J. MALINOWSKI and W. PLATIKANOWA: Concentration of Photoexcited Holes 885

phys. stat. sol. 6, 88.5 (1964)

Institute of Physical Chemistry, Bulgarian Academy of Sciences

Decay of the Concentration of Photoexcited Holes in Silver Bromide

BY J. MALINOWSKI and W. PLATIKANOWA

The reaction between a deposit of silver and the bromine formed by holes migrating to the surface of a silver bromide crystal is used t o verify the existence of mobile holes. The sensitivity of the method is greatly increased by a subsequent chemical treatment of the deposit. The method is used t o study the concentration-decay curve of holes which are generated by a light flash. For the different samples tested, the effective lifetime, as de- termined from the initial slope of the decay curve is found to be about lop4 s. It is shown, however, that a small fraction of the holes remains mobile up to about lop2 s after their generation. This suggests that the concentration-decay is not likely to be described by a simple recombination mechanism.

Die Reaktion zwischen einem Silberniederschlag und Brom, dafl durch Locher, die zur Oberflache eines Silberbromid-Kristalls wandern, gebildet wird, wurde benutzt, um die Existenz beweglicher Locher nachzuweisen. Die Empfindlichkeit dieser Methode, die durch einen EntwicklungsprozeD stark gesteigert werden kann, gestattet die Messung des Abklin- gens der Locherkonzentration, die durch einen Lichtblitz erzeugt wurde. Fur verschiedene untersuchte Proben ist die effektive Lebensdauer der Locher, die aus dem Anfangsstadium der Abklingkurve ermittelt wurde, ungefahr s. Es wird gezeigt, daD ein kleiner Bruch- teil der Locher bis s nach ihrer Erzeugung beweglich bleibt. Deshalb wird vermutet, dafl das Abklingen der Locherkonzentration nicht durch einen einfachen Rekombi- nationsmechanismus beschrieben werden kann.

1. Introduction For understanding the structure of the valence band the mobility and lifetime

of positive charge carriers (holes) are of great importance. Besides having this general meaning, the behaviour of holes in the silver halides has been the subject of numerous speculations connected with the theory of the photographic process. A detailed explanation of the formation of the latent image can be based only upon a thorough understanding of the phenomena occurring after the absorption of a photon. Recently the role of chemical sensitizers in photographic materials has been widely discussed in view of the available information about the properties of holes and electrons [l].

While the generation of photo-electrons in silver halides has been proved beyond doubt [Z to 51, in spite of numerous attempts, photocurrents due to the migration of holes have not yet been observed [6]. Serious evidence exists, however, that a motion of positive charge carriers actually takes place. Already in 1941 this has been demonstrated by STASIW and TELTOW [7], who measured the rate of the bleaching due to bromine vapor in a silver bromide crystal, darkened by traces of siiver sulphide. These authors made also an evaluation of the diffusion constant of holes. Later LUCKEY [S] has shown that the increase of conductivity of a silver

886 J. M.ALIXOWSKI and W. PLATIKANOWA

halide crystal, placed in an atmosphere of the halogen, is due to the migration of holes. HANSON and BROWN [9] have measured the Hall mobility of holes injected into the crystal in this way.

A migration of optically generated holes has been supposed for the explanation of different observations [lo to 121, but direct quantitative measurements of their drift mobility were first published by SAUNDERS, TYLER and WEST 151, and by MALINOWSKI and SUPTITZ [13].

The present paper describes a modification of the method applied by MALI- NOWSKI and SUPNITZ for measuring the drift mobility of optically injected holes. This modification makes possible to follow the decay of the concentration of holes after their production and allows one to determine, in this way, their lifetime in the valence band.

2. Principle of the Method

MITCHELL [14] has shown that the surface of a silver halide crystal is made deve lopable by the presence of about lOI5 atoms per ern2. It was reasonable to assume that the holes, brought up to the surface of the crystal will react readily with the silver deposited there, converting it to silver bromide again. This reaction, which is rendered very sensitive by the large intensification occurring in the process of development, was successfully employed for the detection of minor concentra- tions of holes. It was shown [13] that holes, produced optically near the illumi- nated surface of a silver bromide crystal, can be forced by a suitable potential pulse to penetrate through the volume of the crystal, and are then detected on the opposite surface. In this way the migration of holes in an electric field could be studied, and their drift mobility correspondingly evaluated.

Meanwhile SAUNDERS, TYLER and WEST [5] have employed a similar principle. They were able to show that when optically excited electrons are drawn into the interior of a thin sheet of silver bromide, a developable latent image is formed there. Now by reversing the direction of the field pulse, the latent image is found to be bleached by the holes drawn inwards. Special etching and development techniques have been applied to evaluate the drift mobility of holes and electrons.

These two principally similar methods cannot, however, be directly employed for lifetime measurements. The latter require not only a determination of the path traversed by the holes, but need also certain information about the change in the concentration of the carriers.

It was believed that the internal latent image is too intricate to be quantitatively handled. So in this respect the method employing the bleaching of the silver depo- sited on the surface seemed more suitable for reliable control.

On one surface of the silver bromide sample a succession of narrow parallel strips of silver were deposited by evaporation in vacuum, the concentration of the silver atoms increasing stepwise in a definite manner. The opposite surface was then exposed to short flashes through narrow slits which were arranged perpendicular to the silver strips. Simultaneously with the light flashes a field pulse was now applied. The field pulse was directed so that for appropriate amplitude and dura- tion, the holes generated on the illuminated surface were drawn through the volume of the sample to its opposite side.

As a result, each pulse carries a certain number of holes to the surface with deposited silver. There the holes form bromine atoms (molecules) which react with the silver and decrease its concentration. At the steps where this concentra-

Decay of the Concentration of Photoexcited Holes in AgBr 887

tion becomes smaller than necessary to initiate development (less than atoms per cmz), the crystal surface remains unaltered on immersion in a developer, while tl-e rest is uniformly reduced. Therefore, the length of the bleached slits, correlated to the quantity of silver previously deposited there, is a measure for the concen- tration of the holes which have crossed the crystal and reached its opposite side. If now the electric pulse for each of the successively exposed slits follows with a certain delay relative tow the light flash, the length of each bleached slit will measure correspondingly the relative concentration of the holes which have survived the application of the potential pulse.

3. Experimental The silver bromide used throughout this work was prepared by direct synthesis

of silver and bromine in vacuum [ 15,161, and single crystals were grown in bromine atmosphere following the technique recently described in detail [ 161. The crystals grown in bromine vapour often contain cylindrical voids whose lengths are compar- able with the dimensions of the crystal. On some samples shown in the figures the cross sections of these voids appear as hollow circles.

By means of a circular saw for soft materials, the single crystals were cut into flat disks with diameter and thickness about 15 and 1 mm, respectively. Fastening the disk-shaped specimens by suction, their surfaces were further smoothed mecha- nically. The samples were finally polished to high smoothness on a soft cloth moistened with a 10 per cent solution of potassium cyanide. When required, the eventually present grain boundaries were made readily observable by immersing the samples for several minutes in 40 per cent solution of potassium bromide. The disks were now bathed about 15 min in a dilute aqueous solution of bromine rinsed in distilled water and dried. A controlling treatment of the ready samples for 1 or 2 min in the developer recommended by MITCHELL [I41 did not show any trace of spontaneous reduction.

Immediately before the exposure, silver was deposited by vacuum evaporation on one side of the sample. A specially designed shutter allowed the deposition of parallel steps of silver with increasing concentration. Now the sample, with the deposited silver upwards, was placed between two brass-electrodes pressed against each other by means of a strong spring. The electrodes were electrically blocked by thin covering glass plates. The lower electrode had several slits through which the untreated surface of the crystal was illuminated. These slits could be opened and shut independently.

Light flashes of 2-3 ps duration were obtained from the discharge of a capa- citance through a xenon impulse lamp BGW XI50. The frequency of repetition was purposely lowered to 50 Hz, because certain circumstances, to be explained later, suggested the introduction of a longer dark interval. The effective wave- length of the light filtered through the Jena Glass Filters UG 1 and BG 12 was in the region of 360 nm, and its intensity was about 10'2 photons per flash.

The current in the xenon-lamp circuit formed the trigger signal for the square- wave pulse generator. The system was supplied with a delay device, by means of which the potential pulse could be shifted relative to the light flash from 0 to

The amplitude of the square-wave potential pulse, usually of 20 ps duration, was adjusted so as to provide in the crystal a field strength of about 15 x lo3 Vcm-1 Since the thickness of the crystal samples was about 1 mm and the

1.5 x 104 p.

888 J. MALINOWSKI and W. PLATIXANOWA

drift mobility of holes [13] about 1 cm2 V-l s-l, this field should draw to the opposite surface all holes which survive more than 6 p after the application of the pulse.

The crystal sample was a t ambient temperature, about 20 "C. The time of exposure was varied from several minutes up to an hour. Immediately after exposure the crystal was developed for 30 to 40 s, immersed in acidified stop bath and rinsed with distilled water. While the sample is' wet the developed surface is very sensitive to mechanical damage and should be handled with utmost care.

After drying the lengths of the bleached slits on the developed surface were measured under a microscope. Knowing the concentration scale of the silver deposit, equivalent numbers of bromine atoms, i.e. holes can be computed from the lengths of the slits.

4. Results The method described here is based on the assumption that a simple relation

exists between the number of brominated silver atoms and the number of holes having reached the surface. However, since neither of the two components can be measured directly, it was necessary to obtain a calibration curve. The deter- mination of such a curve is possible in principle if the number of holes reaching the surface is proportional: a) to the total time of exposure, a t constant flash- intensity, or b) to the intensity of the flash, a t constant number of flashes. The experiments described below show that in a certain region of concentrations the expected proportionality could be really observed in both cases.

Preliminary experiments showed that the length of the bleached slits is not sharply defined, diffuse tails being observed in the direction of increasing concen- tration of silver atoms. So it was decided to take as a measure of the length the last step on which no trace of development could be observed. The character of the bleached slits is shown in Fig. 1. On the sample itself, the steps without any

t (min)- Fig. 1 Fig. 2

Fig. 1. Length of bleached slits cxposcd to different numbers of flashes. Concentration of silvcr &-posit incrcssrs to tlir top, tot.al t,ime of exposure rightward. The white cirelc is the cross section of a void. The lower part of the sample was screened so tllat silver has not been deposited there. Development for 30 s. Tho widening of the slits a t lower

Ag-concentration is clearly seen Yig. 2. Xumber of silver atoms per cni' brominated a t different times of exposure. The diffcrcnt sets of points re-

present different cxperimcnts

Decay of the Concentration of Photoexcited Holes in AgBr ss9

traces of reduction could be easily distinguished under a microscope. The widening of the slits a t lower concentrations of silver, which is clearly visible on the picture, indicates a measurable surface diffusion of holes or bromine atoms (molecules).

Fig. 2 represents the dependence of the concentration of silver atoms, deposited on the last thoroughly bleached slit, upon the time of exposure. The different sets of points represent different experiments. It is clearly seen that up to about 8x1015 atoms per om2 the bleaching is proportional to the time of exposure. At larger concentration of the silver deposit, eventually at larger concentration of holes, the efficiency G f bleaching decreases.

I n another series of experiments the number of holes reaching the surface was varied by decreasing the intensity of the flash by means of neutral filters. The concentration of bleached silver was again found to increase linearly with the intensity up to the same concentration of the silver deposit. So in this region a reciprocity law may be regarded as experimentally established. Therefore these results justify the assumption that in the linear part of the curve in Fig. 2 , the number of silver atoms which have been deposited on the last bleached step, is proportional to the number of holes having reached the surface of the crystal.

For the crystals used here the lowest concentration of silver necessary to induce development was about S x 1014 atoms per em2, while the linear part of the curve in Fig. 2 extends to about 8 x atoms per em2. This restricts the range for measuring the hole concentration to within a factor of ten. The established validity of reciprocity, however, makes it possible, by varying the time of exposure, to widen this range considerably. Now, in order to determine the decay curve of the concentration of holes, i t is necessary to expose several slits on the same crystal. For each exposure the delay of the potential pulse relative to the light flash was correspondingly varied. By preliminary experiments the appropriate time of exposure was determined so that the length of each bleached slit remains in the linear part of the curve in Fig. 2 .

Fig. 3 represents a typical example of such an experiment. The concentration of deposited silver increases to the top of the Figure. The time of delay of the potential pulse increases on the right-hand side from 0 to 1000 ps. The time of exposure of the slits increases in the same direction, too, so that for longer delay the lengths of the bleached slits are correspondingly increased. The decay curve of the concentration of holes, computed from this picture, is shown in Fig. 4.

The type of decay curve obtained on different samples was practically the same. I n all of them the rate of decay of the concentration becomes very small after 300 to 500 ps. This long tail of the decay curve made it desirable to lengthen the interval between the light flashes, so that only very small part of the holes would survive until the next flash. Bleaching, however, was observed if the potential

Fig. 3. Change in length of bleached slits with increasing delay of the potential pulse. Time of exposure and delay increasc to the right. The horizontal lines in the lower part have hcen scratched on the sample for orientation purposes. Shadow of the holder and voids are again visible. Develop-

ment for 30 s

58 phydra

890 J. MALINOWSKI and W. PLATIKANOWA

Fig. 4. Solid line: decay of the relative concentration of holes after their generation.

Dashcd linc: linear recombination (exponential decay)

Fig. 5. Bleached slits on a wedge crystal exposed only to light flashcs (no potential pulses have been applied). The long white lines forming the square are the shadow of thc hol- der used in the vacuum evaporating system. Thesilver deposit is the smallest nccessary to induce development and is very

easily damaged. Development for 45 s

pulse was applied with the maximal available delay of 1.5 x lo4 KS after the light flash. The experiments to be described below prove that a measurable concentra- t,ion of holes remains in the valence band even longer.

Fig. 5 shows the upper surface of a wedge-shaped crystal, where, prior t o expo- sure, the minimum concentration of silver necessary to induce development was deposited. Through slits which were parallel to the direction of thickening of the wedge the lower surface was exposed to light flashes for several hours. No poten- tial pulses were applied to the crystal during exposure, but in spite of that bleached slits are clearly seen on the upper surface. At the end of the bleached slits the thickness of the crystal is about 0.4 or 0.5 mm. Some doubt could exist as to this effect being due to long-wavelength radiation transmitted by the filter. Several wedge-shaped crystals were therefore exposed to the radiation of a monochromator transmitting only the 365 nm band and bleaching without the application of electric field was again observed. 99 per cent of this radiation is absorbed in a layer 8 to 10 pm thick. So it seems very reasonable to assume that bleaching is produced by long living holes reaching the upper surface by thermal diffusion through the crystal.

Decay of the Concentration of Photoexcited Holes in AgBr 891

5. Discussion The illustrative results given in the preceding section show that the described

method not only enables one to measure the mean lifetime of optically injected holes in silver bromide, but also to study the decay of their concentration.

For the different samples tested the lifetime of holes, as determined from the initial slope of the decay curve, is found to be between 100 and 300 ps. It is beyond doubt, however, that the experimental curve does not obey an exponential law characteristic for linear recombination. The exponential curve shown as a dashed line in Fig. 4 decreases much faster than the measured curve.

The bleaching observed in the absence of potential pulses also cannot be explain- ed by a simple recombination mechanism. An estimate shows that the observed range of 0.4 to 0.5 em can be covered by thermal diffusion if some holes are free to migrate considerably longer than s.

Any speculations on the detailed mechanism of recombination or trapping seem to be untimely at present. However, the results indicate the presence of some process which conserves part of the injected holes. It is possible to assume the existence of deep traps, or the creation of excitons, both of which could decrease the effective generation rate of free holes, while there may be rather intense re- combination due to some simple mechanism.

The change of conductivity due to illumination, generating n pairs of charge carriers is

The product of lifetime zn by drift mobility ,un for electrons was determined by a method similar to that of SAUNDERS, TYLER and WEST 1151. It was found that for the crystals used here pn z, is approximately 3 x 10-5 em2 V-l, a value compa- rable with published data [3 to 51. Earlier measurements [15] have indicated a value of p p about 1 em2 V-I s-l, while the initial slope of the decay curves obtained here yields values between 100 and 300 [is for the effective lifetime of holes. So the product ,up zp comes out to be not smaller than em2 V-l. If this value is regarded as typical for holes in silver bromide it becomes hard to explain the failure of detecting photocurrents due to the migration of holes [6].

An explanation for the absence of such zt photoresponse may be found in the insufficient resolving power of the method employed here, limited by the duration of the light flash and the potential pulse. It is readily seen from Fig. 4 that the relaxation time of the decay process increases considerably with time. It may therefore be argued that the first check of the concentration is made after the steep initial decay. In this case measurements can only be made in the tail of the curve, for which the lifetime of the relatively small remainder of holes is extremely long.

Another possible explanation involves the assumption that z, varies widely over different samples, and those with long lifetime are rare exceptions. Anyhow, all of the crystals tested here showed relatively long lifetimes. At present the available data are insufficient to decide whether this is connected with some specific property of the silver bromide employed here, which was not prepared by the classical technique of precipitation, but synthesized from the elements in vacuum [15, 161.

s [6], but long lifetimes have been occasionally reported by other authors, too. HAMM [la] estimates an effective lifetime of about 20 ps, while SAUNDERS, TYLER, and

A g = e n ( p n z n + p p z p ) *

It has been supposed that the lifetime of holes is not larger than

559

892 J. MALINOWSKI and It’. PLATIKANOWA : Concentration of Photoexcited Holcs

WEST [ 5 ] note that “some holes are still found to be mobile u p to 30 ps after their production”.

Which, if either, of these explanations will be adequate, remains to be seen. Anyhow, the theory of the photographic process should take into consideration the existence of long living holes. It is hoped tha t their trapping by different sensitizers can be conveniently studied by the method described here.

Acknowledgements The authors acknowledge with pleasure the collaboration of AL. MALINOWSKI

who constructed the pulse generator and maintained it in operating condition. Thanks are also due t o Dr. I?. SUPTITZ for performing exposures of wedge-shaped crystals to monochromatic radiation.

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(Received June 19, 1964)