The photographic process

3 THE PHOTOGRAPHIC

PROCESS

J. F. HAMILTON Research Laboratories, Eastman Kodak Company, Rochester, New York 14650

INTRODUCTION THROUGHOUTthe history of the photographic process, the attention given to the optimization of techniques in the preparation of commercial materials has resulted in impressive increases in photographic sensitivity. Apart from this consistent evolution of sensitivity, however, the technological principles of silver halide photography have undergone relatively few major changes since its inception. With a few notable exceptions--the discovery of spectral sensitization about a century ago, the realization of color photography in the 1930s, and recent innovations in processing (in-camera, dry processes, rapid-access, etc.)-the technological phenomena are much the same. Not so the science related to the process. With the maturing of many branches of science, their applicability to photographic phenomena has become apparent, and the elements of a mechanistic understanding have developed and extended. As this has happened, it has become increasingly evident that this practical technological process entails an unusual and fascinating combination of rather fundamental topics in the chemistry and physics of the solid state. Silver halide photography has proved to be a fruitful medium for the study of such topics as crystal-growth phenomena, dislocations and structural disorder, point ionic defects, surface and colloid chemistry, photoconductive effects, nucleation processes, catalysis, adsorption, spectral sensitization by dyes, and so on. A general mechanistic description of the process may be rather expressly stated, and comprehensive reviews either have appeared or are currently in preparation. <~-4) Consequently, this article will treat the general mechanism only briefly. Without attempting to be comprehensive, it will concentrate on a handful of areas of high current interest in photographic research, in which more general principles are also being evolved in other connections.

THE GENERAL MECHANISM The over-all reactions of the photochemistry of pure silver halides are relatively simple. Throughout their spectral absorption range, the photoproducts are silver and halogen, and 167

168

J . F . HAMILTON

under optimum conditions quantum yields approaching unity may be observed. In the crystalline state, however, the photolysis is not a unimolecular dissociation, but involves both charge and mass transport, so that the products form at separated sites. Silver halide crystals are photoconductors, and the primary absorption act is an electronic excitation forming an electron-hole pair in the conduction and valence bands. Even within the exciton absorption peaks, autoionization is highly efficient, and charge-carrier production has nearly unit yield, ts'6) Owing to the polarizability of the medium, both electrons and holes assume strong polaron character in their motion. In addition, these materials contain thermally activated point defects in the silver ion sublattice, in the form of interstitial silver ions and silver ion vacancies, both with significant mobility. Photolysis involves electronic and ionic migration. A photon is absorbed, the electronic carriers are formed and diffuse about in the crystal, and if they do not encounter one another and recombine, the electron becomes temporarily localized at some appropriate electron-trapping site, and the hole at a corresponding hole trap. The acquisition of the appropriate ionic defect completes the components of the photoproducts at the two centers: an electron and an excess (interstitial) silver ion constitute essentially an atom of silver at the one, whereas a hole and a silver ion vacancy leave in excess a halogen atom at the other. It is significant that the local perturbation of electrical charge which results from trapping either electronic carrier at a site is compensated by the corresponding ionic species which combines with the center. Thus, the trap is, electrostatically at least, reset for trapping of another like electronic carrier, capture of another ionic defect, and so on, in an alternating sequence. Whether or not the alternation of electronic and ionic events follows precisely throughout the process has not been determined. Other possibilities, including singular discontinuities in the pattern, have been proposed by, for example, Mitchell¢7) and Baetzold. ~8) However, these suggestions represent only minor deviations from the alternating sequence. Known ~9) as the Gurney-Mott principle, after the two British physicists t i o, 11) who were responsible for the original formulation, this feature stands as one of the basic elements of the photochemistry of silver halides in the solid state. It is generally found that both the silver and the halogen photoproducts separate in concentrated form. The induced optical absorption caused by the silver is that of colloidal particles, and these are easily revealed by microscopic techniques. The aggregation of the halogen photoproduct is revealed by the production of visible surface pits--the so-called reverse image---demonstrated by West and Saunders¢12) and others, t i a) When a silver-atom aggregate reaches sufficient size it constitutes what is termed a latent-image center, distinguished by its ability to catalyze the chemical reduction of the host silver halide crystal by certain reducing agents used as photographic developers. This development process of photography is a classical example of a catalyzed solid state chemical reaction, Recent evidence ~1~) shows convincingly that, in some cases at least, the catalysis occurs purely by a simple electrode mechanism. The reducing agent, in solution, transfers electrons to the silver metal catalyst, through which they are conducted to the silver-silver halide interface, there to react with silver ions from the silver halide. In the simplest form, the silver ions arrive at the reaction site by motion as interstitials through the silver halide lattice. The precise mechanism of the catalytic effect is not understood, but has been attributed by Trautweiler~l 5) and Jaenicket16) to be the presumed introduction of a vacant electronic state below the level of the electrons of the reducing agent, whereas only levels higher than that exist in unexposed silver halide. Whatever the mechanism, abundant evidence indicates

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169

that this catalytic property is acquired when the aggregate reaches a size in the range of three to six atoms. (17) Thus an efficient aggregation of the silver product is essential to photographic use of the silver halides, in striking contrast with the alkali halides, in which unaggregated F-centers predominate. The high efficiency of aggregation may be attributed to the thermal instability of atomic centers in the silver salts. Both the static and high-frequency dielectric constants are higher by several times than those of the alkali metal salts. This results in a very much stronger shielding of electrostatic attractions by lattice polarizations, and a weakening of the interactions between charged centers and mobile electronic and ionic carriers. Thus coulombic traps for electronic carriers are shallow, and the ionic steps producing single atomic centers are thermally reversible. Only upon formation of a diatomic species at a center is useful thermal stability achieved.

C

AT

ii ETC.

F~o. 1. Schematic diagram of the interactions involved in the photochemicalprocess in silver halides (Hamiltonc22~).

Recombination of electrons and holes competes with the photochemical process, and high photographic efficiency requires its suppression. Owing to peculiarities of the band structure,O a-21) direct band-to-band recombination of electrons and holes must involve phonons to satisfy the momentum requirements. These transitions are unlikely, and processes at shallow trapping levels dominate the recombination. The ionic events which follow carrier trapping alter the electrostatics at these centers so as to reduce the recombination cross-sections. In addition, the two final photochemical products in contact are thermodynamically unstable and if they encounter one another will react again to form silver halide. The back reaction, in which silver is oxidized either directly by halogen, or indirectly by holes, must also be minimized for high efficiency. A schematic diagram of the interactionst ~2) is given in Fig. 1.

170

J . F . HAMILTON IONIC DEFECTS

Throughout the process, it is the part played by the ionic defects which promotes the photochemical reaction and distinguishes the silver halides from other phosphors or photoconductors. The ionic defect structuret23-27) is certainly a topic of prime importance in this regard.

Intrinsic Defects The photographically useful silver halides contain Frenkel-type disorder (interstitialvacancy pairs) in the silver ion sublattice only. Elementary thermodynamic considerations result in an approximate expression for the equilibrium concentration np of defect pairs as follows: np= x/2N.e -w/2kr (1) where N is the number of lattice sites per unit volume, W the energy of formation of a pair, and k T the mean thermal energy. In the high-temperature range, intrinsic pair formation dominates, and expression (1) adequately describes the defect concentration.

Impurity Defects At lower temperature, extrinsic processes become important, and eqn. (1) is no longer adequate. One source of deviation are the residual polyvalent (valence z) metallic impurities3 zs) Many such impurity species can dissolve substitutionally in the lattice, each impurity ion replacing z silver ions. The impurity occupies one lattice site, but the remaining ( z - 1) sites are vacant. At temperatures such that the intrinsic pair concentration is below the concentration of impurity-introduced vacancies, the latter dominates, and the vacancy concentration remains essentially constant as the temperature is further reduced. Nevertheless, the vacancy-interstitial equilibrium is maintained, and, if nl and nv are the concentrations of interstitials and vacancies, respectively, the following relationship holds: nin v = 2 N e - w I l T

(2)

even though ni ¢ nv, contrary to the situation in the intrinsic temperature range.

Surface- or Dislocation-generated Defects Certain physical defects, such as surface kink sites or jogs on dislocations, may also influence the low-temperature concentrations of mobile ionic defects. A number of theoretical treatments of this phenomenon have been reported, tzs-a 5) A kink site ta 6) is the terminus of an incomplete line of ions along a surface terrace. It has an effective long-range electrostatic charge of one-half electronic unit, and may have a positive or a negative sign, depending upon whether the terminal ion is silver or halide. At a positive kink site, an interstitial ion may be generated singly, without creating a corresponding vacancy. The terminal silver ion is thermally excited into an interstitial position, and the kink becomes a negative one, maintaining charge balance. At a negative kink site, a lattice silver ion may be displaced onto the kink, changing the sign of the kink to positive and leaving a silver ion vacancy in the lattice. These processes are illustrated in Fig. 2, from which it may be deduced, based on elementary thermodynamics, that the sum of the forma-

The photographic process

÷

*__

_--

_--

a

171

b

lip

C

wi -Wv V = ~

Distance, x FIG. 2. Diagrams illustrating (a) the formation of an interstitial-vacancy pair, (b) formation of each defect singly from surface sources, (c) the resulting spatial distribution of defects and the electrostatic potential profile.

tion energies (Wi, Wv) of the two types of mobile defects must equal the formation energy of an intrinsic interstitial-vacancy pair: w , + wo = w .

(3)

In general, Wi ~ W~, and the low-energy defect forms in greater concentration than the high-energy one. This leaves the surface (or the dislocation) with a net electrical charge, the counter-charge lacing the excess of the low-energy mobile point defect, which is distributed in a diffuse space-charge region below the surface. The surface m equilibrium is at an electrical potential V with respect to the bulk of the crystal such that Wi-eV

= Wv+eV,

or

wo

v = w,-

(4)

2e The spatial distribution of both types of defect and the electrical potential function may be

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J . F . HAMILTON

derived, and more detailed treatments include the effects of impurities, of two surfaces within interaction range, and of the configuration of the surface.

Experimental Studies One experimental method for investigating surface effects on ionic defect concentrations is the measurement of electrical conductivity. Both interstitial ions and vacancies are mobile (mobility/~i and p~) and the conductivity ¢r of a crystal is given by

tr = e(ndz~+ nja~).

(5)

In any small volume of a crystal, since the product n~ x n~ = n p2 is a constant, the condition for minimum conductivity is that n#t i = nd~, when the contributions of the two carriers are equal. Any deviation from this condition results in an increase in conductivity, by one or the other term of eqn. (5). Within the surface space-charge layer, one carrier is generally far in excess, and the conductivity may be much higher than the bulk value. In an arrangement to measure conductivity parallel to the surface, the space-charge layer constitutes a high conductance path in parallel with the bulk of the crystal which, under favorable circumstances, may be detected and analyzed. Conductivity measurements on silver bromide microcrystals of photographic emulsions have been reported by Hamilton and Brady(37-40) using photographic exposures in pulsed electric fields and electron microscopic observations of results, and by Van Biesen, c41) by means of the Maxwell-Wagner analysis of the frequency dependence of dielectric properties. Conductivities several powers of ten higher than intrinsic were found and attributed to a contribution by the defects in the space-charge layer. The dependence on impurities and photographically active adsorbed agents indicated that the surface was negative, and the excess point defect was the interstitial silver ion. The temperature dependence indicated a value of W~ - 0.1 eV. Conductivity measurements on epitaxial silver bromide films(42) in both {111} and {200} orientations have been made by Trautweiler et al., (43) and by Baetzold and Hamilton.(44) The features observed on {111} oriented films are similar to those noted for emulsion microcrystals. The surface is charged negatively, indicating that interstitial silver ions are the more easily formed defect, and their formation energy was determined to be 0.26 eV. Vacancies introduced by the addition of divalent cadmium as an impurity to these films were found to compensate the excess interstitials, resulting in decreased conductivity at low Cd + + concentrations, reaching a minimum as the Cd ++ concentration was increased, and then increasing again, owing to excess vacancies. The impurity level of the minimum agreed well with the concentration of excess interstitials in the pure films, as determined by their conductivity. Silver bromide films in {200} orientation showed no significant surface component of conductivity. This was interpreted in terms of the analysis by Poeppel and Blakely,(a3) to indicate that these films had a much lower surface-defect population. According to this treatment, the total free energies of formation of the two types of defect must include a contribution from the configurational entropy of the surface itself. Thus

W[ = W , - k T l n

2 - -(NJ2+q/e) \Ns/2_q/e]

(6)

and

W" = W v - k T l n (lvs/2-q/e] \ ~ j

(7)

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173

where Ns is the density of surface sites and q is the surface charge density. These additional terms account essentially for the effects of depletion of the surface sources of the defects. Obviously the number of surface-generated defects can be no more than half the total number of surface kinks, assuming over-all electrical neutrality. From the data one may deduce that the maximum kink-site density is of the order of 10- lO cm-2, or about one in 105 surface lattice sites, on the {200} films. In both orientations, these silver bromide films were found to have extrinsic volume sources of interstitial silver ions which controlled the bulk conductance properties. The {111} films are known to contain double-positioning domain boundaries, and the {200} films have transverse dislocations in high concentrations; these physical defects are presumably the features in question, t#2) Other experimental approaches may be used to investigate imperfection-generated ionic defects. Tan and co-workers~45) applied radioactive-tracer techniques to study lateral silver ion diffusion along the surfaces of similar epitaxial films and obtained results essentially in agreement with those described above. Matejec{46'47) measured conductivity through a silver bromide membrane separating two cells containing electrolyte solutions. Saunders et al. {4s) used microscopic etching techniques to reveal the depth of silver centers and thus determine the equilibrium positions of electrons acted on by an applied electric field opposing the space-charge field. Their results were analyzed by Trautweiler~49) to give the following values for the significant parameters of the system: Surface potential,

V

=

-

140 + 50 inV.

Interstitial formation energy, W~ = 0.32 eV. Electric field strength at surface, 29 (+40, -10) kV/cm. Density of surface charges, 2 (+3, - 1) x 1011/cm2. Slifkin and co-workerstS°) used strain-induced electrical effects and measurements of internal friction to study the charge on dislocations in silver chloride. Their results, unique in dealing with dislocations as opposed to surface defects and with the chloride rather than the bromide salt, also differ in indicating that the silver ion vacancy is formed with lower energy. Conflicting results have been reported on the interaction between double-layer effects in an electrolyte solution in contact with a silver halide surface and the space-charge effects on the solid side of the interface. Fatuzzo and Coppo~~51) measuring an effect on the lowfrequency dielectric constant of silver halide samples caused by the surface space charge, found results which depended strongly on the medium in contact with the surface. Matejec,~46'47) in experiments mentioned above, found a strong dependence of conductivity on the Ag+-Br - ion balance in his electrolyte solutions, whereas Saunders et al. ~4s) and Hamilton and Brady~as~ observed only very small effects. Honig~a-54) has reported effects of the reverse type. He found the solution electrokinetic properties to depend strongly on polyvalent impurities which presumably affect the solid-phase spacecharge properties. Honig's results have been criticized on theoretical grounds by Levine et al., ~5~ and Merrigan et al. ~56~ were unable to confirm an effect from Pb + + impurity. These discrepancies are also probably a consequence of differences in the configuration of the surfaces being studied. If only a small fraction of the defect surface sites are involved in establishing the electrical equilibria, then changes on one side of the interface would not be

174

J . F . HAMILTON

expected to influence the equilibrium in the other phase. Equilibria approaching depletion of one type of site, on the other hand, would be extremely sensitive to the interactions on the opposite side of the interface. In the extreme, this situation becomes the case treated by Grimley and Mott, (57) who assumed that no charge at all resided at the interface. CHARGED DEFECTS AS ELECTRON AND HOLE TRAPS Within the volume of silver halide crystals, photolytic silver is found to separate on dislocations. This effect, in fact, causes microscopically visible decoration of dislocation lines and historically presented the first opportunity to observe dislocation structures within a crystalline solid, t5 s-65) At the silver halide surface, the sites where silver may be produced occur in very high concentrations, (66-67) almost too high to be explained in terms of any particular chemical impurity. Both dislocations and surfaces contain physical imperfections (jogs and kinks) with which are associated effective partial electronic charges. The experimental observations are all fully consistent with the hypothesis that the positively charged physical defects constitute the shallow electron traps at which silver nuclei can form upon illumination. Indeed, in most of the recent literature on the subject, the identification of the predominant electron traps as kinks and jogs is axiomatic. The effect of the high dielectric constants of silver halides in weakening the electrostatic interactions has already been noted, however, and quantitative evaluations of interaction energies cast some doubt upon the effectiveness of charged physical defects as electron traps. F-like centers, involving an electronic carrier in orbit about a fixed opposite charge, have been treated theoretically using models with varying degrees of sophistication. (6s-72) In general, polarization of the lattice between the two point charges introduces the inverse square of the dielectric constant as a factor in the expression for the binding energy. In the silver halides, this polarization so effectively shields the electrostatic interaction that the binding is very weak and the orbital radius is many lattice spaces. At room temperature the interaction energy is less than the mean thermal energy, and even temporary trapping would not occur. Brandt and Brown (71) used a variational technique with a hydrogen-like wave function and the static value of the dielectric constant, and calculated a value for the ls -, to transition in AgBr of 0.03 to 0.04 eV. Their calculated transition energy for the Is ~ 2p excitation was slightly greater than the peak of an exposure-induced infrared absorption which they observed at 9.3°K and identified with that transition of an electron polaron in the coulomb field of a positive center. They suggested that this center was a self-trapped hole.(65.66) Kanzaki and co-workers (6 a, 69) have also studied low-temperature, exposureinduced infrared absorption, most extensively in crystals of mixed halides or those with divalent metal impurities. In addition to the transition at a few hundredths of an electron volt, they also found a higher-energy absorption, which they ascribed to excitation of a trapped hole. In both the calculations and the experimental observations, the trapping centers involved carry a unit electronic charge. The interaction energy for a kink or jog, with an effective fractional charge, would be even weaker. Thus it appears difficult to account for deep enough electron traps at purely physical imperfections to explain the observed tendency for silver to form there. It must be either that the particular electronic states involved with chemical impurities are always involved in the photolysis of real crystals, or else that the

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model systems used both experimentally and theoretically to investigate these energies are not adequate. Consider, for example, an electron orbiting about a fractional positive point charge. The dipolar interaction between the two charges induces an instantaneous polarization of the lattice between them in such a direction as to shield their interaction. The time average of the charge distribution, however, is that of a partial negative charge centered at the trap. The long-range, low-frequency lattice polarization would have the nature of a self-trapping effect, increasing the binding of the electron at the trap, perhaps by a significant amount. It would be enigmatic if a fractional positive charge would provide a deeper trap for an electron than a unit positive charge, because of such an effect. SURFACE STATES Intrinsic surface states, t 7 s-77~ arising simply from the termination of the periodic lattice, and quite apart from surface defects, such as kink sites, are frequently discussed in connection with the silver halides. No clear evidence of their significance has ever been substantiated, however3 TM If such states do exist, their effects would be very difficult to distinguish in the presence of the potential gradient of the ionic space-charge layer and the relatively large numbers of surface imperfections. IMPURITY TRAPPING CENTERS Core electronic states (79~ of a number of charged or isoelectronic chemical impurities have been found to interact to varying degrees with the electronic carriers in silver halides. Generally typical behavior is exhibited by the system AgCI:Cu, which is perhaps the most thoroughly studied of the active impurities38 o-86~ Copper ion can exist as an impurity in AgCI in either of its valence states, Cu ÷ ~ or Cu ÷ 2, in concentrations up to about 10 ~s ions/cm 3. In either state it is substitutional on a cation site, and as cupric ion, it is normally associated with a silver ion vacancy on either a nearest or a next nearest-neighbor cation site. In crystals grown from the melt or annealed in reducing atmosphere, the copper assumes the + 1 state. As such, it effectively sensitizes the volume photolysis of the crystal. Exposure to bandgap illumination results in the appearance of an absorption band due in part to silver particles distributed through the volume. With continued exposure extinction of this band approaches a saturation value which is directly proportional to the Cu + ~ content of the crystal. The exposure-induced absorption spectrum of a crystal of this type includes another band (actually two overlapping bands with peaks at 3.24 and 2.37 eV). This part of the absorption spectrum may be induced in a Cu ÷ 1-containing crystal by annealing in C12 atmosphere to inject holes into the crystal. These observations lead to the conclusion that the Cu ÷ 1 center in a silver chloride crystal acts as a hole trap. Bandgap illumination produces electron-hole pairs, which recombine in a pure crystal. The Cu ÷ ~ centers trap holes and are converted to Cu ÷ 2, with (at room temperature) the liberation of interstitial silver ions from neighboring cation lattice sites. The corresponding electrons become trapped, probably at dislocations, and combine with interstitial silver ions, forming colloidal silver particles. Photoconductivity measurements using light in the impurity absorption bands confirm this interpretation, and luminescence measurements combined with these give information about the energy levels associated with the impurity. Copper impurity in the + 1 state

176

J . F . HAMILTON

induces a weak shoulder on the optical absorption edge of silver chloride. Exposure by light within this shoulder (3.0 eV) produces a photocurrent owing to electrons. The electrons originate in the 3d 1° ground state of the copper ion and are autoionized from the first excited state (3d94s) of that ion, which lies above the bottom of the AgCl conduction band. At liquid-nitrogen temperature the release of the electron is not followed by generation of an interstitial silver ion (as at room temperature) and the lattice polarizes strongly about the residual positively charged center. This center may recapture the electron, which radiatively decays to the ground state. Owing to the strong lattice polarization, the energy levels are changed by relatively large amounts, and the emitted photon has an energy of only 1.4 eV in the infrared. From the equilibrium Cu +2 center holes are liberated by excitation within a band centered at 3.24 eV. An additional nonphotoconductive band at 2.37 eV remains unexplained. Both the Cu +1 center and the Cu+2-vacancy complex, for long-range interaction, are uncharged. Thus it must be that for non-coulombic reasons the Cu + 1 center has a large cross-section for trapping a hole, but the Cu + 2-vacancy center does not interact strongly with either carrier. The iodide center in AgBr or AgCl and the bromide center in AgC1 behave similarly.(74'sT-s9) These halide impurities dissolve substitutionally in the anion sublattice and, because of the difference in electron affinity between the impurity and the host anion, introduce discrete levels within the gap just above the valence band. These isoelectronic impurities thus constitute hole traps, though the levels are shallow, and at room temperature the trapping is temporary, compared with the copper hole trap, which is far more permanent. Other cationic impurities undergo valence changes, and evidently in their polyvalent states have varying propensity for association with vacancies in neighbor positions. The transitions Ni + 2 _~ Ni + 1,(90) Fe + 2 ~ Fe+ a,t9 i~ Cr + a _~ Cr + 2,(92) V + 3 ..~ V + 2(91,93) have been verified by trapping of a hole or an electron, as the case may be. Generally the vacancy concentration changes as expected. (94~ Both nickel and iron have been reported to desensitize the photochemical effect in silver halides, presumably by acting as recombination centers. Moser e t al. (s 1) found no cationic impurities as active as copper in sensitizing the photodarkening of their crystals. Malinowski (95) has devised a technique for ranking the capture cross section of various impurities for trapping electrons and holes. Evaporated films of silver bromide are made with co-evaporated impurity halide deposits at fixed depths in the layer. Electron-hole pairs are generated entirely on one side of the impurity layer by strongly absorbed light, and their ability to diffuse through that region is evaluated by the forward and reverse photographic effects produced on the opposite face. By comparison with control samples without impurities, Malinowski confirmed that Cu + 1 provides hole traps, and found that Pb + 2 causes increased electron trapping and Cd + 2 results in more effective trapping of both carriers. He also found indications that Bi + a traps electrons and Fe +2 has little effect, though both of these latter cases gave problems with reproducibility. It is safe to conclude that most impurities are photographically inactive in practical systems. While it is true that photographic manufacturing practice is geared to the careful exclusion of a few elements known to be detrimental, the over-all purity of chemicals used is not as high as that required for some semiconductor applications, for instance. Many elements are probably present at levels of 10 to 100 ppm, and fluctuations from one batch to another are likely to be large. At even 1 ppm, an average emulsion crystal would contain well over 100 impurity ions. When sensitivities requiring only ten or so photons can be

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controllably achieved, it is unlikely that the inadvertent chemical impurities have much effect. Perhaps this argues for the controlling influence of the physical defects at the surface.

CHEMICAL SENSITIZATION The chemical procedures normally used to reach high sensitivity in practical emulsion systemst 96,97) produce impurities at the crystal surfaces rather than substitutionally in the volume. The common treatments either form monolayer islands of silver sulfide or silvergold sulfide at the surface, or reduce a limited number of silver ions to very small particles of silver. Evidence is that the sulfide deposits are located at imperfections, which would normally act as electron traps. They confer additional stability to silver atomstgs) located at those imperfections, retarding their thermal decay, and may also increase the binding energy of the electron to the trap. t99-1° ~) When gold is part of the sensitizing material, this becomes incorporated in the silver center and increases the catalytic activity.O°2-a) The silver centers produced by reducing agents as sensitizers have been shown to act as traps for holes, t1°4-7} The trapping of a hole followed by release of a silver ion has the effect of reducing the size of the silver aggregate by one atom. Presumably when the residual silver is only a single atom in size it thermally decays, providing an electron which can contribute toward the latent image. The striking difference in behavior between these chemically reduced silver centers and those produced by photolysis has been emphasized by Spencer J ~o s) When present simultaneously, the chemical silver has a tendency to trap holes and be bleached, whereas the photolytic silver traps electrons and grows. An electrostatic charge difference is the most obvious possible explanation, and the type of surface site on which the silver resides could be responsible for the electrostatic condition.

QUANTUM MECHANICAL CALCULATIONS The properties of small silver aggregates--their ability to trap electrons or holes, as well as their catalytic activity during the development processmare features about which only very general inferences can be drawn from experiment. A knowledge of the detailed energetics of these aggregates as a function of size and electrostatic charge would provide immense insight into the mechanisms involved. The technique of molecular orbital calculations is beginning to be directed toward these problems, with considerable success and even greater potential. Some rather primitive methods have been used by Latyshev and Molotskiit1°9-~11) recently, but the most extensive effort is that of BaetzoldJ s' 112-14) He has used both the extended Hiickel method detailed by Hoffmannt ~15) and the CNDO (complete neglect of differential overlap) technique of Pople and co-workers, t116-19) These are both semiempirical quantum mechanical methods, involving atomic wave functions and ionization potentials as input data, and parameterized by comparison with experimental data on diatomic molecules. Beginning with isolated silver aggregates, the results give information about the binding energies, electron affinities, and ionization potentials as a function of aggregate size. Configurational variations may be explored to determine equilibrium forms and bond distances.

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J . F . HAMILTON

For isolated aggregates of silver atoms, the results indicate that a linear chain remains the most stable configuration up to sizes of over 30 atoms. Calculated ionization potentials and electron affinities exhibit a marked oscillatory behavior in the small size range, owing to alternations between single and double occupancy of the highest occupied level. The oscillations diminish and the values of the two levels converge as the aggregate size increases, toward a value approximating the bulk work function of silver. This results in a general trend for the ionization potential to decrease and the electron affinity to increase with increasing size, but neither change is as large as the magnitude of the oscillations superposed on it. Subsequent calculations (1 ~4) have dealt with a limited model of a silver bromide surface and the interface between this surface and silver aggregates placed thereon. Using a rigid lattice of up to thirty-five ions, groups of electronic energy levels are calculated which are reasonable approximations to the AgBr valence and conduction bands. A silver atom moving up to a plane AgBr surface is found to have a lowest-energy position over an interstitial site, but may be more favorably accommodated over a silver ion lattice site than a bromide ion site. Ag atoms placed on the surface are found to become positively charged, to almost the magnitude of the lattice silver ions. This indicates a delocalization of the silver valence electron. The linear geometry is no longer most stable, but the same general trends and the same oscillatory changes in both ionization potential and electron affinity with silver aggregate size are found with and without the AgBr substrate. Results indicate that Ag2 center on a plane surface cannot trap an electron, and if it is to grow, it must do so by first adding a silver ion and then an electron. This can be related to the tendency of chemically formed silver particles to be bleached by exposure rather than to grow. A first approximation to a surface defect has been included in some of the calculations, and the effect is to change the electron affinity of Ag2 (and all even-sized aggregates) so that they can act as electron traps. The thermodynamic pathways found for growth of a silver aggregate on a plane surface and at a surface defect are shown in Fig. 3. The defect considered does not have the exact configuration of a surface kink site, and further changes may be expected as the model is made more realistic. Furthermore, these are acknowledged to be merely the paths of greatest thermodynamic advantage, and kinetic factors might alter the sequence in practice. Ag

J AqAq+ Ag3

ACJ4- ~ Ag5+

J

Ags

Fro. 3a. Calculated thermodynamic paths for collection of silver atoms at a plain AgBr surface.

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A9

A

/

~

Ag 3

j,~Ag4 Flo. 3b. Calculated thermodynamicpaths for collection of silver atoms at a surface defect (Baetzoldta~). Baetzold's approach has several limitations, some of which are subject to modification by refining the model, and some of which are basic to the techniques. At the present time it employs a rigid lattice model, and therefore does not account for low-frequency, ionic lattice polarization or relaxation effects. Perhaps at least a first-order correction for this effect could be made. More basically, existing computer size restricts the substrate model to relatively few ion pairs, and a single defect truly remote from others (e.g. corners and edges) cannot be investigated. The location of electronic carriers is determined by integration of probability density functions over the lattice subcells associated with each ionic core, and weak binding in large diffuse orbits could only be detected by charge trends over still larger volumes. Significant improvements over this situation can only follow radical improvements in computer capacity and speed. Still, even with these limitations, Baetzold's calculations represent at this time the most hopeful approach to a theoretical understanding of electronic states in small centers. SPECTRAL SENSITIZATION One of the most significant technological aspects of the photographic process involves the interactions between the electronic bands in the solid and the localized levels of organic molecules adsorbed at the surface. Spectral sensitizing dyes represent the most common class of such organic molecules, but other chemical species are also important. The principle of using dyes to extend the spectral sensitivity of the silver halides (alone sensitive only in the blue and ultra-violet regions of the spectrum) throughout the visible and even into the infrared spectral ranges was discovered inadvertently about 100 years ago. Since that time an extensive effort has been directed toward synthesizing dyes with specific spectral and chemical properties, and today an immense collection of structures (120> (e.g. the cyanines and substituted cyanines, merocyanines, oxonols, etc.) is available from which to study correlations of properties.

180

J . F . HAMILTON

Although resonance transfer of energyt 121-2) between a dye and the silver halide has been shown to be possible, ~1 2 a-s) the mountingevidence is that in the vast majority of practical instances, actual transfer of electronic Carriers across the interface is involved. For this process, adsorption of the dye to the'surface is of prime importance. Working sensitizing dyes are generally found to adsorb strongly. In some cases cohesive interactions between adsorbate molecules are comparable with subs(rate interactions. Ordered aggregates (126,1 ao) may form in the adsorbed state with corresponding shifts in absorption spectra. Upon aggregation, absorption bands are usually significantly narrowed, and shifts to either shorter wavelength (hypsochromic) or longer wavelength (bathochromic) may be observed. The quantum mechanics~127,1 a 1-4) of simple interacting dipoles predict that the direction and magnitude of the spectral shift upon aggregation is related to the angle between the aggregate axis and the chromophore. Apparently these simple predictions are at least qualitatively correct. Correlations of photographic properties of dyes with energy levels of their ground and excited states have been emphasized in recent years by a number of investigators. (126-s o) In general these correlations have been sufficiently good to produce a unified picture of the over-all process and to explain structure-induced differences in behavior among dyes.

Energy-level Determinations Although a variety of physical and chemical measurements have been used to determine ground- and excited-state levels of dyes, none appears to be without some complication or difficulty. Perhaps the most directly applicable method involves the measurement of the photoelectric emission threshold and employs at most a monomolecular layer of the dye, adsorbed on the substrate in question,t 1 s 1 - 0 In principle this measurement fixes the groundstate level of the dye under the circumstances of the measurement. In practice, a measurement of this type is very sensitive to impurity effects at the dye-vacuum interface. Care must be exercised in preparation of the surfaces in order to obtain reproducible results, and even so, questions remain concerning possible effects of counterions, residual water molecules, and foreign species on the results. Furthermore, the results do not give an abrupt threshold, and some arbitrary criterion must be adopted in assigning a numerical energy value to the ground-state level. Nelson, t 1a s) for example, picks the level at the photon energy for which the emission current is 10-4 of its maximum, and justifies the arbitrary decision by using the same criterion for assigning an excitation energy. It is not at all certain, however, that the same processes control the weak "tail" transitions of the two phenomena, and very small amounts of impurities could be selectively important at the threshold of one or the other excitation. Terenin and Akimov(1 sT) have employed a vibrating-condenser technique to measure potential differences between a palladium electrode and a partial monolayer of dye adsorbed to silver halide. Other methods for energy-level determinations involve dyes in environments different from that in question, and corrections must be applied in order to account for effects of dielectric constant and, when necessary, solvation energy. Data from the photoelectric energy threshold of crystalline dyes,~1s6-9) from the ionization potential of vapors, ~146) and from polarographic determinations of oxidation potential in solution( 146-7,161-7) have been used. When corrections are applied, these results appear to correlate reasonably well with photoemission thresholds from the adsorbed state, where such data exist. The excitation energy of a dye, the energy difference between its ground and excited

The photographic process

181

states, is found from the spectral position of the absorption maximum, or, for continuous or crystalline dye layers, from the photoconductive threshold. The measurement of absorption spectra is quite straightforward, but the identification of the energy with the absorption peak certainly raises questions about rationalization of this measurement with those involving much different threshold criteria. Although chemical reduction of a dye molecule places an electron in the same molecular orbital as the excited-state level, the additional negative charge of the reduced form raises this energy level somewhat. In large organic molecules, however, the change is relatively small. Tani and Kikuchi(136'13s-9) and Gilman~149) have neglected this difference, and taken the electron affinity of a dye to be identical with the energy difference between the vacuum level and the excited state, located in this way. The electron affinity can be obtained experimentally from the polarographic reduction potential~161-7) with the appropriate environmental corrections. For an adsorbed dye monolayer, the electron affinity can be measured by an electronbeam retardation technique,t168) though nonohmic contact problems are reportedly encountered3135) Nelson points out c~35) an alternative approach, which he applies to rhodamine B. In the crystalline state, this dye is a photoconductor with a high density of monoenergetic traps. The trap depth may be measured by the temperature dependence of rise and decay features of the photoconductivity,t169) and Nelson equates this trap depth with the energy difference between the excited-state energy level and that of the reduced form. Both Nelson t135,17 o-1) and later James° 4s~ have emphasized the likelihood of an energy difference between the electron affinity and the excited-state level. Nelson deduces the values of the two levels and finds that the excited-dye level lies below the electronic level of the reduced form by 0.1-0.3 eV. He correlates this energy difference with the temperature dependence of steady-state photoconduction in the corresponding dye layers, with good success. James, on the other hand, suggests inversion of these two levels. In addition to the experimental methods, molecular orbital techniques have been used to calculate ground- and excited-state levels in a variety of dyes. Tani and Kikuchit136) use simple Hiickel semi-empirical techniques, calibrated by experimental properties of naphthalene and anthracene, and find values surprisingly close to experimental data, where available. Similar calculations by Sturmer and Gaugh ~150) have extended the method to even larger numbers of dye structures. Selsby and Nelsont~ 72) employed a Hartree-Fock self-consistent field LCAO-MO method of calculation. All of these methods generate either experimental or theoretical energy values for the ground and excited states of dyes. All involve either some arbitrary criterion or some rather inexact correction for environment or both in order to place them absolutely on an energy scale. All, however, should be fairly reliable in measuring relative energy levels among dyes, at least of related structure. Evidence supporting charge transfer across the interface involves the correlation of photographic effects with the positions of the dye energy levels relative to the valence and conduction bands of the silver halide. The top of the valence band is measured, as for the dye layers, by the threshold of external photoemission, and the value of Taft e t al. ~173) of 6 eV below vacuum for AgBr is that generally used. Assignment of this value also involves an arbitrary threshold choice on a function continuously decreasing with increasing wavelength. Furthermore, recent data by Bauer~174) differ significantly from that value, and show that results depend markedly on specimen preparation and history. The position of G

182

J . F . HAMILTON

the bottom of the conduction band is energetically determined relative to the valence band by optical measurement of the absorption edge. However, the electronic transitions near the absorption edge are temperature=dependent, owing to phonon interactions, and deter= nfination of the energy difference between the band extremes is very indefinite. Probably, with all of the uncertainties currently existing, one should be gratified to be able to find any arbitrary position of the silver halide levels relative to those of dyes, which would consistently correlate with photographic properties of structurally different dyes. It is a little surprising that authors have taken absolute positions as seriously as they have. Nevertheless, there is at least some reassurance in the fact that reasonable adjustments can be made which rationalize the absolute values between the two phases.

Photographic Effects Correlations are very good, with an impressive variety of dyes, not only for the spectral sensitizing properties, but also for interactions with photoelectronic carriers produced directly in the silver halide. Most useful dyes have absorption maxima at wavelengths well beyond the silver halide absorption edge, and exposure to selected spectral regions will either excite the sensitizing molecules or produce electrons and holes in the silver halide, exclusively. Based on relative energy levels, dyes may be classified in terms of the possible electronic transitions across the interface. For spectral sensitization of the normal photographic effect by electron transfer from the dye, the excited-state level must lie at or above the bottom of the silver halide conduction band. Since the excitation energy of practical dyes is less than the silver halide bandgap, this necessarily places the ground level of the dye above the silver halide valence band. The energy-level scheme for such a dye is seen in Fig. 4a. When the dye absorbs light, the excited electrons can transfer across the interface and sensitization occurs. For exposure in the spectral region of the silver halide absorption, photocarriers are produced in the crystal, and the dye molecules are potential acceptors of the holes. The photoelectrons cannot transfer into the reduction levels of the dye. However, when a hole transfers to a dye molecule, it produces a dye radical, with an unfilled ground-state level. This radical state can then move through the dye layer, depending upon the extent to which it is continuous. An electron from the silver halide conduction band, from a surface trapping level or even from a silver atom or aggregate, may fall into the unoccupied level and be lost for photographic effect. In effect the dye behaves as a recombination center,(175-6) promoting an encounter between the photoelectron and an empty ground level. This effect is widely observed in practice, for it is reported ° 77) that almost all working sensitizing dyes cause a loss of sensitivity for light absorbed by the silver halide, particularly when the surface coverage is high. Dyes like that in Fig. 4b, on the other hand, are those referred to as desensitizers. When light is absorbed by the dye, neither electrons nor holes can be directly transferred to the silver halide, and under normal conditions these dyes have almost no spectral sensitization effect. When the absorption is in the silver halide, however, the dye can capture electrons and reduce the photographic sensitivity. (~7a) Holes may also be transferred to such a dye and, depending upon the continuity of the dye layer and the mobility of carriers within that layer, they may meet and recombine. Regardless of this question, however, the electrons transferred to the dye are lost for photographic action. If pre-existing latent development centers exist, at least some of the photoholes will react with these centers and destroy them, thus rendering the grain undevelopable.(95-97)

T h e p h o t o g r a p h i c process

. . . . .

R

'//I///////4 •

183

~~

z~

////////////'

(a)

~/ (b)

"///////?///]

•

'//////~///~

'/////////////

,/ (c)

\ '///j?'//////, FIG. 4. Schematic energy diagrams illustrating the dominant electronic transitions resulting from absorption of a quantum in the dye and in the silver bromide for (a) a sensitizing dye, (b) a desensitizing dye, (c) a hole-injecting dye. G is the dye ground state, E its excited state, and R the level involved in external reduction.

184

J . F . HAMILTON

Dyes having still lower energy levels, such as are illustrated in Fig. 4c, are capable of injecting holes into the silver halide valence band. For light absorbed by silver halide, these dyes act much the same as the desensitizers just described. They desensitize the ordinary photographic effect and promote the destruction of preformed development centers. However, these have the additional property of spectrally sensitizing the development-center destruction by dye-absorbed light. ~179) A few exceptions to these simple pictures can be found. There are some weak sensitization effects caused by injection of either electrons or holes from dyes whose energy levels, as best one can judge, are near but not quite at the values required for a thermodynamically favored transfer directly to the silver halide energy bands. Such effects are explained (149) in terms of transfer to some sort of specific site--an intrinsic surface state, a surface defect, or an impurity--followed by thermal excitation to the energy band. Tani t 1,~z~has proposed that the predominant carrier injected is determined by the relative positions of the Fermi level of the silver halide and what he terms the quasi-Fermi level of the dye, defined as the midpoint between the ground- and excited-state energies. Several environmental factors are known ° 7 ° - z ) to reverse the action of a borderline dye such as phenosafranine from predominantly hole-injecting to predominantly electron-injecting. These include the removal of oxygen, chemical sensitization, the presence of mild reducing agents, and increased concentrations of silver ions in the surroundings. Tani attributes to all of these treatments a change in the silver halide Fermi level. Although Terenin ~~52, ~83) interprets his results as showing that electron transfer cannot be a satisfactory explanation for the spectral sensitization process, Nelson and Selsby~156~ have apparently reconciled his objections in terms of the criterion for threshold assignment. Among the other principal investigators active in this area there has now apparently developed a consensus that the spectrally sensitized photographic effect involves electrons transferred to the silver halide crystals from the excited states of the adsorbed dye molecules. CONCLUSION These few examples demonstrate what a broad collection of scientific areas of current general interest must be considered for a full understanding of the commercial photographic process. It seems certain that this will continue to be the case. As more sophisticated techniques are developed and more fundamental questions are weighed in solid state areas, many corresponding methods and problems will become applicable to the photographic process. Perhaps the scientific successes may be expected in the future to have greater technological impact as well. REFERENCES 1. C. E. K. MEES and T. H. JA~.S, The Theory of the Photographic Process, 3rd ed., Macmillan, New York, 1966. 2. H. b-kIr.S~, G. I-IA~E and E. KLE~, Die Grundlagen der photographischen Prozesse mit Silberhalogeniden, AkademiseheVerlagsgesellschaft,Frankfurt am Main, 1968. 3. J. F. HAMILTONand L. SLn~C_rN,in Solid State Physics, S~Irz, TtrarcBtn_~Land Ernst,,EXert, eds.,

4. 5. 6. 7.

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185

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