Secondary Electron Emission

N. S. Khlebnikov and V. V. Nalimov, Moscow

I. Introduction

In the broad sense, secondary-electron emission is understood as the emission of electrons by various substances subjected to bombardment by charged particles (electrons, ions) or by metastable atoms. Those electrons that are liberated when a substance is acted upon by X-ray quanta are also often called secondary electrons. In this case, what is meant is the method of obtaining X-rays—the bombardment of the tube anticathode by electrons. If, however, one does not think about the origin of the X-ray quanta and turns to the essence of the phenomenon, it will be clear that in this case we are dealing with the photoelectric effect.

The subject of the present review is considerably narrower, since we confine ourselves only to considering secondary emission under the action of electron bombardment and devote special attention to the emission of metals and complex surfaces (photocathodes). We make this choice on the grounds that it is precisely for metals that secondary emission has been studied most fully, and taking into account that in the case of metals and photoelectric surfaces the phenomenon under consideration has found important technical applications. The secondary emission of dielectrics, whose technical significance in connection with the development of new electronic devices (for example, Zworykin’s iconoscope) may also become very great, has been investigated very incompletely. As for secondary emission arising under the action of ions and metastable atoms, these phenomena are of interest only in connection with processes occurring at the cathodes of gas-discharge tubes and are unlikely ever to acquire broader significance.

Among the applications of secondary emission, or, as it is often called, the dynatron effect, we must note the dynatrons developed by Hull¹—electron tubes especially suitable for generating short and ultrashort waves—and especially “electron multipliers,” used for amplifying photocurrents inside photoelectric devices. The appearance of electron multipliers, proposed by Kubetsky² and independently by Farnsworth³, as well as by Iams and Salzberg⁴, represents a complete revolution in many areas of technology connected with photoelectric devices, and above all in television, for which electron multipliers open up enormous prospects both in rela-

of improving existing systems, as well as creating new ones. One of these, belonging to Farnsworth², has already been described in the pages of this journal⁵. Of considerable interest is also the new method of surface investigation proposed by Knoll⁶, based on secondary emission.

II. Historical outline; results of the first works; discovery of electron diffraction

1. The first data on the “reflection” (here, of course, not only reflection in the proper sense of the word was meant, but also secondary emission) of cathode rays were obtained by Starke in 1897–1898. In the first work devoted to this phenomenon, the author showed that when cathode rays fall on a solid body they undergo diffuse reflection, and it was established that the percentage of scattered rays does not depend on the intensity of the primary beam (with the other experimental conditions unchanged).

In the following work⁸ Starke investigated the dependence of the reflection coefficient for various metals (Cu, Al) on the discharge potential, i.e. on the velocity of the primary electrons (Starke worked with a Crookes tube), and found the reflection coefficient to be independent of this factor. This incorrect result (the number of electrons leaving the bombarded surface reaches a maximum at a certain definite velocity of the primary beam) should be attributed to the fact that Starke worked with such primary velocities (4000–11 000 V) for which the secondary-electron yield curve is very flat (the maximum region for most metals is located at 400–500 V).

These works, and especially the work of Austin and Starke⁹, attracted the attention of other investigators to the phenomena of scattering and reflection of cathode rays by solid bodies (as distinct from gases). Interest in this field was stimulated especially by the classical experiments of J. J. Thomson¹⁰ and Lenard¹¹ on the determination of the ratio $e/m$, since the discrepancies in the results observed there, at least in part, could be attributed (and quite justifiably) to the indicated phenomena. Several works by Lenard himself belong to this period,¹², ¹³ as well as the works of Baeyer.¹⁴

1. The investigation of secondary electron streams, beginning with the very first works, was always carried out by measuring currents or charges. The only exception is found in Lenard’s works¹³, whose investigations, devoted to phosphors, led him to the application of the “phosphoroscopic” method, the essence of one of whose varieties is explained by Fig. 1. Here $P$ is the plate under investigation, capable of rotating about the axis $a$, $D$ is a diaphragm through which a beam of primary electrons enters (produced by the action of ultraviolet light on a metallic pla-

tin), and \(H\) is the metallic shell of the chamber. \(\Phi\) is a small metallic sphere coated with \(\mathrm{CaBiNa_2S_2O_3}\) (phosphor), and \(K\) is the metallic mesh surrounding this sphere. Between \(K\) and \(\Phi\) a potential difference of \(4000\text{–}6000\ \mathrm{V}\) was established, accelerating the electrons that entered the space between \(K\) and \(\Phi\), whose impacts caused the phosphor-coated sphere to glow. This electric field had almost no effect outside the mesh \(K\); in any case, at a sufficient distance from it, it had no effect at all. The sphere was arranged in such a way (“in the shadow of the diaphragm”) that primary electrons could not fall on it. The intensity of the glow of the sphere (observed by eye) served as a measure of the number of secondary electrons.

Despite the imperfection of this method of registration, Lenard succeeded in obtaining a number of correct qualitative results. Thus, for example, he was able to establish the general form of the dependence of the number of secondary electrons on the velocity of the primary beam. In order to be able to compare the intensity of the glow, Lenard used a very rapid change (switching) of the voltage accelerating the primary electrons. In this way he established that, for platinum, the number of secondary electrons rapidly increases as the velocity of the primary beam increases from \(0\) to \(100\ \mathrm{V}\), remains almost constant in the interval \(100\text{–}200\ \mathrm{V}\), then immediately increases up to \(400\ \mathrm{V}\), after which it changes hardly at all up to \(1000\ \mathrm{V}\), and, finally, slowly decreases. Similarly, rapid rotation of the plate \(P\) about the axis \(a\) made it possible to study the influence of the angle of incidence of the primary beam. Here Lenard found no differences (for angles of incidence equal to \(75\) and \(90^\circ\)) at all the velocities of primary electrons that he investigated.

Fig. 1. Diagram of Lenard’s experiments.

By applying a positive potential to \(P\), it was possible to find the approximate value of the initial velocity of the secondary electrons (the field created between \(\Phi\) and \(K\) did not act outside \(K\)). In this way Lenard established that the glow of the sphere, with plate \(P\) made of platinum, ceases at \(+10.8\ \mathrm{V}\) on \(P\), and in the case of copper—at \(+7\ \mathrm{V}\) (the velocity of the primary beam in both cases was \(1000\ \mathrm{V}\), and the potential difference between \(\Phi\) and \(K\) was \(6000\ \mathrm{V}\)). This result, as we shall see below, is incorrect, since among the secondary electrons, in addition to a large group possessing small velocities, there are electrons with various velocities up to the primary one. Here the insufficient accuracy of the phosphoroscopic method made itself felt.

Finally, using the plate \(P\), different parts of which consisted of different metals, Lenard, also by rapidly replacing one metal with another (rotation about the axis \(a\)), was able to compare the quantities of secondary electrons emitted by different metals. He established that the greatest emission is given by Al, considerably

a smaller one for Cu, an even smaller one for CuO, whose emission is almost equal to the emission of platinum; the emission of the latter proved to be considerably greater than the emission of platinum black; the smallest emission was found for soot obtained from a turpentine flame.

Lenard also attempted to determine the ratio of the number of secondary electrons to the number of primary ones. In this case, however, he had to abandon the phosphoroscopic method and resort to an electrometer (connecting the grid \(K\) to ground, \(P\)—to the electrometer, and applying a negative potential to \(P\) in order to remove all electrons knocked out). In this way Lenard found that “on the average” (for Pt) there are two secondary electrons for one primary electron. Apparently Lenard, like Starke, who had found an apparent independence of \(\sigma^*\) from the velocity of the primary electrons (see above), considered \(\sigma\) to be one of the constants characterizing a metal.

The work of Baier\({}^{14}\), mentioned above, was undertaken to investigate the causes of errors in Thomson’s experiments on determining the ratio \(\dfrac{e}{m}\). Among the possible sources of error Baier also takes into account the “reflection” of electrons. However, in this work the author establishes only the fact that reflection of electrons from metals undoubtedly exists. In his next work Baier\({}^{15}\) already discovers certain characteristic features of the phenomenon. Thus, he finds that as the velocity of the primary beam increases (beginning with 5 V), the number of reflected electrons (i.e. those having velocities close to the velocity of the primary electrons) rapidly increases, and that with a further increase in velocity secondary electrons appear, having velocities much smaller than those of the primary electrons. The number of these electrons rapidly grows as the velocity of the beam increases, and already at 30 V the total number of reflected and secondary electrons may become equal to the number of primary electrons. Investigating various substances, Baier, like Lenard, established that \(\sigma\) is very small for platinum black and especially for soot. Baier was the first to use thermionic emission to create the primary beam (a heated wire spiral).

1. This work should be followed by mention of the work of Hertz\({}^{16}\), who for the first time investigated in detail the dependence of \(\sigma\) on the velocity of the primary electrons (in the velocity interval from 0 to 500 V) for Al, Pb, Co, Cu, and soot, as well as the distribution of secondary electrons by velocity. Like Baier, he found a very small value of \(\sigma\) for soot (not above 0.5). For metals, \(\sigma\) turned out to have a maximum, which in all of Hertz’s experiments was located near 200 V and at which \(\sigma\) reached values somewhat greater than two. In addition, Hertz discovered that at small primary velocities \(\sigma\) changes non-monotonically, giving a minimum at 11 V and an adjoining small maximum at 5 V. And the existence of a maximum at per—

* Here by \(\sigma\) we denote the ratio of the number of secondary electrons to the number of primary ones, i.e. the average number of secondary electrons knocked out by one primary electron.

SECONDARY ELECTRON EMISSION

...at primary velocities of several hundred volts and the nonmonotonic course of the curve in the region of low voltages are characteristic features of the dependence of $\sigma$ on the velocity of the primary beam, which were consistently observed later.

A study of the velocity distribution of secondary electrons showed that, up to approximately 11 V, the secondary radiation consists only of electrons reflected without loss of velocity. Beginning with 11 V, secondary electrons appear, the majority of which have velocities of 8 V and below. Hertz observed reflected electrons only at primary velocities up to 30 V. This circumstance must be attributed to the insufficient sensitivity of the measuring circuit, since the fraction of reflected electrons in the overall balance of secondary emission falls rapidly with increasing velocity of the primary beam.

1. Campbell arrived at the study of secondary emission by another route, beginning^17 with the investigation of the so-called $\delta$-radiation (as Rutherford called the emission of electrons by metals subjected to bombardment by $\alpha$-particles).

In his second paper,^18 attempting to elucidate the mechanism of the “ionization” of a metal, Campbell investigated the velocity distribution of secondary electrons (emitted this time under the action of electron bombardment). In his third paper,^19 Campbell for the first time investigated a very important circumstance—the influence of the state of the surface on the magnitude of $\sigma$ (for Pt, Ni, Cu, and Al). Campbell found that freshly polished surfaces have the highest value of $\sigma$. Treatment of the surface by discharge in gases and vapors (air, $\mathrm{O}_2$, $\mathrm{H}_2$, kerosene vapor) always lowers $\sigma$. Subsequent electron bombardment causes $\sigma$ to increase, and in the end this quantity reaches a certain limiting value, smaller than the initial one, and further bombardment no longer changes it.

1. The works listed above were followed by a series of further studies devoted almost exclusively to the secondary emission of metals. These works will be considered by us below (IV). In the later papers of this group, special attention was given to the study of the distribution of secondary electrons by velocities and by directions.

As early as 1921, Davisson and Kunsman^20, in studying the angular distribution of electrons reflected from a nickel plate, discovered the existence of certain preferred directions. In the continuation of this investigation (in April 1925), an accident occurred with the apparatus on which Davisson and Germer were working. During the degassing of the plate under investigation, the Dewar vessel with liquid air burst, air entered the vacuum system, and the heated plate became strongly oxidized. To restore the surface, prolonged annealing of the plate was undertaken in an atmosphere of hydrogen and in vacuum at a very high temperature (almost at the melting temperature of nickel). When, subsequently, for the surface cleaned in this way, ...

the curve of the angular distribution of electrons scattered without loss of velocity was taken; it turned out to differ sharply from the curve usually observed for nickel. This new curve had a large number of peaks and in this strongly resembled the intensity-distribution curves obtained upon reflection of X-rays from crystals. The authors attributed this change in the form of the curves to the fact that, as a result of prolonged annealing in the process of surface restoration, recrystallization of the nickel had occurred, and the surface under investigation had changed from polycrystalline into a surface of several (a small number of) large single crystals.

Davisson and Germer showed[^21] that the peaks of the new distribution curve could be explained as diffraction maxima produced as a result of diffraction on a spatial and a plane lattice, with constants corresponding to the lattice constants of nickel. In this case the wavelengths of the diffracted waves turned out to be inversely proportional to the velocities of the electrons and had to be taken equal to

\[ \lambda=\frac{h}{mv}, \]

where \(h\) is Planck’s constant, and \(m\) and \(v\) are the mass and velocity of the electron.

These experiments for the first time revealed the existence of electron diffraction, predicted by Elsasser[^22] shortly after the appearance of de Broglie’s well-known work, and thus constituted the first proof of the existence of de Broglie matter waves.

5. The work of Davisson and Germer mentioned above (as well as the work of Thomson and Reid[^23]) initiated a series of investigations of the diffraction of material particles and pushed the study of secondary emission itself into the background. Interest in this phenomenon was retained by only a few researchers. It became more general only in recent years and especially after the publication of the cited article by Farnsworth[^2], in connection with the much greater practical importance that secondary emission acquired for the amplification of photocurrents.

Recent works on secondary emission are predominantly of an applied character. They are devoted mainly to the use of secondary emission in photocells, to phenomena associated with secondary emission under the operating conditions of instruments, and to the characteristics of photoelectric devices with secondary emission.

III. CHARACTERISTICS OF SECONDARY EMISSION; EXPERIMENTAL METHOD

1. Secondary electron emission, like thermionic and photoelectric emission, is a property characteristic of the emitting surface. We know that from surface to surface \(\sigma\) changes—the number of secondary electrons corresponding to one primary. Since, moreover, for a given surface this quantity depends on the velocity of the primary electrons, it can be likened to the quantum yield of the photoelectric effect,

SECONDARY ELECTRON EMISSION

which, as is known, varies depending on the wavelength of the incident light.

From the practical point of view, $\sigma$ and the dependence of this quantity on the velocity of the primary electrons is the most important characteristic of a surface emitting secondary electrons.

Another, practically no less important property of the emitting surface is the value of the limiting density of the primary (or, what is the same, secondary) electron current attainable without disturbance of the emission properties of the surface. Despite the fact that the use of photodynatron devices is at present limited to a considerable degree by the insufficient magnitude of the output current, emitting surfaces have not been investigated from this point of view.

The question of the distribution of secondary electrons by velocities does not have such direct practical significance. It is, however, very important in principle, since the study of the velocity distribution is one of the ways of elucidating the origin of secondary electrons and the mechanism of their escape. Thereby this characteristic of the secondary-electron flux also acquires great practical interest, since the fabrication of a surface possessing the required emission properties is impossible without understanding the essence of the phenomenon.

From this point of view, the distribution of secondary electrons by directions may also prove to be an important characteristic of the secondary-electron flux, just as this turned out to be the case for reflected electrons. So far, however, there are no indications of this in the literature.

1. With the exception of the phosphoroscopic method described by us above, used by Lenard, which is suitable only for a rough estimate of the observed ratios and is of chiefly historical interest, and of the calorimetric method used by Ham and White,^29 applicable only in the case of large powers of the primary flux, in all investigations of secondary emission the measurement of the current strength (with a galvanometer or electrometer) or of the magnitude of the charge (with an electrometer) has been applied to the study of secondary-electron fluxes.

An apparatus serving to take curves expressing the dependence of $\sigma$ on the velocity of the primary electrons must consist of two parts: a source of primary electrons and an electrode intended for collecting the secondary electrons. This latter electrode (the collector) is very often made in the form of a Faraday cylinder. As for the source of primary electrons, it usually represents an “electron gun” and consists of a thermionic cathode and a system of electrodes creating a sufficiently narrow primary beam. The cathode, as far as possible, is made equipotential. This is especially essential when working with small velocities of the primary beam.

In Fig. 2 are shown the apparatus and the circuit with which Petry^24 carried out measurements. This apparatus consists of a tungsten filament

filament \(F_1\), a series of diaphragms \(SSS\), a Faraday cylinder \(C\), inside which the plate under investigation is placed, and filament \(F_2\), serving for degassing the plate. The secondary-emission current (the current to the Faraday cylinder) is measured by galvanometer \(G_1\); the primary current, by galvanometer \(G_2\). In both circuits the measurement was carried out by the compensation method with an accuracy up to \(0.1\%\). This method of measurement has the feature that the secondary-emission current is measured directly.

In all his numerous works Farnsworth used another method of measurement, in which the secondary-emission current was determined as the difference of two currents\(^{25}\). Fig. 3 shows

Fig. 2. Diagram of the apparatus for measuring secondary emission (after Petri).

the most perfect of the designs of Farnsworth’s apparatus\(^{26,27}\). In the left neck of the glass bulb there is a very carefully constructed\(^{28}\) electron gun. In the right neck is placed the Faraday cylinder \(F\), closed by the protective cylinder \(E\), and insulated from it by means of quartz rings. Cylinder \(E\) serves to prevent electrons from reaching the Faraday cylinder that may arise as a result of multiple reflection from the metallized inner surface of the spherical part of the bulb. Cylinder \(F\) is arranged in such a way that one of its ends is at the center of the sphere \(D\). The plate under investigation is placed inside \(F\) and can be moved (by means of a magnet) from one end of the cylinder to the other.

The curve \(\sigma = f(V_{\text{prim}})\) is taken in the following way: 1) the current \(i_1\) to the plate is measured when it is located at the front end of the cylinder, 2) the current \(i_2\) to the plate is measured when it is at the rear end of the cylinder. Since the plate and the cylinder are connected together and the length of the cylinder is such that in case (2) not a single secondary electron can leave it, the difference \(i_2 - i_1\) gives the secondary-emission current.

Of the other methods of measuring $\sigma$, mention should be made of the calorimetric method, used by Häm and White$^{29}$ in studying secondary emission in a Coolidge tube, when bombarding the anode with high-speed electrons (up to 20 kV). These authors determined the ratio of the number of secondary electrons to the number of primary ones by measuring the difference between the energy supplied to the tube and the amount of heat released at the anode (measured by the temperature of the cooling water). The ratio of this difference to the supplied energy gives $\sigma$.

1. The investigation of the velocity distribution of secondary electrons can be carried out by one of two methods: a) by the retarding-potential method, also known as the spherical-condenser method, and b) by the method of magnetic analysis. Both of these methods have been described more than once, and therefore we shall not dwell on them in detail. A description of them and the corresponding literature may be found, for example, in the book by Hughes and DuBridge$^{30}$, and also in the review by Ramsauer and Kollath$^{31}$. We note that Farnsworth’s apparatus (Fig. 3) is very convenient for measuring the velocity distribution by means of the retarding-field method.

Fig. 3. Diagram of the apparatus for studying the dependence of $\sigma$ on the velocity of the primary beam and the velocity distribution of electrons (after Farnsworth).

We must make several remarks concerning the merits and shortcomings of the one and the other method. In studying the velocity distribution of electrons by means of magnetic analysis, the direct experimental data, expressing the dependence of the number of electrons reaching the collector on the field strength of the analyzing field, already give the distribution of the electrons precisely with respect to velocity. This is easy to see from the linearity of the relation between the strength of the homogeneous magnetic field $H$, in which the electron moves, and the velocity of the latter $v$

\[ v = r \frac{e}{m} H \tag{1} \]

where \(e\) and \(m\) are the charge and mass of the electron, and \(r\) is the radius of the circle along which the electron moves. Thus, in order to obtain here the velocity-distribution curve, it is sufficient to apply a new scale along the abscissa axis.

The situation is different in the case of the retarding-potential method. First of all, as follows from the relation that underlies this method,

\[ \frac{mv^2}{2}=eV \tag{2} \]

where \(v\) is the retarding potential difference, the experiment here gives a distribution not by velocities but by energies. Moreover, the curve expressing the dependence of the current to the collector on the retarding potential does not express the distribution function, but is its integral, since for any value of the retarding potential all electrons with energies from the maximum down to that determined by equation (2) will reach the collector. Therefore, in the case under consideration, in order to obtain the distribution curve it is necessary to differentiate the experimental curve. Meanwhile, very often the integral current–voltage curves are, without any qualification, called distribution curves.

The necessity of differentiation is the most serious source of errors when using the retarding-potential method. In other respects, this method, with the proper design of the apparatus (small dimensions of the spherical or disk-shaped electrode placed at the center of a spherical collector of considerable size), is more reliable than the method of magnetic analysis, the principal drawback of which consists in the low intensity of the electron flux reaching the collector. For this reason, substantial errors may arise here because of electrons reaching the collector as a result of multiple reflections inside the apparatus. This can be combated by weakening the reflection, for example by coating the inner surfaces of the apparatus, and especially the diaphragms, with soot.

1. Since the distribution of electrons by directions at the present time is a field belonging to the study of electron diffraction, we shall not dwell on the instruments and methods of the corresponding measurements. Detailed information on this matter may be found, for example, in the books of Tartakovskii\(^{32}\) and Mark and Wierl\(^{33}\).

IV. Secondary Emission of Metals

1. The study of the dependence of \(\sigma\) on the velocity of the primary electrons, as well as the distribution of secondary electrons by velocities, was begun in 1909 and continues up to the present time. In spite of the fact that much has already been clarified, the extensive experimental material accumulated during this interval is sufficiently contradictory, and even now yet

SECONDARY ELECTRON EMISSION

it is possible to answer a whole series of questions with complete certainty.

The first measurements of the dependence of \(\sigma\) on the velocity of the primary electrons were made by Baier \(^{15,31,35}\), Hertz and Campbell \(^{18,19}\). All these authors found that for all the metals investigated (Pt, Cu, Ni, Pb, Co) the curves \(\sigma=f(V_{\text{prim}})\) are almost completely identical. This entirely incorrect result must be attributed to the fact that at that time both the technique for obtaining a vacuum and the methods for degassing metals were only in a rudimentary state, so that, properly speaking, the objects investigated were not the metals themselves, but the gas films present on their surfaces.

The results of the work of Hull \(^{36}\), Barber \(^{37}\), Horton and Davies \(^{38}\) are likewise in contradiction with the results of later work, and probably for the very same reason.

The first work inspiring confidence with respect to vacuum technique is that of Farnsworth \(^{39}\), published in 1922. Farnsworth investigated the secondary emission of a nickel plate which had first been carefully degassed and placed in a bulb in which the pressure did not exceed \(10^{-7}\) mm Hg. The results of this investigation showed that the course of the curve \(\sigma=f(V_{\text{prim}})\) is determined primarily by the degree of degassing of the metal. Only after heating the plate for several minutes at red heat is a “limiting curve” obtained, which is not altered by further thermal treatment. Thus only this limiting curve is characteristic of a metal surface freed of occluded gases.

Fig. 4. Limiting curve for nickel (after Farnsworth).

The limiting curve for nickel is shown in Fig. 4. The rise of the curve begins at a primary-electron velocity of 0.2 V and continues up to a velocity of 4 V. In the interval of primary-electron velocities from 4 to 9 V the value of \(\sigma\) remains constant. For \(V_{\text{prim}}>9\) V, \(\sigma\) again increases and reaches 1 at \(V_{\text{prim}}\) equal to 260 V.

The energy-distribution curves of the secondary electrons, taken by Farnsworth by the retarding-potential method, show that at primary-electron velocities below 9 V the overwhelming majority of the secondary electrons have velocities close to that of the primaries, whereas at primary velocities greater than 9 V the number of secondary electrons with velocities less than the primary one increases, and their relative number grows as the velocity of the primary beam increases. The sharp change in the course of the curve \(\sigma=f(V_{\text{prim}})\) at a primary-electron velocity of 9 V, as well as the change in the distribution of the secondary

electrons by velocities, which takes place at this point, indicates that at velocities of the primary beam less than 9 V only elastic reflection of the primary electrons occurs; secondary emission proper begins only at \(V_{\text{prim}} = 9\) V.

Fig. 5. Limit curves for copper, silver, and gold (according to Farnsworth).

In his subsequent works\(^{40—43}\) Farnsworth obtained limit curves \(\sigma = f(V_{\text{prim}})\) for copper, silver, gold, tungsten, platinum, lead, magnesium, aluminum, and iron, subjecting these metals to thorough degassing. Some of these limit curves are shown in Figs. 5 and 6. In all cases a rapid rise of the curves is observed at small velocities of the primary electrons, ending in the velocity region from 3 to 11 V, and a further

Fig. 6. Limit curves for lead, platinum, and tungsten according to Farnsworth.

a slower rise. The curves for silver and gold show, in addition, small maxima at 3 V. The curves for copper have two sharp maxima at 3 and 6.5 V and two less sharp ones at 14–20 V. The curve for iron gives sharp maxima at 1.2 and 7 V and sharp minima at 3.7 and 12.0 V. A less sharply expressed maximum and minimum for iron are found at 10.0 and 9.0 V.

The value of σ for aluminum and magnesium turns out to be much greater than for the other metals; thus, for example, for Al σ reaches 1.8 at a primary-electron velocity of 140 V.

The velocity-distribution curves obtained by Farnsworth for the same metals show that at small primary velocities the majority of the secondary electrons have velocities close

Fig. 7a. Curves \(\sigma=f(V_{\text{prim}})\), obtained with the aid of an apparatus of more advanced design for iron (1) and silver (2) (after Farnsworth).

Fig. 7. The same as in Fig. 7a, for copper and nickel (after Farnsworth).

to the primary ones, and that as the velocity of the primary beam increases the relative number of secondary electrons with low velocities increases. Electrons with small velocities appear at primary velocities that vary from metal to metal; the corresponding values of the primary velocities lie, for the metals investigated, in the interval from 9 to 15 V.

Somewhat later Farnsworth repeated the measurement of secondary emission for iron, nickel, silver, and copper, using a more advanced apparatus (Fig. 3), the advantages of which, in comparison with the apparatus used previously, consisted in the following: 1) owing to the new design of the electron gun it was possible to obtain a more intense beam of electrons with low velocities, and 2) the collector of secondary electrons had the form of a sphere whose diameter was much larger than the dimensions of the specimen under investigation, so that the field was close to radial.

The curves \(\sigma=f(V_{\text{prim}})\) for iron and copper, obtained with the aid of this apparatus, proved to coincide with the curves obtained previously; the curves for nickel and silver, however, revealed a larger number of minima and maxima than had been observed earlier. These curves are given in Fig. 7.

The investigation of the velocity distribution of secondary electrons, in agreement with the previous results, showed that, up to a definite value of the velocity of the primary beam, varying from metal to metal, the greater part of the secondary electrons has an energy approximately equal to the energy of the primary electrons. In addition, it was found that, for primary velocities below 35–40 V, for the four metals investigated there are no secondary electrons with velocities close to zero.

Summing up his work, Farnsworth comes to the following conclusion: between the curves expressing the dependence of \(\sigma\) on the velocity of the primary electrons and the curves of the velocity distribution of the secondary electrons it is impossible to establish a correspondence; the maxima and minima of the curves \(\sigma=f(V_{\text{prim}})\) must be attributed to the selectivity of reflection of electrons of definite velocities, determined by the structure of the surface.

Thus Farnsworth, in contrast to other authors (see below), brings to the foreground the properties of the surface, and not the properties of the individual atoms of the substance. In order to confirm this point of view he, in a subsequent paper\(^{45}\), compares the secondary emission of phosphor bronze and of copper single crystals. The curve \(\sigma=f(V_{\text{prim}})\) for phosphor bronze containing 95.4% copper, 4.5% tin, and 0.1% phosphorus proved to be quite unlike the corresponding curve for pure copper. Farnsworth believes that this undoubtedly indicates that the dependence on the velocity of the primary electrons is determined by the arrangement of the atoms, and not by their structure, since in the opposite case almost no difference between the curves for copper and phosphor bronze should have been observed. This view is also confirmed by the fact that the curves \(\sigma=f(V_{\text{prim}})\) for copper single crystals and for chemically pure copper in the form of a polycrystalline specimen also differ strongly from one another. In Fig. 8 are presented the curves \(\sigma=f(V_{\text{prim}})\) for phosphor bronze (I), polycrystalline copper (II), and a copper single crystal (III).

1. A whole series of investigators\(^{46,47,24,48,49}\) adhered to views opposite to Farnsworth’s point of view, considering that the secondary-emission properties of a surface are determined by the properties of the atoms of the substance themselves—by the structure of their electron shells—and attempted in this way to explain the fine structure of the curves \(\sigma=fV_{\text{prim}}\). The same view, as is known, was originally expressed by Davisson and Kunsman\(^{50}\).

Petri, in his first paper\(^{24}\), investigated the secondary emission of iron, molybdenum, and nickel, previously degassed by heating in vacuum. The results of the measurements showed that the curve \(\sigma=f(V_{\text{prim}})\) for iron has 25 small maxima, the curve for nickel—16, and the curve for molybdenum—also 16. Some of the critical potentials (i.e. values of \(V_{\text{prim}}\) corresponding to the maxima) proved to coincide with the energy levels for soft X-rays. Especially good agreement was found for iron, at values of the critical potentials below

40 V, and with the levels found for this metal by Thomas[^51]. Petri’s and Thomas’s data are compared in Table 1.

In his next work[^48] Petri recorded the curves \(\sigma=f(V_{\text{primary}})\) for tungsten, copper, and gold. On these curves, too, small maxima were obtained, which could be compared with energy levels for soft X-radiation, as is seen from Table 2.

Fig. 8. Curves \(\sigma=f(V_{\text{primary}})\) for polycrystalline copper (1), phosphor bronze (2), and a copper single crystal (3) (after Farnsworth).

TABLE 1

Schulman[^47] studied the secondary emission of iron, using a three-electrode tube that had a tungsten cathode, an iron grid, and an iron anode. By the usual interpretation of the curve \(\sigma=f(V_{\text{primary}})\) \((h\nu=eV)\), he obtained the sharply expressed \(M_\alpha\), \(M_\beta\), and \(M_\gamma\) lines of the X-ray spectrum of iron. The calculated series limit proved to lie near 177.4 V.

Krefft[^49] measured secondary emission for tungsten, using an apparatus that made it possible, during the measurements, to keep the plate under investigation in an incandescent state; the gas pressure in the apparatus did not exceed \(10^{-8}\) mm Hg; the measurement data were reproducible with an accuracy of up to 0.1%.

TABLE 2

The curves \(\sigma = f(V_{\mathrm{prim.}})\) were taken at a plate temperature from 1250 to \(1480^\circ\) K and for the interval of primary velocities from 10 to 700 V.

These curves exhibit a maximum at 15.3 V, a minimum at 20 V, and 18 small maxima located between 25 and 600 V. The positions of these maxima agree well with the data of Richardson and Chalklin\(^{52}\) on the soft X-ray radiation of tungsten (\(N\)- and \(O\)-levels).

One should also dwell on the degassing effect, carefully studied by Krefft. Krefft assumes that tungsten annealed at \(1500^\circ\)K cannot be regarded as completely degassed, and considers that the course of the curve \(\sigma = f(V_{\mathrm{prim.}})\) for values of \(V_{\mathrm{prim.}}\) from 10 to 25 V is due to the presence of adsorbed gas. Upon cooling of well-degassed tungsten in the first moments, usually, the maxima of the curve \(\sigma = f(V_{\mathrm{prim}})\) become more sharply pronounced. If the tungsten remains in the cooled state for such an interval of time during which only a very small quantity of gas can be adsorbed, then a number of new maxima appear on the curve. With adsorption of a large quantity of gas, the entire fine structure of the curve disappears.

Thus, both for and against the assumption concerning the influence of the structure of atoms on the secondary-emission properties of the surface there are sufficiently convincing experimental arguments, and it is hardly possible to give preference to one of these points of view. It would be more correct to admit that secondary emission is determined by both factors. In this connection one should mention the later work of Farnsworth,\(^{53}\) devoted to the diffraction of electrons by crystals of copper and silver. Owing to the improvement of the apparatus, Farnsworth was able to detect a fine structure of the diffraction maxima which, despite the similarity of the crystal lattices of silver and copper (differing only in the constant), differed substantially for the two metals. This compelled Farnsworth to express the quite plausible supposition that, in addition to the structure of the lattice, the structure of the atomic shells also plays a role in the diffraction of electrons.

1. Up to now we have spoken about the course of the curves \(\sigma = f(V_{\mathrm{prim}})\) in the region of relatively low values of \(V_{\mathrm{prim}}\). If the dependence of \(\sigma\) on \(V_{\mathrm{prim}}\) is traced at higher primary velocities, it is found that all the curves give a more or less broad maximum in the region of primary velocities of several hundred volts and then gradually decrease. The position of the maximum and the maximum value of \(\sigma\) vary from metal to metal. In Fig. 9 are given the curves \(\sigma = f(V_{\mathrm{prim}})\) for Be, Ba, Mo, and Ta, taken in the interval from 0 to \(5 \cdot 10^3\) V. In Table 3 are given the maximum values of \(\sigma\) and the voltage values corresponding to the maxima for various metals.

Copeland\(^{54,55,56}\) investigated the course of the curves \(\sigma = f(V_{\mathrm{prim}})\) in the region of primary velocities greater than that corresponding to the maximum, and he succeeded in establishing a connection between the course of the curves in this region and

SECONDARY ELECTRON EMISSION

TABLE 3

the atomic number of the corresponding metal. It turned out that the curve in the region beyond the maximum can be represented in the form of an inverse power function of the energy of the primary electrons,

\[ \sigma = k V_{\text{prim}}^{-s} \]

where $k$ and $s$ are constants for the given metal, and $s$ decreases with atomic number. On this basis Copeland

Fig. 9. Curves $\sigma = f(V_{\text{prim}})$ over a wide interval of primary velocities for various metals (after Copeland).

Fig. 10. Distribution curves of secondary electrons by velocities for molybdenum at different velocities of the primary electrons: 1) $V_{\text{prim}} = 10\,\mathrm{V}$, 2) $V_{\text{prim}} = 20\,\mathrm{V}$, 3) $V_{\text{prim}} = 40\,\mathrm{V}$, 4) $V_{\text{prim}} = 100\,\mathrm{V}$ (after Soller).

concluded that the fall of the curves beyond the maximum is due to an increase in the penetration depth of the electrons into the metal.

1. We must now examine in somewhat greater detail the distribution curves of secondary electrons by velocities, which are also important characteristics of the emitting surface

These curves for all metals have, in general, the same form and usually show two maxima: a low and broad one, corresponding to secondary electrons in the proper sense of the word (electrons with low velocities), and a high and very sharp one, referring to electrons scattered without loss of velocity. Fig. 10 gives such curves, obtained by Solmer^57 by the method of magnetic analysis for molybdenum at various primary velocities.

Solmer^57 investigated (on molybdenum) the influence of degassing on the course of the velocity-distribution curve. He found that, when a plate is calcined at a temperature of \(850^\circ\mathrm{C}\) for 20 hours, almost no changes are observed in the course of the distribution curves. Only under considerably stronger thermal treatments (40 hours at \(1250^\circ\mathrm{C}\)) do the curves change appreciably. These changes amount to a weakening of the broad maximum and a strengthening of the maximum for electrons reflected without loss of velocity.

Solmer also investigated the dependence of the height of the maximum for reflected electrons on the velocity of the primary beam. The curves he obtained turned out to have several maxima, and their positions corresponded to the values of the critical potentials found by Petri for molybdenum.

Rudberg^58, using the method of magnetic analysis, investigated the velocity distribution of secondary electrons for calcined plates of copper, gold, silver, platinum, and the oxides of magnesium, calcium, strontium, and barium. His measurements showed that the broad maximum of the distribution curve, referring to secondary electrons with low velocities, must to a significant extent be attributed to the gas film adsorbed on the surface. This follows from the fact that, in the case of curves taken from calcined metals, whose surfaces are certainly free of gas, the broad maximum is found to be considerably weakened, and alongside it several small maxima appear. The positions of these new maxima relative to the peak corresponding to elastically scattered electrons prove to be independent of the velocity of the primary electrons. This indicates that they arise from inelastically reflected electrons, which in reflection always lose the same (absolute) amount of energy. Thus these maxima are already characteristic of the surface of the metal itself.

Following Rudberg’s method (calcined metal, magnetic analysis), Haworth^59, ^60 investigated the velocity distribution for secondary electrons in the case of molybdenum. To obtain a good vacuum Haworth carefully degassed the bulb of his apparatus, heating it for 500 hours at a temperature of \(500^\circ\mathrm{C}\). The molybdenum plate under investigation was degassed by calcination for a total of 3500 hours, and during the last 1000 hours its temperature exceeded \(2100^\circ\mathrm{K}\). At the end of the degassing process the pressure in the apparatus was \(2 \cdot 10^{-8}\) mm Hg at

cooled plate and \(3\text{–}4 \cdot 10^{-8}\) mm Hg—with a heated one. The greater part of the measurements was carried out at a plate temperature of \(1400^\circ\) K.

Haworth’s measurements also showed that, in addition to the usual sharp maximum for elastically reflected electrons, there exists a further series of irregularities in the course of the curve. These new maxima may be classified as follows: 1) maxima for values of the energy of the secondary electrons 10.6, 22, and 48 V less than the primary energy (these maxima were observed by Rudberg); 2) maxima at values of the energy of the secondary electrons of 11, 24, and 35 V. The positions of all these maxima do not depend on the velocity of the primary electrons, and, thus, the groups of maxima (1) must be attributed in a definite way to inelastically reflected electrons, while the groups (2) must be attributed to the selectivity of secondary emission.

Haworth also investigated the relation between the number of elastically reflected electrons and the velocity of the primary beam. It turned out that the corresponding curve exhibits several maxima, some of which correspond to the voltages at which peaks of type (1) occur, while the rest must be ascribed to electron diffraction. The author gives an interpretation of these results based on the modern theory of metals.

Chilinskii\(^{64}\), by means of magnetic analysis, studied the velocity distribution of secondary electrons arising when silver is bombarded by fast primary electrons (with velocities from 2.1 to 30 kV). His measurements showed that the distribution curves have maxima whose positions depend on the velocity of the primary electrons. For voltages up to 10 kV, the maximum in the number of secondary electrons falls in the region of velocities from 0.6 to 0.7 of the initial velocity; at primary-electron velocities of 15–30 kV the maximum already lies between 0.7 and 0.8 of the velocity of the primary beam. The fall of the curve in the region of velocities beyond the maximum occurs the more rapidly, the greater the velocity of the primary electrons. On the side of velocities smaller than that corresponding to the maximum, the fall is characterized by the fact that the ordinate of the curve assumes a value equal to half the maximum at 0.3 of the primary velocity in the case of primary-electron velocities up to 10 kV, and at about 0.5 for higher values of the primary velocities. The form of these curves recalls that of the curves for a continuous X-ray spectrum.

Brinsmade\(^{62}\), also using the magnetic method, investigated the velocity distribution of secondary electrons emitted by aluminum at low velocities of the primary beam (5–175 V). He established the decrease, also observed by other authors, in the relative number of electrons with high velocities that arises as the velocity of the primary beam increases. Thus, according to his data, at \(V_{\mathrm{prim}} = 7\) V the number of secondary electrons scattered without loss of velocity is 95%, at 12 V—90%, at 35 V—10%, and at 175 V—2%.

1. We shall now dwell briefly on works that stand somewhat apart from those cited above, but which are more or less connected with one another.

The work of Baltruschaitis and Starke^63^ (published in 1922) apparently remained unknown to most investigators of secondary emission and had no influence on the general course of research in this field. As in all earlier works, these authors obtained almost identical curves \(\sigma = f(V_{\text{prim}})\) for all the metals studied.

Mac Allister^64^ investigated the secondary emission of copper and copper oxide. He found that \(\sigma\) is greater for copper oxide than for copper, as is also the “ionization potential,” i.e., the value of the accelerating voltage at which secondary emission appears. The experimental technique is of a very questionable character. Becker’s works^65^ were intended to confirm the author’s conviction that the mechanism of secondary emission is identical with the mechanisms of photoelectric and thermionic emission. However, the results obtained by him in no way confirm this point of view.

Tartakovsky and Kudryavtseva^66^ established the connection existing between secondary emission and ferromagnetism, showing that for nickel the secondary emission changes discontinuously at the Curie-point temperature.

Fig. 11. Characteristic of a dynatron

A considerable number of works^67^ is devoted to the study of the interfering action of secondary emission from the grids of cathode tubes. This phenomenon is especially pronounced in the case of oxide and thoriated cathodes, since during activation and in the course of operation of the tube the grid becomes coated with a metal of low work function. Secondary emission from the grid is usually combated by oxidizing it.

A whole series of authors—Moullin^67^, Adams and Campbell^68^, Geiner^69^, Penning and Kruithof^70^, and Ziegler^71^—investigated the Shott effect in secondary emission. We shall not dwell on these works either.

7. As an example of the practical use of secondary emission one should point to Hull’s dynatron^1,73^, in which secondary emission is used to obtain negative resistance. The dynatron is a vacuum tube having a filament, an anode in the form of a grid, and a cylinder surrounding it, which serves as the cathode of secondary emission. A positive potential relative to the filament is applied to the grid; the potential of the secondary-emission cathode must be lower than the grid potential. The characteristic of the dynatron is shown in Fig. 11, where the abscissa gives the voltage on the cylinder (relative to the negative end of the filament), and the ordinate gives the current strength in the cylinder circuit; the positive direction of current is taken to be that for which the electrons go from the filament to the cylinder. At voltages from 0 to 25 V the positive current increases. Beginning at 25 V, secondary emission becomes noticeable, and this current begins to decrease. At 100 V the number of secondary electrons proves to be

equal to the number of primary ones; the current in the cylinder circuit becomes zero. With a further increase of the voltage on the cylinder, the number of secondary electrons continues to grow, and the current in the cylinder circuit changes direction. At a voltage of about 175 V, the potential difference between the anode and the cathode of the secondary emission proves already insufficient to attract all the secondary electrons, and the “negative” current decreases. The curve again intersects the abscissa axis, and the positive current reaches a value corresponding to saturation. In the interval 50–150 V (for the tube to which the characteristic refers) the dynatron represents a negative resistance, varying almost linearly with the change in voltage.

The dynatron can be used as a generator or as an amplifier of current and voltage for almost all audio and radio frequencies.

V. Secondary emission of complex surfaces

1. In the preceding section, when considering the secondary emission of metals, we did not strive to adhere to the chronological sequence of the investigations and arranged the material according to the internal connection between the individual works. This, undoubtedly, was more appropriate and was feasible because the secondary emission of metals has been studied more or less thoroughly and comprehensively. We encounter an entirely different situation when we turn to the consideration of the secondary emission of complex surfaces.

As we have already indicated above, after the discovery by Davisson and Germer of electron diffraction, interest in secondary emission as such declined sharply, and subsequent work proceeded mainly along a new line. The years from 1929 to 1933 provide a minimum in the number of works on secondary emission, and interest in this phenomenon is awakened again only after the publication by Farnsworth[^2] of the remarkable results he achieved in amplifying photocurrents. Let us note that in the USSR the idea of using the secondary emission of photocathodes has an even longer history[^3], and even before Farnsworth’s article appeared, a work had been published devoted to the secondary emission of calcium and potassium-hydride surfaces[^75].

The works of recent years relate almost exclusively to the use of the secondary emission of oxygen–cesium photocathodes for amplifying photocurrents in various photoelectric devices, while the study of the phenomenon of secondary emission itself is carried out only incidentally. Therefore, with regard to the secondary emission of complex surfaces, there does not yet exist either sufficiently extensive experimental material or established viewpoints, and grouping the works by subject is not possible. In view of this, in the present section we shall adhere to another method of arranging the material: first we shall give, in chronological order, an account of the main results of the works, and in conclusion we shall consider the ways of practical use of secondary emission.

1. Oxygen–cesium photocathodes, like others used in modern photocells, are so-called composite surfaces. By this term we now denote a surface layer consisting of alternating layers of metal and dielectric, or layers of different metals.

As is known, the cathode of a cesium photocell consists of a metallic substrate (most often silver), on which, in one way or another, a layer of cesium oxide \(Cs_2O\) is formed, on the surface of which there are adsorbed \(Cs\) atoms. The thickness of the cesium-oxide layer may range from several molecular layers to several hundred molecules and is usually about 100 molecular layers. Photoelectric emission is mainly a consequence of photoionization of the cesium atoms adsorbed on the surface of \(Cs_2O\), but the photoelectric properties of the cathode depend extremely strongly also on the structure of the \(Cs_2O\) layer, since through this layer, from the metallic substrate to the outer surface, new electrons must pass to replace those emitted by the cesium atoms. In order for such replenishment of electrons to take place, cesium atoms and atoms of heavy metals must also be present inside the \(Cs_2O\) layer.^4 Oxygen–cesium cathodes give a very large value of \(\sigma\), which may reach ten.

Fig. 12. Diagram of Groshev’s experiments.

The so-called massive sensitized cathodes (for example, hydride–potassium and sulfur–potassium) have an analogous structure; in them the substrate is the alkali metal itself, the intermediate layer is a compound of this metal with some metalloid (hydrogen, oxygen, sulfur, etc.), and atoms of the alkali metal are present on the surface and inside this layer.

Cathodes of this latter type have scarcely been investigated with respect to secondary emission. The only work in this direction is that of L. V. Groshev,^75 who studied the secondary emission of potassium and of potassium treated by a discharge in hydrogen. The author used an apparatus whose diagram is shown in Fig. 12; here \(H\) is a tungsten filament serving as the source of primary electrons, \(A\) is the anode, by means of which these electrons were accelerated in the direction of the hollow ferrochromium cylinder \(B\), on whose obliquely cut end surface a layer of potassium was deposited, and \(C\) is the collector, which captured the secondary electrons.

Groshev found that for ferrochromium, for potassium, and for potassium treated by a discharge in hydrogen, \(\sigma\) does not depend on the velocity of the primary electrons in the velocity interval from 0 to 2500 V. He also found that a 15-fold increase in the integral sensitivity of potassium as a result of treatment of the surface by a discharge in hydrogen does not change the value of \(\sigma\) to any noticeable extent. The complete independence of \(\sigma\) from the velocity of the primary electrons in so wide an in-

interval is a very unexpected result, all the more so since the dependence on the velocity of the primary electrons is observed both for pure metals and for cesium photocathodes.

Farnsworth’s paper,^2 which marks an epoch in the history of secondary emission, is devoted mainly to questions of amplification of photocurrents by means of secondary emission (see this section below) in connection with a new system of television transmitter.^76 With regard to the secondary-emission properties of cesium cathodes, Farnsworth states only that $\sigma$ in the most favorable cases may reach 6. Farnsworth’s cesium cathodes were prepared in the usual way (cesium was deposited on oxidized silver).

In the work of Iams and Salzberg,^4 who constructed a photocell with photocurrent amplification by means of secondary emission (see this section below), data were given for the first time on the dependence

Fig. 13. Dependence of $\sigma$ on the velocity of the primary electrons for a cesium photocathode (after Iams and Salzberg).

Fig. 14. Scheme of Shmakov’s experiments.

of $\sigma$ on the velocity of the primary electrons for oxygen–cesium cathodes (cesium was deposited on the oxidized surfaces of massive silver plates). The dependence found is represented by the curve in Fig. 13, from which it is easy to see that $\sigma$ increases rapidly in the range of primary-electron velocities from 0 to 300 V, somewhat more slowly in the range 300–900 V, remains almost unchanged up to 1300 V, and then slowly decreases. It is interesting to note that the maximum of $\sigma$ in the case of a cesium cathode is located at appreciably higher voltages than for pure metallic surfaces.

P. V. Shmakov^77 studied the secondary emission of cesium cathodes using an apparatus shown schematically in Fig. 14. Here $K_1$ and $K_2$ are two cesium photocathodes facing one another, formed on silver deposited on the wall of a glass bulb; $A$ is a metallic grid located between the cathodes, which played the role of an electrode to which a voltage was applied that accelerated the primary electrons, torn by the light of the source $L$ (an incandescent lamp) from $K_1$, and at the same time served as a collector of the secondary electrons knocked out of $K_2$; $G_1$ and $G_2$—

galvanometers, \(E_1\) and \(E_2\) are batteries. Shmakov found that \(\sigma\) for a cesium cathode exhibits a maximum at a velocity of the primary electrons corresponding to about 900 V (see Fig. 15, where the numbers beside the curves indicate the magnitude of the collector potential relative to the secondary-emission cathode \(K_2\)), and that the greatest value of \(\sigma\) is 7.3.

With respect to experimental technique, Shmakov’s work is close to the work of Penning and Kruithof \(^{78}\). These authors also used photoemission from a cesium cathode to obtain primary electrons. The cross sections of the photocells they used are shown in Fig. 16. In all cases here \(K\) denotes the photocathode, \(B\) the secondary-emission cathode, and \(A\) a grid anode which simultaneously served as the collector for secondary electrons. The data obtained by these authors on the dependence of \(\sigma\) on the velocity of the primary electrons are shown in Fig. 17. In this case too we see that \(\sigma\) reaches a maximum (\(\sim 9\)) at a high accelerating potential for the primary electrons. Here it is \(\sim 800\) V. The authors attempted to establish a connection between the magnitude of \(\sigma\) and the integral sensitivity of the cathode. They did not succeed in doing so, however. They indicate that in many cases it was possible to reduce the sensitivity of the cathode (sometimes by a factor of 30) without any significant decrease in \(\sigma\).

Fig. 15. Dependence of \(\sigma\) on the velocity of primary electrons for a cesium photocathode according to Shmakov.

Fig. 16. Arrangement of photocells on which Penning and Kruithof investigated secondary emission.

This result fully confirms analogous data obtained by Groshev. The indicated absence of a connection between \(\sigma\) and the integral sensitivity is attributed by the authors to the fact that the sources of photoelectrons and of secondary electrons are not identical. Whereas photoelectrons arise as a result of photoionization of alkali-metal atoms adsorbed on the cathode surface \(^{79}\), secondary electrons can be released from deeper layers of the cathode surface (see above, the beginning of subsection 2 of this section).

In addition to the dependence of \(\sigma\) on velocity, Penning and Kruithof investigated the inertia of their photocells with secondary emission, the influence of small amounts of gas on their operation, and the phenomenon of the Schrot effect in them. We shall touch on the first two of the questions listed below.

Fig. 17. Dependence of \(\sigma\) on the velocity of primary electrons for a cesium cathode, according to Penning and Kruithof.

In considering fluctuations in a photocell with secondary emission, the authors proceed from the assumption that each primary electron releases a whole group of secondary electrons (including also the reflected ones), and that all electrons of such a group reach the collector simultaneously (the latter is true at not too high frequencies). The results obtained by the authors, however, are not sufficiently definite.

Fig. 18a. Change in the dependence of \(\sigma\) on the velocity of primary electrons with gradual thickening of a platinum layer on aluminum (according to Copeland).

Fig. 18b. Change in the dependence of \(\sigma\) on the velocity of primary electrons upon deposition of calcium on the surface of gold (according to Copeland).

The first and, for the time being, the only attempt at an analytical investigation of the secondary emission of continuous surfaces is the rather primitive work of Copeland\(^{80}\). In this work continuous surfaces were studied, consisting of layers of various metals deposited on other metals (Pt on Al, Ca on Au, Li on Ta, Ge on

Au), as well as from layers of machine oil on a gold substrate. The next two figures give curves for the dependence of \(\sigma\) on the velocity of the primary electrons. Fig. 18a refers to the deposition of platinum on aluminum; Fig. 18b, to the deposition of calcium on gold. In Fig. 18a curve 1 refers to pure Al, curves 2, 3—to an increasingly thick platinum coating. From this sequence of curves it is seen how gradually the dependence of \(\sigma\) on the velocity of the primary electrons, from that characteristic of Al (rapid rise at low velocities, rapid fall after the maximum), passes over into the dependence characteristic of Pt (a slower rise in the region of low velocities, a lower maximum situated in the region of higher primary velocities, a slower fall after the maximum). From the series of curves in Fig. 18b a similar transition is seen from the curve for Au to the curve for Ca. Here the changes take place in the opposite direction. As the thickness of the Ca layer increases, the steepness of the curve in the region of low primary velocities increases, the maximum rises, and the steepness of the fall beyond the maximum increases.

This course of change of the curves indicates that, at low primary velocities, emission of secondary electrons takes place closer to the surface than at high velocities. Experiments carried out with the coating of a metallic surface by oil showed that in this case there is an increase in secondary emission over the entire interval of primary velocities, as well as the appearance of a “fine structure” of the curve—the appearance of several smaller maxima.

1. Secondary emission can be used, and is used, for internal amplification of photocurrents. The corresponding devices are called electron multipliers or multipliers, and sometimes photoelements with secondary emission and photodynatrons. By internal amplification we mean an increase in the number of electrons reaching the collector (anode) of the device due to processes not associated with another source of primary electrons. Another kind of amplification of this type, besides secondary emission, is amplification of photocurrents due to ionization, which occurs in gas-filled photoelements.

According to the nature of the power supply, electron multipliers may be divided into multipliers operating on direct current and multipliers operating on alternating (high-frequency) current. Multipliers of the first group, in turn, are subdivided into single-stage and multistage, according to how many times, on its path from the cathode to the collector, the electron stream is directed onto surfaces that give secondary emission.

The single-stage multipliers include the photodynatron of Iams and Salzberg\(^4\), the arrangement of which is shown in Fig. 19; the photoelements with which Penning and Kruithof worked (Fig. 5); and also the photoelement developed at the All-Union Electrotechnical Institute, whose construction is shown in Fig. 20. In Figs. 19 and 20, \(K_1\) denotes the photocathode, \(K_2\)—the cathode of secondary

emission, and \(A\) is the collector of secondary electrons, serving at the same time to create an accelerating field for the primary electrons. Comparing these two types of multipliers, we must recognize that the design shown in Fig. 19 is the more rational one,

Fig. 19. Diagram of the Iams and Salzberg photodynatron.

Fig. 20. Diagram of a photoelement with secondary emission developed at the VEI.

Fig. 21. Diagram of Gerlich’s photoelement with secondary emission.

since the cathode of secondary emission hardly obstructs the access of light to \(K_1\), and, moreover, the closer arrangement of the electrodes makes it possible to use lower voltages.

A similar photoelement was described by Gerlich. A transverse section of this photoelement is shown in Fig. 21, where \(K_1\) denotes the ordinary oxygen–cesium cathode, \(A\) the anode, and \(K_2\) the cathode of secondary emission, consisting of an aluminum or molybdenum plate with a slit \(O\) for the admission of light. The amplification of the primary current obtained by Gerlich was about 2.25.

Fig. 22. Characteristic of the negative resistance of the secondary-emission cathode circuit (after Iams and Salzberg).

Fig. 23. Frequency characteristic of the Iams and Salzberg photodynatron.

Iams and Salzberg carried out a fundamental study of the properties of photoelements with secondary emission (see also Shmakov’s article cited above). We shall present some of their data. Fig. 22 shows the dependence of the negative resistance of the cathode circuit.

of secondary emission on the voltage at the electrodes under a constant luminous flux of 0.1 lm and a constant collector voltage equal to 250 V. The presence of negative resistance makes it possible to use the photodynatron for generating oscillations (this is also indicated by Shmakov; see the article cited above).

Fig. 23 gives the frequency characteristic of the Janes and Zaliberg photodynatron at a collector voltage equal to 250 V, a secondary-emission cathode voltage of 215 V, and illumination by a luminous flux varying according to the law \(\Phi=\Phi_0(1+\sin at)\), with \(\Phi_0=0.15\) lm. Fig. 24 shows analogous data obtained by Penning and Kruythoff\(^{78}\). The line and points in the drawing depict the ratio of the amplitudes of the alternating current in a photoelement with secondary emission and in an ordinary vacuum photoelement, arising under illumination by light whose intensity varied almost sinusoidally, to the frequency of the intensity oscillations. Thus

Fig. 24. Frequency characteristic of a photoelement with secondary emission (according to Penning and Kruythoff).

the inertia in photoelements with secondary emission does exist, but it is considerably smaller than the inertia of gas-filled photoelements.

The same authors\(^{78}\) found that the presence of a small amount of gas in a single-stage multiplier can lead to a very considerable increase in the output of the instrument (up to 70 times compared with the primary photocurrent). Fig. 25 shows the dependence of the current to collector \(A\) on the potential of the secondary-emission cathode \(V_A\), at constant \(V_B\) and at different argon pressures in the photoelement. Such large amplifications, obtained due to the presence of negligible amounts of gas, led the authors to the following explanation of the phenomenon. Most secondary electrons do not reach the collector immediately, but pass through the openings of the grid and then oscillate between cathode \(K\) and secondary-emission cathode \(B\). This motion leads to the effective path of the electron proving greater than the length of its mean free path, and before reaching the cathode it manages to produce a considerable number of ionizations. The fact that the effect is due to the action of secondary electrons is indicated by the existence of a maximum on the curves of Fig. 25, located between the maximum for \(\sigma\) and the maximum of ionization (the latter corresponds to \(V_B=0\)).

Lenning and Kruithof point out that the advantage of such multipliers in comparison with gas-filled photocells is their high amplification with comparatively low inertia (owing to the low gas pressure). At the same time, these instruments also have a number of disadvantages. They are very sensitive to the slightest changes in the gas pressure and the anode potential, and, in addition, the sensitivity of the photocathode rapidly decreases during operation as a result of bombardment by positive ions. The latter disadvantages can be combated by introducing a fourth electrode into the multiplier (grid \(H\) in Fig. 16, IV).

Multistage multipliers also exist in several designs. Fig. 26 shows Farnsworth’s multiplier\(^2\).

Fig. 25. Dependence of the current to the collector on the potential of the cathode of secondary emission at various gas pressures and constant collector potential (after Lenning and Kruithof).

Fig. 26. Arrangement of Farnsworth’s multistage multiplier.

In this type of multiplier, multiple bombardment of the surface giving secondary emission (this is the inner surface of the tube walls between the leads \(K_1\) and \(K_2\), representing an oxygen–cesium cathode) is achieved by the fact that each knocked-out electron comes under the action of two fields—one radial, produced by the potential difference between the cathode on the surface of the bulb and a thin wire stretched along the axis of the instrument, and the other longitudinal, arising owing to the potential difference applied between \(K_1\) and \(K_2\) (for this purpose the layer of silver on which the cesium cathode is formed is deposited not directly on the glass, but on a thin layer of nickel or platinum which does not oxidize when treated with oxygen and has a resistance of \(0.5\)—\(2\text{ M}\Omega\); owing to this, a uniform potential drop is produced along the entire tube). Under the action of

of these fields the primary electron, torn out by the light penetrating into the tube through the window \(O\), strikes the opposite wall at a distance determined by the diameter of the tube and by the ratio of the two fields, and there produces secondary emission. The secondary electrons move farther on in the same manner, and the process continues until the electrons are collected by the funnel-shaped collector located in the lower part of the tube.

Fig. 27 shows the multistage multiplier of the Kubetsky system (Institute of Telemechanics). In this instrument the individual cathodes of secondary emission, likewise located on the inner surface of the bulb, are separated by nonconducting gaps of the glass walls. The direction of the electrons from cathode to cathode is effected by the simultaneous action of electric and magnetic fields. The electric field is produced by a sectionalized battery or by a potentiometer circuit (when operating with a rectifier, as is usually the case), while the magnetic field is produced by means of a permanent magnet; the direction of the magnetic field is perpendicular to the plane of the drawing. Essential disadvantages of this design are the necessity of producing a magnetic field and of arranging a potentiometer circuit. By introducing a thin wire placed axially, the first of these disadvantages can be eliminated.

Fig. 27. Multistage multiplier of the Institute of Telemechanics.

Fig. 28. VEI multiplier.

In Fig. 28 is shown the scheme of a multistage multiplier developed at VEI (Timofeev and Kvartskhava). This multiplier operates without a magnetic field. Electrons released on the upper surface of one of the funnels (each of which is made of silver and treated in the usual manner to obtain a caesium cathode) are carried by the field, created by the next funnel and acting through the opening of the first, onto the surface of the second funnel

SECONDARY ELECTRON EMISSION

etc. This multiplier also requires the use of a sectioned power supply.

Zworykin[^81] has recently constructed a new type of multiplier, likewise operating with only a single electric field, in which electrostatic focusing of the beam is employed. The diagram of this device is shown in Fig. 29. \(K_1\) is a photocathode serving as the source of the primary electrons; \(K_2, K_3 \ldots\) are secondary-emission cathodes. Focusing of the electron stream occurs owing to the action of the electric fields in the spaces between the electrodes \(A, B, C \ldots\). All the cathodes are silver surfaces treated in the usual way with oxygen and cesium. The potential difference between adjacent electrodes is from 200 to 400 V. With a sufficiently large number of stages Zworykin obtained amplification by millions of times, while the output current reached 8 mA. He also proposed several other types of multipliers[^81], both with electrical and with mixed control.

Fig. 29. Diagram of Zworykin’s multiplier.

It is easy to see that, if the properties of the individual stages are identical (the same \(\sigma\)) and the voltages between stages are equal, the amplification factor of the multiplier (i.e., the ratio of the output current to the current from the photocathode) will be

\[ \mu = \sigma^n \]

where \(n\) is the number of stages, i.e., the number of secondary-emission cathodes.

With the aid of the static multipliers described, it proves possible to obtain amplifications of hundreds of thousands and millions of times only in the case when the primary photocurrent is a very small quantity. At large primary currents the amplification turns out to be lower. This occurs, on the one hand, because at high current densities space charges begin to have an effect, and on the other hand because the secondary-emission cathodes cannot withstand significant current densities during prolonged operation and lose their emissive properties. The output currents usually amount to fractions of a milliampere and, in the best case, several milliamperes.

An exception to this rule is the radio-frequency multiplier of Farnsworth[^2], already described in the pages of this journal[^76], by means of which it has been possible to obtain a steady output up to 0.5 A.

Secondary Emission of Dielectrics

1. Secondary emission under bombardment by an electron stream can occur not only in the case of metallic and composite surfaces, but also when dielectric surfaces are bombarded. Phenomena of this kind have so far scarcely been investigated, although they are already encountered in practice.

As early as 1906 Lilienfeld82 discovered an anomalous change in the potential drop in the positive column of a gas discharge, which did not decrease continuously as the gas pressure was reduced, but, beginning at a certain pressure value, again increased rapidly. Lilienfeld83 attributed these phenomena to the existence of positive-charge carriers possessing small mass. Langmuir, repeating Lilienfeld’s experiments, showed, however, that the phenomena indicated are a consequence of positive charging of the walls of the discharge tube, arising as a result of the emission of secondary electrons by the glass. This is indicated, among other things, by the circumstance that the places where the electrons strike the glass (the fluorescing parts of the surface of the tube glass) prove to be strongly heated. This shows that they are charged to a high potential relative to the cathode, which can only be a consequence of the loss by these regions of negative charges, i.e. a consequence of secondary emission, for \(\sigma > 1\).

Fig. 30. Dependence of the secondary emission of glass on the angle of incidence of the primary beam (after Schmidt).

Later, a systematic investigation of the secondary emission of insulators was carried out under the direction of Wehnelt84 in the laboratory of the University of Berlin. Nickel85 repeated Lilienfeld’s experiments and established, in agreement with Langmuir, that the observed phenomena must be attributed to positive charging of the tube walls as a result of secondary emission from the glass.

Wehnelt86 discovered an interesting phenomenon, consisting in the fact that, for oblique incidence of a primary beam of sufficiently fast electrons (1300–3000 V) on an insulator, the number of emitted secondary electrons increases as the angle of incidence increases; this increase continues up to a certain limiting value of the angle of incidence, at which a sudden drop in secondary emission occurs, and then, as the angle continues to increase, a new rise begins (Fig. 30).

This phenomenon was studied in detail by Schmidt87 and Beischlag88. The first of these authors, working with glass, mica, and other insulators, established that the value of the limiting angle is the greater, the greater the velocity of the primary electrons, and that at \(V_{\text{prim}} = 3000\ \mathrm{V}\) the phenomena are in general no longer observed; all the insulators studied behaved in the same way and in the same voltage interval. Beischlag investigated the dependence of the value of the limiting angle on temperature and found that it increases with increasing temperature.

Klemperer89 explained this phenomenon by total reflection of electron waves at the boundary of the dielectric and calculated the internal potential of the dielectric. Ioffe90 showed that the same results can be obtained without resorting to wave mechanics and merely admitting the exis-

SECONDARY ELECTRON EMISSION

existence on the surface of the dielectric of a double layer with its positive side facing outward.

Dane and Shmerwitz \(^{91}\) tested both proposed theories of reflection by measuring the velocity distribution of secondary electrons at the angle of “total reflection,” when all secondary electrons should have velocities close to those of the primary electrons. They, however, did not find electrons with velocities greater than 150 V.

The distribution of secondary electrons emitted by insulators was studied in greater detail by Kalckhoff \(^{92}\) (by the method of magnetic analysis). He established that the distribution curves have a single maximum and in shape resemble a Gaussian curve. The general form of the curve proved to be independent of the velocity of the primary beam and of the angle of its incidence on the surface under investigation. Only the position of the maximum depends on these factors; in the investigated range of angles and primary velocities it lay between 8 and 22 V. When plotting the curve expressing the dependence of the velocity corresponding to the maximum of the distribution curves on the angle of incidence, one obtains the same curve as for the dependence of \(\sigma\) on the angle. A jump in these curves is also observed at primary velocities greater than 1500 V.

Fig. 31. Discontinuity of the current–voltage characteristic of a photocell (after Penning and Moubis).

Secondary emission from glass very often disrupts the normal operation of electronic devices because of the creation of extraneous electric fields. Thus, Molthan \(^{93}\) points out that charging of the glass walls of cathode-ray-tube bulbs is the cause of the existence of “double” characteristics \(I_a - E_a\). The work of this author showed that the transition from one characteristic to another under certain conditions can occur in a jump-like manner. This led him to the idea of using secondary emission from glass to construct tubes capable of serving as almost inertia-free relays.

The presence of secondary emission from glass surfaces was demonstrated very clearly by Penning and Moubis. \(^{94}\) It is known that when current–voltage characteristics of photocells are taken, with the anode voltage varied in small intervals, a jump-like change of current is very often observed (especially in the case of vacuum photocells). An example of such a characteristic (borrowed from the cited work of Penning and Moubis) is shown in Fig. 31. With a gradual increase of the anode voltage from zero to the value \(V_h\), the photocurrent increases gradually. At \(V = V_h\) it instantaneously changes by a finite amount. Conversely, when the anode voltage is decreased from values greater than \(V_h\), there occurs a smooth decrease of the photocurrent down to \(V = V_n\), where it again

changes abruptly, taking on the value corresponding to the lower part of the characteristic.

Penning and Moubis established that the quantity \(V_h\) depends on the intensity and wavelength of the incident light, and also on the duration of illumination. This last quantity, for obtaining one and the same \(V_h\), proved to be inversely proportional to the strength of the photocurrent. All this suggests that the cause of the phenomenon must be regarded as the secondary emission of the glass surface of the bulb. To prove this, the authors used a photoelement in which, opposite the photocathode, instead of a window there was a secondary-emission cathode (cf. Fig. 16), and they investigated the current–voltage characteristics of such a photoelement with the secondary-emission cathode connected to the photocathode through a high resistance (this corresponds to leakage along the glass surface in an ordinary photoelement). As a result, the characteristic of this system proved to be completely identical with the stepped characteristic of an ordinary photoelement.

The abrupt change of photocurrent in an ordinary photoelement must be accompanied by a jump in potential on the inner surface of the window. This was also found by Penning and Moubis. For this purpose they coated the outside of the window with a layer of tinfoil and connected it to one pole of an electrostatic voltmeter, the other pole of which was connected to the cathode. At the moment the photocurrent changed, a change in potential also occurred.

The authors point out that, by means of secondary emission from the surface of the window of a photoelement, one can increase the output of the photoelement; for this purpose (in the case of a vacuum photoelement) it is sufficient to apply a sufficiently high anode voltage.

It should be noted here that, in the case under consideration, we are not dealing with secondary emission of a dielectric in pure form. This is indicated by the fact that here the phenomena take place in the region of very low primary velocities (\(<30\ \mathrm{V}\)), whereas in the experiments of Langmuir, Lilienfeld, and others, voltages of the order of hundreds and thousands of volts were necessary. In photoelements the glass surface is, in all probability, covered with a thin (monatomic) adsorbed film of an alkali metal, facilitating the tearing out of secondary electrons.

VII. Conclusion

Summing up the results of what has been set forth above, we must first of all note that, despite the considerable number of works devoted to secondary emission arising under the action of electron bombardment, this phenomenon has by no means been fully investigated.

Even in the case which at first glance seems the simplest, i.e. in the case of secondary emission of metallic surfaces, on the basis of the available data one cannot form a definite idea of the mechanism of emission.

The presence of fine structure in the curves \(\sigma = f(V_{\mathrm{per}})\) indicates the great importance of the structure of the surface and, probably, also of the properties

of individual atoms. It is quite possible that at higher primary velocities the mechanism of emission differs from that at low velocities.

The major role of the surface layer is also indicated by the strong change in the curves \(\sigma=f(V_{\text{perv}})\), which occurs when the surface is cleaned by degassing metals \(^{95,96}\). The course of this change is qualitatively close to the course of the change in the work function for photoelectric emission, which also occurs during degassing \(^{97}\). This would seem to indicate a direct dependence of secondary emission on the work function; but, on the other hand, comparison of these quantities for different metals \(^{98}\) does not make it possible to establish a connection between them.

Still less is known regarding the secondary emission of complex surfaces. Strictly speaking, with the exception of the dependence of \(\sigma\) on the velocity of the primary electrons, and then only for oxygen–cesium photocathodes, we have no information on the emission of surfaces of this type. Even the question, important for the design of multipliers, of the dependence of \(\sigma\) on the angle of incidence of the primary beam (such a dependence for pure metals was indirectly discovered by Lange \(^{99}\)) has not yet been investigated.

The enormous practical importance that the secondary emission of photocathodes has acquired gives grounds for believing that further investigations of this phenomenon will proceed chiefly along the path of studying the secondary emission of complex surfaces. This direction of work may also yield more for elucidating fundamental questions, since in the case of complex surfaces the experimenter has at his disposal a significantly larger number of factors that can be varied at will than in the case of simple metallic surfaces.

In application to photocathodes, secondary emission, probably, can already now prove useful for investigating their structure and photoemission properties. [Here one should mention the interesting experiments of Dember \(^{100}\), who observed the simultaneous action of photon and electron bombardments and thereby discovered both a change in the total electron yield and a change in the spectral sensitivity of the surface (metallic).] In the future, when the connection between the parameters characterizing a surface and its secondary-emission properties has been established, secondary emission may prove, alongside electronographic and X-ray analyses, to be one of the means for studying the structure of surfaces.

Alongside the secondary emission of photocathodes, in new electronic devices (for example, Zworykin’s iconoscope) the secondary emission of dielectrics plays an essential role. This phenomenon, which has also not yet been studied sufficiently fully, will find interesting applications in electro-vacuum technology.

Note added in proof. In the time that has elapsed since the submission of the manuscript of the present review, a number of new works have been published. Let us note some of them.

Ziegler (M. Ziegler, Physica 3, 307, 1936) published a continuation of his investigations on the proto-effect in secondary emission. Zworykin, Morton, and Malter (V. K. Zworykin, G. A. Morton a. L. Malter, Proc. Inst. Radio Eng. 24, 351, 1936) reported on the study of multistage multipliers carried out in the laboratories of R. C. A. This article contains, among other things, indications concerning the calculation of multistage multipliers. Henneberg, Orthuber, and Steudel (W. Henneberg, R. Orthuber u. E. Steudel, Z. techn. Phys., No. 4, 1936, p. 115) gave the theory of the dynamic multiplier of Farnsworth.

A quantum-mechanical treatment of the emission of secondary electrons for pure metals was made by Fröhlich (H. Fröhlich, Ann. Phys. 13, 229, 1932). The results of his calculations, however, do not give good agreement with experiment^54–56.

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