4141
J . Phys. Chem. 1993,97, 41414148
Time-Resolved Studies of Charge Carrier Relaxation in Chemically Modified Semiconductor Electrodes: n-CdSe/Silane Interfaces W. J. Dollard, M. L. Shumaker, and D. H. Waldeck' Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Received: September 14, 1992; In Final Form: December 22, I992
Time-resolved fluorescence is used to monitor the relaxation dynamics of minority carriers in n-type CdSe semiconductor electrodes. Five different silane compounds are used to chemically modify the interface and change the surface recombination velocity. In order to quantitate the interfacial recombination of charge carriers, a perturbative solution of a nonlinear diffusion equation is developed. These studies are combined with surface analysis and electrochemical studies to identify the nature of the chemically derivatized interface and characterize its electrical properties. This work clearly demonstrates the strong effects of surface treatment on the charge carrier dynamics and the sensitivity of fluorescence in monitoring the dynamics.
Introduction Charge carrier relaxation at interfaces is ubiquitous in nature, and charge carrier relaxation at semiconductor interfaces plays an important role in many technological devices. Charge carrier dynamics is fundamental in photocatalytic and photoconductive processes and in the operation of photovoltaic devices. In a more profound vein, charge carrier relaxation is one of the fundamental chemical events which occur in solid-state media. This work aims to quantitatively model the charge carrier relaxation and, in the longer term, its relationship to material properties and/or the chemical properties of the constituents. The material chosen for these studies is single-crystal n-CdSe, a direct-gap semiconductor (1.7 eV) which has been widely studied as a photovoltaic material.'-3 The interfacial recombination is varied by preparing chemical derivatives of the interface using chlorosilane compounds. The chemical nature of the overlayer is studied using SIMS and XPS surface analysis methods. The electrical characteristics of these electrodes are studied using standard electrochemical methods (photovoltage, photocurrent, capacitance-voltage profiling, and photocapacitance spectroscopy). The silane overlayers are found to have little effect on the steady-state electrical characteristics of the electrodes; however, the charge relaxation as monitored by the fluorescence decay changes by more than an order of magnitude. This work clearly demonstrates that small changes in interfacial properties may have dramatic effects for the charge relaxation. The qualitative aspects of the interfacial recombination are evident in the observed fluorescence decay curves. Similar observations have been reported on n-CdSe and n-CdS with treatment by adsorbed metal ions,4 for the steady-state fluorescence yield when the surface is chemically m ~ d i f i e dand , ~ in other materials as we11.6 In the studies presented here a clear trend of increasing recombination velocity with increasing ionization potential of the substituent is found. Unfortunately, attempts made to quantitate the properties of the interfacial states (e.g., energy difference between interfacial state and the band of the semiconductor) were unsuccessful. In order to quantitate the interfacial recombination velocity, it is necessary to model the bulk properties of the semiconductor adequately. Models used previously to quantitate the decay characteristicshave been shown to be inadequate' for this material. In particular, the influence of self-absorption, nonlinear bulk recombination dynamics, and the space charge potential of the electrode have been shown to be important in the relaxation process. The model used to describe the charge carrier relaxation in this material includes the effects of self-absorption as well as the recombination and trapping of minority carriers in the bulk 0022-3654/93/2097-4 141%04.00/0
of the material. The fluorescence studies in this work were performed with the electrode in contact with air. Consequently, the space charge potential is not well-defined,and it is not included in the modeling. This field can influence the dynamics however, and the recombination velocities reported herein should be considered as upper bounds on the actual value. The emphasis of this study is on the relative change in the surface recombination velocity with chemical treatment. Such comparisons should be valid when the space charge field is independent of chemical treatment. The effect of the space charge field will be discussed quantitatively in a future paper. With this caveat the decays will be analyzed to extract a surface recombination velocity. In the first section of the paper, the model used to describe the trapping in the bulk of the semiconductor is discussed and a perturbative solution of this nonlinear diffusion equation is presented. Second, the experimental details of samplepreparation and the methods used are described. Third, the results of the electrode characterization are presented. Fourth, the timeresolved fluorescence studies of the electrodes are presented and analyzed. Last, conclusions about the interfacial recombination are drawn, and the limits of this analysis are discussed.
Theoretical Modeling The theoretical model used here is based on a general treatment of charge carrier trapping and recombination found to be quite useful in the description of the photoconductive properties of semiconductor materials, and in particular CdSe.8*9Because the material is n-type and the photoinjected minority carrier density may be significant compared to the background concentration of majority carriers, the common description of the radiative recombination as first order in minority carrier density is not appropriate.' Instead, the time-resolved fluorescence decay law is given by r,Jo-dx [exP(-Bx)lP(x,t)(n,
+n(x4)
r,Jomdx [exP(-Ox)lP(x,O)(no
+ n(x,O))
K(t) =
(1)
where yr is the effective radiative decay constant, /3 is the absorption coefficient of the material at the emission wavelength observed, no is the equilibrium density of electrons, and p ( x , t ) is the time-dependent minority carrier population density. The assumptions inherent in the use of a one-dimensional treatment of the population dynamics and the inclusion of self-absorption effects through the use of the parameter B have been discussed previ~usly.~Instead of explicitly treating the dynamics of both 0 1993 American Chemical Society
4142 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993
Dollard et al. density of recombination centers, and NA is the number density of hole traps. The bimolecular rate constants (yrry, xi) in these equations are defined by Figure 1. The term g(r,t) describes the generation of carriers by the laser excitation, and pl is defined by
A
VB
Y
Z=O
Figure 1. This figure shows a schematic drawing of an energy level scheme for the bulk n-CdSe semiconductor electrode. The arrows indicate relaxation pathways which influence the photogenerated carrier’s time evolution.
the photogenerated holes and the electrons it is common to approximate the time behavior of the nonequilibrium majority carriers (in this case electrons) by that of the minority carriers, namely, p ( x , t ) = n(x,t) in eq 1. These two populations are not expected to deviate strongly because of the electric field generated when the particles move apart. In this approximation the diffusion coefficient of the minority carriers is replaced by an ambipolar diffusion coefficient.I0 The discussion here focuses on a model for the minority carrier population density. Figure 1 shows an energy level diagram for an n-type semiconductor in the bulk, i.e., no space charge field is shown at the interface. The levels labeled A near the valence band are acceptor levels which may act as hole traps during the relaxation of the photoinduced minority carrier (hole) population. The energy levels labeled R in this diagram are recombination centers which are believed to lie near the midgap region of the material. The Fermi level lies near the conduction band for an n-type material. Under photoexcitation however the carrier population is perturbed away from equilibrium; Le., the quasi Fermi level for holes drops in energy and may lie near or even below the levels labeled R. A two-state energy level scheme as shown here can lead to very rich b e h a v i ~ r . ~This . ~ type of model was in fact developed to explain the nonlinear intensity dependence of photoconductivity in CdSe and CdS. More recently, this model was shown to describe the temperature- and intensity-dependent emission spectrum of CdSe.” Here the model is extended to incorporate surface effects, Le., the finite absorption length of suprabandgap excitation and the interfacial recombination velocity. The model is solved to find the effective relaxation time of fluorescence. The equations describing transport and kinetics of the carriers in the model indicated by Figure 1 are dn(i,t) -- DnV2n(i,t) + g ( i , t ) - x,,pR(no + n(i,t)) dt
-PA) - y P d l
The first-order decay rate constant 1/r is given by
under low injection conditions, and by XpXnNR -1 = yrn0+ 7
xp
+ Xn
(9)
under high injection conditions. When xn>> xp,these two limits are equivalent. The first-order rate constant has contributions from the radiative recombination and the nonradiative recombination through the states R. The second-order rate constant b is given by
-
Y P A -~TPOJ)(NA ~ -PA) - yr(n0 + ~ V J ) ) P ( ~(4) J)) dPA dt = yp(i,t)(NA
where NVis the density of states in the valence band and E A Ev is the energy gap between the trap state and the valence band edge (note that for holes, discussed here, the valence band energy is greater than the acceptor state energy). These equations can be simplified considerably under conditions appropriate to the experiments. As discussed above, the dynamics of the electrons will not be explicitly treated and the diffusion coefficient for the holes will be replaced by an ambipolar diffusion coefficient, D = 2(DnDp)/(Dn + D,). Moreover, the diffusion coefficient of electrons in CdSe is more than 10 times larger than that for holes such that D = D,. Second, the assumption of a rapid, or quasi, equilibrium between the acceptor states and the valence band is made. This assumption allows the population of holes in the traps to be determined by the hole population in the valence band and an equilibrium constant [namely, PA = ~ N A / NVexp((Ev-EA)/kT)]. This approximation will bevalid when a clear time-scale separation exists between the relaxation of holes into the acceptor states from the valence band and the recombination of carriers between the conduction and valence bands (either directly or through the recombination centers R). When the acceptor levels lie close to the valence band edge in energy, this approximation is expected to work well. In the case of CdSe the defect levels are believed to lie about 0.1 eV above the valence band edge.I1J2 The third approximation is that the recombination through the states R moves rapidly to the steadystate limit so that dpR/dt is small or alternatively that the number of recombination centers available for hole capture is always significant. Lastly, the transport of the minority carrier population is modeled as being one dimensional. The validity of this last approximation has been clearly delineated. 13 With these approximations the set of four coupled equations is reduced to a single equation for the hole kinetics, namely
(5)
where n(r,t) is the concentration of electrons at time t , no is the equilibrium concentration of electrons,p(r,t) is the hole population density at time t , Diis the diffusion constant for particles of type i, p i is the population density of holes in state i , N Ris the number
It is this term which describes the nonlinear dependence of the relaxation on the hole population density. Note that this nonlinear term may lead to either a lengthening or a shortening of the relaxation time of minority carrier population. The shortening arises when the radiative recombination is dominant and can simply be understood as an additional relaxation pathway for the minority carrier population. The lengthening of the decay law arises from changes in the nonradiative relaxation pathways. The traps act as a storage location for holes which are later released
n-CdSe/Silane Interfaces
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4143
to the valence band where they can diffuse readily and recombine. Also the effective concentration of recombination centers may decrease as a result of hole capture. If these latter processes are dominant, then a high population of holes, or a high excitation laser intensity, leads to a slowing of the relaxation over that for the conditions of low laser intensity. Equation 7 can be written in a simpler form by defining a reduced set of units in which time is measured in terms of the inverse first-order decay rate ( 7 ) and length is measured in the diffusion length of minority carriers ( L = 6). In the limit of impulse excitation ( 6 ( t ) ) , the generation term for photoinjection is given by g(x,t) = ZOaT’[exp(-ax)]s(t)
(11)
and eq 7 becomes
that
P b s = B[A: l
exp(-2AX)
exp(-X) - (4A2 - 1)
+
+
2R exp(-(A 1)X) - R2 exp(-2X) A(A 2) 3
+
The coefficient A , is given by AI =
S+2A
(S
2R(l+A+S)
+ 1)(4A2 - 1) - A(A + 2)(S + 1)
+
+
(2 S)R2 (20) 3 ( S + 1) Using reduced variables and the above assumptions, eq 1 for the steady-state fluorescence may be written as
v P 2 ( z T ) (12) where T’is the tranmission coefficient for the excitation light which accounts for reflection at the interface, while Tand X are reduced variables (X=x / L ; T = t / ~ ) An . approximate solution to eq 12 may be found perturbatively in which the expansion coefficient is written in terms of v , namely, p(X,T) = po(X,T) + vpl(X,T) + v2p2(X,T). The zero-order equation is
where k, = y , and ~ G is a proportionality constant containing information about the geometry, collection optics, detector efficiency, etc. Using the perturbation expansion for pss, the fluorescence is given to second order in the laser excitation density
and the solution is ~ e l l - k n o w n . ~The ~ ’ ~first-order -~~ correction is found by solving the steady-state fluorescence intensity is related to the relaxation time by the ansatz
Two boundary conditions are applied in the solution of these equations, namely, that the photogenerated carrier population disappear in the bulk, or
P(X,T)I,=,= 0
(15) and that the net flux of carriers to the interface be matched by their recombination at the interface, or
where S is the surface recombination velocity in reduced units (S= u,T/L;usis the surface recombination velocity). This quantity corresponds to the interfacial recombination rate of charge carriers. If a redox-active species is present at the interface, then Scontains information concerning the interfacial charge-transfer rate. In principle, once these equations are solved, then eq 1 may be used to find the fluorescence decay law. At this juncture the equations are simplified further by assuming the steady-state limit, or dpi/dT = 0. Solution of these equations in the steady-state limit is straightforward and will be used to find an expression for the steady-state fluorescence intensity. Solution of the zeroth-order equation (13) results in PO,,,(x) = B,kXP(-AX) - R exp(-X>l
(17)
and
EOaT‘ R = -S + A Bo = s + 1 (1 - A2) where Eo is the energy per unit area of the excitation source. It may be readily verified that eq 17 is equivalent to performing the time average over the full time-dependent solution of eq 13. The first-order correction is a bit more involved, but it is readily verified
where Z(0) is the fluorescence intensity without any relaxation (Le., in the limit o f t = 0), namely
The expression for Z(0) is found by evaluating the term in the denominator of eq 1 where the initial populations of the carriers are given by the generation term in eq 11. Equation 23 is exact under conditions of low injection. The nonlinearity prevents this relationship from being rigorous at higher intensities. The final expression for the correlation time, within this steady-state approximation, is
4144
Dollard et al.
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993
+
1
1 4 - 1~ ) ( ~2 ~ B ) 2R -- A' (28) A ( A + 2 ) ( A + B + 1) B + 1 The quantity 6 is a quantum yield of fluorescence (4 E -17no) when the nonlinear term is dominated by the radiative recombination. This approximate expression for the intensity dependence of the relaxation time is compared with experimental data later.
H , ( A , B , S )= R2 3(2 + B) (
+
A
40
6
I
Experimental Section The time-resolved fluorescence7 and the electrochemical methodsI5 are standard. The specifics of the apparatuses used have been described previously.16 The SIMS results were performed at Surface Science Labs and at the University of Pittsburgh. The XPS results were obtained at the University of Pittsburgh and in collaboration with W. 1st0ne.I~ The low-resistivity, single-crystalline n-CdSe samples (cleaved perpendicular to the c-axis) were 1-mm thick and were purchased from Cleveland Crystals, Inc. The samples were etched with 0.25% Br2 in methanol for 30 s and then rinsed with methanol prior to use. For electrochemical measurements the crystals were cut into pieces with an area of about 0.1 cm2. Electrical contact was made to the semiconductor by rubbing Ga/In eutectic onto a roughened surface (Se face) and then mounting the electrode on a copper pin using silver epoxy as a bonding agent. The electrodes were subsequently sealed into glass tubing with TorrSeal resin (Varian Associates, Palo Alto, CA). Both theelectrodes and pieces of larger area (0.25 cm2) were used in the fluorescence measurements. The CdSeelectrodes werechemically treated with fivedifferent silane agents [phenyldimethylchlorosilane (PhMezSiCl), methoxydimethylchlorosilane [ (MeO)MeSiCl] ,trimethylchlorosilane (Me&Cl), dimethyldichlorosilane (MezSiClz), and methyltrichlorosilane (MeSiC13)I. After the electrodes were etched in Br2/MeOH solution, they were allowed to sit in air for 10 min or longer so that an oxide layer could form. These samples were subsequently soaked in a solution of the silane in toluene (30% by volume) for approximately 30 min and were then rinsed with toluene. Between treatments, the sample surfaces were polished with alumina to remove the silane. In the fluorescence experiments the excitation wavelength was at 595 nm for which theabsorptioncoefficient is 8.1 X 104cm-1.18 The observation wavelength varied from 700 to 725 nm. The emission was monitored with bandpass filters which have a bandwidth between 8 and 10 nm. The laser intensity was varied over a wide range but never exceeded 20 ccJ/cm2 per pulse. The laser repetition rate was 304 kHz unless stated otherwise. It was found that the form of the decay law changed when the laser repetition rate exceeded 1 MHz, but was independent of repetition rate below this value. A typical collection time for a decay curve was between 15 and 45 min. The electrochemical experiments were performed in two different solutions, 0.09 M KCl/O.Ol M HC1 (pH = 2.3) and 0.25 M K4Fe(CN)6/0.0125M K3Fe(CN)6 (pH = 8). The MottSchottky measurements, capacitance versus bias voltage, were performed in the dark with a 1-kHz modulation frequency and an amplitude of 10 mV or less. The open-circuit photovoltages were measured with the electrode under illumination from a 100-W tungsten-halogen lamp (the average light intensity was 115 mW/cm2).
Results of Electrode Characterization The success of the silane treatment of the electrode surface was verified by both SIMS and XPS studies. Figure 2 shows positive-ion SIMS spectra for an electrode surface before and
MASS (amu) FigureZ. This figure shows SIMS spectra for theuclean" n-CdSeinterface and an interface treated with trimethylchlorosilane.
TABLE I: Electrode Parameters Measured from a Mott-Schottky Analysis electrode/conditions4 VFR(V vs SCEl N,, (cm-9 ~~
~~
untreated dectrcde solution 1 solution 2 Si(C6Hd(C&)2 cap solution 1 solution 2 Si(CH30)(CH3)2 cap solution 1 solution 2
-0.463
1.0 x 10'6 1.3 X 10l6
-0.483 -0.530
1.3 X 10l6 1.9 X I O i 6
-0.489 -0.559
1.0 x 10'6 1.9 X 10l6
-0.489
Solution 1 is 0.09 M KCI/O.Ol M HCI (pH = 2.3). Solution 2 is 0.25 M KdFe(CN)6/0.0125 M K3Fe(CN)6 (pH = 8).
after treatment with trimethylchlorosilane. The surface before treatment with the silane has carbon residue and oxygen. A series of XPS studies, associated with ion etching of the interface to obtain a clean surface, reveal that much of the carbon residue is introduced by the Brz/methanol etchant. Negative-ion SIMS spectra of the electrode after etching reveals both oxygen and some bromine. After treatment with the silane compound the positive-ion SIMS spectrum changes dramatically. Carbon is still present but new features a t higher mass have appeared, namely, peaks at 73 amu [Si(CH&+], 28 amu (Si+), and 43 amu [Si(CH3)+]. Pleasenote the scalechange between the twospectra. Similar observations were found for the treatment with the other silane species. The XPS studies revealed a shift in the binding energy of the cadmium 3d3/2 and 3d512. This shift is believed to be associated with the formation of CdClz on the surface and was verified by treating a sample with Cl2 gas and observing the same changes. These studies clearly demonstrate the presence of the silane on the surface but do not give a quantitative measure of the coverage or the nature of the bonding. Electrochemical studies were also used to characterize the electrodes and to identify any changes in the electrode properties arising from the chemical modification. These studies were performed on the untreated electrode and on two derivatized electrodes, the phenylsilanation and the methoxysilanation. The capacitance/voltage characteristics of the electrodes (MottSchottky plots) were studied in solutions of pH 2.3 and pH 8 (see Table I). In all cases the dopant density, obtained from the amount of space charge capacitance, was found to lie between 1 X 1016 and 2 X 10'6 cm-3. The intercept of the plot of 1/cZ versus bias voltage is typically used to measure the flatband potential of the electrode. The intercept in these studies was -0.5 V vs SCE with an error of 50 mV or more. These values are in reasonable
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4145
n-CdSe/Silane Interfaces
TABLE II: Open-circuit Photovoltaee Measurementss ~
VK (V)
electrode/conditions untreated (MeO)Si(CH& treatment (ChH5)Si(CH& treatment
-0.650 to -0.710 -0.620 to -0.650 -0.620 to -0.650
The redox couple is 0.25 M K4Fe(CN)6/0.0125 M K,Fe(CN)6 (pH = 8). 3000
t
1 0' 10-4
1 '''''''1
'
"'1"'1
10-3
' '''''''1
10-2'
'
'""'1'1
10-1
io0
"""'I
io'
'
INTENSITY (mW)
Figure 4. A fit of the intensity-dependent relaxation time to eq 25 is shown in this figure. The three curves correspond to different values for the excitation density of carriers (the dotted line is 5 X lo6 cm-) mW-I, the solid line is 10'' cm-) mW-I, and the dashed line is 1.5 X 10" cm-3 mw-l).
and Figure 3. The dependence of the fluroescence relaxation time on the incident laser intensity is shown in this figure for emission at 725 nm (0) and at 701 nm (0). The horizontal lines (solid and dotted) indicate the averagevalueoftherelaxation time whenit becomes intensity independent.
agreement with other reported flatband p ~ t e n t i a l s . l ~ An ~J~ example plot of the MottSchottky data may be found in ref 16. The variation in these parameters is considered to lie within the experimental error, and no clear trend is observed between the different electrodes. The open-circuit photovoltage of the electrode was also measured (see Table 11). The change in the photovoltage upon silanation is not significant compared to the error in the measurement. It was observed however that the photovoltage was more stable for the chemically treated surfaces (i.e., less drift in the potential). These studies demonstrate that the chemical treatment does not alter the electrical properties of the interface in a substantial manner, Le., by introduction of surface charge or modification of the space charge region of the material.
Results of Fluorescence Studies Quantifying the Decay. Figure 3 shows a plot of the relaxation time of the fluorescence versus the intensity of the exciting laser light in milliwatts. The relaxation times in this figure were obtained by fitting the decay curve to a sum of exponentials and using those fitting parameters to compute the correlation time, Le., normalized area under the decay law. A 1-mW (3.3 nJ per pulse) laser intensity corresponds to a maximum excitation density of 10l8cm-3 at the surface (obtained using the laser parameters and material parameters reported in the Experimental Section). Clearly, at 1 mW the modeling of the decay law will necessitate nonlinear terms since the background carrier density in these samples is only on the order of 10l6cm-3. As can be seen in the figure, a t laser intensities near 0.01 mW and lower the relaxation time does not change with the laser intensity in agreement with the treatment of the low-injection limit. Clearly then, these experiments are able to span the range from low to high injection. The horizontal lines drawn in Figure 3 correspond to the average value of the measured correlation time at the low excitation intensities, and the relaxation times can be used to compute surface recombination velocities. For this case only the first term in the perturbation expansion for the relaxation time need be used in evaluating the surface recombination velocity. Rearrangement of this term gives
(R)=, ( l + B
1 - :(l
-A2))
(29)
*s
=
A-R L (m);
Using a value of D = 0.5 cm/s2 (ref 20) and T = 20 ns, L is 1 I.tm. A lifetime of 20 ns is close to the lifetime found by fitting the decay curves at very long times to the form eXp(-?/T)/T'/* (refs 7 and 13) and has been reported by others also.4 Using these values and absorption coefficients at 595 nm of 8.1 X 104 cm-I, at 725 of 2.1 X lo2 cm-I, and at 701 nm of 4.1 X lo4 cm-1 (ref 18), the surface recombination velocities found from the correlation times are 3.4 X lo4 cm/s for the 701-nm data and 3.0 X lo5 cm/s for the 725-nm data. These two sets of data correspond to different crystal preparation and represent the sort of variation found experimentally in the polishing and etching of an electrode. Using the measured correlation time at high laser intensity to determine the surface recombination velocity can lead to considerable error. By way of example, a t 1-mW excitation intensity the correlation time for the decay at 701 nm is 560 ps, which via formulas 29 and 30 yields a surface recombination velocity of 5 X lo5 cm/s. This latter number is a factor of 10 higher than the value found under low excitation. In general, if measurements under high injection are used to measure the decay law and the low-injection formulas are used to analyze for a recombination velocity, the recombination velocities obtained will be larger than the true values. It is apparent from this analysis that the measurements at 725 nm yielded higher recombination velocities than those at 701 nm even though the correlation time for the 725-nm data is longer than that for the 70.1-nm data. Because the optical depth at 725 nm is 20 times longer than that at 701 nm, more of the carrier recombination in the bulk of the crystal is monitored, and of course this is less sensitive to the surface recombination velocity. This observation reflects how one may tune the depth measured into the crystal by variation of the observed emission wavelength. In fact, by changing the emission wavelength monitored in the laboratory, it is possible to extend the range of sensitivity of the fluorescence experiment to surface recombination. Figure 4 shows a plot of the same data as is found in Figure 3 at 725-nm emission. The curves on this figure represent the predictions of the perturbation treatment when the values of A , B, S and 7 are determined by the asymptote. The three different curves correspond to eq 25 with different values of the excitation density of carriers [ 5 mW-I for the dashed line, 10 mW-I for the solid line, and 15 mW-1 for the dotted line (normalized to the background value of no)]. The curves shown here demonstrate the sensivitiy of the response to the excitation density. This firstorder treatment appears to extend the range beyond the lowinjection limit by almost a factor of 10in intensity. The excitation density corresponding to the solid line is about a factor of 10 higher than that expected in the steady state, which is given by
Dollard et al.
4146 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993
A
TABLE III: Relaxation Parameters for Chemically Modified CdSe Electrodes"
102
us ( 1O4 cm/s)
8
51
n "
D
0
I
6.6 TIME ( n s e c ) I
I
I
I
I
13.3
I
I
I
I
1311s
electrode
(1)
untreated M e 0 silane Me3 silane untreated Ph silane
532 655 439 915 1862
17.5 8.9 57 4.1 1.o
untreated M e 0 silane Ph silane Me3 silane Me2 silane Me silane
1563b 34 19b 2346b 16Ogb 714b 383b
