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Minority Carrier Trapping and Dye Sensitization1"sb
by R. C. Nelson Department of Physics, The Ohw State University, Columbus 10, Ohio
(Received October 6 . 1964)
The customary criteria for judging the plausibility of the electron-transfer mechanism of dye sensitization in a given case are the production of charge carriers by the sensitizer when illuminated and the sign of the contact potential difference between sensitizer and substrate. These data do not distinguish adequately between sensitizers and nonsensitizers in certain experimental situations, in which there is substantial evidence for electron-transfer sensitization on other grounds. A search for an additional criterion suggests an adverse effect of hole-trapping'in the dye phase when cationic sensitizers are used. The evidence for holetrapping is discussed, as well as its significance for both photochemical and photoconductive dye-sensitized solid state processes. I t is suggested that the effect in the former case may be on the energy of a hole-electron pair in the dye phase, whereas, in the latter, it is involved primarily in the slowing of the relaxation process tending to restore the original conditions after the observation of a sensitized response. This dual expression of its influence would account for the similarities observed between photographic sensitization and sensitization of photoconductivity in cadmium sulfide, in spite of the essential differences between the two experimental situations.
Introduction For more than 25 years, there have been two principal types of mechanisms contesting the field of dye-sensitized, solid state processes. During most of this time, the resonant energy-transfer type of process has had fairly general acceptance while the electron-transfer type was in eclipse. The latter type of mechanism appeals to experiment since its plausibility depends on measurable effects and relationships, and in recent years it has been shown that, for certain sensitizersubstrate combinations, the requirements imposed by these relationships are fulfilled. It is known that, in general, sensitizing dyes in the solid form produce holeelectron pairs on illumination and that, in inany cases, the contact potential difference between sensitizer and substrate is of a sign and magnitude such as to permit spontaneous transfer of electrons from the dye phase to the substrate. There are two experimental results which strongly suggest the validity of the electron-transfer niechanis" for the cases with which they deal. One is the fact that a dye-cadmium sulfide interface shows a photovoltaic effect, and, when this junction is made part of an electrical circuit, a continuous current will flow across it, The Journal of P h y s i c d Chemistry
driven by light absorbed by the dye.2R The second is the fact that a sort of "sensitized photoconductivity" can be observed in glass in contact with a layer of sensitizing dye, in spite of the fact that there is no intrinsic process to which energy could be transferred by resonance.2b However, a difficulty remains; both of these experiments discriminate strongly between good and poor sensitizers, but it is not known upon what basis the discrimination rests since the result cannot be predicted solely upon grounds of being able to produce charge carriers on illumination or upon the sign of the contact potential difference. Clearly, if the electron-transfer mechanism is valid, some criterion must exist according to which the results of these experiments can be anticipated. Thus, a search for such a criterion imposes a test on the electron-transfer mechanism. It is characteristic of this mechanism that it attempts (1) (a) This investigation was supported in part by a Public Health Service research career program award No. GF-560-64 from the Institute of General Medical Sciences and in part by t h e C. F. Kettering Foundation; (b) presented to the International Conference on Photosensitization in Solids, Chicago, Ill., June 22-24, 1964. (2) (a) R. C. Nelson, J . Opt. SOC.A m . , 46, 13 (1956); (b) 50, 1029 (1960).
MINORITY CARRIER TRAPPING AND DYESENSITIZATION
to explain the peculiarities of sensitized systems, not only by consideration of transport phenomena a t the interface but also by application of our knowledge of the processes of charge carrier separation and diffusion in the dye phase. Thus, a possible and hopeful criterion for predicting the efficacy of a sensitizer may be found in considering the energy carried by a holeelectron pair in the dye solid since there are evidently cases of sensitization in which this must assume importance. This paper deals with the applicability of such a criterion to sensitized processes in general and, in particular, with its relevance to the two special cases just mentioned.
The Energy Requirement of a Dye-Sensitized Process
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gested an energy-doubling process which will work only if the energy of a hole-electron pair in the chlorophyll phase is small.6 More traditional types of meGhanisms resemble those of Katz, in requiring that the pair carry a large fraction of the energy of the photon.6 While the significance of the energy of the pair is obvious in a system in which chemical work is done, it is difficult to see why it should be of importance in one in which the only effect expected is an enhancement of photoconductivity because in this case it should suffice that charge carriers of either sign are donated to the substrate under illumination. However, there is a marked parallelism of behavior of sensitizers for the two systems, photographic sensitization and sensitization of photoconductivity in cadmium sulfide, and it is of interest to attempt to uncover the reasons for this, in hope of coming upon a unifying idea.
The resonance mechanism foresees no difficulty with energy; it is an assertion that the energy of the excited The Energy of a Hole-Electron Pair state of the molecule is sufficient to do what needs to be We define the energy of a hole-electron pair to be the done. The form given by Franck and Teller3 is basiseparation on an energy level diagram of the final cally an application of the Franck-Condon principle ; levels occupied by hole and electron when a pair is they note that the lifetime of the excited state of the created. This is the difference in energy between sensitizer is of the order of lo4lattice vibration periods ground and conductive excited states diminished by of the substrate, so that one can hope to carry out the any losses due to trapping of either carrier. The creation of a hole-electron pair with the energy availenergy difference between ground and conductive able by transferring it to a favorable lattice configurastates can be determined by a two-step process. First, tion. This is assumed to be likely to occur a t least we measure, by means of the external photoelectric once during tht: lifetime of the excited state. effect, the energy of an electron in the ground state. Although the electron-transfer type of mechanism We measure the energy of an electron in the conductive rests on a knowledge of the energy level structure of state by the electron-beam-retardation method. If the the system, which can often be worked out, it still is not difference of these two be compared with the energy of a a simple matter to say how much energy must be carried photon a t the photoconductive threshold, the two will across the interface by the hole-electron pair. The be found to be equal, within experimental error, for good primary photographic process is of interest because one sensitizers. For certain other dyes, more complicated can set a lower limit to the energy requirement from relationships are found, but in all cases it is possible to the free energy of the products. If these are silver construct an over-determined, consistent energy level metal and gaseous bromine, then we must transfer a t least 0.8 e.v. of energy to the silver bromide c r y ~ t a l . ~ diagram in which the energy of the threshold photon appears as a difference between two levels, the positions However, the actual energy required will be determined of which can be determined without reference to it.’ by the pathway over which the system moves in energyIn view of the fact that the threshold energy for configuration space and will, thus, depend on rates and photoconduction is somewhat less than that correspondmechanisms. If we suppose that only the transfer of ing to the lowest allowed electronic transition of the an electron from sensitizer to substrate need take place molecule in solution, we must recognize this to be a promptly, that is, within the lifetime of the excited remarkable result which we do not yet understand. Its state of the dye molecule, and that all other processes may proceed slowly enough so that thermal energy may (3) J. Franck and E. Teller, J . Chem. Phys., 6 , 861 (1938). be used to overcome activation barriers, then the total (4) W. F.Berg and J. H. Webb in “The Theory of the Photographic energy requirement need not be much greater than that Process,” C. E . K. Mees, E d . , The Macmillan Co., New York, N . Y., stored in the products. 1954,p. 145. ( 5 ) M. Calvin and G. M. Androes, Science, 138, 867 (1962). I n photosynt)hesis, the luxuriance of hypotheses is (6) E. Katz in “Photosynthesis in Plants,” W. E. Loomis and J. such that, even for the restricted case of electron-transFranck, E d . , Iowa State College Press, Ames, Iowa, 1949,p. 291. fer mechanisms, the energy of a hole-electron pair may (7) R. C. Nelson, J. O p t . Soc. A m . , 51, 1186 (1961);J . Mol. Spectry., appear in different roles. Calvin and Androes have sug7, 439 (1961). Volunze 69. Number 8
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importance for the electron-transfer hypothesis of sensitization is obvious; it also suggests a t least as a possibility that even single dye molecules on the surface of a substrate possessing a photoconductivity of its own might be able to participate in an electrontransfer process. Thus, in the absence of trapping, the energy of B hole-electron pair is nearly that of the least energetic photon which will produce it. We now consider the problem of trapping, confining ourselves to the discussion of cationic dyes, since our knowledge of energy levels in these is rather more extensive than in anionic or nonionic dyes. Many cat,ionic dyes have large densities of electron traps, which lie within a rather narrow range of energy levels, so that they can be considered to be monoenergetic for many purposes. Usually, these traps are about 0.35 to 0.40 e.v. deep so that they represent only about a 25% diminution of the energy of the pair. However, they may affect sensitization by electron transfer by bringing the effective energy of an electron in the dye phase very near the Fermi level in the substrate. These trapping levels are easily accessible to study either by kinetic methods or by an external photoelectric effect arising from electrons occupying them.8 The question of hole traps is a much more difficult one. The writer has suggested that since cationic dyes are usually n-type conductors, the anion may act as a hole trap.9 In the case of the halide ions, their energies as hole traps may be estimated from the electron affinities of the corresponding halogen atoms. Since these lie in the neighborhood of 3.5 e.v., to be compared with energies of the ground states of photoconductive dyes in the range 4.3 to 5.5 e.v., they would act as rather deep hole traps, deep enough so that the energy of the pair would be greatly reduced. Where the hole is a minority carrier, it is very difficult to find out anything about hole traps by ordinary methods. We shall, instead, go at the question indirectly by considering a classical paradox of the field of organic photoconductors concerned with the so-called “intrinsic semiconductivity” of these substances. Many measurements attest to the fact that, if one plots the log of dark conductivity of a dye against the reciprocal of the absolute temperature, the data fall on a straight line, the slope of which is taken to be a measure of the intrinsic forbidden gap between ground and conductive excited states, so that u = uo exp(-E/lcT), where E is the energy of a hole-electron pair. E is usually -1 e.v. and ordinarily not greatly different from one-half the energy of a photon at the photoconductive threshold. If we now estimate the density of The Journal of Physical Chemistry
electrons in the ground state, using the number of molecules, the number of a-electrons, or a density of states in k-space and multiply this by the Boltzmann factor, usually the product is rather a small number, often less than unity. If we attempt to account for the current using this density of charge carriers, we are forced to attribute a very large mobility to the carriers, often -lo4 to lo6 cm.2/v. sec. On the other hand, values of the mobility arrived a t in more direct ways are invariably -1 cm.2/v. sec. or less. Since the number of carriers corresponding to the large mobility is such that shot noise effects should be prominent and these are not seen, it seems more satisfactory to accept the lower range of values. By the same token, we must give up the idea that E can be the energy of a holeelectron pair since, if we take the mobility to be low, we must have a density of carriers several orders of magnitude greater than is consistent with the measured value of E. Because of this state of affairs, we shall refer to this dark conduction as anomalous. This paradox seems to be proof against resolution in any simple way. It cannot be resolved using donor states or any reasonable density of states in the lower level. It does not seem to be due to electrode effects, and there is evidence that it is not ascribable to the presence of the applied field used to measure the conductivity. The writer has investigated the dark conductivities of a number of triphenylmethane dye halides having known energy level structures and has proposed a scheme in which the halide ions appear as deep hole traps. E now has something of the character of the height of an activation barrier over which the distribution of electrons between hole traps and the conductive level is changed as a function of temperature, and the dark conductivity data can be accounted for reasonably well in terms of small mobilities.’O It is not necessary to accept this scheme in order to pursue the argument; it is sufficient to say that, if we take the best values for the mobility, for an anomalous dark conductor, E cannot be the energy of a hole-electron pair, and this energy must indeed be considerably less than E. We now note that there is a strong negative correlation between anomalous dark conductivity and ability to sensitize photoconductivity in cadmium sulfide when the sensitizer is in the form of a “thick” film. The same correlation applies to the ability to sensitize photoconductivity in glass and to the photovoltaic (8) B.-Y. Cho, 499 (1963). (9)
R..C. Nelson, and L. C. Brown, J . Chem. Phys., 39,
R. C. Nelson, ibid., 22, 890 (1954).
(10) R. C. Nelson, ibid.,39, 859 (1963).
MIXORITY CARRIER TRAPPING A N D DYE SENSITIZATION
effect a t a dye-cadmium sulfide interface, the character of which is markedly different for a dye with anonialous dark conductivity. We thus find in the anomalous dark conductivity a characteristic which has diagnostic value for effectiveness of sensitizers in interesting situations. There appears to be a connection between it and the energy of a hole-electron pair. If this should be so, it might be a link between the performance of sensitizers in systems i n which chemical work is done and the less interesting, but more accessible, situations in which only the enhancement of photoconductivity is found.
Sensitization by Thick Dye Films A “thick” dye film in the context of sensitization is one which is much thicker than a monolayer and comparable to the films used to study the photoconductivity of the dye itself. Such systems represent an extreme of the sensitization effect. The simplest sensitized system is one in which the sensitizer is so sparsely adsorbed on the substrate that each molecule can be considered to be isolated. A great many dyes produce an observable effect in this regime. The most useful state, for most purposes, is that in which the dye is adsorbed as a closepacked monolayer, and, for this regime, the number of effective sensitizers is notably less than in the first. I n passing to multilayers, there is a further diminution of the number of effective sensitizers, and such systemsare highly specific and discriminatory. Within the range of sensitizers with whirh the writer has worked, those which perform well in multilayers are also the most satisfactory in monolayers, so that the phenomena are probably fundamentally similar. R!Iultilayers are also of interest as being closely related to the dye-substrate junction cells in which the photovoltaic effect is observed. We now list the most prominent differences in behavior between films which show anomalous dark conduction (HDC) and films which do not (LDC). (1) For HDC films the mobility inferred from the intrinsic semiconduction model is high; for LDC films it is low. (2) LDC films sensitize photoconductivity in cadmium sulfide; HDC films do not. (3) The same is true of the “sensitized photoconductivity” of glass. (4)The photovoltaic effect a t the LDC-cadmium sulfide junction saturates a t low illuminance a t a value numerically equal to the measured contact potential difference; that for the HDC junction is proportional to the log of illuminance over a wide range and tends toward the contact potential difference as a limit. ( 5 ) LDC films show a fast decay of photoconductivity in the dark ( T sec.); HDC films always have a slow component in the decay curve (T lo2sec.). (6) If a cadmium sulfide cell is sensitized with a thick layer
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of LDC film and both are illuminated, the decay of photoconductivity in this system is faster than in the cadmium sulfide cell by itself and is, conversely, slower if the film is HDC. (7) Although the photoconductivity of the HDC film persists in the dark, the photovoltaic effect disappears very quickly from both types when illumination is discontinued. (8) For the HDC film, the photovoltaic effect is very small for a very thick film and can approach the magnitude of the contact potential difference only for a thin film; for a thick film the photo-e.m.f. is of the order of a few millivolts. This effect is not seen with LDC films. (9) HDC films have electron traps 0.3 to 0.4 e.v. below the conductive level; these are inconspicuous or absent in LDC films. Since both dye and cadmium sulfide films may be ntype conductors, we do not consider n-p junction effects. A fairly straightforward account of the phenomena in HDC-cadmium sulfide junction cells can be given on the basis of the observations listed above. The Fermi level in the cadmium sulfide film, as measured by the electron-beam-retardation method, lies in the neighborhood of -3.5 e.v., measured from the vacuum level. The conductive state in many dyes, measured in the same way, is found from -3.0 to -3.2 e.v., so that trapped electrons lie near or a little above the Fermi level of the substrate. We suppose that, before the measurement is made, the Fermi level in the cadmium sulfide has been raised almost to the electron trap energy of the dye phase, possibly by carriers present in the dark or, more likely, excited by a small amount of illumination incidental to the preparation of the cell and pumping it down for measurement. We now illuminate. In a thick dye film, only a small fraction of the dye molecules is illuminated, whereas the excited electrons are trapped throughout the film so that the photovoltage is very small. For thin films and very bright light, we are able to drive the effective energy of excited electrons upward so that the photovoltage may approach the energy difference between the conductive state of the dye and the Fermi level in the cadmium sulfide. Since this effect is due to electrons which are not in thermal equilibrium with traps, it disappears immediately upon cessation of illuniination because there is no longer an energy gradient at the interface. According to this point of view the sensitization effect is not entirely absent but is very small; it could escape observation by the techniques used to detect it. Since the conductivity of HDC filiiis is persistent and the decay is especially slow in the sensitizersubstrate system, only after some time and with great
(11) R. C . Nelson, J . O p t .
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care, would it be possible to observe an energy gradient a t the interface. The absence of electron traps in the LDC films increases the magnitude of the photo-e.m.f. , but the most important factor in establishing the characteristic differences is the fast recovery time of the LDC-cadmium sulfide system. When the system is illuminated, there is a short transient peak in the photo-e.m.f. which apparently is due to the rise in the Fermi level in the cadmium sulfide due to the electrons donated by the dye. The system very quickly comes to a steady state, and the current remains constant. When the photoe.ni.f. is measured, by applying a countervoltage just sufficient to make the current across the junction zero, the recovery is so fast that the Fermi level in the cadmium sulfide is almost independent of the illuminance under the conditions of measurement. In the case of pinacyanole, a particularly effective sensitizer in thick films, the photo-e.m.f. is substantially independent of the illuminance over a range of 100 to 1. For HDC films, not only is the photo-e.m.f. strongly dependent on illuminance, but there are also long-term drifts and fatigue phenomena which are probably to be associated with changes in the Fermi level in the cadmium sulfide due to the process of electron transfer and the slow recovery from it. Presumably, considerations of a similar sort apply to the sensitization of photoconductivity in glass. Although glass is hardly a semiconductor in any ordinary sense, there appears to be a limited number of surface states through which electrons can enter the glass. If one assumes these to be distributed over a range of energies and to be accessible only to electrons more energetic than the highest filled state, they might play a role which simulates that of the Fermi level in cadmium sulfide, leading to a small sensitization effect in the case of HDC films and a large one for LDC material. l 2
Hole-Trapping and Sensitization We have attempted to account for the difference in behavior between the two kinds of film as sensitizers in terms of three characteristics, electron-trapping, presence of carriers in the dark, and relaxation time for photoconductivity. The principal effect is concerned with the last two since the effect of electron-trapping is on the magnitude of the photovoltage. We have already suggested that the anomalous dark conductivity is associated with the presence of deep traps for holes. We now wish to suggest further that the long relaxation time is also ascribable to hole-trapping. In the cationic dyes of which we are speaking, there Seems to be no explicit role for the anion in the processes The Journal of Physical Chemistry
R. C. NELSON
of charge carrier separation and transport. The energy levels connected with these processes are determined by the colored cation and are nearly independent of the nature of the associated anion. The effect of the anion shows in only two ways, being associated with the dark conductivity and with the relaxation time for photoconductivity. For crystal violet , an HDC type material, one can decrease the dark conductivity and the relaxation time for photoconductivity, each by two orders of magnitude, by substituting i o dide for chloride as the anion, without greatly changing the eIectron trap depth, the work function, the electron affinity, or the photoconductive threshold. Considerations of this sort, which emphasize the difference in the roles played by anion and cation, lead to a point of view which encourages one to speak of the domain of anions and that of cations and to visualize them as interacting only weakly insofar as the phenomena of photoconductivity are concerned. Similarly, one is led to associate the role of the anion with the minority carrier since the processes involving transport of electrons can be associated explicitly with the cation. Bearing in mind the negative charge of the anion, its identification as a hole trap is a short step, and the association of the slow decay of photoconductivity with the weak interaction between the two domains is natural. There is also fairly direct evidence of deep trapping of holes in some triphenylmethane dyes, where Petruzzella and Nelson found a rather small p-type photoconductivity in the presence of oxygen, which quenches the ntype conduction seen in vacuo. Since the p-type photoconductivity was very much smaller than the n-type, deep trapping can be i11ferred.l~ If we then suppose that the difference in activity as sensitizers of photoconductivity between the HDC and LDC films is ascribable to trapping of holes in the domain of the anions in the former whereas in the latter they remain untrapped in the domain of the cations, we see that these conditions are also vitally involved in the question of the energy of the hole-electron pair although this energy does not enter directly into sensitized photoconductivity. Thus it seems likely that there will be a good correlation between ability to convey energy to a solid state photochemical system by charge-carrier transfer and the ability to sensitize photoconductivity of cadmium sulfide. Although the immediately operating causes differ, the basic cause, hole-trapping, is the same in both cases.
(12) R. C. Nelson, J . A p p l . P h y s . . 34, 629 (1963). (13) N. Petruzsellaand R. C. Nelson, J . Chem. P h y s . . 37,3010 (1962).
