Cathode Sputtering

N. D. Morgulis

I. Introduction

The sputtering of a metallic surface when it is bombarded by fast positive ions, or cathode sputtering (c. s.), was discovered by Grove as early as 1852. Since the discovery of c. s., many works have been devoted to its study, owing to the fact that this phenomenon is of great interest from both the physical and the practical point of view. Indeed, in studying c. s. we encounter a whole series of interesting elementary processes that occur during the interaction—the impact—of a fast ion with the surface of a solid body. On the other hand, the study of c. s. gives us the possibility of determining the conditions under which the presence of this phenomenon can be reduced to a minimum, which is very important from the standpoint of creating normal and long-lasting operating conditions for modern active cathodes in gas discharges, in devices of the gazotron and thyratron type, in certain glow lamps, etc. Finally, cathode sputtering has found considerable practical application in the technique of producing thin metallic coatings (mirror surfaces, large resistances, etc.).

Of the large number of investigations of c. s., at the present time only works carried out approximately during the last 20 years may be taken into account; this is connected with the requirements of thorough cleaning of the surface under investigation and of the gas filling the lamp, with investigations under conditions in which an auxiliary discharge is present as a source of “monochromatic” ions for sputtering, with more accurate methods for determining the amount of sputtered substance, the sputtering threshold, etc.

The present review has the purpose of giving an idea of the present state of the question of c. s., both from the point of view of the experimental data established up to the present time and of the nature of this phenomenon. The results of older investigations, a more detailed exposition of some experimental data, the technique of c. s., etc., may be found in reviews ¹ that were published on this question in the past. In this connection, experimental investigations of c. s. may be divided into two groups: investigations carried out

with fast ions, which had as its aim the study of the basic regularities of this phenomenon, and investigations carried out with slow ions, near the so-called critical sputtering potential \(v_0\), which had as their aim the study of the conditions under which this phenomenon, in general, can arise; therefore these two cases should be considered separately.

II. SPUTTERING BY FAST IONS

The results of the investigation of c. s. by fast ions, characterized by the so-called sputtering coefficient \(N=\dfrac{N_a}{N_p}\), i.e. the number of atoms sputtered by one ion, were for the most part obtained quite a long time ago. They may be very briefly summarized as follows \(^{1}\):

1. The value \(N\) does not depend on the sputtering time, provided that the properties of the sputtered surface do not change in the process.

2. The value \(N\) does not depend on the density of the ion current sputtering the cathode.

3. The value \(N\) depends approximately linearly on the energy of the sputtering ion \(v_p\) (for not very large \(v_p\)), i.e.

\[ N=A(v_p-v_0), \tag{1} \]

where \(v_0\) is the so-called critical sputtering energy. Some deviations from (1) are nonsystematic in character.

1. The value \(N\) for metals does not depend on the temperature of the cathode, for example in the interval up to \(2000^\circ\ \mathrm{K}\).

2. The value \(N\) usually increases with increasing mass of the sputtering ion.

3. The dependence of the value \(N\) on the nature of the metal is still not sufficiently clear; for example, in an argon atmosphere the metallic cathodes, in order of decreasing \(N\), are arranged as follows: Cd, Ag, Pb, Au, Sb, Sn, Bi, Cu, Pt, Ni, Fe, W, Zn, Si, Al, Mg.

4. The formation of films of adsorbed gases and chemical compounds on the cathode surface affects sputtering in different ways, namely: sputtering of some metals in a hydrogen atmosphere gives anomalies obviously connected with chemical processes (formation of \(\mathrm{SbH}_3\), etc.); insufficient degassing of the cathode (Pt) leads to a decrease in \(N\). The formation of oxide films on the surface leads to a considerable decrease in \(N\); the latter, evidently, also explains the poor sputtering of Al and Mg, which usually have on their surface a stable oxide film, the sputtering of which in the initial stage of the discharge subsequently leads to a noticeable increase in the value of \(N\).

1. During sputtering in a glow discharge, with a gradual lowering of the pressure \(p\), the quantity \(N\) gradually increases as a result of the diminishing role of the return of some of the sputtered atoms back to the cathode upon their collisions with gas atoms; at \(p < 0.1\)—\(0.01\) mm \(N\) reaches its maximum and then constant value, characteristic of the given phenomenon.

2. Under the impact of fast ions, sputtering is possible not only of metals, but also of solid dielectrics, such as, for example, glass, calcite, quartz, fluorite, rock salt, sylvine, mica, etc.

After this very brief summary of the principal empirical data on cathode sputtering, we shall proceed to a more detailed account of certain experimental investigations carried out in recent years, which at the same time have brought much clarity to the question of the nature of this phenomenon.

One of the fundamental questions connected with the nature of cathode sputtering is the question of the nature and velocity of the sputtered particles. To answer this question, Baum \(^{16}\) uses the principle of the Stern and Gerlach experiments on the splitting of a beam of Ag atoms in an inhomogeneous magnetic field, using for this purpose Ag particles obtained by cathode sputtering. The arrangement of the magnets and the traces of the beam of sputtered Ag before (I) and after (II) the magnetic field is switched on are presented in Fig. 1. Having thereby obtained splitting of the beam, the author comes to the conclusion that the sputtered particles have an atomic character, and their deflection in the magnetic field indicates their charging in the discharge space. Further, from an analysis of the deflection of these charged atoms in a homogeneous magnetic field, Baum finds that, in a discharge with a cathode potential drop of 2500 V, these atoms have velocities of the order of 570 m/sec; for comparison we note that at the melting temperature of Ag, equal to \(1234^\circ\)K, the thermal velocity of Ag atoms is 534 m/sec.

(5²² times magnification)

Fig. 1.

The next group of experiments uses for the same purpose the glow of the near-cathode part of the discharge, where the glow of atoms of the cathode material is often observed. Hippel \(^{11}\) drew attention to this; he found spectroscopically that in a discharge with cathodes of Cd, Zn, and Ag, the glow of these elements is observed here; from this Hippel concluded that the sputtered particles have an atomic structure and that they are excited and ionized already in the discharge space. From the relative intensity of this glow he then attempted to estimate the elasticity of the vapors of the sputtered atoms near the cathode. Subsequently Meyer \(^{31}\), when bombarding the surface of Pt coated with a film of Na with Na and K ions, found that a characteristic glow of Na appears at the cathode, spreading over a certain

distance \(d\); for example, for Na ions with \(v_p=600\ \mathrm{V}\) it turned out that \(d=4\cdot 10^{-2}\ \mathrm{cm}\). Assuming that this radiation is associated with the neutralization radiation of excited Na atoms sputtered from the surface, and that for complete fading a time of the order of \(10^{-7}\ \mathrm{sec}\) is required, the author obtains that the velocity of the sputtered atoms is equal to \(4\cdot 10^{-2}/10^{-7}=4\cdot 10^5\ \mathrm{cm/sec}\); this velocity corresponds to a temperature in the sputtered surface element of the order of \(30\,000^\circ\ \mathrm{K}\). Finally, Schlordt \(^{62}\), using Meyer’s refined method, found that, in sputtering in \(\mathrm{O}_2\), the average energies of the sputtered atoms are: for Li—6.9 eV, for Na—4.5 eV, and for Mg—7.0 eV; these values proved to depend little on the nature of the sputtering ions (\(\mathrm{O}_2\), He, and Ar) and on their energy and the gas pressure over wide ranges. From these same experiments it follows that, at \(v_p=2000\ \mathrm{V}\), only one sputtered Na atom in an excited state is produced per 500 ions striking the cathode.

In interesting experiments by Sommermeyer \(^{47}\) it was found that, when potassium iodide is sputtered by Ar ions with energy \(v_p=10\text{–}15\ \mathrm{kV}\), its dissociation occurs simultaneously \((\mathrm{KJ}+Q\rightarrow \mathrm{K}^+ + \mathrm{J}^-)\); one of the dissociation products of KJ, placed at \(H\) (Fig. 2)—\(\mathrm{K}^+\) ions—was collected on a cold filament \(w\). If, after some time of sputtering, the filament \(w\) is instantaneously heated, then, from the ballistic deflection of a galvanometer connected into its circuit, one can determine the number of K atoms deposited on it, which, owing to the phenomena of thermal ionization \((v_i<\varphi)\), fly off from the filament in the form of ions. By finding the quantity of sputtered KJ from the loss of weight and the quantity of \(\mathrm{K}^+\) ions obtained in this way, one can find the degree of dissociation of KJ under sputtering conditions—\(x\); in this case it turned out that \(x\simeq 10^{-1}\), whence it follows that the effective temperature in the sputtered element was of the order of \(3000^\circ\ \mathrm{K}\).

Fig. 2.

In connection with the question of the nature of cathode sputtering (see below), many authors have tried to establish some connection between the sputtering coefficient \(N\) and the physical parameters of the sputtered cathode. It must be pointed out that such attempts should be treated with great caution, for the actual values of these parameters are unknown to us (for example, the coefficient of thermal conductivity, heat capacity, etc.) under real sputtering conditions, and it is not always possible to use their usual values. However, on this matter one may nevertheless note the following interesting facts: the relative values of \(N\) for some metals and dielectrics, under identical sputtering conditions, differ very little from one another.

one another, as, for example, for Ag and AgCl[^47]; from this, in particular, there follows the very important conclusion that the removal of energy from the site where an ion strikes the cathode surface occurs without the participation of conduction electrons (see below). Further, in the case of sputtering of a Bi single crystal it was found that the value of the sputtering coefficient \(N\) becomes anisotropic, depending, in particular, on the direction of the axes of thermal conductivity, so that \(N\) increases as the latter decreases[^17]. Incidentally, in connection with the latter, it may be noted that, in the sputtering of an ordinary polycrystalline surface, it rapidly acquires a very inhomogeneous character, which, for example, is clearly seen from consideration of its microphotography[^16,^24,^71]. Here one may also note attempts to observe c. s. with the aid of an electron microscope, which so far have not yielded any especially interesting results for us.

The role of the nature of the gas whose ions produce sputtering is still not entirely clear. It would seem that, to a first approximation, the experiments[^7,^12] confirm that with increasing mass of the sputtering ion the sputtering coefficient \(N\) should also increase, for in this case the accommodation coefficient \(a\) increases and, consequently, so does the fraction of the energy transferred by the ion to the surface. However, in this respect the matter is somewhat more complicated, as is evident from the following experimental facts. In sputtering a Mo surface by ions and metastable helium atoms with an energy of 800 V[^21], the sputtering coefficient \(N\) in the first case proved to be greater than in the second. Parallel to this experimental fact one should also note another, which showed that, when comparing the sputtering of a surface by the metallic ions Hg, K, and Na with ions of inert gases of approximately the same mass[^7], the value of \(N\) in the first case proved to be smaller than in the second. Both these facts can be connected neither with the role of the charge, nor with the additional influence of the ion neutralization energy \(v_n = v_i - \varphi\), which for atoms of inert gases is considerably greater than for atoms of the indicated metals, just as the kinetic energy of the electrons cannot be used for sputtering metals[^25,^38]; the latter is connected with the fact that both these kinds of energy can be transferred only to the electron gas of the metal, and not to its lattice[^47,^57] (see below), thereby causing the emission of secondary electrons.

Very interesting data were obtained in the study of the structure and properties of the metal deposit obtained during c. s. on a suitably placed screen. Quite long ago a number of investigators[^16,^20] established that the structure of the deposit obtained from the sputtered cathode on such a screen is very closely similar to the structure obtained without discharge, by pure evaporation when the same cathode is heated to a high temperature in the same lamp. However, the most convincing data were obtained by Seeliger and Sommermeyer[^39], who set themselves the task, using

this method, to determine which of the two theories of cathode sputtering—impulse or thermal (see below)—is closer to reality. They studied the deposit obtained on a screen placed from the cathode at a distance less than the mean free path, during sputtering by Ar ions at \(v_p = 10\text{--}15\ \mathrm{kV}\). Fig. 3 presents a diagram of their experiments: the sputtered cathode \(O\) is surrounded by a mica screen \(A\); the distribution of the density of the deposit on this screen is investigated. In this case it turned out that if the cathode is liquid helium with a mirror surface (having a very low vapor elasticity), or matte and polished solid Ag, then, independently of the angle of incidence \((\leq 45^\circ)\) of the ion beam, the deposit on the screen is always distributed in accordance with the cosine law. For an additional verification of this fact, mercury was placed instead of the cathode; its thermal evaporation gave the same character of deposit distribution. In another experiment, where the Ag cathode formed part of a mica cylindrical screen, it turned out that, in accordance with the cosine law, the density of the deposit along the periphery of the screen was constant. These experiments very convincingly support a close correspondence between the phenomena of sputtering and thermal evaporation, although sputtering itself is practically independent of the cathode temperature[^46].

Fig. 3.

It should also be noted that there are indications that deposition on a screen of a deposit, for example of Cd, occurs during sputtering with somewhat greater ease than during thermal evaporation[^33][^34], since in the former case deposition proceeds at any densities of the depositing substance with a rate independent of the screen temperature. At the same time, atoms deposited by cathode sputtering on the surface of glass reveal an ability for surface migration[^34][^69], similar to the case of deposition during evaporation.

Let us now turn to the consideration of several other questions connected with cathode sputtering.

It has long been known that Al and Mg surfaces covered with an oxide film are sputtered considerably more poorly than when their surface is clean; for example, the sputtering coefficient of an MgO surface is approximately \(4\text{‰}\) of the value of this coefficient for pure Mg[^50]. To explain this phenomenon it was proposed that simultaneously with the sputtering of MgO, \(Al_2O_3\), etc., their dissociation occurs \((\mathrm{MgO}\to \mathrm{Mg}^{+} + \mathrm{O}^{--})\), the electric field near the cathode returning the positive metal ions back to the cathode. An attempt to verify this hypothesis[^50][^55], by creating an additional electric field near the cathode with the aid of special grids, did not lead to a positive result—

tate. Then the following experiment was set up: part of the cathode surface made of MgO was covered with a sheet of mica; if, owing to the action of the opposing field, the \(Mg^{++}\) ions return back to the cathode, then, in connection with scattering in collisions with the gas atoms in the lamp, it is not excluded that some of the \(Mg^{++}\) ions will reach the edges of this sheet; however, the experiment revealed no traces of Mg there. Thus, the question of the cause of the poor sputtering of these surfaces remains open.

The question concerning the energy efficiency of cathode sputtering, i.e.,

\[ \eta=\frac{NL}{ev_p}. \]

is not without interest.

This quantity is in general rather small \(^{22, 63}\); for example, at \(v_p=500\ \mathrm{V}\) for the systems: Ni—Ar \(\eta=1.1\%\), Ag—Ar \(\eta=0.9\%\), etc.

In conclusion, let us dwell briefly on the question of the dimensions of that effective region of the cathode from which atoms can fly out during cathode sputtering. The first data on this question are found in the work of Coller \(^{45}\), who, in studying the sputtering of thoriated tungsten Th-W in Hg vapor, found that the value of \(N\) increases strongly with increasing cathode temperature, within the range \(300—1300^\circ K\). The author explains this by the natural assumption (confirmed when other methods of investigation are used) that at \(300^\circ K\) the cathode is covered with a film of mercury vapor, which protects the thorium film from direct impact by ions; however, the presence nevertheless of appreciable sputtering even at \(300^\circ K\) shows that during cathode sputtering emission of atoms occurs not only from the very surface, but also from the layer lying beneath it. Similar data were then obtained also in the bombardment of a thoriated cathode, located in cesium vapor, by cesium ions \(^{70}\), where it additionally turned out that the “protective” effect of the outer film is the greater, the smaller the energy of the sputtering ions; if, for example, one compares the values of \(N\) for a Th-W cathode at a temperature of \(1200^\circ K\) (the protective adsorbed Cs film is absent) and at \(300^\circ K\) (the adsorbed Cs film is present), then it turns out that at \(v_p=100\ \mathrm{V}\) the ratio

\[ \frac{N(1200)}{N(300)} \simeq 3.3, \]

whereas at \(v_p=200\ \mathrm{V}\) it is equal to \(\sim 1.4\). However, this deep transfer of energy from the sputtering ion can hardly be effectively utilized, for, for example, the value of \(N\) proved to be independent (at a constant degree of coverage with thorium) of the concentration of Th atoms in the sublayer, over wide limits of variation of the latter. Otherwise, along with sputtering, outward diffusion would also be observed, which would be reflected correspondingly in the emission of the Th-W cathode.

III. SPUTTERING BY SLOW IONS

The question of sputtering by slow ions is of very great importance in connection with the question of the so-called critical potential, or sputtering threshold \(v_0\), for, as has already been indicated, sputtering occurs only when the energy of the ion \(v_p\) exceeds this value \(v_0\), i.e. when \(v_p > v_0\). Thus, if the question arises of creating such conditions under which the discharge in a lamp would not lead to sputtering—the destruction of its cathode—then it is obviously necessary that the relation \(v < v_0\) hold, which naturally requires reliable knowledge of the magnitude \(v_0\). This question is very important for a whole series of modern gas-discharge devices, especially those operating with an active—oxide thermocathode (for example, thyratrons, tiratrons, gas-filled lamps, etc.), where the cathode emission is associated with the presence on its surface of active films of monatomic thickness. This latter circumstance, along with its fundamental interest, was also one of the chief reasons that gave rise to the appearance of a considerable number of works on this question.

It was established quite long ago that for cathode sputtering, in the region of not very large values of \(v_p\), the principal dependence \(N = f(v_p)\) has the form represented by the empirical formula (1); hence attempts were usually made to determine the value of \(v_0\) by linear extrapolation to the intersection with the abscissa axis \({}^{7,10,40}\). However, this method, in its application to pure metals, cannot claim sufficient accuracy, since in this case measurements of the quantity \(N\) in the region of small values of \(v_p\) can be made with very low precision; the measurements are usually carried out either from the change in the resistance of a filament cathode, or from the change in the weight of the cathode or by determining the weight of the sputtered deposit on a screen, or, finally, by photometry of the sputtered deposit on a transparent screen. The possibility of a sufficiently accurate investigation of sputtering near its threshold \(v_0\) arose only when investigators turned to the use of active cathodes, whose electron emission \(I_e\) is associated with the presence of an active monatomic adsorbed film, the slightest destruction of which can be immediately established with very great accuracy. In this respect the most successful and simple cathode proved to be thoriated tungsten—Th-W, with which almost all the principal investigations of this type were carried out.

The first investigations in this direction, which laid the foundation for almost all subsequent work, were carried out in 1923 by Langmuir and Kingdon \({}^{9}\); these authors performed experiments on the sputtering of Th-W by ions of various gases and metal vapors, obtained by impact ionization by electrons from another filament; the number of sputtered atoms was determined from the change in the electron emission of the cathode \(I_e\). The results obtained in this way are presented in the well-known

Fig. 4, from which, by extrapolating to the intersection with the abscissa axis, one can determine the value of the quantity \(v_0\); these values for three gases (Ag, Ar, and Ne) are presented in the 2nd column of Table I. However, in the same year 1923, Hull and Winter\(^8\), working with a powerful gasotron discharge in Ar, found that appreciable sputtering of the thermocathode from the same Th-W occurs when the potential drop across the lamp exceeds only 25 V. Subsequently, in his detailed work\(^ {19}\), for a powerful discharge with this same cathode, Hull gives the values of \(v_0\) presented in the 4th column of Table I, which, as he indicates, do not depend on the cathode temperature in the interval \(1900—2300^\circ\mathrm{K}\) and which, as we see, differ considerably from the data of Langmuir and Kingdon. On the question of the reason for such a difference in the values of \(v_0\), Hull, in his letter to the author of January 5, 1933, writes: “The difference between our values of the sputtering potential and those obtained by Langmuir and Kingdon is connected with the greater sensitivity of our method. Sputtering is indeed not great at 50 volts if small currents are used, as Langmuir and Kingdon did. However, at the large currents that were used by us in our gas-filled lamps, it (i.e., sputtering) becomes

Fig. 4.

Table I

enormous.” This circumstance cannot but suggest that the measurement of the quantity \(v_0\) is not so simple and that, probably, the values of \(v_0\) given above are apparent—effective \(v'_0\), actually depending on the conditions under which the experiment was carried out. This thought

finds confirmation even in the data of the same paper by Hull[^19], if one considers Fig. 5 for sputtering in Hg, borrowed from there, from which it is seen that the quantity \(v'_0\) has a value different from 22 V, depending, moreover, on the cathode temperature (see also the 5th column of Table 1). Moreover, in the text itself of that paper an example is considered of equilibrium at the surface during sputtering of Th–W (see below), from which it follows that \(v'_0 = 17\) V. All these circumstances compelled us to reconsider this important question anew.

The principal difficulty connected with the observation of sputtering of Th–W and cathodes similar to it consists in the fact that here, along with the sputtering of active atoms from the surface, their continuous arrival at the surface by diffusion from within may simultaneously occur. Therefore, in the general case, the surface film of the active metal (for example, Th), which influences the electron emission of the cathode \(I_e\), with surface density \(n = \vartheta n_1\), will depend on the balance between diffusion from within to the surface at a rate \(D \dfrac{\text{atom}}{\text{cm}^2\,\text{sec}}\) and sputtering at a rate \(R \dfrac{\text{atom}}{\text{cm}^2\,\text{sec}}\), i.e.,[^42]

\[ dn/dt = D - R. \]

Fig. 5.

The onset of c. s. with increasing \(v_p\) is usually determined by the fact that the emission \(I_e\) begins to decrease, i.e. \(dI_e/dt < 0\), and the latter is connected with a decrease of the surface concentration of active atoms, i.e. \(dn/dt < 0\). It is therefore natural that the effective sputtering potential \(v'_0\), at which a noticeable fall of emission will begin, will depend on the relation between the magnitudes \(D\) and \(R\), i.e. on the actual experimental conditions. Indeed, the magnitude \(D\) depends on the cathode temperature and on the distribution of concentrations of active atoms in the substrate, while the magnitude \(R\) depends on the energy and current density of the ions and on the density of atoms on the surface[^42]. This circumstance may be illustrated by the graphs in Fig. 6, where data are given concerning sputtering of a thoriated cathode in mercury vapors[^53] at \(T = \mathrm{const.}\), in the form of curves of the time dependence \(I_e = f(t)\). At the beginning of each curve (if \(v_p > v'_0\)) \(dI_e/dt < 0\), since

\(dn/dt < 0\), i.e. \(D < R\), but then, owing to sputtering, the quantity \(I_e\) gradually decreases; consequently the density of the ion current \(I_p\) produced by ionization also decreases, which in turn leads to a decrease of the very quantity \(R\), until, finally, a state of dynamic equilibrium is reached, where \(R = D\). This state of dynamic equilibrium can be shifted in either direction if the values of the parameters entering into the quantities \(D\) and \(R\) are changed accordingly; this circumstance is clearly illustrated by Table II ^52, which gives us the limiting equilibrium value of the degree of coverage of tungsten with thorium, \(\theta_1\), as a function of the vapor pressure of mercury, \(p\), the cathode temperature, \(T\), and the potential difference at the lamp electrodes, \(v_a\). Everything that has been said is very important for the operation of active thermocathodes in a gas discharge, since ignoring the conclusions following from it may lead to an incorrect interpretation of the experimental data obtained here.

Fig. 6.

Moreover, we can obtain normal and long-lived emission from a gas-discharge lamp; however, it by no means follows from this that sputtering is completely absent; it may exist to a very appreciable degree, being masked, however, by continuous and greater regeneration of the cathode, as, for example, in the case of the mercury thyratron TG-162, for which the normal \(v_a = 20\ \mathrm{V}\), and the neon thyratrons TG-212 and TG-213 with \(v_a = 30\ \mathrm{V}\)*).

Taking these facts into account and exercising greater care in subsequent measurements led to a further decrease in the value of \(v'_0\) for Th-W ^42,46 to a minimum value of the order of 13 V, which in the interval 1350—1750°K proved to be independent of the cathode temperature. Measurements were made by the same method also for carburized thoriated tungsten Th-C-W ^48,

Table II

) Gas-discharge devices.* Glavésprom, 1939, pp. 56 and 58.

which led to the value \(v'_0 \simeq 22\,V\). The indicated data for Th–W and Th–C–W were obtained in a discharge in mercury vapor with an additional filament, whose emission produces ionization of the vapor; the density of the ion current \(I_p\) bombarding the cathode under investigation can be determined with the aid of probe characteristics. An example of the dependence, obtained in this way, of the quantity \(v'_0\) on \(I_p\) is presented in Fig. 7, from which it is seen that the value of \(v'_0\), with increasing \(I_p\), in accordance with the balance equation, gradually falls to a certain limiting value; in this way the minimum value \(v'_0 = 13\,V\) was found for \(v'_0\).*)

Fig. 7.

Somewhat exceptional here are the data of Coller \(^{45}\), given in the 7th column of Table I, obtained, as in Langmuir and Kingdon, by linear extrapolation of the straight line \(N = f(v_p)\). From this it obviously follows, once again, that such a method of determining the value \(v_0\) is incorrect. This is probably connected with the fact that, as is experimentally indicated \(^{42}\), the dependence \(N = f(v_p)\), in its lower part, has a nonlinear character with positive curvature, i.e. is significantly drawn out to the left.

Let us now turn to a consideration of the results of investigations of sputtering of the second class of economical cathodes—oxide cathodes—which are of enormous practical importance in connection with their applications in a large number of modern gas-discharge devices. Unfortunately, despite the great importance of studying the sputtering of these cathodes, we have had almost no systematic investigations here; this is connected primarily with the very great complexity, in comparison with Th–W, of the processes occurring here and with the difficulty of obtaining reliable experimental data. Nevertheless, attempts had already been made in the past to determine the sputtering threshold of an oxide cathode under real conditions of a gasotron discharge. The first attempt, made by Hull \(^{19}\), did not lead to any definite results, and the value usually ascribed to him, \(v_0 = 22\,V\), for sputtering of an oxide cathode in mercury vapor has absolutely no basis. Subsequently Murgulis and Patiokha \(^{44,52}\), in investigating a powerful gasotron discharge in the emission re—

*) By \(v'_0\) in the present measurements we understand the potential drop across the lamp, which differs very little (approximately by the magnitude of the anode potential drop) from the actual energy of the ions bombarding the Th–W cathode.

regime, they found that, when the balance at the surface is shifted toward a decrease in the rate of reactivation \(D\), the effective value of \(v'_0\) gradually decreases to a limiting value of the order of 17 V, as is shown in Fig. 8.

The first, relatively systematic, measurements of the sputtering of real oxide cathodes in mercury vapor^{49} were carried out

Fig. 8.

by determining the time dependences of the emission current \(I_e=f(t)\) under various discharge conditions, similar to that presented in Fig. 6 for a thoriated cathode. In full agreement with the balance equation, the equilibrium value of \(I_e\) can here also be shifted in either direction by changing the vapor pressure \(p\), the cathode temperature \(T\), and the voltage drop across the tube \(v_a\), analogously to the example given above for Th–W. On the basis of these data, at \(T=680^\circ\mathrm{C}\) and \(p=1.8\) and \(6\,\mu\), a limiting minimum value \(v'_0 \simeq 11\) V was obtained. Under similar conditions of sputtering of an oxide cathode in helium^{43}, which has a high penetrating but very low sputtering ability^{9}, it was found that \(v'_0=40\) V.

A new method for studying the sputtering of oxide cathodes, proposed by Koller^{45}, consisted in determining the change in the thermionic emission of a W filament \(I_e\) placed near the sputtered cathode; the active deposit \(\mathrm{Ba}+\mathrm{BaO}\) sputtered from the oxide cathode, settling on this filament, lowers its work function \(\varphi\) and increases \(I_e\). Carrying out such measurements with a cold oxide cathode in neon at \(p=2\) mm, Koller obtains a very strange result, showing that \(v'_0 \simeq 45\) V. However, if the study of sput-

CATHODE SPUTTERING

deposition of a Ba + BaO precipitate on a W filament in argon at \(p = 1\) mm, at different potentials of this filament relative to the discharge plasma, then the decrease in its emission \(I_e\) associated with sputtering begins to be noticed already at \(v_p = 14\ \mathrm{V}\); at \(v_p = 18\ \mathrm{V}\), \(N = 5 \cdot 10^{-4}\ \frac{\text{atom}}{\text{ion}}\). Similar measurements with neon led to \(v_0 = 15\ \mathrm{V}\).

From all these investigations it is still not clear what the sputtering threshold of real oxide cathodes under real conditions of a gas-discharge may correspond to; an attempt to answer this question was recently made by Morgulis and Lyubarskii\(^{66}\), who used for this purpose a modified Coller method, namely: in a lamp with mercury vapor, in addition to the usual normal heated oxide thermocathode, a W filament was also placed. The appearance on the latter of an active deposit from the oxide cathode, in the event of its sputtering, was recorded not by means of the thermionic emission of the filament \(I_e\), but by measuring its contact potential \(v_k\). The latter is more correct and convenient, since here there is no need to heat the W filament, which serves as the anode in these measurements of \(v_k\), nor for the changes in the state of its surface associated with this heating. Special precautions were taken to allow for the deposit obtained through thermal evaporation from the cathode, to allow for possible changes in the temperature regime of the cathode during the gas discharge, etc. Such experiments showed that the value of the sputtering threshold of oxide cathodes lies still much lower than \(11\)—\(12\ \mathrm{V}\), i.e., at a time when the potential drop across the lamp is \(v_a \leq 6\ \mathrm{V}\) (low-voltage arc). This is evident from consideration of the family of current-voltage characteristics for the W filament—anode, shown in Fig. 9; here curves 1 and 2 show the shift caused by pure evaporation from the oxide cathode without a discharge in the lamp, while curves 3 and 4 show the shift of the characteristic caused by switching on the discharge with \(v_a \simeq 5.6\ \mathrm{V}\), a shift considerably exceeding the preceding shift, i.e., indicating the presence of additional sputtering of the cathode. In order to know the actual energy of the ions bombarding the cathode, it is necessary to investigate, under these conditions, the distribution of the potential in the interelectrode space; this work is now being planned by us, and preliminary results show that in the above-mentioned case \(v_p \sim v_a\). Thus, the value of \(v_0\) for oxide cathodes has a very low value, thereby confirming that, from the constancy of the lamp emission, one still cannot draw unambiguous conclusions about the complete absence of sputtering. It should also be noted that such a low value of \(v_0\)

Fig. 9.

for oxide cathodes only at first glance may seem very strange, for this quantity must be directly connected with the evaporation energy of active surface atoms \(L\) (see below), which in the case of oxide cathodes is equal to \(3.4 eV\), whereas for a Th film on W the quantity \(L = 7.5 eV\). In general, however, it cannot be considered impossible that, with a further increase in the accuracy of the measurements, the value \(v_0\) may prove to be still smaller; for here the matter will reduce to an additional energy activation, upon impact of the ion, of those surface atoms which, as a result of ordinary heating, are in the tail of the exponential distribution of their own energies, i.e., so to speak, on the verge of evaporation.

IV. THE NATURE OF CATHODE SPUTTERING

In the light of the results of experimental investigations of the phenomenon of c. s. set forth above, we shall now turn to the question of its nature, which likewise has a very long history. This question has continually arisen throughout all the years of research on c. s., giving rise to the most diverse points of view on this phenomenon, as a result of which the following theories have appeared here1:

1. The chemical theory, which regards c. s. as the result of some chemical reaction of the incident ion with an atom of the surface (even in the case of ions of inert gases).
2. The radiation theory, which connects c. s. with the absorption of radiation produced during the braking of ions at the cathode.
3. The theory of the explosion of occluded gas present in the cathode, leading to its destruction—sputtering.
4. The theory of cumulative sputtering, which regards c. s. as an act occurring in two successive steps.
5. The impact theory, which regards c. s. as the result of direct knocking-out of a surface atom into the volume upon the impact on it of a fast ion.
6. The thermal theory, which regards c. s. as an act of elementary evaporation from an element of the cathode surface briefly heated by the impact of a fast ion.

If, for brevity, we omit the whole history of this question1 and turn directly to its present state, and in particular to the results of modern experimental investigations (Chs. II and III), then the following must immediately be noted. These investigations, for example, for c. s. at large ion energies (Ch. II), show very clearly that in this case the act of c. s. very closely resembles for us the act of thermal evaporation. Indeed, for this it is enough to recall the values of the velocities of the sputtered atoms and of the effective temperature at the point of impact, the character of the deposit obtained during c. s. on a screen, etc. All this has led to the fact that, of all the above-mentioned theories of c. s. upon impact of a fast—

...of ions, the first four, for quite understandable reasons, did not in general gain appreciable currency, and at first only the impulse and thermal theories were retained, and then, up to the present time, only the thermal theory, in a somewhat different variant. The latter is not only the most natural from the standpoint of interpreting the results of experimental studies of cathode sputtering by fast ions, especially in its modern statistical interpretation (see below), but at the same time it is also one of the oldest theories. In its almost modern interpretation this theory was formulated by Stark as early as 1902,^2 and then, after a long oblivion, was in essence again formulated in 1926 by Hippel^13.

As was already indicated above, the thermal theory of cathode sputtering of Stark and Hippel regards cathode sputtering as the elementary evaporation of atoms from a small element of the cathode surface, heated for a very short time to a very high temperature owing to the impact at this place of a fast ion. In formulating this theory Hippel^13 attempts to cast it in quantitative form in the following way. Using the well-known equilibrium exponential formula for the rate of thermal evaporation, i.e., for the number of atoms thermally evaporating in 1 sec from 1 cm² of surface—\(F(T)\), and assuming the existence of some average temperature \(T_0\) during the time \(\Delta t\) in the heated spot—the source of the sputtered atoms, with surface \(\Delta S\),—Hippel arrives at the following expression for the sputtering coefficient:

\[ N = F(T_0)\Delta S\,\Delta t\,\frac{\text{atoms}}{\text{ion}}. \]

However, it is perfectly clear that, owing to the enormous nonstationarity of this phenomenon in time and in space, the quantities \(T_0\), \(\Delta S\), and \(\Delta t\) entering this equation have no physical meaning, and, consequently, no reliable conclusions for comparison with experimental data can be drawn from this expression. Understanding this himself, Hippel^17 subsequently attempted to give a somewhat different, more natural version of the calculation, in which he had to consider certain elementary processes connected with cathode sputtering. However, as a result of this latter calculation as well, the author again arrived at an expression into which the temperature in the heated spot \(T\) explicitly enters, i.e., in this case too the result cannot be used even for a general comparison with experimental data.

Despite such, it would seem, failures, all subsequent theories, for quite understandable reasons, nevertheless proceeded along the path of further improvement of precisely the thermal theory. The first attempt in this direction was made by Morgulis^36, who, in connection with the pronounced nonstationarity of this phenomenon, proposed using for the distribution of temperature in space and time the expres-

…given by the theory of heat conduction from an instantaneous source of heat \(T=f(r,t)\), assuming in this case that at each separate instant at each element of the surface with temperature \(T\) the evaporation is determined, as in Hippel, by the known equilibrium formula \(F(T)\). Thus, the sputtering coefficient proves to be equal to

\[ N=2\pi \int_{0}^{\infty}\int_{0}^{\infty} F[f(r,t)]\,r\,drdt=A v_p^{4/3}, \]

where the quantity \(A\) clearly depends on the physical parameters characterizing the gas ions and the surface being sputtered, and its value can be determined. From this formula there at once follows the nearly linear dependence \(N=f(v_p)\), very close to the experimental data.

Two years after the publication of this work, a paper by Sommermeyer\(^{47}\) was published; proceeding from precisely the same considerations and the same expression for \(T=f(r,t)\), he obtained for the sputtering coefficient \(N\) exactly the same formula, but only with a somewhat different value of the coefficient \(A\); the latter is connected with the fact that Sommermeyer assumed that, as a result of the impact of a fast ion, the temperature in the local spot rises above the critical temperature, where the principal evaporation of the surface atoms occurs according to a different, final, formula \(F(T)\).

Then Izmailov\(^{58}\) further developed this method of calculating the thermal theory of c. s., using the same expression for \(T=f(r,t)\), and obtained for the quantity \(N\) an expression of the same type. For the coefficient of useful sputtering action \(\eta\) he obtains \(\eta=\dfrac{5}{2}N'\left(\dfrac{L}{v_p}\right)\); however, since \(N=A v_p^{4/3}\), then with increasing \(v_p\) the quantity \(\eta\) may also increase without bound, from which the author draws the conclusion that it is necessary to take additional account, in the calculation, of the cooling action of evaporation.

Finally, quite recently\(^{74}\), another theory of c. s. was developed for relatively high gas pressure, in which the thermal variant of the theory of c. s. presented above is again used, with the same expressions for the function \(T=f(r,t)\) and the equilibrium formula for the evaporation rate \(F(T)\). The results thereby obtained are in general agreement with the data of qualitative experiments\(^{72}\) on the sputtering of cold active cathodes in glow-discharge lamps.

Summing up this—the second—stage in the development of thermal theories of c. s., the following should be noted:

There are no grounds, even at the present time, to consider that the basic premises of the thermal theory of c. s. are in any degree incorrect; however, at the same time, there are very serious grounds for questioning the admissibility of pri-

...of the methods of calculation presented above.^57 In fact, the energy transmitted upon impact of a fast ion directly to the atoms of the metal lattice will immediately begin to spread throughout the metal in all directions at a very high rate, for the relaxation time of the thermal conductivity of the lattice \(\tau_a\) is of the order of the period of vibration of the atoms in it, i.e. \(\tau_a \sim 10^{-13}\) sec. The thermal conductivity of the electron gas of the metal should here be neglected, since the energy exchange between the lattice, which directly receives the energy from the striking ion, and the conduction electrons of the metal takes place very slowly; from this, incidentally, it follows that: 1) from the standpoint of heat removal, the value \(N\) should not differ noticeably for metals and dielectrics (see Chapter II); 2) cathodic sputtering of metallic surfaces under electron impact should be regarded as impossible (see below); and 3) the kinetic emission of secondary electrons, when fast ions strike a metal surface, cannot in principle be interpreted as an elementary thermoelectronic effect.^47,57

In view of such a rapid course of the process of heat removal from a local element of the surface, it is naturally impossible to use the formulas given above for evaporation, which pertain to conditions of temperature equilibrium; this, consequently, casts doubt on all the theoretical calculations presented above. In reality, however, the disturbance caused by the ion impact is transmitted rapidly from atom to atom; in this case there occurs a complex, statistical in character, nonstationary transfer of energy, when there is some probability that one or more surface atoms will acquire a “normal energy” exceeding the sublimation energy \(L\), i.e. that an act of sputtering will occur. This very complex statistics, in the particular case of temperature equilibrium, must lead to the usual formulas for evaporation. Thus, the old thermal interpretation of the phenomenon of cathodic sputtering must be replaced by a new, more general one—a statistical interpretation, representing a distinctive synthesis of the old thermal and momentum theories, and covering the entire range of ion energies, from very large down to very small ones close to the critical energy.

Since the quantitative development of such an obviously very difficult theory is still a matter for the future, we undertook an attempt to test this statistical theory of cathodic sputtering with the aid of a mechanical model of a solid.^57 The latter consisted of a box into which, in many layers, 6000 steel balls—“atoms” of the solid—were poured, packed in a definite manner.

From a certain height \(h_p\), other balls—the “sputtering ions”—were dropped onto this model of a solid, and, with the aid of a FED camera, the tracks of the “sputtered” balls-atoms of the solid that flew out upon impact were photographed; it can be shown, using the appropriate criteria, that for the case of cathodic sputtering upon impact

of fast ions, the use of such a model of c.r. is quite admissible and possible. The results obtained in this way may be summarized as follows:

1. The distribution of emitted balls according to “normal energies” in a flat retarding (gravitational) field has an exponential, “Maxwellian” character.

\[ N = N_0 \exp\left(-\frac{h}{h_0}\right), \]

as is seen, for example, from Fig. 10, although it is perfectly clear that there can be no question here of any equilibrium evaporation with some definite temperature. The mean energy \(h_0\) corresponds approximately in magnitude to \(\dfrac{h_0}{h_p}\sim 10^{-3}\), as is the case in real instances of c.r.

1. The dependence of the sputtering coefficient \(N\) on the energy of the “ions” \(h_p\) has, as is seen from Fig. 11, a linear character.

2. With dense packing of the surface atoms, their emission by angles is confined to a narrow cone; however, if, approaching real conditions, the surface is loosened (loose packing, the presence of separate hillocks, etc.), then the aperture of this cone broadens considerably, coming ever closer to the cosine law.

Fig. 10.

Fig. 11.

Thus, the results obtained with this model correspond, in their general character, to the data of experiments on real c.r. by fast ions, and, consequently, one may think that also in the latter case the emission of sputtered atoms actually has a certain nonequilibrium statistical character.

Let us now turn, in a few words, to how one should understand the minimum critical energy \(v_0\), at which c.r. is still possible. This question, too, has been analyzed more than once in the past by various authors, chiefly from the standpoint of various kinds of impulse concepts. Thus, for example, Stark [3] and Holst considered the condition for \(v_0\) from the standpoint of transferring to the surface atom an energy exceeding the evaporation energy \(L\),

although the energy loss connected with the interaction of the sputtered atom with the lattice was not taken into account (see below). Then Langmuir \(^{9}\), in a very artificial way, considers this process as two-stage, i.e. 1) the formation of a micro-well on the surface, due to the impact of the first ion, and 2) the reflection from the bottom of this micro-well of the second ion, with the knocking-out—sputtering—from its edge of a surface atom. A certain variant of these theories is found in the work of Hertz \(^{30}\), who considers cathode sputtering as the dissociation of surface molecules, for which (metal!) he regards activation, dissociation by a cumulative path, and allowance for the energy of neutralization of the sputtering ion in the overall energy balance during sputtering as possible.

Finally, in the most recent works of this direction \(^{41}\), the phenomenon of sputtering is considered in the following way. When an ion strikes a surface atom (a hard individual collision), a certain energy \(v_a = av_p\) is transferred to the latter (\(a\) is the accommodation coefficient). However, before flying out, this atom, in its motion within the sphere of interaction with the lattice, gives up to it some fraction of its energy \(\gamma v\), where \(\gamma < 1\), i.e. the condition for the existence of cathode sputtering will be

\[ (1-\gamma)v_a = (1-\gamma)av_p > L. \]

Hence the condition corresponding to the minimum sputtering energy \(v_0\) will refer to a central (optimum for energy transfer) impact, i.e. \(a_0(1-\gamma)v_p > L\), or

\[ v_0 = \frac{L}{a_0(1-\gamma)}. \]

Unfortunately, at present we lack data concerning the magnitude of \(\gamma\), and consequently the possibility of comparing this formula with experimental results. This rather simplified calculation does not take into account the intrinsic energies of the surface atoms, especially in the case of a heated thermionic cathode, when, as was already indicated above, naturally, the sputtering boundary may become somewhat indefinite and sufficiently small. The situation arising here is, in character, analogous to the known case of the photoeffect of metals near the red limit at high temperatures, according to Fowler and DuBridge.

It should be noted that, in essence, all the considerations set forth here concerning \(v_0\) are a special case of the general statistical theory presented above, only applied to very small limiting energies of the sputtering ion. Therefore the future quantitatively developed theory of cathode sputtering will indeed be very general, embracing this phenomenon at all possible energies of the sputtering ions \(v_p\) and including all the cases set forth above, both individual and particular.

V. CONCLUSION

From the research results on cathode sputtering set forth above, it is clear that considerable progress has recently been achieved in the study of this phenomenon, as a result of which a number of interesting questions have been clarified, although, of course, a number of others still require further investigation. In connection with these further investigations, it should be noted that it is necessary to bring to full completion the question of the threshold energy of sputtering, in particular for economical cathodes; to create a unified quantitative theory of cathode sputtering covering the entire range of energies of the sputtering ions; to study the energy balance and the excitation associated with the impact of a heavy particle (ion or atom) on a solid surface; to study the cathode sputtering of semiconductors and dielectrics, etc. It should be noted that this last question—the cathode sputtering of semiconductors and dielectrics—is very interesting not only because a number of modern efficient cathodes, such as, for example, the barium-oxide thermocathode of gas-discharge devices, oxide-cesium and other photocathodes of gas-filled photocells, etc., are semiconductors, but mainly because in this case one may already expect the partial utilization, for cathode sputtering, not only of the kinetic energy of the heavy particle—ion or atom—but also of its potential excitation energy, the energy of photons, and the kinetic energy of electrons. In this case the phenomenon of cathode sputtering will occur similarly to the phenomenon of photodissociation or the dissociation of molecules by electron impacts, and this is possible only with discreteness of the electronic levels of the sputtered surface atom, which we do not have in the cases of metals studied up to now. It is therefore unquestionable that the undertaking of all these investigations is highly desirable and promising from the standpoint of the interesting results of both physical and practical character expected here.

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