalized luminescence intensity defined by
where Qois the total flux of photons in a laser pulse (photons/cm2). The results are presented for various values of S and with two values of the parameter Ps defined by
ps = 61/62
(9)
(Experimentally, a larger value of Pa means a deeper penetration of the exciting laser beam into the semiconductor effected by an increase in the wavelength of the exciting light.) It has been assumed in Figure 1 that the time-dependent generation function go(t) is 6 ( t ) and that the detection system has a 6 ( t ) impulse response as well. The following parameters, typical for CdS crystals, are used for the plots in Figure 1: D* = 0.8 cm2/s, 6 , = 7.3 x cm, and Tb = 2.5 x s. In Figure la, Pa = 0.39 and in Figure l b Pa = 0.105. The penetration depths corresponding t o the excitation and the edge emission wavelengths were based on data given in the literature.12-14 The value of D* is (12) Segal, B.; Marple, D. T. F. In "Physics and Chemistry of 11-VI Compounds"; Aven, M.; Prener, J. S., Eds.; North-Holland Publishing Co.: Amsterdam, 1967; Chapter I.
Figure 4. Experimental (solid lines) and simulated (dashed lines) photoluminescence decay curves for CdS single crystals obtained for excitation wavelength of 450 nm (Pa = 0.39): (a) crystal immersed in distilled water, following chemical etching in concentrated HCI; (b) crystal immersed in aqueous solution of 0.1 M hydroquinone.
calculated from averaged drift mobilties of electrons and holes, as given in the literature.15t16 The values of Tb was found for the CdS crystals used in our experiments by fitting the experimental photoluminescence decay curves to the simulated curves (see be1ow)i. Figure 2 shows the simulated results obtained for material parameters identical with those used in Figure 1, but using a genera tion function with a Gaussian shape, having full width at half-maximum (fwhm) of 25 ps. It was also assumed that the impulse response function of the detection system is a Gaussian with a fwhm of 50 ps. The other parameters are as mentioned for Figure 1. Figure 3 presents simulated plots of In PI vs. time calculated from eq 2 and with 6(t) functions for both the generation function and thle impulse response of the detection system. The semilog (13) Moss, T. S. 'Optical Properties of Semiconductors"; Academic Press: New York, 1961; p 124. (14) Parsons, R. B.; Wardzynski, W.; Yoffe, A. D. Proc. R.SOC.London, Ser. A 1961, 262, 120. (15) Wolf, H. F. "Semiconductors"; Wiley: New York, 1971; p 33. (16) "CRC Handbook of Chemistry and Physics"; 55th ed.; CRC Press: Boca R.aton, FL, 1974-1975; p E103.
6216 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 1.01 ' 1
9
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Evenor et al.
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Figure 5. Experimental (solid lines) and simulated (dashed lines) photoluminescence decay curves for CdS single crystals obtained for excitation wavelength of 352 nm (pa = 0,105): (a) crystal immersed in distilled water, following chemical etching in concentrated HCI; (b) crystal immersed in aqueous solution of 0.1 M hydroquinone.
I 0.4
0
1650 t(ps1 Figure 6. Experimental (solid line) and simulated (dashed line) photoluminescence decay curves for etched CdS single crystal immersed in an aqueous solution of 2 M NaOH, following immersion in distilled water. Excitation wavelength was 352 nm (pa = 0.105).
plots are given for two values of Ps: 0.39 and 0.105. It can be seen from Figure 3 that, even for the simplest case when S = 0, the decay of the luminescence does not have a simple exponential form and requires, therefore, an exact analysis. This is to be contrasted with phenomena like photoconductivity, which are linearly proportional to the concentration of the carriers," and may be, therefore, associated with a simple exponential decay under such conditions.
Experimental Results Figures 4 and 5 show the experimental photoluminescencedecay curves (solid lines) obtained for CdS single crystals at two different excitation wavelengths. In Figure 4 A,, = 450 nm (Pa = 0.39) and in Figure 5 A,, = 352 nm (Ps= 0.105). The dashed lines represent simulated curves, employing parameters specified in the captions. All the plots are arbitrarily normalized, taking the peak intensity as I = 1. Figures 4a and 5a show results for the chemically etched crystal immersed in distilled water. The value of the surface recombination velocity which gave the best fit was S B 5 X lo3cm/s for both the excitation by 450- and by 352-nm pulses. r,, was evaluated as 2.5 X lo4 s. Figures 4b and 5b give the results of the luminescence decay from the same etched crystal when immersed in an aqueous 0.1 M hydroquinone solution. The values evaluated for the surface recombination velocity for this system were 3 X lo4 and 1 X lo5 cm/s for the two excitation wavelengths, respectively. In this case the values obtained for S a t the two wavelengths agree to within a factor of three, which gives some indication on the accuracy of the values obtained for S by this method. Figures 6 and 7 present a series of experiments performed with a CdS crystal, for evaluating the influence of a basic sulfidepolysulfide solution (2 M NaOH, 0.1 M So, 0.5 M Na2S) on the surface recombination rate. Figure 6 shows the luminescence of the etched crystal immersed in an aqueous solution of 2 M NaOH. In this solution the surface recombination velocity was very low (S d 5 X lo3 cm/s). Figure 7a shows the result for a crystal immersed in the basic sulfide-polysulfide solution immediately after etching in HCl. The surface recombination velocity evaluated in this case was 9 X IO5cm/s. Figure 7b shows the luminescence transient for the crystal immersed in the basic sulfide-polysulfide solution after being previously immersed in the 2 M N a O H solution for 2 h. In this case the surface recombination velocity was lower: 2 x IO4 cm/s. (17) Tyagi, M.S.; Nus, J. F.; Van Overstraeten, R. J. Solid-State Electron. 1982, 25, 411.
t( ps) Figure 7. Experimental (solid lines) and simulated (dashed lines) photoluminescence decay curves for a CdS single crystal immersed in a basic sulfide-polysulfide solution (2 M N a O H , 0.1 M So, 0.5 M Na2S): (a) immersion in the sulfide-polysulfide solution immediately after chemical etching; (b) immersion in the sulfide-polysulfide solution after the crystal was previously immersed in a 2 M N a O H solution for 2 h. Excitation wavelength was 352 nm (pa = 0.105).
Discussion Conclusions from Simulations: The Effect of Various Parameters on the Form of Photoluminescence Decay Curves. The conditions of the photoluminescence decay experiments are quite different from those of the electrical transient measurements reported by us before in which small perturbations were always employed to simplify the analysis.2 In the present work the large power of the exciting laser results in a concentration of lozocm-3 of photogenerated electron-hole (e-h) pairs, which is about four orders of magnitude larger than the equilibrium concentration of majority carriers. This large population of photocarriers (which is required at the moment to obtain easily measurable luminescence intensities) eliminates the effect of the field at the surface by complete band flattening. As a result, the decay of the luminescence will not be affected by (preexisting) band bending, and is expected to be controlled by the combined processes of ambipolar diffusion of the photogenerated e-h pairs and by their bulk and surface recombination kinetics as described above. It can be seen from Figures 1 and 2 that as the surface recombination rate increases the decay of the photoluminescence becomes faster. However, in the case presented in Figure 1, at
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 6217
Photoluminescence from CdS Crystals t = O+ all the curves with the same values of Pa have the same height irrespective of S. This quantity is derived directly from eq 2 and given by P,(t=O+) = 1/(2
+ P*)
(10)
For the ideal case of a 6 ( t ) excitation pulse, the initial height of the simulated luminescence intensity is seen here to decrease slightly with increasing Pa,apparently because as the penetration of the excitation pulse becomes deeper the profile of the photogenerated carriers is more spread out in the semiconductor phase. (At t=O+ the recombination processes have no effect as yet on the profile when a 6 ( t ) pulse is assumed.) Figure 2 reveals the strong effects of the finite width of the excitation pulse and the impulse response of the detection system on the form of the luminescence decay curve: Firstly, the effect of the surface recombination velocity is now clearly seen on the height of the photoluminescence peak, since a significant fraction of the carriers will recombine at the surface during the period of photogeneration when the width of the pulse becomes significant. The effect of the surface is more pronounced for smaller values of Pa,i.e., when a larger fraction of the carriers is generated closer to the surface. It can be realized from a comparison of Figure 1 and 2 that the extent of the recombination and transport processes which take place within the time of the excitation is such that the generation function and the impulse response of the detection system must be taken into account. In the case of a finite pulse width, the effect of Pa is in an opposite direction to that shown in Figure 1: As 61 (and therefore Pa)becomes smaller (in our case due to an increase in excitation energy), the peak of the photoluminescence curve decreases significantly, even when S = 0. This can be understood in the following way: The gradient of the excess carriers (dAc/ax) increases when 6, decreases, causing the excess carriers to diffuse more rapidly to the interior of the semiconductor. Thus, the extent of carrier dilution which takes place within the finite time of the generation pulse would increase as Padecreases, resulting in a smaller photoluminescence peak. It also should be noted that as S becomes larger and Pa becomes smaller, the quantum yield (defined by the area under the photoluminescence decay curve) decreases markedly. Our simulations show that when S is very small, Le., S 6 5 X lo3 cm/s, the form of the luminescence decay curve is not very sensitive to the exact value of S. This is so because in the lower limit the surface recombination is too slow compared to the other processes contributing to luminescence decay (bulk recombination and diffusion). A similar insensitivity of the decay curve is found when S is large, Le., S 2 IO6 cm/s, because in the high limit the rate of the overall surface recombination process becomes effectively controlled by diffusion. As time progresses, the carriers move deeper and deeper into the semiconductor and, thus, recombine primarily in the bulk rather than at the surface, making the effect of recombination at the surface less and less important. Furthermore, the local gradients of the excess carrier concentration decrease with time, and diffusion plays, therefore, a less significant role in the last portion of the decay. The bulk recombination process has thus the dominant effect in the tail of the decay. In fitting the experimental results to the simulated curve, this part of the decay is the more sensitive to the value of rb. These phenomena (surface reaction, bulk recombination, diffusion) and their interaction are discussed in detail in ref 11, The Effect of Surface Morphology and Composition on the Apparent Surface Recombination Velocity. The measured decay times of the edge luminescence emitted from the CdS semiconductor crystals were found bef0re~9~ to be very sensitive to the morphology of the crystal surface. The luminescence after mechanical polishing by 0 . 0 5 - ~ malumina was of the order of 100 ps. The quantum yield and the decay times were shown to be significantly increased by chemical etching, which removes the surface layer damaged by mechanical polishing2and, thus, reduces the rate of the recombination processes at the surface. It can be seen from Figures 4 and 5 that, after surface etching, the optimized fit of the simulated data to the experimental luminescence decay
curve reveals a low surface recombination velocity: S C 5 X lo3 cm/s. It should be noted that even the upper possible value of S = 5 X lo3cm/s is very small and corresponds to a concentration of recombination centers on the surface of ca. 10l2 cm-2. The hydroquinone and polysulfide solutions were tested in this work to probe the effect of redox couples in solution on the rate of recombination processes that occur at the semiconductor-solution interface. The case of the sulfide-polysulfide system is particularly important in the study of photoelectrochemical cells.’* It can be seen from Figure 7 that the sulfide-polysulfide system strongly enhances the rate of the measured photoluminescence decay, corresponding to an increase of S to lo6 cm/s. Sulfide ions are known to be efficient photohole acceptors from CdS and are also known to adsorb at the surface of this cry~ta1.l~ A species in solution which is known to adsorb at the surface and to improve the steady-state performance of an illuminated semiconductor-electrolyte junction may either passivate an “intrinsic” recombination center or may enhance the surface reactivity by serving as a mediating center in the process of photocharge transfer to acceptors in s o l ~ t i o n . ’Previous ~ work by Heller and co-workersZ0J1demonstrated examples of the first case, Le., of semiconductor surface passivation by adsorption from solution. The adsorption in those instances was not of an active redox component but rather of a metal ion (Ru3+ or Ag+). The results presented here provide an opposite example: Apparent activation of the surface is acheived by exposing the semiconductor to an electrolyte solution containing a redox system which is known to adsorb and to be active in the steady-state photocharge transfer process. In the framework of the photoluminescence decay experiment, the activation of the surface is revealed by the increase of S. However, the apparent value of S is a function of the individual surface capture velocities for holes and electrons which are of interest for the elucidation of the kinetics of photocharge transfer at the same semiconductor-electrolyte interface. It follows from the Hall-Shockley-Read statistics that, under conditions of high injection, and when the concentrations of electrons and of holes near the surface are equal, the following relationship holds:**
where S is the measured apparent surface recombination velocity and Sp,o and Sn,O are the individual surface capture velocities of holes and electrons, respectively, both of which apply to low injection conditions. Thus, when the conditions specified for the validity of eq 11 are met, each of the individual surface capture velocities is equal to or higher than the measured apparent S. Actually, the condition (AC),,,~= (AC),,,~,required for the strict are validity of eq 11, is not necessarily fulfilled when S,,o and Sp,o both very large and different. However, rigorous solutions of the continuity equation for the individual instantaneous profiles of electrons and holes, as obtained by digital simulation (without then it is assuming electrone~trality),~~ show that if S,,o # Sn,O and Se02 lo6 cm/s in order to account required that both Sp,o for the decay curve measured in the presence of sulfide. If we recall that the upper limit for either Sp,o or Sn,O is set by the thermal (18)(a) Hodes, G.;Manassen, J.; Cahen, D. Nature (London) 1976,262, 403. (b) Ellis, A. B.; Kaiser, S.W.; Bolts, J. M.; Wrighton, M. S.J . Am. Chem. Soc. 1976,98,1635. (c) Miller, B.; Heller, A. Nature (London) 1976, 262,680.(d) Inoue, T.;Watanabe, T.; Fujishima, A.; Honda, K.; Kohayakuwa, K. J . Electrochem. Soc. 1977,124, 719. (19)Wilson, R. H. In “Photoeffects at Semiconductor-Electrolyte Interfaces’’; Nozik, A. J., Ed.; American Chemical Society: Washington, DC, 1981;p 103. (20) Nelson, R. J.; Williams, J. S.; Leamy, H. J.; Miller, B.; Kasey, Jr., H. C.; Parkinson, B. A,; Heller, A. Appl. Phys. Lett. 1980,36,76. (21)Heller, A.; Leamy, H. J.; Miller, B.; Johnston, Jr., W. D. J . Phys. Chem. 1983,87,3239. (22) McKelvey, J. P. ‘Solid State and Semiconductor Physics”; Harper and Row: New York, 1966;Chapter 10. (23)Such separate rigorous solutions of the continuity equations for electrons and holes call for extremely long computer calculations. They were thus generated only in some limiting cases for the verification of the results obtained according to the much simpler approach, defined by eq 1 and 3.
6218
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
velocity of free carriers in the semiconductor ( lo7 cm/s at room temperature), the measured rate of interfacial charge capture by sulfide anions is very high, in accordance with previous predictions by Wi1s0n.l~ This high rate is apparently due to a partial bonding between the adsorbed anionic acceptor and the semiconductor solid. Such bonding allows a fast inelastic charge transer from the semiconductor band to the anionic surface state, which is accompanied by multiphonon emission.24 Gratzel and Frank25 noted that in cases of bimolecular charge transfer processes, as studied between colloidal semiconductor particles and ions in solution, the maximum observable heterogeneous charge transer rate constant is only 10 cni/s, since for higher charge transfer rates the process becomes diffusion controlled. Gratzel and coworkers have reported also very high rates of photocharge transfer to species adsorbed at CdS colloidal particles by observing the instantaneous product formation signal during a nanosecond wide laser pulse.26 The results presented here show that by employing a picosecond laser technique such extremely high surface capture rates can be evaluated quantitatively. When mediation of charge transfer by an adsorbed anionic state is con~idered,'~ the overall process of charge transfer from semiconductor to solution includes two stages, e.g.
where the form S-ads in step a is equivalent to a hole trapped in an anionic surface state, and step b describes the subsequent process of hole transfer from the surface state to the sulfide ion in solution. (The polysulfide product is designated here by Soaq.) The apparent surface recombination velocity measured in our experiment gives direct information on the rate of process a, Le., capture of a photogenerated carrier by an anionic surface state. As for the overall rate of the sequence of steps, (a) followed by (b), step b could be obviously rate controlling, due, for example, to mass transport limitations of reactant and/or product in solution. However, it has been noted that the rate of charge transfer proper in step b should be high: The small gap in this case in
Evenor et al. electron energy between donor state (adsorbed sulfide) and acceptor state (sulfide in solution) should result in a large probability of charge transfer.*' As a result, the activation of the CdS surface by adsorbed sulfide anions leads, under steady-state illumination and significant band-bending conditions, to the required large ratio between the overall rates of photocharge transfer and of recombination processes. When the CdS crystal is immersed in a NaOH solution prior to the immersion in the basic sulfide-polysulfide solution, the surface recombination velocity measured in the presence of sulfide becomes much lower (see Figure 6). It is conceivable that this phenomenon is caused by the formation of an hydroxide layer on the CdS crystal during the immersion in the NaOH solution, thus preventing to some extent the adsorption of the sulfide anions at the surface. Another possibility is a lowered rate of recombination of photocharges via the surface states which may still exist on the outer surface of the oxide layer. This may be due to a limited transport rate through the film, which lies between the photogenerated carriers and the surface recombination centers. Conclusion It has been shown that time-resolved photoluminescence in the picosecond time domain can be an efficient tool for quantitative evaluation of high surface recombination rates. The front surface collection geometry employed in this work allows such measurements on surfaces of bulk crystal samples. We found that adsorbed ionic acceptors, such as sulfide on CdS, are active recombination centers under conditions of high injection (flat bands) and conclude from these results that they serve as active charge mediators to acceptors in the solution phase under regular-steady illumination conditions. Acknowledgment. S. Gottesfeld and S. W. Feldberg gratefully acknowledge the support of this work by a grant from the US.-Israel Binational Science Foundation (BSF, Jerusalem). This work was supported in part by the Division of Chemical Sciences, U.S. Department of Energy, Washington, DC, under Contract NO. DE-AC02-76CH00016. Registry No. CdS, 1306-23-6; NaOH, 1310-73-2; S, 7704-34-9; Na2S, 13 13-82-2; HC1,7647-01-0; water, 7732-18-5; hydroquinone, 123-31-9.
(24) Henry, C.H.; Lang, D. Phys. Rev. B Solid State 1977, IS, 989. (25) Gratzel, M.; Frank, A. J. J. Phys. Chem. 1982, 86, 2964. (26) Duonghong, D.; Ramsden, J.; Gratzel, M. J . Am. Chem. SOC.1982, 104, 2917.
(27) Morrison, S . R. 'Electrochemistry at Semiconductors and Oxidized Metals Electrodes";Plenum Press: New York, 1980; p 106.
