SEMICONDUCTORS AS CATALYSTS OF CHEMICAL REACTIONS

F. F. Volkenshtein

1. INTRODUCTION

The technical applications of semiconductors, as is known, are very diverse. There is, however, one area of the practical use of semiconductors which until recently remained outside the field of view of physicists. This is the use of semiconductors as catalysts of chemical reactions.

Such typical semiconductors as cuprous oxide, zinc oxide, and vanadium pentoxide are at the same time typical catalysts. Semiconductors serve as catalysts for many chemical reactions. These include oxidation reactions, hydrogenation reactions, and many others.

Some metals also act as catalysts. However, oxygen, as well as hydrogen and nitrogen, when in contact with a clean metallic surface, even at low temperatures, are very rapidly and strongly absorbed by it. As a result, the metallic surface becomes covered with a film of a binary compound, the removal of which, for most metals, is known to be a very difficult task. Thus, in most cases metals prove to be clothed in a semiconductor casing, and chemical processes that we consider to occur on the surface of a metal in fact often occur on the surface of a semiconductor. Therefore, when one speaks of the catalytic action of a metal, one is in reality dealing (not always, but very often) with the catalytic action of this semiconductor casing, while the metal located beneath this casing practically does not participate, or almost does not participate, in the process.

The catalytic action of semiconductors was discovered long before the very concept of a semiconductor appeared. Chemists have long been engaged in catalysis, but until recently they did not know (and often still do not know) that the majority of catalysts,

with which they deal are semiconductors. At the same time physicists engaged in semiconductors often do not know that semiconductors, in addition to their other properties, possess catalytic action and have long been used in the chemical industry as catalysts.

At the present time it is obvious that the electronic processes developing in a semiconductor and determining its electrical, optical, and magnetic properties at the same time also determine its chemical properties, in particular its catalytic properties. The problem of catalysis is a problem situated at the junction of two sciences: physics and chemistry. Until now this problem has been entirely in the hands of chemists. Recent years are characterized by the fact that the attention of physicists is being directed to the problem of catalysis to an ever greater and greater extent.

Below we shall consider the basic phenomena and the basic concepts with which one deals in catalysis. At the same time we shall formulate those basic questions that confront semiconductor physics in connection with the problem of catalysis.

The present article was written at the suggestion of the editorial board of UFN in connection with the All-Union Conference on Semiconductors, held in Leningrad in November 1955. At this conference there was a special section on “Semiconductor Catalysis.” In the history of semiconductor conferences such a section appeared for the first time. This fact in itself is remarkable.

2. ACTIVITY AND SELECTIVITY OF A CATALYST

Let us imagine that we have a mixture of gases between which some chemical reaction takes place. If a solid body—a catalyst—is introduced into this medium of reacting gases, then the rate of the reaction increases. The relative increase in the rate characterizes what is called the “activity” of the catalyst. In a number of cases we are dealing with an acceleration of the reaction by hundreds and thousands of times, so that the introduction of a catalyst can lead to a very vigorous development of a reaction which, in the absence of the catalyst, practically does not proceed at all or proceeds very slowly.

An example may be the oxidation reaction of carbon monoxide, leading to the formation of carbon dioxide,

\[ 2\mathrm{CO} + \mathrm{O}_2 \to 2\mathrm{CO}_2. \tag{1} \]

In the absence of a catalyst this reaction proceeds at a barely perceptible rate and, moreover, only at very high temperatures (of the order of several hundred degrees). In the presence, however, of such catalysts as \(\mathrm{MnO}_2\), \(\mathrm{Ag}_2\mathrm{O}\), \(\mathrm{Co}_2\mathrm{O}_3\), this reaction proceeds at a high rate even at temperatures below room temperature (down to \(-60^\circ\mathrm{C}\)).

At temperatures of about 100° C and higher, CuO and NiO are also catalysts for this reaction.

One and the same catalyst has different activity with respect to different reactions. While active with respect to a given reaction, it may prove to be completely inactive with respect to some other reaction.

Thus, for example, reaction (1) is not accelerated at all by zinc oxide, whereas zinc oxide is an excellent catalyst, for example, for the dehydrogenation reaction of isopropyl alcohol:

\[ \mathrm{C_3H_7OH \to CO(CH_3)_2 + H_2}. \]

Every reaction, as a rule, consists of a number of successively proceeding intermediate stages. A catalyst changes the rates of the individual stages of a reaction, and not to the same extent. Thus, since the rate of the overall reaction is determined by the rate of its slowest stage, in the presence of a catalyst this slowest (limiting) stage may prove to be a different stage than in the absence of the catalyst.

Moreover, the role of the catalyst may be manifested in a change in the stages themselves. Thus, if in the absence of a catalyst a given reaction is decomposed into certain stages, then in the presence of a catalyst the same overall reaction may prove to consist of other stages.

If the reacting substances participate in several parallel reactions, as often happens, then the rate of each of these reactions may be changed by the given catalyst to a different extent. In other words, the activity of a catalyst, generally speaking, may be different with respect to different parallel reactions.

This means that under the influence of a catalyst practically the very direction of the reaction may change. This ability of a catalyst to change the direction of a reaction is called the “selectivity of the catalyst.” The concepts of “activity” and “selectivity” are fundamental concepts in catalysis.

Thus, if as a result of some complex reaction we obtain various products, then under the influence of a catalyst not only the absolute magnitude of the yield of each product may change, but the relative yields of these different products may also turn out to be changed. Thus, for example, the decomposition reaction of isopropyl alcohol \(\mathrm{C_3H_7OH}\) can proceed in two directions:

in the direction of dehydrogenation:

\[ \mathrm{C_3H_7OH \to CO(CH_3)_2 + H_2} \tag{2} \]

and in the direction of dehydration:

\[ \mathrm{C_3H_7OH \to C_3H_6 + H_2O}. \tag{3} \]

In the first case the reaction products are acetone \(\mathrm{CO(CH_3)_2}\) and hydrogen \(\mathrm{H_2}\); in the second case, propylene \(\mathrm{C_3H_6}\) and water \(\mathrm{H_2O}\). The catalyst \(\mathrm{ZnO}\) conducts the reaction mainly in the first of these two directions (in the direction of dehydrogenation), whereas \(\mathrm{Al_2O_3}\) is a typical catalyst for the second direction (for dehydration)\(^1\).

The catalytic activity of a semiconductor (with respect to a given reaction) can be substantially changed (increased or decreased) as a result of one or another external action upon the semiconductor. Thus, when the temperature is raised, the activity of a catalyst, as a rule, increases sharply. The introduction into a catalyst of negligible amounts of a foreign impurity may lead to a considerable change in its catalytic activity.

An impurity that lowers the activity of a catalyst is called a “poison.” In this case we are dealing with “poisoning” of the catalyst. Impurities which, on the contrary, increase catalytic activity are called “promoters.” In this case one speaks of “promotion” of the catalyst. Let us note that one and the same impurity, with respect to one reaction, may be a poison, and with respect to another reaction, a promoter. Moreover, one and the same impurity, with respect to one and the same reaction, may act as a poison in one temperature interval, and as a promoter in another temperature interval. At one and the same temperature, with respect to one and the same reaction, one and the same impurity may be a poison or a promoter depending on the concentration of this impurity introduced into the catalyst. We shall speak in more detail below about the influence of impurities on the catalytic activity of a semiconductor (see § 8).

By introducing impurities into a catalyst one can regulate not only the activity, but often also the selectivity of the catalyst. Thus, as we have already indicated, \(\mathrm{ZnO}\) mainly causes the dehydrogenation of isopropyl alcohol [reaction (2)] and only to an insignificant extent conducts the reaction toward dehydration [reaction (3)]. The more excess zinc there is in zinc oxide, the more strongly the first direction of the reaction is expressed in comparison with the second\(^1\).

The catalytic activity of a semiconductor is determined not only by its nature, but also by its biography, i.e. it depends on the method of preparation of the given specimen and, to a certain degree, on those external actions to which the given specimen has been subjected throughout its entire previous life. In other words, the catalytic activity of semiconductors, like many of their other properties, belongs to the category of so-called “structure-sensitive” properties\(^2\).

Let us note that a solid body catalyzing a reaction, i.e. changing its rate, is not a passive but an active participant in the process. Its role as a catalyst is due to the fact that it parti-

participates in the intermediate stages of the reaction as one of the components of the reaction. It is characteristic, however, that upon completion of the act of reaction it is completely regenerated, i.e., it emerges from the reaction in the same form in which it entered the reaction. This feature is a characteristic and distinctive property of a catalyst and may be regarded as a strict definition of the very concept of a catalyst.

However, in many cases encountered in practice, the composition of the catalyst itself changes to one degree or another during the reaction. Thus, for example, the catalyst is often poisoned by the reaction itself, so that in the course of the reaction its activity gradually decreases. As an example let us again point to the oxidation of CO, catalyzed by various solid oxides (see above), which often proceeds not only at the expense of gaseous oxygen, but to some extent also at the expense of oxygen belonging to the crystal lattice of the catalyst itself. As a result, in the course of the reaction the catalyst is gradually reduced and, after the end of the reaction, has a somewhat different stoichiometric composition than before the start of the reaction.

The same occurs, for example, in the decomposition reaction of methyl alcohol, $\mathrm{CH_3OH}$. In the presence of ZnO, methyl alcohol decomposes almost completely into CO and $\mathrm{H_2}$. In this process the catalyst is noticeably reduced. This can be detected from the sharp increase in its electrical conductivity. ZnO, which before the start of the reaction possessed a typical semiconductor electrical conductivity, in the course of carrying out the reaction acquires the electrical conductivity of a metal type.^3

Thus, in the ideal case the catalyst is completely regenerated after the reaction is completed. In practice, however, it gradually changes in the course of operation and, in the end, after having worked for a sufficiently long time, may fail altogether.

Be that as it may, in both cases the catalyst that causes the acceleration of the reaction itself participates in the chemical process. And it is precisely in this that its action as a catalyst is hidden.

3. ADSORPTION AS A STAGE OF CATALYSIS

Every chemical reaction catalyzed by a solid always includes adsorption and desorption as obligatory stages. Adsorption and desorption are the first and last stages of every heterogeneous catalytic process.

The adsorbing body is called the adsorbent. The adsorbed substance is called the adsorbate, and the adsorbed substance—adsorptive. Gas molecules are first adsorbed on the surface of the solid; then, while remaining in the adsorbed state, they enter into reaction with one another or with molecules arriving from the gas phase, after which the reaction products are desorbed. Thus

Thus, upon introducing a catalyst into a mixture of reacting gases, the reaction is practically transferred from the gas phase to the surface of a solid. A catalytic reaction is a reaction proceeding at the interface of two phases (solid and gaseous). The mechanism of a heterogeneous catalytic process cannot be fully understood until the mechanism of the intermediate stages of this process—the stages of adsorption and desorption—has been deciphered. Therefore the theory of heterogeneous catalysis inevitably begins with the theory of adsorption.

One should distinguish two types of adsorption: physical adsorption and chemical adsorption (chemisorption). The difference between them reduces to the difference in the nature of those forces which hold the adsorbed molecule on the surface of a solid. These may be van der Waals forces, forces of electrostatic polarization, or forces of electrical image attraction. In this case we are dealing with physical adsorption. If, however, the forces responsible for adsorption are of a chemical nature (exchange-type forces), then in this case we speak of so-called chemical adsorption.

Chemical adsorption, in contrast to physical adsorption, is characterized by a considerably larger heat of adsorption. The binding energy of an adsorbed molecule with the surface of a solid in the case of physical adsorption is \(0.01—0.1\) eV. In chemical adsorption this quantity reaches an order of magnitude of \(1\) eV. Further, chemical adsorption, in contrast to physical adsorption, is characterized by a considerably smaller equilibrium distance (the distance between the adsorbed molecule and the surface of the adsorbent). If the wave functions of the adsorbed molecule and of the adsorbent lattice may be regarded as practically nonoverlapping, we are dealing with physical adsorption. If this overlap cannot be neglected, we pass into the region of chemical adsorption.

Physical and chemical adsorption, under theoretical consideration, require essentially different approaches to the problem. In the case of physical adsorption, the adsorbed molecule and the adsorbent lattice may be considered as two independent systems. The action of the adsorbent on the adsorbate may be treated as a weak perturbation, and the problem may be solved within the framework of perturbation theory. In chemical adsorption the adsorbed molecule and the lattice form a single quantum-mechanical system and must be considered as one whole.

The adsorption with which we deal in catalysis is, as a rule, chemical adsorption. This is adsorption that constitutes a chemical combination of a gas molecule with a solid.

Chemical adsorption, as a rule, requires a certain activation energy. Therefore such adsorption is often called activated adsorption. It should be noted, however, that the presence of an activation energy is not a necessary characteristic of chemical adsorption. Chemical

adsorption in some cases can also proceed without activation energy.

Activated adsorption differs from ordinary (nonactivated) adsorption in the character of its kinetics. In the absence of activation energy, adsorption proceeds very rapidly, so that equilibrium between the adsorbent and the gas phase is established almost instantaneously. The lower the temperature, the faster equilibrium is established. In the case of activated adsorption, however, equilibrium is established slowly. Adsorption proceeds at a measurable rate and, moreover, the faster the higher the temperature. In this case heating accelerates adsorption.

The origin of the activation energy in adsorption is usually explained by introducing the idea of a potential barrier on the adsorption curve. Such adsorption curves are shown schematically in Fig. 1. They represent the dependence of the energy of the system \(W\) on the distance \(r\) between the surface and the adsorbed molecule. Fig. 1,a refers to ordinary adsorption, proceeding without activation. Fig. 1,b corresponds to activated adsorption. The depth of the well in Fig. 1,a

Fig. 1.

and 1,b characterizes the heat of adsorption \(q\). The height of the barrier in Fig. 1,b represents the activation energy \(E\). The role of the barrier amounts to the fact that it blocks access to the surface for all molecules whose energy is sufficiently small. Only those gas molecules incident on the surface whose kinetic energy (in the direction normal to the surface) exceeds the height of the barrier are adsorbed.

Let us note that the concept of a potential barrier on the adsorption curve (the very appearance of which requires explanation) is not obligatory for explaining activated adsorption. A theory of activated adsorption can also be constructed without the pre—

ideas about a potential barrier.^4 The origin of the activation energy in adsorption may be due to certain specific properties of the adsorption centers located on the surface and taking up gas molecules. Adsorption centers are certain special points on the surface at which, according to modern ideas, chemisorption takes place. In Taylor’s opinion, such centers are geometrical inhomogeneities of the surface (peaks, vertices, and edges of crystallographic faces, etc.). They may also be various surface microdefects, for example atoms or ions of the crystal lattice thrown by thermal motion from lattice sites onto the surface of the crystal.^5 The functions of such adsorption centers in chemisorption may, as can be shown, also be performed by free electrons or holes on the surface of a semiconductor.^4

If one assumes that the concentration of adsorption centers on the surface does not remain constant but increases exponentially with temperature, then all the regularities of activated adsorption can be obtained without introducing the idea of a potential barrier on the adsorption curve. In this case the activation energy in adsorption is nothing other than the energy of formation of an adsorption center.

Thus, if in the theory of activated adsorption, which deals with a potential barrier near the surface of a crystal, the number of gas molecules incident on the surface increases exponentially with temperature, while the number of adsorption centers accepting these molecules remains unchanged, then in the case under consideration, on the contrary, the number of accepting centers increases exponentially with temperature, while the number of incident molecules remains practically constant.

In Langmuir’s elementary theory of adsorption, the question of the physical nature of the adsorption centers is not considered at all. These adsorption centers, whatever their nature, are nevertheless ascribed definite properties. It is assumed that the number of centers on a given surface is constant and fixed once and for all. It is determined only by the nature of the surface and by its history. It is further assumed that the adsorption centers are localized on the surface. The topography of the adsorption centers does not change with time. Finally, it is assumed that all adsorption centers are identical, i.e., with respect to gas molecules of a given kind they are characterized by one and the same bond energy (heat of adsorption). It is assumed that the strength of the bond of an adsorption center with an adsorbed molecule remains unchanged throughout the entire time that the molecule stays in the adsorbed state. Such are the initial premises of Langmuir’s theory.

In a number of cases Langmuir’s theory is in satisfactory agreement with experiment. In the majority of cases, however, the regularities observed experimentally deviate substantially from the regularities,

predicted by the Langmuir theory. To explain these deviations, one usually proceeds by revising the initial assumptions of Langmuir’s theory. Thus, for example, the idea is introduced that there exists on the surface not one, but several different kinds of adsorption centers, differing in the strength of their bond with the adsorbed molecule. In this case one speaks of an energetically inhomogeneous surface. The theory of adsorption on an inhomogeneous surface has recently received detailed development in the works of S. Z. Roginskii and his school[^6]. This theory makes it possible to explain many regularities that are actually observed.

The same experimentally observed regularities can be obtained if one preserves the Langmuir concept of a homogeneous surface (adsorption centers of only one kind), but operates not with a constant number of adsorption centers, fixed once and for all, but with a variable number of adsorption centers, depending on temperature and changing as the surface is filled[^5]. We have already spoken of these ideas above.

Finally, deviations from the Langmuir regularities observed experimentally can also be explained in the case where the surface is regarded as homogeneous and the number of centers as constant, but where one also takes into account the circumstance that, during the time a molecule remains in the adsorbed state, the strength of its bond with the given adsorption center may change. We shall see below that this circumstance, which must indeed be taken into account, is due to electronic processes occurring on the surface during chemisorption[^7],[^8].

The question of the nature of adsorption centers and of their properties is central in the theory of chemical adsorption and, at the same time, in the theory of heterogeneous catalysis. Later (see § 6) we shall return once more to this question.

Let us note in conclusion that in chemical adsorption dissociation of the molecule often takes place: at the moment of adsorption the molecule breaks into two parts. Usually a simple (single) bond is broken, joining in the molecule two atoms or two groups of atoms. Thus, formation of a chemical bond between the molecule and the surface (with an adsorption center) leads to rupture of a bond within the molecule. As a result, it is not the molecules themselves that turn out to be adsorbed on the surface, but fragments of these molecules. Such dissociation of a molecule, occurring in the very act of adsorption, may at present be regarded as an experimentally established fact. Thus, for example, adsorbed hydrogen is found, as a rule, not in the molecular but in the atomic state. Adsorption of the molecule \(H_2\) is accompanied by its dissociation. Conversely, recombination of adsorbed hydrogen atoms leads to desorption of the molecule \(H_2\). We note that for such adsorption, accompanied by the rupture of the molecule into separate atoms or radicals, it is characteristic, as can be shown

recognize,⁹ the presence of an activation barrier on the adsorption curve (see Fig. 1,b). Thus, in the present case we are dealing with activated adsorption.

Chemical adsorption is of interest to us in its own right, and not only as a stage of catalysis and not only from the point of view of the theory of catalysis. Indeed, chemical adsorption is the simplest type of heterogeneous reaction: it is the reaction of combination of a gas molecule with a solid, which in this case acts as a single system.

4. ELECTRONIC PROCESSES IN CHEMISORPTION

In the theoretical interpretation of adsorption phenomena, the layer of adsorbed molecules is often treated as a two-dimensional gas. Such an interpretation is very widespread in theoretical works on adsorption. It is quite legitimate and fruitful so long as we are dealing with physical adsorption. The picture of a two-dimensional gas becomes, however, unacceptable as soon as we pass to chemical adsorption, in which the adsorbed molecule and the adsorbent lattice form a single quantum-mechanical system and must be considered as one whole.

In the case of chemical adsorption, when the wave functions of the adsorbed particle and of the lattice overlap to a sufficient degree, the adsorbed atoms and molecules situated on the surface of a semiconductor may be regarded as “impurities” that disturb the strictly periodic structure of the lattice. In the energy spectrum of the crystal they may be represented by local levels (acceptor or donor levels) situated in the forbidden region between the valence band and the conduction band.

Such a treatment was first carried out by the author.¹⁰ In this case the adsorbate and the adsorbent appear for the first time as a single system, and the participation of the adsorbed atoms and molecules in the electronic economy of the lattice is thereby automatically ensured. Let us note that such an interpretation of chemisorbed atoms and molecules as “impurities” on the surface of a semiconductor by no means presupposes a rigid localization of the adsorbed particles. The adsorbed atoms and molecules retain the ability to creep along the surface.

Figure 2 shows a local level \(A\) corresponding to a certain chemisorbed molecule. By \(v\) is denoted the distance between this level and the lower boundary of the conduction band; by \(u\), the distance between the conduction band and the valence band. Let us suppose that the level \(A\) in Fig. 2 is an acceptor level. An electron situated on this level is characterized by a wave function that has a maximum near the corresponding chemisorbed molecule and decreases with distance from it. The deeper the level \(A\) is situated (the larger \(v\) in Fig. 2), the more

the sharper this maximum, and hence the stronger the localization of the electron belonging to this level.

The position of level \(A\) (i.e., the distance \(v\) in Fig. 2) is determined by the nature of the lattice and by the nature of the adsorbed molecule. Other conditions being equal, it depends on the distance between the molecule and the surface of the crystal. As the molecule moves away from the surface, the acceptor local level \(A\) in Fig. 2, as can be shown, is drawn toward the conduction band ( \(v\) decreases), while the lattice electron sitting on this level is gradually delocalized, since its wave function becomes more and more spread out. In the limit, at infinite removal of the molecule from the surface, the local level proves to be drawn into the band. The electron sitting on it thus becomes completely delocalized and thereby returned to the family of free electrons.

Fig. 2.

Thus, if an acceptor local level \(A\), corresponding to some adsorbed molecule, is occupied by an electron, this means that the lattice electron is localized near this molecule, i.e., the adsorbed molecule is in a charged state (it carries a negative charge).

Let us now suppose that the adsorbed molecule is represented not by an acceptor but by a donor local level. Removal of an electron from such a level means localization of a hole near the chemisorbed molecule. The molecule thus proves to be associated with a positive charge, i.e., again brought into a charged state.

Let \(N\) be the total number of molecules of a given kind adsorbed per unit surface. A certain part of these molecules (let the number of such molecules be denoted by \(N'\)) is always in a charged state, i.e., is associated with an electric charge (with an electron, if the molecule is represented by an acceptor level, or with a hole, if it corresponds to a donor level).

Let us introduce the notation

\[ \eta = \frac{N'}{N}. \]

This quantity shows what fraction of the molecules of the given kind is charged, or, in other words, what the probability is that a given adsorbed molecule will be in a charged state. Put another way, the quantity \(\eta\) characterizes the absolute value of the electric charge concentrated on the adsorbed molecule (expressed in units of the electron charge).

The quantity \(\eta\) depends on the temperature and on the position of the chemical-potential level (the level \(\varepsilon\) in Fig. 2). If the local level \(A\) is an acceptor level, then we have

\[ \eta=\frac{1}{1+e^{\frac{\nu_{\varepsilon}-\nu}{kT}}}. \]

If, however, the level \(A\), corresponding to the chemisorbed molecule, is a donor level, then

\[ \eta=\frac{1}{1+e^{\frac{\nu-\nu_{\varepsilon}}{kT}}}. \]

The meaning of the notation adopted here is clear from Fig. 2.

Figure 3 schematically shows how the quantity \(\eta\) changes as the level \(\varepsilon\) is displaced along the energy spectrum of the crystal\(^{12}\). Fig. 3a refers to the case in which the level \(A\) is an acceptor level.

Fig. 3.

Fig. 3b corresponds to the case in which the level \(A\) is a donor level. The different curves in Figs. 3a and 3b correspond to different temperatures; the broken-line curve \(abcd\) corresponds to \(T=0\).

We see that molecules represented by acceptor local levels and molecules represented by donor levels behave in opposite ways. The quantity \(\eta\) for molecules of the first type is the larger, and for molecules of the second type the smaller, the higher the chemical-potential level \(\varepsilon\) is located (i.e., the closer it is to the conduction band).

What, then, determines the position of the level \(\varepsilon\)?

It depends, above all, on the nature and concentration of the molecules chemisorbed on the surface of the crystal. Thus, the probability that a given adsorbed molecule will be in a charged state depends on the total number of adsorbed molecules. Each adsorbed molecule, as it were, “feels” the presence of the others[^12].

The position of the level \(\varepsilon\) also depends on the nature and concentration of impurities contained inside the crystal. When the content of a donor impurity is increased, the level \(\varepsilon\) shifts upward; an acceptor impurity acts in the opposite way. Thus, the probability that a molecule chemisorbed on the surface of a crystal will be in a charged state depends, other conditions being equal, on the nature and quantity of the impurities introduced into the crystal. In this way the properties of the bulk are reflected in the properties of the surface[^13].

We see that the appearance of chemisorbed molecules on the surface of a semiconductor leads to charging of the surface. The absolute value of the surface charge caused by chemisorption is equal to \(\eta N\). As a result, between the surface and the bulk of the semiconductor there arises a certain potential difference. We shall denote it by \(V_0\). The consequence of this is the bending of the energy bands near the surface.

Fig. 4.

Figure 4 shows the energy diagram for a semiconductor containing a donor impurity (an \(n\)-type semiconductor). The plane \(x = 0\) is the adsorbing surface. In Fig. 4 the surface energy bands due to the very fact of the lattice termination are not shown. Here we shall ignore (as many authors do) the existence of these surface bands.

Below we shall discuss the role they play in chemisorption phenomena. Fig. 4, a corresponds to the case of a clean surface \((N=0)\), when the semiconductor surface is electrically neutral. Fig. 4, b refers to the case when molecules of the acceptor type are adsorbed on the semiconductor surface. In this case the surface becomes negatively charged. Fig. 4, c corresponds to the adsorption of donor molecules. In this case the surface proves to be positively charged.

Fig. 5.

The course of the potential inside the semiconductor is determined from Poisson’s equation:

\[ \frac{d^{2}V}{dx^{2}}=\frac{4\pi e^{2}}{\chi}\rho(x), \tag{1} \]

where \(\chi\) is the dielectric permittivity of the semiconductor, and \(\rho(x)\) is the density of the volume charge arising in the semiconductor. This volume charge compensates the surface charge arising as a result of chemisorption. The boundary conditions have the form

\[ \left(\frac{dV}{dx}\right)_{0}=\pm \frac{4\pi e^{2}}{\chi}\gamma_{1}N,\qquad \left(\frac{dV}{dx}\right)_{L}=0. \tag{2} \]

Here the upper sign corresponds to the adsorption of donor molecules, and the lower sign to the adsorption of acceptor molecules; \(L\) is the half-thickness of the crystal.

Surface energy bands, if they are taken into consideration, lead to the following effect. The surface of a semiconductor turns out, generally speaking, to be charged even in the case when it is clean, i.e. even in the absence of chemisorbed molecules. Such charging of the surface, due to the presence of surface bands, is shown in Fig. 5. In this case the role of the chemisorbed molecules is reduced to changing the magnitude of this surface charge[^13].

The bending of the energy bands that occurs as a result of chemisorption has as its consequence the following two effects, which are observed experimentally.

First of all, under the influence of adsorption the work function must change. Let us return to Fig. 4. In this figure the work function is denoted by \(P\). Adsorption of acceptor molecules must lead to an increase, and adsorption of donor molecules to a decrease, of the work function \(P\), as is evident from a comparison of Figs. 4, a, 4, b, and 4, c.

The change in the work function under the influence of adsorption has in fact been observed by a number of authors. As an example let us cite the data of V. I. Lyashenko and I. I. Stepko[^14], who stud-

observed the adsorption of \(O_2\), CO, and \(CO_2\) on CuO. The adsorption of oxygen led to a noticeable increase in the work function. The same effect was also observed upon adsorption of carbon monoxide. Carbon dioxide, on the contrary, caused a certain decrease in the work function. These data (as well as some others on the influence of adsorption on the work function) were reported by the authors at a conference in Leningrad.

From the change in the work function one can judge the acceptor or donor nature of the adsorbed molecules. An increase in the work function upon adsorption may be regarded as an unambiguous criterion that we are dealing with acceptor molecules. A decrease in the work function indicates the donor nature of the adsorbed molecules.

Another consequence of band bending is a change in the electrical conductivity of the semiconductor \(\sigma\). Indeed, the concentration of free electrons in the conduction band (we shall denote this concentration by \(n\)) and the concentration of holes in the valence band (we shall denote it by \(p\)) are determined by the position of the level of the chemical potential \(\varepsilon\). We have (see Fig. 4)

\[ \left. \begin{aligned} n &= A e^{-\frac{v_e}{kT}},\\ p &= B e^{-\frac{u-v_e}{kT}}, \end{aligned} \right\} \tag{3} \]

where \(A\) and \(B\) are constants that need not concern us here. (These formulas are valid under the assumption \(v_e \gg kT\) and \((u-v_e)\gg kT\).) In the presence on the semiconductor surface of chemisorbed molecules, the quantity \(v_e\) turns out to be a function of \(x\), as is seen from Fig. 4, б or 4, в. Thus, in different sections parallel to the adsorbing surface (i.e., at different \(x\)), the electrical conductivity of the semiconductor proves to be different. We see that chemisorption can cause a noticeable change in the electrical conductivity in the near-surface layer of a semiconductor. In the case of sufficiently small crystals this may be reflected in the total electrical conductivity of the specimen under investigation.

Acceptor molecules cause depletion of the near-surface layer in electrons and enrichment of it with holes. Donor molecules act in the opposite manner. Thus, in the case of an \(n\)-semiconductor, adsorption of acceptor molecules should lead to a decrease, and adsorption of donor molecules to an increase, in conductivity. In the case of a \(p\)-semiconductor, on the contrary, acceptor molecules should cause an increase, and donor molecules a decrease, in conductivity.

The influence of adsorption on the electrical conductivity of a semiconductor has been studied by a number of authors. We note the work of Gray\(^{15}\) on the adsorption of \(O_2\) on CuO and on MnO, the work of Heiland\(^{16}\), who observed

decrease in the electrical conductivity of ZnO upon adsorption of O$_2$, the works of V. I. Lyashenko and I. I. Stepko$^{14,17}$, and also the works of S. Yu. Elovich and L. Ya. Margolis$^{18}$, who investigated the adsorption of a series of gases (O$_2$, CO, CO$_2$, C$_2$H$_6$, C$_3$H$_6$) on MnO$_2$.

According to S. Yu. Elovich and L. Ya. Margolis, reported at the conference, the adsorption of oxygen, studied at 20° C, has an equilibrium and reversible character; moreover, as the surface is filled with adsorbed molecules, the electrical conductivity of manganese dioxide increases monotonically, which once again testifies to the acceptor character of the local levels arising upon oxygen adsorption (since MnO$_2$ is a $p$-type semiconductor). Adsorption of C$_2$H$_6$ also leads to an increase, while adsorption of C$_3$H$_6$, on the contrary, leads to a decrease in the electrical conductivity of MnO$_2$.

A report by I. A. Myasnikov was devoted to the same question. I. A. Myasnikov dealt with the adsorption of oxygen on ZnO. He observed a decrease in electrical conductivity under the influence of adsorption (let us note that ZnO is a typical $n$-type semiconductor). He investigated in detail the kinetics of adsorption and desorption. From the change in electrical conductivity it was possible to judge the amount of adsorbed oxygen. Thus, the change in the electrical conductivity of the adsorbent may be regarded as a kind of indicator of the degree of filling of the surface with adsorbed molecules.

Let us note that, in studying the influence of adsorption on electrical conductivity, a certain caution should be exercised. One must be sure that one is really dealing with adsorption, and not with the penetration of gas molecules or atoms into the volume of the crystal. In the latter case the crystal is enriched with an “impurity,” and the accompanying change in electrical conductivity is trivial.

Special mention should be made of the results obtained by S. Yu. Elovich and L. Ya. Margolis$^{18,19}$ in studying the adsorption of oxygen on various adsorbents (MnO$_2$, Cu$_2$O, V$_2$O$_5$). If on MnO$_2$ and on Cu$_2$O oxygen behaves as an acceptor, then in adsorption on V$_2$O$_5$ it apparently acts as a donor. The authors were deliberately working in the region of impurity (and not intrinsic) conductivity. The V$_2$O$_5$ specimens with which they dealt were electronic semiconductors. This was directly established from the sign of the thermoelectric emf and was also confirmed by the fact that the introduction of oxygen into the crystal caused a decrease in electrical conductivity. However, oxygen introduced not into the interior of the crystal, but adsorbed on the surface, led not to a decrease but, on the contrary, to a certain increase in conductivity. This apparently indicates that in this case the adsorbed oxygen is bound not to an electron but to a hole.

In recent years a number of theoretical works have appeared abroad (Ehrén and Duke$^{20}$, Weisz$^{21}$, Germain$^{22}$, Engel and Hauffe$^{23}$),

in which the bending of the energy bands near the surface of the semiconductor, caused by chemisorption, is considered, and the influence of this effect on various adsorption regularities is investigated (the kinetics of activated adsorption, the decrease of the differential heat of adsorption with coverage, etc.). All these works are grouped under the general name of the “contact theory of adsorption” (Randschichttheorie der Adsorption). The question of the nature and mechanism of formation of the chemical bond between the adsorbed molecule and the semiconductor lattice is not considered at all in this theory. The theory proceeds from the idea of chemisorption as a factor causing charging of the surface, and examines the consequences that follow from this.

All works in this direction are based on the assumption that the adsorbed molecule is always charged, i.e., on the assumption that $\eta = 1$. Thus, according to this theory, neutralization of the adsorbed molecule, i.e., delocalization of the lattice electron (or hole) bound to it, means desorption of the molecule, whereas in reality, as can be shown$^{7}$ and as will be seen from what follows, this means not desorption, but merely a change in the character of the bond of the adsorbed molecule with the lattice.

According to the contact theory, a molecule remains in the adsorbed state only so long as it is held at the surface by an electron (or hole) localized near it, and loses its bond with the surface as soon as this electron (or hole) proves to be delocalized, i.e., transferred from the local level into the conduction band (or, correspondingly, into the valence band).

The dependence of the magnitude $\eta$ on the position of the chemical-potential level $\varepsilon$, shown in Fig. 3, according to the contact theory has the form of the broken line $abcd$ (which corresponds to $T = 0$; see Figs. 3a and 3b), i.e., depending on the position of the level $\varepsilon$, $\eta$ has the value $\eta = 1$ or $\eta = 0$. In the adsorbed state $\eta = 1$, while the value $\eta = 0$ corresponds to the absence of any bond between the molecule and the lattice.

From this there follows the following incorrect conclusion, yet one characteristic of the contact theory. Since, as the surface is filled by adsorbed molecules of some given kind $A$, the chemical-potential level $\varepsilon$ always approaches the local level $A$ (as a result of charging of the surface and bending of the energy bands; see, for example, Fig. 4b), there must always exist some limiting degree of coverage that cannot be exceeded. This maximum coverage is determined from the condition that the level $\varepsilon$ intersects the level $A$, which, according to Weisz’s calculations$^{21}$, occurs already at coverages of the order of 0.004. (By coverage is meant the fraction of the surface occupied by adsorbed molecules.) Upon reaching such very small coverages

chemisorption ceases. Further chemisorption according to the contact theory proves impossible.

This limitation is, of course, automatically removed if one assumes that, for a molecule in the adsorbed state, changes of $\eta$ from $\eta = 1$ to $\eta = 0$ are possible, i.e., if one takes into account a form of adsorption in which the adsorbed molecule remains uncharged. Indeed, a molecule in the adsorbed state may, but need not, carry an electric charge (an electron or a hole), since, as can be shown^24,25, the bond of a molecule with the surface may also be effected without the participation of electrons (holes) of the crystal lattice (the so-called “weak” homeopolar bond; see below).

This circumstance was taken into account in the work of V. V. Sandomirskii^26, reported by him at a conference, and also in the joint work of V. V. Sandomirskii and the author^13. In these works, which are closely related to the contact theory, the effect of chemisorption on electrical conductivity and on the work function of a semiconductor was theoretically studied, as well as the influence of impurities introduced into the interior of the crystal on the magnitude of $\eta$.

5. DIFFERENT TYPES OF BONDING IN CHEMISORPTION

Thus, a molecule adsorbed on the surface of a semiconductor may be in an electrically neutral or in a charged state. A molecule represented by an acceptor local level becomes negatively charged (binding with a lattice electron). A molecule represented by a donor level becomes positively charged (binding with a hole). Whether a given molecule acts as an acceptor or as a donor is determined by the nature of the molecule. Thus, for example, an $\mathrm{O}_2$ molecule is a typical acceptor, whereas a $\mathrm{CO}_2$ molecule is apparently (according to the data of V. I. Lyashenko and I. I. Steiko^14) an example of a donor. According to theoretical considerations, however, in a number of cases one and the same molecule on one and the same adsorbent may be represented simultaneously by both an acceptor and a donor level, i.e., may act simultaneously in two roles. In other words, in some cases one and the same molecule may serve as a localization center both for an electron and for a hole. Certain experimental data apparently support these theoretical concepts (for example, the data of S. Yu. Elovich and L. Ya. Margolis on the adsorption of oxygen on $\mathrm{V}_2\mathrm{O}_5$, which were mentioned above).

Defects of this kind, possessing both acceptor and donor properties simultaneously, are well known in solid-state physics. An example is the so-called $F$-center in an ionic crystal (an electron in a vacant metalloid site). As

As is known, an \(F\)-center can capture a free electron, turning into an \(F'\)-center. In this case the \(F\)-center acts as an acceptor. With respect to a free lattice electron it may be represented as an acceptor local level. At the same time, an \(F\)-center can give up its electron to the conduction band (dissociation of the \(F\)-center), or capture a free hole from the normal band. These are processes which, as is known, lead to bleaching of the crystal. In this case the \(F\)-center acts as a donor and may be represented as a donor local level.

The acceptor-donor properties of an adsorbed molecule lead to the existence of different forms of chemisorption. Indeed, in a number of cases one and the same chemisorbed molecule may be in an electrically neutral, negatively charged, and positively charged state. These states may be regarded as different forms of chemisorption. Transitions between these states are possible. Localization and delocalization of an electron or a hole on the adsorbed molecule transfer it from one state to another.

At equilibrium, of the total number of molecules of a given kind adsorbed per unit surface, a certain fraction of the molecules is found in each of these states. The relative content of the various forms of adsorption corresponding to equilibrium is determined by the nature of the adsorbent, the nature of the adsorbed molecules, and also by external conditions (pressure, temperature, etc.). The degree of charging of the surface, i.e. the magnitude and sign of the total electric charge concentrated on the surface at a given coverage (i.e. at a given surface concentration of adsorbed molecules), depends on the relative content of these different forms of adsorption.

The relative content of the various forms of adsorption can be changed as a result of external actions on the crystal, for example as a result of heating or of changing the concentration of impurities contained inside the crystal. Thus, for a given total number of adsorbed molecules, the relative number of molecules of a given kind bound to an electron, or bound to a hole, or in an electrically neutral state can, within certain limits, be artificially regulated \(^{27}\). This is very important from the point of view of catalysis, for, as theoretical investigation shows, depending on which of these possible states the adsorbed molecule is in, it is bound to the surface by bonds of different character and different strength. Consequently, in these different states its reactivity, i.e. its ability to enter into chemical combination with other adsorbed molecules or with molecules impinging from the gas phase, proves to be different.

Let us explain this with a concrete, deliberately simplified example. Let us take, as the adsorbent, a purely ionic crystal (for example, an NaCl crystal). As the adsorbed particle we shall consider a monovalent atom possessing one electron above a closed shell (for example, an Na atom). The following types of bonding of the Na atom with the NaCl lattice are possible: 1) the so-called “weak” homeopolar bond, corresponding to the neutral state of the Na atom; 2) the so-called “strong” homeopolar bond, formed as a result of capture by the adsorbed Na atom of a free electron of the lattice; 3) an ionic bond, formed when the Na atom captures a free hole.

Let us consider each of these types of bonding.

1) So long as the Na atom is sufficiently far from the surface of the crystal, its valence electron is its own property. If, however, the Na atom is located on the surface (as shown in Fig. 6, a), then its electron no longer belongs to it alone. Strictly speaking, it belongs to the entire system as a whole.

Fig. 6.

Calculation shows^24,25 that the valence electron of the Na atom is then, to a greater or lesser extent, drawn away from the Na atom into the lattice. In other words, the electron cloud surrounding the positive core of the Na atom and possessing, in the case of an isolated atom, spherical symmetry, is now deformed and, to some degree, drawn into the lattice. The wave function has a decaying character: it decreases inside the lattice as the distance from the center of adsorption increases. In the present case one of the Na$^+$ ions in the surface layer of the lattice serves as such a center (Fig. 6, a).

This pulling of the electron cloud into the lattice is what accounts for the bond between the adsorbed Na atom and the crystal. Thus, the bond is effected at the expense of the valence electron of the Na atom. The Na atom, together with the Na\(^+\) ion of the lattice serving as the adsorption center, forms the quasimolecule Na\(_2^+\). Here we have a bond of the same type as in the molecular ion H\(_2^+\). This is a one-electron bond. We shall call such a bond a “weak” homeopolar bond.

Let us note that a Na atom which is in the state of such a “weak” homeopolar bond with the surface retains its free valence unsaturated.

2) It can be shown\(^{11}\) that such an atom, bound to the lattice by means of its own valence electron, plays the role of a “trap” with respect to a free electron of the lattice, i.e., it serves as a localization center for this electron. In other words, in the energy spectrum of the crystal such an atom is represented by an acceptor local level.

Let us note that a free electron in the lattice may be treated as a free positive valence wandering through the crystal. Indeed, the presence of a free electron in the NaCl lattice means that one of the Na\(^+\) ions of the lattice is neutralized (converted into a neutral Na atom). This neutral state can move through the lattice, being transferred from one Na\(^+\) ion to a neighboring Na\(^+\) ion. The Na\(^+\) ion has a closed electron shell, i.e., it has the structure of a noble gas. A free electron in the lattice is thus an extra electron placed on a Na\(^+\) ion over and above the closed shell and therefore performs the function of a free valence.

If a free electron of the lattice drops from the conduction band to a local level, this means that such an electron ceases to be free and is localized on the surface of the crystal near that Na\(^+\) ion of the lattice on which the adsorbed Na atom sits. This is shown in Fig. 6, b. In this case, as can be shown\(^{11}\), a rather strong two-electron bond is formed between the Na atom and the lattice. Two electrons participate in this bond: the valence electron of the adsorbed Na atom and an electron of the crystal lattice itself, borrowed from the family of free electrons.

The electron of the lattice and the adsorbed atom are then bound by exchange forces. These exchange forces are in the present case the adsorption forces holding the adsorbed Na atom on the surface and, at the same time, holding the lattice electron near the adsorbed atom. We obtain the quasimolecule Na\(_2\) (see Fig. 6, b). Here we have a two-electron bond of the same type as in the H\(_2\) molecule. We shall call such a bond a “strong” homeopolar bond.

Let us note that the valence of an adsorbed atom in the state of a “strong” homeopolar bond is saturated. It is saturated by a free valence of the lattice. In this case the adsorbed atom (together with the adsorption center) is an electrically charged entity.

3) Alongside the “weak” and “strong” homeopolar bonds, a third type of bond is also possible[^27]. The possibility of this third type of bond is due to the fact that a Na atom in the state of a “weak” homeopolar bond with the lattice is, as can be shown, not only a localization center for a lattice electron, but at the same time also a localization center for a free hole. The presence of a hole in an NaCl crystal means the presence of a neutral Cl atom among the Cl\(^{-}\) ions of the lattice. Such a neutral state is, of course, not localized, but is capable of wandering through the crystal, being transferred from one Cl\(^{-}\) ion to a neighboring Cl\(^{-}\) ion. Thus, a free hole is the absence of an electron at one of the Cl\(^{-}\) ions. The Cl\(^{-}\) ion possesses a closed electron shell. The presence of a hole means that one electron has been removed from this closed shell. Consequently, the hole may be interpreted as a negative free valence. Localization of the hole near an adsorbed Na atom in the state of a “weak” homeopolar bond with the lattice leads to the formation of a quasimo­lecule NaCl, as is seen from Fig. 6, v. The adsorption center in this case is a Cl\(^{-}\) ion of the lattice with a hole localized on it. We have here a bond of ionic type. Indeed, the hole may be regarded as having been displaced onto the adsorbed Na atom, as is shown in Fig. 6, v′ (Fig. 6, v′ replaces Fig. 6, v).

In this case, as in the case of the “strong” homeopolar bond, the valence of the Na atom is saturated. However, now the positive valence of the Na atom is saturated not by a positive, but by a negative valence of the surface. In this case the adsorbed atom proves to be positively charged (ionized).

The ionic bond, just like the “strong” homeopolar bond, is therefore a state with saturated valence, in contrast to the “weak” homeopolar bond, in which the free valence of the Na atom remains unsaturated.

The mutual saturation of two like valences (the positive valence of the Na atom plus the free positive valence of the surface) leads, as usual, to the formation of a homeopolar bond. The mutual saturation of two unlike valences (the positive valence of the Na atom plus the free negative valence of the surface) leads to the formation of an ionic bond.

If, in the transition of an adsorbed Na atom from the state of a “weak” bond to the state of a “strong” homeopolar bond, the adsorbed atom acts as an acceptor, then in the transition to the state of an ionic bond this same atom acts as a donor.

6. REACTIVITY OF ADSORBED MOLECULES

Thus, the various forms of chemisorption differ in the character of the bond between the adsorbed atom (molecule) and the lattice of the adsorbent. The possibility that different types of bond may be realized for one and the same atom (or molecule) with one and the same adsorbent is a characteristic feature of chemisorption. In this respect chemisorption, which is a chemical compound of a gaseous atom or molecule with a solid body, differs from ordinary chemical compounds formed between atoms or groups of atoms when molecules are produced from them. The bond between two atoms or two groups of atoms within a molecule always has a quite definite character, uniquely determined by the nature of both components entering into the bond.

In the preceding section, various types of bond were considered using the example of a Na atom adsorbed on the NaCl lattice. In the final analysis, the existence of different types of bond in this case is due to the binary character of the adsorbent. It is due to the fact that either of the two components of the lattice can participate in the bond, provided it bears a free (unsaturated) valence: a Na\(^+\) ion with an electron localized on it, or a Cl\(^-\) ion with a hole localized on it.

Semiconductors used as catalysts are likewise, as a rule, binary compounds with a more or less pronounced ionic character of bonding (like the NaCl lattice). These include numerous solid oxides and sulfides (ZrO, ZnS, V\(_2\)O\(_5\), Cu\(_2\)O, etc.). The variety of possible forms of adsorption is reduced, however, in those cases where we are dealing with homopolar lattices built from atoms of one and the same kind (for example, in the case of Ge or Se).

In chemisorption we obtain different types of bonds depending on whether free electrons and holes of the crystal lattice do or do not participate in these bonds; these act, respectively, as positive and negative free valences of the surface.

Everything said in the preceding section concerning the Na atom, which possesses one positive valence, i.e. contains one electron beyond a closed shell, can be fully transferred to the case of an atom possessing negative valence, i.e. characterized by a deficiency of an electron in a closed shell. The Cl atom may serve as an example. In this case, however, the words “electron” and “hole” must everywhere be interchanged. Moreover, everything said can also be transferred to the case of any radical, i.e. a molecule possessing a free (unsaturated) valence. The hydroxyl group OH may serve as an example of such a radical.

Let us now consider the adsorption not of a free atom or radical, but of a saturated molecule. Here again, and moreover with particular clarity, the role of free electrons and holes of the lattice as the free valences of the surface is manifested.

Let us first turn to a molecule built from two atoms or two groups of atoms joined by a simple (single) bond. Such are, for example, the molecules \(H_2\), \(Na_2\), \(Cl_2\), the molecule of any saturated hydrocarbon \(C_nH_{2n+2}\) (where \(n\) is any integer), in which all atoms are joined by simple bonds, and the molecule of any alcohol \(ROH\), built from a hydrocarbon radical \(R\) and a hydroxyl group \(OH\), joined by a simple bond. Such a molecule, placed on the surface of a semiconductor, is capable of capturing a free electron (or hole). As a result of such capture, a strong bond is formed between the molecule and the lattice, but at the same time, as can be shown, one of the bonds inside the molecule is broken. As a result the molecule proves to be divided into two parts (into two radicals).

Fig. 7.

One of these radicals remains adsorbed and, in doing so, bound to the electron (or to the hole) that caused the dissociation of the molecule. This electron (or hole) thus proves to be captured by one of the products of dissociation and thereby localized. The other product of dissociation, retaining its valence unsaturated, passes into the gas phase or is adsorbed on the surface, binding to it by a “weak” bond. This is depicted in Fig. 7, \(a\), \(b\), \(c\), in which the successive stages of the process are presented. In Fig. 7, \(a'\), \(b'\), \(c'\) the same mechanism is shown with the aid of symbolic valence strokes.

We see that a free electron of the lattice (or a free hole) here performs the function of a free valence. This free valence of the surface causes the rupture of a valence bond within the molecule and is saturated at the expense of the liberated valence of one of the dissociation products. The crystal itself (as a whole) acts here in the role of a free radical (in the role of a molecule possessing a free valence), and the dissociation reaction upon adsorption may be written as an ordinary reaction with the participation of a free radical:

\[ \mathrm{Na}_2 + \dot L \to \dot{\mathrm{Na}} + \mathrm{Na}L, \]

where \(L\) is the symbol of the lattice, and the dot over the letter denotes a free valence.

Let us now consider a molecule in which two atoms or two groups of atoms are bound not by a simple bond, but by a multiple (for example, double or triple) bond (examples may be the molecules \(\mathrm{O}_2\), \(\mathrm{N}_2\), \(\mathrm{SO}_2\), etc.), and let us suppose that during adsorption one of these bonds is ruptured.

In this case, in contrast to the preceding one, the act of adsorption is not yet accompanied by dissociation of the molecule. On the surface we obtain a radical possessing one free valence and held on the surface by an electron or a hole, as is shown, for example, in Fig. 8 for the molecule \(\mathrm{O}_2\).

Fig. 8.

We see that the free valence of the surface, in binding with the molecule, does not disappear, but is reborn in the form of a free valence of the adsorbed molecule. As a result of the very act of adsorption, the saturated molecule is transformed into a radical. This transformation is the result of the capture by the adsorbed molecule of a free electron or hole. Thus the adsorbed molecule is transformed into an electrically charged formation (the so-called “ion-radical”).

Let us note that radicals are always more reactive than saturated molecules. We see that the very act of chemisorption, with which every heterogeneous catalytic process begins, leads to an increase in the reactivity of the molecules participating in the process. Is this not where the clue to the catalytic action of the semiconductor lies?

The theory, some qualitative results of which have been briefly set forth here (§ 6 and § 5), is usually called the “electronic theo-

“theory” of catalysis and adsorption^28,29. This theory studies the mechanism of the chemical interaction of a gas molecule with a solid body, which is here treated as a single whole. According to this theory, the free electrons and holes of the crystal lattice prove, as we see, to be direct participants in the chemical processes developing on the surface of the semiconductor. Moreover, in a number of cases they prove to be regulators of these processes.

Thus a path is opened toward understanding the connections between the adsorption and catalytic properties of a semiconductor, on the one hand, and its electronic properties, on the other. A conference report by F. F. Vol'kenshtein was devoted to questions of the electronic theory of catalysis.

Let us note that the so-called “contact theory” of adsorption, discussed in the preceding chapter, is one of the branches of the “electronic theory.” In the “contact theory” only one side of the matter is considered: the influence of the bulk on the surface. The question of the mechanism and types of bonds in chemisorption, as we have already noted, remains, however, outside the framework of the “contact theory.”

In the “contact theory,” as has already been said, the possibility of a “weak” homeopolar bond in chemisorption is ignored. In other words, those states of the chemisorbed molecule in which the molecule remains electrically neutral are ignored. Such an approximation is permissible when the “weak” homeopolar bond is indeed weak or, in other words, when the chemical-potential level lies sufficiently high above the acceptor local levels or sufficiently deep below the donor local levels corresponding to the adsorbed molecules.

In this approximation the free electrons and holes of the crystal lattice act as adsorption centers. In other words, the free valences of the adsorbent, wandering over the surface and taking up gas molecules, act in this role. In this approximation each act of chemisorption is accompanied by the rupture of a valence bond within the molecule (the transformation of the molecule into a radical or its dissociation into two radicals).

Let us note that the concentration of the electron and hole gas in a semiconductor under ordinary conditions is very small. In other words, the concentration of adsorption centers on the surface of the crystal should be regarded as negligibly small. From this it would seem to follow that, within the framework of the approximation under consideration, the surface can take up only a negligible quantity of gas molecules.

This, however, is not so. It can easily be shown^4 that, as the surface is filled, ever new adsorption centers are created. The supply of free adsorption centers is depleted very slowly owing to the supply of new centers to the surface. Therefore the number of adsorbed molecules may substantially exceed the initial number of adsorption centers.

The conception of free electrons and holes as adsorption centers was proposed and developed by the author\(^{12, 4, 28, 29}\). Proceeding from these conceptions, it proved possible to explain a number of the basic regularities of so-called activated adsorption\(^{4}\). From these same conceptions, in fact, follows the “contact theory.” The interpretation of free electrons and holes as adsorption centers is contained (although not always explicitly) in all works on the “contact theory.”

7. ADSORPTION CAPACITY OF THE SURFACE

How many gas molecules can be retained, under given conditions, on the surface of a semiconductor?

Let us suppose that the adsorbent and the adsorbate are in equilibrium. This means that on the given surface, over a given interval of time, as many molecules are adsorbed as are desorbed. The surface concentration of adsorbed molecules then remains constant. It depends on the conditions (on the temperature \(T\) and on the pressure \(p\)), and also on the nature of the adsorbent and on the nature of the molecules being adsorbed. Let \(N\) be the number of molecules of a given kind retained per unit surface at given \(T\) and \(p\). The number \(N\) characterizes what may be called the “adsorption capacity of the surface” with respect to molecules of the given kind.

According to the elementary Langmuir theory we have

\[ N=\frac{N_{0}}{1+\frac{a}{p}e^{-q/kT}}, \tag{4} \]

where \(N_{0}\) is the number of adsorption centers (per unit surface); \(q\) is the heat of adsorption, i.e., the binding energy of an adsorbed molecule with an adsorption center; \(a\) is a factor which need not concern us here. We see that the adsorption capacity \(N\) depends on the concentration of adsorption centers \(N_{0}\) and on the strength of the bond \(q\). The more adsorption centers there are on the surface, and the stronger the bond of the adsorbed molecule with the surface, the more molecules are retained on the surface under the same external conditions.

The adsorption capacity of a surface can be changed by subjecting the adsorbent to one or another external action. An example of such an action may be any treatment of the specimen that leads to a change in its stoichiometric composition or to a change in the nature and amount of the impurity contained in it. The adsorption capacity of the surface is extremely sensitive to the slightest structural disturbances created inside the crystal and distorting the strictly periodic structure of the lattice.

Let us cite, as an example, the work of Hedvall and Nord^30, who studied adsorption on various samples of HgS differing in stoichiometric composition. They found that the adsorptive capacity of a crystal (other conditions being equal) is the greater, the more strongly its stoichiometry is disturbed. The influence of impurities on adsorptive capacity was observed by Lux, Bodart, and Rens^31, as well as by a number of other authors.

Another factor changing the adsorptive capacity of a surface is illumination. In this case it is not all frequencies of the irradiating light that are active, but only definite regions of the spectrum. The action of light in different cases proves to be opposite. In some cases illumination increases the adsorptive capacity of the adsorbent (photoadsorption); in other cases, on the contrary, it suppresses the adsorptive capacity (photodesorption). This depends on the nature of the adsorbent, on the nature of the adsorbate, and on the frequency of the irradiating light.

Let us note that in a number of cases the influence of illumination on adsorptive capacity is only apparent. Indeed, illumination can cause a photochemical reaction in the gaseous volume, i.e., in the adsorbate itself, as a result of which the nature of the molecules participating in adsorption proves to be changed. In this case the adsorptive capacity of the surface may change not as a result of the direct action of light on the adsorbent, but as a result of a change in the chemical composition of the adsorbate. Thus, for example, Lux, Bodart, and Rens^31 observed an increase in the adsorptive capacity of ThO\(_2\) upon illumination of the system by the light of a mercury lamp. The adsorbate was a mixture of hydrogen with mercury vapor. In these experiments, apparently (as the authors themselves also note), there occurred dissociation of gaseous H\(_2\) molecules photosensitized by mercury vapor. Here there were apparently no effects due to the direct action of illumination on the adsorbent.

The influence of light on adsorptive capacity may be apparent for another reason as well. Illumination can cause heating of the adsorbent. An increase in temperature, however, always leads to a decrease in adsorptive capacity, as is seen, for example, from Langmuir’s formula (4). Desorption caused by illumination is not, in such cases, photodesorption. Here light acts as an indirect factor.

At present, however, there is a whole series of experimental works in which it has been shown beyond doubt that in a number of cases the role of light is not merely indirect, and that light can exert a direct influence on the adsorptive capacity of a crystal. This may be due either to a change in the number of adsorption centers, or to a change in the strength of the bond of the adsorbed molecules, occurring under the influence of illumination. Such effects are in complete agreement with the concepts of electron-

…of the theory of chemisorption. Indeed, according to these ideas (see §§ 5 and 6), the free electrons and holes of a semiconductor take a direct part in bond formation. Enrichment of a semiconductor with free electrons or holes, occurring upon absorption by the crystal of photoelectrically active radiation, should lead to an increase in its adsorptive capacity. On the other hand, absorption of radiation that in one way or another leads to the liberation of electrons or holes localized on adsorbed molecules, i.e., increases the share of the “weak” bond (as compared with a “strong” homeopolar or ionic bond), should lead to desorption, i.e., to a decrease in adsorptive capacity^4,32.

As early as 1934, A. N. Terenin^33 discovered, and subsequently L. N. Kurbatov^34 investigated in detail, an increase in the adsorptive capacity of TlJ with respect to iodine vapors when the adsorbent was illuminated with a certain region of the visible spectrum. This was precisely the spectral region that produced photoconductivity in TlJ. In 1943 A. K. Vishnevskii^35 studied the adsorption of J₂ on KJ enriched with excess-stoichiometric potassium, i.e., containing so-called “color centers.” He likewise observed an increase in the adsorptive capacity when the adsorbent was illuminated with photoelectrically active radiation, i.e., radiation absorbed by the “color centers” and producing conductivity. Let us also note the already cited work of Hedvall and Nord^30, who observed an increase in the adsorptive capacity of HgS caused by illumination. The authors dealt with the red modification of HgS, which is a typical semiconductor. In this work as well, the maximum of adsorption sensitivity proved to coincide with the spectral maximum of photoconductivity. Finally, mention should be made of the recent work of Kobayashi and Kawai^36. The authors dealt with a ZnS phosphor activated with copper. Illuminating a crystal, placed in an oxygen atmosphere, with frequencies lying in the characteristic absorption band, the authors observed an increase in the adsorptive capacity of the crystal (with respect to oxygen) and, at the same time, a decrease in the work function. The effect increased with increasing oxygen pressure and with decreasing temperature.

In all these works (and in a number of others), the authors, in investigating the increase of adsorptive capacity under illumination, were naturally dealing with adsorption equilibrium. Until now, unfortunately, no one has investigated the influence of illumination not on the equilibrium but on the kinetics of chemical (activated) adsorption. From the standpoint of the concepts of the electron theory, such an influence should occur.

Photodesorption, i.e., a decrease in adsorptive capacity under illumination, has also been observed by a number of authors. At the conference of eth—

Myasnikov’s report, devoted in its well-known part to this question.

I. A. Myasnikov and S. Ya. Pshezhetskii \(^{37}\) caused desorption of \(O_2\), previously adsorbed on \(ZnO\), by illuminating the adsorbent with frequencies belonging to the region of intrinsic absorption of zinc oxide. In this, an increase in the conductivity of the specimen was observed.

Photodesorption caused by frequencies lying in the band of intrinsic absorption, i.e., as a rule, photoelectrically inactive frequencies, may have an exciton mechanism. In this case the primary act of light absorption leads to the appearance of an exciton in the lattice. The exciton, wandering through the crystal, encounters lattice defects and is annihilated at these defects. The energy liberated in such annihilation, i.e., in other words, the energy of the exciton, is used in this process to transfer an electron or a hole localized at the defect from a bound state into a free state. This last act thus leads to the occurrence of photoconductivity.

Such an exciton mechanism for the occurrence of impurity photoconductivity in semiconductors was considered by V. E. Lashkarev \(^{38}\) and, simultaneously with him, by V. P. Zhuze and S. M. Ryvkin \(^{39}\). The latter authors used this mechanism to explain the internal photoeffect in \(Cu_2O\), which they studied experimentally.

This same Lashkarev—Zhuze—Ryvkin mechanism may lead to desorption when the lattice defects at which excitons are annihilated are not impurity atoms located inside the crystal, but foreign molecules adsorbed on its surface. Indeed, the removal of an electron or a hole from an adsorbed molecule, i.e., its transfer from a charged state to an electrically neutral state, leads, as we have seen, to a weakening of its bond with the crystal. This in turn has, as its consequence, a decrease in the adsorption capacity of the surface. As a result, some of the adsorbed molecules leave the surface and pass into the gas phase (desorption).

The increase in the conductivity of the specimen that accompanies photodesorption, observed by I. A. Myasnikov and S. Ya. Pshezhetskii, is quite natural. Indeed, as a result of desorption, the charge concentrated on the surface is partially removed and the curved energy bands shown in Fig. 4, b or 4, c are straightened to a certain extent. In the case of acceptor molecules \((O_2)\) and an electronic semiconductor \((ZnO)\), this should lead to an increase in conductivity.

Whatever the detailed mechanism of photoadsorption and photodesorption may be, the very fact of the influence of light (light absorbed by the crystal itself) on the adsorption capacity of the crystal testifies to the electronic nature of the adsorption bonds realized in chemisorption.

8. CATALYTIC ACTIVITY AND THE ROLE OF IMPURITIES

Up to now we have been speaking about chemical adsorption on the surface of a semiconductor. Let us now turn directly to questions of catalysis.

Let us have a mixture of gases \(A_1, A_2,\ldots,A_n\) in contact with the surface of a semiconductor (catalyst). Suppose that a chemical reaction takes place between these gases, as a result of which, instead of the molecules \(A_1, A_2,\ldots,A_n\), the molecules \(A'_1, A'_2,\ldots,A'_m\) are formed. The reaction equation has the form:

\[ \nu_1 A_1+\nu_2 A_2+\cdots+\nu_n A_n \to \nu'_1 A'_1+\nu'_2 A'_2+\cdots+\nu'_m A'_m, \tag{5} \]

where \(\nu_i\) and \(\nu'_k\) are stoichiometric coefficients indicating how many molecules of each given kind participate in the reaction act (here \(i=1,2,\ldots,n\) and \(k=1,2,\ldots,m\)).

Let us denote by \(p_i\) and \(p'_k\) the partial pressures, respectively, of the gases \(A_i\) and \(A'_k\). Obviously, \(p_i\) and \(p'_k\) are proportional to the concentrations of the corresponding molecules \(A_i\) and \(A'_k\). The quantity

\[ g=-\frac{1}{\nu_1}\frac{dp_1}{dt} =-\frac{1}{\nu_2}\frac{dp_2}{dt} =\cdots =-\frac{1}{\nu_n}\frac{dp_n}{dt} = \]

\[ =\frac{1}{\nu'_1}\frac{dp'_1}{dt} =\frac{1}{\nu'_2}\frac{dp'_2}{dt} =\cdots =\frac{1}{\nu'_m}\frac{dp'_m}{dt} \]

we shall call the reaction rate. This quantity shows the rate at which the concentration of the molecules \(A_1,A_2,\ldots,A_n\) entering into the reaction decreases, or the rate at which the molecules \(A'_1,A'_2,\ldots,A'_m\), which are the reaction products, accumulate.

The reaction rate \(g\) depends on the temperature \(T\) and, generally speaking, on the partial pressures \(p_i\) and \(p'_k\) of all the gases participating in the reaction,

\[ g=g(T;\ p_1,p_2,\ldots,p_n;\ p'_1,p'_2,\ldots,p'_m). \]

Generally speaking, \(g\) increases as \(p_1,p_2,\ldots,p_n\) increase and decreases as \(p'_1,p'_2,\ldots,p'_m\) increase. In other words, the accumulation of reaction products leads to inhibition of the reaction.

In the case where the partial pressures of all gases participating in the reaction are sufficiently small, i.e., in the case where the coverages of the surface by adsorbed molecules of each given kind may be regarded as sufficiently small, we have

\[ g=K\cdot p_1^{\mu_1}p_2^{\mu_2}\ldots p_n^{\mu_n}. \tag{6} \]

The exponent \(\mu_i\) in (6) is called the “order of the reaction” with respect to the component \(A_i\). Usually we have:

\[ \mu_i=\nu_i. \]

The constant \(K\) in (6) is called the “rate constant” and characterizes the activity of the catalyst with respect to reaction (5).

Usually the rate constant \(K\) satisfies the Arrhenius law

\[ K=K_0 e^{-E/kT}, \tag{7} \]

where \(E\) is the activation energy of the reaction, and \(K_0\) is the pre-exponential factor, whose dimension is determined by the order of the reaction with respect to each of the components [i.e., by the exponents \(\mu_1,\mu_2,\ldots,\mu_n\) in (6)].

In the coordinates \(\ln K\) and \(\dfrac{1}{T}\), the Arrhenius law (7) is represented by a straight line which, however, in some cases undergoes bends similar to the bends that are observed on electrical-conductivity straight lines. In other words, the activation energy \(E\) and the pre-exponential factor \(K_0\) in different temperature regions may have different values. This is illustrated in Fig. 9, taken from the work of L. Ya. Margolis and O. M. Todes \(^{40}\), who investigated the oxidation reaction of ethylene

\[ \mathrm{C_2H_4}+3\mathrm{O_2}\to 2\mathrm{CO_2}+2\mathrm{H_2O} \tag{8} \]

on magnesium–chromium and copper–chromium catalysts.

Fig. 9.

The introduction of an impurity into a semiconductor leads to a change in the values both of the activation energy \(E\) and of the pre-exponential factor \(K_0\) in the Arrhenius law (7). As a result, the reaction rate constant \(K\) changes, i.e., the catalytic activity of the semiconductor with respect to the given reaction changes.

It is noteworthy that the Arrhenius straight lines for different samples of one and the same semiconductor, differing in impurity content, may intersect, as is shown, for example, in Fig. 10. This

figure pertains to the reaction of ethylene oxidation (8) on \(MgO \cdot Cr_2O_3\) catalysts with an admixture of \(Na_2SO_4\), which was studied by O. V. Krylov and L. Ya. Margolis \(^{41}\).

Let us consider, for example, straight lines No. 1 and No. 5 in Fig. 10. Straight line No. 1 corresponds to the sample with the smaller, and straight line No. 5 to the sample with the larger, content of the admixture. We see that the addition of the admixture in this case lowers the activation energy \(E\) and increases the pre-exponential factor \(K_0\). Thus, at low temperatures (to the right of the point of intersection of straight lines No. 1 and No. 5 in Fig. 10) the activity of the catalyst, as a result of introducing the admixture, as we see, increases, whereas at high temperatures (to the left of the point of intersection of straight lines No. 1 and No. 5), on the contrary, it decreases. In other words, one and the same admixture, taken in one and the same amount, at low temperatures may promote the catalyst, i.e. accelerate the reaction, while at high temperatures, on the contrary, poison the catalyst, i.e. retard the reaction proceeding on it.

Fig. 10.

It is noteworthy that even at one and the same temperature one and the same admixture may exert either a promoting or a poisoning action, depending on its concentration. This is evident from the same Fig. 10, if one notes that the straight lines in this figure are renumbered in the order of increasing admixture content in the sample. This is seen especially clearly from Fig. 11, which shows the activity of the catalyst (the rate constant \(K\)) at a specified temperature as a function of the concentration \(Z\) of the admixture contained in it—

mixtures. Fig. 11 relates to the decomposition reaction of hydrogen peroxide

\[ 2\mathrm{H}_2\mathrm{O}_2 \longrightarrow 2\mathrm{H}_2\mathrm{O} + \mathrm{O}_2 \]

on MgO crystals containing \(\mathrm{Sb}_2\mathrm{O}_3\) as an impurity. Fig. 11 is taken from the work of G. M. Zhabrova and E. A. Fokina \(^{42}\).

Thus, we see that \(K = K(T, Z)\). The ratio

\[ M(T, Z) = \frac{K(T, Z)}{K(T, 0)} \]

may be called the “modification coefficient.” This quantity shows how many times the rate constant of a catalytic—

Fig. 11.

—reaction changes when a given amount of impurity \(Z\) is introduced per unit volume of catalyst. If \(M(T, Z) > 1\), the impurity is called a “promoter.” If, however, \(M(T, Z) < 1\), the impurity is called a “poison.”

In many cases, however, for one and the same kind of impurity, as we have seen, we have the condition \(M(T, Z) > 1\) in one range of values of \(T\) and \(Z\), and the condition \(M(T, Z) < 1\) in another range of \(T\) and \(Z\), i.e. one and the same impurity acts as a promoter or as a poison depending on its concentration \(Z\) and the temperature \(T\) of the catalyst. Thus, the promoting or poisoning—

ing effect of an impurity is determined not only, and not so much, by its nature as by the experimental conditions. The concepts of “promotion” and “poisoning” are at present often replaced by the more general concept of “modification.” The phenomenon of modification (i.e., promotion by poisons and poisoning by promoters) was discovered in 1940 in the catalysis laboratory of the Institute of Physical Chemistry of the Academy of Sciences of the USSR. At present this phenomenon has been fairly well studied experimentally[^43].

Let us note, in conclusion, that between \(K_0\) and \(E\), which change as the content of impurity \(Z\) changes, there is, as a rule, a simple linear relation, observed by many authors for different reactions on different catalysts:

\[ \ln K_0 = A + BE. \tag{9} \]

As an illustration of this empirical law, Fig. 12 is given, constructed from the data of L. Ya. Margolis and O. M. Todes[^44], who studied the oxidation reaction of isooctane:

\[ \mathrm{C}_8\mathrm{H}_{18} + 12\tfrac{1}{2}\mathrm{O}_2 \to 8\mathrm{CO}_2 + 9\mathrm{H}_2\mathrm{O} \]

on a magnesium–chromium catalyst modified with an admixture of \(\mathrm{H}_3\mathrm{PO}_4\). The points in Fig. 12, corresponding to different specimens, are numbered in the order of increasing impurity content in the specimen.

Fig. 12.

Law (9) recalls the well-known empirical Meyer–Neldel law for electrical conductivity. The temperature dependence of electrical conductivity, as is known, has the form:

\[ \sigma = \sigma_0 e^{-u/kT}, \tag{10} \]

where in a number of cases, as was established by Meyer and Neldel[^45], the parameters \(\sigma_0\) and \(u\) in (10) turn out to be connected by a linear relation:

\[ \ln \sigma_0 = a + bu. \tag{11} \]

Let us note that the value of the coefficient \(B\) in law (9) coincides with the value of the corresponding coefficient \(b\) in the Meyer—Neldel law[^11]. Thus, according to the data of A. B. Shekhter and Yu. Sh. Mashkovskii[^2], for the decomposition reaction of methanol \(\mathrm{CH_3OH}\) on zinc oxide samples calcined to different extents, the coefficient \(B\) has the value \(B = 0.35\) mole/kcal. The corresponding coefficient \(b\) in the Meyer—Neldel law for the same zinc oxide has the value \(b = 0.30\) mole/kcal.

The question arises: in what way do impurities, introduced into a semiconductor in negligible amounts, exert such a substantial influence on the rate of chemical reactions occurring on its surface?

From the standpoint of the electronic theory, the matter is that the introduction of impurities changes the concentration of the electron and hole gas in the semiconductor, and this concentration, in turn, determines, as we have seen (see § 6), the reactivity of molecules adsorbed on the surface of the semiconductor, and thereby its catalytic activity. The semiconductor crystal, together with the foreign molecules adsorbed on its surface and the impurity atoms introduced into its volume, forms a unified system with an established electronic equilibrium. The electron gas in the semiconductor effects, if one may put it this way, a connection between its volume and its surface.

A number of theoretical works[^10],[^12],[^13],[^46] are devoted to the explanation of modification phenomena from the standpoint of the electronic theory of catalysis.

9. CATALYTIC ACTIVITY AND ELECTRICAL CONDUCTIVITY

From the standpoint of the electronic theory of catalysis, one should expect a definite correlation between the electrical conductivity of a semiconductor and its catalytic activity. In connection with this theoretical prediction[^12],[^13],[^46], in recent years a whole series of experimental works have appeared whose purpose is to reveal this correlation.

In investigating the connection between electrical conductivity and catalytic activity, different authors, however, put different meanings into this concept and understand their task in different ways. In this connection all works of this kind should be divided into two groups.

To the first group belong those works in which the connection between electrical conductivity and activity is understood as the connection between two characteristics of the sample: its specific electrical conductivity \(\sigma\) and the reaction-rate constant \(K\), characterizing the catalytic activity of the given sample with respect to the given reaction.

According to the electronic theory, the activity of a semiconductor is determined, other conditions being equal, by the concentrations of the contained ...

in it of free electrons and holes. Therefore, factors causing changes in \(\sigma\) must at the same time lead to changes in \(K\). Thus, different specimens of one and the same semiconductor, prepared in different ways and possessing different electrical conductivity \(\sigma\), must at the same time possess different activity \(K\). A certain parallelism should exist between these two characteristics.

It should be emphasized that, according to the electronic theory, it makes sense to expect this parallelism only in those cases when changes in \(\sigma\) and \(K\) are caused by the action on the semiconductor of one and the same factor, while all other conditions remain unchanged. An example of such a factor is an impurity introduced into a given semiconductor in various concentrations. There is, however, no basis for expecting any parallelism in changes of \(\sigma\) and \(K\) when comparing different semiconductors that differ in their chemical nature. In these cases such parallelism may be completely veiled, since the expression for catalytic activity includes not only the concentrations of free electrons and holes, but also other parameters characterizing both the nature of the semiconductor and the nature of the molecules participating in the reaction.

Among the experimental works belonging to this group, we shall note the work by N. P. Keier, S. Z. Roginskii, and I. S. Sazonova\(^{47}\), reported at the conference; they studied the oxidation reaction of carbon monoxide (1) on different NiO specimens differing in impurity content. Li\(_2\)O was introduced as the impurity. According to de Boer and Verwey\(^{48}\), an NiO crystal may be represented as built of Ni\(^{++}\) and O\(^{--}\) ions. As a rule, NiO is a hole semiconductor. The presence of a hole in such a crystal means the presence of an Ni\(^{+++}\) ion among the Ni\(^{++}\) ions of the lattice. Current transfer is provided by the displacement of the Ni\(^{+++}\) state from one Ni\(^{++}\) ion to a neighboring Ni\(^{++}\) ion:

\[ \mathrm{Ni}^{+++} + \mathrm{Ni}^{++} \to \mathrm{Ni}^{++} + \mathrm{Ni}^{+++}. \]

The NiO crystals with an addition of Li\(_2\)O with which N. P. Keier, S. Z. Roginskii, and I. S. Sazonova dealt were solid substitutional solutions in which the doubly charged Ni\(^{++}\) ions belonging to lattice sites were partially replaced by singly charged Li\(^+\) ions. Such a Li\(^+\) ion, replacing an Ni\(^{++}\) ion, is an acceptor defect, i.e., a defect that holds a hole near itself, as is shown in the schematic Fig. 13, \(a\). This hole can be freed (the probability of release increases with temperature), after which, having lost its connection with the defect, it acquires the ability to wander freely through the crystal (Fig. 13, \(b\)). In this way the crystal is enriched with additional current carriers. Consequently, the introduction of Li into NiO should lead, and does lead, to an increase in conductivity. The authors investigated the temperature

the behavior of the electrical conductivity for different specimens differing in lithium content. Law (10) was well obeyed for all specimens over a wide temperature range (from room temperature to \(350^\circ\)C). The more lithium had been introduced, the greater was the electrical conductivity \(\sigma\) of the specimen (at each given temperature) and the smaller the ionization energy \(u\) in formula (10).

On the same specimens the catalytic activity with respect to the reaction of oxidation of carbon monoxide was measured. The greater the initial conductivity of the specimen, the smaller proved to be its

Fig. 13.

activity. Lithium introduced into the crystal acted here as a poison, lowering the catalytic activity of the semiconductor. Figure 14 shows the temperature dependence of the rate constant \(K\), which, as we see, satisfies the Arrhenius law (7). The different straight lines correspond to specimens with different lithium contents. As the lithium content increases, the catalytic activity \(K\) (at a given temperature) falls, while the activation energy \(E\) [in formula (7)] increases.

Thus a distinct correlation is found between the conductivity \(\sigma\) of the specimen and its catalytic activity \(K\). This evidently indicates that the catalytic activity really depends (other conditions being equal) on the concentration of the electron (in the present case—hole) gas in the semiconductor.

Let us now turn to another group of experimental works, in which the connection between catalytic activity and electrical conductivity is understood as the change in electrical conductivity occurring during operation of the catalyst. In investigations of this type, the rate of the catalytic reaction proceeding simultaneously is measured

SEMICONDUCTORS AS CATALYSTS OF CHEMICAL REACTIONS

on the surface of the semiconductor, and the electrical conductivity of the semiconductor, changing in the course of the reaction.

Such a change in electrical conductivity (an increase or a decrease) under the influence of the reaction itself, discovered and investigated by a number

Fig. 14.

of authors for different reactions and different catalysts, may be due to two natural causes.

In the course of the reaction the relative content on the surface of the adsorbed molecules entering into the reaction and of the molecules that are reaction products changes. The coverage of the surface by reactants gradually decreases, while the coverage by reaction products increases. In other words, the nature and concentration of the adsorbate change. This circumstance may cause, as we have seen (§ 4),

change in electrical conductivity. In this case, the change in electrical conductivity that reflects the course of the reaction is the result of the influence of adsorption on electrical conductivity, the mechanism of which we have already considered (see § 4). This effect can be avoided under appropriate experimental conditions. If the reaction products are removed and the pressures of the gases participating in the reaction are kept constant, so that the coverage of the surface by adsorbed molecules (of each given kind) remains unchanged during the reaction, then the changes in electrical conductivity caused by this reason will be reduced to zero. The value of the electrical conductivity established at the beginning of the reaction will remain constant during the reaction.

Another cause that may give rise to a change in electrical conductivity under the influence of a reaction consists in a change in the chemical composition of the catalyst itself, which often occurs during the operation of the catalyst. If in the first case the change in electrical conductivity is caused by a change in the composition of the adsorptive, then in the present case it is caused by a change in the adsorbent itself. Thus, many reactions catalyzed by solid oxides are, as a rule, accompanied by oxidation or, conversely, reduction of the catalyst. In the course of the reaction, the degree (and sometimes also the character) of stoichiometric deviations in the semiconductor gradually changes, which is, of course, reflected in its electrical conductivity. The change in electrical conductivity observed during the reaction may thus be caused by a quite trivial reason. This effect can be eliminated by a proper choice of the system and of the experimental conditions under which the stability of the catalyst during its operation would be ensured (i.e., the invariability of its structure and composition).

Among the works of this group we note the work of G. K. Boreskov and K. I. Matveev^3, which we have already mentioned. The authors studied the reaction of decomposition of methyl alcohol on ZnO:

$$ \mathrm{CH_3OH}\to \mathrm{CO}+2\mathrm{H_2}. $$

The electrical conductivity of the samples increased in the course of the reaction and acquired a metallic character (the dependence of electrical conductivity on temperature disappeared). The increase in conductivity in these experiments is due to the reduction of zinc oxide under the influence of methyl-alcohol vapors. In the course of the reaction, zinc oxide became enriched with superstoichiometric zinc, which led to the appearance of an electron gas (i.e., to metallic electrical conductivity). The increase in conductivity was accompanied by a sharp rise in catalytic activity (for individual samples—by more than 100 times). This indicates, as the authors themselves note, the correlation of changes in catalytic activity and in the concentration of free electrons in zinc oxide. Different samples, prepared in different ways and differing greatly in the magnitude of their conductivity, in the course of carrying out the reaction (i.e., in the process of reduction) po

SEMICONDUCTORS AS CATALYSTS OF CHEMICAL REACTIONS

were gradually compared both with respect to the magnitude of their electrical conductivity and with respect to their catalytic activity. This means that, strictly speaking, the process of preparing the samples could not be considered complete by the moment the reaction began. In the course of the reaction itself there occurred, if one may put it so, an “after-preparation” of the sample.

Let us also note the work of I. A. Myasnikov and S. Ya. Pshezhetskii49, who dealt with the same catalyst (zinc oxide) and with a reaction of the same type (dehydrogenation of isopropyl alcohol):

\[ \mathrm{C_3H_7OH \longrightarrow CH_3COCH_3 + H_2} \]

The authors investigated in parallel the catalytic activity and the electrical conductivity of zinc oxide, changing upon introduction into the reaction mixture of a small amount of oxygen. The introduction of oxygen led to a simultaneous decrease both in catalytic activity (with respect to the dehydrogenation reaction of isopropyl alcohol) and in electrical conductivity. The decrease in electrical conductivity was due in this case to the adsorption of oxygen. Indeed, adsorption of oxygen (which is an acceptor) on zinc oxide (which is an electronic semiconductor) must lead, as we have seen (see § 4), to a decrease in electrical conductivity. Oxygen, adsorbed in one amount or another, served in this case as a factor making it possible to vary the electrical conductivity of the samples. The catalytic activity changed symbatically with the electrical conductivity, which indicated that these two phenomena are probably based on one and the same cause. According to the electronic theory, it consists in a change in the number of free carriers (in this case electrons) in the semiconductor crystal. The work of I. A. Myasnikov and S. Ya. Pshezhetskii to a certain extent belongs both to the second and to the first group of works on the investigation of the connection between activity and electrical conductivity.

Finally, let us note the works of the Polish investigators A. Belyanski, I. Dereń, and G. Haber50, 51. They studied changes in the electrical conductivity of the catalyst during its operation and its connection with activity. The catalysts were crystals of \(\mathrm{MgO \cdot Cr_2O_3}\) of various composition, which are hole semiconductors. The reaction of dehydrogenation of ethyl alcohol was investigated50. In another work the reaction of oxidation of ethyl alcohol was studied on \(\mathrm{ZnO \cdot Fe_2O_3}\) catalysts51, which are electronic semiconductors. The activity of the catalyst was characterized by the yield of the reaction products. Upon introduction of the reacting gases, the electrical conductivity of the catalyst changed sharply, became established at a new level, and thereafter, in the course of the reaction, remained constant. The magnitude of this change depended on the temperature and on the composition of the catalyst. The reaction yield, characterizing the activity of the catalyst, also depended on the temperature and on the composition of the catalyst. In all cases:

strict concordance was observed between changes in activity and changes in electrical conductivity.

This same group of works includes the work of V. I. Lyashenko and I. I. Stepko, the results of which were reported at a conference (see also \(^{14}\)). The authors studied the electrical conductivity of CuO, situated in an atmosphere of the gases CO and \(O_2\), as a function of temperature. The dependence of \(\ln \sigma\) on \(\frac{1}{T}\) was expressed by a straight line. However, this straight line underwent a break, and precisely at the temperature point at which the reaction between CO and \(O_2\) occurred:

\[ 2\mathrm{CO} + O_2 \to 2\mathrm{CO}_2, \]

as was revealed by the appearance of the reaction product \(CO_2\).

At present we already have a whole series of experimental works in which the connection (in one or another understanding of this word) between the electrical conductivity and catalytic activity of semiconductors has been discovered and investigated. All these works have appeared during the last three or four years and, to one degree or another, confirm the correctness of those initial conceptions on which the electronic theory of catalysis is based and to which it leads.

10. CONCLUSION

The ultimate task facing researchers engaged in catalysis is the task of selecting catalysts. What is meant is the preparation of sufficiently active catalysts for particular concrete reactions. The importance of this task will be obvious if one recalls that almost all modern chemical industries are based on the use of catalytic processes. Almost all industrial chemistry is catalytic chemistry.

The task, in the final analysis, consists in learning to control the activity and selectivity of catalysts, i.e., in learning to change them to the required degree and in the required direction. This task cannot be fully solved and cannot be taken beyond the limits of crude empiricism until the mechanism of action of the catalyst is understood. To solve this task it is necessary to reveal the elementary (microscopic) mechanism of the catalytic act.

The facts presented in this article testify sufficiently that the catalytic properties of semiconductors are most closely connected with the electronic processes taking place inside and on the surface of the semiconductor and, ultimately, are determined by them. Therefore the problem of catalysis, being a chemical problem, may at the same time be regarded as one of the problems of the physics of semiconductors.

The catalytic process, in the final analysis, has an electronic mechanism. In the enormous chemical literature devoted to the ques—

of catalysis itself; this circumstance, however, until very recently was almost not reflected at all. Some interest in the question of the connection between catalytic properties and the electronic properties of semiconductors has appeared among chemists only in recent years, apparently in connection with the emergence and development of the electronic theory of catalysis.

The electronic theory of catalysis on semiconductors, whose aim is to reveal the elementary mechanism of the catalytic act and which is based, on the one hand, on the theory of semiconductors and, on the other hand, on the theory of chemical bonds, is at present only just coming into being. When we speak of the electronic theory of catalysis, we are not speaking of some completed theory (such a theory does not yet exist), but only of a definite direction of theoretical and experimental work in the field of catalysis.

This new line of work arose about ten years ago in the catalysis laboratory of the Institute of Physical Chemistry of the Academy of Sciences of the USSR on the initiative of S. Z. Roginskii. We do not count here the pioneering works in this direction, belonging to L. V. Pisarzhevskii and his students, carried out in the twenties of our century. These works were based on Bohr’s theory and, naturally, did not go beyond the bounds of that theory. They belong to the period when quantum mechanics and the modern theory of semiconductors did not yet exist, and at the present time they are of only historical interest to us. Several years later the electronic direction found a response abroad, and at the present time a number of foreign laboratories and individual investigators (physicists and physical chemists) are working in this direction.

For the present time there is characteristic (this is especially characteristic of Soviet work) a certain lag of experiment behind theory. A number of theoretical predictions still remain experimentally unverified. At the same time, the actual experimental material from which a theory could proceed and on which it could be based is still insufficient. An expansion of experimental work in this direction is urgently necessary. We mean experimental work aimed at investigating the connections between the electronic and catalytic properties of semiconductors. Connections of this kind are at present established, but so far they have not yet been sufficiently investigated.

The theories of catalysis that have circulated among chemists up to the present time have been, for the most part, phenomenological in character. This, however, in no way diminishes their significance or the role that they played at the corresponding stages in the development of the doctrine of catalysis. A genuine physical theory of heterogeneous catalysis, i.e., a theory that would reveal the physical mechanism of catalytic processes, still does not exist.

The so-called electronic theory of catalysis is taking its first steps in this direction. The emergence of the electronic theory of catalysis

marks the entry of modern physics into the problem of catalysis. Entering this territory, which until now belonged to physical chemistry, modern physics naturally brings with it its own apparatus and its own instruments. The electronic theory of catalysis, dealing with a physicochemical problem, nevertheless considers this problem as a physical task, approaching it from the standpoint of the modern theory of semiconductors.

The existing theories of heterogeneous catalysis and the future physical theory of catalysis, not yet fully constructed, stand in approximately the same relation to one another as the theory of the chemical bond of the past century, which operated with valence strokes (and had nothing in its hands except these strokes), and the modern quantum-mechanical theory of the chemical bond, which has filled the valence strokes of old chemistry with physical content and thereby revealed the physical nature of chemical forces.

CITED LITERATURE

1. O. V. Krylov, Collection “Heterogeneous Catalysis in the Chemical Industry,” p. 437, Goskhimizdat, 1955.
2. A. B. Shekhter and Yu. Sh. Moshkovskii, DAN 83, No. 6, 1075 (1953).
3. K. I. Matveev and G. K. Boreskov, Collection “Problems of Kinetics and Catalysis” 8, 165 (1955).
4. F. F. Vol’kenshtein, ZhFKh 27, 159, 167 (1953); UFN 50, 253 (1953).
5. F. F. Vol’kenshtein, ZhFKh 23, 917 (1949); Collection “Problems of Kinetics and Catalysis” 7, 360 (1949).
6. S. Z. Roginskii, Theory of Adsorption on Nonuniform Surfaces, Publishing House of the Academy of Sciences of the USSR, 1948.
7. F. F. Vol’kenshtein, ZhFKh 28, 422 (1954).
8. V. L. Bonch-Bruevich and F. F. Vol’kenshtein, ZhFKh 28, 1219 (1954); Collection “Problems of Kinetics and Catalysis” 8, 218 (1955).
9. Lennard-Jones, Trans. Farad. Soc. 88, 333 (1932).
10. F. F. Vol’kenshtein, ZhFKh 22, 311 (1948).
11. F. F. Vol’kenshtein, ZhFKh 23, 1462 (1952).
12. F. F. Vol’kenshtein, ZhFKh 24, 1068 (1950).
13. F. F. Vol’kenshtein and V. B. Sandomirskii, Collection “Problems of Kinetics and Catalysis” 8, 189 (1955).
14. V. I. Lyashenko and I. N. Stepko, Collection “Problems of Kinetics and Catalysis” 8, 180 (1955).
15. T. Y. Gray, Disc. Farad. Soc., No. 8, 331 (1950); Collection “Semiconductor Materials,” p. 238, IL, 1954.
16. G. Heiland, Zeits. f. Physik 133, 459 (1954).
17. V. I. Lyashenko and I. N. Stepko, Izv. AN SSSR, ser. fiz., 211 (1952); V. I. Lyashenko, Trudy IFAN USSR, No. 4, 33 (1953).
18. S. Yu. Elovich and L. Ya. Margolis, Report at the Conference on Semiconductors, Leningrad, November, 1955.
19. S. Z. Roginskii, Report at the Conference on Semiconductors, Leningrad, November, 1955.
20. P. Aigrain und C. Dugas, Zeits. f. Elektrochem. 56, 363 (1952).
21. P. B. Weisz, J. Chem. Phys. 21, 1531 (1953).
22. J. E. Germain, C. R. 238, 236, 345 (1954); J. Chimie phys. 51, 263 (1954).

1. H. I. Engel und K. Hauffe, Zeits. f. Elektrochem. 57, 762 (1953); H. I. Engel, Halbleiterprobleme, No. 1, 249 (1954); K. Hauffe, Angew. Chem. 67, 189 (1955).

2. F. F. Vol’kenshtein, ZhFKh 21, 1317 (1947).

3. V. L. Bonch-Bruevich, ZhFKh 25, 1033 (1951).

4. V. B. Sandomirskii, Candidate dissertation, Institute of Physical Chemistry, Academy of Sciences of the USSR, 1955.

5. F. F. Vol’kenshtein and S. Z. Roginskii, ZhFKh 29, 485 (1955).

6. F. F. Vol’kenshtein, collection Problems of Kinetics and Catalysis 8, 79 (1955).

7. V. V. Voevodskii, F. F. Vol’kenshtein, N. N. Semenov, collection Questions of Chemical Kinetics, Catalysis, and Reactivity, p. 423, Publishing House of the Academy of Sciences of the USSR, 1955.

8. J. A. Hedwell u. S. Nord, Zeits. f. Elektrochem. 49, 467 (1943).

9. A. Luyskx, J. Boodart, G. Rens, J. Chim. phys. 39, 139 (1942).

10. F. F. Vol’kenshtein, collection Problems of Kinetics and Catalysis 8, 68 (1955).

11. A. N. Terenin, ZhFKh 6, 189 (1935).

12. L. N. Kurbatov, ZhFKh 14, 1049 (1940).

13. A. K. Vyshnevskii, Candidate dissertation, State Optical Institute, 1943.

14. A. Kobayashi and S. Kawaji, J. Phys. Soc. Japan 10, 270 (1955).

15. I. A. Myasnikov and S. Ya. Pshezhetskii, collection Problems of Kinetics and Catalysis 8, 34 (1955).

16. V. E. Lashkarev, memorial collection for S. I. Vavilov, p. 324, Publishing House of the Academy of Sciences of the USSR, 1952.

17. V. P. Zhuze and S. M. Ryvkin, DAN 77, 241 (1951).

18. L. Ya. Margolis and O. M. Todes, ZhOKh 18, 1043 (1948).

19. O. V. Krylov and L. Ya. Margolis, ZhOKh 20, 1991 (1950).

20. G. M. Zhabrova and E. A. Fokina, Izv. AN SSSR, ser. khim., No. 6, 963 (1955).

21. G. M. Zhabrova, UKh 20, 450 (1951).

22. L. Ya. Margolis and O. M. Todes, DAN 58, 421 (1947).

23. W. Meyer und Neldel, Phys. Zeits. 38, 1014 (1937).

24. F. F. Vol’kenshtein, ZhFKh 25, 1244 (1951).

25. N. P. Keier, S. Z. Roginskii, and I. S. Sazonova, report at the Conference on Semiconductors, Leningrad, November 1955.

26. J. H. de Boer, E. J. W. Verwey, Proc. Roy. Soc. (L) 49 (extra part) (1937); J. W. Verwey, P. W. Haamyman, F. C. Rornein, Chem. Weekblad 44, 705 (1955).

27. I. A. Myasnikov and S. Ya. Pshezhetskii, collection Problems of Kinetics and Catalysis 8, 175 (1955).

28. A. Belyanskii, I. Deren’, G. Taber, Bull. Polish Acad. Sci., No. 3, 491 (1955).

29. A. Belyanskii, I. Deren’, G. Taber, Bull. Polish Acad. Sci., No. 4, 221 (1955).