J . Phys. Chem. 1989, 93,1975-1971
the barrier. The results are shown in Figure 2. The ab initio surface favors a slightly off-collinear attack but has a cone of no reaction similar to that of the empirical surface. Hence, the role of reagent alignment is somewhat reduced for the computation using the ab initio barrier but is otherwise quite similar for the two surfaces. The barrier functionality in itself is thus not the prime reason for the lack of dependence on the laser polarization for HC1 excited to u = 2. The essential difference between the O(3P) + HCI(u=2) and O(3P) HCl(u=l) results (shown in Figure 3) is due, in the trajectory computations, to the higher reactivity within the cone of acceptance in the former case. This reflects the higher energy available at the barrier (or, equivalently, the lower barrier for a stretched molecule). There is therefore a good test case for the effect of yibrational excitation on the cone of reaction: Measure dald(E.2) for 0 HCl(u=l) a t the same ET as for 0 + HCl(u=2). Our original prediction'* for 0 HCl(u=l) based on a kinematic model has since been supported by trajectory computations of both othersz3 and ours. Both trajectory com-
+
+
+
(23) Loesch, J. J. Faraday Symp. Chem. SOC.1989, No. 24.
7975
putations and more approximate model results (Figure 2 vs Figure 10 of ref 18) thus show differences in the reactivity of aligned HC1 in u = 1 and 2, respectively. Trajectory computations showing the dependence of the reaction cross section on the angle of attack, y (as defined, e.g., in ref 9 and 14), are shown in Figure 4. Note however that due to the range of impact parameters contributing to the reaction, the cross section shown in Figure 4 is no: Grectly measurable, since the relation between y and the angle E-2 is not then 1:l. Thelrejults shown in Figures 1 and 3 suggest that measuring da/d(EZ), even at only two angles, but for HCl in both u = 1 and 2 and at the same ET would be revealing. Acknowledgment. We thank Prof. R. N. Zare and Dr. K. G. McKendrick for many comments about their experiment. We thank Prof. M. S. Gordon for the prepublication communication of this ab initio computed barrier to reaction. This work was supported by the US.-Israel Binational Science Foundation (B.S.F.), Jerusalem, Israel. The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munich, BRD. Registry No. 0, 17778-80-2; HC1, 7647-01-0.
Time-Resolved Luminescence of Electron-Hole Pairs in CdS, Se,, Semiconductors
Graded
Jennifer K. Hane, Michael G. Prisant,t Charles B. Harris,* Department of Chemistry, University of California at Berkeley, Berkeley, California 94720
Gerald J. Meyer, Larry K. hung, and Arthur B. Ellis* Department of Chemistry, University of Wisconsin at Madison, Madison, Wisconsin 53706 (Received: September 8, 1989) Time-resolved photoluminescence (PL) from graded CdSSe,, samples that exhibit spatially resolved PL has been used to study the dynamics of nonequilibrium distributions of electron-hole pairs in air at 295 K. Samples have been studied with the band gap increasing both toward the surface (CdSe/S) and toward the bulk (CdS/Se). Decay times ( l / e )in PL spectra for CdS/Se and CdSe/S samples, measured between -500 and 740 nm, occur over roughly 100-400 ps and are strongly dependent on detection wavelength, reflecting carrier dynamics. The decay traces show a nonmonotonic dependenceon detection wavelength. Graded samples of n-CdS,Sel, have been shown to exhibit color-coded photoluminescence (PL) that permits identification of the spatial origin of e--h+ pair recombination in continuous illumination experiments.I The observed PL is derived from the band edge emission characteristic of the alloy compositions comprising the graded zone A, (nm) = 718 - 210x (1) The band gaps of these materials are direct and increase monotonically from 1.7 eV for CdSe to 2.4 eV for CdS. By use of Auger electron spectroscopy and Ar+ sputter etching, the locations of alloy compositions that contribute to the observed PL spectral distributions can be identified. Samples can be prepared with alloy band gaps increasing either toward the surface or toward the bulk by diffusing S into CdSe (CdSe/S) or Se into CdS (CdS/Se), respectively. Because the emission wavelength is related to the composition, which in turn is related to the distance away from the surface into the bulk, these graded solids are ideally suited for direct study of the carrier dynamics. Recombination of e--h+ pairs at various depths beyond the near-surface region where they are first created can be temporally resolved and thus give information on the 'Present address: Department of Chemistry, Duke University, Durham, NC 27706.
0022-3654f 89f 2093-1975$01.50/0
diffusion times from the surface to the bulk. The feasibility of such studies with graded CdS,Se+, samples is demonstrated. Specifically, we show that PL decay times occur over roughly 100-400 ps and are strongly dependent on detection wavelength, reflecting carrier dynamics. The decay traces also show a nonmonotonic dependence on detection wavelength. Samples of CdSe/S and CdS/Se were prepared as previously described from single-crystal CdS and CdSe substrates.'-* The graded CdS$el, samples have 1-~m-thickgraded regions. For CdSe/S specimens, the graded zone comprises virtually all of the alloy compositions (0 Ix I1); for CdS/Se, the compositions vary from x 0.2 at the surface to x = 1 in the substrate. Sample excitation using a picosecond laser system at 3 15 nm creates a nonequilibrium distribution of e--h+ pairs with a density of lOI4 ~ m - ~At. this excitation wavelength the incident light is estimated to be absorbed within -0.1 Fm of the s ~ r f a c e . ~The , ~ temporal decay of the luminescence at a given wavelength is measured by using time-correlated single-photon counting techniques.s
-
-
-
( I ) Carpenter, M. K.; Ellis, A. B. J. Electroanal. Chem. 1985,184, 289. (2) Carpenter, M. K.; Streckert, H. H.; Ellis, A. B. J . SolidState Chem. 1982, 45, 5 1. (3) Dutton, D. Phys. Reu. 1958, 112, 785. (4) Parsons, R. B.; Wardzynski, W.; Yoffe, A. D. Proc. R. SOC.London, A 1961, 262, 120.
0 1989 American Chemical Society
Letters
7976 The Journal of Physical Chemistry, Vol. 93, No. 24, 1989 Fi
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Figure 1. CdSe/S photoluminescence. (A) PL decays for 500-620 nm
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R Data on graded CdSe/S samples are illustrated in Figure IA,B. Incident excitation is absorbed in CdS and S-rich alloy strata (x L 0.7). The decay functions are clearly dependent on detection wavelength and become longer as expected from 500 to 620 nm, corresponding to the spreading distribution of carriers. However, in the 620-700-nm region the trend is reversed. Here the decay functions are faster at longer wavelengths. This is unexpected. One possible explanation is that fast surface recombination events are biasing the decays observed at these wavelengths. Further studies are required to determine the extent of such effects. Overall, the decay functions have l / e time constants of 100-400 ps. Thus, the diffusion process is occurring on a time scale that is competitive with characteristic band-to-band recombination lifetimes for direct band gap semiconductors.6 The observed decays, however, yield information about transport, rather than merely reflecting differences in intrinsic lifetimes of the materials comprising the graded region. This conclusion is supported by extending the study to CdS$e,-, materials with the opposite composition gradient. These results, as discussed below, demonstrate that the l / e decay constants are not the same a t a given wavelength for the two materials, as they would be if only the lifetime were being measured. Instead, the decays show a dependence on factors such as band gap gradient and distance from initial excitation. The appearance of carriers removed from the S-rich regions of the CdSe/S material is illustrated with "gated" PL spectra, Figure 2A. The spectra reflect only events that occur in a given time window of 400 ps. As this window is shifted in time, the resulting spectra show an increase in relative intensity at longer wavelengths, consistent with the picture of carrier diffusion into deeper regions. As a rough check on the diffusion interpretation, the mobility of the minority carrier (ph) was estimated from the time scale of the decay functions. Using the difference in I/e decay constants from 500 to 620 nm, the depth profile, and the potential drop across the depth profile, one can obtain an approximate value for ph
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Figure 3. CdS/Se photoluminescence. (A) PL decays for 500-620 nm
become longer at shorter wavelengths, corresponding to increased distance from initial excitation. (B) The 620-740-nm region shows a reversal of the previous trend. This value is in accord with the mobilities for CdS and CdSe materials.' As indicated, further study was performed on CdS$e,, material that possesses the opposite composition gradient, Le., Se-rich region near the surface (lower band gap) with CdS substrate (higher band gap). The steady-state PL of this material indicates ~that the ~ excitation is absorbed significantly in regions of mixed (7) Madelung, O., Schulz, M., Weiss, H., Eds. In Londolt-Bornstein Numerical Data and Functional Relationships in Science and Technology; Hellwege, K.-H., Editor-in-Chief;Springer-Verlag: Berlin, 1982; New Series, Vol. 17b, pp 190, 217.
J . Phys. Chem. 1989, 93. 7977-7978
composition. However, the time-resolved PL decay functions still reflect the appearance of e--h+ pairs at compositions far removed from the initial excitation. The results are shown in Figure 3A,B. The "gated spectra" in Figure 2B demonstrate an increase in the relative intensity at shorter wavelengths corresponding to the appearance of carriers in the deepest regions, Le., toward the bulk. Hence, the observed trends in decay functions for this material are reversed with respect to the oppositely graded CdSe/S material. In particular, the decay functions for the deepest region (620-500 nm) become longer with decreasing wavelength (increasing depth or distance from initial excitation). This trend is observed even though appearance of e--h+ pairs in the CdS region involves transport up a band gap gradient of at least -0.35 eV (assuming significant absorption occurs to the region of roughly CdSo,,Sq,5composition). It appears, therefore, that diffusion down the carrier concentration gradient is sufficient to drive the e--h+ pair transport. In the 620-740-nm region the decays become longer at longer wavelength. This trend presumably reflects both diffusion in the carrier concentration gradient and the band gap gradient. Furthermore, since the band gap increases away from the surface, self-absorption and reemission effects will contribute to longer decays for wavelengths characteristic of the near surface region. Although it is clear that the system is appropriate for studying e--h+ transport, it is not straightforward to map the observed trends into position and time-dependent equations (diffusion and continuity equations) for the number of carriers. Transport in a graded semiconductor has been treated in the special case of doping to eliminate space charge (i.e., internal electric fields).* In this case it can be shown that the diffusion of electrons (and holes) is described by two terms dE i = -D dn Dn (3) dx k T dx where i is the particle current, D the diffusion constant, n the number of particles, x the position, T the temperature, and E the conduction (or valence) band edge energy. The first term is the standard Fick's diffusion, and the second term indicates transport to lower band edge regions. In the current experimental situation, with arbitrary doping profile, it is not clear what effects space charge regions have on carrier dynamics. However, if these effects were extremely important, carriers would probably not reach the deepest regions, since internal electric fields move electrons and holes in opposite directions. The transport mechanisms described by eq 3 yield particle currents in the same direction for both electrons and holes and therefore can account for smooth trends in the characteristic decay times and appearance of carriers in the deep regions. A further complication involves specifying a position-dependent recombination rate that couples continuity equations for the electron and hole populations. Finally, the graded semiconductor system provides an opportunity to study another phenomenon, the effect of local potential (8) Van Ruyven, L. J.; Williams, F. E. Am. J . Phys. 1967, 35, 705.
7977
fluctuations due to S/Se substitution on e--h+ pair dynamics. In a graded semiconductor where the composition changes slowly relative to the lattice spacing, the environment at a given depth can be considered to be that of a homogeneous semiconductor layer with a particular mole fraction x . An understanding of transport properties associated with this composition requires knowledge of the band edge states. In an alloy material the description is complicated by the random substitution of the lattice sites, which does not produce a periodic potential. Further deviations from periodicity arise through geometric constraints imposed by differing lattice constants. Although both CdS and CdSe crystallize in a hexagonal wurtzite structure, CdS has lattice constants a = 4.14 and c = 6.72 A, while CdSe has a = 4.30 and c = 7.01 A. However, if the de Broglie wavelength of carriers is long relative to the potential fluctuations, it has been shown that a valid picture can be obtained when the statistical distribution of unit cells is replaced by an array of average unit cells. The potential associated with this average unit cell then determines the band gap energy. The linear shift in emission maximum for homogeneous samples with a particular x supports this picture of the band edge states. However, time-dependent measurements have established that, for an alloy material such as CdS,Se,-,, trapping in regions of low potential will occur.9 The picture of radiative recombination occurring from band edge states with wavelength corresponding to a given composition is an oversimplification in this case. Since the decay functions include all radiative transitions with a particular energy, they will reflect local fluctuations from a (possibly) broad range of compositions. The resulting form should be highly nonexponential, as observed. Further experiments are in progress to determine the extent of localization, as well as the effect of smoothly varying x, and thus the amount of disorder, with depth. In summary, the graded CdS>e,-, semiconductors provide an interesting system to probe the effects of band gap distortion over a macroscopic distance on the dynamics of excess e--h+ pairs. The luminescence decay functions for systems with both increasing and decreasing band gap reflect diffusion in concentration and band gap gradients as expected, although some features remain unexplained. The overall time scale of the decays is fast (hundreds of picoseconds), indicating transport is competitive with recombination and making quantitative description difficult. The system also looks promising for studying the effects of local potential fluctuations in a partially disordered material, since changes in the composition fraction x correspond to differing degrees of substitutional disorder. Acknowledgment. This work was supported by the Office of Naval Research. We also acknowledge the US.Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division, under Contract No. DE-AC03-76SF00098 for some specialized equipment used in these experiments. (9) Gourdon, C.; Lavallard, P.; Permogorov, S.; Reznitsky, A.; Aaviksoo, Y . ;Lippmaa, Y . J . Lumin. 1987, 39, 111.
Reevaluation of the Bond-Dissociation Energies (AH,,,) H-0, H-00-, and H - 0 0
for H-OH, H-OOH, H-00-,
Donald T . Sawyer Department of Chemistry, Texas A & M University, College Station, Texas 77843 (Received: August 3, 1989) The thermodynamic redox potentials for H+, HOH, 02,HO;, O;-,'OH, and 0'-,when appropriately combined, provide accurate values for the dissociative bond energies (AHDBE) of H-OH (1 19 kcal), H-OOH (90), H-0' (106), H-0- (1 16), H-OO- (80), and HOO' (59). The latter two values are 21 and 12 kcal greater, respectively,than their long-accepted values. O W ,
The hydrogen-oxygen dissociative bond energies (AH,,,) of H-OH, H-OOH, H-0', H-0-, H-00-, and HOO' are a mea0022-3654/89/2093-7977$01.50/0
sure of the hydrogen atom abstraction reactivity of the HO', 02*-, and '02* radicals, respectively. Values for HOW, *O',0'-, 0 1989 American Chemical Society
