SECONDARY ELECTRON EMISSION OF METALS UNDER ELECTRON BOMBARDMENT

N. D. Morgulis, Kiev

1. Introduction

As is known, when a metallic surface is bombarded by a beam of fast primary electrons, secondary electrons are knocked out of it, the number of which may under certain conditions exceed the number of primary electrons[^1]. This long-known phenomenon of secondary electron emission from metals has already been investigated many times, as a result of which certain general regularities have been established; these, however, in their individual details have often agreed very poorly with one another. Even the investigations of recent years, in which quite exceptional measures—primarily of a vacuum-technical character—were employed in order to carry out the experiment in as pure a form as possible, have still not brought clarity to a whole series of questions concerning this phenomenon. The theory of this question is likewise still insufficiently developed; at present it is in fact limited to only a single work by Fröhlich[^2], which treats, approximately, only the emission of pure metals. Meanwhile the phenomenon of secondary emission is of considerable interest not only from the point of view of elucidating the physical processes occurring in it, but also from the point of view of its role in the technology of electron-vacuum devices. This phenomenon—the dynatron effect—was encountered long ago in the operation of electron tubes, where it was combated and attempts were made to eliminate it as a factor adversely affecting the normal operation of the tube. The attempt, however, to construct an electron tube using this phenomenon—the Hull dynatron—nevertheless did not lead to practically significant results[^3]. During the last approximately two years, however, we have observed enormous progress in the direction of the practical use of secondary electron emission for the purpose of amplifying weak primary currents, progress which has led to designs of electron-vacuum devices that are entirely new in type and exceptional in their properties, and, above all, to the so-called photodynatrons[^4]. It is enough to point out that in a modern multistage photodynatron it proves possible to obtain amplification of a weak primary photocurrent in the same tube by mil-

lion times. Such development of the technique of tubes with secondary-electron amplification in turn gives a new impetus to investigations of this phenomenon. What is now very essential is not so much the investigation of the emission of pure metals as that of metals covered with various films, which correspondingly affect the phenomenon of interest to us. Unfortunately, at present we have a very limited number of studies devoted to the secondary emission of metals covered with films, and, undoubtedly, in the near future one should expect very strong activity on the front of these investigations. Therefore the task of the present review is to give a summary of the data now available on secondary emission, primarily of metals covered with films. As regards the secondary emission of pure metals, here we shall confine ourselves to a very condensed survey of these works, since this question has already been discussed more than once in the past[^1].

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2. Secondary emission of pure metals

As was already indicated above, despite the numerous investigations of the secondary-electron emission of metals, at the present time we still do not always obtain wholly unambiguous results of the investigations. One of the main reasons for this is that the surface of the metal under study must be very well cleaned of contamination, which in particular requires exceptional thoroughness in its degassing. In modern work serious attention is paid to this point, and it is not surprising that here we quite often encounter indications that, say, the pumping and degassing of the tube with the object of investigation continued for several days in succession, or even longer.

When fast primary electrons strike the surface of a metal, we observe the emission from it of electrons which, roughly speaking, may be called secondary. In fact the matter is, of course, considerably more complicated, and the beam of emitted electrons consists approximately of three groups of different nature, namely: 1) elastically scattered primary electrons, which in this process have retained almost all their primary kinetic energy \(V_p\); 2) inelastically scattered primary electrons, which upon scattering in the metal have lost part of their primary kinetic energy \(V_p\); and 3) actual secondary electrons, i.e. electrons of the metal knocked out of it by the impact of the primary electrons. The simplest indication that these secondary electrons are really present among the emitted electrons may be the circumstance that the current intensity of the secondary electrons \(I_s\) can sometimes exceed the current intensity of the primary electrons \(I_p\), i.e. in this case
\[ \sigma=\frac{I_s}{I_p}>1. \]
On the other hand, evidence for the presence of elastically scattered primary electrons may be the presence, in the spectrum of the velocity distribution of the emitted electrons, of such a group whose velocities correspond to the velocities of the primary electrons. In the furth—

in the following, when speaking of secondary emission, we shall almost always understand by this the total effect of all three indicated groups.

Fig. 1 shows the distribution of the potential at the surface and inside the metal. Here \(W_a\) is the total potential jump at the metal surface, \(W_i\) is the maximum kinetic energy of the electrons in the conduction band inside the metal at \(0^\circ\) K. In addition to the conduction electrons, which densely occupy all energy levels in the metal (at \(0^\circ\) K), for whose energy we have

Fig. 1.

\[ 0<\varepsilon<W_i=\frac{h^2}{2m}\left(\frac{3n}{8\pi}\right)^{\frac{2}{3}}, \]

there also exist in the metal bound atomic electrons, situated, as shown in Fig. 1, on discrete or slightly broadened (for levels close to the conduction band) energy levels.

A primary electron having kinetic energy \(V_p\), upon entering the metal, will have there the energy \(V_p+W_a\). This energy, or a part of it \(\Delta V\), it can give up to the electrons of the metal, and here the following two cases should be distinguished (assuming that the metal is at \(0^\circ\) K):

1. The energy \(\Delta V\) is transferred to a conduction electron, and if \(\varepsilon\) is the initial energy of the conduction electron, it is necessary only that the level \(\varepsilon+\Delta V\) be free, i.e. at \(0^\circ\) K \(\varepsilon+\Delta V>W_i\). For this primary conduction electron to escape immediately beyond the limits of the metal, it is necessary that \(\varepsilon+\Delta V>W_a\), or \(\Delta V>W_a-\varepsilon\).

2. The energy \(\Delta V\) is transferred to an atomic electron bound on a discrete level—in this case this energy may have not any arbitrary, but a discrete value, or, more precisely, a band of values; i.e. here \(\Delta V>\varepsilon_a+W_i\), where \(\varepsilon_a\) is the “excitation” energy of the given atomic electron, the magnitude of which is determined as shown graphically in Fig. 1. For the direct escape of this atomic electron from the metal, naturally, the condition \(\Delta V>\varepsilon_a+W_a\) is necessary. However, if \(\varepsilon_a+W_i<\Delta V<\varepsilon_a+W_a\), we can nevertheless observe the emission of secondary electrons owing to the following process: the atomic electron will first be excited, i.e. transferred to one of the levels of the conduction band; however, immediately a redistribution of electrons will occur, and the vacated level will at once be occupied by one of the electrons passing to it from the conduction band. In this process a quantum of soft X-radiation is emitted, which can be absorbed by one of the conduction electrons, which may lead to a photoelectric effect, i.e. to the escape of this electron from the metal, provided only that the energy of the quantum is greater than \(W_a-\varepsilon\). Thus, in this case the emission of secondary electrons is effected by a more complicated path, establishing a connection

between this phenomenon and the phenomenon of absorption of soft X-rays in a metal.^5 A number of authors have drawn attention to this connection,^6 and in modern experimental studies considerable attention is devoted to it.

Then, from all that has been said, it is clear that an increase in temperature should lead to an increase in secondary emission; however, if one recalls how relatively little the energy distribution of electrons in a metal changes when the temperature is raised to approximately 1000–1500°K, it follows that the secondary emission should also change only to a very slight, practically imperceptible degree, which is fully confirmed by experimental data.

Experimental study of the secondary emission of pure metals is usually carried out in tubes that differ little from one another in principle. Fig. 2 shows a tube typical for this case, with its circuit, which Warnecke^7 used for studying the secondary emission of tantalum. The electrons from the gun pass inside the spherical electrode and strike the surface of the metal under investigation. This surface can be degassed and heated during the investigation to the required temperature by means of an incandescent spiral placed behind it. The total current to the surface under investigation and to the sphere is the current of primary electrons \(I_p\), while the current to the sphere alone is the current of secondary electrons \(I_s\), in the simplified sense indicated above, i.e. actually the current of all electrons leaving the surface. On the other hand, the spherical-condenser system implemented in this case makes it possible to measure not only the secondary-emission yield

\[ \sigma = \frac{I_s}{I_p} \]

for various experimental conditions, but also the velocity distribution of the secondary electrons; sometimes deflection in a magnetic field is used for this purpose.

Fig. 2.

Let us now turn briefly to the most essential results obtained in experimental studies of the secondary emission of pure metals.

First of all let us address the question of how secondary emission depends on the energy of the electrons in the primary beam—on \(V_p\). This question has been studied many times for different metals, and approximately unambiguous results have been obtained here, namely: the dependence of the secondary-electron current \(I_s\), or of the yield

\[ \sigma = \frac{I_s}{I_p}, \]

on the magnitude of \(V_p\) has, for all metals, the form shown graphically in Fig. 3 for molybdenum in the non-degassed \((A)\) and degassed \((B)\) states.^8 Secondary emission

(Fig. 3) appears in general at \(V_p\) slightly greater than zero, then rapidly rises to a maximum and, finally, begins gradually to decrease. For most pure metals the maximum value of the quantity \(\sigma\) corresponds approximately to 1.2—1.5; this maximum lies at values \(V_p = 300—600\ \mathrm{V}\), and, finally, \(\sigma = 1\), or \(I_s = I_p\), at \(V_p = 150—200\ \mathrm{V}\). An un-degassed surface, as is seen from Fig. 3, can give considerably altered data, and in particular the value of \(\sigma\) is then usually greater than for a perfectly pure metal with a well-degassed surface.

Fig. 3.                  Fig. 4.

A typical curve of the distribution of the initial energies \(V_0\) of secondary (i.e. in the sense of all electrons leaving the metal) electrons is presented in Figs. 4 and 5 for molybdenum\(^9\), for regions of small and large values of \(V_0\). Its main characteristic features are as follows: among the emitted electrons there are almost none that would have velocities sufficiently close to zero; then this curve gives a broad maximum in the region of relatively small values of \(V_0\), corresponding to a large group of slow secondary (in the actual sense of the word) electrons (Fig. 4); after this the curve decreases slowly, but nevertheless extends to values corresponding to the velocities of the primary electrons, thereby indicating the presence among those leaving the metal of elastically scattered primary electrons (Fig. 5).

In Figs. 3, 4, and 5, against the general background of smoothly running curves, we sometimes observe peculiar anomalies, apparently of the same nature. Curves of the type of Fig. 3 often reveal the presence of a “fine structure,” i.e., in other words, of very small local maxima and minima not visible in Fig. 3. On the other hand, the velocity-distribution curve usually gives, against the general continuous background, a number of fairly noticeable maxima. Both these phenomena are at present customarily associated with the discrete character possessed by

of the phenomenon of excitation of soft X-rays upon excitation of a bound atomic electron by the impact of a fast primary one, with the subsequent emission of a secondary electron upon absorption in the metal of a quantum of this radiation—this process has already been analyzed by us above\(^{6}\). It should be noted that, in this respect, the matter is still confined only to qualitative comparisons, since the results of experimental investigations still often give quantitatively rather substantial contradictions—in particular, in the present case an extremely important role is played by very good degassing of the metal. As an example one may cite the investigation of the secondary emission of tungsten, i.e. a metal that is relatively easy to degas, where at first Krefft\(^{10}\) pointed out the presence of a large number of local maxima in the curve \(\sigma=f(V_p)\), in the region \(V_p<600\ \mathrm{V}\), whereas subsequently Ahern\(^{11}\) found, in approximately the same region, only 4 local maxima for tungsten, which moreover partially disappeared upon further degassing of the tungsten. It follows, therefore, evidently, that although the number and relative magnitudes of such anomalies in the curves of Figs. 3, 4, and 5 may raise certain doubts in one or another specific case, nevertheless, taking into account their evident nature indicated above, the existence of this phenomenon should apparently be regarded as sufficiently natural.

Fig. 5.

The general character of the curve of the dependence \(\sigma=f(V_p)\) obtained by us and presented in Fig. 3 can easily be explained from the standpoint of the most general considerations in the following way: as the energy of the primary electrons \(V_p\) increases, an ever greater number of electrons of the metal can be excited by the impact of the primaries and, under suitable conditions, escape outward, thereby creating the secondary-electron current \(I_s\). However, alongside this, another factor gradually begins to play an ever more important role, namely that, as is known already from the work of Lenard, as the magnitude of \(V_p\) increases, the fast primary electrons, being scattered less and less, will penetrate ever more deeply into the metal, and consequently the majority of the secondary electrons created by them will arise at an ever greater depth below the surface and will at the same time possess somewhat smaller initial velocities. Owing to their relatively small initial velocities, the secondary electrons will be strongly scattered in their motion from the place of their origin toward the surface. Their scattering will increase with the growth of their path in the metal, i.e., in other

In other words, as the value of \(V_p\) increases. From all that has been said it follows that in the left branch of the curve in Fig. 3 the predominant role will be played by the first of the indicated processes, and in the right branch by the second. Some proof of the correctness of such an interpretation of the course of the curve in Fig. 3 may be furnished at least by the fact that, as Copeland showed\(^{12}\), for the right descending branch of the curve \(\sigma=f(V_p)\) in Fig. 3 the quantity \(k=\frac{\Delta \sigma}{\Delta V_p}\), characterizing the relative decrease of \(\sigma\) when \(V_p\) is increased by some constant amount, say by 1 volt, for different metals increases linearly with an increase in their density. Incidentally, for the same reasons it is clear that if the primary electrons are directed at an acute angle to the surface of the metal, the secondary emission will thereby increase.

Fig. 6.

We shall now omit a whole series of other facts established for secondary emission, such as, for example, its change at the moment when, in varying the temperature, we pass through the Curie point\(^{13}\) (although ordinarily secondary emission is practically independent of temperature), etc., and shall dwell a little on a rather old but nevertheless very interesting work of Dember\(^{14}\) concerning the influence exerted by bombardment of the surface of aluminium by a beam of primary electrons on its photoelectric effect. The lamp he used is shown in Fig. 6. Electrons from the heated filament were accelerated by a diaphragm-anode and bombarded the surface of an aluminium plate situated at the center. On the other hand, this same plate could be illuminated through a quartz window by radiation from a mercury arc. First, the pure photocurrent to the grid \(I_1\) was measured separately, then the pure secondary current in the absence of illumination \(I_2\). If now the Al surface is simultaneously illuminated and bombarded by electrons, it turns out that, all other conditions being equal, the resulting current \(I_3\) now obtained will be greater than the sum of the two preceding ones \(I_1+I_2\). The difference \(I_4=I_3-(I_1+I_2)\), the so-called additional photocurrent, turns out to be a quantity many times exceeding the strength of the pure photocurrent \(I_1\) and depending on the strength of the secondary current \(I_2\) in the following way. With a continuous increase of the secondary current \(I_2\) at unchanged photocurrent \(I_1\), the additional photocurrent \(I_4\) at first increases rapidly, then more and more slowly, passes through a maximum, and then begins to decrease; its maximum value exceeds the strength of the pure photocurrent \(I_1\) by approximately 148 times. The presence of such a maximum shows that, despite the bombarding action of the electron beam, by illumination of a definite

of light we are still able to tear out of the metal only a definite number of electrons. On the other hand, the dependence of the strength of the additional photocurrent \(I_4\) on the intensity of the light, at unchanged strength of the current of the bombarding electrons \(I_2\), gives a characteristic curve with “saturation.” This obviously indicates that the bombarding electrons are able to “excite” only a definite, though very large, number of additional photoelectrons. Finally, Dember also established that such bombardment strongly shifts the limiting frequency of the photoeffect \(A\) far toward the red wavelengths, which is reflected correspondingly in the value of \(I_4\). There is no doubt that Dember’s article is of great interest to us, although the interpretation of the results obtained by him still appears difficult, owing to the absence of sufficiently detailed experimental data on this question. The most natural interpretation of this process seems to be that, under the impacts of the primary electrons, additional excitation of the metal electrons to higher energy levels occurs, from which they are more easily detached in the simultaneously occurring photoeffect; such an interpretation will in its idea be very close to the explanation of the influence of an increase in temperature on the photoelectric effect, according to Fowler’s theory\(^{15}\).

In conclusion of this chapter we shall dwell briefly on contemporary theoretical investigations of the problem of the emission of secondary electrons from pure metals. In this direction we have as yet the single work of Fröhlich\(^{2}\), which is limited only to the knocking out of electrons from the conduction band and does not consider inelastic impacts of primary electrons on the lattice with direct emission of secondaries or with excitation of soft X-rays. To obtain the escape of conduction electrons outward, it is necessary to take into account their connection with the potential field of the metallic lattice; in general, our phenomenon proves to be very similar to the phenomenon of electron emission from a metal upon absorption in it of soft X-rays\(^{5}\). Fröhlich considers the interaction of primary and secondary electrons, introducing thereby into the Schrödinger equation the Coulomb perturbation potential

\[ V=\frac{e^2}{R-r}. \]

Solution of this equation, taking into account the fact that only those secondary electrons can leave the metal whose total energy \(\varepsilon+\Delta v\) as a result of such interaction becomes greater than the value \(W_a\), leads to conclusions which may be briefly summarized as follows:

1. The lower limit of secondary-electron emission is obtained on the basis that, for a metal at \(0^\circ\) K, all levels with energies \(\varepsilon \leq W_i\) are occupied. In this case the primary electron can give up a maximum energy \(V_p+W_a-W_i\), and, consequently, the energy \(\Delta V\) acquired by the secondary electron must satisfy the inequality

\[ V_p+W_a-W_i>\Delta V>W_a-\varepsilon, \tag{1} \]

whence, for \(\varepsilon = 0\), we obtain \(V_p > W\), i.e. the lower boundary of emission. The level of the emitted electron which thereby remains free will immediately be occupied by another, and the distribution of electrons will return to the initial one.

1. The velocity distribution of secondary electrons \(V_0\) does not depend, in the first approximation, on the energy of the primary electrons \(V_p\). For example, for silver it satisfies the inequality \(V_0 \ll 25\ \mathrm{V}\). In the second approximation, as the magnitude of \(V_p\) increases, the distribution curve \(V_0\) shifts slightly toward higher velocities.

2. The dependence of the yield coefficient \(\sigma\) on the energy of the primary electrons \(V_p\) has the following character. For small values of \(V_p\), close to the threshold energy,

\[ \sigma \sim V_p^{\frac{1}{2}}, \tag{2} \]

i.e. it increases with \(V_p\). On the other hand, for large values of \(V_p\) one obtains

\[ \sigma \sim \frac{\ln \dfrac{V_p}{W_a}}{V_p^{\frac{3}{2}}}, \tag{3} \]

i.e. \(\sigma\) decreases as \(V_p\) increases. The general course of this dependence, in which the influence—considered above—of absorption and scattering of primary and secondary electrons at different depths is still not taken into account, agrees in character with that observed experimentally (Fig. 3).

1. Finally, a comparison of the theoretically obtained absolute values of the quantity \(\sigma\) with those obtained experimentally was carried out for the case of ordinary metals at \(V_p = 100\ \mathrm{V}\). In qualitative agreement with the experimental data, one obtains here that \(\sigma \sim 1\); in general, however, this value of the quantity \(\sigma\) depends on the conditions at the surface.

Summarizing now the data of Fröhlich’s work, one may say that, despite a number of defects present in it—connected in particular with the failure to take into account secondary emission due to inelastic collisions of primary electrons with the atoms of the metal, etc.—it nevertheless represents a first and important step forward toward analyzing some of the processes occurring in the emission of secondary electrons from pure metals.

As regards energy losses in the inelastic collision of a primary electron with metal atoms with the direct emission of a secondary electron or the excitation of a quantum of radiation, here one may make use of the corresponding data known for free atoms[^16]. In this case the effective cross section of such a

the interaction proves to be equal to

\[ \Phi=\frac{\lambda^{2}}{\pi}\sum_i Z_i \lg \frac{V_p}{A_i}, \tag{4} \]

where \(\lambda\) is the wavelength of the primary electron, \(Z_i\) is the number of electrons in the \(i\)-th shell of the atom, and \(A_i\) is the mean excitation potential. For ordinary metals, at \(V_p=100\ \mathrm{V}\), for the quantity \(\Phi\) we obtain a value of the order of \(10\ \text{\AA}^2\). Taking into account the magnitude of the absorption coefficient, one may obtain that in a layer one atom thick approximately half of the primary electrons passing through undergo a collision. This, perhaps even exaggerated value, must of course lead to a noticeable role of secondary emission excited in this way.

3. Secondary emission of metals covered with films

Let us now turn to our central question of the ejection of secondary electrons from metals whose surface is covered with films or has been treated in an appropriate manner, since the path toward increasing secondary emission lies precisely in this direction. However, as the few investigations have shown, which we shall analyze in detail below, the character of the processes obtained in this case differs substantially from the character of the processes associated with the enhanced emission of thermoelectrons and photoelectrons from metals covered with active films.

The first, fairly detailed investigation of the question of the influence of covering the surface with an active multiatomic film on the emission of secondary electrons—a film which very strongly affects the thermoelectron emission of a metal—was carried out by Siksus \(^{17}\). The author studied the secondary emission obtained when primary electrons bombarded a filament of thoriated tungsten under various conditions of its activation. The lamp constructed by him is shown in Fig. 7. Inside the bulb were placed two electrode systems consisting of tantalum anodes, along whose axes filaments were stretched: \(A\)—of pure tungsten, \(B\)—of thoriated tungsten. The anode of filament \(A\) and the middle (working) anode of filament \(B\) have slits placed opposite each other. The lamp was very thoroughly evacuated and degassed; then a magnesium getter was evaporated in it, and during the measurements it was immersed in liquid air. In the known manner \(^{18}\) it was possible easily to activate the thoriated filament to any required degree, while the electron work function could vary from the value \(4.52\ \mathrm{V}\), corresponding to pure tungsten \((\theta=0)\), to the value \(2.63\ \mathrm{V}\), corresponding to tungsten covered with a complete monoatomic film of thorium \((\theta=1)\). With such activation the thermoelectron emission of this

the filament at \(1655^\circ\mathrm{K}\) increased \(10^5\)-fold. The degree of activation of the thorated filament was determined by the usual methods and, first of all,

Fig. 7.

Fig. 9.

from the known Langmuir relation \(\theta=f(\varphi_a)\), or \(\theta=F(\lg i_a)\). The measurement scheme used by Sykstus is shown in Fig. 8, which requires no additional explanation. A very serious difficulty in this case was the following circumstance. At sufficiently large values of the potential that imparted velocity to the primary electrons, a considerable majority of them passed by the thin thorated filament, whose diameter was \(50\,\mu\), and reached its anode; therefore the measurement of the current presented considerable difficulties in this case. The author attempted to circumvent this difficulty indirectly, introducing here an analogy with the question of the relation between grid current and anode current in a triode, using Lange’s expression\({}^{19}\) for this relation. The application of such a method cannot, of course, be considered sufficiently justified, as a result of which the data obtained by the author should be regarded as having only a qualitative character. A complicating circumstance in this case is also the fact that the primary electrons struck the surface of the thorated filament at different angles to it. Despite all this, the work of Sykstus

Fig. 8.

should be considered very valuable, as referring to the case when the work function of the bombarded surface can easily be varied within considerable limits, with easy control of its absolute value and with a simultaneous comparison with the thermionic emission of the same cathode.

Fig. 9 presents the graph obtained in this case of the relation between the yield coefficient of secondary emission \(\sigma=\dfrac{I_s}{I_p}\) and the energy of the primary electrons \(V_p\). We see that for \(\theta=0\), i.e. for a completely deactivated cathode, the maximum value of \(\sigma\) is equal to 1.81 and lies at \(850\ \mathrm{V}\), whereas for \(\theta=1\), i.e. for a fully activated cathode, we obtain \(\sigma_{\max}=2.21\) at \(V_p=750\ \mathrm{V}\). Thus we arrive at the basic conclusion that in this case the value of \(\sigma_{\max}\) increases by only about 20%, although the work function decreased by 1.9 V, and the thermionic emission increased by \(10^5\) times.

The author tries to explain this in the following way. In a very rough approximation he assumes that the secondary electrons emerging have a Maxwellian velocity distribution, and therefore for the secondary-electron current he writes the following expression, analogous to Richardson’s for thermoelectrons,

\[ I_s=\frac{Nc}{2\sqrt{\pi}}\sqrt{2\frac{e}{m}V_0}\,e^{-\frac{\varphi}{V_0}}, \tag{5} \]

where \(V_0\) is the initial energy of the electrons; \(\varphi\) is the electron work function, \(Nc\) is the number of electrons in \(1\ \mathrm{cm}^3\) of metal excited upon impact by the primary electrons. If it is assumed that the quantities \(Nc\) and \(V_0\) depend only on the energy of the primary electrons \(V_p\), then from (5) we obtain

\[ V_0=\frac{\varphi_1-\varphi_2}{\ln\frac{I_2}{I_1}}, \tag{6} \]

i.e. at \(V_p=\mathrm{const}\) the dependence \(\lg I_s=f(\varphi)\) should give a straight line. When this is checked, it turns out that indeed at \(\theta\leq 0.6\) straight lines are obtained, whose angular coefficients give us values of \(V_0\), listed in Table 1, which in order of magnitude agree with those obtained by other methods. Using further this relation (5), we can explain the results of the study of thoriated tungsten in the following way. With complete activation of this cathode the value of \(\varphi\) changes by \(\Delta\varphi\), approximately by \(2\ \mathrm{V}\). If we are speaking of thermoelectrons, whose initial velocities are of the order of \(0.2\ \mathrm{V}\), then with such activation

\[ \ln\frac{I_1}{I_0}\simeq \frac{\Delta\varphi}{V_0}=10, \]

i.e. \(I_1=I_0e^{10}\). If, however, we are speaking of secondary electrons, which have relatively large initial velocities of the order, say, \(V_0\sim 10\ \mathrm{V}\), then in this case

\[ \ln\frac{I'_1}{I'_0}\simeq \frac{\Delta\varphi}{V_0}=0.2, \]

i.e., \(I_1' = I_0' e^{0.2}\). Thus, owing to the much higher initial velocities, the secondary emission upon activation of the cathode increases to a considerably smaller degree than the thermionic emission, since for it a change of \(\varphi\) by 2 V plays a much smaller

Fig. 10.

TABLE 1

role than for thermoelectronic emission. Finally, the last fact noted by Sixtus consists in the practical independence of secondary emission from the temperature of the thoriated cathode in the interval \(300—1000^\circ\) K. Thus, as we see, this rather old work of Sixtus gives us at once a certain answer to a whole series of questions that are now of great interest to us.

Sixtus then attempted, by a similar method, to determine the secondary emission of technical oxide cathodes as well. Here, however, he encountered additional difficulties of the following kind. The heated cathode he used, after being remounted from a technical electron tube into the one under investigation, continuously emitted gas, and its activation could be brought only to such a limit that the work function \(\varphi\) was \(2.56—2.28\) V; this figure, in comparison with \(\varphi \ll 1\) V for well-activated oxide cathodes, indicates a very imperfectly activated state. The large transverse resistance of the oxide layer, if it was not in an incandescent state, also had a distorting influence. Therefore the results obtained by Sixtus with the oxide cathode were unreliable and poorly reproducible. In Fig. 10, nevertheless, the curve is also given for this case (\(\varphi = 2.28\) V), giving at 1100 V a value of \(\sigma\) equal to 3.4; in this case \(\sigma\) had not yet reached its maximum.

We find a certain further development of this line of investigation in a short note by Treloar \(^{20}\). This author, treating Hauers’s data \(^{9}\) on the secondary emission of pure molybdenum, established that the law of distribution of the energy corresponding to the components of the velocities of secondary electrons normal to the surface, \(\varepsilon_n\), for \(\varepsilon_n < 5\) V, corresponds approximately to a Maxwellian one.

Thus the number of emitted electrons \(N_s\), for which \(\varepsilon_n > U\), is given by a formula of the form

\[ \lg N_s = A - bU, \tag{7} \]

where \(A\) and \(b\) are constants; moreover in this case (pure Mo) \(b = 0.070\), if \(U\) is expressed in volts. According to Treloar, this formula (7), which shows what number of electrons will pass through a potential barrier of height \(U\) volts, must consequently also describe the analogous change in the quantity \(N_s\) with the work function \(\varphi\), i.e. approximately in the same way as we have in the case of thermoelectrons. To verify this Treloar measured the secondary emission of molybdenum, gradually covered with an active barium film, at an unchanged primary-electron energy \(V_p = 300\ \mathrm{V}\). The change in the work function of molybdenum, due to the deposition of Ba on it, was determined from the contact potential difference relative to pure tungsten. The experimental data obtained indicate that the dependence \(\lg N_s = f(\varphi_\theta)\) does indeed give a straight line, whose angular coefficient turned out to be 0.067, i.e. coincided with the theoretical one, thereby showing that the secondary electrons emerge from the molybdenum core. As the author points out, a similar result is obtained also in the case of a tungsten surface covered with an adsorbed oxygen film, when \(\varphi > \varphi_0\) and where the secondary emission proved smaller than that of pure tungsten. All these relations hold only for films no thicker than a monatomic one, i.e. for \(\theta < 1\); in the case \(\theta > 1\), deviations are obtained, connected with the fact that the secondary electrons arise partly already in the film itself, whereas the above calculation reduces the role of the film only to the corresponding change of the potential barrier at the surface. At this point it should be noted that although the secondary emission of the Ba—Mo surface also increases exponentially with a decrease of the work function \(\varphi\), this increase (similarly to Sixtus’ data) proceeds very slowly. From the above Treloar formula it follows that

\[ \frac{\Delta N_s}{N_s} = -0.16\,U, \]

i.e. when the work function changes by \(1\ \mathrm{V}\), the secondary emission changes only by 16%.

Even fewer data than for comparison with thermionic emission are available at present for comparing secondary emission with photoelectric emission, although this question is of primary importance precisely for the technology of photodynatron tubes. In this direction there are now only certain indications of an orienting character. Thus, for example, Groshev\(^{21}\) compared the secondary emission and the total photoelectric emission obtained from pure and activated—hydrided—potassium. He found that while such activation of the potassium surface leads to an increase of its photoelectric emission by approximately 15 times, a similar process has practically no effect on the secondary emission. Subsequently the same behavior of photoactivated surfaces was also established in the work

Penning and Kruithof,^22 in the case of a cesium cathode of the Ag—Cs$_2$O—Cs type. These authors indicate that in this case they were unable to establish any connection between secondary emission and photosensitivity. They had cases in which the photosensitivity decreased greatly (by approximately a factor of 30), while the secondary emission remained unchanged. Incidentally, they also refer to an unpublished work by Bruning, who likewise was unable to establish any regular connection between

Fig. 11.

secondary and thermionic emission. The dependence $\sigma=f(V_p)$ subsequently obtained by these authors in the case of their cesium cathode is presented in Fig. 11, from which it is seen that at $V_p=800$ V the maximum value of $\sigma$, equal to approximately nine, is obtained. These insignificant data exhaust everything that we now know about the connection between secondary and photoelectron emission, not to mention that in the latter case, when the photocathode is activated, one must distinguish the effect caused by a shift of the red boundary toward greater wavelengths and by the appearance of a selective maximum.

Finally, let us also note that Zworykin^23 carried out a study of the secondary emission of a whole series of surfaces having as cores: Ag, Be, Ta, Ni, Al, Zr, Ca, W, Cr, etc., and coated with films of Na, K, Rb, Cs. In this case the greatest secondary emission was found for surfaces of Ag, Be, or Zr oxide coated with a Cs film. In this case it turned out that at $V_p=400$—$600$ V the value $\sigma_{\max}=8$—$10$.

Also of considerable interest is Copeland’s work^24 on the secondary emission of metals coated with various films, but of such considerable thickness that the work function practically corresponds to the bulk material of the film. The arrangement of the electrodes in his tube is shown in Fig. 12, where $A$ is the bombarded surface, $F_1$, $F_2$ are metal filaments which, when heated, could evaporate and deposit on the surface $A$. Figure 13 presents data for an aluminum surface, coated ...

covered with a Pt layer of different thickness; curve 1 corresponds to pure Al, curves 2, 3, etc.—to coating with platinum of an increasingly thick layer. We see that at first the quantity \(\sigma = \dfrac{I_s}{I_p}\) decreases throughout

Fig. 12.

Fig. 14.

Fig. 13.

the whole range of measurements, but subsequently, as the thickness of the Pt layer increases, in the author’s opinion, the following can seemingly be established. At small values of \(V_p\), the secondary emission in its character corresponds to Pt in the film, while at large values of \(V_p\) it corresponds to the Al core. Such a statement, however, is not entirely obvious, since in this case one would have to expect the reverse arrangement of the curves in Fig. 13. As regards

of the thickness of the Pt layer, the author merely indicates that for curve 6 it corresponded to \(7.5\cdot 10^{-6}\) cm. The author obtained something somewhat different for a calcium film on gold. In this case, as the thickness of the Ca layer increases, the secondary emission (Fig. 14) increases continuously, but the curves \(\sigma=f(V_p)\) then show a sharper rise in the left-hand part and a fall in the right-hand part; at the same time the maximum of the curve seems to shift somewhat toward smaller \(V_p\). Results of the same character were obtained by the author also for Li on Ta and Ge on Au. Generally speaking, it may be said that for complex surfaces the value of \(\sigma\) differs both from the value corresponding to the core and from the value corresponding to the film.

Of very great interest to us is a recently published note by Malter \(^{25}\) on the anomalously large secondary emission obtained by him. The object of the investigation was electrolytically oxidized aluminum, the surface of which was suitably treated with cesium. It turned out that the secondary electron current from this surface to a special collector could in some cases be several thousand times greater than the primary current to the surface. However, this secondary current had a number of strange features not characteristic of what we usually had in the case of other surfaces, namely: after the primary beam was switched off, the secondary current to the collector \((I_s)\) slowly decreased and in some cases could be detected even after 24 hours. The white light of a tungsten filament caused a considerable decrease in \(I_s\), as well as a more rapid change in the characteristics of the decay and growth of the current. The author attempts to explain the nature of the effect he observed as follows: during treatment and activation, a surface having a high coefficient of secondary-electron emission is formed on the oxide film with high resistance. Since under bombardment \(I_s>I_p\), the surface becomes positively charged, which causes the appearance of a large potential gradient in this oxide film, owing to which a large secondary emission is obtained. Irrespective of the fact that in this work we still have too little data for characterizing the processes occurring here, it is of great interest.

These few works exhaust everything that we have at present in the direction of investigating secondary emission of different types of active cathodes.

As for theoretical investigations devoted to this question, unfortunately, in this direction we still have nothing. True, in the case of coating a metal with a monatomic film, whose role is practically reduced only to the corresponding change in the potential barrier at the surface and which has little effect on the main process connected with the formation of secondary electrons deep beneath it, one may try to use the data of Fröhlich’s theory \(^{2}\). If in this case the role of the film is reduced only to the corresponding change in the magnitude of the potential jump at the surface \((W_a)\), then from the data of Fröhlich’s theory one can obtain that, when the work function of elec-

tron ($\varphi$) or in the value of \(W_a\) by about 2–3 V at mean energies of the primary electrons of several hundred volts, the secondary emission increases only to an insignificant degree. All this is in agreement with the experimental data set forth above.

4. Conclusion

What conclusions can we draw from the investigations now available that are devoted to secondary emission, and in particular from the point of view of the problems of interest to the technology of high-vacuum devices with secondary-electron amplification? These conclusions may be summarized as follows.

Despite a number of shortcomings in the works of Siksus[^17] and Treloar[^20], it may be regarded as established that coating a metal surface with an active monoatomic film affects its secondary emission only to a very small extent, although the same coating would have a very strong effect on thermionic or photoelectric emission. In the present case one can evidently agree with Siksus that the reason for this may, in particular, be the relatively large initial velocities of the secondary electrons as compared with photo- and thermoelectrons, when a change in the work function by 1–2 \(v\) will not play an essential role; all the more so since the secondary electrons arise rather deep below the surface. It is true that the quantitative application of a Maxwellian-type formula (5) or (7) should still be regarded as far from justified. Therefore, if further investigations confirm the data obtained by this author, it will become clear that the path to obtaining surfaces with large yield coefficients \(\sigma\) lies in another direction. One may try to judge the nature of this direction if, for example, attention is paid to the fact that the most characteristic representative of surfaces that emit secondary electrons well is the photoactive cesium surface of the type \(\mathrm{Ag}—\mathrm{Cs}_2\mathrm{O}—\mathrm{Cs}\).[^22] A surface of this kind may be interpreted as consisting of a metallic core (Ag), on which there is a rather thick layer of \(\mathrm{Cs}_2\mathrm{O}\)—a substance that is probably an electronic semiconductor[^26] (with a possible inclusion in it of atoms of metallic cesium)—and, finally, with a film of atomic cesium on the surface. In this case the primary electrons bombarding the surface will knock secondary electrons not out of the metallic core, but out of the semiconductor \(\mathrm{Cs}_2\mathrm{O}\), and this, evidently, is the principal difference in the magnitude and behavior of the secondary emission. Whereas in the case of a metal the secondary emission occurs to a large extent at the expense of conduction electrons, which are present here in very large numbers, in the case of an electronic semiconductor the presence in the conduction band of only a small number of free electrons should have led to still smaller secondary emission than in the case of metals. The fact that experiment gives precisely the opposite result compels us to ascribe the chief role in the emission of secondary electrons not

free electrons rather than with bound electrons, preferably, of course, with the lowest possible binding energy. In this case, in an electronic semiconductor, only a rather small energy is usually required to transfer an electron from the band where it is in the bound state into the conduction band; but still the main point, evidently, lies not in this, but in the specific character of the energy exchange itself between the fast primary electron and the group of bound electrons. Owing to this, the energy of the primary electron \(V_p\) may ultimately be better used for exciting a possibly larger number of bound electrons of the semiconductor, thereby also leading to a greater yield of secondary electrons. It should, incidentally, also be noted that, as Sixtus established, the secondary emission even of his poorly activated oxide cathode (Fig. 9), which is an electronic semiconductor \(^{27}\), was considerably greater than that of, say, a fully activated thoriated cathode. As to a possible connection between secondary emission and the photoelectric effect, its outlines are still very unclear. The point is that each of these phenomena has its own specific features, not identical in every case. For example, the large photoelectron emission of cesium cathodes, associated both with a considerable shift of the red limit toward long wavelengths and with the presence of a selective maximum, the causes of which are certain optical conditions at the surface of the cathode and inside it, possible photoionization of surface cesium atoms, etc. \(^{28}\), may evidently have no direct connection with the causes producing a large emission of secondary electrons.

Addendum

Since this article was submitted for publication, a whole series of works devoted to secondary emission has appeared; some of them we shall note briefly here.

1. In a new paper by Malter (L. Malter. Phys. Rev. 50, 48, 1936) detailed data are given characterizing the effect he found of increased secondary emission from cesiated aluminum oxide, already mentioned above. A number of peculiar phenomena observed here, for the most part already noted above, are explained, in the author’s opinion, by the fact that, owing to the considerable knocking-out of secondary electrons from the active cesiated film formed on the surface of aluminum oxide (\(\delta > 1\)), the outer surface of the aluminum oxide, which is a good insulator, thereby becomes positively charged. This leads to the formation here of a considerable potential gradient, producing significant autoelectronic emission, which is what we perceive as increased secondary emission. In addition to aluminum oxide, a whole series of oxides of other metals was then also investigated, but positive results were obtained only with cesiated beryllium oxide and an oxide cathode. In the author’s opinion, from the point of view of the idea developed by him here, the necessary condition for the presence

of the effect are the greater resistance of the metal oxide and the impossibility of decomposing it by the cesium admitted during activation. It should be noted that the work nevertheless contains a whole series of unclear points which undoubtedly require further development.

1. In Shmakov’s work (P. Shmakov, Zh. T. F. 6, 1261, 1936), processes connected with the simultaneous illumination and bombardment of an ordinary cesium cathode by photo- and thermoelectrons were investigated. It was found (in agreement with the above-cited work of Dember) that simple summation of the photoeffect and the dynatron effect not only does not take place, but a number of new interesting phenomena are observed; for example: if the current of primary and secondary electrons to the cesium emitter under investigation is balanced so that the resulting current in its circuit is equal to zero, then additional illumination of this emitter may cause the appearance of an additional current in both directions, depending on the conditions in the external circuit. Further, under certain conditions of bombardment of the surface of the cathode-emitter, when the current of secondary electrons exceeds the current of primary ones, additional illumination of it causes not an increase but a decrease of the emission, at times to a very considerable degree. The explanation of this interesting phenomenon requires the further accumulation of experimental material, which appears very desirable, not to mention the possibility of its practical use.

2. In Lukyanov’s work (S. Lukyanov, Zh. T. F. 6, 1256, 1936) an attempt is made to calculate the dependence \(\delta = f(V_p)\), and then also the gain coefficient of a multistage multiplier. The author’s conclusions are based on the empirical use of the following two non-obvious assumptions: that both the number of secondary electrons obtained inside the metal and the mean depth of the place of their origin will be proportional to the first power of the energy of the primary electrons. Then, using for the probability of escape of secondary electrons to the outside the expression \(De^{-\beta x}\), the author obtains that

\[ \sigma = A V_p e^{-\mu V_p} \]

Comparison of this expression with experimental data, with preliminary determination of the empirical constants \(A\) and \(\mu\), shows that it conveys rather satisfactorily the general form of the experimental dependence \(\sigma = f(V_p)\), presented in Fig. 11. From this the author then obtains both expressions characterizing the gain coefficient of a multistage multiplier and the optimum conditions of its operation; see also: V. Zworykin, G. Morton and L. Malter, Proc. Inst. Radio Eng. 24, 351, 1936.

1. In connection with the above, it should be noted that even in Mac Allister’s old experimental work (L. Mc Allister, Phys. Rev. 21, 122, 1923) it was qualitatively shown that the secondary emission from the surface of copper oxide is greater than from pure copper.

1. In Rudberg’s work (E. Rudberg, Phys. Rev. 50, 138, 1936) the energy distribution of inelastically scattered electrons was investigated by the method of magnetic analysis, at \(V_p = 50—400\ \mathrm{V}\). In this case the metals Cu, Ag, and Au give distribution curves very similar in character to one another and practically independent of \(V_p\). On these curves two maxima are obtained at \(V < 10\ \mathrm{V}\), which qualitatively correspond to regions of strong optical absorption, thereby indicating the kinship of these phenomena. Then, from the study of distribution curves obtained with films of Ca, Ba, CaO, and BaO of different thicknesses on an Ag core, the author attempts to estimate the depth of penetration into the emitter of the scattered electrons. It turns out that, as the thickness of the film increases, the maxima characteristic of its material in the distribution curve, indicating that the incident electrons already begin to scatter here and not in the core, appear at thicknesses of the order of several atomic layers. For example, in the case of CaO—Ag the maxima characterizing the CaO film already appear at \(\vartheta < 0.5\), while the maxima of the Ag core disappear at \(\Theta \sim 5\). Thus this work gives us indications concerning the depth of penetration of primary electrons into the metal and the location of that zone from which inelastically scattered and probably also, to a considerable extent, secondary electrons arise.

2. Finally, in the work of Rudberg and Slater (E. Rudberg a. J. Slater, Phys. Rev. 50, 150, 1936), the conditions for the excitation of electrons in a crystal under bombardment by external electrons are investigated theoretically; in the case when the excitation energy \(V_a\) is small in comparison with \(V_p\), the probability of this process corresponds to the probability of excitation upon absorption of radiation. Applying then the data of this theory to the case of copper, under the condition that the initial state of the electron in the crystal corresponds to a discrete atomic level, and the final state—to free electrons in the conduction band, the author calculates the distribution curve of inelastically scattered electrons; it turns out that in the case of small \(V_a\) it is in agreement with the experimental data of the preceding work by Rudberg.

LITERATURE

1. For reviews on the question of secondary emission see K. Compton and I. Langmuir, Rev. Mod. Physics, 2, 171, 1930. O. Klemperer, Einführung in die Elektronik 1933, p. 165. A. Becker, Die Physik, 2, 1934. W. Bothe. Handb. d. Physik XXII/2, 1933.
2. H. Fröhlich, Ann. Physik, 13, 229, 1932.
3. A. Hull, Proc. Inst. Radio Eng., 6, 5, 1918.
4. P. Farnsworth, J. Frankl. Inst., 218, 411, 1934. H. Jamsand B. Salzberg, Proc. Inst. Radio Eng., 23, 55, 1935. P. Shmakov, ZhTF 5, 1220, 1935. F. Penning und A. Kruithof, Physica 2, 793, 1935. P. Görlich. Z. Physik, 96, 588, 1935. L. Kubetskii. Avtomatika i telemekhanika, No. 1, p. 17, 1936. V. Zworykin, G. Morton a. L. Malter. Proc. Inst. Radio Eng. 24, 351, 1936.

1. R. Kronig and W. Penney, Proc. Roy. Soc., A 133, 255, 1931.
   A. Sommerfeld und H. Bethe, Handbuch der Physik, XXIV/2, p. 461, 1933.
2. See, e.g., O. Richardson, Proc. Roy. Soc., A 119, 531, 1928.
3. R. Warnecke, J. de phys. et de rad., 5, 267, 1934.
4. R. Petry, Phys. Rev., 26, 346, 1925.
5. L. Haworth, Phys. Rev., 48, 88, 1935.
6. H. Krefft, Phys. Rev., 31, 199, 1928.
7. A. Ahearn, Phys. Rev., 38, 1858, 1931.
8. P. Copeland, Phys. Rev., 40, 122, 1932.
9. P. Tartakowsky und W. Kudrjawzewa, Z. Physik, 75, 137, 1932.
10. H. Denber, Z. Physik, 33, 529, 1925. See also I. Langmuir, Science, 58, 398, 1923.
11. R. Fowler, Phys. Rev., 38, 45, 1931. L. du Bridge, Phys. Rev., 39, 108, 1932.
12. A. Sommerfeld und H. Bethe, Handbuch der Physik, XXIV/2, p. 499, 1933.
13. K. Sixtus, Ann. d. Physik, 3, 1017, 1929.
14. See, e.g., S. Dushman, Rev. Mod. Physics, 2, 398, 1930.
15. H. Lange, Z. Hochfrequenztechn., 31, 105, 133, 191, 1928.
16. L. Treloar, Nature, 137, 579, 1936.
17. L. Groshev, JETP, 4, 363, 1934.
18. F. Penning und A. Kruithof, Physica, 2, 793, 1935.
19. V. Zworykin, American Technology and Industry, 13, 96, 1936.
20. P. Copeland, Phys. Rev., 48, 96, 1935.
21. L. Malter, Phys. Rev., 49, 478, 1936.
22. J. de Boer und M. Teves, Z. Physik, 74, 604, 1932; 83, 521, 1933.
23. See, e.g., A. Reimann, Thermionic Emission, p. 188, 1934.
24. See, e.g., R. Suhrmann, Erg. d. exakt. Naturwiss., 13, 148, 1934.