ELECTRON-TRANSFER MECHANISM OF SPECTRAL SENSITIZATION
2517
Electron-Transfer Mechanism of Spectral Sensitization’
by R. C. Nelson Department of Physics, The Ohio State University, Columbus, Ohio 4 Z ? l V
(Received December 13, 1866)
Precise measurements of energy levels in sensitizer dyes adsorbed on cadmium sulfide show that the energy of a conduction electron in the dye phase is 0.1-0.4 ev higher than that of the excited “optical electron” of the dye molecule, so that charge-carrier separation in the dye phase is unlikely. The mechanism in which sensitization by singly adsorbed molecules and by adsorbed monolayers takes place by tunneling of the excited “optical electron” through a barrier into the substrate is consistent with the measured energies and analogous to the generation of charge carriers in the solid dye. Evidence is given that for efficient sensitization, the electron affinity of the substrate should lie above a point midway between the ground and excited states of the dye molecule and below the excited state.
Introduction The long controversy over the mechanism of dyesensitized photoconductivity, while perhaps not finally resolved, has reached a point such that it can be said that charge-carrier transfer undoubtedly makes a contribution to the process, whereas the role of pure energy transfer remains speculative. However, much of the evidence for electron transfer has been obtained on systems which are not realistic in the context of sensitization as it is ordinarily carried out and by methods which are not free from concealed assumptions. Characteristically, the charge-transfer hypothesis rests upon detailed consideration of the situation at the dye-substrate interface-its geometry and the system of energy levels of dye and substrate referred to a common zero. The fact that only adsorbed dyes sensitize makes possible reasonable assumptions about orientation and distances; the appropriate energy levels can be measured and one expects to be able to discuss a particular system in terms of these data and a few elementary principles. What follows is an attempt to clarify and define the roles of these energy levels and to examine some familiar aspects of the problem from just such a semipoint Of view. We bring to this task Some new self-consistent energv level schemes for a few dyes, - . as Well as a considerable amount of unpublished work on sensitizers and sensitization. While the primary emphasis will be on the sensitized photoconductivity II
of cadmium sulfide, we shall also attempt to relate these phenomena to the corresponding ones in silver halides and zinc oxide.
Energy Levels in Sensitizers The energy levels which are of interest in the electron-transfer mechanism of sensitization can be defined in terms of three operations performed on dye molecules adsorbed on the sensitized substrate. Following the usual convention, the values associated with each operation are defined so as to be positive, but the energy levels themselves are negative and are measured down from the zero of the free electron at rest at a distance. The lowest, or ground state, of the molecule is given by its ionization energy, which is measured by the threshold of the external photoelectric effect from the adsorbed dye molecules.2a The energy of the excited “optical electron” in the molecule lies above the ground state by an amount equal to the threshold energy for the sensitized ph~toeffect.~The energy of a free conduction electron in the dye phase is measured by the (1) This work was supported by the U. S. Public Health Service through Research Career Program Award No. K3-GM-21946 and also throueh Research Grant No. GM-12835. both from the Institute of GenerafMedical Sciences. (2) (a) R. C. Nelson, J . Opt. Soe. A m . , 5 5 , 897 (1965); (b) R. C. Nelson, K. Drexhage, F. Schiifer, and H. Kuhn, J . Phys. Chem. 27. 1189 (1966). . , .
I
(3) R. C. Nelson, J . o p t .
SOC.
A m . , 48, 948 (1958).
VoEume 7 1 , Number 8
July 1967
R. C . NELSON
2518
electron beam retardation method and hence is equal in magnitude to the electron affinity.4 The first two operations can be performed on systems in which the surface density of sensitizer molecules is so low that they are singly adsorbed or on those which approach close-packed monolayers. The third is necessarily confined to systems of high surface density because of the difficulty of correcting for the effect of the exposed substrate when this is a large fraction of the area. These energy levels are shown in Figure 1 using pinacyanole on cadmium sulfide as an illustrative example and showing levels for both singly adsorbed molecules and adsorbed monolayer aggregates. The ground state G is found to be very nearly the same for both systems, within a few hundredths of an electron volt.2* F,, the energy of the excited “optical electron,” lies roughly 0.1-0.2 ev higher for the single molecule than for the aggregate because of the shift to the red in sensitization threshold associated with aggregatio11.~ E,, the level in the substrate to which the electron is transferred, identified as the bottom of the conduction band, and F,, the energy of a conduction electron in the dye phase, are measured by the electron beam retardation method. F , and F , are to be understood as Fermi energies appropriate to the consideration of transfer of electrons from sensitizer to substrate. The use of a Fermi energy associated with a single molecule is perhaps unfamiliar, but it is convenient and suitable for the discussion of transfer of electrons across an interface. F d is correspondingly a Fermi energy appropriate to the consideration of transfer of electrons from sensitizer to substrate by molecules in the ground state. It is located midway between G and F,, as in an intrinsic photoconductor in the dark. These energy levels have been known approximately for a number of dyes for some time. The older data are unsatisfactory for detailed consideration of mechanisms because they are for the most part measured on solid dyes, rather than on the state in which the sensitizer actually functions, adsorbed on the substrate. Furthermore, they are not sufficiently good to distinguish between two possible modes of sensitization, that in which charge carriers separate in the dye phase and are then transferred to the substrate or that in which the excited molecule acts as electron donor; that is, to a fair approximation, the energy of the conduction electron and of the “optical electron” are indistinguishable in these data. The principal problem in improving the values is the construction of a self-consistent scale of energies to which they can be referred. This problem is not trivial because the energy levels are determined in The Journal of Physical Chemistry
0
0
Figure 1. Energy levels in pinacyanole in relation to cadmium sulfide: left, dye in singly adsorbed state; center, bottom of conduction band in cadmium sulfide; right, dye as adsorbed aggregated monolayer.
ways which are mutually independent and we do not have a broad enough understanding of the details of the phenomena involved to give a theoretical basis for the scale. Hence it is necessary to approach the problem empirically. Since we may define one of the energies arbitrarily, we define the ionization energy to be that for which the yield of electrons per photon is loM4times that at the peak yield in the region below 6 ev. This sensitivity is directly attainable experimentally for most cases and gives values not greatly different from those already published. The threshold for Sensitization may be defined similarly and the same threshold criterion is specified. This threshold can be determined directly in favorable cases, although with difficulty; where this is not possible, an extrapolation of -0.1 ev can be made using the good approximation that the quantum yield decreases logarithmically with decreasing photon energy near the threshold. This operation is made difficult by the fact that the characteristics of the substrate under very low levels of irradiation are involved. The plots of yield vs. energy have somewhat different slopes for the ionization energy and the sensitization threshold, but the value of (G - F,) changes by only about 0.05 ev for a change in threshold criterion from lod4to and for the present purpose discrepancies of this magnitude are not intolerable. The fitting of the electron affinity to this scale presents a different sort of problem, since we must relate it t o the wavelength calibration of the monochromator which forms the basis for the other energies. A further difficulty for dyes adsorbed on cadmium sulfide is that the contact between cadmium sulfide and the pal(4) R. C. Nelson,
J. Opt. Soe. A m . , 46, 1016 (1956).
ELECTRON-TRANSFER MECHANISM OF SPECTRAL SENSITIZATION
ladium film onto which it is evaporated is never exactly ohmic and after a film has been used a number of times, with heating in air at 350” to clean it each time, the deviations from ohmicity become fairly large. Fortunately, it is possible to arrive at the energy of a conduction electron in certain dyes without recourse to the electron beam retardation method. An example is rhodamine-B where, even in monolayers, there is a large density of monoenergetic “traps” from which electrons can be excited to the vacuum photoelectrically. The threshold for this process, once more using the criterion of peak yield, gives the energy of the trapped electron as -3.75 ev. The depth of the trap, 0.54 ev, can be determined thermally in several ways;6 thus, the energy of the conduction electron is -3.21 ev. We use rhodamine-B as a standard for the determination of the total lumped correction from all sources in the electron beam retardation procedure. For a fresh cadmium sulfide film, this correction is typically -0.02 to -0.05 ev, rising with continued use to a few tenths of an electron volt. Hence the standardization procedure must be carried out at frequent intervals. It is somewhat laborious to establish the full energy level scheme of a dye in this way and, for various reasons, it may not be possible for some dyes. We have done so for a few sensitizers to permit a full discussion of their properties; these new data appear in Table I. We shall also use less elaborately measured values of energies in this paper where great precision is unimportant. Table I: Energy Levels of Dyes Adsorbed on Cadmium Sulfide
Pinacyariole 3,3‘-Diethylthiacarbocyanine 3,3‘-Diethylthiadicarbocyanine 3,3’-Diethylthiatricarbocyanine Rhodamine-B A = F,
G
Fe
-4.67 -5.14
-3.20 -3.49
-3.05 -3.13
0.15 0.12 0.36 0.31
-4.76
-3.39
-3.25
0.14 0.19
-4.60
-3.46
-3.33
0.13 0.11
-5.25
-3.50
-3.21
0.29 0.24
FC
Aa
EB
2519
ture on photoconductivity which could be represented by a Boltzmann factor containing an activation energy of a few tenths of an electron volt. The agreement between A and E , confirms the usual point of view that this represents a thermal energy which is required in addition to the optical excitation energy for the formation of a hole-electron pair and shows that such considerations must apply even for the generation of charge carriers in two-dimensional domains of dyes.
Direct Sensitization There are two principal regimes of sensitization, that in which the sensitizer molecules are effectively singly adsorbed and isolated on the substrate and that in which they are aggregated into close-packed monolayer domains. Theh ighest efficiency is associated with the first regime, but for good sensitizers there is not apparent any discontinuity in passing from one regime to the other. We shall consider the sensitizer molecule in the general framework of the Kuhn model as a gas of electrons in a potential well.’ A photon is absorbed and the molecule passes into an excited state which we may visualize as the appearance of a hole and an energetic electron in the well; this state has a lifetime 1O-lo sec. The term “direct sensitization” designates the process in which the excited “optical electron” in the dye molecule adsorbed on the substrate, whether singly or as part of a monolayer aggregate, transfers to the substrate by tunneling through the barrier of the potential well. (See Figure 2 . ) I n general the electron will either gain or lose energy during this process. The problem of transfer of an electron and a phonon through a barrier is properly one in second-order perturbation theory, but a classical and semiclassical treatment can give order-of-magnitude estimates of efficiency. For this purpose we assume that tunneling must be horizontal on the energy coordinate diagram and that the fraction of electrons which may undergo such tunneling is fct/ (7-l fct) or
-
+
- F,.
In addition to levels determined in this way, the table gives values of the “activation energy for photoconductivity” E , for these dyes, measured by the effect of temperature on the steady-state photoconductivity at constant irradiance.* It has been known for many years that in general there was an effect of tempera-
where t is the transparency of the barrier, f c is the classical frequency of the electron in the potential well, and T is the lifetime of the excited state. (5) R. C. Nelson, J . Chem. Phys., 22, 885 (1954). (6) N. Petruzzella, S. Takeda, and R. C. Nelson, submitted for publication. (7) H . Kuhn, J . Chem. Phys., 17, 1198 (1949).
Volume 71 iVumber 8 I
July 1967
R. C. NELSON
2520
For the present purpose we require only the results that for barrier geometries which are reasonable in terms of molecular dimensions, efficient transfer may be possible and that the efficiency decreases rapidly when the final state lies higher on the energy diagram than the energy of the “optical electron.” Direct comparison of energy levels of sensitizer and substrate shows that for good sensitizers, the optical electron is able to lose energy in tunneling through the barrier, making p z 1. If we approximate t by exp [-2a(2kfEb/&2)1’2]where t is the transparency of a barrier of thickness a and height Eb and take the classical freqiiency of the electron in the well to be 1015/sec,we find that for barriers of thickness 5 A and height 3.4 ev, pi is of the order of 1, while for a thickness of S A, pl is only about 0.01. Since a < 5 A is reasonable for barrier thickness, we see that the electrontransfer process has in it the potentiality for efficient sensitization. On the other hand, we see that it is very sensitive to both barrier thickness and energy difference and hence is capable of accounting for the well-known high specificity of sensitization phenomena. While the efficiency of sensitization may vary continuously through the transition between single adsorption of dye molecules and adsorption as aggregates, there are cases in which singly adsorbed molecules sensitize and adsorbed aggregates do not sensitize a t all. In terms of the electron-transfer hypothesis, there are two straightforward possible causes of such behavior. We have noted in the case of pinacyanole that F , lies higher for the single molecule than it does for the aggregate. Here both are safely above E,, but there may be cases in which the difference becomes critical. This is probably the reason why the efficacy of malachite green as sensitizer drops catastrophically upon aggregation.3 F , for aggregated malachite green is 3.60 ev; it should not sensitize cadmium sulfide with E, of 3.5 ev. However, the threshold for absorption by singly adsorbed malachite green is about 0.15 ev higher and sensitization is possible. A second possible cause is to be found in an increased thickness of barrier when the molecules pass from the broadside adsorption, usually associated with single adsorption, to the edge-on adsorption of aggregates. This may be a gross effect as with nonplanar molecules in which large substituents introduced to force the molecule out of planarity will also lead to the r-electron cloud being held far from the substrate in edgewise adsorption. The rather small difference in distance which one might reasonably associate with the transition from broadside to edgewise adsorption might also
-
Figure 2. Transfer of electron from excited state of dye through a barrier into the substrate.
I n general, thermal energy must also be gained from or lost to the lattice. From a quasi-static point of view, the fraction of electrons which can tunnel horizontally is the fraction of a Maxwellian distribution centered on the initial state having energies equal to or greater than the final state on the other side of the barrier. That is, we assume that vibrational energy is adequately coupled to the electron transfer. A time-dependent formulation is also possible. We take as the temperature-dependent part of the probability that the electron in the well will tunnel the ratio of the rate at which molecules acquire enough lattice energy to tunnel horizontally to the sum of this rate and the rate at which excited molecules disappear by all other causes, or 1, exp(-AE/kT)/[r-’ fe exp (-AEIkT)], sothat
+
pz
-
fe
1
+
exp(-AE/kT)r f e exp(-U/kT)T
where fe is an effective lattice frequency. Classically, f, is the frequency of an acoustic wave in the dye phase having a wavelength twice the length of the molecule and is lO”/sec. Since the classical frequency of the electron in the well is much greater than the effective lattice frequency, we may take the probability of the whole process to be the product of the probabilities of the temperature-independent and temperature-dependent parts, because it implies that the electron is in effect continuously testing the barrier while its energy fluctuates because of lattice vibrations, so that
-
The Journal of Phyaical Chemistry
ELECTROK-TRASSFER MECHANISM OF SPECTRAL SENSITIZATION
2521
be of importance in systems in which a layer or two of adsorbed water or other nonsensitizer material intervenes between sensitizer and substrate, increasing the thickness of the barrier between them into the region in which p l decreases very rapidly with increasing distance.
Indirect Sensitization We understand by this a process in which charge carriers are separated in the dye phase, followed by tunneling of the electron into the substrate; sensitization by thick films ordinarily takes place in this way.8 It has no applicability to sensitization by singly adsorbed molecules. We examine the likelihood of such a process contributing to sensitization by a closepacked monolayer. We assume charge-carrier generation in the dye phase to take place by a localized process entirely analogous to that described for direct sensitization, except that the electron tunnels to an adjacent dye molecule, appearing in the level F,. The data of Table I show that the separated or conduction electron is always more energetic than the optical electron, the difference A being 0.1-0.3 E'V. Using eq 1 to estimate the yield of conduction electrons per photon in the dye phase of a system sensitized by pinacyanole, we find for a barrier thickness of 5 A a value of approximately 3%, representing a rather small contribution. It should be pointed out that this value may well be substantially too high for the following reason. Indirect as well as direct sensitization requires that the barrier between dye phase and substrate have a good permeability to electrons. When this is the case, charge-transfer deactivation in direct sensitization may significantly reduce the lifetime of the excited state. In principle, the fact that F , lies above F, opens the door for a possible case in which sensitization by monolayer aggregates could be observed when singly adsorbed molecules of the same dye were ineffective. The writer is not aware that any such case has ever been reported. For the many good sensitizers in which A is about 0.3 ev, indirect sensitization can play only a negligible part in the process. Specificity of Sensitization One of the more intriguing problems of sensitization arises from the fact that silver bromide and cadmium sulfide behave rather similarly in sensitization, while zinc oxide is at least superficially very dissimilar. Eosin, the best single sensitizer for ZnO, is a mediocre sensitizer of the first two, while pinacyanole, a good sensitizer of CdS and AgBr, is a poor one for ZnO. I t is interesting to see whether an explanation can be
I
nFe
Figure 3. Transfer of an electron from the ground state of the dye through a barrier into the substrate.
constructed in terms of the energy levels which are fundamental to the electron-transfer hypothesis as presented here. In what follows, as elsewhere in this paper, we assume that the dye molecule, even in a monolayer aggregate, acts as an almost isolated entity except for purely electrostatic effects of its surrounding~.Za,~ We consider a system consisting of substrate and adsorbed dye in the dark before it has been illuminated at all. There exists in principle the possibility that an electron could be transferred from dye to substrate even in the dark by thermal activation of an electron in the ground state, as shown in Figure 3. In general, transferring an electron from dye to substrate will lower the Fermi level in the former and raise it in the latter. Thus, if F, lies below F d , the process is more likely to take place than if the converse is true. However, in practice, we find an effect associated with E,, the energy associated with the bottom of the conduction band in the substrate. Below is a series of sensitizers together with values of F d for each one, inserting at appropriate positions the values of E , for several substrates. These are, in fact, all the sensitizers for which the necessary data are at present available: eosin, 4.6 ev; erythrosin, 4.6 ev; rose bengale, 4.6 ev; rhodamine-B, 4.4 ev; auramine, 4.3 ev; 3,3'-diethylthiacarbocyanine, 4.3 ev; zinc (8) R. C . Nelson, J . Opt. SOC.Am., 51, 1182 (1961). (9) R. C . Nelson, J . Mol. Spectry., in press.
Volume 7 1 , Number 8
July 1967
R. C. NELSON
2522
oxide,1° 4.3 ev; 3,3’-diethylthiadicarbocyanine, 4.1 ev; pinacyanole, 4.0 ev; 3,3‘-diethylthiatricarbocyanine, 4.0 ev; kryptocyanine, 3.6 ev; cadmium sulfide, silver bromide, 3.5 ev; methylene blue, 3.4 ev. All these dyes are at least moderately good sensitizers of cadmium sulfide except methylene blue, which shows only a small effect. The dyes coming before zinc oxide are good sensitizers of it with ratings on a sensitometric scale of 25-9. Those coming after it are poor to very poor sensitizers with ratings of 1-0.1. There is also a moderately good correlation between position in the series and effectiveness of sensitization of zinc oxide. The case of methylene blue is of particular interest since it is known to cause fogging of silver halide emulsions in the dark. Our present hypothesis casts it in the role of a chemical reductant of silver halide by a thermally activated process. We propose the following explanation of this effect. I n general the Fermi level in the substrate will lie below E , and there will in general be a tendency for a freshly prepared sensitized substrate to receive electrons from the sensitizer in the dark. These electrons are “extra” electrons in the substrate and its Fermi level will rise and may rise a considerable distance, since practical sensitizable systems are typically rather pure substances and have a large surface-tovolume ratio, so that a considerable number of dye molecules are associated with a unit volume of substrate. If F d is large, the substrate Fermi level need only rise a little for the process to cut off and only a little sensitizer will be lost. As F d is decreased, the losses of sensitizer from this cause become greater, since more charge must be transferred to raise the substrate Fermi level to F d . However, when the Fermi level comes to E , at the bottom of the conduction band, it will rise very slowly because of the much greater density of states in the conduction band than in the forbidden region and thus the chances of exhausting or almost exhausting the dye layer by the dark process are greatly enhanced. Thus, the most dramatic change in effectiveness comes a t the point a t which the value of F d becomes less than E,. We wish to suggest as a conjecture the rule that a necessary but not sufficient condition for a good sensitizer-substrate pair is that the bottom of the conduction band of the substrate should lie below F,, the energy of the optical electron in the excited state of the dye, and above F d , the midpoint between F , and the ground state. We know of no exceptions to this rule, although it is evident that it rests upon a small number of cases. We recognize that doping with a large density of electron traps might alter this rule. This is not customary The Journal of Physical Chemistry
with photographic materials and Sorensen’s data are for zinc oxide of good commercial purity.
Discussion We have attempted in this paper to remove some of the ambiguity which has been characteristic of the earlier descriptions of electron-transfer sensitization. The ambiguity arose out of the fact that the energy of the excited electron in the dye molecule and that of the conduction electron were indistinguishable within experimental error, making it impossible to distinguish between direct and indirect processes. Since much of the earlier work rested on studies of the interface between a bulk dye phase and the substrate. it was natural to assume that indirect sensitization by carriers formed in the dye phase was an important process. The realization that there exists a thermal energy requirement for generation of charge carriers even in monolayers calls for a change in point of view; it now appears that sensitization by thick dye layers is atypical and that sensitization by singly adsorbed molecules and by monolayer aggregates are fundamentally similar processes. The most satisfactory aspect of the charge-transfer mechanism of sensitization is that it is usually possible to submit a hypothesis to quantitative experimental test; one need no longer rely completely on plausibility arguments. Unfortunately, the measurements are diffcult and the problems numerous. The data on the vinylogous series of thiacarbocyanines are of some interest, even though the series is not complete. As the chain lengthens, the ground state rises and the energy of the conduction electron diminishes; the optical excited state stays at about the same level. They suggest a reason for the difficulties which accompany infrared sensitization. As the ground state rises, so does F d , enhancing the tendency of the dye to reduce the substrate and fog it chemically. Another possible effect is that the thermal energy for separation of charge carriers in the dye phase becomes less as one goes to longer chains. This may have an unfavorable result in that if the lifetime of the electron in the dye before transfer to the substrate is long enough, it may be quenched by ambient oxygen, which may in turn lead to the formation of deep traps in the dye and consequent desensitization. The objection posed by Terenin12 to the electron(10) H. Meier, J . Phys. Chem., 69, 719 (1965). (11) The writer wishes to thank Dr. David Sorensen of the 3.M Co. for permission to refer to his data on the effectiveness of sensitizers of zinc oxide. The data are also in reasonable agreement with those of H. Frieser and M. Schlesinger, Phot. Korr., 101, 133 (1965). (12) A. Terenin and I. Akimov, J . Phys Chem., 69, 730 (1965).
ELECTRON-TRANSFER MECHANISM OF SPECTRAL SENSITIZATION
transfer mechanism, that a dye which is a p-type photoconductor may sensitize an n-type substrate, disappears in the present scheme, since we suppose that in general charge-carrier separation in the dye is unimportant. This would be true for the p-type eosin, for example, where the thermal activation energy for charge-carrier generation is about 0.3 ev. However, the energy levels in eosin are such that direct sensitization of zinc oxide or cadmium sulfide is possible. The present study has further weakened the grounds for supposing that there is a close connection between sensitization and the photovoltaic effect at a sensitizersubstrate junction. The experiment is important in that it shows that the barrier a t the interface is permeable to electrons, but there seems to be no great diagnostic value attributable to the details of the behavior of the junction. The writer’s conjecture that a “well-behaved” junction was simply one at which the rate of recombination at the interface was high13has been confirmed by Schaer14and it would appear that the relationship between this behavior and efficient sensitization is indirect and in some measure coincidental. We have not, considered the question of desensitization, which has been dealt with earlier in similar termin~logy.’~It would appear that if F , lies above F,, transfer of carriers from substrate to dye should be
2523
possible. The characteristic “trapping states” of dyes like the triphenylmethanes may also participate, although we understand too little of their nature to be certain. We are also unable t o contribute toward the problem of supersensitization. The character of Rilott’s explanation is such that it should be equally pertinent to electron-transfer sensitization. l6 We have examined the energy levels in auramine and can find no reason to relate the supersensitization of pinacyanole by this dye to energy differences; the effect might be associated with the character of the barrier between dye and substrate at the singularity. Another omission is discussion of the fate of the hole. The evidence from sensitization of photoconductivity in cadmium sulfide suggests that there is no hole transfer and that recombination takes place across the interface. In the case of the primary photographic process, it would appear that if chemical free energy is indeed stored, the hole must be transferred, although not necessarily to the valence band. (13) R. C. Nelson, J. Phye. Chem., 69, 714 (1965). (14) F. M. Schaer, M.S. Thesis, The Ohio State University, 1965. (15) R. C. Nelson, J. Opt. SOC.Am., 48, 1 (1958). (16) R. W.Gurney and N. F. Mott, Proc. Roy. SOC.(London), A164, 151 (1938).
Volume 71, Number 8
Julv 1967
