Selective Photoelectric Effect

M. V. Savostyanova, Leningrad

The nature of the selective photoelectric effect, which has found the widest application in the technology of photocells, remained unexplained for a long time, despite a very large number of experimental investigations. Only in the last two years can one note a certain shift in this respect, owing to a number of systematic works by American and German investigators. Some questions already appear to be sufficiently clarified; others still await the completion of a series of studies, but in any case it is now already possible to form a sufficiently clear picture of the phenomena underlying the selective photoelectric effect. The present article is an attempt to systematize the material accumulated in recent years, which has not entered, or has entered only partially, into special monographs. In doing so we have confined ourselves to works of the last two or three years, setting forth chiefly the results of the latest works in each series of investigations and departing from chronological order: the development of the work proceeded at such a rapid pace that results published in 1930–1931 are often already obsolete.

Fig. 1.

As is known, the concept of the external photoelectric effect includes two kinds of phenomena: the normal and the selective photoelectric effect.

In the normal photoelectric effect, the number of electrons per unit of incident energy does not depend on the position of the electric vector (the polarization of the light); it increases smoothly with frequency, beginning from some critical value of it (the threshold of the photoelectric effect) (see curve a in Fig. 1). Since the extraction of electrons occurs in the very surface layer of the metal, the curve of the spectral distribution, referred to a unit of incident energy, must evidently reflect the peculiarities of the variation of the optical constants of the metal with wavelength. This circumstance was in fact noted by Hlučka[^1], who studied the spectral distribution of the external photoelectric effect for a number of metals (Cu, Pt, Ni) in

in the region of their own oscillations (about 200 mμ) and obtained sharply expressed maxima of the photocurrent. A maximum of the same kind for aluminum had already been observed in 1913 by Richardson and Compton² (at 220 mμ), and for calcium by Pohl and Pringsheim³. A more thorough investigation of the photoeffect from the surface of silver was carried out by Ives and his collaborators, and also by Suhrmann in connection with their work on the selective photoeffect; Ives succeeded in showing the complete correspondence of the curves of the spectral distribution of the photocurrent with the course of the optical constants of silver. These works will be set forth below. The latest data on the theory of the normal photoeffect are presented in the article by L. Linford¹.

In some cases, for a special state of the surface, especially one easily attained in the alkali metals, against the background of the normal—

Fig. 2.

Fig. 3. Potassium on platinum.

effect there is observed a sharp increase in the quantum yield (by 100 or more times) in a definite part of the spectrum (see curve b in Fig. 1). This phenomenon is called the selective photoeffect.

The principal difference between the selective effect and the normal one consists in the fact that it depends on the direction of the electric vector in the light beam: the maximum appears only in the case when the oscillations of the vector occur in a plane parallel to the plane of incidence (Fig. 2) \((E \parallel)\); if the vector oscillates in a plane perpendicular to the plane of incidence \((E \perp)\), the curve of the normal photoeffect is observed.

In the first case \((E \parallel)\) the photocurrent also strongly depends on the angle of incidence of the light; a typical curve is given in Fig. 3.

Following the terminology of the American authors (Suhrmann, Ives), we shall call this phenomenon, first discovered by Elster and Geitel³, the vector effect.

The vector effect always accompanies the spectral one, but, evidently, can be detected only on sufficiently mirror-like

surfaces; photoelectric layers do not always satisfy this condition.

Both effects—the vectorial and the spectral—were studied in detail on the surfaces of alkali and alkaline-earth metals by Pohl and Pringsheim \(^{3}\), who connected them together and gave the aggregate of both effects the name “selective.” It was found that both the intensity of the effect and the position of the maximum depend to a very high degree on the state of the metal surface; as a result of a long series of investigations it was established that the selective effect is connected not with the metal itself, but with its surface layer. This became especially clear after a sharply expressed selective photoeffect was discovered on thin (invisible) films of alkali metals on the most varied substrates.

At the present time photoelectric surfaces may be divided into two types:

Ia. Thin (invisible) films of alkali metals on metallic substrates.

Ib. Thin films adsorbed on nonmetallic surfaces.

Fig. 4.

IIa. Complex colored photocathodes.

IIb. Complex di- and triatomic layers.

The phenomena occurring in photocathodes of types Ib and II are closely connected with the properties of colored salts, familiarity with which is necessary for clarifying the processes under consideration.

Referring the reader for a detailed exposition of these properties to other reviews by the author \(^{6}\), we shall recall here only the basic propositions, chiefly from the work of R. Pohl’s Göttingen school. Although these results were obtained predominantly on alkali-halide salts, they may also be transferred to other halide compounds.

All these salts have strong absorption in the ultraviolet region (the left-hand part of Fig. 4). When a crystal is illuminated by rays corresponding to this region, and also by large quanta of X-rays and \(\gamma\)-rays, electrons are torn from the atoms of the halide; these electrons neutralize metal ions, as a result of which uncharged atoms of the metal and of the halide are separated inside the lattice. The atomic distribution of the metal causes a change in the optical properties of the crystal; a new absorption band appears (the right-hand part of Fig. 4), in most cases in the visible part of the spectrum, and the crystal becomes colored. Thus rock salt becomes yellow, KI bluish-green.

The electrons that cause neutralization of the ions may be introduced into the lattice from outside,—indeed, besides the above-mentioned

besides the photochemical method of coloration there are also other ways: bombardment by a beam of electrons in a cathode tube and the so-called additive coloration, in which the crystal is brought into contact with the vapor of an alkali metal. Electrons, released for one reason or another at the point of contact, can at a sufficiently high temperature (50–600°) penetrate into the crystal and neutralize ions.

When a crystal is illuminated by rays absorbed in the visible region, the following phenomena occur:

a) Bleaching, accompanied by the appearance of yet another new absorption band in the near ultraviolet; it is also observed upon heating to 100–200°.

b) A change in the form of the absorption curve, which is lowered and broadened (curve \(b\), Fig. 5) (the so-called “Erregung”—excitation). When the crystal is illuminated with wavelengths corresponding to the new region of absorption, and also upon heating, the initial curve is restored.

Fig. 5. Optical absorption (\(a\)) and the internal photoeffect (\(e\)) in yellow rock salt.

Fig. 6. Optical absorption in rock salt: \(a\)—unexcited, \(b\)—excited.

c) Formation of larger colloidal particles.

The first two phenomena are accompanied by the transfer of electrons (internal photoeffect). The curves of the spectral distribution of absorption and photocurrent run parallel (Fig. 6). The phenomenon of excitation is connected with the formation of positive charges inside the lattice. All processes of the appearance and disappearance of color centers proceed in complete agreement with Einstein’s law: each absorbed quantum tears away one electron and produces or destroys one color center.

The quality of the lattice plays an essential role in the processes described: the more damaged places there are in the crystal (Lockerstellen), the stronger the coloration, and the greater the excitation.

A colloidal distribution occurs at a considerable con—

trations of coloring centers, which coalesce into larger particles. This is obtained especially easily with additive coloration, and also under the action of cathode rays. Particles of each size have their own absorption band, producing one or another coloration of the salt, sharply different from the atomic one. Thus rock salt, colloidally colored by dispersed sodium, is blue in color (particles \(40—80\,m\mu\)); upon heating it turns violet (\(20—40\,m\mu\)) and red (\(20—5.0^*\,m\mu\)). The absorption curves can be calculated from Mie’s theory; their form and position are determined by the values of the optical constants of the salt and the metal. Thus, as the author of the present article has shown \(^{7}\), for the system Na—NaCl the absorption lies in the visible part, while for K—KCl it lies in the infrared, in complete agreement with experiment. Absorption in colloidal systems is caused by two reasons: scattering of light (conservative absorption) and the proper absorption of the electromagnetic wave inside the metallic particles (consumptive absorption). For the photoelectric effect, of course, only the second is of importance. The scattering of colloidal systems can also be calculated, and in this way the part of the consumptive absorption can be separated out. For large particle sizes scattering predominates, while for very small ones the absorption is almost exclusively consumptive; thus red rock salt appears optically empty in the ultramicroscope.

A colloidal distribution of the metal is possible also in the case where the metal is in a finely divided state on the surface of another medium—for example, glass. In this case the medium is air. Such layers also appear brightly colored. Thus Schulze \(^{30}\) observed, on thin metallic films, a sharp change of color when the thickness of the layer was decreased, which evidently corresponds to a change in the structure of the film and a transition from a continuous layer to a surface covered with colloidal particles. Further, the colored silver mirrors of Kundt \(^{31}\) and the films of alkali metals of Wood \(^{32}\) also belong here; it should be noted that these films possess very sharply expressed dichroism, i.e., they absorb light only for one position \((E\parallel)\) of the electric vector. Mie’s theory has not yet been applied to these films.

We shall now proceed to consider phenomena in photocathodes of various types.

Ia. Thin (invisible) films on metal surfaces

The method of investigating the photoelectric effect in thin films is essentially as follows: in a high vacuum, in a quartz or Pyrex vessel, a certain quantity of the purest metal (most often silver) is sublimed; onto this mirror, which forms the cathode of the photocell, traces of one or another alkali metal are distilled. The photocathode is illuminated with polarized monochromatic light (double decomposition) through nickel or two-

refracting prism; the strength of the photocurrent is measured with a sensitive electrometer.

The photoelectric effect from thin films, first observed by Geitel\(^8\) at the anode of his photocell, was then studied in detail (1924–1933) by Ives\(^9\) and his collaborators in a series of brilliant works, which are classics not only for the subtlety and elegance of the experiment, but also for the novelty of the ideas; the successful completion of this series, ending with an explanation of the process of the photoelectric effect in thin films, was promoted, on the one hand, by the proper combination of experiment and theory, and on the other by the parallel study of both sides of the photoelectric process—the electrical (emission of electrons) and the optical (calculation of absorption).

Fig. 7. Potassium on silver. Film thickness: I less than monoatomic, IV greater than monoatomic, II and III intermediate.

The picture of the phenomenon established by the work of Ives, and also by certain works of Suhrmann\(^ {10}\) and his collaborators, is basically as follows. There is a fundamental difference in the behavior of photolayers whose thickness is less than monoatomic (the atoms are arranged in isolation or in separate groups) and those which consist of several atomic or molecular layers. This dependence on the thickness of the film, especially carefully investigated also by Brady\(^ {11}\), who with the aid of a molecular beam obtained films of known thickness, is well illustrated in Fig. 7, taken from Suhrmann’s article: when the film consists only of a small number of adsorbed atoms, we have the curve of the normal photoelectric effect corresponding to the metal from which the photocathode is made, but shifted toward longer wavelengths. Thus, in curve I of Fig. 7 we have the curve of the photoelectric effect from a silver cathode covered with a potassium film whose thickness is less than monoatomic. The threshold of the photoelectric effect is shifted from 2600 Å for pure silver to 4000 Å. As the number of atoms increases, the threshold at first moves into the red region and then returns back (curve IV); simultaneously with this, a selective maximum begins to grow. According to Brady, the smallest work function is obtained for a layer thickness of from 1.5 to 3 atoms*, maxi-

* This coincides with the data for thermionic emission: for thoriated metal, the work function reaches its smallest value when the heated wire is covered with a monoatomic layer of thorium.

minimal photoelectric emission—for K at 22 layers, for Na, Cs, Rb at five layers.

According to Ives, joined also by Zhurman, this dependence on the thickness of the layer is caused by the fact that in one case we have the photoeffect from the atoms of the alkali metal, whereas when the layer thickness is less than monatomic, the electrons are emitted still from the substrate (the normal photoeffect), and the role of the atoms

Fig. 8. Thin films of sodium on silver, successive stages. Angle of incidence of light 60°.

of the alkali metal is reduced only to decreasing the work function.

The following experimental facts confirm this idea:

1. The spectral curves of the photoeffect for light polarized parallel and perpendicular to the plane of incidence in the first moments of formation of the film differ hardly at all from one another; as the film grows they gradually diverge (Fig. 8) (Ives) \(^{9c}\).

2. These curves for light polarized perpendicular to the plane of incidence, in the first stage of development of the film, display the course (with wavelength) of the optical constants of the substrate, which is especially noticeable in the case of silver with its characteristic minimum of reflecting power at 3160 Å (Fig. 9 and Fig. 8, \(a\)) (Ives \(^{9b}\) *).

Fig. 9. Thin films: sodium on platinum and sodium on silver.

As the film develops, the “saddle” disappears, and a maximum grows in another place, near 3500 Å (Fig. 8, \(c\)). This new maximum is observed also on platinum, which, as is known, exhibits no optical anomalies; in both cases it is evidently caused by the photoeffect from the atoms of the alkali metal.

* A certain discrepancy between these and other curves is fully explained theoretically by Ives (see below).

Ib. Thin films adsorbed on nonmetallic surfaces

Under this heading falls the field of phenomena being developed by the Dutch scientists de Boer and Teves[^12], who use as a substrate a metallic surface coated with a layer of one or another salt \((\mathrm{CaF}_2,\ \mathrm{BaCl}_2,\ \mathrm{Cs}_2\mathrm{O})\); photocathodes of this kind, with layers of oxides of the alkali metals, were also used by Klug and Rupp[^13b], as well as by Koller[^14] and Campbell[^15].

Fig. 10. Thin invisible films of alkali metals on silver.

Just as in films of the first type, here too we have to do with a certain optimum layer thickness, at which the threshold of the photoeffect is shifted most strongly into the red region and at which the photocurrent has its maximum value. A distinguishing feature of these layers is their high photosensitivity in the visible and even infrared part of the spectrum, caused by the favorable position of the selective maximum in the spectrum and by small values of the work function; in some cases the threshold of the photoeffect reaches \(1.4\,\mu\).

Some data relating to various combinations of substrate and alkali metal for types Ia and Ib are given in Table 1 and in Fig. 10.

Consideration of these data leads to the following questions: a) what causes one or another position of the spectral maximum? b) what is the reason for the shift of the threshold of the photoeffect?

The first question has been studied in considerable detail in a series of papers by Ives, an account of which is given in the last paragraph of the present article; the second question is dealt with by de Boer and Teves[^12].

The starting point of their arguments is the idea that, in the present case, we are dealing with a process of photoionization of individual atoms adsorbed on some surface. The ionization potential of atoms of the alkali metals is, as is known, about \(200\text{–}300\,\mathrm{m}\mu\); if the ionized atom is adsorbed by the surface of the substrate more strongly than the neutral atom, then the tearing away of the electron is facilitated and energy is gained in the process,

TABLE 1

equal to the difference in the adsorption energies in the two cases. The photoeffect (or photoionization) will therefore occur at smaller quanta than is the case for free neutral atoms. De Boer and Teves \(^{12b}\) estimate the order of magnitude by which the photoeffect threshold may be shifted, and obtain for Cs on \(\mathrm{CaF_2}\) an adsorption-energy difference of about \(2\ \mathrm{V}\), which corresponds to a photoeffect threshold

\[ h\nu = 3.88 - 2 = 1.9\ \mathrm{V} \]

(where \(3.88\ \mathrm{V}\) is the ionization potential of the neutral free Cs atom), whereas direct measurements give about \(1.76\ \mathrm{V}\) (\(700\ \mathrm{m}\mu\)).

This influence of adsorption forces is also manifested in metals (type Ia), but it is most markedly expressed in salts, where, as the authors have shown, the surface is covered with negative ions attracting the ionized atoms. Indeed, as is seen from Table 1, the shift of the threshold on salt substrates is expressed more strongly than on metallic ones*.

Obviously, the magnitude of the adsorption forces must be strongly influenced by the state of the surface, the mutual arrangement of negative and positive charges. The most favorable conditions may be expected when the ionized atom is attracted not to one, but to a whole row of negative ions, which will occur not on an ideally smooth crystal surface, but on a surface furrowed with cracks and covered with corners and protruding parts. This imperfection of the crystal lattice, which, as we have already seen, plays an essential role in the coloration of salts, will be expressed more strongly in thick layers than in thin ones, and, indeed, by increasing the thickness of the layer de Boer and Teves succeeded in shifting the photoeffect threshold from \(900\ \mathrm{m}\mu\) to \(1200\ \mathrm{m}\mu\). In this, however, an undesirable decrease in the photocurrent strength occurs, since the access of electrons from the metallic substrate, which replace the torn-off electrons, is hindered; the layer becomes poorer in electrons, and strong positive charges are obtained, which impede the further tearing-off of electrons. This circumstance can be helped by creating such conditions under which electrons could be torn off inside the salt: as we have seen, colored salts possess such a property, exhibiting an internal photoeffect under illumination. De Boer and Teves make use of this circumstance, additively coloring the substrate layer. To increase the effect they first contaminate the salt with impurities of heavy metals; such phosphors with a strongly loosened lattice are colored especially intensely. For such surfaces they obtained exceptionally large values of the photocurrent—of the order of \(100\) or even \(200\ \mu\mathrm{A}/\mathrm{Lm}\), which corresponds to a quantum yield of about \(0.20\). There are, however, grounds to suppose that in surfaces of this kind the increase in emission is caused by the superposition of two effects—the type Ib discussed above and type IIa.

* See below the experiments of Lukirsky and Ryzhanov.

IIa. Complex Photocathodes

Since, in the use of complex photocathodes, we have a considerable increase in sensitivity in comparison with the surface of a “pure” metal, it is customary to speak of a “sensitization” of photocathodes. This sensitization may take place in various ways and by means of various substances; the usual method consists in the following: one or another alkali metal \((M)\) is distilled onto the surface of the photocathode \((X)\), and then traces of a sensitizing substance are introduced into the photoelement, such substances usually being hydrogen and oxygen; sulfur, selenium, and tellurium are also used. At this stage the photoelement is still only slightly sensitive; the increase in sensitivity occurs during further treatment, which consists either in the fact that traces of alkali metal are secondarily distilled onto the surface, or in the fact that, by one means or another—by passing a silent discharge, by the action of cathode rays—the coloring of the layer is achieved.

In this case we have a change of the photosensitive layer itself, whereas in the first case, in all probability, the formation of a thin film on a complex surface takes place (type 16).

Fig. 11. Complex layers.

The photosensitivity may thereby be increased by tens of times.

The spectral distribution of complex photocathodes varies very strongly with the composition of the layer; thanks to the systematic investigations of Kluge \(^{13}\) (Germany), and also of Olpin \(^{10}\) (America), the following types of complex layer can be established:

a) hydrides \(X—MH\), b) oxides \(X—M_2O\), where \(X\) is the photocathode metal, \(M\) is an alkali metal.

Data for various photocathodes are collected in Table 2; a number of curves are given in Fig. 11.

Hydrides give simple maxima (with a hint of a rise in the ultraviolet part), whose position depends on the kind of alkali metal; these maxima coincide with the long-studied maxima for “pure” surfaces of alkali metals: evidently, their surface is always covered with hydrides.

In contrast to hydrides, oxides usually give two maxima: one of them, situated in the visible and even infrared part \((Cs)\) of the spectrum, depends on the kind of alkali metal,

TABLE 2

whereas the other, apparently for all metals, has one position—about 410 mμ. The first maximum appears by no means always; a comparison of the curves in Fig. 11 with the curves of Bur and Teves shows that in both cases we have the same nature of layer; in all probability, it is a combination of type Ib with type II (adsorbed atoms on a colored salt).

Sulfur, selenium, and tellurium apparently belong to the oxide type, giving two maxima or one maximum, the latter being located in the same place (about 400 mμ) as for the oxides. Ol’pin \(^{16a}\) carried out sensitization with a series of organic substances and dyes (about 2000 photocells were investigated by him); in all these cases he obtained one maximum, lying near 435 mμ for potassium and near 350 mμ for sodium, i.e. in the same place where the maxima for the hydrides are located. This compels him in all these cases to ascribe the sensitizing action to one agent common to all the substances—most probably, hydrogen.

If the picture of the phenomena in photocathodes of the first type is at present more or less clear, this can by no means be said of complex layers: with a high degree of probability one can only assert that the phenomenon is closely connected with the coloration of the layer. This circumstance was noted as early as 1897 by Elster and Geitel \(^{20a}\), who discovered that when NaCl salt deposited on a cathode and other alkali-halide salts were exposed to cathode rays and thereby became colored, a sharp increase in the photocurrent was observed.

In 1910 the same authors \(^{20a,c}\) repeated these experiments with layers coated with potassium, sodium, and cesium hydrides, and established that colorless crystals of the hydride are not photosensitive, but become so only after exposure to cathode rays or the passage of a silent discharge. In this process they become brightly colored: KH becomes violet, NaH—yellow-brown, changing on heating to blue, CsH—greenish.

Pohl and Pringsheim \(^{3}\) then showed that a silent discharge causes the appearance of a selective photoeffect, and studied its spectral distribution at various positions of the electric vector.

As is known, the subsequent history of the selective photoeffect proceeded in two directions: on the one hand, on the basis of the first experiments of Elster and Geitel, the technology of photocells developed widely, while on the other—thanks to a series of works by Pohl and Pringsheim \(^{3}\), the basic laws of the spectral and vectorial photoeffect were established step by step. The abundance of qualitative material and the absence of a guiding idea forced Pohl to take a somewhat different path and to proceed to the solution of the simpler problem—the study of the photoeffect within the medium. Thus there developed an extensive field of the internal photoeffect, which made it possible to establish the basic laws of the interaction of light quanta and electrons

(checking Einstein’s law), which still await clarification for the case of the external photoelectric effect.

At the time of Elster and Geitel, the properties of atomic and colloidal distribution of the metal had not yet been studied; it was clear only that the coloration is connected with a finely divided state of the metal. This circumstance was noted by them: on the basis of the observation that, when a silent discharge is passed over the surface of potassium hydride, coloration of the layer is accompanied by the evolution of large quantities of hydrogen, they conclude that in this case decomposition of the hydride takes place; the remaining metal, separated out in a finely divided form, possesses a sharply expressed selective

Fig. 12.

Fig. 13. Electronogram of a hydride layer KH. (green-colored layer).

absorption and therefore emits electrons especially readily when illuminated.

This proposition was again put forward by Pohl², who returned to the topic of the selective photoelectric effect; he bases it on the following experiment of Gudden and Pohl²²: traces of potassium \((K)\) are distilled onto a not quite clean surface of a quartz plate \((J)\), serving as one of the electrodes; another electrode \((B)\) is pressed against this layer (Fig. 10). Upon illumination, a photocurrent can be detected in the circuit, and the maximum of the spectral distribution is quite analogous to the maximum of the selective photoelectric effect with potassium. An essential circumstance is that the phenomenon does not depend on the direction of the field; this clearly shows that the effect is associated not with the quartz plate, but with the layer filling the space between the electrodes, into which potassium particles are embedded. Evidence for this proposition is the fact that the effect disappeared as soon as precautions were taken to clean the plate.

In 1931, Klug and Rupp¹³ᵃ carried out a parallel investigation of the photoelectric effect from colored photocathodes and a study of their surface structure by means of the electronographic method;

the results fully confirmed Pohl’s idea. The experiment was carried out as follows. Degassed potassium was distilled onto a silver or gold plate serving as the cathode, so that a continuous layer was obtained (state \(a\)). Then a certain amount of hydrogen was admitted into the vessel (\(b\)), and, finally, a glow discharge was passed (\(c\) and \(d\)). For each state of the surface the spectral curve of the photocurrent and the reflection curve of the electron beam were recorded. In Fig. 13 one of the curves for the KH surface is shown; here the abscissa gives the electron velocities in volts, and the ordinate gives the corresponding current strengths in the receiver. In the general case the curves obtained had sharply expressed peaks, which corresponds to a surface consisting of a multitude of randomly arranged small crystals, as in the experiments of Davisson–Germer. The positions of the peaks for metallic potassium could be predicted from the potassium lattice on the basis of X-ray analysis data, and from this the other peaks could also be identified.

As a result, 12 peaks could be ascribed to potassium, 8 peaks—to a crystal with a cubic lattice with constant \(5.40\ \text{\AA}\), in all probability KH. Four peaks, corresponding to a lattice of \(2.9\ \text{\AA}\), could not be identified.

TABLE 3

Table 3 gives some final data. These data shed some light on the conditions for the appearance of the selective photoeffect: the presence is necessary not only of pure finely divided potassium, but also of such a crystalline lattice (in this case—potassium hydride) with which this potassium is in some way connected.

How the alkali metal is distributed in photoelectric layers has not yet been clarified. Elster and Geitel \(^{20a}\) mention that they obtained a photoeffect both with yellow (atomic) and with blue (colloidal) rock salt. Gudris and Kulikova \(^{23}\), using Millikan’s method, observed in the visible region the emission of electrons only from yellow salt. Klafeke \(^{24}\) indicates that the salts \(PbCl_2\) and \(CdI_2\), insensitive in the visible region

of the spectrum, acquire this property after preliminary illumination with ultraviolet rays (from the region of intrinsic absorption). The action of long waves causes a diminution of the effect. These phenomena are expressed the more strongly, the more damaged places there are in the salt crystals. Klafeke explains their appearance by atomically dispersed metal (photochemical coloration) and by the subsequent bleaching of the crystals.

Klug and Rupp[^13a] insist that in their experiments we are dealing with colloidal coloration; atomic distribution would not give electronic interferences. They also attempt to establish a connection between the intensity of the effect and the size of the particles (the color of the surface), basing themselves on the results of calculations by M. V. Savost’yanova[^7] for colloidally colored rock salt. This attempt, however, is entirely unfounded, since, as was indicated above, the position of the absorption curves for the systems K—KH and Na—NaCl, determined by the course of the optical constants of the metal and the salt, may in the two cases be entirely different; the violet coloration of the hydride by no means corresponds to the violet coloration of rock salt. There is even reason to suppose that it is caused by atomically dispersed potassium; as the authors indicate, it very easily disappears under the action of an electron beam (bleaching upon heating).

Some indications that in other cases as well we are dealing with atomic coloration may be drawn from the observations of de Boer and Teves[^12c] on the “fatigue” of photocells. This phenomenon consists in a decrease in the sensitivity of the photocathode under the influence of prolonged illumination and is caused by an accumulation on its surface of positive ions, owing to an insufficient supply of electrons from the substrate. This circumstance causes, on the one hand, a decrease in the strength of the photocurrent, and, on the other, a shift of the photoeffect threshold into the violet region, since the ions accumulating on the surface increase the work function. The effect is expressed the more strongly, the more “Lockerstellen” there are in the layer. The thought naturally suggests itself of a connection with the phenomenon of “Erregung”; indeed, “fatigue” can be eliminated by the same causes as “Erregung,” i.e. by heating and by illumination with long waves.

Since “Erregung” is observed only in atomically colored crystals, this is a direct indication that here, too, we are dealing with an atomic distribution. A complete solution of the question of the nature of the active centers in the selective photoeffect of complex layers will be obtained only when, on the one hand, the selective photoeffect of atomically and colloidally colored alkali-halide salts has been studied, and, on the other, an investigation has been made of the optical properties of colored hydrides and oxides. So far, unfortunately, no such parallel investigations on the same objects have been carried out.

IIб. Complex two- and three-atomic layers

An intermediate position between complex and monoatomic films is occupied by layers studied by Lukirskii and Ryzhanov[^23]; depositing successively a series of layers of atomic hydrogen and atomic potassium on a metallic substrate, they followed the simultaneous change in their photoelectric properties. In this way two types of adsorption of atomic hydrogen by potassium were established: at first, as the authors suppose, the hydrogen atoms penetrate under the surface monoatomic layer of potassium; since hydrogen is more electronegative than potassium, it decreases the work function, as a result of which the photocurrent increases up to a certain maximum value. With further treatment of the surface with hydrogen, the latter is already located above the potassium, increasing the work function; photoemission decreases (Fig. 14). By heating one can remove the second layer; then the photoemission again increases to its maximum value. By distilling alternately first potassium, then hydrogen, the authors obtained layers of the type H–K–H, H–K–H–K, etc., the photocurrent fluctuating between maximum and minimum values (Fig. 15), depending on what was on top—potassium (maximum) or hydrogen (minimum).

Fig. 14. a) dependence of the photocurrent on the time of treatment of a potassium surface with atomic hydrogen; b) curve of the total number of absorbed hydrogen atoms.

Fig. 15. Curve of the photocurrent as a function of the arrangement of the K and H atoms.

Obviously, in this case we are approaching layers of the complex type IIa or IIб; unfortunately, the authors worked with undecomposed unpolarized light and could not trace the conditions for the occurrence of selectivity.

The selective photoeffect as an optical phenomenon

The question of the nature of the selective photoeffect arose repeatedly throughout the study of this phenomenon. There were attempts to interpret the selective photoeffect as a resonance phenomenon. Lindemann[^26], Campbell[^27], and Fowler[^28], on the basis of the ideas of wave mechanics, calculated the probability of an electron wave passing through a potential barrier at the surface

of the metal, and found that at a certain frequency of the incident light a selective emission of electrons would be observed. Olpin \(^{16a}\) attempted to apply this theory to complex layers (oxides and hydrides), and obtained satisfactory agreement with experiment. Later, however, it was shown \(^{29}\) that this agreement is accidental, since in his calculations Olpin used incorrect data for the crystal lattice; moreover, there are several fundamental objections to applying this theory to complex layers, which compel one to regard Olpin’s reasoning as erroneous (see, for example, Lukirsky \(^{25}\), Linford \(^{4}\)).

All these theories placed the very mechanism of photoemission at the center of their arguments and ascribed the appearance of selective maxima to one or another condition for the escape of electrons. At best, however, they confined themselves only to predicting the position of the maximum; the dependence on polarization, on the angle of incidence, and the very shape of the curve remained unexplained.

Alongside these theories, the idea had long since arisen that the selective photoeffect might be reduced to the purely optical phenomenon of selective absorption of light; this is indicated by the characteristic form of the curves of the selective photoeffect, which very strongly resemble the curves of light absorption in colored media, as well as by the fact that photosensitive layers (of type II) are always brightly colored.

This idea was expressed as early as 1926 by Pohl \(^{21}\), who pointed out that, in measuring the curve of the selective photoeffect, we are thereby measuring, by electrical means, the absorption curve of the adsorbed atoms of the alkali metal.

With such an interpretation of the phenomenon we should expect, first, that the strength of the photocurrent, referred to a unit of absorbed energy (the quantum yield), will have one and the same value for all wavelengths—as is the case in the internal photoeffect for colored salts—and, second, as a consequence of this, that selective absorption will be observed only for the vector \(E_{\parallel}\); for the other direction of the electric vector the film must be almost transparent, in other words, it must be dichroic. The absorption and photocurrent curves must run parallel, and the quantum yield must be close to one electron per quantum.

There are two ways to verify this proposition: the experimental way—direct measurement of the amount of absorbed energy—and the theoretical one. Pohl, and after him all other investigators except Ives, used experimental methods. Three such methods were employed: the black-body method, in which the photocathode is given the form of a hollow sphere; the method of reflection from the mirrored surfaces of the photocathode; and the method of direct measurement of the amount of light transmitted through the film.

Obviously, this method is inapplicable to complex layers and, on the contrary, proves very successful for thin films,

In all these methods we encounter the following fundamental difficulties: first, not all electrons torn away by the absorbed light can reach the surface and manifest themselves in the photoelectric current; obviously, the thinner the film, the larger this number. Second, energy may be expended not only on tearing away electrons: thus, for example, the absorption of light in colored colloidal systems containing large particles (blue rock salt) is caused (according to Mie’s theory) almost exclusively by the scattering of light by these particles (conservative absorption). The separation of “active” absorption appears to be very complicated. Finally, yet another shortcoming, pertaining to the reflection method, consists in the inevitable imperfection of the mirror surfaces of the photocathode, which, if one takes into account the picture set forth above, have the structure of complex layers, a microcrystalline structure. However ideally mirror-like such a surface may appear to the eye, its microscopic structure will nevertheless affect the quality of the reflected light, whose laws of reflection will be quite different than in the case of smooth metallic surfaces.

Indeed, when we have normal reflection from a mirror surface, the intensity in the reflected beam constitutes the fraction

\[ R=\left(\frac{n-1}{n+1}\right)^2 = \frac{\nu^2(1+\chi^2)+1-2\nu}{\nu^2(1+\chi^2)+1+2\nu} \]

of the intensity of the incident light, where \(n=(1-i\chi)\), and \(\nu\) and \(\chi\) are the optical constants of the mirror. By this formula, together with the expression \(J=J_0 e^{-\frac{4\pi \nu \chi}{\lambda_0}}\), the absorption \(K=\frac{4\pi \nu \chi}{\lambda_0}\) is also calculated. As is known, the absorption maximum almost coincides in its position in the spectrum with the reflection maximum, being only slightly shifted toward shorter waves.

In the case when the surface is insufficiently smooth, the matter becomes considerably more complicated and begins to depend on the form of the irregularities present. In the limiting case, if these irregularities consisted of the smallest spheres, as occurs in colloidal dispersion, we could calculate the absorption directly by Mie’s theory; but to judge the absorption by the scattering in the given case does not appear possible, in view of the very complex dependence between the one and the other. In any case, we have no possibility of asserting that in the case of imperfectly smooth surfaces the course of the absorption curve will correspond to the course of the reflection curve, as it does in the case of perfect mirrors.

All these reasons make it extraordinarily difficult to obtain exact quantitative data; at best we have qualitative indications of a parallelism between the curves of the photoeffect and absorption. Let us give several examples.

Complex layers (types Ib and II)

The question of converting the photocurrent per unit of absorbed energy was first posed by Pohl and Pringsheim,^3 who in 1913, using the black-body method, obtained a series of curves for Ca, K, Na. Fleischer^33 in 1927, by means of the reflection method, obtained similar curves for potassium (Figs. 16 and 17). In both

Figs. 16 and 17. Optical absorption and photocurrent in a layer of K treated with oxygen.

cases the authors note that the photocurrent maximum recalculated for the absorbed energy (at 436 μ) is manifested still more strongly. However, this assertion should be regarded as a misunderstanding: although the absolute magnitude of the photocurrent, of course, becomes larger, the maximum broadens and becomes flatter, as should have been expected. This circumstance is caused by the fact that the absorption measured in the experiment is composed, as we have already noted, of the “active” absorption in the photo-layer and other energy losses (Fehlabsorption). It is very probable that these losses take the form of a certain uniform background superposed on the selective absorption maximum. If, in Fleischer’s curves, one tries to ...

partly this background, the curve will rise still more; in the limiting case, when the absorption curve will correspond completely to the photocurrent curve, we shall have a uniform curve corresponding to a quantum yield equal to unity. This is indeed what we see when comparing Fig. 16 with Fig. 17: the maximum at 313 mμ evidently corresponds to a very thin layer of potassium, when “Fehlabsorption” is not of such great significance; in this case the recalculated curve comes out quite monotonic.

Fig. 18. Photocurrent and reflection of light on a complex layer. Ag—Cs₂O—Cs.

Klugе obtained a similar result in his latest work[^13c], who also used the reflection method. In contrast to Fleischer, he does not calculate the absorption coefficient, but directly plots the measured data for the reflection coefficient. As was to be expected (see above), this curve appears broadened and shifted relative to the curve of the selective maximum (toward shorter waves) (Fig. 18), which compels the author to conclude that there is a complete discrepancy between the absorption and photocurrent curves. Such a conclusion is too hasty: the surface is obviously insufficiently specular, as indicated by the presence of photocurrent even at \(E_{\perp}\), and under such circumstances, as we have already noted, we could not expect any other course of the reflection curve. That the minimum of reflection is nevertheless connected with the selective maximum follows from the curves obtained for a photocathode with a poorly expressed layer (type I); here the reflection curve runs quite smoothly, in accordance with the absence of a long-wavelength maximum (Fig. 19).

Fig. 19. Photocurrent and reflection of light on an Ag—Cs photocathode.

Purely qualitative results are obtained for combined de Boer and Teves layers[^12]: upon adsorption of alkali-metal atoms the surface of the salt became brightly colored, and the absorption band lay approximately in the same place as the photocurrent maximum.

All these results show that in complex layers there is an undoubted connection between absorption and the photoelectric effect.

Thin films (type Ia).

In this case more definite results may be expected, since, in all probability, here almost all the energy goes into the ejection of electrons. Moreover, here direct measurement of the absorption is possible. Almost simultaneously (in 1931) two papers appeared in which this method was used.

Fleischer[^18] obtained an extremely thin layer of potassium on semitransparent gold foil; measuring the amount of light transmitted through the foil before and after deposition of the potassium layer, he could determine the energy absorbed in the layer itself. It turned out that such a layer absorbs about 4% of the incident energy. Measuring the photocurrent at the same time, he could calculate the quantum yield, which for \(\lambda = 436\,\mathrm{m\mu}\) proved to be equal to \(38 \cdot 10^{-2}\ \mathrm{coul/cal}\), which for the given wavelength corresponds to the emission of one electron for 4 absorbed quanta. This number is of the order of unity. This conclusion is valid only if one assumes that all photoelectrons are ejected only from the potassium; since Fleischer worked at optimal film thicknesses corresponding to maximum sensitivity, there is reason to believe (see above) that in this case the role of the substrate was negligible.

The maximum of the absorption curve, according to Fleischer, occurs in the same place as the photocurrent maximum (\(436—440\,\mathrm{m\mu}\)); unfortunately, he does not give data for all wavelengths. A second shortcoming of his work is that he used unpolarized light.

This shortcoming is remedied in the work of Fleischmann[^35], carried out in Pohl’s laboratory (Göttingen): obtaining extremely thin layers of potassium on quartz (on the flat wall of a quartz cuvette), he established not only that films invisible at normal incidence of light appear brightly colored at oblique incidence, but also that they are dichroic (the color is noticeable only for \(E \parallel\); for \(E \perp\) it disappears), which is direct proof of its connection with the selective photoelectric effect. Fleischmann measured, in transmitted light at oblique incidence, the absorption of these films, taking into account the losses due to reflection and to absorption by the quartz itself. The selective maximum is observed only for one position of the electric vector; in all other cases we have uniform absorption, caused probably by larger metal particles and independent of

directions of vibration. Both the position of this maximum and its shape fully correspond to the selective maxima of the photoeffect from potassium.

Unfortunately, in Fleischmann’s work the second, photoelectric part of the investigation is absent, as a result of which he could not carry out a recalculation to the absorbed energy.

Thus we see that, as a result of all the experimental work carried out up to the present time, we have only qualitative indications—though rather convincing ones—of the presence of parallelism between the absorption curves and the selective photoeffect; the experimental method of direct measurement of absorption, which in some cases, for example for thin films on a metallic substrate, is not applicable at all, has proved unable to give an exhaustive quantitative answer to the question posed above concerning the optical nature of the selective photoeffect.

As we shall see below, the only correct path is the path of calculating the absorption in the active layer; in complex layers and in thin films the approach, obviously, must be different.

Complex Layers

In this area we as yet have no data; the formulation of the question reduces to the following considerations.

A number of the facts cited above indicate that, in the case of the photoeffect from colored layers, the detachment of electrons occurs from particles of the alkali metal, distributed atomically or colloidally within the salt lattice. The absorption curves of colored salts of this kind are in many cases (alkali-halide salts) well studied, and in others can be investigated; thus we have before us the elementary problem of comparing the photoeffect curves with absorption curves known in advance. However, here one must take into account the complicating circumstance that, in the external photoeffect, the electron must overcome the work function, as a result of which here one may expect a displacement of the curves of the external photoeffect and of absorption in comparison with the corresponding curves for the internal photoeffect. We encounter a phenomenon of this kind in the photoionization of free atoms (ultraviolet region) and of atoms adsorbed on the surface of a salt (see above the experiments of de Boer and Teves), or embedded in a crystal lattice (atomic coloration). Thus the problem reduces to a preliminary calculation of this displacement on the basis of knowledge of the work function, and consequently to clarification of the connection between the internal and external photoeffect—this question, noted by Lukirsky^34 as early as 1926, has recently emerged in other fields as well, for example in the study of the barrier-layer photoeffect.

Thin Films

The problem is reduced to a preliminary calculation of the absorption of individual atoms adsorbed on the surface of a metal. In doing so, however, we must take into account the circumstance that the film is under the action of two beams of light—the incident and the reflected. As Wiener had already shown, the interference of these two beams gives a system of standing waves above the surface of the metal; in the case of an ideal conductor, the node would be at the very surface. Owing to the finite values of the conductivity of metals, the node is shifted, so that at the very surface we have finite values of the electric vector, which, however, will differ depending on the wavelength, the angle of incidence, and the polarization of the light. This curve for the distribution of the light intensity is superposed on the curve of the intrinsic absorption; knowing both of these curves, one can find the intensity of the light \(I = I_0 e^{-kb}\), whose distribution over wavelengths and angles of incidence determines one or another course of the curve of the number of emitted electrons.

Fig. 20.

This problem was solved by Ives jointly with Fry9d, who developed the optical side of the phenomenon. Referring readers to the original article by these authors, a translation of which is given below, we shall dwell only on the final results.

The calculation was carried out on the basis of the formulas of Maxwell’s classical electromagnetic theory according to the following scheme: first the distribution of the energy density above the surface of the metallic substrate was calculated; then a correction was introduced for the discontinuity in the normal component of the electric vector caused by the presence of the alkali-metal film. Finally, the intrinsic absorption of the film was calculated, taking into account the distribution of intensity within the film itself; of course, in conclusion the distribution of energy in the spectrum was taken into account. Calculations of the intensity distribution were made for various distances from the metallic substrate for the spatial pattern of standing waves.

In Fig. 20, on the left, is shown the course of the energy distribution for a wavelength at an angle of incidence of \(60^\circ\) at various points of interferen-

one picture, for two positions of the electric vector; as we see, at different distances from the surface different ratios are observed between the intensities of light polarized parallel and perpendicular to the plane of incidence: at a certain point they are equal, and then we have a picture opposite to that observed at the surface. At this point we would have to expect a “reverse” selective photoeffect. To verify this proposition, Ives measured the photocurrent from a film placed at various distances from the substrate (a cesium film on a quartz wedge, the first part of Fig. 20), and indeed obtained

Fig. 21. Cesium film on quartz; a—photocurrent, b—calculated absorption in the film.

a peculiar course of the photocurrent curves, quite analogous to the course of the calculated curves (Fig. 21).

From these data it follows that the curves of the selective photoeffect in thin films are by no means characteristic either of the alkali metal or of the substrate, but are caused exclusively by the course of the optical constants of both. This circumstance is especially pronounced in the case where silver, with its characteristic minimum of reflecting power in the ultraviolet region, serves as the substrate. As was noted above, the photocurrent curves do not run fully parallel to the reflection (or absorption) curves of silver; the minimum of the photocurrent from a thin film of sodium on silver is observed not at 316 mμ, but at 326 mμ, and for perpendicularly polarized light a maximum is observed at this point (Fig. 22). For still thinner films the minimum shifts toward shorter waves (310 mμ) (Fig. 8,a).

All these features receive their explanation if one calculates the energy distribution. In Fig. 23 are shown calculated curves giving: a) the distribution of intensity above the surface of silver (corresponding to the experimental photocurrent curves of Fig. 22) and b) the absorption in the very surface layer

its edge (corresponds to Fig. 8,a). Fig. 23,c gives the absorption in massive metal. As is seen from the comparison of the experimental (photoelectric) and calculated (optical) data, the agreement obtained is remarkable.

Fig. 22. Photocurrent from a sodium film on silver.
Angle of incidence \(60^\circ\).

Thus, by the work of Ives and Fry the optical nature of the selective photoeffect, at least for thin films, is proved. It is not excluded, of course, that the mechanism of photoemission itself may also play some role—as Lukirskii \(^{25b}\) indicates, one must take into account the circumstance that, upon illumination with different frequencies, the initial velocities of the photoelectrons inside the body will be different; very slow electrons have little chance of escaping outward, which is especially noticeable near the boundary, and this explains the different course of the absorption and photocurrent curves in the long-wavelength region (Figs. 23,a and 22). However, the predominant role, apparently, is nevertheless played by the optical side of the phenomenon, which determines the dependence both on the wavelength and on the polarization of the light.

Fig. 23. Optical properties of silver, calculated for an angle of incidence of \(60^\circ\); \(a\)—energy density at the surface of silver, \(b\)—absorption of light in the very surface layer, \(c\)—absorption of massive silver.

As we see, the method applied by American scientists of parallel study of optical and photoelectric properties, with the proper combination of theory and experiment, has proved very fruitful: by transferring the study of the phenomenon from the plane into space and showing that the observed course of the phenomenon is only a special case of a more general spatial picture, it has yielded much more than could have been expected of it. It remains to extend this method to the case of layers on nonmetallic substrates, which the authors intend to do in the near future.

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