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600 1000 1400 1800 2200 Curing time after quench, hr. Fig. 2.-Annealing of excess conductivity after quenching. The conductivity, in ohm-’ cm.-’, is 6 X 10-7 times the dissipation factor. The temperature wm raised three times during the anneal.
200
point, the subsequent room temperature ionic conductivity is high relative to that of the slow-cooled crystal by a factor of about 50. It a pears that the effect is due to a quenchingin of Schottk derects from high temperature, most of which are a s s o c i a d m vacancy pair “molecules,” or divacancies, at room temperature. I n equilibrium with these pairs is a “vapor pressure” of a few dissociated vacancies; the silver ion vacancies are mobile enough t o contribute to the conductivity and the chloride ion vacancies serve to hold the silver vacancies in solution. Figure 2 shows the decrease of this extra conductivity aa a function of annealing time, the temperature being increased three times during the annealing run. From these curves,
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we may obtain several useful data concerning the Schottky defects. First, from the increases in conductivity that occur whcn the temperature is raised, we deduce an effective activation energy of 13 kcal./mole. For equilibrium between divacancies and dissociated vacancies, and assuming a small degree of dissociation, then this activation energy must consist of the mobility activation ener of the silver vacancy (8.6 kcal./mole, from reference I3yplus one-half the dissociation or binding energy of the divacancy.’ We thereby deduce the binding energy of the divacancy to be 9.8 kcal./ mole. From the temperature dependence of the rate of anneal ( L e . , from the changes in slope of the curves of Fig. 2 upon raising the temperature) it also was possible to obtain the activation energy for the migration of the divacancies. The value of this migration energy is 23 kcal./mole. Since we do not know whether the divacancy migrates aa a unit or by dissociation and migration of the separate vacancies, we can conclude only that the 23 kcal./mole corresponds to the energy of migration of either the divacancy or the chloride vacancy, whichever is the more mobile. We also can estimate the concentration of Schottky defects that have been quenched-in. The magnitude of the ionic conductivity just after quenching corresponds to a fractional concentration of free vacancies of 2.5 X IO*. Having determined the divacancy dissociation energy and estimating the structural contribution to the dissociation entropy to be of the order of 1to 2 entropy units, then we obtain a fractional concentration of divacancies of 0.1%. This must be the concentration of Schottky defects present at high temperatures (Le., near the melting temperature). It is sufficiently small compared to the Frenkel defect concentration at high temperatures that it is not in conflict with the deductions of Friauf.14 It is also of the same order of magnitude as the vacancy concentrations found in metalsI6 and is just the value that was estimated for silver halides much earlier by Seitz .* R. J . Friauf, J . Phyr. Chem., 88, 2380 (1962). (15) R. Simmons and R. Bslluffi, Phys. Re%., 126, 8132 (loo?). (14)
SOME REClEST TRENDS I N THE THEORY OF SPECTRAL SEMITIZATIOX BY W. WEST Research Laboratories, Easfmnn Kodak Company, Rochester Q, A’. Y . Received June 80. 196.8
The present situation in the theory of spectral sensitization of the photographic process is reviewed. It seems probable that spectral sensitization involves the participation of energy-rich swface states of the silver halide a t energies within the gap between the conventional valence and conduction bands. Conduction electrons are formed in the dye-sensitized process with properties similar to those excited by self-absorption bv the silver halide. Positive holes derived from surface states, however, may be expected to be relatively immobile, and preliminary experiments showing the difficulty of observing displacement of positive holes by electric fields in dyed crystals exposed to light absorbed by the dye, without any corresponding difficulty when the same crystal is exposed to near-ultraviolet light, suggest that few mobile holes are formed in the sensitized process. Recent experimental data on the threshold wave lengths for the external photoelectric effect in sensitizing dyes show that the ground levels of crystalline dyes are situated some 1.5 to 2 e.v. above those for the corresponding isolated molecules, and, if it is assumed that the ground levels of cooperative adsorbed monolayers of sensitizing dyes are similar to those for the three-dimensional crystal, sensitization by electron transfer from the excited dye layer to the conduction band of the silver halide becomes energeticallv possible. It is doubtful, however, that electron transfer is energetically possible from isolated adsorbed molecules of sensitizer, which appear to sensitize at least as efficiently aa cooperative monolayers. The selective loss of photographic sensitivity within the spectrally sensitized region a t low temperature suggests the participation of some thermal activation process in sensitizaton, which, however, is not influenced essentially by the position of the absorption band of the dye. Comparative estimates of the fluorescence and phosphorescence yields of sensitizing dyes adsorbed to silver halides and to other substrates suggest that the excited singlet state rather than the triplet state of the sensitizer is involved in the sensitization.
This paper is intended to review some salient points in the theory of spectral sensitization as it appears to stand at present. There can be little doubt that the primary motess induced by the absorption of a photon by silver halide crystals is the creation of a mobile electron and of a mobile positive hole in the crystal. The photo-production of mobile charge-carriers in emulsions is signalled clearly by the observed photocon-
ductivity of emulsions, and experiments of the type introduced by Haynes and Shockley,1-5 involving the displacement of print-out and of latent images in silver halide crystals placed in pulsed electric (1) J. R. Haynes and W . Shockley. Phys. Rev., 121 82, 935 (1951). (2) J. H. Webb, J . A p p l . Phys., 28, 1309 (1955). (3) J. F. Hamilton, F. A. Hamm, and L. E. Brady. ibid., 27, 8 7 t (19.56). (4) .I. F. Hamilton and L. E. Brady, ibid., SO, 1893 (1059). (5) I’. Soptitz, 2. Physik, 163, 174 (1958).
Dee., 1962
RECENT TRENDS IN THE THEORY OF SPECTRAL SENSITIZATION
fields synchronized with light flashes, show that the latent image induced by the absorption of light by the crystals is formed through the intermediary of mobile electrons liberated by the light. Similar experiments in appropriately directed electric fields show the mobility of positive h01es.~J In thin macroscopic crystals of silver bromide, the mobility of the positive holes was found to be 1.5 v.-l set.-', a few per cent of the value of 67 v.-I see.-’ found for the mobility of electrons in the same material.’ Even in the absence of applied fields, exposure of t.hin macroscopic crystals forms latent-image centers in the interior, indicating the diffusion of photoelectrons from sites near the surface of incidence where they are liberated.8.9 In the dye-sensitized photographic response to light of wave lengths absorbed only by the adsorbed layer of sensitizing dye a t the surface of the silver halide crystallite, the photoelectrons also are free, as is indicated by a sensit’ized photoconductivity whose spect’ral sensitivity and response to supersensit+izersand antisensitizers runs parallel to the corresponding characteristics of the photographic sensitivity.lOJ1 The formation of internal lat,entimage centers in emulsion grains, induced by light absorbed by sensitizing dyes, shows that electrons migrate into the interior from tneir points of origin a t the crystal surface; in dyed macroscopic t’hin crystals, exposed t o light absorbed by the dye, the appearance of internal latent-image centers 20 to 40 p from the dyed surface shows the diffusion of dye-induced free electrons over relatively great distances. The mobility of the positive hole associated with the dye-sensitized photographic process is not so clearly established as that of the electrons. Some mechanisms of spectral sensitization t.o be discussed later suggest that the positive hole associated with the dye-sensitized photographic process should initially appear at a surface site which probably is localized. The observed bleaching of sensitizing dyes adsorbed to silver halides during exposure both to light absorbed by the halide and to light absorbed by the dye, and the inhibition of the bleaching on the addition of halogen acceptors t’o the system,12 suggest attack of the dye, directly or indirectly, by bromine release during exposure t,o light both in the region of self-absorption and in the spectrally sensitized region, but do not in themselves show that the positive hole associated with the sensitized process can move through the crystal lattice. The motion of positive holes in thin sheet cryst,als of silver bromide, exposed to flashes of light absorbed by the crystal synchronized with an appropriately directed electric iield, can be shown by the displacement in the field of t’he (6) F. A. Hanim, J. Appl. Phys., 30, 1468 (1959). (7) V. I. Saundera, R. W. Tyler, a n d W. West, J . Chem. Phys.. 37, 1126 (1962). (8) P. W. McD. Clark and J. Pi. Mitchell, J . Phot. Sei.,4, 1 (19X). (9) W.Wpst and V. I. Saunders. J . Phya. Chem., 63, 45 (1959). (10) W. \Test and B. H. Carroll, J . Chem. Phys.. 15, 529 (1947). ( 1 1) IV. \Yeat, “l’iindilrnentul hlechanisms of 1’hotogr:tphic Sensitivity,” J. IT. RIitcliell. Ed., Butterx.orths Scientific Publications, Ltd.. London, 1951. p. 99. (12) S. E. Sheppard, R. H. Lambert, and R. D. Walkor, J. Chem. Phus.. 7 , 426 (1939).
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bleaching effect of the holes on latent-image centers introduced before the flash.’ Recent experiments performed with V. I. Saunders and R. CV. Tyler at the Research Laboratories of the Eastman Kodak Company show that when silver bromide sheets which have been dyed on the surface of incidence by a monolayer of sensitiaing dye are exposed in this way to light absorbed by the silver halide, the motion of positive holes in the field is readily demonstrated, at the same exposure level as required to show the motion of electrons by the corresponding displacement of latent-image centers in an electric field of opposite polarity. When, however, the flash exposure is made to green and yellow light, absorbed by the dye, no such motion of positive holes is indicated. On the other hand, when the field is directed so as to displace electrons into the crystal, motion of the electrons excited by exposure of the dyea crystal to green and yellow light is readily seen. There therefore seems to be strong evidence that the positive holes associated with the spectrally sensitized process lack the freedom of motion of those induced by self-absorption of the silver halide, consistent with trapping of the holes involved in spectral sensitization a t localized surface sites. A decade or so ago, a fundamental problem in discussions on spectral sensitization was the source of the energy which enabled the dye to induce the formation of latent imaFe essentially similar to that formed in the imsensitized process bv utiliziny quanta of so much smaller energy. This problem appears to have been resolved by the recognition that the long wave length of appreciable absorption by the silver halide need not necessarily represent the minimum energy necessary to excite an electron into the conduction band of the crystal. Seitz has pointed out the possibility of radiationally forbidden transitions from levels in the valence band of the lattice above those from which radiational transitions of electrons to the conduction band can occur with appreciable inten~ity.’~,’~ In addition, on analogy with the hetter known surface states in homopolar crystals like germanium, it is expected that the silver bromide surface should possess occupied energy levels in the gap between the lattice valence band and the conduction band, associated with the surface as Such, with crystalline imperfections and impurities and with adsorbed layers. From these levels, an electron can be excited into the conduction band with the expenditure of less energy than corresponds to the long-wave limit of strong absorption by the silver halide. Unfortunately very little is known, either theoretically or experimentally, about the nature of the levels in the energy gap of ionic crystals, and a t present they are little more than a concept which secures conservation of energy in spectral sensitization on the assumption that the smaller quantum absorbed by the dye excites an electron to the same energy state as does the larger quantum absorbed by the crystal. It is still uncertain whether the electron which appears in the coilduetion band of the silver halide (13) F. Seitz, Reo. M o d . P h y s , 2 3 , 3 2 8 (1051). (14) F. C . Brown and F. Bertz, “Photographlo Sensltivity.” Vol. 2, Tokyo Symposium, 1957, Maruzen Co., Ltd., Tokyo, 1958, p. 11.
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as the result of the sensitization process is transferred from the dye, with the formation of a free radical ion in place of the dye molecule, or is excited from a site in the surface of the silver halide following some sort of resonance energy transfer between the excited dye molecule and a surface st,ate. Both mechanisms require the participation of surface states to account for the low energy of activation experimentally observed for spectral sensitization. I n the energy-transfer mechanism, the excited dye molecule must interact with a surface site from which an electron can be raised to the conduction band with the electronic energy available in the excited dye molecule.'5 A positive hole, which may be initially localized, is left at the surface site, while the dye reverts to its ground state. Mitchell visualizes the transfer as the passage of an electron from an energy-rich surface bromide ion t,o the vacancy in the ground orbital of the excitaed dye molecule, with the simultaneous passage of an electron from the excited orbital of the dye to a surface silver ion, from which it is thermally eject,ed into the conduction band.I6 If the sensitizing transfer is to be repeat>ed,t,he surface state in the halide must again be occupied by an electron, or the dye must be able to find an equivalent filled st,at,e. Since the adsorbed dye molecule is in contact with several surface sites, it. could possibly t,ransfer energy several t,imes before depleting the surface of st,ates with which it can interact,. In the elecbron-t,ransfer process, surface statres may be invoked to regenerate the dye molecule from the free radical ion left after t*hepassage of an electron from the dye into the conduction An electron can pass from a surface bromide ion site to the dye radical, regenerating the dye, and leaving a positive hole, probably initlially localized, in the surface. The migration from t'he iieighborhood of the site of a mobile surface silver ion as an interstitial ion in the latt,ice would discharge the hole as an adsorbed bromine atom, which might react, with the dye, in a side reaction unconnected with the sensitizing t,ransfer, in the absence of a more effect,ivehalogen acceptor. The charge of the photoelectron is now balanced by that of the interstitial silver ion. In the energy transfer scheme, there are no restrictions on t,he energy levels of the dye relative to t,he conduction band of t,he silver halide--the energetic restrict3ionis that the dye find a surface level from which an electron can be excited t,o the conduct,ion band (or t80a level sufficient'ly near the conduct,ion band for tmhejump into t'he band to be accomplished by a small thermal activation) wit,h the energy available in the excit,ed dye molecule. Elect,ron transfer, however, requires that t,he excited dye .level hr not, much lower t'han the lowest level of thci c.onduc4on I)and, about i3.5 e . x ~ . brlow the vaciiuni level for silver bromide. The ground level of an $sorbed dye that sensit,izes a t wave length 6000 A . , equivalent t,o an exrit.ation energy (1,i) N.1'. AIotI,, I ' h d J.,88B, 11!) (1!~18j. ( 1 G ) J. W. lfitchell, .I. P h o t . S c i . , 6 , 57 (1038). 1:. Matt and R. W. Gurnay, "Electronic 1'rucesut.s i n Ionic 2nd rd., Oxford Univ. Prcss, 19-18, p. 242. :IS) .J. l';ggert, r ~ n n .Physik, [7] 4, 140 (19.59).
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of 2.15 e.v., must, therefore, be not much lower than about 5.6 e.v. below the vacuum level. The external photoelectric threshold frequency for the adsorbed dye must be equivalent to an ionization energy or work function not much above 5.6 e.v. Measurements of the external photoelectric thresholds of layers of crystalline dyes by Fleischmann19 and more recently by Vilesov and Terenin20 -22 and by Nelsonz3 indicate ionization energies of crystalline sensitizing dyes between 4.7 and 5.8 e.v. From these data it appears tlhat the first excited singlet level of several crystalline dyes, including some photographic desensitizers like phenosafranin, lie above the bottom of the conduction band of silver bromide. The values of phot,oelectric t,hresholds of the vapors of some of these dyes, determined by Vilesov and Terenin,20q21 show that the ionization energy of the crystalline dye is about 1.5 to 2 e.v. less than that of the vapor. A similar relation has been found for condensed ring hydrocarbons.24 I n normal photographic practice, sensit.izingdyes are adsorbed as incomplete cooperat,ive monolayers on the surface of the emulsion grains. Cooperative layers constitute two-dimensional crystals, and if the ionization energy of these adsorbed layers approxirnat.es that of the corresponding normal crystal, spectral sensitization by electron transfer becomes energetically possible. The only data on the ionizat,ion energy of an adsorbed dye layer of a sensitizing dye refer to erythrosin on Sn02,22for which the value 6.7 e.v. was found. It is not certain whether this value applies to a cooperative layer or to a layer mostly consist'ing of approximately isolated dye molecules. Terenin and Akimov22 consider an energy transfer more probable than an electron transfer in the dye sensitization of photoconductivity of semiconduct,ors, and in the absence of further dat,a on the ionization energy of adsorbed layers, the quest'ion of the energetic possibility of the electron-transfer mechanism of spectral sensitization must be left open. In any case, spectral sensitization of the photographic process can occur wit,h undiminished efficiency, and sometimes with increased efficiency compared with that of a cooperative layer, under conditions of very small coverage of the silver halide surface by dye when the dye appears to he adsorbed essentially as isolated molecules.25 I n t,his state, the ionization potential of t.he adsorbed dye probably would difYer relatively litt'le from that of the gas. Even if spectral sensitization of t,he photographic process by a cooperative layer of sensitizing dye by electron transfer is energetically possible, there is considerable doubt, that all observed cases of dye sensitization can occur by this mechanism. Contact potential differences het8ween a relai'ively thick layer of a cyanine dye and silver (19) R. Fleisehinann, Ann. Physik, I,73 (1930). (20) F. I. Vilesov, Dokl. Bkad. Nauk S S S R , 132, 632 (1960). (21) F. I. Vilesov a n d A. N. Terenin, ibid.,133, 1060 (1960); 134. 71 (1960). ( 2 2 ) 1-01. 2 c o r ~ i p r e l i e i ~ sdisciiqaitiii. i~~ w e ;i. \ . 'Vweiiin :I,II
