STRUCTURE AND PHYSICAL PROPERTIES OF THIN METAL LAYERS

A. T. Aitselov, Leningrad

I. Introduction

The metallic state of matter, in the broad sense of the word, is characterized by high conductivity for electricity and heat and by strong absorption and reflection of light1. The metallic properties are most vividly expressed in true metals, which in their behavior differ sharply from nonmetallic substances.

It should be noted that these properties are characteristic of a special aggregate state, in which metals exist under ordinary conditions and which we call the metallic state. When the aggregate state of metals changes, their physical properties change sharply. Thus, the electrical conductivity of metals upon transition to the liquid state decreases by a factor of 1.5–2 (with isolated exceptions). In the vapor state, however, metals in general do not exhibit the properties of the metallic state as defined above. Experiment and theory have together led to two basic conceptions concerning the metallic state, namely, it has been established that: 1) substances in the metallic state are crystalline and 2) there are free electrons in the metal lattice. The hypothesis of free electrons, proposed by Riecke and Drude and developed by the latter and by other investigators on the basis of classical physics, led to good agreement between theory and experiment only for certain phenomena in metals (the Wiedemann–Franz law, the Richardson effect).

However, the theory of free electrons, which was based on the Maxwell–Boltzmann distribution, could not overcome certain difficulties, for example, on the question of the heat capacity of metals. All attempts to improve or modify this theory within the framework of classical physics failed, and theo-

...theory was abandoned. Only with the development of the new physics was the electron theory of metals revived and did it achieve great successes. Even while retaining Drude’s physical ideas, the application of Fermi–Dirac statistics to the electron gas made it possible to overcome the difficulties of the old theory. The further development of the electron theory of metals is connected with taking into account the interaction of the electrons in a metal with its ionic lattice. The theory constructed in this way already explains the basic phenomena in metals quite satisfactorily and offers greater possibilities for elucidating, from the observed electrical properties, the material processes occurring in metals.

Metals exhibit the properties of the metallic state over a very wide temperature interval. A sharp change in properties occurs only either at very high temperatures (near the melting temperature), or at temperatures close to absolute zero, where the phenomenon of superconductivity is observed. Within this temperature interval the physical properties of metals, although they change as a function of temperature, do so very smoothly and in an explicable manner. However, in thin metallic layers (with thicknesses of the order of several millimicrons) there has been established a sharp change in the properties of metals under ordinary temperature conditions, going beyond the framework of the metallic state, where massive metals behave normally. Such anomalous behavior is observed especially clearly in electrical, magnetic, and optical properties. It is possible that other properties, for example mechanical ones, also undergo sharp deviations; however, their investigation in thin layers presents great difficulties and therefore is not undertaken.

The change in properties always occurs in such a way that the metallic layer approaches a dielectric in its behavior. In this sense, the change in the electrical conductivity of thin metallic layers as a function of thickness is very characteristic. In thick layers the specific electrical conductivity is practically independent of thickness. But when the thickness is decreased to a certain limiting value, the electrical conductivity begins to fall sharply and reaches values hundreds of thousands of times smaller than the electrical conductivity of the massive metal. In Fig. 1 the change in the resistance of a platinum layer as a function of thickness is presented (the curve is taken from Pogany’s paper^[1]^).

The change in electrical conductivity has been studied for most metals by many authors. The values of the critical thickness, even for one and the same metal, are then obtained as different. What is essential, however, is that all the curves have the same form as the curve shown in the figure.

We observe a similar picture for the change in the optical constants \(n\) and \(k\) of thin metallic layers as a function

^[1]^ See also works ^57, 60, 104^.

…on the thickness. In Fig. 2 the corresponding curves are presented (from the same paper by Pogany^54 for platinum)^1).

Such anomalous behavior of thin metallic layers is of considerable interest for investigation from various points of view. The study of these anomalies may be very useful, if only for refining our still imperfect ideas about the metallic state in general. A whole series of other important physical phenomena—such as, for example, the mechanism of condensation of metal vapors on solid surfaces, and the influence of structure on the physical properties of a layer—may likewise be elucidated in the study of the anomalous properties of thin layers.

Fig. 1

In addition, from the practical point of view as well, the problem of thin layers is highly topical. It is known that thin metallic layers find extensive application in practice, for example as reflecting surfaces in interference, astronomical, and generally optical apparatus, in the manufacture of photocells, and in other fields. For these reasons thin layers are the object of very extensive investigations.

Fig. 2

In evaluating work on thin layers, one must unfortunately state that, despite the enormous number of investigations devoted to this question over the course of several decades, the results achieved are very modest. Indeed, the ultimate aim of any investigation should be, first, a complete understanding of the processes taking place in the object under study, and, second, such control of these processes as would make it possible to use the object in our practical activity.

^1) See also 15, 83, 89, 150, 188.

In reality, we not only lack an unambiguous explanation of the observed phenomena, but even on the factual side encounter contradictory data. It goes without saying that these circumstances considerably restrict the range of application of thin metallic layers.

The slow progress in the problem under consideration is explained by the fact that, until the last decade (and in part even now), theoretical conceptions of the metallic state and the experimental capabilities of physicists for investigating thin layers were insufficiently advanced. Thin metallic layers are an extremely delicate object of investigation; here the results depend on many extraneous, sometimes quite unexpected circumstances which, in view of the smallness of the effects caused by the layers themselves, distort the true picture and make the solution of the problem difficult.

Recent advances in physics have created conditions that have sharply increased the effectiveness of investigations of thin layers. We have in mind here the electronographic method for determining the structure of substances. With the development of this method it became possible to study the connection between the properties of a layer and its structure, as determined by an independent method. The influence of structure on layers, following at least from general considerations, had of course been observed even before the advent of electronography; however, notable successes in this direction were obtained only after electronographic investigations. In recent years several works have appeared which are of great interest for the field of phenomena under consideration; although they do not solve the problem, the results obtained make it possible to draw very important conclusions both about the nature of the phenomena and about the path along which further investigations should be directed. The exposition of these works is the aim of the present article.

II. Methods of Obtaining Thin Metallic Layers

Thin metallic layers are deposited on transparent (glass, quartz, crystals) or metallic surfaces by various methods: electrolytically, by chemical precipitation, by evaporation of colloidal solutions, and by condensation of metal vapors. For the thinnest layers practically only vapor condensation is used, since it provides the best conditions for obtaining, preserving, and investigating the layers. We shall therefore confine ourselves to the characterization of this one method, all the more so since in the works whose results are presented, other methods were not used.

The production of the metallic vapor itself is carried out in two ways: 1) by thermal evaporation of the metal in a high vacuum, 2) by cathodic sputtering of the metal.

Both the first and second methods are not faultless and have their disadvantages. The choice is usually determined by the aims of the investigation. Thermal evaporation is carried out in a high vacuum and is effected in a closed…

depending on the individual properties of the metal, in different ways. Refractory metals are introduced into the vacuum apparatus in the form of wire or ribbon and are heated by a current passed through them. Other metals (gold, silver, etc.) are first deposited electrolytically onto a wire of refractory metal, or are even simply suspended in the form of a loop. High-frequency furnaces are also used for evaporating the metal. The positive aspects of this method are its comparatively simple realization and the purest experimental conditions in comparison with other methods. However, some investigators (Kramer) believe that in certain cases the method of cathodic sputtering is preferable, since in thermal evaporation: 1) the rate of evaporation cannot be controlled with more or less exact dosing, 2) the atoms fall on the receiving surface with high velocities (and may cause local thermal effects), and 3) there is thermal radiation from the heated metal. All these circumstances, in Kramer’s opinion, may sometimes cause distortion of the results.

In cathodic sputtering the metal under investigation is introduced into the apparatus usually in the form of a plate and serves as the cathode. Between the cathode and the anode a substrate for the layer is placed. The voltage is taken as 1500–2000 V. Sputtering is carried out in the presence of some gas. With this method it is possible to work at any deposition rates, since this is achieved by simply feasible regulation of the pressure, voltage, and current strength.

Here it is quite probable to suppose that at small current densities the velocity and thermal effects will practically not affect the results. However, in this case too there are sources of error that are difficult to control. Sputtering is carried out in the presence of some gas, which under the conditions of an electric discharge is activated and may, generally speaking, in one way or another influence the layer being formed. Thus, Ingersoll[^52] observed that nickel films deposited by the method of cathodic sputtering contain more gas than the same films obtained by thermal sputtering at the same gas pressure.

In addition, with energetic cathodic sputtering aggregation of the metal vapors is possible already in the volume, so that not metal atoms but very small particles will be deposited on the substrate. Let us note that in all the preceding considerations it is assumed that in the process of sputtering vapors, and not metal particles, fly off from the cathode. This point of view was put forward by Gillpearl[^39], who represents the mechanism of sputtering as follows: upon the impact of an ion on the cathode, strong local heating of the latter occurs, accompanied by evaporation of the metal. Such a mechanism of sputtering is confirmed by the investigations of Seeliger and Sommermeyer[^132] and, apparently, is now generally accepted (although there also exists another point of view, according to which, upon the impact of an ion on the cathode, as a result of mechanical destruction, not atoms but particles of the metal fly off from the latter).

III. Methods for Establishing the Structure of Thin Metallic Layers

Modern physics has various possibilities for assessing the structure of matter. Foremost among the means of analysis in this respect should be placed such means as X-rays and electron beams, which are methods for the direct determination of structure. For the study of thin layers these methods are also applicable, although to differing degrees. X-rays are scattered very weakly; therefore their application to thin layers is not advantageous. Electron beams possess an enormous scattering power in comparison with X-rays and therefore allow the analysis of extremely thin layers in a very short time. For this reason, after electron beams—recently discovered and soon transformed from an object of study into an instrument of research—began to be applied to thin layers, they completely displaced radiography from this field (although the latter had previously been applied very little precisely to thin layers).

The electron-beam method is applicable to layers beginning with extremely thin ones; the upper limit of thickness for the application of electron beams is of the order of 100 mμ. Thus the entire range of thicknesses interesting from the standpoint of anomalous properties is covered by this method. The method makes it possible to clarify very fine details of the structure of the object under investigation. It reveals not only the crystallinity of the structure of the specimen, but also gives an indication of the orientation of the crystallites, their size, and the character of the surface of the specimen. Investigation can be carried out both in reflected and in transmitted beams. In terms of execution, it is simplest (and for some purposes, for example for determining the size of crystallites, also the most advantageous) to work in transmitted electron beams. However, this method of investigation is extremely limited by the following circumstance. Electron beams are strongly absorbed; therefore, in transmitted beams it is possible to study only layers deposited on very thin celluloid or collodion films. Meanwhile, for practice it is most important to study layers on comparatively thick glass, quartz, or crystalline substrates. In the latter case one must work exclusively by the reflection method.

The question of assessing the structure of thin metallic layers may also be approached from another side. The electrical properties of massive metals have been studied rather well. Therefore, knowing the dependence of the electrical conductivity of a massive metal on its temperature and lattice state, and considering these laws valid also for thin layers, we can proceed by the reverse route, i.e., in the direction of the change in electrical conductivity depending on the thickness of the layer and on its temperature, to form an idea of the structure of the layer. This method is, of course, indirect, but according to the assertion of some investigators, in particular cases it even has advantages

before direct methods of determining structure. In our opinion, there are at present insufficient materials for such an assertion, and we leave it to the responsibility of these investigators; but there is no doubt that the results of investigating metallic layers according to this principle are of considerable interest, and we shall briefly recall here the foundations of such an approach to the study of layers.

Such a foundation is Matthiessen’s rule, established experimentally and justified in modern theory. As is known, it consists in the following: if any impurity is added to a metal, the electrical conductivity of the metal decreases (even if the added impurity itself has a greater electrical conductivity than the base metal). This effect remains also in the case where the disturbance of the normal crystal lattice is produced not by an impurity, but, for example, by deformation of the metal. In this case the additional resistance does not depend on temperature, in contrast to the resistance of a pure metal, which increases with temperature. Thin metallic layers are obtained under conditions in which the formation of a normal lattice is rather unlikely; therefore the property of electrical conductivity that we have indicated may be a very sensitive reagent for structural changes in the layer.

Finally, let us dwell also on optical methods of observation. Optical investigations of thin metallic layers are very numerous. They may be divided into two groups. The first group includes observations whose aim is the determination of the optical constants: the refractive index \(n\) and the absorption index \(k\). It should be borne in mind that methods for determining the optical constants of thin metallic layers are based on the electromagnetic theory of light, into which these constants enter as purely phenomenological concepts. Therefore, knowledge of \(n\) and \(k\) gives only the possibility of reducing various optical phenomena characteristic of layers to a certain pair of numbers, but says nothing about the nature of the layer. From this, however, one should not conclude that optical methods are of little effectiveness. First, knowledge of the optical constants is important in itself for practical purposes. Secondly, comparison of the optical constants with data from other methods makes it possible to draw a conclusion about the connection of the optical properties with the structure of the layer, and knowledge of this kind is highly significant for many reasons. In particular, this dependence can be used for judging processes in layers when other methods of investigation are inapplicable. There is also one more circumstance that requires knowledge of the optical constants. It is known that on the surface of thin metallic layers, under certain conditions, foreign films arise. The fact of the formation of such foreign films on metallic surfaces was established long ago. It is also known that these surface films change the optical properties of a thin metallic layer. Therefore there arises the necessity of studying their

properties and conditions of formation. For this purpose, Drude developed in optics a method that makes it possible to determine the refractive index and thickness of a transparent film formed on the surface of a metal, provided that the optical constants of the pure metal (free from the surface film) are known.

The second group of optical observations is, in idea, most directly related to the problem under consideration. Here we are speaking of attempts to apply the optical theories of colloidal solutions of metals to thin metallic layers.

The general theory of the optics of colloidal solutions of metals has been developed by many investigators. The attainment of definite practical results in this direction is associated chiefly with the names of Maxwell-Garnett \(^{8,10}\) and Mie \(^{13}\). Considering colloidal solutions of metals consisting of metallic spheres suspended in a solvent, Maxwell-Garnett—and later, for a more general case, Mie—gave working formulas that make it possible to calculate the optical properties of such systems, if the optical constants of the dispersed metal in the massive state, the refractive index of the medium surrounding the particle, and certain constants characterizing the structure of the system are known (in Maxwell-Garnett, the “filling factor”—the volume of metallic spheres per unit volume of solution; in Mie, the particle diameter). In this way it was possible, to some extent, to explain a number of optical properties of colloidal solutions of metals. We shall not here compare the two indicated theories from the standpoint of their correspondence to real phenomena in solutions, since this is not required for our purposes. Let us note only that Mie’s theory is more perfect and agrees better with experimental data in the case of solutions. We shall dwell in greater detail, however, on the question of the possibility of extending the formulas of Maxwell-Garnett and Mie to thin metallic layers \(^{1}\).

Two circumstances (apart from that indicated in the note) impel investigators to proceed precisely along this path. The first is that, in an optical sense, colloidal solutions of metals and thin metallic layers exhibit analogous properties, namely: the color of both, and its change, can be treated from a single point of view. The second circumstance lies in the great effectiveness of this method. Indeed, the formulas relate the optical constants of the object being studied to constants characterizing its structure. Thus, from optical observations it is possible to draw quantitative conclusions about the structure of the layer and its influence on its physical properties, and this is one of the decisive questions of the whole problem. This also explains why already

\(^{1}\) By this it is already assumed that the layers have a finely crystalline structure. We note that in most cases precisely such a structure is observed. In those cases where we are dealing with another structure, these views, of course, are not applicable.

Maxwell-Garnett himself, and subsequently many other investigators, applied the representations of Maxwell-Garnett and Mie to thin metallic layers.

However, a number of difficulties arise here. The considerations given above are quite insufficient to draw a conclusion about the admissibility of identifying layers and solutions in the sense of the indicated theories. On the contrary, from the fact that the surrounding medium for a metal particle in a solution and in a layer is completely different, doubts may arise about the validity of such a step in general. This becomes clearer from a consideration of the basic premises of Maxwell-Garnett and Mie. Both authors assumed that: a) the metal is present in the solution in the form of spherical particles, b) the particles are surrounded by one and the same medium, and c) the particle diameters are small in comparison with the distances between them1 (the latter leads to the fact that the intensity of absorption or scattering by any volume is equal to the intensity for one particle multiplied by the number of particles in the volume. The validity of such a method of calculation was theoretically justified by Trinks[^134]).

It is easy to see that these conditions are far from being fulfilled in thin metallic layers. It follows from this that the use of this apparatus will be fully justified only in the event that it is shown that the deviation of the particle shape from a sphere, the change in boundary conditions, and the closer arrangement of particles in a layer, as compared with a solution, either do not affect the optical properties of the colloidal system, or affect them in a manner known to us.

Attempts to solve some of these questions have been made. Thus, Trinks[^134] solved the problem for the case when the distances between particles are commensurable with their dimensions; Gans[^17] and Moglich[^44],[^82a]—for particles of ellipsoidal form. However, the results of all the authors for particles of finite dimensions are so complex that it is practically impossible to use them. The question of the effect of replacing a liquid medium by the boundary of a solid body—air, so far as we know, has not been subjected to serious theoretical investigation at all.

Thus the state of theoretical investigations (at the present time) does not allow us to decide unambiguously the question of the limits of applicability of the Maxwell-Garnett and Mie formulae to optical phenomena in thin metallic layers. Nevertheless, such an application is being made, and this is a quite expedient step. The point is that the physical similarity of solutions and layers in the sense of these theories, which follows, as was already said above, from their optical behavior, and also from ultramicroscopic observations, suggests that within certain, albeit very limited, limits the Maxwell-Garnett and Mie formulae also describe the phenomena in layers. And since we do not have a more accurate theory, then, consequently,

as a first approximation we are compelled to use even an imperfect theory. In doing so, one must only remember the limitations of the analogy and approach the evaluation of the results with due caution.

IV. Results of Observations

1. Electronographic Studies

We shall confine ourselves here to a detailed presentation of the results only of those works that have been published in recent years. Earlier, very interesting works by Kirchner and by the Russian investigators Gen, Zelmanov, and Shalnikov have already been covered in our literature (see the monograph by Yu. B. Khariton and A. I. Shalnikov) ^111; therefore here we shall only briefly recall their principal results.

Kirchner ^73, ^191 studied thin layers of Au, Ag, Bi, and of certain metal compounds and established that metallic layers exhibit a crystalline structure down to extremely small thicknesses, when the absorption amounted to only 2% of the incident light. However, in the thinnest layers the interference rings are very strongly blurred, which indicates an extremely small size of the crystallites forming the layer. With increasing thickness the rings become sharper, which indicates an increase in the crystallites. The structure of thin layers proves to be unstable, and recrystallization of the layers is observed (growth of the crystallites and sometimes their ordering). With increasing temperature, recrystallization is accelerated.

Gen, Zelmanov, and Shalnikov ^81 investigated the dependence of the structure of Cd, Hg, Ni, and Fe on the temperature of the substrate. The investigations were carried out by the reflection method; the films were deposited on a glass surface at the temperature of liquid air. In all cases a crystalline structure of the layers was likewise found, the layers obtained at low temperature consisting of very small crystallites (less than \(10^{-7}\) cm); with increasing temperature, recrystallization was also observed, i.e. an increase in the crystallites. This process proceeds more readily for cadmium layers than for nickel layers. It was also found that an increase in the rate of deposition decreases the dispersity of the layer; for cadmium layers an orientation of the crystallites on the substrate was observed.

Lassen and Brück ^122 studied the influence of the nature of the substrate and of its temperature during deposition on the structure of the layer and showed that it can be very considerable. They sought conditions under which monocrystalline layers of metal could be obtained. The investigations were first performed in transmitted, and then also in reflected, rays on silver layers. It turned out that layers deposited on a crystal of rock salt (a fresh cleavage surface), heated to a temperature above 100°, show the pattern of monocrystalline layers. They did not give more precise indications of the substrate temperature on this page.

To the article by A. T. Ascheulov

Fig. 3.

Fig. 4.      Fig. 5.      Fig. 6.

Fig. 7.

On the article by A. T. Ashcheulov

Fig. 8.

Fig. 9.          Fig. 10.

Fig. 11.    Fig. 12.    Fig. 13.

do not lead to this. In Fig. 3 a photograph of one such layer is presented, the thickness of which is 30 mμ.

In this case such a structure was observed over the entire extent of the specimen, which is proved by the fact that, when the specimen was moved in a plane perpendicular to the beam, the interference pattern did not change. The orienting influence of the substrate—a rock-salt crystal—was also observed by the authors at room temperature, although to a lesser degree. With further deposition onto such a silver layer the layer grew as a single-crystalline one even at room temperature. According to the authors’ conclusion, such single-crystalline layers can be obtained with any thickness. Experiments both in transmitted and in reflected rays gave identical results (for investigations in transmitted rays the layer was washed off the substrate with water and deposited on a metal frame). Layers obtained under the same conditions on thin celluloid films do not show such orientation.

Very interesting are the results of the work of G. Hass²⁰², published in 1938. The author investigated films of silver and antimony. He set himself the task of determining the optical properties of thin metallic layers as a function of their structure. For this purpose he made preliminary structural determinations in the indicated metals, which he deposited in high vacuum on collodion films. The experiments were carried out in transmitted electron rays. The structure was observed as a function of the temperature of the substrate. Hass established a very interesting phenomenon. When he cooled in high vacuum the layers obtained, which up to that point had given a good interference pattern of crystalline layers, the layers became covered with a transparent foreign layer, the thickness of which reached more than 100 mμ. To eliminate this he made the following device: he surrounded the layer with a metal jacket with an aperture, everything being arranged so that this protective device was cooled earlier and to a lower temperature than the layer under investigation; owing to this one could expect that foreign vapors would condense not on the layer but on the protective device. This device did indeed eliminate condensation of the film on the layer.

The nature of the phenomenon can be judged from Figs. 4, 5, and 6. They show electronograms of one and the same silver layer. The photograph in Fig. 4 was made from a layer cooled for 10 min to −180° in the presence of the protective device. The photograph corresponds to a crystalline metal. The photograph in Fig. 5 was made from the same layer, cooled for 1 min to −180°, but without the protective device. The pattern changed noticeably. The photograph in Fig. 6 corresponds to the same layer, but cooled to −180° for 10 min without the protective device. The pattern of the crystalline metal disappeared altogether. By an optical method the author established the refractive index and the thickness of these surface layers. The nature of these layers has not been established precisely. In the case of...

when heated to room temperature they disappear. These experiments are extremely important and may introduce serious corrections into previous investigations.

Then, under conditions ensuring the absence of a covering extraneous layer, the structure of metallic layers was investigated. The dependence on temperature is clearly visible from the photographs that we present. In Figs. 7 and 8 electron diffraction patterns are shown of two silver layers, each approximately 50 mµ thick. The first was deposited at \(-175^\circ\), the second at \(+150^\circ\). From the nature of the interference pattern it is immediately evident that, with an increase in the temperature of the substrate, the size of the crystallites increases. The influence of temperature on recrystallization is observed very clearly for antimony layers.

Figs. 9 and 10 are electron diffraction patterns of antimony layers approximately 50 mµ thick; the first photograph corresponds to a layer deposited at \(-175^\circ\), and the second to the same layer heated to room temperature. In the first case the layer is crystalline, but highly dispersed. In the second case we already have a coarse-crystalline structure. The influence of temperature depends on the thickness of the layer. This dependence is clarified by Figs. 11, 12, and 13.

Fig. 11 is an electron diffraction pattern of an antimony layer 10 mµ thick, deposited at \(-150^\circ\) and heated to room temperature. Comparing Figs. 11 and 10, we see that in thin layers the influence of temperature is manifested less clearly. For the same transformation of a thin and a thick layer it is necessary to heat the former to a higher temperature than the latter.

In Fig. 12 there is an electron diffraction pattern of the same layer heated to \(+100^\circ\). The last photograph (Fig. 13) relates to an antimony layer approximately 70 mµ thick, deposited at \(+150^\circ\). The pattern corresponds to a monocrystalline layer. Hass also established that the higher the deposition rate, then, other conditions being equal, the larger the crystallites of which the layer consists.

The dependence of the structure of thin metallic layers on heating of the substrate during deposition was investigated by Krautkrämer \(^{203}\) in reflected electron beams. He deposited layers of gold and silver on quartz plates in a high vacuum. The temperature of the substrate during deposition was varied from 20 to \(300^\circ\). As a result Krautkrämer found that for both metals there exists a certain thickness interval, depending on the temperature of the substrate during deposition, in which the layers show increased submicroscopic roughness (Rauhigkeit). Thus, in agreement with the preceding, in this case too an increase of crystallites with increasing substrate temperature is observed.

The observations cited, made by all the authors at different times, agree very well with one another and give a sufficiently complete picture of the structure of thin metallic layers and of their dependence on various conditions. Let us briefly summarize the results of these investigations:

1. Thin metallic films obtained by condensation in vacuum always exhibit the crystalline structure of an ordinary metal.

2. While remaining crystalline, their structure is strongly dependent—in terms of ordering and of the size of the crystallites forming the film—on the individual properties of the metal, the temperature of the substrate during deposition, the nature of the substrate, the thickness of the film, and the rate of deposition.

3. The dispersion of the film increases: a) with increasing melting and boiling temperatures of the metal, b) with decreasing substrate temperature during deposition, c) with decreasing deposition rate, and d) with decreasing film thickness.

4. The orientation of crystallites improves for crystalline substrates and with increasing temperature.

5. Very often the structure of thin films proves to be unstable, and therefore the phenomenon of recrystallization is observed, both spontaneous and induced, for example, by heating.

2. Electrical Conductivity of Thin Metallic Films

In the introduction it was already stated that anomalous electrical conductivity occurs in thin films. This fact has been established by numerous observations and is quite indisputable; we shall not give more detailed information on this question. Here the question of anomalous electrical conductivity is treated from another point of view. As we saw above, the influence of the temperature of a film on its structure is very considerable. Some investigators have attempted to obtain information about the structure of the film from the temperature dependence of electrical conductivity and to explain the anomalous properties of thin metallic films. As a result of investigations of this kind, Kramer\(^{76,190}\) arrived at a conclusion that differs from the conclusions reported above on the basis of electronographic determinations. In our opinion, Kramer’s experiments are of considerable interest, and we shall dwell on the principal ones.

Kramer deposited films at low temperatures and observed the change in the electrical conductivity of the films as the temperature was raised. In doing so he succeeded in finding that at a certain temperature \(T_u\), which he calls the transformation temperature (Umwandlungstemperatur), the electrical conductivity increases abruptly and irreversibly. This is observed especially clearly for antimony films, as can be seen from Fig. 14.

For other metals such a sharp break is not observed, but with a careful increase of temperature Kramer also found a point there corresponding to the transformation temperature. We give the curve for nickel obtained by Kramer in Fig. 15.

Kramer further observed the temperature dependence of electrical conductivity and found that up to the transformation temperature \(T_u\), with increasing

of temperature the electrical conductivity increases, i.e. the temperature coefficient of resistance is negative; this increase is reversible; above the transformation temperature it is positive, i.e. it differs from the coefficient for normal metals only quantitatively.

These experiments are difficult to explain in any way if the layers are regarded as crystalline up to the transformation temperature; therefore Kramer proposed that, before the transformation temperature is reached, the layers were not crystalline but amorphous, and that at the transformation temperature \(T_u\) the amorphous modification of the metal passes into the ordinary crystalline one.

Fig. 14.

Fig. 15.

In a number of subsequent works Kramer develops this point of view and gives some new evidence in its favor. Very interesting is his experiment with the simultaneous determination of the electrical and magnetic properties of an iron layer. In Fig. 16 the course of the electrical conductivity and magnetic permeability of such a layer is presented.

At the transformation temperature the electrical conductivity of the layer rises sharply; at the same time the magnetic properties at this moment only appear and then increase vigorously. Kramer explains the experiment as follows: during the condensation of atoms from metal vapors, for each metal one can obtain, at a certain low temperature, a layer of the metal in the amorphous state. In this state the atoms are not ionized, i.e. there are no free electrons, and the lattice is also absent. At the transformation temperature a sudden ionization of the atoms occurs; free electrons appear, and a sharp increase in electrical conductivity sets in1; the formation of the lattice also begins at the transformation temperature, but proceeds slowly, and therefore the magnetic properties, conditioned by the presence of the lattice, grow after \(T_u\) has been reached. In sufficiently thick layers the temperature \(T_u\), according to Kramer, is a material constant and does not depend on the thickness.

TABLE 1

Table 1 gives the values of $T_u$ found by Kramer. But $T_u$ is independent of thickness only in thick layers; in thin layers $T_u$ depends on the thickness. It is the higher, the thinner the layer, and lies between $T$ as a material constant and the ionization temperature of an atom of metallic vapor. Therefore thin and very thin metallic layers can be amorphous even when they are produced at comparatively high temperatures.

Fig. 16.

Considering the conditions of the surface atoms, Kramer believes that surface layers have a very high transformation temperature and can exist in the amorphous state even if the layer is crystalline inside; moreover, according to Kramer, preservation of an amorphous metallic layer on a massive metal is possible, if it should in some way form there. Kramer also explains the anomalous physical properties of thin metallic layers by the amorphous structure of thin metallic layers.

Similar experiments on the study of the electrical conductivity and optical properties of thin metallic layers were carried out by Zuurman and Bart165 to verify Kramer’s results. They investigated layers of Cu, Ag, Au, Cd, Pb, and Bi, condensed in a high vacuum at low temperatures (at 30 or 80°K). However, neither from the electrical properties nor from the optical ones could these authors detect a transformation temperature. In these observations the electrical conductivity, with the temperature raised to room temperature, gradually increased irreversibly. The course of the change in the electrical conductivity of a copper layer 115 mµ thick, condensed at 20°K, is shown in Fig. 17.

The experiment was carried out as follows. The layer was condensed at \(20^\circ\mathrm{K}\) and had a resistance at this temperature of \(3.96\,\Omega\) (point \(A\)). The layer remained at this temperature for 2 hours; its resistance changed hardly at all \((A)\). With an increase in temperature an irreversible fall in resistance began, which at \(78^\circ\mathrm{K}\) was equal to \(3.48\,\Omega\) \((B)\). Reverse cooling of the layer to \(20^\circ\mathrm{K}\) reversibly reduced the resistance to \(3.33\,\Omega\) \((B_1)\), and with a new increase in the temperature of the layer to \(80^\circ\mathrm{K}\) the resistance was \(3.39\,\Omega\) \((B_1)\). Further, these experiments were repeated toward higher temperatures, as indicated in the figure.

Fig. 17.

As is evident both from this curve and from the curves for other metals, one cannot conclude that there exists a temperature at which an abrupt irreversible increase in conductivity occurs. The temperature coefficient of resistance

\[ \alpha=\frac{1}{R}\frac{\Delta R}{\Delta T}, \]

computed by these authors from the experimental data for the copper layer, is as follows:

\[ \begin{aligned} 78^\circ\mathrm{K} &\ —\ 0.028\cdot 10^{-2}\\ 138^\circ\mathrm{K} &\ —\ 0.054\cdot 10^{-2}\\ 192^\circ\mathrm{K} &\ —\ 0.061\cdot 10^{-2}\\ 297^\circ\mathrm{K} &\ —\ 0.141\cdot 10^{-2}\\ 416^\circ\mathrm{K} &\ —\ 0.240\cdot 10^{-2} \end{aligned} \]

(for normal copper \(\alpha=0.440\cdot 10^{-2}\)).

The course of the change in the resistance of Ag, Au, and Cd was similar to that observed in the case of copper.

The authors processed the data on the temperature dependence of the resistance and obtained the remarkable result that layers condensed at low temperatures possess a certain additional resistance almost independent of temperature. This additional resistance decreases when the layer is heated. Taking Matthiessen’s rule into account, the authors explain this fact as follows: metals in thin layers condensed at low temperatures are in a disordered state, which, with increasing temperature, passes into the ordinary crystalline state. The authors do not indicate in detail what exactly should be understood by the “disordered state” of thin layers. By

the Matthiesen rule consists only in the fact that here a disturbance of the crystal lattice takes place. An example of a “disordered state,” according to the authors, is such a state when there are individual centers in the layer in which the atoms are in a denser spherical packing than in neighboring places. At the same time the authors note that such a picture does not contradict electronographic measurements, since, in their opinion, even without the presence of a microcrystalline structure it gives the observed blurred rings1).

Measurements of electrical conductivity thus give results that are in part mutually inconsistent. Kramer, in recent articles (in 1937), again discusses the question of the amorphous state of metals. He believes that the amorphous state is denied only because in experiments one does not take into account the circumstance that this state is very unstable and, for the most insignificant reasons, can pass into the metallic one. In particular, he points out that in the course of investigation by electron beams it may be disturbed, since electron beams possess great energy; therefore, in order to detect it, it is better, in his opinion, to use measurements of electrical conductivity. As one of the reasons why \(T_u\) is not observed in many experiments, he indicates the following circumstance. It is extremely difficult to create conditions for obtaining only the amorphous phase. Therefore a mixed phase is often obtained, when, for example, crystalline formations are embedded in an amorphous mass. In such a case detection of the amorphous phase is extremely difficult. To prove this proposition he cites the results of the work of Munif and Gelebi[^186], who investigated the conductivity of amorphous carbon. Amorphous carbon, obtained by the usually recommended method, i.e. in the form of soot from a gas flame, upon heating shows the dependence of electrical conductivity on temperature as is seen from Fig. 18.

Fig. 18.

The curve proceeds quite smoothly, and it is plainly impossible to indicate here a transformation temperature. According to Gelebi and Kramer, the reason is that carbon obtained by this method in fact also contains a certain crystalline part, which obscures the true picture of the transformation of amorphous carbon into crystalline carbon.

Geleb succeeded, by another method, in obtaining amorphous carbon that was much more homogeneous (by the action of sulfuric acid on sugar). For such specimens of amorphous carbon an entirely different picture is observed. In Fig. 19 the dependence of the electrical conductivity of such carbon on temperature is presented. Here one can clearly determine the temperature at which this transformation occurs. According to Kramer, analogous phenomena should also occur in metallic layers, with the difference that there the processes obscuring the true picture are more difficult to avoid. Kramer considers cathodic sputtering the best method for obtaining amorphous layers (Surmann and Barth obtained layers by the thermal method).

Fig. 19.

Fig. 20.

In the works set forth above, the electrical conductivity of layers obtained at room temperature or at a lower temperature was studied. In view of the discrepancies discovered, the study of the electrical properties of layers obtained at higher temperatures is very important. It should be noted that this question had until now hardly been investigated, and only quite recently was it examined in Krautkremer’s article, in which he measured the resistance of gold and silver layers deposited on a heated substrate. In Fig. 20 the course of the resistance of gold layers as a function of their thickness is presented for different substrate temperatures. It is striking that, when the substrate temperature is raised, the anomalous electrical properties shift toward greater thicknesses. The same picture is also observed for silver layers. Whereas the jump in resistance for layers obtained at \(20^\circ\) begins at a thickness of \(6\)—\(7\,m\mu\), layers obtained at \(200^\circ\) already show anomalously high resistance at \(37\)—\(39\,m\mu\).

Krautzkremer, on the basis of the above-cited results of his electronographic determinations, explains these facts by saying that in layers consisting of a large number of very small crystallites, contact between the crystallites occurs at smaller thicknesses than in layers consisting of a smaller number of large crystallites. Let us note that such a point of view had already been expressed earlier by other investigators as well.

3. Optical observations

Of the enormous number of optical investigations that have been carried out on thin metallic layers, we shall cite only a very few. For the reasons already discussed above, conclusions about the structure of a layer from the results of optical observations are usually not very convincing, unless, in parallel with the optical properties, the structure was determined by other methods. There are very few such works, and the principal ones are presented here.

In the above-cited work of Sürmann and Barth, simultaneously with measurements of electrical conductivity, the reflection of light from layers of the same metals was also determined. In Figs. 21 (for \(E_\perp\)) and 22 (for \(E_\parallel\)) the dependence of the reflecting power of a copper mirror on temperature is given for different wavelengths. The layer had a thickness of 115 m\(\mu\) and was condensed at \(20^\circ\mathrm{K}\).

Fig. 21.

Curve 1 was measured at \(20^\circ\mathrm{K}\), curves 2, 3, and 4 at \(80^\circ\mathrm{K}\) after the layer had first been heated respectively to 192, 296, and \(416^\circ\mathrm{K}\). The course of the curves does not reveal a sharp, jump-like change in reflecting power, but confirms the same character of change in the layer as does the course of the electrical conductivity. For Cu, Au, and Ag, an increase for \(E_\parallel\) in the long-wavelength region was observed in particular.

Hass also observed optical properties. Among his results, the optical behavior of antimony is very interesting. Layers obtained at low temperature, i.e. highly dispersed ones, exhibit a lower reflecting power in comparison with layers prepared at a higher substrate temperature. Thus, if during deposition of the layer the substrate was located

when \(\sim 0^\circ\)C and the rate of spraying was not high, the reflection coefficient of such a mirror was \(46\)—\(59\%\). A layer obtained on the substrate at room temperature and at a high rate of spraying reflected \(64.5\)—\(67.5\%\). Finally, for layers obtained on a substrate heated during spraying to \(250^\circ\)C, we obtain \(74\%\) for the reflecting power. The dependence is quite clear and is just what one should have expected. For silver and aluminum layers the author did not observe such a sharply expressed dependence.

The results of these experiments, which are of great practical importance—since the quality of optical mirrors is judged precisely by their reflecting power—lead to a quite definite conclusion about the influence of the structure of the layer on its optical properties as well.

To the same degree, the influence of structure is noticeable also in the study of the absorbing power of thin metallic layers. It is known that thin metallic layers of a number of metals are vividly colored; their color changes depending on the thickness and, up to a certain limiting value of the latter, differs from the color of the massive metal. Observations on colored films were already made by Faraday \({}^{1}\), Bilby \({}^{6}\), Wood \({}^{5,7,25}\), and many others. Naturally, the question of the physical nature of the coloration could not fail to attract attention. There is no need to cite all the detailed statements on this subject. We shall point out that the explanation of the coloration was given from two points of view: the interference one (in recent times it was supported by Edwards \({}^{62}\)) and the structural one. The interference picture of the coloration was rejected with complete justification already by Wood and is now entirely abandoned. At present, everyone explains the coloration by the structural features of thin metallic layers. In particular, Wood attributed the colors of thin layers of metals to their granular\({}^{1}\) structure; Maxwell-Garnett—to colloidal structure.

Fig. 22.

\({}^{1}\) The terminology used by some authors to define the structure of thin metallic layers is not entirely successful. For example, a crystalline structure is sometimes opposed to a colloidal one, identifying the colloidal and the amorphous, etc. In this article we make use of generally accepted terminology. Namely, by the amorphous structure of a metal is understood such a structure in which the metal has no crystalline lattice

In recent years a number of investigators have likewise adopted the structural, namely colloidal, point of view. We may mention, for example, the work of Dreisch and Rotten2, who investigated absorption by Ag and Au films in the near infrared region, and a number of papers by Smakula3, who measured the absorption of light by films of various metals in the ultraviolet and visible regions of the spectrum.

However, the assertions of these authors are rather qualitative in character. Recently several attempts have been made to apply the above-mentioned theories of Mie and Maxwell-Garnett to thin metallic layers, in order to obtain also a quantitative dependence of the optical properties of thin metallic layers on structure.

Fig. 23.

In doing so, as has already been said, one has to use the Rayleigh—Mie formulas constructed for solutions. This theory, as applied to the optical properties of colloidal solutions, gives us the following indications:

a) The absorption curves (and also the scattering curves) of colloidal solutions of metals exhibit great variety in the position and intensity of the maxima, depending on the optical constants of the metal. In Fig. 23 a series of absorption curves is presented, calculated by Savostianova4 from the Rayleigh—Mie formulas for cop—

particles (diameter $< 5\,m\mu$) of various metals, colloidally distributed in one and the same medium (NaCl), at one and the same concentration ($10^{-6}$). The sharp character of the absorption maxima enables us to conclude that the corresponding colloidal solution must be colored. As we see, the brightest colors should be expected for sodium, silver, calcium, and also gold, one of whose maxima, although weaker, is likewise located in the visible region ($525\,m\mu$). On the contrary, Zn, Pt, and most other metals give absorption maxima in the ultraviolet region and, in colloidal distribution, should give brown and gray tones.

c) With an increase in particle size the absorption maximum, generally speaking, shifts toward the red end of the spectrum. This shift is likewise not the same for different metals; it is especially sharply expressed for Na and Ag, which, consequently, should display in colloidal distribution a great variety of shades.

As Savostyanova has shown, all these circumstances are fully confirmed experimentally for colloidal solutions of metals in liquid and solid media. Their validity also for metal films should serve as evidence of their colloidal structure.

Fig. 24.

We shall cite two works in which such a point of view was applied to thin metallic layers. Fuchs[^148] investigated films of mercury, cadmium, and zinc, obtained in a high vacuum at low temperatures and at different rates of deposition. He measured the scattering of light and compared the experimental and calculated—

TABLE 2

computed according to Mie theory. In doing so, agreement between experiment and theory was found, as is seen from a comparison of Figs. 24 and 25 and Table 2. In Fig. 24 the curves of light scattering as a function of the thickness of a mercury film obtained by slow deposition are plotted; in Fig. 25, the curves for a mercury layer calculated by Mie theory are shown (particle diameters are plotted along the abscissa).

Fig. 25.

Already from the figures one notices the similarity of the first maxima. The agreement between theory and experiment is seen more clearly from Table 2.

The diameters and thicknesses are taken from the first maxima of the curves presented.

From the data given, Fukuroi calculated the distance between the particles and found that it exceeds the mean radius of the particles by more than a factor of 10.

Very important results were also obtained in experiments with mercury layers deposited rapidly (in the first case the deposition rate was 1.6 mµ/min). The experimental curves for a mercury layer deposited at a rate of 20 mµ/min are presented in Fig. 26. Here the character of the curve differs considerably from the preceding one. It is known that such a course of the curves in colloidal systems is observed for comparatively large particles. And indeed, calculations made by Fukuroi using Hobst’s formulas for larger particles give a curve (Fig. 27) that is very similar

Fig. 26.

experimental (on the abscissa axis here is plotted the quantity \(\dfrac{2\pi\rho}{\lambda}\), where \(\rho\) is the radius of the particle1).

Thus Fuchs’s observations show that mercury films behave as colloidal systems; the optical phenomena in them are described quite satisfactorily by Mie’s theory, so that even quantitative conclusions about the size of the particles forming the film are possible.

Krautzkremer also made an attempt to solve the question of the structure of metallic films by an optical method. He investigated the optical properties of gold and silver films; from measurements of the intensity of the light transmitted and reflected by both surfaces of the film he determined the optical constants of the film and compared them with constants calculated from formulas based on the Maxwell-Garnett theory. In doing so, Krautzkremer deposited the film on a substrate which, during deposition, was heated to various temperatures (or else was not below room temperature). In this connection we note that as early as 1936 (Krautzkremer’s work appeared in mid-1938) A. Asheyulov5 established curious features of the influence of heating the substrate on the optical properties of silver and gold films. Thus, Asheyulov found that with an increase in the temperature of the substrate during deposition the anomalous optical properties shift toward greater thicknesses. This process depends, moreover, on the rate of deposition, and the rate of deposition acts in the opposite direction; by increasing the rate of deposition one can make the effect of heating the substrate disappear. In addition, Asheyulov found that silver films obtained in this way, after some time in air, undergo a change, namely: they return to the state in which they would have been if they had been obtained on a substrate at room temperature. This is observed especially well in silver films. Krautzkremer’s observations also established a shift of the anomalies toward greater thicknesses and a change of thin films with time. In addition, Krautzkremer established that the surfaces of such films scatter light strongly.

Fig. 27.

Krautkremer calculated, according to the Maxwell–Garnett theory, the optical constants of layers and established that the greatest agreement between the calculated and experimental constants is observed at higher temperatures. In Fig. 28 the curves are presented for the dependence of the constants \(n\) and \(k\) on wavelength for gold layers obtained at a temperature of \(300^\circ\) [the hatched curves are theoretical for three values of the “filling factor”; the solid curves are experimental for layers of thickness \(5.3\ \mathrm{m}\mu\) (1) and \(8.8\ \mathrm{m}\mu\) (2)].

Here, too, however, the agreement of the theoretical assumptions with the observed facts is less clear than in the preceding case.

The results of Fukuroi and Krautkremer, in our opinion, show that this line of optical research may render substantial assistance in the investigation of the properties of thin metallic layers and therefore should be developed more intensively than hitherto.

Fig. 28.

V. Discussion of Results

Structural, electrical, and optical observations consistently lead to the view that sufficiently thick metallic layers condensed on uncooled substrates have the crystalline structure of an ordinary metal. The dependence of the structure on various factors is likewise established unambiguously by all methods, namely: with a decrease in the rate of deposition and in the thickness of the layer, and with a lowering of the temperature of the substrate, the size of the crystallites forming the layer decreases. However, with regard to the limit of crystallite diminution there are discrepancies. Most investigators believe that in all cases, even in the thinnest layers and at the temperature of liquid air, the layers nevertheless remain crystalline, although highly disperse. At the same time, it has been established by electron diffraction that a change in the lattice constant is observed only in isolated cases, and then by only a few tenths of a percent1. Others have come to the conclusion that an amorphous structure of metals is also possible and that in thin layers we are dealing precisely with such a structure. Accordingly, the physical properties of thin metallic layers are derived either from the features of the crystalline structure or from the amorphous constitution.

The principal facts requiring explanation, as was already said above, are, first, the anomalously low electrical conductivity and its anomalous temperature dependence; second, the irreversible, jump-like increase in the electrical conductivity of layers obtained at a low substrate temperature; and third, the anomalous colors of thin metallic layers.

The microcrystalline structure of thin metallic layers has been demonstrated by almost all electronographic investigations. It is in good agreement with optical observations, because, as we have seen, the formulas of Maxwell-Garnett and Mie are based on the assumption that the layer consists of crystallites with the optical constants of the massive metal. Such an assumption makes it possible to explain also the optical anomalies of thin metallic layers. In many cases such a conception of the structure likewise does not contradict the observed electrical properties. In particular, the low electrical conductivity of thin metallic layers can be explained with sufficient plausibility by poor contact between the crystallites. However, this conception does not encompass the entire aggregate of phenomena. From this point of view it is difficult to understand the anomalous temperature dependence of the electrical conductivity. Tammann’s idea[^133] that the coalescence and growth of crystallites occurring when the layer is heated (indisputable in this respect) is in general not very convincing and contradicts, first, the reversibility of the anomalous electrical conductivity up to the transformation temperature and, second, the fact that the anomalously high electrical conductivity shifts toward greater thicknesses in layers obtained on heated substrates. It is also difficult, while remaining within this conception alone, to imagine the mechanism of a jump-like, irreversible increase in electrical conductivity upon passing through a certain temperature.

The hypothesis of an amorphous structure of thin metallic layers rests mainly on measurements of their electrical properties. Kramer, the most consistent exponent of this point of view, explains the entire aggregate of anomalous properties of thin metallic layers by the presence of a complete or partial amorphousness of the metal structure. On this question it should be noted that a number of observed phenomena fit very well within the framework of this hypothesis; however, here too great difficulties arise. The main weakness of this view is insufficient experimental substantiation. The point is that the decisive fact speaking in favor of this hypothesis—the irreversible, jump-like change in electrical conductivity—has been very little studied. In essence we have here the observations of Kramer alone. In other investigations, even those set up specially for this purpose, the phenomenon was not detected. True, from the work of Suhrmann and Barth it follows, as we have seen, that with lowering of the substrate temperature there occurs an ever greater disturbance of the lattice and an increase in the additional, temperature-independent resistance, which to a certain degree may also serve-

serve as proof of the validity of the amorphous hypothesis. However, the different behavior of this disordered state as reported by different authors gives rise to certain quite legitimate doubts and requires careful experimental verification, all the more so since the conclusions of other investigators in favor of an amorphous structure are, in our opinion, not very convincing, since the phenomena on the basis of which such conclusions have been drawn also admit another interpretation.

In addition to these considerations, there are a number of others that limit and even exclude an amorphous structure of metallic layers. In discussing this question one should remember that the hypothesis of an amorphous structure, as applied to thin metallic layers, consists, strictly speaking, of two independent assertions, namely: 1) the possibility of the existence of a metal in the amorphous phase in layers of any thickness obtained at low temperatures, and 2) the amorphous structure of thin metallic layers obtained at ordinary (room) temperatures. The first follows from experimental observations of the electrical properties of thin layers. It is, however, contradicted by electron-diffraction observations, which show a crystalline structure even in this case. To remove this contradiction, Kramer put forward the supposition that, in the course of the investigation, the electron beams transform the amorphous structure into the normal one. So far this supposition has not been verified, and, consequently, the question in this part remains open for the time being. Let us note only that electron-diffraction studies nevertheless show that, with a decrease in temperature, the dispersity of the layer increases, and from this point of view they do not exclude the possibility of the existence of a metal in an amorphous phase. Greater difficulties exist for the second assertion. It is, in fact, rather logical than factual, and already in this lies its weakness. Moreover, an experiment is known which apparently excludes this part of the amorphous hypothesis. We have in mind the fact that the anomalous properties shift toward greater thicknesses in layers obtained on heated substrates. These layers can in no case be regarded as amorphous; meanwhile, in both electrical and optical respects they behave analogously to the thinnest layers, for which, according to Kramer, an amorphous structure is precisely characteristic. The final resolution of this question, however, for the sake of caution, should also be postponed until it is shown that the nature of the anomalies in these cases is the same.

Thus, neither from the crystalline point of view nor from the amorphous one has it so far been possible to encompass the entire totality of phenomena unambiguously and with complete persuasiveness. In particular, the question of the anomalous electrical and optical properties of thin metallic layers remains unresolved. This, of course, also hampers the understanding of the processes of condensation of metal vapors and of the behavior of metal atoms on a solid surface. That migration of atoms over the surface takes place here follows from many observations1.

But a number of questions—the possibility of the existence of a metal in the form of a highly compressed vapor, quantitative data on migration—remain unclear. It is very likely that, in order to solve the problem in general, the indicated ideas are insufficient, and that other factors must also be taken into account. Such a factor, in particular, is the influence of gases1. A number of investigators have observed that, during the formation of layers and during their subsequent preservation, interaction of gases with the metal in the layer takes place. Depending on the conditions, this interaction has a different character (chemical compound, absorption) and affects the properties of the layers in different ways.

Therefore many have tried to explain anomalies in thin layers precisely by the influence of gases. It seems to us that such a direction of research is not fruitless and may clarify much. In any case, in our opinion, a number of phenomena in layers could be interpreted, taking into account the influence of gases, considerably more simply than at present.

For completeness, let us also recall here other attempts to reconcile the observed phenomena with theory. Thomson[^3], and later Tissa[^70], tried to start from the idea that the mean free path of electrons in the layer is a function of thickness, and from this obtained a dependence between electrical conductivity and the thickness of the layer. Perucchi assumed that the concentration of free electrons in the layer decreases toward the surface, reaching there a zero value, and by this explained the peculiarities of the layers. It should be pointed out that no especially valuable conclusions could be drawn from this.

Let us dwell once more on the question of methods for studying thin metallic layers. In our opinion, the necessity of some change in working procedures is now clear. The point is that any of the methods used for investigation is, to a certain extent, unsatisfactory and may in some cases raise doubts. Meanwhile, when studying the literature, it is striking that in the majority of works only either optical, or electrical, or electron-diffraction measurements were made on one and the same specimen. Such an overly differentiated approach is not very effective and raises many doubts on a number of questions. Several works of recent years have been carried out on a different principle, and it is significant that precisely these works compare favorably with the preceding ones. We believe that in the future one should abandon excessively narrow investigations and, as far as possible, study one and the same specimen comprehensively.

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1. On this question, see 179, 174. ↩↩↩↩↩↩↩↩

2. visible reference number in the source text. ↩

3. visible reference numbers in the source text. ↩

4. visible reference number in the source text. ↩

5. Asheyulov’s work was reported at the conference on surface properties at the Leningrad State Optical Institute in May 1936. ↩