J. Phys. Chem. 1991, 95,9961-9965
9961
Surface-Trapped Charge at CdS Electrode in Aqueous Solution As Observed by Photoreflectance Spectroscopy Seiichiro Nakabayashi and Akira Kim* The Institute of Physical and Chemical ResearchYRIKEN), Wakoshi, Saitama 351 -01, Japan (Received: February 19, 1991)
The photoreflectancespectra of the cadmium sulfide single crystal electrode in contact with aqueous electrolyte were measured for excitation with an intensity-modulated argon ion laser. The distribution of the lifetime of photoinduced surface-trapped charges, the optical cross section, and the two-dimensional density of the states were evaluated by the frequency dispersion and the fluence dependence of the photoreflectance spectrum intensities.
Introduction Electronic states peculiar to the semiconductor/electrolyte interface are regarded as a very important clue for understanding the mechanism of interfacial electron transfer and for controlling electrode reactions. The characterization of such states, especially in situ, draws attention. Impedance and admittance spectra of the interface have been discussed by several groups.'-9 The modulation spectroscopy'O also provides useful information on the interface. Electrolyte electroreflectance (EER) spectroscopy is a modulation spectroscopy which is a powerful method in semiconductor physicsI0 and has been successfully applied to electrochemical system."-'4 By this method, T~mkiewicz'l-'~ and Gerischer14 have studied the surface-state distribution at the semiconductor-liquid interface. E,ER is a typical technique to obtain the optical absorption difference induced by the electrostatic field in the space charge layer. The length of the space charge layer on a normally doped semiconductor electrode is a few micrometers or less. When the surface-state density is low, the electrode potential drops within the space charge layer and the electrostatic field strength is more than the order of IO6 V m-'. It is well-known that the high electrostatic field affects a spectral shape of the optical absorption of a semiconductor, which is called a Franz-Keldysh effect.I5 Thus, the EER spectrum relates to the electrostatic field in the space charge layer. As the surface states induce the potential drop between the surface states and the Helmholtz layer in so1ution,l6 ( I ) Shen, W. M.; Tomkiewicz, M.; Cahen, D. J . Electrochem. SOC.1986, 133, 112. (2) Tomkiewicz, M. J. Electrochem. SOC.1979, 126, 2220. (3) Schroder, K.; Memming, R. Ber. Bunsenges. Phys. Chem. 1985,89, 385. (4) Nagasbramanian, G.; Wheeler, 8. L.; Hope,G. A.; Bard, A. J. J. Electrochem. Soc. 1983, 130, 385. (5) Fmlyason, M. F.; Wheeler, B. L.; Kakuta, N.; Park, K.-H.; Bard, A. J.; Campion, A.; Fox, M. A.; Webber, S. E.; White, J. M. J . Phys. Chem. 1985.89. 5676. (6) Nagasbramanian, G.; Wheeler, B. L.; Bard, A. J. J. Elecrrochem. Soc. 1983, 130, 1680. (7) Nakabayashi, S.; Kira, A. J . Phys. Chem. 1990, 94, 7571. (8) Nakabayashi, S.; Kira, A.; Ipponmatu, M. J . Phys. Chem. 1989, 93, 5543. (9) Nakabayashi, S.; Kira, A. J . Phys. Chem. 1987, 91, 4460.
(IO) Cardona, M. Modularion Specrroscopy; Seitz, M., Turnbull, D., Ehrenreich. H.,Eds.; Solid State Physics Supplement 1 I; Academic Press: New York. 1969. ( I I ) Tomkiewicz, M.; Siripala, W.; Tenne, R. J . Electrochem. Soc. 1984, 131. 736. (12) Shen, W.M.; Siripala, W.; Tomkiewicz, M.; Cahen, D. J . Electrochem. Soc. 1986, 133, 107. (13) Silberstein, R. P.; Lyden, J. K.; Tomkiewicz, M.; Pollak, F. J . Vac. Sci. Technol. 1981, 19, 406. (14) Soltz, G. A.; Gerischer, H. J . Elecrrochem. SOC.1985, 132, 1643. ( I 5) Pankove, J. 1. Oprical Process in Semiconductor. Dover Publications: New York, 1971; Chapter 3. (16) Bard, A. J.; Bocarsly, A. B.; Fan, F. R. F.; Walton. E. G.; Wrighton, M. S. J . A m . Chem. Soc. 1980, 102, 3677.
0022-3654/91/2095-9961$02.50/0
the density of the surface states is estimated from the difference between the potential drop estimated by EER and the applied potential."-14 Recently, Frese and Memming and other^'^-^' have suggested that the photoexcitation of some semiconductor electrodes induces a reversible shift of the flat band potential from the one in the dark. The origin of the shift is the photocreated surface charge, probably trapped on the surface states of the Under a fixed electrode potential, the shift in the flat band potential can be utilized for modulation of the electrostatic field in the space charge layer. A modulation spectroscopy based on the photocreated surface-trapped charge is known as photoreflectance spectroscopy, which has been used in the study of solidsolid
interface^.^^-^^ Figure 1 illustrates a mechanism of electrostatic field modulation by surface charge of n-type semiconductor. The solid line stands for the system in the dark and the dotted line the one under photoexcitation by which positive charges are accumulated on the surface. The surface charge shifts the flat band potential of the electrode to the anodic direction (a). Under a fixed electrode potential, the length of the space charge layer is reduced by the surface charge (b). Then, the electrostatic field changes as shown in (c).
Experimental Section The semiconductor electrode was a CdS single crystal purchased from Eagle-Picher Research Laboratory, mounted in a Kel-F electrode holder. The ohmic contact of the electrode was made by lubricating gallium-indium alloy on the back side of the crystal. The donor density of the crystal was 2 X 10l6~ m - The ~ . surface of the electrode was cut perpendicular to the c axis. The counter and the reference electrodes were platinum and silver, respectively. The electrode potential will be represented with respect to the silver quasi-reference electrode. Before each experiment, the electrode (17) Freese, K. W. J. Elecrrochem. SOC.1983, 130, 28. (18) McEvoy, A. J.; Etman, M.; Memming, R. J . Electroanal. Chem. 1985, 190, 225. (19) Prybyla, S.; Struve, W. S.; Parkinson, B. A. J . Elecrrochem. Soc. 1984, 131, 1587. (20) Etman, M. J . Phys. Chem. 1986, 90, 1844. (21) Allongue. P.; Blonkowski, S.; Lincot, D. J . Elecrroanal. Chem. 1991, 300, 26 1. (22) Shay, J. L. Phys. Rev. B 1970, 2, 803. (23) Bhattacharya, R. N.; Shen, H.; Parayanthal, P.; Pollark, F. H.; Coutts, T.; Aharoni, H.Phys. Rev. B 1988, 37,4044. (24) Kanata, T.;, Sugawa, H.; Matunaga, M.; Takakura, H.; Hamakawa, Y.: Kato. H.: Nishino. T. Phvs. Rev. B 1990. 41. 2936. (25) Parayanthal, P.; Shen, H.;Pollak, F. H.; Glembocki, 0. J.; Shanabrook, B. V.; Bread, W. T. Appl. Phys. Leu. 1986, 48, 1261. (26) Shen. H.:Paravanthal. P.: Pollak. F. H.:Tomkiewicz.. M.:. Drummond,'T. J.; Schulman,-J. N. Appl. Phys.'Lerr. 1986, 48, 653. (27) Shanabrook, B. V.;Glembocki, 0. J.; Breard, W. T. Phys. Reo. B 1987, 35, 2540.
0 1991 American Chemical Society
Nakabayashi and Kira
9962 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
Y
I
i ’
T
I
-
I I I
I h
. ~
PL
pc
OS
a
,’
d\
I
L 1
_
Figure 1. Schematic representation of the space charge region of the potentiostatic n-type semiconductor electrode: (a) the energy band; (b) the charge density R; (c) the electrostatic field t ; (dotted line) on laser irradiation: (Nd) donor density; (Qs)positive surface charge.
surface was mirror-polished by a Kulzer-Technotron polishing disk, etched in HCI aqueous solution, and rinsed with distilled water. The electrolyte was an aqueous solution of 0.1 M Na2S0, and 1 M Na2S03, which prevents the anodic photocorrosion of the CdS crystal s u r f a ~ e . ~The * ~ ~electrochemical ~ cell has a large optical window for the incident light of a solid angle of approximately r,which is convenient for photoreflectance measurements. The electrode potential was controlled by a Toho-Giken 2020 potentiostat. In the EER measurements, the electrode potential was modulated with a square wave by using the potentiostat connected to a Hewlett-Packard 81 12A pulse generator. The probe beam for both photoreflectance and EER was the xenon arc lamp (1 50 W) light monochromated by a Jovan-Yvon H-20 monochrometer with wavelength scanner MICl1. The pump beam for the photoreflectance experiments was a 458-nm line from a Lexel Model 95 argon ion laser. The pump beam was frequency-modulated by using a Stanford Research System SR540 light chopper. The intensity of the beam was contrslled by neutral density filters and monitored by a PIN photodiode calibrated by Laser Instrumentation Model 5273 laser p w e r meter. The light reflection was detected by a Hamamatu Photonics R-928 photomultiplier, and the signal was fed into a N F Circuit Block LI 575 lock-in amplifier with a BX-31 preamplifier. The ratio of the synchronous component to the total reflected light intensities (AR/R) was calculated on a Stanford Research System SR245 analog processor and recorded on a Riken Denshi SPG3C recorder.
Results Line Shape of Photoreflectance and EER Spectra. A typical EER spectrum measured at a modulation frequency of 18 Hz is shown in Figure 2. Below 1 kHz, the spectrum was independent of the frequency of the electrode potential modulation. The intensity at the peak wavelength of the spectrum linearly increases with increasing modulation amplitude, as shown in Figure 3. V-l for 497 and 510 nm, Slopes are 2.5 X and 1.4 X respectively. Figure 4 shows profiles of the photoreflectance spectra for different laser fluences. The 497-nm peak coincides with that in the EER spectrum, but the 5 IO-nm valley is opposite to the EER peak. The line shape is the same as spectrum a in Figure 4 at laser fluences below 3.0 X 1Om m-2 s-I. At higher laser fluences, the valley at 510 nm increases in depth with decreasing height of the 497-nm peak. (28) Ferrer, 1. J.; Salvador, P.Ber. Bunsenges. Phys. Chem. 1987, 91, 314. (29) Inoue, T.; Watanabe, T.; Fujishima, A.; Honda, K.;Kobayakawa, K. J . Electrochem. Soe. 1971, 124, 719.
600
I
I
I
550
500
450
A
400
nm
/
Figure 2. Typical EER spectrum at CdS/electrolyte interface. 1
I
0
0.1
1.3
I
I
I
0.2
0.3
Vmod / V
Figure 3. Peak heights of the EER spectra plotted as a function of modulation amplitude. Peak wavelengths: (a) 495 and (b) 507 nm.
550
500
450
h / nm
Figure 4. Laser fluence dependence of photoreflectance spectra. Flus-’. ences: (a) 2.2 X IOz0. (b) 8.0 X IOzo, and (c) 16.0 X 10”
The dependence of the spectral shape on the laser fluence was reproducible for repeated change of the fluence; therefore, the
The Journal of Physical Chemistry, Vol. 95, NO. 24, 1991 9963
Surface-Trapped Charge at CdS Electrode I
I
A
i
7 I /--. . . " 3.0
2.0
2
5.0
d
- I
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1
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0
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4.0
6.0
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Figure 5. Modulation frequency dispersion of photoreflectance spectrum intensities at 497-nm peak. Electrode potential: 0.4 V vs Ag. (Inset)
Photoreflectance spectrum at this potential.
2 -
d
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j
1
01 0
I
2.0
I
4.0 Log ( f/Hz )
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Figure 6. Same as Figure 5 , except the electrode potential is 1 .O V vs Ai3.
change in the shape is not ascribed to the change of the surface photocorrosion. The mechanism of the change in the line shape is not elucidated at the present stage. Discussion for the photoreflectance spectra will be limited to the results for low laser fluences, where the line shape is identical to spectrum a in Figure 4. For the comparison between EER and photoreflectance experiment, the 497-nm peak will be used on the assumption that the origin of this peak is identical for both EER and photoreflectance spectra. Frequency Dispersion of Photoreflectance Intensity. The photoreflectance intensity depends on the modulation frequency of the laser pumping. Typical results are depicted in Figures 5 and 6, where intensities of the 497-nm peak of the photoreflectance spectrum are plotted as a function of the (natural) logarithm of the modulation frequency. The laser fluence is 2 X lozom-z s-I, common to both, but the electrode potentials are 0.4 and 1.O V vs Ag for Figures 5 and 6, respectively. The frequency dependence suggests that the modulation in the electrostatic field in the space charge layer, which is the origin of photoreflectance spectroscopy, delays in time from the laser excitation of the electrode. Since the electrostatic modulation is caused by the surface-trapped charge, the dependence must contain the contribution from the kinetics of the photocreation and dark neutralization of the surface-trapped charge. The frequency dependence is featured by the response over a wide frequency range over 2 orders of magnitude. If the frequency response were characterized by a single lifetime, the response should change steeply within the frequency of the same order of magnitude as the reciprocal of the lifetime. The observed wide-range response suggests that there is dispersion in the lifetime. Comparison between Figures 5 and 6 indicates that the electrode potential does not affect the frequency dependence of the pho-
toreflectance intensities, although it affects the spectral shape appreciably as shown in the inset. As the spectral response almost vanishes at ca. 500 Hz,the lifetime of the surface charge is on the order of a millisecond. The certain value of the lifetime of photocreated holes on the top of the valence band is not known, but the experiments conducted on the CdS colloid suggest that the lifetime of the hole is in the nanosecond or picosecond domain.3b33 If such a fast component of the photoreflectance appears in the picosecond or nanosecond domain, it cannot be detected by the present lock-in detection system. Thus, at least at the frequency domain below 1 kHz, the contribution of the holes to the photoreflectance spectrum is probably negligible. The origin of the photoreflectance spectrum in this frequency domain cannot be assigned to the hole on the valence band but to another entity which is probably the charge trapped in a surface state. Evidence supporting this assignment is that the electrode current for the slow process, which will be calculated a t the end of Discussion, is very small compared with the total photoinduced current due to a major process, which is probably electron transfer from an electron-donating solute to the hole on the valence band. Laser Fluence Dependence of Photoreflectance Intensity. At the laser intensities for the constant photoreflectance line shape, the spectral intensity was measured with the laser fluence varied at a fixed electrode potential of 0.1 V vs Ag. In Figure 7, the intensities at the 497-nm peak are plotted as a function of the fluence of the 458-nm laser line. The plot shows a saturation over a fluence of 2 X 1020 m-2 s-l. The plot enables us to evaluate the two-dimensional density of the surface charge and the optical cross section for the photocreation of the charge are evaluated, as will be described later.
Discussion Frequency Dependence. Formulation was made for the frequency dependence of the photoreflectance spectral intensity on the basis of the model as described in Figure 1 and on the assumption of a distribution for the lifetime of surface charge. The relation between spectral intensity and the electrostatic field modulation is given by34 A R / R = Ag2L(hu) where L(hv) denotes the line-shape function of the spectrum, which relates the band structure of the semiconductor, and A,$ is the modulating amplitude of the electrostatic field in the space charge layer. A( is caused by the modulation of the electrode potential (in EER) or by the photocreation of the surface charge (in photoreflectance). (30) (31) (32) (33) (34)
Rossetti, R.; Brus. L. E. J. Phys. Chem. 1986, 90, 558. Nosaka, Y.; Fox, M. A. J. Phys. Chem. 1986, 90, 6521. Nosaka, Y.;Fox, M. A. J . Phys. Chem. 1988, 92, 1893. Morgan, J. R.; Natarajan, L. V. J . Phys. Chem. 1989, 93, 5. Aspens, D. E. Phys. Reu. Lett. 1972, 28, 913.
Nakabayashi and Kira
The Journal o j Physical Chemistry, Vol. 95, No. 24, 1991
9964
1.5 1
I
'TABLEI: Electrode Potential Dependence of Fitted Parameters in Modulation Frequency Dispersion of PR Spectra Intensities EIV vs AP,
0.10 k
f A R / R ~ n / 1 0 - 3 1.0 3.7 0.54
'"'
&/mS
v
P
M
0.40
0.65
0.70
1.0
1.4
1.3 2.6 0.49
1.3 1.9 0.48
2.6 4.5 0.35
2.6 2.1 0.48
1.3 1.6 0.41
0 b
IC=-
6
1.o
0
2.0
I
%dJx
-
/ f, Figure 8. Typical shape of the distribution of lifetime calculated in terms of eq 6. t
For the space charge layer of the n-type semiconductor electrode, the potential is given by35936 v(X)= eNdX2/2€Co (2) where e, N,, e, and eo represent the electronic charge, the donor density, the dielectric constant of the electrode, and the permittivity of the free space, respectively. If the penetration length of the probe light is smaller than 0.2x0,where xo is the thickness of the space charge layer, eq 1 is recast as A R / R = (2eNd/cto)vsc0L( hv) (3) where VK0 denotes the potential at the surface of the electrode. By Gauss's law, the surface charge is related to the surface potential, and eq 3 is rewritten as A R / R = (1 /eto)2Q,ZL(hv) (4) where Q, represents the two-dimensional surface charge density. On the assumption of exponential decay characterized by a lifetime T , the time evolution of the surface charge after the laser excitation is cut off is represented by Nmc(t) = ~ m c q J ~ g ( 7 exp(--t/7) ) d7
n
VI
I!
'
I
+1.6
(5)
where Nmcq denotes the densities of the surface charge in the photostationary state, N,,(t) is the density at time t after the light is cut off, and g ( r ) is the distribution function of the lifetime, T g(T) = sin @ r / r r ~ ( y+f ly-8 + 2 cos 0s) (6) where y = 7 / 7 0 and ro is the average lifetime. Equation 6, proposed by Cole and is a convenient function, because, by a single parameter, 6, it can represent extremely different lifetime distributions as depicted schematically in Figure 8. Equation 5 describes the kinetics in the time domain. To analyze the experimental result of the frequency dispersion, eq 5 is tranformed into the frequency domain by Fourier transformation Nmc(w) = Nmcq/ [ 1 + (i~70)'I (7) where i2 = -1 and w is a modulation frequency multiplied by 27~. Substituting Q,in eq 4 by e", one obtains the final equation in the frequency domain: A R / R ( w ) = (eNm,~/eeo)2[1/1+ ( i w ~ ~ ) f l ] ~ L ( h(8) v) The solid curves in Figures 5 and 6 represent simulations in terms of eq 8. Table I lists the values of parameters T~ and @ that give the best fit with the experimental data for several electrode potentials. Crude averages are 3 f 1 ms for so and 0.5 f 0.1 for ~~~
~~~
~
~~
~~~~
~~
~~
~
(35) Gerischer, H. In Advances in Electrochemistry and Electrochemical Engineering. Interscience Publischers: New York, 1961; Vol. 1. (36) Memming, R. Charge Transfer Processes at Semiconductor Electrodes. In Electroanalytical Chemistry; Bard, A. J., Ed.; Dekker: New York, 1979; Vol. I I . (37) Cole, K. S.;Cole, R. H. J . Chem. Phys. 1941, 9, 341. (38) Shimizu, H.J . Chem. Phys. 1965, 43, 2453. (39) Yoshimitu, K.; Matubara, T. Prog. Theor. Phys. Suppl. 1968, 109.
(40) Marcus, R . A. J . Chem. Phys. 1965, 43, 694.
Surface-Trapped Charge at CdS Electrode
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9965
pression used for simulations for X = 0.7 eV, u = 0.4 eV, A / (47rk7')'/* = 1, and N0/(27r)1/2= 1: gT(7) = 2
2.5Zexp-l.3{Em, - Erdox- 0.7 n- I
+ (-1)"[(1/12)
In 1.2r]'/2)2
(13) Graphs of eq 13 for some selected values of E, - Edox are depicted in Figure 9. Simulations indicate that distributions qualitatively similar to the experimental one (for j3 = 0.5 in Figure 8) appear in the region 0.4 < (E,, - ,Fredox) < 1 for the above conditions. A probable estimation for is 0.3 V vs EbB which indicates that the E,, is located in the region from 0.7 to 1.3 eV below the conduction band; Le., the surface charge is trapped by an interband state. The above simulation refers to a single-electron transfer. The oxidation of the real electron donor, Sol2-, is known to proceed ~ ~ nothing ~'~~ irreversibly on multielectron-transfer p r o c e s ~ e s , but has been studied on the slow electron transfer which is discussed here. If two different electron donors, e.g., Sol2-and its one electronically oxidized form, are concerned with the observed lifetime, two different distributions of the donor level should be taken into account, and the equations should be modified. The above formulation, however, shows that the distribution of the lifetime can be explained qualitatively or semiquantitatively in terms of the electron-transfer theory. Fluence Dependence. The laser fluence dependence of the reflectance is analyzed for evaluation of the density and the optical cross section of the surface state. The rate of the photocreation of the surface charge, Le., the photoionization, is given by dN,,/dt = 41pb- kN,, (14) where 4 denotes the quantum efficiency of the photoionization, I,, the photondensity absorbed at the surface, and k the average rate constant of the neutralization of the surface charge which is equal to 1 / T ~ . The total density of the surface states, No, is given by
+
(15) No = N,, N,, where N,, is the density of the reduced form of the surface state. Equations 14 and 15 combined with the Lambert-Beer law lead to
dNmc/dt = 4411 - exp[-pc(No - "JII - kNmc (16) where p denotes the optical cross section of the surface state. The MacLaurin expansion of the right-hand side of eq 16 is combined with the photostationary condition to lead to Nmcq = 4IGNo/(k
+ 410~)
(17)
Equation 4 is recast in terms of eq 17 as [AR/R(Io)]-1/2 = [ceo/L(hv)1/2eNo](l+ k/p410) (18) (41) Foerster, A.; Friessner, A. Ber. Bunsenges. Phys. Chem. 1902, 35, 2515. (42) Friessner, A. 2.Elekrrochem. 1904, 10, 265. (43) Yokosuka, F.; Okuwaki, A.; Okabc, T. Nippon Kugaku Kaishi 1975, 1722.
LA i
0.5 0
2.5
5.0
1.5
( 1 / Io ) / m ' sec Figure 10. Plot of the data of Figure 7 in terms of eq 18.
The value of e is 10 for CdS.44 The value of L(hv) at 497 nm is estimated as 3.5 X lo-'' m2 from the slope of Figure 2 and eq 3. The vertical intercept of Figure 10, combined with these values, gives the density No = 1.6 X lOI5 m-2. As T~ is 3 ms as shown in Table I, the slope leads to 4p = 19 A2 on k = 1 / =~ ~ 3 X lo2 s-l. As the quantum efficiency 4 is not known, a value of 19 A2 is the lower ilmit of the optical cross section p. The density is too low to cause the Fermi level pinning,I6 which occurs above a surface-state density of 101'-101* m-2; therefore, the potential drops within the space charge layer in the electrode, which is consistent with the linear relation between EER and the modulation height as shown in Figure 3. By using the values obtained above, the rate of the electron transfer is calcualted in the form of current density: i = eNo/To = 7 (pA/cm2)
The observed total photocurrent is about 2 orders of magnitude as large as this value. The slow process that gives such a small current cannot be a major process-the oxidation of SO,2- by the hole on the valence band.
Conclusions This is the first experimental study of the application of photoreflectance spectroscopy to the semiconductor-electrolyte interface. Although EER and photoreflectance spectroscopy are classified in the same category in modulation spectroscopy, photoreflectance spectroscopy has the potential to develop into kinetic spectroscopy for the photocreated surface charges. This study is concerned with the kinetics in the millisecond region. The application to faster kinetics for evaluation of the hole transfer on the top of the valence band is now in progress by direct time-resolved measurement using a nanosecond pulsed laser. Registry No. CdS, 1306-23-6; Na2S04,7757-82-6; Na2S03, 775783-7. (44) Berlincourt, D.; Jaffe, H.; Shiozawa, L. R. Phys. Reu. 1963, 129. 1009.
