NEW DATA ON SECONDARY EMISSION

N. S. Khlebnikov, Moscow

I. INTRODUCTION

1. The heightened interest in secondary emission was aroused by the work of L. A. Kubetsky1 in the USSR and later of P. T. Farnsworth[^2] in the USA. These authors created electronic devices, now widely known under the name of electron multipliers, or multiplicators, by means of which it proved possible to amplify (weak) electron currents. Thus a new method of amplifying weak signals was discovered. Multipliers have found their widest application in the amplification of photocurrents, and only recently have reliable indications appeared in the literature that this method can also be successfully used in amplifier tubes.[^3]

2. The most attractive feature of electron multipliers is the possibility of obtaining, in a single vacuum device of comparatively small dimensions, enormous amplifications—in the millions and billions of times. It would seem that replacing a large and cumbersome multistage tube amplifier by a single secondary-electron tube should always be desirable. In reality this proved not to be so, for several reasons.

The chief of these reasons was the absence of materials for secondary-electron emitters. Until very recently all materials that had been used were so unstable with respect to temperature that they did not permit the emitter temperature (arising as a result of electron bombardment because the energy efficiency of the emitter is very low) to be raised above 50–100° C. Exceeding this temperature led to a catastrophic reduction in the service life of the multiplier. Thus insufficient temperature stability limited the output power of the device, which could reach no more than 1 W and, as a rule, was considerably lower. The small permissible output power obviously determines the amplification limit of a given primary current and thereby restricts the possibilities of using this new method of amplification. On the oth—

on the other hand, a power of less than 1 W is insufficient to actuate most devices with which the output of the amplifier is loaded, as a result of which there arises the need for additional amplification by means of ordinary tube amplifiers. Thus the absence of suitable emitting materials compels one, instead of a simplified amplifier circuit, to turn to a more complicated one. The advisability of using a combination of a highly sensitive electron multiplier with electron tubes is limited to very few cases, and therefore at present the field conquered by the electron multiplier is limited to sound motion pictures.

At first glance it seems that for highly sensitive electron multipliers there is another extensive field—the field of amplification of very weak primary electron currents, which appears very valuable above all for the registration of weak light fluxes. It turns out, however, that here too there are limitations of the highest degree of unpleasantness. The first of them is imposed by the existence of so-called “dark currents,” caused by thermionic emission from the photocathode and the first emitters and amplified on a par with the useful signal. These dark currents, in the case of photocathodes with a low work function (for example, the usual oxygen-silver-cesium photocathode and the same emitter), reach considerable values even at room temperature (for Cs—O—Ag of the order of \(10^{-11}—10^{-12}\ \mathrm{A/cm^2}\)) and, accordingly, are much larger at higher temperatures. Taking as the lower limit of a distinguishable useful signal its value equal to the magnitude of the interference, a photocathode sensitivity equal to \(10\,\mu\mathrm{A}/\mathrm{Lm}\), and a cathode area equal to \(1\ \mathrm{cm^2}\) (average figures for the sensitivity and the magnitude of the cathode surface in existing multipliers), it is easy to see that the lower limit of the registered luminous flux at room temperature will be \(10^{-7}\ \mathrm{Lm}\). This limit increases linearly with the growth of the cathode area and exponentially with temperature. The presence of dark current is a fundamentally ineradicable defect of amplification by means of secondary emission, and in this respect the given method is inferior to the method of tube amplification, where there is always the possibility (in any case in principle) of excluding the dark current as a constant (or comparatively slowly varying) component by working with a modulated primary beam. To reduce dark currents one may, generally speaking, make use of replacing photocathodes with low work function by cathodes with large values of it. However, this path is not always possible, for both technological and fundamental reasons.

The difficulties arising for the method of secondary-electron amplification in the region of weak primary currents are not exhausted by the presence of dark currents. The point is that the lower limit of the useful signal is determined, along with them, also by the noise level. The nature of noise in electron multipliers has not yet been sufficiently clarified. The available data suggest that the cause of their

New Data on Secondary Emission

causing it are fluctuations in the photocurrent (and in the thermoelectronic current of the photocathode) and in the secondary currents of the first stages. The operating conditions of electron multipliers (the absence of space charges in the first stages) are favorable for the full development of this effect. Moreover, the noises apparently increase with increasing gain faster than the useful signal.

Both of the circumstances indicated force us to believe that the main region of practical applications of electron multipliers is the region of medium primary electron currents, in which, as we saw above, these devices cannot be successfully used without the creation of more stable emitters. Therefore we consider the central problem of secondary emission to be the problem of emitters, which, in addition, is of considerable interest also from the fundamental point of view. The task of the present article is to consider this problem in the light of new data, a significant part of which was obtained in our Union.

For completeness in outlining the existing state of affairs in the field of the use of electron multipliers, it is also necessary to dwell briefly on the question of the power supply of electron multipliers. Owing to the fact that for all emitters the values of the secondary-emission coefficient $\sigma$ have a magnitude substantially exceeding unity (2.5–3 and higher) at values of the primary-electron energy $V_p$ lying within the limits 50–200 V, the total supply voltage of a highly sensitive electron multiplier is 1000–2000 V and proves to be the higher, the greater the gain one wishes to obtain. Such high supply voltages are undoubtedly an argument not in favor of electron multipliers, and here this new device at present clearly yields to the electron tube in respect of safety, reliability, and convenience in handling.

Rectifiers are most widely used as power sources; their voltage is applied to the stages of the multiplier through voltage dividers. It is quite obvious that this is the most compact, simple, and reliable device of all those existing at present (galvanic and storage batteries, high-voltage direct-current machines), but it requires the presence of an alternating-current mains supply and therefore, in its turn, greatly limits the range of applications of multipliers.

In view of what was said above about noises and output powers, as well as the difficulties arising in the supply of highly sensitive multipliers, we believe that the greatest practical effect from the use of the secondary-electron method of amplification can be obtained if one does not strive for the complete elimination of electron tubes, but uses multipliers with a small number of electrodes only as the first stages of the amplifier, using electron tubes thereafter. In this way it seems possible, in particular, to remove the acuteness of the question of power sources for electron multipliers, and probably also to encompass the region of very weak primary currents.

II. DEVELOPMENT OF WORK ON SECONDARY EMISSION

1. As was indicated in detail in our earlier review4, before the publication of the results obtained by Kubetsky and Farnsworth, the study of secondary emission was carried out almost exclusively on pure (both truly pure and insufficiently pure) metals. The principal aim of these works was to clarify the micromechanism of secondary emission by establishing a connection between the characteristics of secondary emission (the dependence of the yield of secondary electrons on the energy of the electrons of the primary beam, the distribution of electrons by velocities and the angular distribution), on the one hand, and the constants characterizing the metal (X-ray levels, work function, atomic number), on the other. Although such a correspondence could be established only to a limited extent, these works have retained their significance in this respect up to the present day, since the elucidation of the details of the process still remains a matter of extensive work that has only just begun.

2. The investigations mentioned, however, also had another significance, not directly physical. The fact is that a whole series of works in one direction exerted a certain influence on the interpretation and methodology of subsequent investigations of secondary emission, adversely affecting later works in which effective emitters were studied, i.e., those emitters for which the secondary-emission coefficient \(\sigma\) substantially exceeds unity at primary-electron energies of \(100\text{–}200\ \mathrm{V}\). The essence of the viewpoint that took shape—although it was never expressed directly anywhere, since it was taken as something self-evident—amounted to the idea that the secondary emission of any material is completely determined by the so-called process of the “formation” of secondary electrons, i.e., by those processes that lead to the appearance, in the emitting layer, of electrons with an excess of energy at the expense of which they can leave the boundaries of the emitter—in other words, by processes of transfer of the primary electron’s energy to the electrons of the emitter. This process, however, does not exhaust the whole phenomenon even in the case of metals; it is still less adequate, as will be seen below, for an exhaustive description in the case of complex surfaces, which are materials with large values of \(\sigma\). This circumstance also affected the habit of regarding phenomena of electron emission as phenomena connected exclusively with the surface, which is incorrect already with respect to the photoelectric effect of complex surfaces5, as was shown with particular clarity in the case of the new semiconducting (cesium-antimony) photocathodes6,7, and, in fact, is incorrect even in the case of the photoelectric effect of pure metals, as Tamm showed8.

This point of view is pursued especially consistently in the work of Khvarts khava9, where the author attributes the secondary emission of a complex surface (oxygen–silver–cesium) exclusively to the surface layer.

1. Meanwhile, already rather old works^10,11, as well as two of the very first works on complex surfaces^12,13, showed that the role of the surface in secondary emission is in any case not a determining one. Sikscius^10 and Treloar^11 established that a considerable lowering of the work function of a metallic surface by adsorption of metals with a low work function (Th on W and Ba on Mo), which increases thermionic emission many times over, has almost no effect on the emission of secondary electrons (in the experiments of Sikscius, for example, an increase in thermionic emission by \(10^5\) times was observed and—for the same surfaces—an increase in \(\sigma_{\max}\) by 15–20%).

Groshev^12 found that treatment of a potassium surface by a discharge in hydrogen, leading to a 20–30-fold increase in photoemission, does not increase the secondary emission by more than 15–20%. Similarly, Penning and Kruithof^13 found that a 30-fold decrease in the photoemission of an oxygen–silver–cesium cathode is not associated with appreciable changes in the value of \(\sigma\).

In this connection, Luk’yanov^14 put forward (as applied to complex oxygen–silver–cesium surfaces) the supposition that secondary electrons arise in the bulk of the intermediate layer, whence they “diffuse” to the surface. Somewhat later an analogous view was expressed (this time as applied to metals) by Bruining^15. This correct point of view was subsequently shared by the overwhelming majority of authors; however, for almost two years no further steps were taken toward elucidating the basic features of the phenomenon. Here, too, the one-sidedness in considering the phenomenon, mentioned above, made itself felt. In particular, an overestimation of the role of processes of production is present in the new work of Bruining and de Boer^19.

1. Two further circumstances also played a considerable role in the absence of further progress. The first of them was that almost all work on the investigation of complex surfaces was carried out with primitive experimental devices of the three-electrode photocell type^17,18,20. As we have already noted elsewhere^16, this extremely limited the possibilities of experimentation and reduced the reliability of the results obtained.

The latter circumstance, which hindered the possibility of generalizing the data on secondary emission, consisted in the existence of a number of incorrect experimental data, repeated several times and therefore acquiring the appearance of reliability. These include both old and more recent results obtained by Copeland^21,22, and also by Warnecke^23. According to these authors, certain “pure” metals (Be, Ca, Ba, Al) possess, unlike the overwhelming majority of metals, values of \(\sigma_{\max}\) of the same order as complex surfaces (for example, for pure Be Copeland gives a value of \(\sigma_{\max}\) of about 5.5).

Thus it seemed that there exist two classes of effective emitters having nothing in common with each other: complex surfaces and certain metals, i.e., two groups of substances possessing—

yielding identical properties with respect to secondary emission and entirely different ones with respect to all other physical properties. This was sufficiently surprising. The point here was that the authors mentioned regarded as clean those metallic surfaces which in fact were by no means such. This misunderstanding was clarified by Bruining and de Boer 19 and—independently—by us 24. It is interesting to note that in this case as well the misconception was a consequence of deficiencies in experimental technique (the authors mentioned considered as clean surfaces those obtained as a result of annealing in vacuum; however, in the case of the metals listed such annealing, and it was rather weak, does not give the usual results).

All the circumstances listed led to the fact that, despite the large number of experimental works, generalizing points of view were lacking (this found very vivid expression in the character and even in the very structure of the two most recent reviews on secondary emission—those of Kollath 25 and Luk’yanov 26). The absence of a general point of view seemed extremely unsatisfactory not only in principle. It caused substantial damage to practical work in this field, since it did not make it possible to carry out systematic work toward developing emitters with the required properties and often forced one to work by trial and error.

III. EXPERIMENTAL TECHNIQUE

1. In view of the fact that in many of the most recent works the possibilities of experimentation and, consequently, the significance of the data obtained were greatly limited by the excessive primitiveness of the apparatus employed, it seems desirable to us to devote some attention to the requirements that must be imposed on experimental instruments in order to eliminate this shortcoming, and also to the simplest practical means of realizing them.

The inapplicability of three-electrode photocells as experimental instruments for the investigation of secondary emission follows above all from the circumstance that in such instruments, when the energy of the primary electrons is changed, a number of other conditions change at the same time—the distribution of the primary current over the surface of the emitter, the current density, the potential of the walls of the bulb (owing to the appearance of charges of one sign or the other as a result of electron bombardment 27). In addition, the observed value of the secondary current depends to an extremely large degree on the potential of the collector of secondary electrons. These circumstances lead, for example, Kollath 25 to regard—and quite correctly—many results obtained with instruments of this type as unreliable. These considerations determine the geometry of a rationally constructed experimental instrument and indicate the necessity of working with narrow primary beams.

The second major defect of three-electrode photocells

is that there the source of primary electrons is the photocathode. Since ordinary instruments of this kind are made of glass, only photocathodes sensitive to visible light can serve as the source of primary electrons. This thereby excludes from the range of experiments a number of substances and, in particular, pure metals. However, the identity of the primary and secondary cathode is an obstacle to a sufficiently deep study even in the case of photocathodes, since it limits such possibilities of acting on the emitter as lead to the destruction of photosensitivity (for example, oxidation). Still less, of course, are experimental devices made in the form of multistage multipliers suitable for obtaining serious results.

Fig. 1. Designs of experimental instruments

a  b

2. The designs of instruments used by us, apart from certain technical improvements, are not original, since they have been used many times before. Fig. 1 shows two typical designs, differing in the arrangement of electrode $E$, onto which the material under study is deposited. In design a the arrangement of this electrode (which consists of

a glass tube with an approximately flat end surface) provides the possibility of varying the temperature of the emitting surface within the limits of approximately from \(-190^\circ\) (liquid air) to \(+300^\circ\)C. Cooling of the layer is effected either by blowing air cooled by passage through a spiral glass tube immersed in liquid air, or by introducing liquid air, carbon dioxide with ether, and other cooling mixtures into the tube \(M\). For heating, blowing with hot air is used. In construction \(b\) the temperature interval of the emitting surface extends from room temperature to \(\sim 1000^\circ\). Heating to \(300\)—\(400^\circ\) is easily effected by simple incandescence of the filament \(F\); higher temperatures are attained by electron bombardment \(E\) with electrons from the same filament \(F\). Control of the surface temperature is carried out in construction \(b\) by means of thermocouple \(T\), and in construction \(a\) by means of a thermocouple introduced into \(M\), the junction of which is located directly at the inner surface \(E\).

In both drawings the letter \(C\) denotes the collector of secondary electrons, usually consisting of a layer of chemically deposited silver covering the entire inner surface of that part of the bulb where the emitting layer is located, with the exception of the window \(W\), which serves for observing the surface \(E\). The collector is led out by means of a platinum wire sealed into the wall of the bulb. The spirals \(S\), sealed on stems into the side tubes, serve for depositing metals on \(E\) by evaporation. Alkali metals are also obtained in the side tubes and can be introduced into the bulb by heating the whole instrument or only the corresponding side tube.

As is easy to see, instruments of such a design, for all their simplicity, provide broad possibilities for experimentation. With their aid it is possible: a) to obtain on the electrode layers of any materials permitting evaporation in vacuum, b) to investigate the temperature characteristics of these materials over a wide temperature range, c) to investigate the influence of chemical actions on the emitter material. The latter possibility is ensured by the fact that the source of primary electrons is the thermionic cathode of the electron gun, located in the neck \(G\) of the instrument. Such a cathode may consist both of pure and of thoriated tungsten, and may also belong to the type of oxide cathodes. We used chiefly cathodes of the latter type.

Further, instruments with spherical bulbs can readily be used for investigating the distribution of electrons by velocities. For this it is necessary to select the ratio of the dimensions of electrode \(E\) and the diameter of the bulb so as to ensure the desired accuracy, and, moreover, to have collector \(C\) not of silver but of a layer with as low a value of \(\sigma\) as possible. Such include many metallic oxides, aquadag, etc.

A small but essential innovation in the design of our instruments is that the entire surface of the bulb serving as ...

...which is a collector, is a homogeneous layer deposited on glass. This is especially important in the study of the distribution of electrons by velocities, since it ensures equality of the contact potential difference between the emitter and all points of the collector1. Another improvement is the introduction into the electron gun (the construction of which was in the main borrowed by us from Farnsworth[^28]) of a third cutting diaphragm. This made it possible to obtain narrower beams, almost perfectly homogeneous in velocity (the fraction of slow electrons not more than 0.1%). In Fig. 2 a drawing of such an improved gun is given (dimensions are in millimeters).

Fig. 2. Construction of the electron gun

Finally, in these constructions the strong dependence of the magnitude of the secondary current on the collector potential is eliminated, since complete saturation of the secondary current usually occurs already at low voltages (not above 5–10 V).

It is interesting to note that the constructions of these instruments, in conceptual respects, completely coincide with two constructions described in the recent work of Bruning and de Boer[^19]. The instruments of these authors are technically more perfect, with the exception of the electron guns. In addition, we consider it an advantage of our methods that we always worked with instruments under pumping, and not with sealed-off ones, as did the authors mentioned. This ensures much greater speed and flexibility in carrying out the experiments.

1. The measuring circuits used by us coincide with that described at one time by Petry[^29]. Such a circuit is shown in Fig. 3. Here the Roman numerals $I$, $II$, and $III$ denote the electrodes of the electron gun. The velocity of the primary beam with such a connection scheme is determined by the potential of cylinder $III$; cylinder $II$ plays an auxiliary role, drawing electrons out of the space near the cathode. The Wehnelt cylinder $I$ is usually connected to the negative end of the thermionic cathode. As in Fig. 1, the letters $C$ and $E$ denote the collector and the emitter respectively. The rectifiers are denoted by $r_{II}$ and $r_{III}$.

The advantage of this circuit is that in it the primary and secondary currents are measured directly (galvanometers \(G_1\) and \(G_2\), respectively). This, in particular, simplifies the calculation of \(\sigma\), since to determine this quantity here it is sufficient to take the ratio of the readings of galvanometer \(G_2\) to the readings of \(G_1\) and multiply this ratio by a constant coefficient for the given pair of galvanometers, equal to the ratio of the division value of \(G_2\) to the division value of \(G_1\). This is considerably simpler than performing calculations by the formula for instruments in the form of three-electrode photocells.

Fig. 3. Measuring circuit

The same circuit can also be used in investigating the distribution of secondary electrons by velocities; for this purpose, a commutator must be introduced into the collector—emitter circuit, allowing the field between \(E\) and \(C\) to be switched.

IV. CONDITIONS FOR THE EXISTENCE OF HIGH SECONDARY EMISSION

1. There is no doubt that the dependence of the coefficient of secondary emission \(\sigma\) on the energy of the primary electrons \(V_p\), expressed by the curves \(\sigma = f(V_p)\), constitutes the most important characteristic of the emitter from both the practical and the theoretical points of view.

The practical significance of these characteristics is clear without special discussion. Indeed, for use in electron multipliers, only that material is suitable for which \(\sigma\) has a value of several units at not too high values of \(V_p\) (50–200 V). Only in the case where this condition is fulfilled is it of interest to establish other properties of the emitter—the dependence of \(\sigma\) on temperature, the values of permissible loads, etc.

The theoretical significance of these characteristics, in our opinion, has been underestimated. In any case, they have not been used to the extent that they could have been. There have even been assertions\(^{20}\) that these characteristics have no theoretical significance. However, assertions of this kind, as became clear upon careful consideration of their foundations, were based on a kind of indeterministic conception of the curves \(\sigma = f(V_p)\). Thus, for example, it was stated\(^{20}\) that for one and the same surface the position

NEW DATA ON SECONDARY EMISSION

the maximum of the curve \(\sigma = f(V_p)\) can vary within rather wide limits. At the same time, it was overlooked that the identity of the surfaces was purely nominal, since the process of their preparation contains a large number of factors that are controlled only very roughly. This indeterminism, as was pointed out elsewhere\(^{16}\), is ultimately a consequence of defects in the experimental technique, namely, that it does not permit an exhaustive formulation of the experiment.

The dependence of \(\sigma\) on \(V_p\) cannot fail to have theoretical significance, for the simple reason that it is one of the few experimental results concerning the secondary emission of a given material as such; all the more so because, being an integral curve with respect to the distribution curves of secondary electrons by velocities (energies) and angles, it most fully expresses the secondary-emission properties of the material. The shortcoming of this characteristic is the difficulty of its interpretation, due to the fact that the curve \(\sigma = f(V_p)\) is determined by the combined action of all the factors responsible for secondary emission. Therefore it would be quite hopeless to try to interpret it by assuming, for example, that secondary emission is determined only by the processes of the formation of secondary electrons. It was precisely the fact of the scatter of the characteristics \(\sigma = f(V_p)\) for (nominally) identical surfaces, together with the firm conviction that there are no effects without a cause, that compelled us not to regard these characteristics as something given, but to strive to establish a connection between them and the structure of the emitting layer. This determined the entire course of the work, including the experimental technique.

1. First of all, it was, of course, of great interest to establish the factors responsible for the high values of \(\sigma\) for the oxygen–silver–cesium emitter, since, despite the fact that most studies on complex surfaces dealt with this emitter, there was complete lack of clarity on the question, and different authors expressed opposing opinions\(^{9,17}\). The reason for this was the impossibility, noted above, of carrying out decisive experiments with primitive experimental instruments.

Our instruments made it possible to carry out a number of series of experiments\(^{16,22}\), the results of which left no doubt that the principal factor responsible for the high \(\sigma\) for emitters of this type is the alkali metal contained in the intermediate layer. This was shown first of all by the fact that sufficiently strong oxidation of oxygen–cesium and oxygen–silver–cesium emitters invariably leads to \(\sigma\) taking low values (\(\sim 1\)) over the entire range of primary velocities (50–1200 V). In Fig. 4 a group of curves \(\sigma = f(V_p)\) is given, showing typical changes under sufficiently strong oxidation. The order of numbering of the curves corresponds to the increase in the amount of oxygen in the layer. On the other hand, the introduction of a new alkali metal into the layer (by heating the emitter in vapors

of an alkali metal) again leads to large values of \(\sigma\). Fig. 5 gives typical results of experiments of this kind. Curve 1 refers to a layer obtained by very strong oxidation, curve 2—to the same layer after heating it in cesium vapor. Experiments with oxidation also showed that, in order to obtain high \(\sigma\), it is necessary that the cesium be distributed in a dielectric medium (cesium oxide). This follows from the fact that, with weak oxidation of metallic cesium, \(\sigma_{\max}\) remains very small (Fig. 6, where, as before, the numbering of the curves goes in the order of increasing oxygen content, curve 1 referring to a layer of metallic cesium not subjected to oxidation).

Fig. 4. Changes in the dependence of \(\sigma\) on \(V_p\) for an oxygen–cesium layer with high oxygen content

Fig. 5. Restoration of high values of \(\sigma\) as a result of introducing cesium into a cesium-oxide layer

All the experiments described were carried out with layers containing only cesium oxide and cesium and containing no silver. The purpose of this was to establish the role of various metallic inclusions. What was common to all the curves observed in these experiments was that they had steeper maxima located at smaller values of \(V_p\), in contrast to the curves for ordinary layers containing, besides cesium and oxygen, also silver. The introduction of silver into such oxygen–cesium layers by depositing it on the finished layer by evaporation, followed by heating or without it, invariably led to a displacement of the maximum toward larger \(V_p\)—to where the maximum lies for an ordinary oxygen–silver–cesium emitter. The nature of such changes is clear from Fig. 7, where curve 1 refers to a layer without silver, curve 2—to the same layer after the introduction of Ag. We cannot dwell on other data of this work\(^ {16}\), but we must note one more very important fact, namely that, in order to bring the curve \(\sigma=f(V_p)\) to a form similar to curve 3

...Fig. 4, in the case of a layer not containing silver, considerably higher oxygen pressures and exposure times were required than in the case where the layer was an oxygen–silver–cesium emitter prepared in the usual way. The product of the exposure time and the pressure in the first case was 20–30 times greater.

1. Along with the investigation of complex emitters, we also carried out work^24 with those metals which, according to Copeland^21,22 and Warnecke^23 in the pure state have \(\sigma_{\max}\) of several units. The first of these metals to be investigated was beryllium. In this case the very first experiments destroyed the myth of the high secondary emission of pure metals. It turned out that if the metal is obtained in a truly pure state [deposition of a layer by evaporation of the metal from the spiral \(S\) (Fig. 1) in vacuum], then \(\sigma_{\max}\) becomes less than unity. But if this layer is acted upon by a gas, for example oxygen (simply keeping the metal in a gas atmosphere), then \(\sigma_{\max}\) increases several times. In Fig. 8 (p. 314) curve 1 refers to a layer of pure beryllium, curve 2—to the same layer subjected to the action of oxygen, and curve 3—to this same layer subjected to a short, weak heating. Thus the last curve shows that the sharp increase in secondary emission is not a consequence of the formation of compounds (since the beryllium compounds possible under the conditions of these experiments are extremely stable with respect to temperature). Thus in this case we are dealing with the influence of the presence of gas as such (in the adsorbed and dissolved state).

Fig. 6. Secondary emission of pure and oxidized cesium

Fig. 7. Change in the form of the curve \(\sigma=f(V_p)\) as a result of introducing silver into an oxygen–cesium emitter

Curves of an entirely different kind are obtained in the case where the gas is in contact with the heated metal. In Fig. 9 (p. 314) curve 1 shows the dependence of \(\sigma\) on \(V_p\) for beryll...

…of beryllium annealed in the presence of hydrogen. It is extremely noteworthy that in this case it is practically impossible to remove the gas from the layer. Curves 2 and 3 of the same figure show the insignificance of the changes occurring as a result of prolonged annealing. These results shed light on the reasons why Warnecke\(^{23}\) and Kollath\(^{21,22}\) obtained their erroneous data.

As is seen from curve 3 of Fig. 8, the same changes also occur in the case of the action of oxygen at a high temperature of the layer.

Fig. 8. Changes in the shape of the curve \(\sigma = f(V_p)\) for beryllium under the influence of oxygen and partial degassing

It should be substantially noted that all these basic data were obtained by us as early as the beginning of 1937—before the appearance of the preliminary communication by Brüning and de Boer\(^{30}\), which, like the latest article by these authors\(^{19}\), contained, from the experimental point of view, only a statement of the fact that the action of a gaseous atmosphere on electropositive metals is the cause of high values of \(\sigma\), whereas these metals themselves, in the pure state, are characterized by low secondary emission.

1. The cause that produces the displacement of the maximum of the curve \(\sigma = f(V_p)\) toward larger \(V_p\) is the penetration of the gas, at high temperature, into the body of the emitter to a greater depth than in the case when the gas merely comes into contact with the surface. This can be verified by obtaining a thick layer of metal, so to speak “impregnated” with gas at low temperature. If onto a layer of pure beryllium (low \(\sigma_{\max}\)) …

Fig. 9. Secondary emission of beryllium annealed in hydrogen

act on it with oxygen (a higher \(\sigma_{\max}\)) and again evaporate beryllium, the curve assumes the form characteristic of the pure metal. If this new surface is again subjected to the action of oxygen, an even larger \(\sigma_{\max}\) is again obtained, but the maximum lies already at larger \(V_p\). A series of such curves is shown in Fig. 10. The sequence of numbering is clear from what preceded. The continuation of such an alternation of operations has the consequence that the maximum is shifted ever farther toward larger \(V_p\).

As it turns out, this displacement of the maximum is due to the fact that the gas-containing metallic layers possess a greater “transparency” for secondary electrons arising in the depth than does a layer of pure metal. This is easily seen from the series of curves in Fig. 11. Here curve 2 refers to a Be layer with hydrogen dissolved in it (curve 1 is the curve for pure Be), curve 3 was obtained for a layer differing from the preceding one in that onto it an additional very thin layer of Be had been evaporated. Curve 4 was obtained after this new layer had been acted upon by oxygen. The essential result here is that the curve has a form similar to the initial one, and not to the curves characterizing the usual surface action of oxygen (as in Figs. 8 and 10).

Fig. 10. Changes of the curves \(\sigma=f(V_p)\) with double deposition of the metal and treatment of it with gas

Fig. 11. Restoration of the initial curve \(\sigma=f(V_p)\) as a result of increasing the transparency of the surface layer

Thus, in the present case the action of oxygen was manifested mainly in an increase of the “transparency” of the layer for secondary electrons arising in the depth, usually

the same effect of oxygen manifested itself only in an increase in the steepness of the initial part of the curve.

These experiments showed that the “surface” action of the gas is apparently not limited to the surface, but extends over a certain thickness of the layer. To verify this, we addressed the question of the resistance of such thin layers. The experiments consisted in depositing, by evaporation in a special bulb in vacuum, a thin layer of metal on glass, possessing considerable resistance, and observing the change in the resistance of this layer (from the change in current at constant voltage) when gas was introduced into the bulb. It turned out that the resistance of the layer increases strongly and instantaneously, changing only slightly thereafter. In Fig. 12 the results of experiments of this kind with several metals are shown. For clarity of the figure, the scale of the abscissa axis in the interval \(0\)—\(1\) sec. has been enlarged 10 times. The course of the curves during the first second after admitting the gas is given very approximately, since the current was measured with a galvanometer of large period. As it turned out, the influence of hydrogen on the magnitude of the resistance is considerably smaller than the influence of oxygen.

Fig. 12. Changes in the conductivity of thin metallic layers under the action of gas

The increase in resistance is a consequence of a decrease in the concentration of free electrons, which, in our opinion, is caused by the appearance in the metal of dissolved gas binding a part of the free electrons. Here, of course, the formation of compounds is also possible, but the fact that slight heating of Be completely removes the sharp peak of the curve, and also the fact that equally strong changes of resistance occur for Ni and especially Ag (which at room temperature is not oxidized by molecular oxygen), indicate that the principal role is played precisely by the dissolution of gas. This view is further confirmed by some of our other experiments.

1. From the series of facts presented above, namely from the fact that: a) the secondary emission of pure metals is small, b) secondary emission depends almost not at all on the work function and in any case is not determined by it, c) the presence of dissolved gas in the metal increases secondary emission, d) this increase is connected with an increase in the resistance of the layer, caused by the binding of electrons pro-

conductivity—it follows that secondary emission is determined by processes occurring in the bulk of the emitter, and also that processes connected with the motion, within the emitter, of the secondary electrons that have arisen play the most important role. Indeed, the presence of a layer of pure metal on the surface, giving high values of \(\sigma\), lowers the secondary emission, and conversely—the action of such a gas coating, leading to an increase in the specific resistance, reveals the secondary-emission properties of the underlying layers.

Thus it turns out that the reason for the low secondary emission of pure metals is the high concentration in them of conduction electrons. The reason for this is easily understood if one imagines that the creation of secondary electrons, i.e. the appearance of electrons with excess energy, takes place along the entire path of motion of the primary electron in the metal, so that these electrons that have arisen are forced to move among the other conduction electrons, which possess lower (thermal) energies. Motion in this electron gas is inevitably associated with loss of the acquired energy, chiefly owing to the Coulomb interaction between these and other electrons. The basic role of the Coulomb interaction between electrons in these losses is due to the fact that conduction electrons can acquire any amounts of energy, and also to the fact that its effective cross section is very large (in the first approximation equal to infinity). The role of the lattice ions is incomparably smaller, above all because of the mass ratio for this case, which, for the velocities of the secondary electrons that have arisen, smaller than the ionization potential, ensures an elastic (or nearly elastic) character of the interaction.

Thus, from all that has been set forth above, it follows that in order to obtain a material with a large coefficient of secondary emission one should choose one with as low a concentration of conduction electrons as possible. However, the use of dielectrics is evidently not possible because some concentration of conduction electrons is necessary to replenish the electrons that have been lost; without this, stationary emission is impossible. Therefore the class of substances in which effective emitters should be sought is the class of semiconductors; moreover, as we shall see below, only electronic semiconductors can be of practical interest.

This new point of view on secondary emission, which arose on the basis of our experiments, was reported by us at the March session of the Academy of Sciences of the USSR, 1938[^31]. Since then, both in our laboratory and elsewhere, several works have been carried out that fully confirm it. Let us also note that quite definite confirmation of it consists first of all in the trivial fact that effective emitters of the oxygen-silver-cesium cathode type are precisely electronic semiconductors[^32].

V. SOME PROPERTIES OF EFFECTIVE EMITTERS

1. Insufficient attention to the physics of secondary emission has been reflected, above all, in the fact that complex surfaces, of the type of complex photocathodes—which until recently were the only class of materials for emitters in multipliers—had not been investigated at all. Thus, for example, in Kollat’s review[^25] it is indicated that it would have been highly desirable to study the influence of temperature on their secondary emission; while in Lukyanov’s more recent review[^26] on the question of temperature dependence it is stated only that the influence of temperature is difficult to take into account because of possible changes in the structure of the layer, and the data of Timofeev and Pyatnitskii[^17] are cited on the observed increase of secondary emission at the temperature of liquid air.

The considerations set out above enabled us to make a number of predictions,[^5],[^24] both concerning the influence of temperature on the secondary emission of effective emitters and on other questions. In particular, it was to be expected that, for such emitters, when the temperature is varied within sufficiently wide limits (and at constant \(V_p\)), as the temperature rises there will be observed at first an increase in secondary emission (an improvement in replenishment owing to an increase in the concentration of conduction electrons in the electronic semiconductor) and then a decrease (caused by the same increase in the concentration of free electrons already beyond the limits within which the dominant role begins to be played by the increase in energy losses suffered by the secondary electrons), these changes being reversible in character, provided that in this temperature interval no irreversible changes occur in the composition (for example, evaporation of the alkali metal) and in the structure of the layer.

Fig. 13. Dependence of \(\sigma\) on temperature for an oxygen-silver-cesium emitter

The existence of precisely such a dependence was first discovered by us in the already mentioned work of Timofeev and Pyatnitskii.[^18] The corresponding curves for an oxygen-silver-potassium layer are shown in Fig. 13a, where curve 1 was taken during an increase of tem-

...temperature, curve 2—on lowering. Here there is a very sharply expressed drop at high temperatures, and irreversible changes are also found (probably connected with redistribution of the alkali metal). Unfortunately, the temperature interval below zero was investigated here only down to \(-80^\circ\), so that only the beginning of the decrease of \(\sigma\) is observed.

The expected character of the dependence of \(\sigma\) on temperature (at constant \(V_p\)) was subsequently established in our laboratory[^34] for several other semiconductors (also effective emitters).

1. Of very great interest was the study of the secondary-emission properties of a peculiar semiconductor, namely the antimony–cesium photocathode first described by Görlich[^35] and investigated in detail by us.[^36]

For antimony–cesium layers it was not possible to obtain completely the curve of the dependence of \(\sigma\) on \(T\), since with a strong increase in temperature excessively large irreversible changes already occur.[^37] However, with moderate heating it was possible to observe changes in which a reversible part predominates. Among these reversible changes it was possible to observe also a strong decrease of \(\sigma\) with increasing \(T\) (Fig. 13b). Figure 14 shows a series of curves referring to one and the same layer before (curve 1), during (curve 2), and after (curve 3) heating. Curve 2 corresponds to \(T \approx 97^\circ\text{C}\), for curves 1 and 3 \(T \approx 25^\circ\) (room temperature). As is easy to see, curves 1 and 3 differ from one another, but the discrepancy from curve 2 is much greater. This latter discrepancy corresponds to reversible, the former to irreversible changes in the properties of the layer (the layer in state 3 had, in particular, a lower resistance than in state 1). Such a character of the change of \(\sigma\) with temperature shows that, in the given temperature interval, the effect of improved replenishment of depleted electrons due to an increase in the concentration of conduction electrons predominates over the effect of their retarding action.

Fig. 14. Changes of the curves \(\sigma = f(V_p)\) under the influence of temperature changes for an antimony–cesium emitter

In the same work it was established that the magnitude of the coefficient of secondary emission depends substantially on the density of the primary beam. Figure 15 presents curves characterizing this dependence. Of these, curves 1 and 2 refer to the case,

when the Sb—Cs layer was located directly on the glass, curve 1 corresponding to \(V_p = 200\ \mathrm{V}\) and curve 2 to \(V_p = 500\ \mathrm{V}\). Curve 3 of the same figure was obtained for the case when the Sb—Cs layer was not directly on the glass, but on a metallic (silver) substrate; here \(V_p\) was equal to 500 V. The difference between these two cases consists, first of all, in the fact that whereas in the second case the potential drop across the layer exists only in the direction perpendicular to the surface, in the first case there is also a voltage drop along the layer [we note that the character of the change of the curves with temperature (Fig. 14) is the same in both cases]. Below we shall have occasion to speak further about these dependences in connection with the question of the use of emitters in electron multipliers.

Fig. 15. Dependence of \(\sigma\) on the density of the primary beam for an antimony-cesium emitter

1. Bruning and de Boer \(^{30}\) pointed out that quite appreciable \(\sigma\) can be obtained by subjecting dielectric layers deposited on a metallic substrate (for example KCl) to electron bombardment. In the work cited above \(^{16}\) we put forward the (erroneous) assumption that such layers are structures analogous to ordinary complex surfaces, i.e. they consist of a dielectric containing inclusions of an alkali and a heavy metal, which was possible under the conditions of their preparation. To check this assumption and to clarify the causes responsible for the high secondary emission for emitters of this kind, work was undertaken in our laboratory on the study of the secondary emission of such layers \(^{38}\). In the course of the investigations a number of interesting data were established, making it possible, in particular, to express certain considerations about the microscopic processes in secondary emission. In addition, it was possible to obtain very large values of \(\sigma_{\max}\)—about 20, which until now apparently had not been

Fig. 16. Changes of the secondary emission of KCl with temperature: curve 1 \(T = 175\text{—}200^\circ\); curve 2 \(T = 250\text{—}300^\circ\); curve 3 \(T = 300\text{—}350^\circ\); curve 4 \(T = 375\text{—}400^\circ\)

obtained. The data of this work also fit completely into the ideas on secondary emission developed above.

The secondary emission of some dielectrics has also recently been investigated by Budynskii^39 in an interesting work, the results of which once again confirm the correctness of the point of view developed here. Budynskii established that the secondary emission of obvious dielectrics, NaCl, KCl, and others, small at ordinary temperatures \((\sigma_{\max} \sim 1)\), can reach very high values \((\sigma_{\max} \sim 5—7)\) at sufficiently high temperatures.

In Fig. 16, borrowed from Budynskii’s work, are shown the changes in secondary emission that occur when the temperature of KCl is raised. An essential feature of these changes, along with the increase in \(\sigma_{\max}\), is the shift of the maximum toward larger \(V_p\), emphasized by the author. This increase is a consequence of the fact that, on heating, the substances indicated become ionic semiconductors, as a result of which the possibility of replenishing the electrons appears. From this, it might seem to follow that a good emitter may be not only an electronic semiconductor. However, this is not so, because to all the disadvantages of electronic semiconductors as emitters there is added in this case the presence of electrolytic processes leading to irreversible changes in the properties of the emitter. These changes are very sharply noticeable in the case of thin dielectric layers^38.

Finally, it is necessary to note here that Morgulis and Nagorskii^40a arrived at the same views as a result of studying the secondary emission of oxide-barium cathodes; we shall discuss their work in more detail in the next section, in connection with questions of the theory of secondary emission.

VI. ON THE MECHANISM OF SECONDARY EMISSION

1. The most essential result of all the experiments described is the establishment of the fact that secondary emission depends in the strongest way on factors which previously, as a rule, had been underestimated. These factors are: the ability of the emitter material to absorb the secondary electrons that have arisen and the conductivity of the layer. It is quite clear that a correct theory of secondary emission must take these factors into account together with the one which until now has received exclusive attention, namely, the transfer of the energy of primary electrons to the electrons of the emitter. The task of the theory is to establish the connection of all these factors, taken together, with the characteristics of the emitter (the dependence of \(\sigma\) on \(V_p\), the distribution of electrons by velocities, etc.), on the basis of definite ideas about the mechanism of all the processes that make up the phenomenon of secondary emission.

Such a theory does not exist at present. A formal quantum-mechanical treatment of the secondary emission of pure metals was made by Fröhlich^40, but with such considerable simplifications that, in our opinion, it is far from the real processes

in a real metal almost nothing remains.^1) And in any case the data of this work can in no way contribute to the elucidation of the causes producing large secondary emission, or to the establishment of a broad view of this phenomenon, embracing all three categories of substances (metals, semiconductors, dielectrics), for which there is now considerable experimental material requiring generalization in order to make it possible to approach the practical use of secondary emission with open eyes.

In this respect, i.e. in the sense of creating a general scheme of the phenomenon, in our opinion the other views that have been expressed are of no greater value. Thus, for example, in the recent work of Bruining and de Boer^19 the authors confine themselves, in essence, to the assertion that high values of \(\sigma\) are a property of compounds (as distinct from metals), attributing this difference to the conditions under which secondary electrons arise in the one case and the other. On the other hand, Timofeev and Pyatnitskii^17,18 attempt to explain the properties of complex surfaces by a redistribution of alkali-metal particles in the dielectric of the intermediate layer. It is easy to see that this supposition cannot explain, for example, reversible temperature changes of \(\sigma\) and cannot be extended to emitters of other types (homogeneous layers), as a result of which it cannot serve as the basis for a general point of view.

In the case of secondary emission, the situation with the theory of the phenomenon is the same as in the case of the photoeffect. In the field of the photoeffect, a formal quantum-mechanical theory is not at present capable (owing to the insufficiency of information about the substance and to the diversity and complexity of the phenomena to be described) of giving a picture of the phenomenon in complex photocathodes. The theory of the complex photocathode was constructed (by de Boer^32) on the basis of extensive experimental material, with the use of quantum mechanics as applied to those parts of the general scheme where it can be used with confidence. De Boer’s theory, even if it is not exhaustive, in any case has the merit that it makes it possible to orient oneself in the phenomenon. This is what practice requires of a theory above all.

It seems to us that the experimental material presented above and the conclusions that were drawn from it may serve as a basis for creating a theory of secondary emission similar to de Boer’s theory for the photoeffect, i.e. a theory representing above all practical value.

In order to accomplish the creation of such a theory, some refinement of the concepts of the processes in secondary emission is necessary. This refinement can be carried out in various ways, one of which, appearing to us the best only on pri—

^1) This work of Frenkel was subjected to thorough criticism at the conference on problems of secondary emission and the photoeffect (held January 20–22, 1939, in Leningrad) in reports by A. Vyatskin and A. Kadyshevich.

...the visibility of the picture obtained, we shall outline below. In addition, much further work is needed to collect experimental material. The existence of a general scheme, however, will make it possible to orient the work expediently in this latter direction as well.

1. On the basis of what has been set forth above, it should be considered that the principal processes in secondary emission are those occurring within the bulk of the emitter. There are two such processes:

a) The motion of the primary electron from the surface into the depth of the emitter, accompanied by the loss of energy by the primary electron as a result of the interaction of the primary electron with the electrons and atoms (or ions) of the emitter. These energy losses lead to the appearance within the emitter of electrons with increased energy (“generated” secondary electrons).

b) The motion of the generated secondary electrons, which takes place in all directions, including toward the surface.

We regard precisely these two processes, taking place in the bulk of the emitter, as the principal ones, because the processes associated with the surface play a significantly smaller role. This is evidenced, on the one hand, by the insignificance of the fraction of the secondary current accounted for by elastically reflected electrons, and, on the other, by the negligible change in \(\sigma\) for considerable changes in the work function.

1. The transfer of energy by the primary electrons to the emitter may in general occur in several ways. Energy may be transferred to conduction electrons, atoms forming the emitter may be ionized, or secondary ionization of ions may occur, and X-radiation may be excited, leading to the photoelectric release of electrons. There is no doubt that all these modes of occurrence exist simultaneously, but the weight of each of them is different for different materials. Thus, for example, for metals, where the concentration of conduction electrons is high, the principal mode should be the transfer of energy to conduction electrons. For dielectrics the decisive form is ionization; for semiconductors, one or another compromise between the two modes.

The initial directions of motion of the generated secondary electrons are distributed depending on the mode of energy transfer. In the case of ionization, and especially photoionization, the angular distribution will be closer to uniform than in the case of energy transfer to free electrons.

The transfer of energy to free electrons, because of the unfavorable angular distribution (the predominance of directions of motion of the generated secondary electrons in the direction of the primary beam), is the first of the factors responsible for the low secondary emission of metals. However, the direction of motion subsequently undergoes changes as a result of the interaction (collisions, Coulomb interaction) of the generated secondary electron with the elements of the emitter structure. Therefore, if one neglects the losses of energy during the motion of the generated secondary electrons, then one can

one may consider that, for electrons arising at some distance from the surface, there are no preferential directions of motion, so that approximately half of the electrons (for points of origin sufficiently far from the surface) have components of velocity in the direction toward the surface. However, such homogenization of the angular distribution is possible only on the condition that, in collisions with the elements of the lattice and especially in the intervals between these collisions, the secondary electron that has arisen does not lose energy. Since the greatest role is played by losses due to Coulomb interaction with the conduction electrons, the greatest approximation of the angular distribution of the secondary electrons that have arisen to a uniform one should occur in dielectrics, and the least in metals. This is the second factor responsible for the low secondary emission of this latter group of substances.

Since the concentration of conduction electrons in semiconductors is considerably lower, for them the percentage of secondary electrons that have arisen with components in the direction toward the surface is considerably greater. Therefore, for semiconductors, the simultaneous fulfillment of the laws of conservation of energy and momentum is a less obligatory condition for the presence of secondary electrons that have arisen with velocities directed opposite to the velocities of the primary electrons than it is for metals. Thus, as applied to the processes of generation, favorable for high secondary emission is not so much the presence of bound electrons as the absence of free ones.

1. Secondary electrons moving toward the surface are scattered by the lattice and experience a retarding action on the part of the conduction electrons. As a result, some of the electrons that have reached the surface prove unable to overcome the potential barrier and are reflected back, and only a part penetrate outward, forming the stream of secondary electrons. This process of “diffusion” of the secondary electrons that have arisen also depends primarily on the concentration of conduction electrons, and the large energy losses associated with this process in metals are the third factor responsible for their low secondary emission. As is evident, all three factors reduce to one and the same basic cause—the high value of the concentration of conduction electrons.

In the case of dielectrics and semiconductors, the principal property of the emitter is also this quantity, which now figures not in three but in four ways: directly (the processes of generation), as determining changes in the angular distribution, as determining the diffusion of the secondary electrons that have arisen, and as determining the conductivity (the processes of replenishment of the electrons leaving).

1. In order, in the crudest approximation, to interpret qualitatively the curves \(\sigma = f(V_p)\), it is sufficient to consider secondary emission as processes of generation upon which...

laid on processes of diffusion. In such a scheme it is also possible to take into account the influence of replenishment processes.

It is obvious that the general course of the curve \(\sigma=f(V_p)\) (if one disregards the “fine structure” of these curves, and also restricts the region of primary energies from below to that value of \(V_p\) at which secondary electrons in the proper sense of the word appear, i.e., electrons with energies much smaller than the energies of the primary ones), i.e., the position and height of the maximum, the steepness of the rise and fall, will depend on the relative energy losses of the primary and secondary electrons per unit path length. For clarity, it is more convenient to consider two quantities—the “limiting depth of generation” \(D_0\) and the “limiting depth of diffusion” \(D_d\).

The first of these quantities is equal to the distance from the emitter surface to which primary electrons penetrate while still capable of giving to the electrons of the emitter amounts of energy sufficient for escape to the outside. It therefore depends on the magnitude of \(V_p\), increasing together with it, and is related by a certain inverse dependence to the magnitude of the energy losses per unit length. Thus it depends on the material constants of the emitter (lattice constant, concentration of free electrons, atomic number). As for the quantity \(D_d\), it should be regarded as determined by the constants of the material, and only a weak dependence on \(V_p\) may be assumed. We shall consider it independent of \(V_p\). With the aid of these two quantities one can qualitatively explain the course of the curves \(\sigma=f(V_p)\), and also clarify the changes in the form of the curves observed experimentally.

The curves expressing the dependence of \(\sigma\) on \(V_p\) begin with a more or less steep rise, the steepness of which gradually decreases, becomes zero (maximum), and takes on negative values, gradually decreasing in absolute magnitude. According to what has been set forth above, the rise of the curve to the maximum occurs because, with increasing \(V_p\), the limiting depth of generation \(D_0\) increases, remaining less than the limiting depth of diffusion \(D_d\). The maximum corresponds to the equality \(D_0=D_d\). The gradual decrease in the steepness of the ascending branch of the curve is due to two factors. The first of these is the presence of a surface potential barrier of unchanged magnitude, which, as \(D_0\) increases, is approached by an ever larger number of electrons incapable of overcoming it1. The second factor is what may be called a decrease in the effective cross section of generation. The presence of this decrease follows from the very existence of the descending branch of the curve. Indeed, after \(D_0\) has become greater than \(D_d\), the generation of secondary electrons still—

...has a place only within the limits of \(D_d\) (secondary electrons arising deeper can no longer pass beyond the emitter). Since each primary electron traverses in this case the same active distance \(D_d\), this means a decrease in the number of formations over the segment \(D_d\). For ionization processes the decrease in the number of formations may be a consequence of a decrease in the probability of ionization\(^ {42}\). In the case of transfer of energy to conduction electrons it may occur as a result of a decrease in the amount of energy transmitted to the secondary electron being formed, owing to a decrease in the “collision time”\(^ {43}\).

The scheme outlined has a number of substantial and obvious shortcomings. In it, for example, the knocking-out of electrons from the primary beam as a result of scattering is not taken into account; it does not take into account the distribution of the secondary electrons formed by angles and the changes

Fig. 17. Changes of the curves \(\sigma = f(V_p)\) as a function of the angle of incidence of the primary beam for carburized nickel

Fig. 18. Changes in the conditions of formation and diffusion of secondary electrons as a result of changes in the angle of incidence of the primary beam

in this distribution; it does not take into account the distribution of the secondary electrons formed by velocities and by modes of formation. Nevertheless, since it is at the level of the experimental material available at present, it does not contradict experiment and makes it possible to interpret visually the curves \(\sigma = f(V_p)\) and their changes. As an example one may cite the changes of the curves \(\sigma = f(V_p)\) with change in the angle of incidence. This dependence was studied by Bruining\(^ {15}\) and Müller\(^ {15a}\) (for metals) and by Luk’yanov and Bernatovich\(^ {44}\) for complex surfaces. In Fig. 17 are shown the curves \(\sigma = f(V_p)\) obtained by Bruining for carburized nickel at various angles of incidence of the primary beam. Increase of the angle leads to an increase of \(\sigma_{\max}\) and a shift of the maximum toward larger \(V_p\). This is precisely what,

which is to be expected on the basis of our scheme.\(^1\) The displacement of the maximum is a consequence of the fact that the equality \(D_0 = D_d\) occurs, in oblique incidence, at large \(V_p\) (Fig. 18); the increase in \(\sigma_{\max}\) is a consequence of the fact that, in oblique incidence, for \(D_0 = D_d\), the number of origins within the limits of \(D_d\) increases (in addition, in the same direction there also acts the fact that, in oblique incidence, the number of secondary electrons produced which have velocity components in the direction toward the surface increases). For the same reasons (traversal of a smaller thickness of the absorbing layer), the values of \(\sigma\) in oblique incidence, for any \(V_p\), turn out to be larger.

1. In the same way one can readily explain all changes in the curves \(\sigma = f(V_p)\) observed when gases act on a metal. Above, curves were given showing changes of two kinds. In Figs. 8 and 10 the positions of the maxima for the pure metal and for the metal subjected to the action of oxygen scarcely differ. In these cases the gas acted only on the layer of metal nearest to the surface. In those cases in which the gas penetrated to a greater depth (successive deposition of Be and treatment with oxygen—Fig. 10, and saturation of Be with hydrogen—Fig. 9), the maximum shifts toward larger \(V_p\).

For the course of the curve \(\sigma = f(V_p)\), what is essential is not the absolute magnitudes and changes of \(D_0\) and \(D_d\), but their ratio and their changes relative to one another. A decrease of \(D_d\) relative to \(D_0\) must lead to a shift of the maximum toward smaller \(V_p\) and, conversely, an increase of \(D_d\) relative to \(D_0\)—to a displacement of the maximum in the opposite direction. Changes in the positions of the maxima must, generally speaking, be accompanied by corresponding changes in \(\sigma_{\max}\), since a relative change of \(D_d\) also means a change of the same sign in the number of origins within the limits of \(D_d\). Superposed on these changes may be changes of the surface potential barrier (changes of the work function under the action of the gas), which can be allowed for as changes of \(D_d\), since a decrease in the work function, other conditions being equal, means the possibility of escape for slower among the electrons produced, and conversely.

The introduction of gas into the bulk of a metal has as a consequence, first, an increase of the resistance,\(^2\) which should be ascribed to a decrease in the concentration of free electrons, the result of which is an increase of \(D_d\). But, in addition, the presence of gas atoms in the lattice increases the absorption of the primary beam and, consequently, dimin—

\(^1\) To explain the dependence of \(\sigma\) on the angle of incidence (at unchanged \(V_p\)), this scheme was first used by Müller,\(^{15a}\) in whose terminology \(D_0\) is denoted as the “depth of penetration” (Eindringtiefe) of the primary beam, and \(D_d\) as the effective path length (wirksame Weglänge). In Kadyshevich’s work,\(^{52}\) reported at the conference mentioned above, the ratio of the path lengths of the primary and secondary electrons (in the metal) is already, as in our scheme, the basis for explaining the form of the curves \(\sigma = f(V_p)\).

\(^2\) An increase in the resistance of metals as a result of annealing in hydrogen was observed, for example, by Pirani.\(^{45}\)

decreases \(D_0\). Thus the presence of gas in the bulk of the metal should lead to changes in the course of the curves \(\sigma=f(V_p)\), as found in Fig. 9. Under surface action of the gas, its dissolution in a thin surface layer takes place. This leads to an increase of \(D_0\) for this layer, which is revealed with particular clarity (owing to the small thickness of the deposited Be layer and, consequently, its complete treatment with oxygen) in Fig. 11 (see also Fig. 10). In the case of a pure metal, however, since \(D_d\) changes only for a thin surface layer, the conditions for the entire region of production change little, and the increase of \(\sigma_{\max}\) is a consequence of an increase in the number of events of production in the layer nearest to the surface. The shift of the maximum toward larger \(V_p\) for oxygen-cesium cathodes after silver has been introduced into them (Fig. 7) is a consequence of a decrease of \(D_0\) as a result of the increased scattering by the newly introduced particles. This is also evidenced by the greater ease, mentioned above by us (IV, 2), of destroying high secondary emission for layers containing silver.

There is no doubt that the secondary emission of surfaces of the type \([\mathrm{Ag}]—\mathrm{Cs_2O}, \mathrm{Ag}, \mathrm{Cs}—\mathrm{Cs}\)-cathodes is due to the presence of a free (alkali or alkaline-earth) metal in the intermediate layer. However, the question remains unclear as to what role these metallic inclusions play. Initially we assumed\(^{16}\) that the atomically dispersed metal constitutes the centers of production of secondary electrons. However, new data—above all, the high secondary emission of dielectric films in which such metallic impurities are absent—compel one to think that the role of the inclusions consists chiefly in creating conditions for replenishing the depleted electrons, i.e. in ensuring a sufficiently high conductivity of the layer, which is a consequence of the presence in the layer of conduction electrons appearing as a result of thermal ionization of internally adsorbed atoms.

The concentration of cesium atoms in an oxygen-silver-cesium cathode is very considerable, since its intermediate layer \((\mathrm{Cs_2O}, \mathrm{Ag}, \mathrm{Cs})\) possesses a large number of structural defects of the main lattice (for each molecule of \(\mathrm{Cs_2O}\) there are 2 Ag atoms). This circumstance is probably one of the reasons why the oxide-barium cathode, similar in structure, possesses considerable secondary emission only at high temperatures. Another reason is the large ionization work of the Ba atom.

1. In considering the secondary emission of metals (pure and containing gases) there is no need to take into account the influence of electron replenishment, since the small thickness of the layers ensures its unhindered occurrence. This, in particular, is manifested in the absence of a dependence of \(\sigma\) on the density of the primary beam\(^{46}\). The presence of a strong dependence on beam density for effective emitters (Fig. 15) shows that in this case the influence of replenishment cannot be neglected. In the \(D_0—D_d\) scheme it can be taken into account as a decrease of \(D_d\), due to the occurrence of a potential difference-

of traps in the emitting layer, and also as a result of an increase in the concentration of conduction electrons. The few data that exist at present apparently confirm this possibility. Thus, for example, in Fig. 14 the maxima of the curves corresponding to room temperature lie at smaller \(V_p\) than the maximum for the curve corresponding to high temperature. Since in these experiments an increase in temperature led to an increase in \(\sigma\), despite the increase in the concentration of conduction electrons, here, evidently, the increase in the energy losses of the secondary electrons that had arisen was overcompensated by a decrease in the resistance of the layer. The experiments of Budynskii\(^{39}\) also show that insufficient replenishment of electrons is equivalent to a small value of \(D_d\), since in the curves of Fig. 16 the maximum shifts to the right with increasing temperature (i.e., conductivity), and here the influence of conduction electrons is excluded, since at the temperatures considered KCl is an ionic semiconductor.

Thus positive temperature effects, depending on the kind of semiconductor, may be a consequence both of changes in the concentration (of free electrons) and of mobility (of ions). Negative temperature effects (a decrease of \(\sigma\) with increasing temperature, for example, in Fig. 13) are always the result of an increase in the concentration of conduction electrons. This is indicated in particular by experiments with pure metals (see, for example, Kollath’s review\(^{25}\)), where no temperature dependence of \(\sigma\) is observed up to temperatures \(\sim 2000\), despite considerable thermal disordering of the lattice. The fact that a considerable increase in resistance in this case has no effect on \(\sigma\) shows that, for secondary emission, not changes of resistance in general are essential, but only those changes that are due to changes in the concentration of conduction electrons.

In concluding this section, we should dwell on two other fairly clearly formulated points of view on secondary emission. The first of them, belonging to Morgulis and Nagorskii\(^{40a}\), set forth in connection with the study of secondary emission of oxide-barium cathodes, differs in no way from ours, except that the authors believe that in emitters of this type the sources of the secondary electrons that arise are only metallic inclusions in the intermediate layer. Considering the process of their production as impact ionization, the authors assume the necessity of homogenization (in their terminology—symmetrization) of the unfavorable initial angular distribution of the secondary electrons produced. The authors consider the reason for the high secondary emission of complex surfaces to be the low concentration of conduction electrons, assuming that their influence may be neglected under the condition \(\lambda \ll \dfrac{1}{\chi}\), where \(\lambda\) is the free path of the electron in the emitting layer and \(\dfrac{1}{\chi}\) is the Debye screening radius. This condition is fulfilled for an oxygen-barium cathode up to

temperatures of \(\sim 800^\circ\mathrm{K}\), but, as follows from Fig. 13, for complex surfaces containing alkali metals, the range of its applicability is bounded above by \(T \sim 120^\circ\mathrm{C}\), and for Sb—Cs layers by an even lower temperature\(^{37}\).

Dutch authors view the phenomenon differently. They\(^{53}\) divide substances, from the standpoint of secondary emission, into a) metals, b) metal compounds, and c) dielectrics, the second group being divided into metal compounds with low and with high ionization work. The low secondary emission of metals is attributed to the comparatively weak absorption of fast (primary) electrons together with strong absorption of slow (secondary) electrons, i.e., in our notation, to a small relative value of \(D_a\) (the condition for low emitter efficiency). For the secondary emission of compounds, the decisive factor is considered to be the arrangement of the occupied and unoccupied bands with respect to one another and with respect to the surface potential barrier.

Fig. 19. Scheme of energy levels for a substance with a high (a) and low (b) secondary-emission coefficient (after Bruining)

In Fig. 19, scheme \(a\) refers to a compound with high secondary emission, while scheme \(b\) refers to a compound having a low \(\sigma_{\max}\) (\(\sigma_{\max} \sim \leq 1.4\)). In this connection, on the basis of data from works on the photoelectric properties of compounds, the first group includes metal compounds with low ionization work (chiefly alkali-halide compounds), while the second includes \(\mathrm{MoS}_2\), \(\mathrm{MoO}_2\), \(\mathrm{WS}_2\), \(\mathrm{Cu}_2\mathrm{O}\), \(\mathrm{Ag}_2\mathrm{O}\). The difference between the two cases (Fig. 19) is that high secondary emission is possible only when (case \(a\)) the free band (\(II\)) nearest to the band of occupied levels (\(I\)) is located above the potential barrier. In this case, the secondary electron produced can leave the emitter. If, however (case \(b\)), the nearest free band (\(II\)) is located lower, then the secondary electrons that enter it cannot leave the emitter; only those of them that are thrown into the next free band (\(III\)) are able to do so.

Since the probability of transition to band \(III\) is less than to band \(II\), and, moreover, the lifetime of an electron in band \(III\) is shorter than in band \(II\) (band \(II\) is located above the band of occupied levels, band \(III\) above the free band), the probability of escape

NEW DATA ON SECONDARY EMISSION

the secondary electron that has arisen beyond the limits of the emitter proves to be smaller. As is easy to see, this scheme, despite its elegance, suffers from one essential shortcoming: in essence it takes into account only one of the three processes that make up the phenomenon of secondary emission (the process of generation), and therefore cannot explain all the experimental data. Thus, for example, it does not make it possible to understand the temperature changes of secondary emission in the case of ionic conductivity (Budinskii’s experiments). Indeed, no matter how the zones are arranged, if the emitting layer is on a dielectric substrate, stationary secondary emission is absent. Therefore this scheme must first of all be supplemented by the condition for the existence of electron replenishment.

In the case of replenishment due to electronic conductivity this means such a close mutual arrangement of zones $I$ and $II$ (or $III$, if $II$ is absent) that a transition of electrons between them would be possible as a result of thermal excitation; in other words, for this we must have an electronic semiconductor. If, however, such a transition is impossible, as occurs, for example, in the case of alkali-halide compounds, then high secondary emission at normal temperature (when ionic conductivity is absent) can take place only under the condition that “induced” electronic conductivity arises[^38] (i.e., at the expense of those electrons transferred into zone $II$ which have not left the emitter) throughout the entire thickness of the layer. This is possible only when the primary beam produces ionization throughout the entire thickness of the emitter, i.e., in the case of sufficiently thin layers. This circumstance is quite definitely confirmed by the experiments of Budinskii[^39], Bruining and de Boer[^30], and Korshunova[^38].

Furthermore, if one does not take into account the process of “diffusion” of the secondary electrons that have arisen, it is impossible to understand either the temperature dependence of $\sigma$ or the dependence of $\sigma$ on the density of the primary beam in electronic conductivity. If, however, one takes into account that every secondary electron that has arisen, before leaving the emitter, must traverse some path inside it, over the course of which it will lose its energy through interaction with conduction electrons, then these properties become understandable. Indeed, with increasing temperature the probability of transition of electrons into zone $II$ and their concentration in it increase. The electrons in zone $II$ behave, with respect to the secondary electrons that arise, as conduction electrons, i.e., they rapidly take away their energy. Thus the transition into zone $III$, from which the electrons can be emitted, is hindered. Since at the same time these same electrons of zone $II$ improve the conductivity, then, in the case of a sufficiently wide temperature interval, we must observe a curve of the dependence of $\sigma$ on $T$ having a maximum. The dependence on the density of the primary beam is a consequence of the fact that, with increasing $j_p$ (the density of the primary beam), the increase in the concentration of electrons in zone $II$ increasingly hinders the transition of the secondary electrons that arise into zone $III$.

Thus this scheme is directly applicable only to metals for which there is no need to take replenishment into account (high conductivity), and in which the concentration of free electrons is constant. In the case of metals, zone II is part of zone I (alkali metals), or both zones overlap.^54

That this scheme does not exhaust the whole phenomenon is indicated by several experimental facts in addition to those mentioned above. Thus, for example, antimony–cesium photocathodes quite undoubtedly have between the zone of occupied levels (I in Fig. 19) and the emission zone (III) at least one zone of photoconductivity (II).^6,7 Nevertheless they possess high secondary emission. Further, as it turns out, a compound such as Cu₂S also gives a value of \(\sigma \sim 5\text{—}7\). Therefore we believe that the most important physical factor which decisively determines the properties of an emitter is the concentration of conduction electrons; and it seems to us that the energy scheme given in Fig. 19 is only a first approximation, although an extremely useful one, since it illuminates the question from a new angle.

1. As one of the areas in which the energy scheme may be of exceptionally great benefit in explaining the phenomenon, mention should be made of the effects observed under the simultaneous action on an emitter of light and of an electron beam. Three such effects are known. Dember^55 observed, upon illuminating an aluminum emitter (probably with an oxide film on the surface), a resulting current greater than the sum of the photocurrent and the current of secondary electrons, the additional current arising under illumination exceeding the photocurrent proper many times over. Shmakov^56 discovered the inverse phenomenon for an oxygen–silver–cesium emitter: a decrease of the resulting current in comparison with the sum of the two currents, this decrease likewise exceeding the photocurrent. Similar observations were made by Malter^57 in the investigation of “anomalous secondary emission.”

At the above-mentioned conference on the photoelectric effect and secondary emission, the existence of the Shmakov effect was called into question on the grounds that some authors had not succeeded in observing it on the same oxygen–silver–cesium emitters. Such a tendency to “close” this effect seems to us insufficiently justified. Indeed, in connection with what was said above, it follows from the scheme of Fig. 19 b that if the emitter possesses appreciable photoconductivity (a broad band II, situated close to I), then, as a result of the action of light, a considerable lowering of secondary emission should take place. The discrepancy with Shmakov’s results should, in our opinion, be attributed to differences in the structure of the emitters, since such difficult-to-control factors as the concentration of cesium in the intermediate layer, which very strongly alter all the properties of the cathode,^32 cannot fail to affect its properties as a photoconductor. A significant internal photoelectric effect should be exhibited by those photocathodes in which there is an atomically distributed alkali metal. In the same case when

under the manufacturing conditions the predominant component is colloidal inclusions, the photoconductivity will be expressed considerably less definitely. Accordingly, in the first case the conditions for the existence of the Shmakov effect are more favorable than in the second.

VII. PRACTICAL CONSEQUENCES

1. Establishing the properties of effective emitters and classifying them are of primary importance for practice, since, on the one hand, they indicate the limits of applicability of modern devices with secondary emission and make it possible to establish certain of their peculiarities which have usually been taken for properties of the constructions, and, on the other hand, make it possible to outline the main paths to be followed in creating more perfect emitters.

We therefore consider it a great mistake that, up to the present, insufficient attention has been paid to fundamental questions. Their timely solution would have made it possible to carry on work in the field of the practical use of secondary emission more fruitfully.

2. Since the question of the applicability of emitters begins with the question of the magnitude of \(\sigma\), the only group of substances suitable as materials for emitters are electronic semiconductors. Ionic semiconductors fall away as materials for which prolonged operation with unchanged properties is impossible because of irreversible (electrolytic) changes connected with the passage of current. The use of homogeneous semiconductors, i.e., semiconductors not belonging to the type similar to complex photocathodes, where the basis of the structure is a dielectric lattice and the semiconductor properties are due to the presence of inclusions with a low ionization work, is especially desirable. For semiconductors of this latter type, considerably greater deviations of properties are inevitable even under identical manufacturing conditions, as a result of which a greater scatter of the parameters of the devices is also inevitable.

The influence of temperature on the magnitude of the coefficient of secondary emission limits, above all, the possibility of maintaining the constancy of the parameters of devices (multipliers) over wide intervals of external temperatures. The changes in the parameters will be the greater, the larger the number of multiplication stages. Thus the least technically reliable devices are all “supersensitive” multipliers (not to mention the fact that for them the problem of supply is especially complicated). Still more important are the changes caused by heating of the multiplier electrodes as a result of electron bombardment. These changes may have either a temporary (reversible) character or be irreversible—as a result of changes in the structure of the emitter. In any case, every change in load is inevitably reflected in the parameters of the device. These changes again show themselves most sharply for multistage multipliers. The permissible specific load limits the power at the output of the multiplier. In modern multipliers it cannot, without a sharp

the shortening of the service life may be greater than approximately 1 W. Thus the creation of “powerful” electron multipliers is not at present feasible.

Further, both temperature effects and the influence of replenishment lead to a decrease of $\sigma$ from cascade to cascade. Therefore the formula by which the total amplification given by a multiplier is usually determined, $\mu=\sigma^n$, where $\mu$ is the total amplification and $n$ the number of multiplication cascades, is inapplicable not only because of the “losses” of electrons in passing from cascade to cascade, but also, even with the best focusing, because of changes in $\sigma$ itself, and in general must be replaced by the following: $\mu=\sigma_1\sigma_2\ldots\sigma_n$. Thus the very nature of modern effective emitters is the cause of properties of electron multipliers that are extremely undesirable for technical instruments: scatter of parameters, susceptibility to external influences, and changes of parameters during operation.

3. All this makes it possible to regard as truly full-fledged technical instruments with secondary emission only those in which there is no striving to obtain extreme values, i.e., only those in which the phenomenon is used as far as possible within reasonable limits. Such applications include multipliers with a small number of cascades, successfully used, for example, for amplifying pulses from the mosaic of an iconoscope. In this case the gain is obtained by virtue of the fact that a weak signal is amplified without superposing on it fluctuations in the communication channel and in the input resistance of the tube. Further, the use of three-electrode photocells^47 and multipliers with a small number of cascades is undoubtedly worthy of attention, since in this way inertialess amplification can be obtained, likewise without superposing fluctuations on the weak signal. Such photocells are used in mechanical television. Finally, the ingenious use of secondary emission, opening new prospects for the development of electronic commutators, was recently described by D. V. Zernov.^48

VIII. POSSIBILITIES FOR FURTHER DEVELOPMENT

1. From all that has been said it does not follow that one should draw the conclusion that broader applications of devices with secondary emission are hopeless than is expedient at the present moment. The conclusion that should be drawn is that up to now too little attention has been paid to the fundamental side of the question, as a result of which nothing has yet been done to adapt the phenomenon itself for its successful use, and it has been used in its crude form—in the form in which it was discovered.

An example of the opposite state of affairs is the use of the photoelectric effect. First discovered on heavy metals and in ultraviolet light,^49 the photoelectric effect found important applications only when complex photocathodes sensitive to visible and even infrared light^50 were created. This path

was traversed as a result of extensive, but rather unsystematic, work over the course of almost 40 years. This lack of system was forced, since the work was carried out without sound guiding viewpoints, for ideas about the photoelectric effect changed radically more than once during this interval of time. Therefore the existence of a correct, even if only primitive, theory seems so necessary to us—and above all for practice.

1. Since the phenomenon is based on the semiconducting properties of emitters, one must first of all strive to find such semiconductors which, as far as possible, would exhibit their semiconducting properties less sharply, and also use semiconductors under such conditions where these properties are least manifested. Since both the temperature changes of the resistance and the dependence on the density of the primary current will, in general, be the greater the greater the resistance, this means an orientation toward the thinnest possible emitting layers. Further, since it is always desirable to have a small \(D_0\), semiconductors should be used which strongly scatter the primary flux. This condition can be realized both by creating additional scattering centers \(^{16}\) (Fig. 7), and by using semiconductors with heavy atoms.

A decrease in the working thickness of the emitter \(D_0\) also has another important advantage. For emitters with small \(D_0\), the efficiency of the emitter \(\eta\) should be higher. The quantity \(\eta\) is determined by the ratio of the energy carried away by secondary electrons to the energy arriving with the primary beam. Owing to the character of the velocity distribution of secondary electrons \(^{41,51}\) (a considerable predominance of slow electrons), for all emitters \(\eta\) proves to be of the order of a few percent. An increase in \(\eta\) will have as a consequence an increase in the stability of the emitter with respect to both reversible and irreversible changes. The theoretical upper limit for a simple emitter, i.e., one in which all directions of motion of the generated secondary electrons (after homogenization) are equally probable, is \(\eta = 50\%\). However, if conditions are created for a predominance of the motion of the generated secondary electrons toward the surface, one may also think of larger values of \(\eta\).

Finally, a very essential question at present is the insufficiently clear question of the noise level in devices with secondary emission. The noise level determines the sensitivity threshold and, consequently, the advantages of the secondary-electron or ordinary (tube amplifier) method of amplifying weak signals and, thereby, the value of electron multipliers, for example, as indicators of radiant energy.

All the questions listed require, for their solution, extensive and careful research work using experimental technique at the level of the problems to be solved.

REFERENCES

1. L. A. Kubeckii, patent, 1930.
2. R. T. Farnsworth, J. Frankl. Inst., 218, 411, 1934.
3. Jonker and Overbeek, Wireless Engineer, 15, 150, 1938.
4. Uspekhi fizich. nauk, 16, 467, 1936.
5. Izvestiya OTN AN SSSR (in press).
6. N. S. Khlebnikov and N. S. Zaitsev, Uspekhi fizich. nauk, 19, 278, 1938.
7. N. S. Khlebnikov and N. S. Zaitsev, Journal of Technical Physics (in press).
8. I. Tamm, Z. Physik, 68, 97, 1931.
9. I. F. Kwarzhava, Sov. Phys., 10, 809, 1936.
10. K. Sixtus, Ann. Phys., 3, 1017, 1929.
11. L. Treloar, Nature, 137, 579, 1936.
12. L. V. Groshev, Journal of Technical Physics, 5, 1220, 1935.
13. F. M. Penning and A. A. Kruithof, Physica, 2, 793, 1935.
14. S. Yu. Lukyanov, Journal of Technical Physics, 6, 1256, 1936.
15. H. Bruining, Physica, 3, 1046, 1936.
    15a. H. O. Müller, Z. Physik, 104, 475, 1937.
16. N. S. Khlebnikov and A. S. Korshunova, Journal of Technical Physics, 8, 500, 1938.
17. P. V. Timofeev and A. I. Pyatnitskii, Journal of Technical Physics, 6, 1645, 1936.
18. P. V. Timofeev and A. I. Pyatnitskii, Journal of Technical Physics, 7, 2138, 1937.
19. H. Bruining and J. H. de-Boer, Physica, 5, 17, 1938.
20. A. Dobroliubsky, Sov. Phys., 10, 242, 1936.
21. P. L. Copeland, Phys. Rev., 46, 166, 1934.
22. P. L. Copeland, Phys. Rev., 48, 96, 1935.
23. R. Warnecke, J. Phys. Rad., 7, 270, 1936.
24. N. S. Khlebnikov, Journal of Technical Physics, 8, 995, 1938.
25. R. Kollath, Physik. Z., 38, 202, 1937.
26. S. Yu. Lukyanov, Journal of Technical Physics, 8, 671, 767, 1938.
27. F. M. Penning and J. Moubis, Physica, 2, 55, 1935.
28. H. E. Farnsworth, Trans. IOSA, Rsl, 15, 290, 1927.
29. R. Petry, Phys. Rev., 26, 346, 1925.
30. H. Bruining and J. H. de-Boer, Physica, 4, 473, 1937.
31. N. S. Khlebnikov and N. S. Zaitsev, DAN (in press).
32. J. H. de-Boer, Electron Emission and Adsorption Phenomena, ONTI, 1936.
33. N. S. Khlebnikov, Izvestiya OTN AN SSSR (in press).
34. D. S. Afanas’eva (unpublished); G. A. Kuz’min (unpublished).
35. P. Görlich, Z. Physik, 101, 335, 1936.
36. N. S. Khlebnikov and N. S. Zaitsev, Journal of Technical Physics (9, 1939); Uspekhi fizich. nauk, 19, 278, 1938.
37. N. S. Khlebnikov, Journal of Technical Physics (in press).
38. A. S. Korshunova and N. S. Khlebnikov, Journal of Technical Physics (in press).
39. M. M. Vudynskii, Journal of Technical Physics, 8, 790, 1938.
40. H. Frölich, Ann. Phys., 13, 289, 1932.
    40a. N. D. Morgulis and Yu. O. Nagorskii, Phys. Zap. AN USSR, 7, 147, 1938.
41. T. Soller, Phys. Rev. 36, 1212, 1930.
42. K. Ramsauer and R. Kollath, Uspekhi fizich. nauk, 14, 957, 1934; 15, 128, 407, 1935.
43. E. J. Williams, Sc. Progr., No. 121, 1936.
44. S. Yu. Lukyanov and V. N. Bernatovich, ZhETF, 7, 856, 1937.
45. M. Pirani, Z. Elektrochem., 11, 555, 1905.
46. Rao, Proc. Roy. Soc., A 128, 41, 1930.

1. Simon and Zourman, Photoelements and Their Application, ONTI, 1936.
2. D. V. Zernov and A. I. Parfent'ev, Film-Photo-Chemical Industry, No. 6, 34, 1938.
3. A. L. Yuz and L. A. Dubridge, Photoelectric Phenomena, ONTI, 1938.
4. A. R. Olpin, Phys. Rev., 36, 251, 1930.
5. A. I. Pyatnitskii, Journal of Technical Physics, 8, 1014, 1938.
6. A. E. Kadyshevich, ZhETF (in press).
7. H. Bruining, Diss. Leiden, 1938.
8. B. Gudden, Advances in Physical Sciences, 15, 703, 1935 (Fig. 3).
9. A. Dember, Z. Physik, 33, 529, 1925.
10. P. V. Shmakov, Journal of Technical Physics, 6, 1261, 1936.
11. L. Malter, Phys. Rev., 50, 46, 1936.

1. This circumstance has direct confirmation in the data of Soller[^4], who found an increase in the relative number of slow electrons in the total flux of secondary electrons, occurring with increasing \(V_p\). ↩↩↩

2. Uspekhi Fizicheskikh Nauk, vol. XXI, no. 3 ↩