The Influence of Adsorption on Electrical and Magnetic Properties of Thin Metal Films

Chapter 5

The Influence of Adsorption on Electrical and Magnetic Properties of Thin Metal Films J . W. GEUS Central Laboratory, StaatsmijnenjDSM, Geleen, The Netherlands I. INTRODUCTION I I . THEORETICAL

III.

327 328

A. ELECTRICAL CONDUCTIVITY OF METALS

329

B. FOREIGN ATOMS IN METALS C. EXPERIMENTAL EVIDENCE FOR THE EFFECTS OF FOREIGN ATOMS ON THE ELECTRONIC PROPERTIES OF METALS . .

343 354

D. INFLUENCE OF COLLISIONS WITH THE METAL-VACUUM INTERFACE ON THE MOTION OF CONDUCTION ELECTRONS .

363

E. THEORETICAL ASPECTS OF THE EFFECTS OF ADSORPTION ON THE ELECTRICAL CONDUCTANCE OF METALS . . .

372

E F F E C T S OF ADSORPTION ON ELECTRICAL AND MAGNETIC PROPERTIES OF VAPOUR DEPOSITED METAL F I L M S . . .

398

A. STRUCTURE AND ELECTRICAL PROPERTIES B . EFFECT OF ADSORPTION ON ELECTRICAL RESISTANCE . C. EFFECT OF ADSORPTION ON FERROMAGNETIC PROPERTIES . D. EFFECT OF ADSORPTION ON THE HALL COEFFICIENT . . REFERENCES

398 415 472 479 481

I.

INTRODUCTION

Although thin metal films were studied in the 19th century byFaraday and Drude (Mayer, 1955), the profound effect of the interaction of the film surface with gas molecules on the physical properties was clearly recognized only much later. Since the presence of residual gas molecules t h a t react rapidly with surfaces of many metals could not be avoided by early workers, their results on thin metal films are unreliable for many purposes. I n the thirties, the first studies of gas adsorption on metal films were published by de Boer and Kraak (1937), 327

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J. W. GEUS

shortly followed by the start of the extensive work at the Shell Laboratory at Emeryville by Beeck and co-workers (Beeck, Smith and Wheeler, 1940, Beeck, 1950). The study of the modification of physical properties by chemical surface interaction is important in two respects: on the one side, knowledge of this is a prerequisite for a proper interpretation of important physical phenomena such as the anomalous skin effect. On the other hand, data obtained by studying adsorption on clean film surfaces considerably add to the understanding of the chemisorptive bond, especially as to the effect of adsorption on the structure of the metal surface (for instance, on the bond between surface and subsurface layers). Nowadays, many subtle techniques are available t h a t enable a detailed study of surface phenomena (flash desorption, field-electron and field-ion emission, low-energy electron diffraction, and electron probe surface mass spectrometry). However, we hope to demonstrate in the following t h a t a study of the effect of adsorption on electrical and magnetic properties of thin metal films gives information which cannot be obtained in other ways. This review can be divided in two parts. I n section I I the electronic properties of bulk metals are discussed together with the electronic configuration around impurity atoms. Then, the special phenomena occurring at the metal-vacuum or metal-gas interface will be dealt with. I n section I I I the effects of adsorption on the electrical conductance of island-like and coherent films are surveyed, and the effect of adsorption on ferromagnetic properties of films will be briefly examined.

II.

THEORETICAL

To account for the effects of adsorption on the electrical and magnetic properties of metals, many authors use a simple version of the rigid band model. This model in which electrons are simply added to or removed from an invariable continuous set of energy levels was very attractive in view of the extremely complicated phenomena with which the workers in this field were faced. First a description of the electronic structure of ideal metal and alloy crystals is complicated and up till now a controversial subject of solid state quantum mechanics. Secondly, due to the relatively large density of lattice defects present in evaporated films and the large surface-to-volume ratio, the physical problem is rendered even more intricate; this is the more so since a variety of crystallographic planes can be present in the surface, each of which might give rise to another effect on the electrical conductivity. If, finally, we are engaged with the problem of chemisorption on this complicated system,

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all difficulties connected with the description of chemical bonding in two-dimensional structures are added. All labour arising from the above factors can be saved, if the rigid band model would be applicable. As will be demonstrated in this section this model is, however, not adequate to describe the influence of adsorption on surfaces. To arrive at a description as well founded as possible, we start with a discussion of the electronic structure of pure metals. This is followed by a consideration of the motion and scattering of conduction electrons in metals. There is a considerable body of theoretical and experimental work on the distribution around foreign atoms inside metals. These data can be used very well to guide the interpretation of the phenomena induced by putting foreign atoms on to the metal surface, which is done in adsorption experiments. Therefore, a review of the results obtained for foreign atoms inside metals is presented. Next the nature of collisions of conduction electrons with metal surfaces is investigated; before the results obtained can be used for the explanation of the effects of adsorption on the conductance of metals, the structure of real metal surfaces must be considered. This section is concluded by a survey of the effects of adsorption on the electrical conductance of metals t h a t can be expected on the basis of the data discussed earlier. To simplify the argument the admittedly complicated structure of evaporated metal films is ignored here; it is assumed t h a t the films are thin sheets of metals bounded by parallel flat planes. Before the mechanisms by which adsorption can affect the conductance are reviewed, some characteristics of adsorption on metals have to be dealt with. Finally the two mechanisms by which the conductance of the hypothetical film can be affected, viz. changes in the reflection of the conduction electrons against the metal surface and in the conductivity of the surface layer will be discussed. A . ELECTRICAL CONDUCTIVITY OF METALS

1. Motion of Electrons in Periodic Structures To discuss the influence of adsorption on the structure and physical properties of metals, both the dynamics of electrons in metals and the cohesive energy of metals has to be considered. For a first introduction into the physics of metals and metal bonding, we refer to the well-known treatises by Kittel (1967), and by Mott and Jones (1939), while a deeper understanding of the cohesive energy of metals can be gained from Ramies' monograph (1962). Here we restrict ourselves to a summary of the most essential points t h a t are needed to follow our discussion. The motion of conduction electrons through metallic lattices can be

330

J . W. GEUS CD

4

c

c

o O-

|«

position in metal-

F I G . 1. Metal idealized as a potential box with flat bottom and infinitely high walls.

explained very well if the metal is idealised as a potential box with a flat bottom (Figure 1). In this free electron model, the Schrödinger wave equation is, [ - | ^ V ^ + V(r)]iA = EiA

(II)-(l)

where h = h/27r, m is the electronic mass, ψ is the wave function, E the energy, r indicates the position in the metal, and V(r) the potential energy. This model assumes V(r) to be zero inside and infinite outside the metal. After introduction of cyclic or periodic boundary conditions to avoid a consideration of the scattering of the electrons against the infinite potential wall, equation (II)-(l) can be easily solved to \

φ(τ)

e

ik.r

- ( * ) 3 where L is the volume of the metal, and k is the wave vector.

(Π)-(2)

F I G . 2. Energy as a function of wave vector according to the free electron model.

The energies corresponding to this solution are given by Ek =

h2k2 2m

(Π)-(3)

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331

and the allowed values for the magnitude of the wave vector are

k = 2π£

(Π)-(4)

n being a positive or negative integer (Figure 2). In view of the macroscopic dimensions of the metal, the energy levels given in equation ( I I ) (3) are quasi-continuous. The approximations inherent to the free electron model are: smearing out of the periodic potential due to the ion cores to a continuous flat potential t h a t is taken to be zero, and we neglect the electrostatic interaction between the electrons. Hence, the only energy term involved is the kinetic energy of the electrons. The band theory of solids improves the foregoing assumption of a constant potential inside the metal by introduction of potential minima at sites where the ion cores are located in the metal. These potential minima now scatter the plane waves associated with the motion of the electrons through the metal. With arbitrary values of the wave vector, k, the scattered waves have no mutual phase relationship, which causes them to have a negligible intensity. If, however, the Bragg reflection condition is fulfilled k = ^ (II)-(5) a where n is an integer and a is the distance between neighbouring lattice points, the scattered waves are in phase. Now the intensity of the totally scattered wave e" i k r is equal to that of the forward wave e i k r , which leads to wave functions and

φ ~ e i k r + e- ik - r = cos k.r φ ^ eik.r _ e -ik.r

=

gJn

fc r

(H)-(6)

The resulting waves, equations (II)-(6), are standing waves, which implies t h a t the kinetic energies of electrons the motion of which is given by the values of k corresponding to equation (II)-(5) are forbidden. Stated more formally, the degeneracy of an energy value which corresponds to + k and — k is lifted for those k-values for which equation (II)-(5) is valid, and the energy is split up into two separate levels (Figure 3). The fact t h a t energy ranges are obtained t h a t cannot be realized for the kinetic energy of the electrons, easily explains t h a t some wellordered solids (e.g. diamond) are non-conductors. I n these solids the energy levels are filled up to the forbidden energy range without any

332

J. W. GEUS

overlap in different directions. Therefore, the energy of the conduction electrons cannot be increased by arbitrary amounts by an external electrical field.

♦E,

forbidden energies

FIG. 3. Energy as a function of wave vector, k, according to band theory. Owing to the interaction with the lattice, the degeneracy at ± k i and ±1$:2 is lifted, which leads to two forbidden energy ranges.

The free electron and the more refined band theory poorly account for the electrostatic interactions between ion cores and electrons; V(r) in equation (II)-(l) is set equal to zero. Consequently, it is not possible to arrive at a cohesive energy by these theories; the only energy considered is the kinetic energy of the electrons. Inasmuch as the mean value of the kinetic energy is proportional to the number of conduction electrons per unit volume, condensation of metals from their gaseous to their solid state (large atomic distances become small ones) increases the energy of the system according to these theories. However, the problems we are faced with in a consideration of interactions of gas molecules with metal surface atoms can only be solved by using as a framework of thinking a theory in which the cohesive energy is included. If a chemical bond between one or more surface metal atoms and a gas molecule is established, it is indispensable to take into account also possible modifications in the bonds between the chemisorbing metal atoms and their neighbours. Interaction of the valence electrons with the ion cores can be included by starting from a wave function (Bloch function), ψ{τ) = u k ( r ) e i k - r

(Π)-(7)

were Uk (r) accounts for the interaction with the ion cores. I n view of the symmetry of metal lattices, it can be shown quite generally that any

THE INFLUENCE OF ADSORPTION ON METAL FILMS

333

wave function describing the behaviour of electrons inside metal lattices should be of the form as given in equation (II)-(7). The tight-binding theory takes for Uk(r) the wave functions corresponding to the free atoms. This approximation is reasonable only if the potential energy in regions in the metal, where the wave function has appreciable values, does not differ much from the potential energy in the free atom (Figure 4). This asks for a relatively small overlap of the wave functions on neighbouring metal atoms; consequently, the tightbinding method only gives reliable results for wave functions extending over relatively small distances from the ion cores, as for instance the atomic eZ-wave functions. wave function

-difference Δ potential energy

isolated atom

metal

\potentiaI energy in metal

FIG. 4. Potential energy and wave function in an isolated atom and in a metal. The tightbinding approximation is realistic only if the indicated difference in potential energy for the metal and the isolated atom, Δ, is small.

I n the tight-binding method, two other energy terms arise besides the ionization energy of the free atoms. The first is derived from the fact t h a t the potential energy in the metal is lower than t h a t in the free atom, due to the presence of neighbouring metal atoms. This difference, which has to be small to allow application of this theory, leads to a decrease in energy below that of the ionization energy of the free metal atom. The second term is due to the overlap of wave functions on neighbouring metal atoms, which is assumed to be small too. The latter term depends on the wave vector k and, hence, on the kinetic energy of the electrons. As appears from the assumptions underlying the tight-binding theory, it can be applied with small interaction energies only. Therefore, it cannot be used to obtain more than a qualitative notion of the appreciable cohesive energy of metals. As will be shown later on, it is however very apt for describing the electrical conductance and magnetic properties of electrons present in wave functions situated relatively close to the ion cores. o*

334

J . W. GEUS

In the Wigner-Seitz cellular theory (Seitz, 1940), the function Uk(r) in equation (II)-(7) is obtained in a much more realistic way. Therefore this theory leads, after suitable corrections, to a cohesive energy well in accordance with the experimental data for simple metals, besides accounting for the motion of the conduction electrons. (The cohesive energy is the difference in energy between a state with the metal atoms infinitely separated and the metallic state with the metal atoms occupying their equilibrium lattice positions.) In view of the symmetry


dh-

■-6

F I G . 5. Wigner-Seitz cells for a simple cubic lattice. r b is a vector from the mid-point of a cell ending on a boundary.

present in a plane which perpendicularly bisects the lines connecting nearest neighbours in the metal, the factor ut(r) associated with a value k = 0, u0(r) has to fulfil the condition

FPL-

(II)-(8)

where r = r^ indicates a position on the above bisecting planes (Figure 5). Since f.c.c. and b.c.c. metal lattices have a high symmetry, the polyhedra formed by the bisecting planes can be approximated by a sphere with volume equal to the atomic volume. The wave equation now becomes

[ - s s (r2 έ) + V(r)]Uo(r)=Euo(r)

(IIH9)

THE INFLUENCE OF ADSORPTION ON METAL FILMS

335

where u0(r) has to fulfil equation (II)-(8) at r = rs. In equation (II)-(9), r is the distance from the centre of the sphere and rs is the radius of the sphere. V(r), the potential in the sphere can be taken from self-consistent field calculations or from the experimental energy levels of the atom, for instance by the quantum defect method (Raimes, 1962). The approximation of the polyhedra by a sphere has a very small effect on the potential and kinetic energy of the electron in the sphere (Mott and Jones, 1939). It implies, however, that no directed bonds are included in the theory. Therefore, the theory cannot account for the lattice structure of the metals. The reliability of the approximation for different f.c.c. metals can be judged from the stacking fault energy, which is generally small compared with the cohesive energy (Dillamore andSmalman, 1965).

free sodium atom

wave A function metallic sodium <^

> Γ

FIG. 6. Wave function for an isolated sodium atom (top), and for metallic sodium as calculated according to the Wigner-Seitz Theory (bottom).

The wave function resulting from equation (II)-(9) is represented in Figure 6 together with that of the free atom for sodium. It turns out that for this metal the wave function is practically constant over about 90% of the atomic volume. Hence, the free electron model is a very good approximation to describe the motion of valence electrons inside metallic sodium. Although especially for transition metals, the flat part of the wave function is appreciably smaller, the character of the wave functions obtained by the Wigner and Seitz method nevertheless rationalizes the success of the free electron theory in the description of the motion of the conduction electrons. The wave function, u0(r), obtained as indicated above, corresponds to a wave vector k = 0. As this wave function extends through the

336

J . W. GEUS

complete lattice and the Pauli principle interdicts association of more than two electrons with the same wave function, the valence electrons in the metal have to be endowed with kinetic energy connected with motions through the lattice. This requires the value of k in equation (II)-(7) to be different from zero; in t h a t case, the wave function is no longer flat between the ion cores but displays a relatively slight curvature (Slater, 1965). If the dependence of Uk(r) on k is neglected, i.e. if ut(r) is replaced by u 0 (r) for all values of k, the kinetic energy associated with the motion of the electrons through the lattice is fi2k2 Ek = - ^

(H)-(IO)

If the assumption is made t h a t only one electron is present per sphere for monovalent metals, which causes the mutual electrostatic interaction between the ion cores and t h a t between the valence electrons to be small, the cohesive energy, E c , can be approximated by E

C

= E + av-I

(Π)-(Π)

Here E is the energy given by equation (II)-(9), which comprises the kinetic and potential energy of the valence electron in the sphere; av is the mean kinetic energy of the electrons associated with motion through the lattice. The above mentioned definition of the cohesive energy requires the subtraction of I, the ionization energy. I n Figure 7 the terms of equation (II)—(11) are represented as a function of the interatomic distance in the metal, r a . The potential

1

«

■

■

■

'

2 A, 6 8 IO ^ ra^Bohrunit=0-53A/; F I G . 7. Behaviour of E and av of Equation ( I I ) - ( l l ) as a function of the interatomic distance, r a , for sodium. D, the difference between E —I and av is the cohesive energy.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

337

energy of the valence electrons in the cell is decreased on decreasing the interatomic distance, since the electrons can approach the nuclei more closely. The kinetic energy of the valence electrons in the cell is increased, as the cell volume is decreased. Eventually the increase in kinetic energy dominates, which leads to a minimum for E as a function of r a . The kinetic energy connected with motion through the lattice increases only on decreasing the interatomic distance. The energy E + av traverses a minimum at a distance slightly larger than the distance corresponding to the minimum for E. Equation (II)—(11) yields values for the cohesive energy and equilibrium distance of the alkali metals that are in very good agreement with the observed values, provided the relative mass m* is substituted for the electron mass, a quantity t h a t will be explained below. Since the approximations about the interactions between valence electrons and ion cores in different cells are rather crude, this seems to be accidental. Indeed, an elaborate treatment of exchange (between electrons with like spins) and correlation (between electrons with unlike spins) interaction of the valence electrons shows t h a t the omitted terms in the cohesive energy approximately cancel (Nozieres and Pines, 1958). The above discussion demonstrates that it is possible to account quite well for both the cohesive energy of metals and the motion of conduction electrons in metals, although the Wigner-Seitz theory is much more difficult to apply quantitatively with metal atoms that have valence electrons in orbitale with symmetries other than s-symmetry. I n cases where the calculations are difficult to carry out accurately, the motion of the conduction electrons can be rationalized by the concept of the effective mass (Kittel, 1967). As said above, the interaction with the lattice is accounted for by the factor Uk(r) in the Bloch function Uk(r)eik,r. The energy values resulting from this Bloch function can be obtained by applying the Hamiltonian -|-V*

+

V(r)

to Uk(r)elk,r. I t can be verified t h a t Uk(r) must satisfy

[ - K - = k * + H U k ( r ) - (El - S:> ( r ) I t turns out (see Bardeen, 1938), t h a t to a good approximation E

fi2k2 * = 2 ^

<ΠΗ13)

is valid, where m* is a quantity with dimension mass, which is defined as

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J . W. GEUS

the effective mass of the conduction electrons in the lattice. The resulting expression for the kinetic energy has the same character as in the free electron theory. Experimentally, the effective mass m* can be determined by, for instance, cyclotron resonance experiments. 2. Scattering of Conduction Electrons The above discussion shows t h a t the motion of valence electrons in a strictly periodic structure t h a t is described by wave functions of the Bloch form, Uk(r)eik-r, is not accompanied by a transfer of energy from the electrons to the lattice. This is also true when the interaction of the electrons with the ion cores extends over larger distances, which causes the deviation from free electron behaviour to be large. Then the electrons are still moving in conservative fields, where no energy is dissipated into the lattice. An ideally ordered metal therefore does not exhibit electrical resistivity. The electrons are accelerated by an external field till their wave vector reaches the value corresponding to the forbidden ranges of kinetic energy t h a t arise in the band theory. Then the electrons are reflected to the opposite k-value and start again to be accelerated, since the energies imparted by an external electrical field are too small to enable the electrons to traverse a forbidden energy range (Figure 8).

electric field E

D

|^T

F I G . 8. Two-dimensional Brillouin zone. An electron with its wave vector at P is accelerated b y the indicated electric field, E, till it collides with the zone boundary at A, where it is reflected to B , etc.

Real metals however do not have a strictly periodic structure but contain deviations from periodicity both permanently and momentarily. The latter deviations originate from the thermal vibrations carried out

THE INFLUENCE OF ADSORPTION ON METAL FILMS

339

by the ion cores around their equilibrium positions. The permanent deviations are caused by the presence of lattice defects and impurities. The non-periodicity brings about a transfer of kinetic energy from the conduction electrons to the lattice, which leads to an increase in temperature of the metal and a constant mean velocity of the electrons in an external electrical field. The correlation between scattering of conduction electrons in a metal and its conductivity is made most simply by introduction of a relaxation time, T, which accounts for thermal and structural imperfections in the lattice. I n a stationary state, the drift velocity of the conduction electrons, vD, is constant, which leads via

m and

( ^ + v ) = -eE

(IIH14)

dv„ _ dt

to VD

=

eEr ^ "

(II)-(15)

where m is the electron mass and eE is the force exerted by the field E on an electron. The drift velocity, equation (II)-( 15), corresponds to a conductivity, σ, σ =

ne-r m

ne-1 mv

=

n is the number of conduction electrons per unit volume, 1 is the mean free path of the conduction electrons, and v is the velocity of the electrons at the Fermi level. If the interaction with the potentials of the ion cores cannot be neglected, m in equation (II)-(16) has to be replaced by m*, the effective mass. I n Table 1 values for the mean free path in some metals at 273 °K are collected. TABLE 1

Mean Free Path of Conduction Electrons at 273 °K Metal

Na Cu Ag Ni Fe Pt

Mean Free Path, 1 (Ä)

350 420 570 133 220 110

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J. W. GETJS

The data of Table 1 show t h a t at 273 °K conduction electrons can pass along many ion cores before being scattered. The connection between the relaxation time, r, and the effective cross section for scattering of conduction electrons, Qd, is made by means of the relation known from gas kinetics T = (NvQd)- 1 (Π)-(17) where N is the number of ions per unit volume, and v is the velocity of electrons with the Fermi energy (Weisskopf, 1943). The scattering cross section is assumed to be uniform in equation (II)-(17). The scattering cross section is governed by the local deviation of the potential energy, U(r), from the potential energy, V 0 (r), in the unperturbed lattice U(r) = V(r) - V,(r)

(II)-(18)

where V(r) is the actual potential. The deviation, equation (II)-(18), can be either structural or thermal. Structural deviations are caused by lattice defects and impurities. Impurity atoms also lead to a locally different potential energy if substitutionally present at regular lattice positions. This effect, which is particularly important in studies of adsorption on metallic surfaces (introduction of foreign atoms into the surface layer), will be dealt with separately. I n lattice defects, metal atoms are permanently displaced from their equilibrium lattice positions. The contribution of lattice defects to the electrical resistivity is difficult to estimate accurately. The calculation of the potential energy around displaced atoms in metal lattices is complicated; if the displaced atoms are forming dislocations, interference between waves scattered from neighbouring atoms has to be included. To indicate the physically important characteristics, we give a simplified treatment, in which it is assumed t h a t the electronic structure of the displaced ion is equal to that of the corresponding gaseous ion. Then, the effective cross section Qd of a metal atom displaced over a distance d from its equilibrium position for scattering of conduction electrons from a state with wave vector k into a state with k', is given by Qd = [(k - k').d] 2 Q s

(Π)-(19)

where Q s is the scattering cross section of the gaseous metal ion. Since, generally, a range of displacements d is present, Qd in equation (II)-(19) has to be averaged before insertion in equation (II)-(17). The thermal motions of the ions in the metal lattice cause them to deviate momentarily from their equilibrium positions. This gives rise to a contribution to the electrical resistivity t h a t depends on the temperature, in contrast to that due to lattice defects and impurities. To arrive

THE INFLUENCE OF ADSORPTION ON METAL FILMS

341

at an approximation for the temperature dependent resistivity, we proceed from equation (II)-(19) too. If the mean square deviation from the equilibrium position is d2, equations (II)-(16), (17), and (19) lead to a temperature dependent conductivity, στ,

(IIH2

- "(1) (iSjfe)

°»

where k p is the wave vector at the Fermi level, and one conduction electron per metal ion is assumed. At temperatures high compared with the Debye temperature ΘΌ of the metal, the mean square deviation is onPK2

< π >-< 21 )

^-TS-*

where M is the mass of the metal ions, and kB is Boltzmann's constant. Insertion of equation (II)-(21) into equation (II)-(20) leads to p 2 Mk 0 2

1

<πΗ22)

*-«ϊ£·ΐ

Hence, this very simple theory predicts a resistivity increasing proportionally with the absolute temperature. In real metals, both lattice defects and impurities, and thermal motions are present. Although not completely exact, the probabilities for scattering by structural and thermal defects, l/r R and 1/ττ, respectively, can be added. This gives rise to a probability for scattering of conduction electrons

i-i + i and to a resistivity P - ft, +

ft

(ΠΗ23)

Equation (II)-(23) is known as Matthiessen's rule; it demonstrates t h a t the temperature dependence of the resistivity, d/o/dT, does not vary with the defect and impurity concentration in metals. Matthiessen's rule, which will be used for the explanation of the effects of adsorption on the electrical conductance of metals, is obeyed very well experimentally (Donovan, 1967). I t can be seen from equation (II)-(16) t h a t the electrical conductance is proportional to both the concentration of charge carriers, n, and their mobility, which is given by βτ/m. The sign and the concentration of the charge carriers can be obtained from a measurement of the Hall effect

342

j . w. GEUS

(Purcell, 1965). This effect originates from the transverse force exerted on moving charges by a magnetic field, H, oriented perpendicularly to the electrical current density, J, as indicated in Figure 9.

F I G . 9. Determination of the sign and mobility of charge carriers by means of the Hall effect. J, current density; H, magnetic field; δν drift velocity of electrons.

For an electron with drift velocity, δν, and charge — (e/c) emu, this force, K, is K

(II)-(24)

-δν χ Η c

If no permanent current can flow in the direction of the force, K, an electrical field, E H , is established, given by (II)-(25)

EH = - - δ ν x H

The direction of δν and, hence, the orientation of E H depends on the sign of the charge carriers. The drift velocity, δν, is connected with the current density, J, which can be determined experimentally. For electrons, the relationship is (II)-(26)

J = — ηβδν

The Hall constant, R H , defined by the equation EH

=

RHH

(Π)-(27)

x J -1

is, therefore, for free electrons equal to —(nee) . This value is experimentally rather well confirmed for alkali metals and liquid metals; most other metals however show values for the Hall constant t h a t have to be rationalized by more involved arguments (Kittel, 1966).

THE INFLUENCE OF ADSOBPTION ON METAL FILMS

343

B . FOREIGN ATOMS IN METALS

1. Distribution of Electrons around Foreign Atoms One of the main objectives of this review is to elucidate the mechanisms by which chemisorption can affect the electrical conductance of metal films. Chemisorption onto a metal surface can be considered as formation of a two-dimensional adsorbate-metal compound. Hence, much insight can be gained from a consideration of the effect of foreign atoms, interstitially or substitutionally present, on the electrical condictivity of metals. The conductivity of bulk metals and alloys as well as its temperature dependence can be accurately measured, while it is possible to ascertain the structure of the specimens by standard X-ray techniques. Consequently, theoretical explanation of the effects of small amounts of foreign atoms present at known crystallographic positions asks for much less conjecture than that of the way in which a generally badly defined surface compound influences the conductance of a metal film with an involved structure. A crucial point in the discussion will be the question if the electronic properties of a metal can be modified homogeneously by chemical interaction of only the surface. It is well established that chemisorption on metals does not change the structure of the metal except possibly the region within two or three atomic diameters from the surface. To answer the above question, therefore, we shall consider the electrical conductivity of metals in which foreign atoms are dissolved without bringing about a deviation from the structure of the pure metal. To accomplish this, the atoms of the solvent and the solute have to fulfil some requirements most clearly expressed by Hume-Rothery (1963). For atoms substitutionally dissolved, the diameter must differ by not more than 15% from that of the solvent atoms, whilst for atoms present interstitially, the diameter has to be smaller than about 0.6 of that of the solvent. The electronegativity of solvent and solute atoms cannot diverge too much to avoid formation of ordered compounds with an ionic character and a completely different structure, as e.g. Mg3Sb2. Finally, the overall concentration of the valence electrons of the resulting alloy has to meet some requirements, which at present are not completely understood. The above arguments imply that we should consider dilute alloys to solve the above question. For a large number of metals and solute atoms, it is ascertained that the insertion of a small number of foreign atoms into metals without changing their structure leads to an increase solely of the temperature independent part of the resistivity. Addition of foreign atoms causes an increase of the resistivity due to structural defects, pR, as given in equation (II)-(23), without affecting markedly

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J. W. GEUS

the thermal resistivity, pT. This implies t h a t (i) the effective number of conduction electrons and (ii) the thermal vibrations of the metal atoms are hardly changed by the addition of a small number of foreign atoms. To account for the effects of foreign atoms on the conductivity, Mott set up a theoretical treatment which was later on substantially extended and improved by Friedel (1952, 1954). Finally, Blatt (1957) and Mott (1962) introduced some important refinements, whilst Daniel (1962) dealt with transition metal solutes. Inasmuch as these theoretical results are of paramount importance for the interpretation of the effects of adsorption on the electrical conductance of metal films, we shall give here a short survey of this work. Insertion of a foreign atom into a metal has three effects: (i) an ion core with a valence different from t h a t of the matrix is introduced; the extra charge has to be screened by a locally modified electron density; (ii) the unit cell into which the foreign atom is inserted changes its size; (hi) the change in size leads to a local average ionic charge density different from t h a t in the matrix, which brings about a redistribution of the electrons too. If a foreign atom with the same valence as the host metal is introduced, the effects (ii) and (iii) only are present. As will be argued later on, the effects (i) and (iii) leading to a different charge distribution are the most important in regard to scattering of conduction electrons. I n view of the spherical symmetry of the potential due to an additional charge in a metal, we use spherical polar coordinates to describe the modification of the electronic wave functions. The periodic boundary conditions, t h a t give rise to a quasi-continuous energy distribution using a rectangular coordinate system, are now replaced by the angular conditions known from the treatment of the hydrogen atom and the requirement t h a t the wave function is zero at the surface of a large sphere with radius R, centered around the foreign charge. Since the spherical symmetrical charge distribution affects only the radial part of the wave function, it suffices to consider this, viz. ψ\(τ) = yi(r)/r, where r is the distance from the foreign atom. This part of the wave function has to satisfy the wave equation

[»♦{St--™)-^}]»«-· cw«) E is the energy of the state considered, and V(r) is the potential energy, The term 1(1+ l)/r 2 is due to the angular momentum, hVl(l + 1 ) ? of the electron around the foreign charge. I t can be shown (Mott and Massey, 1949; Schiff, 1955) t h a t if the poten-

THE INFLUENCE OF ADSORPTION ON METAL FILMS

345

tial energy tends to zero more rapidly than r - 2 with increasing r, the asymptotic form of yi(r) for large r is yi(r) ~ sin(kr +

Vl

- £1π)

(Π)-(29)

I n equation (II)-(29), k is connected with the radial momentum. As can be concluded from equations (II)-(28) and (29), the energy of the radial motion is

£_.-yW-»!!L+i>

(IIH30,

Since we are interested in the effect of introducing the foreign charge giving rise to V(r), we have to compare the solutions of equation (II)-(28) with those of the field-free situation. I n t h a t case the wave equation is

For large r, the solutions of this equation are y i (r)

~ sin(k n r - \\π)

(Π)-(32)

differing by a term ηλ in the argument of the sine function. At distances from the foreign atom large enough for V(r) to be negligible, the values of k and k n corresponding to the same energy E are equal. With wave functions not satisfying boundary conditions, a continuous range of values allowed for k and k n corresponding to a continuous range of energy levels results. However, when as said above the wave functions must be zero at the surface of a large sphere, a set of discrete values is allowed for k and k n and discrete energy levels are obtained. I t will be shown below t h a t the values of k and k n satisfying the boundary condition are different and lead to diverging energy levels. The meaning of the phase shift, ηϊ9 can be demonstrated most easily by a square potential well extending to r = a (Figure 10). If an electron enters the region r < a, its kinetic energy and, hence, its k-value increases. This implies t h a t the wave function oscillates more rapidly inside the potential well, whereas outside the well the oscillations of the wave function are equal to those in the field-free case. Therefore, the values of k and k n in equations (II)-(29) and (32) t h a t are solutions of the wave equations for large values of r, are not different. Since, however, the wave function as well as its derivative should be continuous everywhere, the values of the wave function on both sides of r = a should be matched. This requires insertion of the phase shift, ηϊ9 in equation (II)-(29). As the number of oscillations of the wave function

346

J. W. GEUS

increases for an attractive potential, a positive phase shift ηλ is necessary to match the wave functions. In Figure 10 the behaviour of the wave function for 1 = 0, which is a sin function also at low values of r, is represented for a square well. o Q.fc)

o

a

r . -V

h^o^x/v -v=o

FIG. 10. (top): Potential energy as a function of the distance r from the scattering centre. (middle): Simplified wave function, y 0 (r), for an electron with positive energy E = V/3; wave function inside square well y0(r) ~ sin kr = sin 2k n r, outside well y0(r) ~ sin k n r. (Much more involved wave functions are required to describe adequately the behaviour inside a three dimensional square well). (bottom): Phase shift, η0, for the field-free asymptotic wave function (r ->oo).

If the potential energy around the foreign charge is only moderately lower than in the pure metal, the value of ηλ tends to zero as k approximates zero, since the wave function oscillates very slowly then. The same is valid for very high energies and, hence for high k-values; now the period of the rapid oscillations is hardly aflfected by the relatively small increase in radial kinetic energy in the potential well. I n Figure 11 the dependence of η λ on the energy is given qualitatively. If the potential well is rather deep, the possibility of bound states arises. I n t h a t case the phase shifts, ηϊ9 tend to ηπ(η = 1, 2, 3 ) for k approximating zero; n increases with the strength of the attractive potential (Figure 11). Now a qualitative argument will be developed t h a t illustrates the fact t h a t the attractive potential must have a minimum value to allow the presence of bound states. We consider an electron in a square potential well extending to r = a without an angular momentum

THE INFLUENCE OF ADSORPTION ON METAL FILMS

347

(1 = 0). Inside the well the wave function is y0(r) ~ sin ar with

E

«=7>- >

FIG. 11. Phase shifts, rji, for attractive potentials according to Morse (1932). A potential after Thomas and Fermi (see section II.B.2) is assumed, V = (Z/r) exp(— qr), where z is the valence difference between foreign and host atoms, ß indicates the strength of the potential, j82 = Z/q.

^potential energyj wave function

—

—

-

r

A potential energy. wave function

FIG. 12. (top): Shallow square potential well which does not allow bound levels. (bottom): Deep square potential well which can accept electrons in bound levels.

348

J. W. GEUS

If, as indicated in Figure 12, the energy of the electron E is negative, the wave function outside the well has t o be y 0 (r) ~ e"fr with

-ß '-·/£■ This implies t h a t the sine function has to be descending at r = a to arrive at a continuous behaviour of the wave function. Evidently, this requires oca > 7T/2 and consequently,

Since for a bound state, the maximum value of E is zero, this leads to 2m 4 The effect of introducing a foreign charge on the density of occupied states of the metal is very important (Ziman, 1964). The density of states is derived from the boundary condition yi(R) = 0, where R is the radius of the large sphere centred around the foreign charge. With equation (II)-(29), this leads t o k= (n+ i lK_^) XV

xi

with n = 0 , 1, 2, 3 As discussed above and shown in Figure 11, the phase shifts η χ depend on the value of k; hence ^ ( k ) . With the same boundary condition, equation (II)-(32) leads t o ^ . O i + W f

(II)_(34)

From equations (II)-(33) and (34), it is apparent t h a t the density of states per unit length of k-space is the same for the perturbed and the pure metal, viz. R/π states per unit length. Moreover, there is a one-toone correspondence between t h e k-values and, hence, between t h e energy levels in the perturbed and the field-free situations. Owing to the phase shifts, ην t h a t are positive for attractive potentials, as was argued above, the momentum space is, however, compressed. We now shall investigate this compression of the momentum space quantitatively. B y introduction of t h e foreign charge, t h e distance

THE INFLUENCE OF ADSORPTION ON METAL FILMS

349

between two k-values, kx and k2, k ni and kn2 respectively, is changed by R This leads to a change in the number of states of ^i(ki) - Vi(K) π

The density of states connected with the angular motion of the electrons is not influenced here, as said above. If 771(0) is zero (small attractive or repulsive potentials), the total increase in the number of states up to the Fermi surface is ^(k¥)jn for the states with angular momentum hvl(l + 1). kF is the k-value at the Fermi surface. If one bound state is present in the perturbed metal, the phase shift for k = 0 is π. Consequently, the state with k n = π/R corresponds with k = 0 in the perturbed metal, whilst the state with k n = 0 corresponds with the bound level. This implies that the bound level is subtracted from the Fermi A energy (-k

2

)

k

n= 31 j4.

kn=2Tj/ Rm

k

n =2TT A

k n =H/ R

kn=TV6,

FIG. 13. Displacement of states with 1 = 0 around an attractive foreign potential in a metal. The states above kp are filled by mobile electrons screening the foreign charge.

350

J . W. GEUS

distribution; the decrease in the occupied part of the Fermi distribution is again ^i(kp)/7r states, as is represented in Figure 13. I n this figure the situation in the perturbed metal is represented for r < R, whilst for r > R t h a t of the unperturbed metal is given. If the degeneracy of the 1-levels, viz. (21 + 1), and the spin in degeneracy, viz. 2, is taken into account, it follows t h a t the total number of states, n, emptied by insertion of the foreign charge is 00

n =^(2\

+ l)Vl(kr)

(Π)-(35)

1=0

At this point the following two general principles valid for small concentrations of foreign charges are taken into account: (i) the wave vector at the Fermi surface at large distances from the foreign charge has to be equal to t h a t of the unperturbed metal and (ii) an electrical charge originating from a foreign atom or a vacancy in a metal has to be screened by a surplus of electrons within a finite distance. I t is remarked that these two principles are in accordance with the above mentioned observation t h a t only the residual resistivity is affected by small concentrations of impurities. The range of concentrations where the above principles are valid will be investigated below. Application of the first principle shows t h a t extra electrons have to be supplied to the region near to the foreign charge. The number of these electrons is given by equation (II)-(35). The second principle, on the other hand, relates the number of screening electrons to the valence or the valence difference of the foreign atom. If this atom is present interstitially a charge of Z atomic units has to be screened, where there is a charge of Z = Z ' — Z " equal to the difference in valence of the solute, Z', and the solvent, Z " , atoms for a substitutional impurity. Since the number of states to be filled to reach the wave vector of the pure metal, kF, is given by equation (II)-(35), the following expression is valid 00

Z = ^ ( Ά

+ l)VlQt,)

(Π)-(36)

1=0

which is the well-known Friedel sum rule. If a foreign atom with the same valence as the solvent metal is introduced, the charge to be screened originates from the difference in size of the two kinds of atoms. Suppose t h a t an impurity atom with atomic radius rA is inserted into a metal with radius r 0 . The free electron wave function, which is a constant in the pure metal, is normalized in the atomic volume ^πτΐ. In a volume f πν\ which is taken up by the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

351

foreign atom in the distorted metal, (1 + «0 electrons are present, where r3

_ L

r3

§y V

A

0

SV is the difference in atomic size between solute and solvent. For 8V < 0 a positive charge has to be screened. If both a valence difference, Z, and a difference in atomic volume, SV, is present, the charge that has to be screened is N = Z- ^ V

(II)-(38) 0

As the phase shifts, ^1(k), are determined by the potential V(r), which is in turn determined by the charge N that has to be screened, equations (II)-(36) and (38) can be used for a self-consistent calculation of the potential around a given impurity. 2. Bange of Screening As mentioned in the beginning of this section, it is very important to know if the electronic properties of a metal can be changed homogeneously by interaction with foreign atoms. The theory developed so far, shows that this is not possible; there is always a heap-up of electrons either in bound levels or belonging to the Fermi distribution around a foreign charge in a metal. Experimental evidence for this will be dealt with later on. This question being answered, it now remains to evaluate the range over which the screening is effected. For this, equations (II)-(29) and (32) can be used, which enable us to calculate the range over which the deviation, 8n(r), from the mean electron density in the metal extends. It can be shown (Ziman, 1964) that oo

8n(r) = ^ 2 1=0

r*

(

21

+ !)

{sin*(kr - $„ + Vl) - sin^kr - 11*)} I dk 0

e 2 2 (21 + 1) ( - I)* sin Vl 2i~21=0 .

C S(2k

°

g

+

*>

(IIH39)

It is gratifying that an analogous screening distance results on application of the many-body theory, which is much more involved. Owing to the Coulomb interaction between the electrons, the long-range oscillation of the electron density governed by the cosine-factor is reduced by a factor in the range 1.4 - 1.9. In Figure 14, results of Langer and Vosko (1959) obtained by using many body theory are represented.

352

J. W. GEUS

The dimensions are relevant for a metal like copper or silver. I t appears t h a t the screening is almost complete within a distance of about 3Ä. Very small oscillations in the charge density extend to about 10Ä; these oscillations are manifest only in very subtle experiments like nuclear magnetic resonance. Since it is difficult to handle the many-body theory as well as to use equation (II)-(39), it is useful to have a good approximative calculation. This is provided by the Thomas-Fermi approximation, which will be explained below. I n Figure 14 the exact results are compared with those calculated according to the Thomas-Fermi method. Although the latter method leads for r approximating zero to infinite charge density and does not display the minute oscillations at larger distances, the main features of the screening are well reproduced.

0-20 OI6 CO-I2

<

0-ΟΘ 0O4 °0

Ϊ

2

R

3

4

Fig. 14. Displaced electron density, Δη, around an inserted charge as a function of the distance R. according to the Thomas and Fermi approximation, according to many body theory. (After Langer and Vosko, 1959.) Data relevant for copper or 8 -1 silver; kF = 1.2 - 1,4 x 10 cm . R is expressed in units of kp, An in units of electronic charge per volume of kF - 8 .

I n the method of Thomas and Fermi (Raimes, 1962) it is assumed t h a t the density of states is not changed by the introduction of a foreign charge with potential energy V(r). I n Figure 15 the change in the electron density is represented schematically for a potential attracting electrons. The potential around the foreign charge, V p , is derived starting from the Poisson equation V 2 V P = 4πβ(η - n 0 )

(II)-(40a)

I n the pure metal the density of the positive charge and the electrons

THE INFLUENCE OF ADSORPTION ON METAL FILMS

353

energy

pure metal foreign charge FIG. 15. Basis of the approximation of Thomas and Fermi.

is n 0 e; if n(r) is the electron density around the foreign charge, the resulting negative charge density is e(n—n 0 ). Since the potential energy, V p , in the pure metal can be taken to be zero, the electron density n 0 is n0 = ^ ( 2 m E K ) « i « where E M is the energy at the Fermi surface. By an electron-attracting potential, Vp, the density is modified to n = =

3^

[ 2 m ( E M + e V ) ] 3 / 2

Hence,

- n o _ /1 , ^ V \ 3 / 2 EM/ n0 \ which can be approximated to n — n0 3 eV p 2 EM e2Vp (II)-(40b) EM The solution of equation (II)-(40b) satisfying the boundary conditions

which leads to

V 2 V,

θπη,

V p (r) = 0 , r - * oo ) n

V p (r) = ^ , r IS

o

Vp = - - ? e x p ( - q r ) (II)-(41)

with EM

354

J. W. GEUS

Since both n 0 and E M can be related to the atomic radius, r s , we obtain for a metal with N conduction electrons per atom q = 2.13 x l O ^ N ^ / r s ^ J c m - 1 For most metals, r s is of the order of 1.5 Ä, which leads for monovalent metals to a value for q of 1.78 x 108 cm - 1 . This large value reflects the finding of the more exact calculations t h a t the screening is almost complete over distances of some few Angstroms. Since E M contains the mass of the free electrons, it is apparent from equation (II)-(41) t h a t this screening length is very small for transition metals, which display a high effective mass m* (see equation (II)-(13)). I n the above discussion, it was assumed t h a t there is no interaction between the electron clouds screening the foreign charges. If the screening clouds overlap, the electrons of the foreign atoms cannot be completely accommodated around the impurity atoms. Then part of these electrons contribute to the Fermi energy, which is consequently modified. I n this case the electron density is still far from uniform; a considerable part of the electrons added with the solute atoms is concentrated around the ion cores with the higher charge. Experimental evidence for this will be given below. Since screening is effected over distances of the order of some Angstroms, whilst for transition metals this is only about one atomic diameter, modification of the Fermi surface asks for very high concentrations of solute atoms. Evaporated metal films may be highly porous: an upper limit to the specific surface area, which is attained for tungsten films, is about 107 cm 2 /cm 3 . This implies t h a t in cases where the sorption process is restricted to monolayer coverage ( ~ 1015 atoms cm - 2 ), the overall ratio of adsorbate-to-metal atoms is at most 0.15. For transition metals which mainly give rise to high specific surface areas, this is not enough to influence the electronic structure of the interior part of the metal. A change in the Fermi energy can only be expected for very small metal particles (diameter 10 to 20 Ä) t h a t have a large fraction of the metal atoms situated in the surface.

C. EXPERIMENTAL EVIDENCE FOR THE EFFECTS OF FOREIGN ATOMS ON THE ELECTRIC PROPERTIES OF METALS

The validity of the above theoretical results now will be substantiated by a review of the relevant experimental evidence. We shall discuss here work on the electrical conductivity of dilute alloys, on ferromagnetic alloys and on soft X-ray spectra of alloys.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

355

1. Electrical Conductivity The fact that the temperature-independent part of the resistivity only is increased by addition of small amounts of impurities was mentioned earlier, together with some important implications. The theory developed above enables one to account quantitatively for the effect on the resistivity. It can be shown that the increase in resistivity, Δ/>, due to addition of an atomic concentration, c, of foreign atoms is given by Ap = J ^ - 21.8 V 1 e i n 2 ^ ! K F Ila

£-4 1=1

ηι)

(μ ohm cm)

(II)-(42)

where n a is the number of conduction electrons per cm3 of the solvent metal, and kp the wave vector at the Fermi level (cm-1) is expressed in atomic units (0.53 xl0~ 8 cm). It was demonstrated by de Faget de Casteljau and Friedel (1956) that this expression describes very well the increase in the resistivity of, for instance, copper by the addition of non-transition metal atoms such as zinc, gallium, etc. Blatt (1957) showed that the theory is markedly improved if the screening due to a difference in atomic size of solvent and solute is taken into account. Now cases where only a size difference is present, as e.g. copper in silver, can also be covered successfully. No effect due to the strain in the lattice around the foreign atoms was observed. Later on, Harrison (1966) rationalized this by working with the pseudo-potential theory. This author concluded that the effects of distortions on the resistivity may be appreciable; however, compared with the influence of foreign charges, distortions lead to relatively small effects. If interstitial atoms that give rise to large lattice distortions are inserted into the metal—a case that we excluded so far in our discussion—this may no longer be valid. As argued by Jongenburger (1955) and later on by Overhausen and Gorman (1956), the scattering by the displaced metal atoms neighbouring the interstitial can predominate. Insertion of transition metal atoms into non-transitional metals leads to increases in resistivity that are more difficult to explain, since the d-levels can be split up by exchange interactions. Daniel (1962) used results on magnetic properties to assess a split-up of the phase shifts, 772, with 1 = 2. In this way, he could remarkably well account for the resistivities of gold and copper alloyed with first series transition metals. 2. Magnetic Properties Unequivocal evidence for the presence of localized screened charges in metals is provided from neutron scattering experiments. By this

356

J. W. GEUS

technique, differences in atomic magnetic moments present in an alloy can be determined. The first experimental results on alloys were published by Shull and Wilkinson (1955). These authors observed in FeCr, NiFe, and CoCr alloys different magnetic moments for the two kinds of atoms present. Later on this work was extended by Collins and Wheeler (1963), and Collins and Forsyth (1963). Collins and Wheeler found t h a t the atomic magnetic moments of cobalt and nickel are not changed in cobalt-nickel alloys. I n iron-cobalt alloys, the moment of the cobalt atoms remains unchanged, whereas t h a t of iron increases with increasing amounts of cobalt. In iron-nickel alloys, the atomic moment of iron increases, while t h a t of nickel decreases with increasing nickel content. These results clearly show that in binary alloys, even if both constituents are present in about equal amounts, the electron density around the atoms is different resulting in different atomic magnetic moments. The concept of a common d-band filled to the same level homogeneously throughout the alloy as is assumed occasionally in the rigid band model, is certainly erroneous. 3. Soft X-Ray Spectra Soft X-ray spectra also demonstrate beyond doubt t h a t the electron intensity f

M levels (empty) Ψ//^/////////λ

Μ

levels (OCCUpied)

I I

emission/ftabsorption

i / 1^ ι

-IO

O

IO

1

20

energy (eV)

1

30

intensity - V r (2S)

c O

o

.a O

t

absorption

fv

ion/ V emission - 2 0 -15 - I O

IO

energy (eV)

15

20

-U-K(.s) FIG. 16. (left): Emission and absorption of X-rays. (right, top): L n i emission and absorption spectrum for Na. (After Parratt, 1951). (right, bottom): K emission and absorption spectrum for Ti. (After Nemnonov and Kolobova, 1966).

THE INFLUENCE OF ADSORPTION ON METAL FILMS

357

density around different atoms in alloys diverges. Soft X-ray spectroscopy studies transitions to or from energy levels corresponding to electrons situated close to the nucleus. The spectra are indicated according to the inner energy level involved, spectra resulting from a transition to or from states with principal quantum number n = 1 , 2 , 3 , . . . . are denoted K, L, M, . . . . spectra, respectively. Inasmuch as the inner energy levels are sharp, the spectra obtained from transitions to or from these levels reflect the energy and the density of the states corresponding to much more loosely bound electrons. Emission of X-rays is brought about by transitions of electrons from outer states to an inner vacancy created by electron bombardment. Consequently, emission spectra scan the distribution of the filled energy levels. Absorption of X-rays is brought about by transition of electrons from inner levels to unoccupied outer levels; in this case, the unoccupied part of the energy band is investigated. Although interpretation of soft X-ray spectra is hampered by a number of complications, investigations of these spectra is one of the most valuable tools for investigating band structures. As said above, the rigid band model assumes that the only significant change in the density of states caused by insertion of foreign atoms in a metal without affecting the crystallographic structure, is a shift of the Fermi surface. Soft X-ray spectra are ideally suited for testing this assumption. In Figure 17 the situation is given as though a common energy band corresponding to a homogeneous distribution of valence

absorption

emission

absorption

v A

KB

•K. absorption χ*-^> B ,' /emission* / / Λ A / y Ε

κΒ

Ε

κΑ

τ

absorption* A ^

energy

FIG. 17. Absorption and emission of X-rays according to the rigid-band model.

358

J . W. GEUS

electrons in an alloy containing atoms A and B. Then, transitions to or from a common band to different inner levels belonging to atoms A and B would occur. In t h a t case, two bands identical in width and shape are expected, shifted over a distance corresponding to the difference in energy between the sharp inner levels of A and B atoms. Actually, this has never been observed. Even copper-nickel alloys, which should be ideally suited to display rigid-band characteristics, do not behave in this way as can be seen, for instance, from the work of Azaroff and Das (1964). I n all cases investigated so far, binary alloys show spectra for the two kinds of atoms t h a t are different in width and shape. The spectra of non-transition metal alloys display pronounced

o

10 2 0 30

o

10 20 30

energy eV

energy eV

>*

/ Λ / \ //V-oCu N } *Zn

4-» 0) L. V

t!

/ Y j

_y

/

2*Zn7iCu lOeV

k-»i

energy F I G . 18. X-ray K absorption spectra for Cu-Ni and Cu-Zn alloys. (Reproduced with permission from Azaroff and Das (1964). Phya. Bev. 134, 747; and Yeh and Azaroff (1967). J . Appl. Phya. 38, 4034.)

differences from those of the pure metals when the composition is changed beyond the range where interaction of the screening clouds is expected. As was argued above, the distance needed for complete screening of the foreign charge is short for transition metals owing to the high effective electron mass. I n accordance with this, the spectra of

THE INFLUENCE OF ADSORPTION ON METAL FILMS

359

transition metal atoms only change slightly on alloying. This is in keeping with the relatively small changes of the atomic magnetic moments evident from the neutron diffraction experiments. The high potential energy of the ion cores of transition elements t h a t leads to the high effective mass also causes the electrons to remain close to the nucleus. Therefore, the electrons are only slightly influenced by the environment of the atoms. Azaroff and coworkers (Azaroff and Das, 1964; Azaroff, 1967; Donahue and Azaroff, 1967; Yeh and Azaroff, 1967) carefully investigated the effects of varying the composition of binary alloys of transition metals within wide ranges on the soft X-ray spectra of the constituent atoms. Small differences were observed when the composition was changed which can easily be traced to small modifications in the screening charge clouds around the atoms. The experimental evidence presented above clearly demonstrates the applicability of the theory described. In many chemisorption studies elements such as hydrogen, oxygen, or nitrogen are used as adsorbates. I t is thus interesting to investigate the modifications in the electronic structure of metals brought about by dissolution of the above elements. Nemnonov and coworkers determined the effects of dissolution of nonmetal atoms on the X-ray spectra of metals most extensively (Nemnonov, 1960; Nemnonov and Finkel'shtein, 1960; Nemnonov and Kolobova, 1966); effects of oxidation to the corresponding oxides on the X-ray spectra of first series transition metals were recently also studied by Bonnelle (1966), and Fischer (1965). The effects observed on oxidation to non-conducting compounds are most easy to deal with. I n contrast to alloying with other metal atoms, this profoundly affects the K X-ray spectra, whereas the L n and L m spectra are hardly influenced. As said above K spectra are due to transition involving ls-electrons. Only transitions between s- and p-states can lead to intense bands in these spectra according to the selection rules. If there is a strong interaction between electrons present on neighbouring metal atoms, the energy corresponding to electrons in outer states are considerably broadened. The result is that at the energy level of the unperturbed 3<#-state states with p symmetry are also present. Owing to this, K X-ray absorption spectra of transition metals display a rather high intensity at wavelengths corresponding to energies just above the Fermi surface. In a non-conducting oxide, mutual interaction between metal atoms is strongly decreased, and hence the broadening of the ^-levels too. Consequently, the energies of the ^-levels are much closer to that of the unperturbed 4p-level; this brings about a shift of the onset of the K X-ray absorption edge to shorter wavelengths. The L n and L n i X-ray

360

J. W. GEUS

spectra are connected with transitions between p and d, or p and s levels. Since these transitions are much less influenced by the broadening of the p-leveh, the effect of oxidation on the L n and L n l spectra is much smaller; the shift in the latter spectra being of the order of 1 eV, whereas the K X-ray absorption edge is shifted by about 10 eV. The effects of reaction with elements to form conducting compounds is very interesting in view of the connection with chemisorption experiments. As was mentioned above, foreign atoms can be interstitially 3d 4 s 4 p hybridised energy levels

4p

A-——*

J4s 3d

0)

c +-» c

■ I I I

1 I I

R^~^ Jf Is

* 1—

Fe

^ -

FeO

O 20 4 0 60ΘΟ

energy (eV) ■K

metal

•K oxide

FIG. 19. Comparison of K X-ray spectra for a metal and its corresponding oxide. (left): Schematic representation. (right): K X-ray absorption spectrum for Fe and FeO, and Fe and Fe 3 0 4 . (After Nemnonov, 1960.)

dissolved in metals without changing the structure of the metal if the size of the dissolving atoms does not exceed 0.6 times the diameter of the metal atom. Moreover, the difference in the electronegativity of solvent and solute atoms has to be small to prevent formation of ionic compounds of a deviating structure. Owing to the latter, interstitial alloys of hydrogen, boron, carbon, and nitrogen can be obtained from transition metals that have relatively high electronegativities only. In these compounds the distances between the metal atoms are not much increased by the presence of the nonmetallic atoms. Consequently, the interaction between electrons on

THE INFLUENCE OF ADSORPTION ON METAL FILMS

361

neighbouring metal atoms remains large, with the result t h a t the metallic conductivity is largely maintained (see also section I I . E . l ) . The effect of reaction of titanium with oxygen (to conducting TiO), boron, carbon, nitrogen and hydrogen on the K X-ray spectra was investigated by Nemnonov and Kolobova (1966).

-20

-IO

O

energy

IO,

N 20

(eV)

FIG. 20. K X-ray absorption and emission spectra for titanium and titanium compounds: emission; absorption. (After Nemnonov and Kolobova, 1966.)

These authors observed a new band in the emission spectra at low energies, while the main emission band was shifted to lower energies if compared with t h a t of pure titanium. The strong maximum in the absorption spectra just above the Fermi surface was strongly decreased. Guided by theoretical results on the band structure of the carbon, nitrogen, and oxygen compounds from Ern and Switendick (1965), Nemnonov and Kolobova ascribe the differences in the spectra of the above compounds and the pure metal to the presence of strongly directed bonds between the metal and non-metal atoms. These bonds are due to electrons in orbitals hybridized from a 2^p-orbital centred on the non-metal atom and a (3cZ4p)-orbital centred on the metal atom. In this hybrid wave function, two of the five 3d-orbitals of the metal atom are engaged, viz. the two with e^-symmetry (dx2_y2, dz*). I n titanium carbide the electrons present in this hybrid orbital are about

362

J. W. GEUS

equally shared by the metal and the non-metallic atom. I n titanium nitride and considerably more in titanium monoxide, the electrons are shifted towards the non-metal atoms, which results in a bond with more ionic character. The band in the emission spectrum at low energies was ascribed to electrons in a (2s4p) hybridized wave function.

d 2 2 u

x-y

Cg-orbitals

ixz

°yz *2g— orbitals

«xy

FIG. 21. Symmetry of d wave functions.

Inasmuch as the electrons present on the metal atom in d-orbitals with £ 2g -symmetry and in the 4s-orbital t h a t is not involved markedly in the bonding with the non-metallic atoms still strongly interact, their energy levels are broadened, which leads to electrical conductivity. Owing to the interaction with the non-metal atoms, the energy of the metal 4p-wave function is decreased below that of the Fermi surface. Therefore, transition of ls-electrons to empty levels with ^-symmetry in the energy range of the atomic d-levels can no longer occur. This explains the decrease in the absorption just above the Fermi surface. The conclusions presented above can be applied to all interstitial compounds of transition metals and non-metallic atoms with valence electrons in p-orbitals. Starting from magnetic properties and electrical

THE INFLUENCE OF ADSORPTION ON METAL FILMS

363

conductivity data, Goodenough (1963) developed a description for the bonds in these compounds that is essentially the same as given above. This author considered, for instance, nickel nitride and nickel-iron nitride. Intermetallic bonds have a small directional dependence; besides from the ductility of metals, this can be concluded also from the success of the Wigner-Seitz theory. By insertion of small atoms with valence electrons in^-orbitals, strongly directed bonds between the two kinds of atoms are established. This leads to an increase in the hardness and sublimation energy beyond those of the pure metals, which is most pronounced for the carbide where the covalent character of the bond is largest. D. INFLUENCE O FCOLLISION S WIT HTH EMETAL-VACUUMINTERFAC E ONTH EMOTIONO FCONDUCTION ELECTRONS

1. Surfaces with an Undistorted Crystallographic Structure The preceding discussion has demonstrated that modifications in the electronic properties of the metal brought about by interactions at the surface will be restricted to a region comprising about five atomic layers from the surface. Before a prediction can be made of the influence on the electrical conductivity of a modification of this layer by chemical or physical interaction of the surface, the effect of the pure metal-vacuum interface on the motion of the conduction electrons has to be known. The effect of collisions of conduction electrons with the metal boundary planes can be predicted completely, if the fraction, p, of the electrons that is reflected specularly is known. For specular reflection the momentum distribution of the mobile electrons is not modified by the boundary (see also the discussion by

bulk metal

thin film with specularly reflecting boundaries

F I G . 22. Comparison of the distances covered by a conduction electron in a bulk metal and in a thin metal film with specularly reflecting boundaries.

364

J . W. GEUS

Brandli and Cotti, 1965); if, on the other hand the reflection is diffuse, the incident electrons loose their momentum and are scattered in a manner analogous to the scattering by impurities or thermal or structural lattice defects. The presence of a diffusely reflecting boundary therefore leads to an increase in the temperature independent resistivity, pR. If one or two of the dimensions of a metal specimen (film or wire respectively) are of the order of the mean free path of the conduction electrons, diffusely reflecting boundaries increase the resistance considerably over the value calculated from the bulk resistivity and the geometry of the specimen. Fuchs (1938) was the first to investigate theoretically the increase of the resistivity due to boundary scattering. Later on, his results were extended by Sonderheimer (1952) and Brandli and Cotti (1965). For different values of p, the fraction specu-

10"1

1

10

102

10 3

F I G . 23. Electrical resistivities, p, of thin metal films as a function of thickness, d. 1, mean free p a t h of conduction electrons; p», resistivity of corresponding bulk metal; p, fraction of conduction electrons specularly reflected at film boundaries.

larly reflected, these authors calculated the relative increase in the resistivity brought about by the small dimensions of a metal specimen as a function of the ratio of the thickness (for films) or the diameter (for wires) and the mean free path. Theoretical prediction of the fraction, p, specularly reflected requires knowledge of the structure of the metal surface down to an atomic scale. This is needed in view of the very small value of the wavelength, λζ, associated with the motion of the electrons at the Fermi surface through

THE INFLUENCE OF ADSORPTION ON METAL FILMS

365

the metal; for most metals, this wavelength is of the order of 10 Ä. Since the structure of metal surfaces has been investigated only quite recently to a sufficiently detailed extent, most workers in the field introduce the fraction p as an empirical parameter, which has to be determined experimentally. Ziman (1962) connected p with the roughness of the surface, which he described with a statistical auto-correlation function; in view of the lack of knowledge of the actual structure of metal surfaces he did not apply his results to real surfaces. Soffer (1967) improved Ziman's model by including oblique incidence, by using a more exact auto-correlation function, and by satisfying the flux-conservation requirement. This work was more related to the actual structure of the surface than that of Parrott (1965) and Brandli and Cotti (1965) who introduced a cut-off angle; electrons incident at an angle larger than the cut-off angle are specularly reflected, whereas the other electrons are diffusely scattered. These theoretical results too were not applied to real surfaces. Müser (1954) only envisaged the atomic structure of metal surfaces; his work has not drawn much attention, however. This author starts by remarking that electrons will be reflected specularly by a crystallographic plane in which the interatomic distances are smaller than the wavelength of the electrons at the Fermi surface. It can be derived that

Af

= a Uj

for a metal with one conduction electron per metal atom, where a is the lattice constant, and n is the number of atoms per unit cell. For f.c.c. metals λ^ = 1.279a, whilst this is 1.612a for b.c.c. metals. Consequently close-packed crystallographic planes, for which the nearest-neighbour distances are smaller than a, display specular reflection. Every crystallographic plane with higher indices (hkl) can be conceived as an arrangement of lamellae consisting of close-packed planes. Hence, the theory developed for optical diffraction on echelette gratings can be used to derive the orientation dependence of the reflected radiation. Application of the complicated expressions for echelette gratings show that the specularly reflected beam is suppressed over a considerable range of angles of incidence if the spacing of the crystallographic plane is markedly larger than the wavelength, λ^. This is valid for electrons incident at grazing angles too; these electrons will be reflected at large angles from the surface into the metal. In view of the bearing of Müser's results for the interpretation of the experimental data to be discussed later on, we reproduce here his qualitative argument. In Figure 24 an echelette grating is represented, p*

366

J . W. GEUS

the geometry of which is given by s, d, and φ, where tan φ = s/d. We consider an electron beam incident perpendicularly; the orientation of the crystallographic plane is given by the plane passing through the outside atoms. As said above, the lamellae with length cos φ/d are composed of close-packed planes. This implies t h a t the partial waves scattered by the atoms of one lamella in the direction making an angle 2φ with the incident beam have no mutual phase differences. (These waves are specularly reflected by the lamellae; owing to the difference in orientation of the lamellae and the crystallographic plane considered,

F I G . 24. Echelette grating.

the directions of specular reflection do not coincide for the two kinds of planes.) For a reflection maximum, the waves reflected by the small close-packed segments have to interfere constructively; this requires d sin 2φ = ηλ,

η = 1, 2, 3, . . .

Since tan φ = s/d, this leads for the first order (n = 1), to 2s cos2 φ = λ

(H)-(43)

The condition for suppression of the zeroth order, which is reflected perpendicularly, is cancelling of the waves scattered by the atoms of one close-packed segment. The waves scattered by the left half of a segment are cancelled by t h a t from the right half if 2s = λ

(Π)-(44)

s can be taken roughly equal to the distance between two close-packed planes; this is 0.577a for the {lll}-planes and 0.500a for the {100}planes of the f.c.c. lattice, whilst for the b.c.c. lattice the distance between the {110}-planes is 0.707a. Since λ^ is 1.279a for a f.c.c. and 1.612a for a b.c.c. lattice, condition (II)-(44) for suppression of the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

367

specularly reflected beam is almost fulfilled. In view of the fact that φ is often small, a large fraction of the incident beam will be scattered in the first order. Consequently, the considerations of Müser show that crystallographic planes with distances between neighbouring surface atoms larger than 1.279a for f.c.c. and 1.612a for b.c.c. lattices will scatter conduction electrons to a large extent diffusely. Specular reflection against the surface will occur, if the distances between neighbouring surface atoms are below the value for λζ. This implies that the {HI}, {100}, and {110} planes of the f.c.c, and the {110}, {100}, {211}, and {111} planes of the b.c.c. lattice reflect conduction electrons specularly. Inasmuch as the latter planes have the minimum number of broken nearest-neighbour and next-nearest-neighbour bonds, they have the lowest surface energy and are, hence the most stable planes. Before discussing what is presently known about the structure of real metal surfaces, we have to extend the consideration of Müser to flat surfaces of very small dimensions, viz. of the order of some tens Angstroms. This is necessary, since evaporated metal films can be composed of metal particles with diameters of this order of magnitude. In the films, these particles are either intimately connected via grain boundaries, or more or less isolated with a large fraction of their surface accessible for gas molecules. It is well known from optical theory that radiation incident on a plane with dimensions of the order of the wavelength of the radiation is reflected over a wide range of angles; this I

Ψ v y y v v A intensity

->sinS FIG. 25. Reflection of a plane wave by a plane of small dimension, d.

occurs also if the plane is completely flat. Figure 25 illustrates this behaviour; radiation is incident perpendicularly on a plane with width d. It can easily be seen that the radiation reflected by the left half of the plane is cancelled by that reflected from the right half if the reflected radiation makes an angle e with the normal to the plane, where sin « = g

(Π)-(45)

368

J . W. GEUS

The intensity of the radiation reflected is also given in Figure 25; the first minimum is given by equation (II)-(45), which corresponds to a larger angle e as d approximates λ. Consequently, metal particles so small t h a t they are bounded by facets of dimensions of the order of λζ will display diffuse scattering of conduction electrons at their boundaries. 2. The Structure of Seal Metal Surfaces The above discussion showed t h a t metal specimens composed of crystallites t h a t are not too small and which are bounded by stable crystallographic planes should reflect the conduction electrons specularly, provided the structure of the surface layer does not deviate markedly from t h a t in the bulk metal. Since the co-ordination of the metal atoms situated in the surface is much less than t h a t in the bulk, either a distortion at the surface may be present t h a t is maintained at 0 °K, or the thermal vibrations of the surface atoms may have an amplitude much larger than t h a t of bulk atoms. This may lead to an appreciable increase of the fraction of conduction electrons scattered diffusely at the surface. Since it is difficult to reach reliable conclusions about this point from a priori considerations, we shall first review the experimental evidence. Very reliable information can be gained presently from field-ion emission and low energy electron diffraction (LEED) experiments. Field-ion emission work has not revealed any deviation in the structure of metal surfaces from the bulk structure up till now. The field-ion emission pattern could be reproduced quite well by computer calculations on models based on the bulk crystallographic structure (Moore, 1962; Moore and Ranganathan, 1967). More accurate information can be gained from L E E D experiments. Different crystallographic planes in the surface of quite a number of metals have been studied already by this technique. I n all cases reported, surface structures were observed at temperatures below 250 °C that are in accordance with the bulk structure; the dimensions parallel to the surface are always as calculated from the bulk lattice constants within the experimental accuracy. There has been some dispute about the spacing perpendicular to nickel surfaces. I t was shown by Park and Farnsworth (1964a) t h a t for both (110) and (111) nickel surfaces this spacing is equal to t h a t in bulk nickel within about 2%. Silver, gold, palladium, and platinum at temperatures above 250 °C show L E E D patterns t h a t do not correspond with the bulk crystallographic structure of the metals. About the origin of these patterns there is still much discussion. Some authors ascribe the deviating patterns to reaction of the surfaces with impurities, whereas others

THE INFLUENCE OF ADSORPTION ON METAL FILMS

369

believe t h a t they reflect intrinsic surface properties (Fedak and Gjostein, 1967; Palmberg and Rhodin, 1967). As porous metal films are not stable it is difficult to investigate effects of adsorption on the electrical conductance of metal films at temperatures above 250 °C. We therefore can safely conclude t h a t the structure of metal surfaces is not permanently distorted in the temperature range t h a t is used in the work under review. The above techniques, viz. field-emission and low energy electron diffraction show, however, t h a t it is extremely difficult to obtain atomically clean surfaces. Especially carbon contamination is very difficult to remove, which is very inconvenient since there are strong indications that carbon migrates preferentially to the surface layer. Hence, ultrapure metals with a carbon content in the p.p.m. range can still have surfaces completely contaminated by carbon. Carbon contamination can only be avoided by extreme precautions and severe pretreatment, viz. alternate heating in oxygen and hydrogen, ending with hydrogen; or ion bombarding and finally moderate annealing in ultrahigh vacuum. 3. Thermal Vibrations of Metal Surface Atoms Thermal vibrations of metal surface atoms have been investigated both experimentally and theoretically. In experimental work the diffraction of low energy electrons was used, while some Mössbauer experiments were also directed to a determination of the vibrations of surface atoms. The effect of the temperature on the intensity of the reflected electrons can be used to determine the Debye-Waller factor. From this factor the mean-square displacement in the direction bisecting the angle between the incident and reflected electron beam can be calculated; for comparison purposes the Debye temperature is often given which is proportional to the root mean-square displacement. Since the penetration of electrons decreases strongly with decreasing energy, the extent to which their scattering is determined by the surface atoms can be controlled by varying the energy of the electrons used. MacRae (1964) determined the thermal vibrations of surface atoms in a (HO)-nickel plane in different directions using electrons of 35 and 40 eV. This author observed t h a t the mean-square displacement perpendicular to the surface was about a factor of three larger than that in the bulk; this was found also for the vibrations in the [001] direction, which is parallel to the surface and perpendicular to ridges of closely packed atoms. The mean-square displacement in the direction of the ridges, the [lTO] direction, is only a factor 1.2 larger than that in the bulk. In other work the mean-square displacement of the surface atoms

370

J. W. GEUS

was obtained by determining the temperature dependence of the reflected intensity at continuously decreasing electron energies. At sufficiently low electron energies. Debye temperatures characteristic of the surface atoms were determined. Lyon and Somorjai (1966) investigated the thermal vibrations perpendicular to the surface for platinum (100), (111), and (110) surfaces, while Goodman, Farrell and Somorjai (1968) worked with (100) and (111) planes of palladium and the (111) plane of lead. Finally, Jones, McKinney and Webb (1966) measured the mean-square displacement perpendicular to the surface for the (111) plane of silver (see also McKinney, Jones and Webb, 1967). The results are collected in Table 2; it appears that the mean-square displacements perpendicular to the surface are larger than those in the bulk by a factor of two to five. Clark, Herman and Wallis (1965) calculated the mean-square displacements of surface atoms in face-centered cubic lattices theoretically. These authors arrived at values about a factor two larger than that in the bulk for the perpendicular vibration. This is in very good agreement with the results obtained for the silver (lll)-plane, whereas the experimental data for the other metals are higher than those theoretically predicted. To evaluate the effect of the thermal vibrations at the surface on the scattering of the conduction electrons, we include in Table 2 the mean free paths of the electrons at 273 °K in the bulk and on the surface. The latter is calculated by means of equations (II)-(16) and (21) assuming that only the mean-square displacement perpendicular to the surface is increased compared with that of the bulk. From a comparison of both mean-free paths it appears that the effect of the thermal distorTABLE 2

Thermal Vibrations of Metal Surface Atoms Ni(100)

Mean free path at 273 °K (A) bulk surface

Pd(100)(lll)(O

Pb(lll)( c >

Ag(lll)(d)

220 220 310

no±io

140±10

55±10

155±15

390

234

273.4

90.3

225

3.2

4.5

3.8

2.7

2.1

130 75

110 51

110 56

—

570 415

(a) MacRae (1964) (b) Lyon and Somorjai (1966)

(c) Goodman, Farrell and Somorjai (1968) (d) Jones, McKinney and Webb (1966)

THE INFLUENCE OF ADSORPTION ON METAL FILMS

371

tion on the surface is still rather modest at 273 °K. Although the conduction electrons are relatively more scattered in the surface layer, they are evidently not scattered by every surface atom. 4. Some Experimental Data From the above discussion specular reflection of the conduction electrons against close-packed surfaces has to be expected. Since the close-packed surfaces are thermodynamically the most stable, it can be anticipated that most metal specimens will have predominantly closepacked crystallographic planes in their surfaces. Consequently, most metal specimens should display a high fraction of conduction electrons specularly reflected by the boundary planes. However, a considerable body of evidence points to a diffuse scattering of conduction electrons against metallic boundaries. The evidence is both from anomalous skin effect experiments and from investigations into the effect of finite dimensions of metals on their resistivity. Anomalous skin effect work is discussed by Sondheimer (1952) and by Pippard (1965); all experimental results are in accordance with only diffuse scattering of the conduction electrons against the metal boundary plane with the one exception of bismuth. The conduction electrons in this metal, however, have a very long wavelength, which makes specular reflection very likely. Friedman (1967) demonstrated by electrical conductivity measurements that the reflection of conduction electrons against the boundaries can be made more diffuse by roughening the surface; a quantitative account of the experimental data could not be given, however. Almost all other experiments in which the effects of the small dimension of metal specimens on their conductivity were investigated, showed diffuse scattering of the conduction electrons against the boundaries. Although the experimental results obtained in this way are not very likely to give accurate information about the fraction of conduction electrons reflected specularly, as has been recently stressed by Nossek (1966), the majority of the data nevertheless evidences a large fraction of electrons diffusely scattered at the boundaries. In most cases the origin of the discrepancy between the experimental results and what is expected theoretically is due to contamination of the surfaces of the samples used. As will be discussed later on, chemisorption on metal surfaces generally destroys their ability to reflect conduction electrons specularly. In all anomalous skin effect experiments no attempts were made to prevent chemisorption, which is indeed very difficult; moreover, carbon contamination of the surface has to be eliminated too, which requires elaborate pretreatments as discussed above with the LEED results. The same is valid for experiments in

372

J. W. GEUS

which thin metal specimens were obtained by cold rolling to desired thickness or by forcing the molten metal into narrow capillaries. Experimental data on vapour-deposited metal films will be dealt with in Section I I I . B . E . THEORETICAL ASPECTS OF THE EFFECTS OF ADSORPTION ON THE ELECTRICAL CONDUCTANCE OF METALS

The modifications of the electronic structure of metals by insertion of foreign atoms and the reflection of conduction electrons against boundaries of metal specimens were dealt with in previous sections. Now the results obtained will be used to explore the mechanisms by which adsorption, t h a t is, bonding of foreign atoms to the metal surface atoms may affect the electrical conductance of metals.

FIG. 26. Model of a metal film.

At this stage we consider metal films t h a t are not porous and bounded by two parallel flat planes (Figure 26). 1. Adsorption on Metals Since this review is concerned with the effects of adsorption on the physical properties of metals, a short survey of some of the main characteristics of adsorption on metals is indispensable. Usually physical adsorption and chemisorption are distinguished. The distinction is mostly based on the energy of the adsorption bond (Hayward and Trapnell, 1964). Here we will use a more basic criterion. Adsorption is considered to be physical if the adsorption can be accounted for to a first approximation by a model in which all electrons remain under control of the nuclei to which they belong before establishment of the adsorptive bond. A first approximation to the chemisorption energy requires a model in which a considerable transfer of control of electrons is included. Physical adsorption can be ascribed to van der Waals forces. Since physical adsorption does not lead to a considerable transfer of electrons between adsorbent and adsorbate, the distribution of electrons around the metal surface atoms will not be markedly changed. In a chemisorption process a chemical bond is established between the adsorbate

THE INFLUENCE OF ADSORPTION ON METAL FILMS

373

and the adsorbing surface. Though generally chemisorption is specific, clean metal surfaces are very reactive, with the result t h a t many gas atoms are strongly bonded to the surface. This is obvious for foreign metal atoms having their valence electrons in orbitale with the same symmetry as the metal surface atoms. Moreover, many non-metal atoms such as hydrogen, carbon, nitrogen, and oxygen are strongly bonded to clean metal surfaces. This is however only apparent for many non-metal/metal combinations after previous atomization of the species to be adsorbed, since the non-metal atoms are generally present as very stable molecules like H 2 , N 2 , 0 2 , CO, C0 2 , H 2 0 , NH 3 , or CH 4 . Therefore, adsorption of the non-metal atoms on metal surfaces can be prevented by thermodynamic or kinetic factors. These two factors now will be considered. 2. gas atoms without interaction

o! o '

r

• «I

.o a. u o

■olihydrogen ~ 100-

■

§6 ioxygen 1

c ! 200-

1

\

i 1 1

< c

& ε

Έ

-C

JZ

υ

u

)

chemisorbed atoms

(b

1 Z^777777^777777777777777777777/ V77s, Cb nitrogen metal surface

gaseous molecules

F I G . 27. Schematic energies of two atoms as: gaseous diatomic molecule, gas atoms, and atoms chemisorbed on a metal surface.

The large dissociation energies of the above gas molecules ask for very high adsorption energies to make adsorption of the constituent atoms thermodynamically favoured. I n Figure 27 a schematic energy level diagram is given. The bonding for hydrogen and oxygen atoms has to exceed 52 and 59 kcal a t o m - 1 respectively. High dissociation energies are also required for molecules like water, ammonia, carbon monoxide, and methane. The high dissociation energy of a nitrogen molecule even requires adsorption energies above 120 kcal atom - 1 . Consequently, dissociative adsorption of such gas molecules is possible only if the constituent atoms are bonded very strongly to the metal surface. Besides the possibility of complete dissociation of gas molecules and

374

J . W. GEUS

adsorption of the resulting atoms, adsorption of the complete or partially dissociated molecules has to be envisaged. There is evidence t h a t hydrogen and oxygen are bonded strongly to metal surfaces only as atoms; for nitrogen, on the other hand, there are strong indications t h a t molecular species can be bonded too with considerable energy to some metal surfaces (Ehrlich, 1961a; Ehrlich and Hudda, 1961; Delchar and Ehrlich, 1965; Ermrich, 1967; Robins, Warburton and Rhodin, 1967). Though some authors postulate a disproportionation of carbon monoxide to adsorbed carbon atoms and carbon dioxide molecules (Edmonds and Pikethly, 1969), most evidence for this molecule points to a non-dissociative adsorption (Gomer, 1967; Ehrlich, 1961b; Brennan and Hayes, 1965). This can be anticipated from the unsaturated character of the molecule; in the following, more arguments to account for strong bonding of undissociated carbon monoxide to some metal surfaces will be presented. I t is likely t h a t this is valid too for the unsaturated nitric oxide molecule, the adsorption properties of which are less extensively studied (Yates, Madey and Payne, 1967). The evidence for more complex molecules like water, carbon dioxide, methane and ammonia is less unambiguous owing to kinetic factors which will be discussed now. If gas molecules with high bonding energies are to be adsorbed dissociatively to metal surfaces, it might be expected t h a t the chemisorption process requires a considerable activation energy. This expectation stems from the fact t h a t in the usual gas-reactions, the bonding in the configurations t h a t have to be traversed before the stable reaction products are obtained, is mostly weak. The energies of the transitional configurations are consequently large, which leads to high activation energies for reactions between stable molecules like hydrogen and oxygen, and hydrogen and chlorine. Often therefore these reactions proceed via radicals as intermediates (Semenov, 1958). Though in the older adsorption experiments, activated adsorption of hydrogen was observed owing to surface contamination, it was ascertained already in the thirties t h a t adsorption of a monolayer of hydrogen atoms is very rapid and does not require a marked activation energy (Roberts, 1935). Later on, Gomer and coworkers demonstrated the chemisorption of hydrogen on nickel and tungsten to be very rapid even at 4.2 °K (Wortman, Gomer and Lundy, 1957; Gomer, Wortman and Lundy, 1957). A very low activation energy was also observed for the chemisorption of oxygen on tungsten (Gomer and Hulm, 1957). The fact t h a t no configurations with high energies have to be traversed in the dissociative adsorption of hydrogen and oxygen on metals can be rationalized by the fact t h a t the bonding energy to the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

375

metal surface does not vary much with the position on the surface and with the structure of the adsorbing molecules. The small variation of the bonding energy over the metal surface can be inferred from the relatively small activation energies for migration of adsorbed atoms over metal surfaces. For the more complex molecules like water, ammonia, methane, and carbon dioxide, the evidence available now points to an activated dissociative adsorption at least at higher coverages; since, however, extensive physical adsorption is possible at temperatures around 77 °K, it is difficult to ascertain chemisorption in this temperature range. The evidence for nitrogen is more difficult to explain. On tungsten, nitrogen is dissociatively adsorbed even at 77 °K almost instantaneously; however, the amount of nitrogen t h a t is atomically adsorbed remains much smaller at this temperature than at room temperature (Ehrlich, 1961a). We believe that this is due to a factor that has not been considered up till now, viz. the distortion of the metal surface. I n the establishment of the chemisorptive bond, the distribution of the valence electrons of both the adsorbate and the chemisorbing metal atoms is changed. A change in the electron density around the chemisorbing metal atoms necessarily implies t h a t the bonding of these metal atoms to the remainder of the metal is affected. If the distribution of the valence electrons around the chemisorbing metal atoms is strongly influenced, the structure of the metal surface will be appreciably changed. The extent to which the electronic configuration around the chemisorbing metal atoms has to be modified in order to chemically bond the adsorbate atoms depends on the symmetry of the orbitale of metal and adsorbate atoms, the occupation of the orbitals, and the electronegativity of the reacting atoms. Before discussing the implication of the latter factor, we shall argue that the distortion of the metal surface required to accommodate the adatoms can also be the ratedetermining step in establishing the thermodynamic equilibrium. The most obvious evidence for the role played by the energy needed to break the intermetallic bonds can be found in cases where reaction of the metal to the bulk-adsorbate compound is thermodynamically favoured. A good instance is adsorption of carbon monoxide on metals t h a t are capable of forming gaseous carbonyls. Adsorption of carbon monoxide on, for instance, tungsten and iron at about 273 °K should lead to formation of tungsten and iron carbonyls; nevertheless the interaction stops after adsorption of about one monolayer. Inasmuch as the adsorbate does not need to be dissociated here, the origin of the slow process is the activation energy required to break the intermetallic bonds. For nitrogen adsorption on tungsten the evidence is also

376

J . W. GEUS

conclusive. As demonstrated by Ehrlich (1961a), the fraction of nitrogen atomically adsorbed increases at increasing adsorption temperatures. The adsorption of nitrogen proceeding at higher temperatures only is accompanied by a marked distortion of the metal surface. This follows from the fact t h a t the increased ability for adsorption of atomic nitrogen is maintained after desorption of nitrogen by flashing. Readsorption of nitrogen at low temperatures on the tungsten surface flashed below 1500 °K leads to a much higher take-up of atomic nitrogen. Only after annealing at temperatures around 2400 °K, the surface distortion is removed, and the amount of nitrogen adatoms is the same as measured before heating in nitrogen at higher temperatures. Usually however, distortion of the metal surface by interaction with adsorbing molecules is difficult to ascertain. We believe t h a t data on the effects of adsorption on the electrical and magnetic properties of clean metal surfaces can give the most reliable information. To arrive at a sound interpretation of the experimental data, however, we must have at least a rough classification of the effects t h a t can be expected in different cases. To tackle this problem, we shall consider the structure and properties of the corresponding bulk compounds. This attack has already been used to investigate the effects of the presence of foreign charges on or in metals on the behaviour of the valence electrons of the metal. To separate the effects on the electronic properties from other influences, we restricted the discussion of section I I . B to cases where the metal structure itself was not affected. Here we shall focus attention on the structure of the bulk compounds and their electrical properties. First we shall demonstrate t h a t a comparison of bulk and chemisorption compounds can give reliable results provided the thermodynamically less stable state of the metal surface atoms is taken into account. Adsorption of foreign metal atoms on metal surfaces is relatively simple. Since the symmetry of the relevant orbitale of adsorbate and adsorbent is essentially the same, the reorganization of the electronic structure of both kinds of atoms is likely to be small, as is consequently, the distortion of the metal surface. If, however, formation of alloys is possible, place exchange between adsorbate and metal surface atoms can proceed. A good instance is copper-nickel. Neugebauer (1961) demonstrated t h a t on a nickel film kept at 77 °K copper can be deposited without formation of a copper-nickel alloy. On the other hand, Sachtler and coworkers obtained evidence t h a t a copper-rich surface alloy is formed with a composition deviating from the bulk composition by heating codeposited copper-nickel to about 500 °K (Sachtler and Dorgelo, 1965; Sachtler and Dorgelo, 1965; van der Plank and Sachtler, 1967). Earlier Tuul and Farnsworth (1961) published L E E D evidence for the forma-

THE INFLUENCE OF ADSORPTION ON METAL FILMS

377

tion of a copper-rich surface phase on copper-nickel alloys (see also Yamashina and Farnsworth, 1962). We shall now compare the adsorptive properties of metals for nonmetal atoms or compounds with their ability to form bulk compounds with non-metals. I n Figure 28 the characteristics of adsorption by metals as far as data are available are collected. Since carbon monoxide according to most of the present evidence does not dissociate, the data for this molecule are the most unambiguous (Gomer, 1958; Ehrlich, Z

H

Na

Mg

K

ΪΕ

]v

v

γτ

"W

w I

'

\3

©

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^

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^

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^

JB

T[B

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7n

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AI

Si

Cu Zn

®(^)^)).Ag Cd

© @®©®®

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Au Hg

Ge

Sn Pb

(Th)

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Chemisorption of nitrogen, hydrogen and carbon monoxide observed

Xj) Chemisorption of hydrogen & carbon monoxide observed ( x ) Chemisorption of carbon monoxide observed ( 7 ) Chemisorption of hydrogen x

observed

No chemisorption of molecular hydrogen nor of carbon monoxide observed FIG. 28. Pattern of adsorptive behaviour of metals.

1961b; Brennan and Hayes, 1965; Bell and Gomer, 1966). I n compiling Figure 28, adsorption up to a coverage of about one molecule per two metal surface atoms with a heat of adsorption well above 10 kcal mole - 1 is taken as a criterion for carbon monoxide chemisorption. As argued above, adsorption of atoms from diatomic molecules only indicates t h a t twice the bonding energy to the surface is larger than the dissociation energy. In Figure 28 for hydrogen and nitrogen, adsorption of about one and about one third of a monolayer, respectively, is used as a criterion. This figure, consequently, indicates for which metals the chemisorptive bond energies are larger than critical values. Adsorption of oxygen is displayed by every metal except gold. The metal atoms able to form carbonyl compounds are collected in Figure 29. I t can be seen t h a t carbonyl compounds are known for transition metals with incomplete <#-shells only. As discussed by Cotton and

378

J . W. GEUS

Wilkinson (1966), the chemical bond is due to electrons from the carbon monoxide forming a σ-bond with the e g -orbital of the metal, together

Ϊ I I SUE V Cr Mn Fe Co Ni Mo

Ru Rh

W Re Os I r F I G . 29. Metals with known carbonyls.

with a donation of metal electrons from t 2g orbitale to empty antibonding orbitale of the carbon monoxide which results in a π bond (Figure 30). To accommodate the electrons from the carbon monoxide, the metal d orbitals have to be incompletely filled. Carbonyl compounds with strong intermetallic bonds are also known, such as Fe 2 (CO) 9 , Co4(CO)12,

(±70 0 *2g

© Θ<®&

Φ

F I G . 30. Bonding in metal carbonyls with linearly bonded carbon monoxide.

and Rh 6 (CO) 16 . From the existence of these compounds it can be concluded t h a t metal atoms can be bonded both to carbon monoxide and to other metal atoms. Though the clusters of metal atoms in the carbonyl compounds are very small, their stability points to the possibility of adsorption on a metal surface without breaking the intermetallic bonds to a large extent. I t is not possible to predict the effects of adsorption of carbon monoxide on the intermetallic bonds more quantitatively. Since the distance between the iron atoms in Fe 2 (CO) 9 is equal to t h a t in metallic iron, viz. 2.46 Ä, whereas in Fe 3 (CO) 12 it is markedly larger, viz. 2.80 Ä, both a small and a larger increase in the distances between the metal atoms of the adsorbent can be anticipated. A comparison of Figures 28 and 29 finally shows t h a t there is a close agreement between the metals t h a t are able to adsorb carbon monoxide and those t h a t can

THE INFLUENCE OF ADSORPTION ON METAL FILMS

379

form carbonyl compounds. I n Table 3 the heats of adsorption of carbon monoxide, as determined by Brennan and Hayes (1965) are compared with the heats of formation of the corresponding carbonyl compounds. In all cases the heats of formation are smaller than the heats of adsorption (calculated per mole of carbon monoxide). The differences demonTABLE 3

Comparison of H e a t s of A d s o r p t i o n of C a r b o n Monoxide w i t h t h e H e a t s of F o r m a t i o n of C a r b o n y l C o m p o u n d s

Metal

Mo W Fe Ni

Heat of adsorption* integral heat kcal (mole CO)" 1 60 80 35 40

Carbonyl compound

Heat of formation kcal (mole CO)" 1

Mo(CO)6 W(CO) e Fe(CO) 5 Ni(CO)4

36 42 28 35

♦From Brennan and Hayes (1965)

strate t h a t the intermetallic bonds are not completely broken on adsorption in contrast to the formation of indicated carbonyl compounds. I t is, therefore, reasonable t h a t the range of metals capable of adsorption of carbon monoxide is slightly larger, viz. the metals of the second, third, and fourth column, as well as palladium and platinum adsorb carbon monoxide, whereas the carbonyl compounds of these metals are not known. I t is very significant t h a t neither magnesium, nor copper, silver, and gold adsorb carbon monoxide strongly (Culver, Pritchard and Tompkins, 1959). This points to the fact t h a t for chemisorption of carbon monoxide empty eZ-orbitals are also a prerequisite. We shall now compare the ability of metals to bond hydrogen atoms strongly to their surface with their ability to form bulk hydrides. I n Figure 31 the metals of which bulk hydrides are known are indicated. Two types of bulk hydrides can be distinguished: salt-like and metallic hydrides (Gibb, 1962). Whereas the salt-like hydrides have an ionic character, the metallic hydrides show a high electrical conductivity which decreases with increasing temperature. I n Figure 31 both types of hydrides are marked differently. The character of scandium, yttrium, and lanthanum hydride is intermediate between ionic and metallic. I t appears t h a t palladium which forms a stable metallic hydride, is rather unusual. However, nickel can be converted also into a metallic hydride, though this is stable at very high hydrogen pressures

380

J . W. GEUS

only. Copper forms an unstable hydride too, the properties of which are not well known. I t is apparent from Figures 28 and 31 t h a t strong adsorption of hydrogen extends further to the right side of the periodic table than formation of bulk hydrides. This can be ascribed to the expansion of the metal lattice required to incorporate hydrogen into the metal; for adsorption of hydrogen onto the metal lattice the effect on the intermetallic bonds will be much smaller. Moreover, the energy of metal surface atoms will be higher owing to the lack of a number of neighbouring metal atoms. At the left side of Figures 28 and 31 there is another Τ Τ Τ Π Γ Υ ϊ ν Γ γ Π [NO)

@

Ε

0

"νϊϊΓ

T B ΤΓΒ ΊΤΓΑ AI

Ο

©

®

(Cr)

[Rb| |§r] 0 © ®

Ξ @G3@®

n

Mn

°

Fe

Co (H\J(CU)

Tc Ru Rh

w Re

°

s lr

©

*

Zn

Ga

A Cd In

9

Au H

9

Tl

(X)

Metallic

ivX )

Unstable metallic hydrides

[Xl

Salt-like

Q(J

Hydrides intermediate between metallic and salt-like

_ y

X

hydrides

hydrides

No solid hydrides F I G . 31. Pattern of formation of metal hydrides.

discrepancy: whereas the alkali and alkaline-earth metals form salt-like bulk hydrides, these metals do not adsorb molecular hydrogen. Inasmuch as salt-like hydrides are formed, the metal structure is strongly affected. Evidently, the activation energy required to dissociate the metal and to convert the metal atoms into ions cannot be provided at room temperature. If hydrogen molecules are dissociated before adsorption, the hydrogen atoms react rapidly with sodium to sodium hydride as shown by Anderson and Ritchie (1966). The stable nitrides of metals are surveyed in Figure 32; the metals capable of forming oxides displaying a metallic conductivity are also included. Like the hydrides, the nitrides and oxides can be classified into metallic and salt-like compounds, the latter having a more ionic character. As can be concluded from Figures 31 and 32, formation of oxides

THE INFLUENCE OF ADSORPTION ON METAL FILMS

381

and hydrides with metallic character is largely confined to the fourth and fifth groups of the periodic system, whilst the elements of the sixth group and manganese can form metallic nitrides. As far as is known from data now available, nitrogen is adsorbed by the same metals t h a t can form metallic nitrides. Iron dissolves nitrogen exothermally in the f.c.c. form only, which is stable in nitrogen above about 500 °C. Whereas adsorption of hydrogen is displayed by metals t h a t do not form metallic hydrides, adsorption of nitrogen is shown only by metals capable of forming metallic nitrides. Moreover, adsorption of nitrogen is at least partly activated, whereas hydrogen and oxygen are instantaneously taken up in amounts corresponding with about a monolayer.

H Jii

1

JV y YL YIL

VIM IBJIBJILA

Na (fig)

Al

^^©WliilSis00 Rb @

Y ( z H (Nb) @

Ni

Cu (Zn) Ga

Tc Ru Rh Pd Ag ( 3 ) In

Cs (Sr) La (Hf)nb) [w] Re Os I r Pt Au

Tl

Εΐϋ] [Pal J 3 (χ)

Nitrides with ionic character

QQ

Both nitrides and oxides with metallic properties

\χ\

Nitrides with metallic properties ( n in fee only)

X

No oxides or nitrides with metallic properties Nitrides with covalent character not considered

F I G . 32. Pattern of formation of metal nitrides and oxides with metallic properties.

We believe t h a t the differences in behaviour of oxygen and hydrogen on the one hand, and nitrogen on the other are due to differences in the symmetry of the orbitale containing the valence electrons and in the electronegativity. Hydrogen has its valence electrons in a Is orbital, which has the same character as the orbitale t h a t contain at least part of the valence electrons of the metal atoms. To bond hydrogen atoms, consequently, a rehybridisation of the orbitale of the metal atoms is not required. As insertion of hydrogen atoms between metal surface atoms is not required strongly to bond hydrogen atoms to the metal surface,

382

J. W. GEUS

the intermetallic bonds are hardly affected unless the difference in electronegativity is large. While the electronegativity of hydrogen is 2.1, t h a t of the alkali and alkaline-earth metals ranges from 0.86 for cesium to 1.23 for magnesium. This large difference has the result t h a t the metal electrons are shifted considerably towards the hydrogen atoms; consequently, the metal structure is strongly affected and salt-like hydrides result. Though the electronegativities of the transition metals ranging from 1.22 for zirconium to 1.75 for nickel are still appreciably smaller than t h a t of hydrogen, these metals have enough valence electrons to maintain a considerable intermetallic bonding after insertion of the hydrogen atoms to form metallic hydrides. The same reasoning can be applied to the bonding of hydrogen atoms onto the surface of transition metals, which therefore will proceed also without a strong effect on the metal structure. Bonding of oxygen onto a metal surface or into a metal will affect strongly the electron distribution around the bonding metal atoms. I n view of the high electronegativity of oxygen, viz. 3.5, a substantial transfer of metal electrons to oxygen atoms must be expected, which results in the formation of charged oxygen and metal atoms. The bond between oxygen adatoms and the metal surface will therefore have a strong ionic character; bonds of this type do not have a strong directional dependence. The result of this is t h a t insertion of oxygen into the metal surface can proceed rather easily. Moreover, oxygen atoms are known to be multiply-bonded to one metal atom in many compounds like FeOCl, WOCl 4, MoOCl3. There is evidence t h a t in the first stage of the adsorption process oxygen atoms are bonded on top of the metal surface atoms, and in the following stages penetrate between the metal surface atoms. The above arguments can be used to rationalize the fact that oxygen is rapidly sorbed by metals, while the intermetallic bonds of the metal surface atoms are strongly affected. Though the electronegativity of nitrogen is only slightly smaller than that of oxygen, viz. 3.1 and 3.5 respectively, it only can form covalent bonds with a strong directional dependence. To bond nitrogen atoms, metal electrons must therefore be shifted to the nitrogen atoms and the metal atoms must take up positions satisfying the bond directions of nitrogen. From the structures of metallic nitrides it can be expected t h a t the nitrogen atoms must be present between two metal atoms. For most closely packed metal surfaces, insertion of a nitrogen atom between two metal surface atoms requires a displacement of the metal atoms. To bind nitrogen atoms, therefore, metal surfaces must often rearrange in much the same way as metals do in the formation of bulk nitrides. The conditions for adsorption of nitrogen atoms are thus

THE INFLUENCE OF ADSORPTION ON METAL FILMS

383

analogous to those for the formation of bulk nitrides. This, moreover, explains why dissociative adsorption of nitrogen requires an activation energy. Since the extent of rearrangement necessary to accommodate the nitrogen atoms changes from one crystallographic plane to another, the activation energy will vary. I n accordance with this argument, Ehrlich and Hudda (1961) and Delchar and Ehrlich (1965) demonstrated that no nitrogen atoms are adsorbed on the closely-packed (110) plane of tungsten at 300 °K or lower. We now want to consider more closely the tendency displayed by a number of metals to form hydrides, nitrides, and oxides with a metallic conductivity. Much information can be obtained from an investigation of the extension of the wave function of isolated metal atoms. Earlier in this section, the method of Wigner and Seitz for the calculation of the cohesive energy of θ-type metals was discussed. I t was argued t h a t the electron density was shifted towards the ion cores by the highly symmetrical mutual environment of the metal atoms. This leads to a decrease in potential energy, which brings about the cohesive energy. Doubtless the radial parts of the wave functions of isolated atoms and atoms in metals differ markedly. Nevertheless the mutual chemical interaction between atoms can be judged rather accurately from the maxima in the radial parts of the unperturbed wave functions and the interatomic distance. This treatment is justified by the extensive theoretical work on the bond of the hydrogen molecule. As discussed by Slater (1963), the LCAO treatment which uses the wave functions of the isolated atoms, leads to results qualitatively correct for the hydrogen molecule. By exact calculations, Watson (c.f. Slater, 1960) determined the maxima in the radial parts of the wave functions for (inter alia) the first long period transition metals. These results are plotted in Figure 33, which includes also the interatomic distances in the corresponding metals; the maxima for both the 4s and the 3d wave function are given. I t is, moreover, important t h a t the 3d wave functions of neutral atoms decrease appreciably more slowly at increasing distance from the nucleus than hydrogenic 3d wave functions as shown by the calculations of Watson. If the metal atom is ionized, the maximum of the wave function remains at the same position, but it approaches zero much more rapidly. The difference in energy between the dn~2s2 and dn~1s configuration decreases as the nuclear charge goes up. For iron, cobalt, and nickel the energies of the 3cZn_24s2 and 3eZn-14s configurations are about equal. Hence the s character of the valence electrons decreases on going from titanium to nickel. In metals this trend is not much different;

384

J . W. GEUS

ferromagnetic data point to less than one 4=s electron in iron, cobalt, and nickel. I n Figure 34 the heats of atomization for (inter alia) the first long period transition metals are presented. From this figure as well as from the interatomic distances of Figure 33, it can be concluded t h a t neither

K Ca Sc Ti V CrMn FeCoNi Cu Zn F I G . 33. Positions of maxima of radial parts of 3d and 4s wave functions for metals of the first transition period (c.f. Slater, 1960). □ , 3d; Q> 4s; X, interatomic distance in metals.

F I G . 34. Heats of atomization of the transition metals.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

385

the cohesive energy, nor the bond length varies erratically. (We neglect the peculiar minimum displayed by manganese, which is not shown up by the metals of the following long periods.) On the other hand, Figure 33 shows t h a t the overlap of the 3d and 4s wave functions decreases going from titanium to nickel, as does the number of more strongly interacting 4s electrons, as said above. Consequently, there is a delicate balance between the number of valence electrons and the mean interaction per valence electron going from titanium to nickel. The data of Figure 33 can be used to account for the fact t h a t the metals from titanium to manganese are able to bind non-metal atoms while retaining their metallic properties. Owing to the relatively large extension of the 4s wave functions in these metals, a slight increase in the intermetallic distance does not destroy the large overlap of the wave functions. Electrons in (3deg — 4p) wave functions bind the non-metal atoms, while electrons in 3dt2g — 4s) wave functions provide the metalto-metal bonds that are strong enough to give rise to metallic properties (see Figure 21). This explanation links up with the discussion presented earlier. For metals like nickel the overlap of the 4s wave functions is smaller, as is the number of electrons in this state. If valence electrons are shifted towards inserted non-metal atoms, the 3d wave functions, moreover, shrink owing to partial ionization. The smaller extension of the metal wave functions and the increased distance between the metal atoms caused by the non-metal atoms now decrease the metal-to-metal bonds to such an extent t h a t the metallic properties are lost. Recently results of calculations of the maxima in the radial charge density for the elements of the second and third transition series have been published (Waber, 1965; Herman and Skilman, 1963). I n Slater's book (1965) the computed radii of maximum charge density are compared with the atomic radii obtained from experimentally known bond lengths. I t appears t h a t the atomic radii for the second transition period are of the same order of magnitude as the radii of maximum charge density for the elements up to silver. On going from palladium to silver there is a sudden increase in the atomic radius, whereas the radius of maximum charge density still decreases. The same behaviour is displayed by the elements of the third transition series, where the atomic radii become gradually larger than the radius of maximum charge density from iridium on. From the above results, it can be concluded that the overlap of the valence electrons in the metals of the second and third periods is larger than in the metals of the first transition period. This is reflected by the fact t h a t the heats of atomization of the metals of the second and third period are markedly larger than t h a t of the first period (Figure 34). Brewer (1967; 1968) and Goodenough (1966)

386

J . W. GEUS

arrived at the same conclusion from a consideration of, inter alia, the electrical and magnetic properties of the transition metals. From the above discussion it is apparent that the electrical properties of the bulk metal-non-metal compounds give interesting information about the chemical bonds in these compounds. I t now will be argued that the effects of adsorption on the electrical conductance of metals can provide this information about the bonding in metal surfaces covered with gas atoms. 2. Survey of the Mechanisms by which Adsorption can affect the Electrical Conductance of Metals In this section the mechanisms by which adsorption can influence the electrical conductance of our model film will be surveyed, together with their implications for the film conductance as determined experimentally.

U)^

ΤΜΜΜΜΜΜΜ,

wimrnmrmTrrmm,

Nip p αι

?

t

ΨΠΠ7Τ7ΤΠ7Π7Τ7ΤππΓί

before adsorption

after adsorption

F I G . 35. Effects of adsorption on the electrical conductance of metals.

In view of the above discussion on the properties of metal alloys and the reflection of conduction electrons against metal surfaces, only the following two possibilities need be envisaged: (i) an effect on the fraction of conduction electrons specularly reflected against the metal surface; (ii) a change in conductivity of a restricted number of atomic layers at the surface of the metal. One of the effects usually invoked to explain the effects of adsorption on the conductance of metals, viz. a uniform change in the density of conduction electrons is not considered. In view of the distances over which foreign charges in metals are screened, a change in the number of

THE INFLUENCE OF ADSORPTION ON METAL FILMS

387

charge carriers homogeneous over the metal specimen asks for very thin films (thickness about 5Ä). As discussed in Chapter 3 continuous films with thicknesses of this order of magnitude cannot be prepared. A metal surface that reflects conduction electrons diffusely is equivalent to a structural defect. According to Matthiesen's rule, the diffusely reflecting surface contributes to a first approximation only to the residual resistivity. Consequently, a change in the fraction of conduction electrons diffusely reflected against the metal surface will lead to a change in the residual resistivity of the metal film. As said above, the metal surface can be converted over a certain depth into a compound with a resistivity different from that of the bulk metal. Since the resistances of the surface compound and the unperturbed part of the metal film are connected in parallel, it is most easy to use the electrical conductance, λ, of the film. If the resistivity, p09 of the film is changed by an amount dp owing to a change in the reflection of the conduction electrons, and if the original thickness of the film, t0, reacts over a depth, dt, to a compound with resistivity, pB9 the change in conductance, dA/A0, is

_^

dA = An

+

Po

(i_Mdt \

(dt<0)

(II) _ (46a)

PB/ *>O

It can also be conceived that a conducting layer with a resistivity pa, and thickness, dt, is added to the metal; this can arise if another metal is adsorbed onto a metal surface. Then the change in conductance is given by ^

Ao

=

_ ^

Po

+

*>^

PB t 0

(dt>0)

(II)-(46b)

It is also possible that the adsorbing metal is converted over a depth dt 2 into an alloy with adsorbate metal atoms. If the thickness of the alloy is dt x and its resistivity pB, the change in conductance is

ψ Λ0

=

_ dp + Po dt, + dt, PQ

PS JjQ

( d t i > 0j d t a < 0)

(n)_(46c)

T/Q

This can occur for instance on adsorption of copper onto nickel above room temperature. The change in the reflection properties of the surface leads to an effect on the residual resistivity. To a first approximation this effect will not vary with the temperature. Hence, the change in resistance, AR,will not depend on the temperature, whereas the relative change in conductance, dA/A0, will clearly vary with the temperature. If the surface layer of the metal is converted into a compound with a

388

J . W. GEUS

resistivity p8 that is large compared with p0, the thickness of the conducting part of the metal film is decreased. I n view of the small thermal expansion of metals (about 10~5 °C_1) the change in the thickness of the film brought about by a temperature difference of 200 °C will be 0.2% only. I t can therefore be assumed t h a t t 0 , the thickness of the film does not vary with the temperature; this is valid also for the decrease in the thickness of the conducting phase, dt. The relative change in the conductance, dA/A0, connected with a large increase in the resistivity of the surface layer therefore does not depend on the temperature. For Ps > Po, determination of the effect of adsorption on the conductance at different temperatures enables us to calculate the change in the residual resistivity and the thickness of the metallic phase separately. This will be demonstrated in section I I I . I t is possible t h a t the experimental films have surfaces rough on a scale larger than the wavelength of the conduction electrons; the surfaces of these will reflect the conduction electrons diffusely. This is also valid for films consisting of metal particles bounded by closepacked crystallographic planes with dimensions of the order of the wavelength of the conduction electrons. For these films, the resistivity, p8, of the surface layer only can be influenced by adsorption. 3.

Effect of Adsorption on the Reflection of the Conduction Electrons against the Metal Surface Adsorption on a metal surface can be visualized as putting foreign charges onto the surface. The effect of these foreign charges on the motion of the conduction electrons is governed by: (i) the screening of the foreign charges and (ii) the locations and number of different types of foreign charges. We shall now first focus our attention on the origin of foreign charges at metal surfaces, and on the screening of these charges. Foreign charges at metal surfaces can arise from: (i) adsorbate atoms, and (ii) surface metal atoms. If the electron density around a surface metal atom is not substantially changed in the establishment of binding at the surface, the potential energy of the ion core of the surface atom is about the same as t h a t of bulk metal atoms. If this is so, foreign charges at the metal surface only originate from foreign adatoms. This holds with physical adsorption. A small effect on the electron density around the metal surface atoms is likely also for adsorption of foreign metal atoms and hydrogen, provided the difference in electronegativity is not too large. If, on the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

389

other hand, bonding of the adatoms requires a rehybridization of the wave functions of the metal atoms and a considerable shift of valence electrons, the potential energy of the ion core of the adsorbing atoms will be different from that of the bulk metal atoms. This is presumably valid for adsorption of oxygen, nitrogen, and carbon monoxide. As given in equation (II)-(42), the scattering by a foreign charge is determined by the phase shifts, ην that are in turn dependent on the potential around the foreign charge (see Figure 11). Since the valence electrons around a physically adsorbed atom are not markedly shifted, the charge of this atom is screened within the atomic diameter. This implies that the constant q in equation (II)-(41) has a large value. As can be seen from Figure 11 the phase shifts, ην for large values of q are zero, except for 1 = 0, where η0 = ηπ. Consequently, a number of states corresponding to the number of valence electrons of the adatoms is subtracted from the bottom of the Fermi distribution, while the distribution itself remains unchanged (the spacing of the k-values being TT/R). Since phase shifts η0 = ηττ- and ^(1 ^ 1) = 0 do not lead to an increase in the resistivity according to equation (II)-(42), physically adsorbed atoms do not increase the fraction of conduction electrons diffusely scattered by the metal surface. Hence the residual resistivity, pR, of the metal is not affected by physically adsorbed molecules to a first approximation. If foreign atoms are chemisorbed on a metal surface, the charge of their ion cores is not screened within the atomic diameter, since the valence electrons are shifted to or from the metal atoms. The charges due to chemisorbed atoms give rise to scattering of the conduction electrons, just like foreign charges inside metals do. The phase shifts, ην that determine the scattering, also depend on the distance over which the charge is screened and the momentum of the conduction electrons at the Fermi surface. As shown by Greene (1966), and Greene and O'Donnell (1966), however, the angle of incidence on the surface now influences the scattering too; the fraction of electrons scattered diffusely decreases as grazing incidence is approached. Adatoms more electropositive than the surface metal atoms, e.g. alkali metal atoms on transition metals, repulse the mobile electrons. Adatoms more electronegative than the surface metal atoms, on the other hand, attract the mobile electrons. If the difference in electronegativity is small, bound levels capable of containing more electrons than the valence electrons of the adatoms will not be generated. The attractive potential is screened by mobile electrons only. For adatoms appreciably more electronegative than the metal atoms, transfer of metal electrons in bound levels around the adatoms is likely. This can occur for instance Q

390

J . W. GEUS

on adsorption of oxygen and nitrogen; with these adsorbates not only a transfer of electrons but also a rehybridization of the wave functions on the metal atoms is likely. The transfer and the rehybridization lead to a change in the electron density around the metal surface atoms. This has a twofold effect: the ion core potential of the adsorbing metal atoms becomes different from that of the bulk metal atoms and the metal surface atoms take up other positions owing to the decrease of the intermetallic bonding energy. Both effects bring about scattering of the conduction electrons. I t is difficult to predict the relative importance of scattering by the deviating ion core potential and by the displacement of the surface atoms. As said in section II.C.l, scattering by the difference in potential dominates for substitutional alloys, whereas in interstitial alloys scattering by the displaced metal atoms surrounding the interstitial is presumably larger. Since the extent of the distortion of the metal surface on adsorption is not precisely known, the data for bulk alloys, which are themselves not conclusive, cannot be simply used for adsorbing metal surfaces. Experimental evidence supporting the above theoretical discussion can be found in the results of Kamins and MacDonald (1968). At the interface of a metal-semiconducting oxide structure both the number of scattering charges and the density of charge carriers can be varied. Since the density of charge carriers determines the screening distance of the surface charges, the effect of the screening can be systematically investigated. Kamins and MacDonald observed a surface mobility varying as predicted theoretically by Greene and O'Donnell (1966) for a Si-Si0 2 interface, which demonstrates the applicability of the above theory. Effects of adsorption on the reflection of conduction electrons against metal boundaries can be expected only for atomically flat surfaces. Inasmuch as the scattering charges are concentrated in or on these flat planes, the possibility of constructive interference of the scattered electron waves has to be taken into account. The interference is governed by factor (ii) mentioned in the beginning of this section, viz. the locations and number of different types of foreign charges. If an atomically flat metal surface is covered with identical scattering charges with mutual distances equal to or smaller than the wavelength of the conduction electrons, it will reflect the electrons specularly. The metal surface will, on the other hand, loose its ability to reflect the conduction electrons specularly to a larger or smaller extent in cases where identical scatterers are present on sites with mutual distances larger than the wavelength of the conduction electrons. Covering an atomically flat metal surface with scattering charges can, consequently, only increase the residual

THE INFLUENCE OF ADSORPTION ON METAL FILMS

391

resistivity of the metal if the spacing of the scatterers is larger than the wavelength of the conduction electrons. The residual resistivity, which reflects the surface scattering, is hence susceptible to the presence of scattering charges and their distribution over the metal surface. The above discussion shows that investigation of the effects of adsorption on the residual resistivity of a metal specimen with atomically flat boundaries can be an important tool for studying the character of the adsorptive bond. As mentioned previously, physical adsorption does not affect strongly the residual resistivity, whereas chemisorbed atoms provided their spacing is not too small, increase it. By the effect on the residual resistivity, therefore, weak chemisorption can be distinguished from physical adsorption, while chemisorption can be detected also at low temperatures where extensive physical adsorption also occurs. Moreover, the presence of differently bonded chemisorbed species can be demonstrated in cases where the density of adatoms is equal to the density of metal surface atoms or where all metal surface atoms can react strongly with adsorbates. Adsorption of hydrogen is a good instance of a case where often a coverage equal to the number of metal surface atoms is easily reached. A strong effect on the electron density around the metal surface atoms can be expected for carbon monoxide. This molecule can react with two metal surface atoms so that at a coverage equal to one half of the density of metal surface atoms every surface metal atom interacts with an adsorbate molecule. If the resulting surface structure is thought as containing identical scatterers with a spacing that is equal to that of the metal surface atoms before adsorption, the residual resistivity will not be markedly different from that of the uncovered metal. Especially for carbon monoxide, however, there is much evidence pointing to induced heterogeneity; this implies that empty sites adjacent to sites already covered are not able to bind the adsorbate atoms in the same way. The resulting structure of the completely covered surface then contains identical scatterers with a spacing larger than the wavelength of the conduction electrons so that the residual resistivity of the fully covered metal specimen is larger than that of the clean metal. If the fully covered surface displays again specular reflection to the same extent as the clean surface, the formation of the adsorbed layer can be studied by determining the residual resistivity at increasing coverage. If the adatoms are not mobile over the surface, adsorption proceeds at random during the first stages of the covering process. Since this gives rise to large distances between the adsorbate atoms, the diffuse reflection of the conduction electrons at the metal surface will increase. In the following stages the gaps in the adlayer are gradually

392

J . W. GEUS

filled in, which leads to a decrease in the diffuse reflectivity and, hence, a decrease in the residual resistivity (Figure 36). For mobile adatoms, on the other hand, the forces between the adsorbed species can become apparent. If there is a repulsive interaction between the adatoms effective over a range of the order of the wavelength of the conduction A

A A

AA

A AAA A

^residual resistivity

AAAAAAAAAAAA coverage

immobile adatoms

B

B

B

B

^ residual resistivity

B B B B B B

-7777777777777777777777.

BBBBBBBBBBBB Ύ777777777777777777777.

mobile adatoms repulsive interaction

CC CCCC

CC

Λ residual resistivity

CCCC

CCCCCCCCCCCC mobile adatoms attractive interaction

coverage

F I G . 36. Schematic representation of dependence of residual resistivity on coverage for some types of adsorption behaviour.

electrons, a configuration with widely spaced adatoms will be established first. Thereafter, the sites between the adatoms are filled in. The larger degree of ordering in the adlayer if compared with random adsorption leads to a strong maximum in the residual resistivity. Finally with mobile adatoms that display an attractive interaction, the residual resistivity only traverses a very slight minimum.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

393

4. The Electrical Conductivity of the Metal Surface Layer after Adsorption As given in equation (II)-(46) adsorption can affect not only the nature of the reflection of conduction electrons against the metal surface, but also the resistivity ps of the surface layer of the metal. I n the latter case, adsorption converts the metal surface over a depth dt into a compound with a resistivity different from that of the bulk metal. The resistivity ps is the (hypothetical) value of an infinitely extended compound with the same structure as the converted surface layer; p s , therefore, does not contain a contribution due to the boundary scattering. The change in the thickness of the conducting phase, dt, can be positive, negative, or zero (Figure 37). If the resistivity ps of the metal

dt>C

■ dt=0

■dt<0-

F I G . 37. Effects of adsorption on the electrical resistivity of the surface layer of the metal.

surface after adsorption equals that of the bulk metal, dt is zero. If dt > 0, the conduction electrons can penetrate into the layer above the original metal surface. For dt < 0, the resistivity of the surface layer can be larger or smaller than that of the bulk metal; for ps > p0 conduction electrons cannot penetrate into the surface layer after adsorption. The above discussion demonstrates that information about the resistivity of the surface layer after adsorption can be obtained. The nature of the electrical conductivity of a solid (metallic, semiconducting, or insulating) reflects the electronic structure of the material. Hence, determination of the nature of the conductivity of a metal surface covered with adsorbate is important in ascertaining the nature of the adsorptive bond.

394

J . W. GEUS

In a series of papers Mott (Mott, 1956, 1961; Mott and Davis, 1968) discussed the conditions to be fulfilled by a solid to display metallic conductivity. Mott argues that a crystalline array of atoms in which there is an incomplete shell does not display necessarily metallic conductivity as is suggested by the band theory. This is due to the longrange attraction between an ionized atom and an electron. The attractive potential energy always leads to bound levels that are filled at 0 °K. If there is, however, a sufficient concentration of free electrons the Coulomb attraction, leading at large distances, r, to a potential energy e2//cr (K dielectric constant), is screened. As derived above, the screened potential can be represented by (e/r) exp (— qr) according to Thomas and Fermi (equation (II)-(41)); this screened potential does not always lead to bound levels. There is hence a critical concentration of free electrons which leads rather abruptly to a transition from a semiconducting to a metallic state. The number of free electrons in a crystalline array can be estimated from the contribution of ionic states to the cohesive energy. This estimation can be made reliably for the hydrogen molecule (Goodenough, 1963) and for a six-membered ring of hydrogen atoms (Mattheis, 1961; Slater, 1963). Results for these systems show that ionic terms are not important at interatomic distances larger than twice the equilibrium distance. The growing importance of ionic states with decreasing interatomic distances shows that the number of free electrons increases too. Consequently, a critical interatomic distance can be indicated below which the number of free charge carriers is large enough to screen potentials sufficiently to give rise to metallic conductivity. This critical distance will depend on the overlap between the wave functions on neighbouring metal atoms. In section E . l the ability of metals to form interstitial alloys with non-metal atoms such as oxygen, nitrogen, carbon, and hydrogen was discussed. I t appeared that mainly metals of the 4th, oth, and 6th groups of the periodic system form these alloys. I t was argued that in the interstitial alloys the non-metal atoms were bonded by electrons in 3deg wave functions, while electrons in the (3rfi2g — 4s) wave functions are providing intermetallic bonds. The (3dt2g — 4s) wave functions shrink toward the nucleus as the nuclear charge goes up; consequently, the overlap of the wave functions and, hence, the number of free carriers decreases on going from titanium to nickel (Goodenough, 1966, 1967). This explains why titanium monoxide and the high-temperature form of vanadium monoxide are metallic conductors, whereas manganese monoxide and nickel oxide, which have also a sodium chloride structure are insulating or semiconducting. The same transition can be seen in

THE INFLUENCE OF ADSORPTION ON METAL FILMS

395

the oxides with a corundum structure of which the high-temperature form of vanadium (III) oxide is metallic, whereas chromic oxide is insulating. The electrical properties of the interstitial oxides have been investigated in most detail (Howe and Fensham, 1967; Goodenough, 1963). As is to be expected, the overlap of the wave functions and, hence, the band width of the metallic oxides is smaller than that of pure metals. This leads to a large effective mass (equation (II)-(13)), which is confirmed by the relatively small mobilities. For vanadium (III) oxide a mobility of 0.2 cm 2 V _ 1 sec" 1 is quoted and for titanium monoxide 1.0 cm 2 V - 1 sec - 1 , whereas for metals like copper and sodium mobilities of 30 cm 2 V ^ s e c - 1 are found (Feinleib and Paul, 1967). The large effective mass means that the conductivities of the metallic oxides are appreciably smaller than those of normal metals, viz. 104 ohm _ 1 cm _ 1 against 106 ohm _ 1 cm- 1 , respectively. I t is, therefore, likely that the resistivity of the surface layer of a metal that has reacted with oxygen is markedly larger than that of the corresponding metal though the conductivity of the surface layer can still be metallic. The resistivities of metallic nitrides and hydrides have been studied much less than those of the oxides. This is due to the fact that it is difficult to prepare specimens of these materials with a known composition; the nitrides, moreover, are very brittle, which makes it difficult to obtain specimens with known dimensions. As far as data are available, it can be concluded that the resistivities of the metallic nitrides and hydrides are not markedly different from those of the corresponding metals (Matthias, 1963; Williams, 1964). There are indications that the resistivities of stoichiometric or nearly-stoichiometric hydrides and nitrides are either equal to or slightly smaller than the values for the corresponding metals. For titanium nitride at about 300 °K a lower resistivity (about 22 x 10~6 ohm cm) is quoted than for pure titanium (about 47 x 10 - 6 ohm cm) (Pascal, 1963). Since titanium hydrides with crystallographic structures appreciably different from the structure of the pure metal are obtained depending on the hydrogen content and the temperature, the resistivities of the hydride and the pure metal cannot be easily compared. Ames and McQuillan (1956), therefore, investigated the resistivity of ß-titanium; as can be seen from Figure 38 this structure is displayed both by the pure metal (above 880 °C) and by the metal hydrides. In Figure 38 the resistivities at 780 °C are also represented. Above it was argued that the resistivity is determined by the electronic structure of the compound and the degree of order. These two factors are apparent in the results of Figure 38.

396

J . W. GEUS

At a composition around T i H 0 5 the disorder is largest, whereas the order increases if either the pure metal or the composition TiH is approached. (The fact that the TiH phase is ordered points to a repulsive interaction between the dissolved hydrogen atoms). Moreover, from the extrapolation, it is evident that the ordered hydride has a resistivity that is lower than that of the pure metal; owing to this, the maximum in the resistivity versus hydrogen concentration curve is shifted to the left. This points to a different electronic structure of the hydride.

IOOO nu

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hydrogen concentration (at%)

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hydrogen concentration (at/£)

F I G . 38. (left): The phase diagram for the titanium-hydrogen system. (Reproduced with permission from McQuillan (1950). Proc. R. Soc. A204, 309.) (right): Resistivity of titanium-hydrogen alloys at 780 °C.

A resistivity of the metal hydride lower than that of the pure metal was observed at temperatures between 1000 and 1200 °K also for zirconium and yttrium (ZrH 2 20 x 10~6 ohm cm, Zr 41 x 10~6 ohm cm) (Savin, Andrievskii, Boika and Lyutikov, 1967). At room temperature the resistivity of zirconium hydrides with a composition up to ZrH 2 traverses a slight maximum, but remains above that of the pure metal. The hydride most investigated is palladium hydride. Up till recently, only increases in the electrical resistance at increasing hydrogen contents were observed; there is evidence that the increase is due to a larger residual resistivity (Schmidbauer, 1966). Recently, however, Baranowski and Wisniewski (1968) published measurements carried out at hydrogen pressures up to 16 x 103 atm. I t appeared that from a pressure of about 103 atm the resistance decreases linearly with increasing pressures till at about 16 χ 103 atm the resistance of the pure palladium is obtained again. The authors were

THE INFLUENCE OF ADSORPTION ON METAL FILMS

397

unable to determine the hydrogen content of their samples at the high pressures used. The difference in the resistivities of metallic oxides on the one hand, and metallic hydrides and nitrides on the other, points to an electron transfer towards the non-metal atoms t h a t is much larger for oxygen than for nitrogen and hydrogen. Owing to this, the radial extension of the wave functions on the metal atoms is larger for nitrides and hydrides than for oxides. This leads to a smaller effective mass for the conduction electrons in nitrides and hydrides. The evidence presented above suggests that at low concentrations of hydrogen or nitrogen, the resistivity increases owing to disordering. Accordingly, Wagenblast and Arajs (1968) found a strong increase of the resistivity of iron on dissolution of up to 0.18 at % of nitrogen (about 7 x 10- 6 ohm cm/at.%). Grabke (1967) investigated at 773 °K the effect of a further slight increase in the nitrogen content of an iron specimen with the composition FeN 0 . 25 ; this author arrived at an increase of about 10 x 10~6 ohm cm/at%. This suggests a linear increase in the resistivity up to a composition of about FeN 0 . 25 , which is also displayed by the titanium hydrogen system. Wagenblast and Arajs (1968) determined the resistivities of their nitrogen-containing iron samples at 4.2° and 78 °K. I t appeared that Matthiesen's rule is not completely obeyed; at lower temperatures the increase in the resistivity is smaller than at higher temperatures. According to Campbell, Fert and Pomeroy (1967) this is due to shielding of the impurity atoms by d electrons, which is to be expected as mentioned earlier. From a very thorough investigation of the resistivity of a- palladium hydride (compositions up to PdH 0 . 1 0 ), Lindsay and Pement (1962) concluded that Matthiessen's rule is also inapplicable to this system. At this moment, it is difficult to account for this deviation. From the data available for bulk compounds, it consequently can be expected that the metal surface layers will have a markedly decreased conductivity after interaction with oxygen. At coverages where the proportion of hydrogen and nitrogen to metal surface atoms is too small to lead to ordered structures without a large number of vacancies, the conductivity of the surface layer is likely to be low. At high coverages under conditions where ordered structures can be formed, on the other hand, a conductivity equal to or higher than that of the bulk metal can be expected. The behaviour of the conductivity of the metal surface on interaction with carbon monoxide is difficult to predict as no comparable bulk compounds are presently known.

398

J . W. GEUS III.

E F F E C T S OF ADSORPTION ON ELECTRICAL AND MAGNETIC P R O P E R T I E S OF VAPOUR DEPOSITED METAL F I L M S

In section I I the effects that adsorption can have on the electrical conductance of a continuous parallel-sided film were dealt with. In this section we first shall consider briefly the structure and electrical properties of vapour deposited metal films. These considerations will be used in the central part of this section, where the experimental evidence concerning the change in electrical conductance of metal films caused by adsorption will be surveyed. Conclusions drawn from the effects on the electrical conductance will be substantiated and amplified in a discussion of the much less extensive experimental data on the change in ferromagnetic properties of evaporated metal films brought about by adsorption. Finally, some results on the effect of adsorption on the Hall effect of metal films will be discussed. A.

STRUCTURE AND ELECTRICAL PROPERTIES

Since the formation and structure of vapour-deposited metal films is discussed elsewhere, we shall confine ourselves here to a brief summary of the main features which are relevant to the subsequent discussion. As dealt with in Chapter 3, deposition of metal atoms onto a non-metallic substrate first gives rise to isolated small metal crystallites. Further deposition leads to a network of contacting metal particles, which grows out to a continuous layer covering the substrate completely. Since many experiments have been carried out with continuous metal films, it is important to understand the electrical properties of these films. As conduction electrons are scattered at grain boundaries, the crystallite size is one of the factors determining the electrical conductance of continuous metal films. Knowledge of the crystallite size in films of varying thicknesses is therefore important. To estimate the dimensions of the crystallites, investigation in the electron microscope is very suitable, and film thicknesses may be estimated non-destructively by X-ray fluorescence. Specimens for transmission micrographs may be prepared by stripping the film from the substrate by reaction with hydrofluoric acid (Pyrex) or water (rocksalt) (Anderson, Baker and Sanders, 1962). Films thinner than about 200 Ä may be stabilized by covering with an evaporated carbon film. As observed by Suhrmann, Gerdes and Wedler (1963) and by Wiedenmann and Hoffmann (1965), the dimensions of the crystallites as found from replicas and from transmission micrographs are about equal. In a poly crystalline film one may readily see small crystallites having the same orientation making contact with each other, and crystallite coalescence becomes more extensive

THE INFLUENCE OF ADSORPTION ON METAL FILMS

399

as the deposit thickens. The degree to which metal crystallites coalesce increases with increasing temperature, but the cohesive energy of the metal is also important. As dealt with in Chapter 3 the activation energy for surface self-diffusion of metal atoms is correlated with the cohesive energy. Consequently, the merger of small metal crystallites remains restricted for a metal such as tungsten which has a very high cohesive energy. There is thus a general trend for crystallite size to be smaller in films formed from metals with high cohesive energy. A typical table of comparative crystal sizes is given in Chapter 7. Metal films used in adsorption studies are preferably highly porous. Figure 39 shows the surface area of some metal films as a function of the 15000h

E

S 10000

3 5000 LU CD

^ 50 Volume of metal in film (cm3 x 104)

100

F I G . 39. Surface area, as measured by adsorption of xenon at 90 °K, of metal films deposited on Pyrex kept at the indicated temperatures as a function of the volume of the metal in the film. Surface areas calculated according to the BET-theory at relative pressures from 0.05 to 0.30 based on a surface area of 22.4 A 2 for an adsorbed xenon atom, x , W 283 °K; ■ , Fe 273 °K; + , Fe 77 °K; O , Ni 77 °K; Λ, Ti 77 °K.

volume of the metal in the film. Though as usual with evaporated metal films, the scatter of the experimental points is large, especially for nickel, the surface area increases approximately linearly with the amount of metal deposited. The specific surface area depends on: the cohesive energy of the metal—cf. tungsten and iron on Pyrex kept at about 273 °K—, the structure of the metal—cf. nickel and iron on Pyrex kept at 77 °K—, and the substrate temperature—cf. iron on

400

J . W. GEUS

Pyrex kept at 273 °K and 77 °K. A comparison of the B E T surface area of the substrate, about 600 cm 2 , and that of the films demonstrates the films to be highly porous. We now must consider the shape and the orientation of the interstices giving rise to the large internal surface area of the metal films studied. A technique developed by Nieuwenhuizen and Haanstra (1964) allows a direct study of the interstices in vapour-deposited metal films. For a description of the technique we refer to the above paper of Nieuwenhuizen and Haanstra and that of Kooy and Nieuwenhuizen (1966), and an example of a result with an aluminium film is shown in Chapter 1. In Figure 40 a micrograph of a replica taken from a fractured iron film is represented. The thickness of the film was about 8000 Ä. The same type of columnar structure observed by Haanstra and by Kooy and Nieuwenhuizen for aluminium is also displayed by iron films, as is apparent from Figure 40. We hence can conclude that vapour deposited films contain narrow interstices oriented approximately parallel to the direction of incidence of the metal atoms. Figure 40 suggests that the metal layer at the substrate contains smaller crystallites than at the external surface, while beyond a thickness of about 3000 Ä the crystallite size does not increase appreciably. Since, however, the fracturing does not necessarily occur along a flat plane normal to the substrate, this conclusion is not unambiguous. The result obtained above will now be used to account for the electrical properties of vapour-deposited metal films. As dealt with in Chapter 3 all experimental evidence about the structure of thin metal deposits on non-metallic substrates points to the formation of individual small metal particles in the first stage of the deposition. The range of mean film thicknesses where films comprise isolated metal particles— island stage—strongly depends on the ratio of the mobilities of metal atoms over the metal and over the substrate surface, which is affected strongly by the substrate temperature and the cohesive energy of the metal. Much theoretical and experimental work has been devoted to the electrical conduction in metal films having an island structure. As was mentioned in section I I , the resistivity of bulk metals increases with rising temperature owing to a larger phonon scattering. The behaviour of the resistance of films with an island structure is completely different: the resistance of these films falls with rising temperature (negative temperature coefficient of resistance). Since the conduction process in island films is thermally activated, Mostovetch and Vodar (1951) ascribed the charge transport to thermionic emission between the islands. Later on Neugebauer and Webb (1963) combined Nifontoff's (1953)

THE INFLUENCE OF ADSORPTION ON METAL FILMS

401

F I G . 40. Micrograph taken from a replica of a fractured edge of an iron film with a thickness of about 8000 A. Specimen prepared according to Nieuwenhuizen and Haanstra (1964). Magnification x 28,000.

402

J . W. GEUS

calculations on tunnelling of charge carriers between metal particles with the suggestion of Gorter (1951) and Darmois (1956) that there is a marked electrostatic energy barrier to charge transport due to the charging of the small metal particles. The electrostatic energy must be included in the theory as quantum mechanical tunnelling is not an activated process. Hill (1969) also derived the activation energy accompanying the tunnelling process from electrostatic considerations; he arrived at the activation energy at low fields as being due to the difference in potential between a charged particle and the nearest neighbouring particles. Hartman (1963), arguing t h a t the spacing of the electronic energy levels increases for metal particles with smaller dimensions, associated the energy difference between the highest energy level occupied at absolute zero and the first excited level with the activation energy for electrical conductance. Herman and Rhodin (1966) finally postulated that charge transport proceeded through the non-metallic substrate. van Steensel (1967) and Hill concluded that both tunnelling and thermionic emission can play a role in the charge transport in island films. I t is obvious t h a t at high temperatures thermionic emission is more important than tunnelling. Small gaps between the metal particles lead to tunnelling being the more important, whereas at larger separations between the particles thermionic emission dominates. When the metal particles are smaller, the activation energy connected with tunnelling is large, which tends to favour thermionic emission. A high potential barrier between the particles, on the other hand, tends to favour tunnelling. Both van Steensel and Hill can explain their experimental data most readily by assuming t h a t charge transport between the particles occurs via the substrate. Van Steensel prefers thermionic emission, whereas Hill uses tunnelling to describe his results. I t is very difficult to discriminate between the above mechanisms, since vapour deposited films always present a distribution of particle dimensions and gap widths. If, however, charge transport goes exclusively through the substrate, adsorption would not be likely to affect the electrical conductance since only the work function at the metal/gas interface should be affected. Van Steensel tried to establish experimentally that no charge is transported through the vacuum between metal particles by depositing a layer of silicon monoxide over platinum island films. The effect on the conductance appeared to be very small if compared with that expected for silicon monoxide filling completely the gaps between the particles. Filling the gaps with silicon monoxide should lead to a reduction of the potential barrier between the particle.i and, consequently, to a large increase in the conductance. However, Caswell and Budo (1964) found that a 2600 Ä silicon monoxide film

THE INFLUENCE OF ADSORPTION ON METAL FILMS

403

deposited on to a tin film had no measurable effect on the annealing or agglomeration of the film, though it protected the metal film against interaction with oxygen. This shows that silicon monoxide is not able to penetrate to an appreciable extent into the gaps between metal particles. We therefore believe t h a t van Steensel's result is not conclusive. Milgram and Lu (1968) observed a decrease in the resistance of chromium films by overcoating with silicon monoxide. Silicon monoxide only affected the resistance when, during deposition, the metal film was kept at temperatures above about 150 °C, and the effect on the resistance was greater the higher the film temperature during silicon monoxide deposition. This may indicate that the mobility of silicon monoxide at 150 °C becomes sufficient to afford penetration between metal particles. The electronic properties of very small metal particles are difficult to study. As mentioned above, Hartman assumed that the differences between electronic energy levels corresponding to different kinetic energies become marked as the diameter of metal particles decreases to values of the order of some tens of angstroms. Doremus (1964, 1965, 1966) experimentally investigated the electrical properties of small metal particles by determining optical absorption spectra; he studied gold particles dispersed in glass or water, or present in very thin films on glass, and silver particles in glass. Doremus established that for gold, optical properties determined by interband transitions of electrons are unchanged down to small particle sizes. The experimental results could be accounted for by application of the optical constants of bulk gold down to a particle diameter of about 85 Ä. Since at 25 °C the mean free path of conduction electrons in bulk gold is about 370 Ä, the applicability of bulk optical constants points to specular reflection of conduction electrons at the particle surfaces. For colloidal gold particles in water, the experimental data were in poorer agreement with the bulk optical constants. This is at least partly due to adsorption of impurities on the surfaces of the gold particles, which leads to diffuse reflection of conduction electrons. Doremus' results for gold particles with diameters below about 85 Ä point to a mean free path of conduction electrons being proportional to the diameter of the geld particles. I n section I I it was argued that surfaces with dimensions t h a t are not large if compared with the wavelength of the conduction electrons scatter conduction electrons diffusely. We therefore believe t h a t for the gold particles studied by Doremus the critical dimensions of metal surfaces for diffuse scattering are reached at a particle diameter of about 85 Ä. The data for silver particles embedded in glass point to diffuse scattering of conduction electrons at the surfaces of particles with diameters up to about 100 Ä. The mathematical description of the

404

J . W. GEUS

optical properties for larger silver particles is too complicated to establish the nature of the reflection of conduction electrons. Since silver surfaces are, moreover, much more reactive than gold surfaces, it must be doubted if the surfaces of Doremus' silver particles are sufficiently free from adsorbed impurities to reflect conduction electrons specularly. The electrical resistance, R, of a metal film with length L, width B, and thickness t is η = ρ^

= Ρο

(ΐιΐ)-(ΐ)

where p is the resistivity of the metal in the film, and G a factor describing the geometry of the metal specimen. Knowledge of the resistivity, p, affords a calculation of the geometric factor of metal films from their resistance. However, vapour deposited metal films have a high density of grain boundaries that depends strongly on experimental conditions such as substrate temperature, residual gases, rate of deposition and film thickness. Consequently the resistivity of vapour deposited metal films cannot be estimated sufficiently accurately. Matthiesen's rule dealt with in section I I states that scattering by phonons proceeds independently from that by lattice defects and impurities (p = pR + pT). As a result the variation of the resistivity due to phonons with temperature, dp T /dT, does not depend on the defect and impurity concentration of a metal, which determine pR, the residual resistivity. If Matthiesen's rule, which is obeyed very well for bulk metals, is valid also for vapour deposited metal films, the geometric factor of films can be calculated from (Buckel and Hilsch, 1952) G = (dR f /dT)/(dp B /dT)

(HI)-(2a)

In equation (III)-(2a), Rf is the resistance of the film and pB is the resistivity of the bulk metal containing a negligible amount of defects and impurities. Equation (III)-(2a) can also be written G = ARf/ApB

(III)-(2b)

where ARf is the difference in the film resistance measured at two temperatures and ΔρΒ is the difference in the resistivity of the bulk metal at the same two temperatures. Von Bassewitz and von Minnigerode (1964) used equation (III)-(2b) to estimate the thickness of lead and copper films. They compared the thickness calculated according to (II)-(2b) with the values obtained by means of Tolansky multiplebeam interferometry (Tolansky, 1960). After elimination of experimental errors, the thicknesses found by both techniques were equal for lead films and for copper films deposited on quartz kept at temperatures

THE INFLUENCE OF ADSORPTION ON METAL FILMS

405

above 200 °K. Copper films deposited on substrates kept at lower temperatures are known to be markedly porous, which leads to the thickness determined by the Tolansky technique to be higher than t h a t corresponding with a compact film. Von Bassewitz and von Minnigerode as well as Broquet and Nguyen Van (1967) investigated the detailed validity of equation (III)-(2) for thin metal films. Though scattering by phonons and by lattice defects or impurities in bulk metals occurs independently, scattering at the boundaries of parallel-sided metal films is affected by thermal scattering at low temperatures. This is due to the fact t h a t at very low temperatures the energy of phonons is sufficient only to scatter conduction electrons over small angles. I n bulk metals, consequently, the scattering of electrons and hence the resistivity decreases with the temperature. I n thin metal films, on the other hand, electrons moving parallel to the film plane carry most of the current. Scattering of these electrons over small angles under conditions where the mean free path is comparable with or larger than the film thickness causes them to collide with the film boundaries. Phonon scattering at low temperatures, which deflects electrons over small angles, consequently leads to strong scattering at the boundary planes of the film (Olsen, 1958; Blatt and Satz, 1960; Azbel and Gurzhi, 1962). Owing to the above asymmetric scattering by the film boundaries, the effect of phonon scattering and, hence, of the temperature on the electrical resistance of thin films is stronger than on the resistivity of bulk metals. Von Bassewitz and von Minnigerode as well as Broquet and Nguyen Van demonstrated t h a t the corrections to be applied to equation (III)-(2) are negligible at temperatures above the Debye temperature and with film thicknesses larger than the mean free path of the conduction electrons. Since metal films used in adsorption studies are often not deposited or annealed at high temperatures, they have a high density of grain boundaries. Scattering of conduction electrons at grain boundaries leads to a relatively small mean free path, owing to which equation (III)-(2) can be applied without correction. As dealt with earlier, porous metal films contain many crystal boundary planes perpendicular to the substrate surface (e.g. Figure 40). Owing to this, the scattering of conduction electrons at the film surfaces is much more isotropic than for a parallel-sided film. Geus and Koks (unpublished) determined the geometric factor, G, of metal films the surface areas of which are given in Figure 39. The results are collected in Figure 41, where the ratio of the experimental geometric factor and t h a t calculated from the geometrical surface area of the substrate and the weight of the evaporated metal is given as a function of the film thickness. The B E T surface areas of the substrates R

406

J. W. GEUS

exceeded the geometrical surface area by factors varying from three (tungsten films and most of the iron films) to four (nickel films). That the experimental geometric factors exceed the theoretical values by factors that are markedly below three and four, indicates that the substrate surface is not completely covered by the metals. Since contact

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(5 3 O 2

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500 1000 Film thickness (Ä)

FIG. 41. Ratio of geometric factor determined experimentally according to equation (III)-(2) and calculated from the weight of metal deposited and the geometrical surface area of the substrate, as a function of the film thickness. The geometrical surface area of the substrate amounted to 220 cm 2 , whereas the BET surface area varied from about 650 cm 2 for the tungsten and most of the iron films to about 900 cm 2 for the nickel films. Film thicknesses calculated using the BET surface area of the substrate. Iron films were deposited on glass kept at 77 °K ( # ) and 273 °K (O); nickel films ( x ) on glass kept at 77 °K and tungsten films ( Δ ) on glass kept at 283 °K.

electrodes are melted on the Pyrex substrates t h a t were, moreover, frequently cleaned from metal films used in previous experiments, the substrates are likely to contain narrow crevices t h a t are not filled up by metal crystallites. Whereas the experimental geometric factors of iron and nickel films do not vary markedly with the film thickness, the values for tungsten films tend to increase with the film thickness. This may be due to contact resistances between metal columns in the films. As indicated in Figure 42 the surface area of the contacts between metal particles in thick tungsten films may be small if compared with the cross-sectional area

THE INFLUENCE OF ADSORPTION ON METAL FILMS

407

of the metal columns. As derived by Went (1939), a relatively small contact area gives rise to a resistance R c = />/4a, where a is the radius of the contact area, which is taken to be circular. When a is appreciably smaller than the film thickness, the film resistance will be higher than that displayed by a compact film containing an equal metal volume.

Top-view.

Side-view.

FIG. 42. Model of vapour deposited tungsten film. The surface area of the contact spots between the metal columns is small compared with that of the cross section of the columns. The equipotential curves are no longer oriented perpendicularly to the substrate surface.

This is due to the fact t h a t now part of the metal does not contribute to the electrical conduction. From the geometric factor G of a film, its resistance R f , and the bulk value pB of the resistivity which is characteristic of an almost defect free metal, the residual resistivity pR of the film can be calculated, according to R P*=-^-PB (ΠΙ)-(3) For the film resistance and the bulk resistivity, values at the same temperature must be used in equation (III)-(3). The residual resistivities of the films for which the B E T surface areas and the geometric

408

J . W. GEUS

factors are given in Figures 39 and 41 respectively, are represented in Figure 43. The values for tungsten films, which show a considerable scatter, are much larger than the resistivity of bulk tungsten at 273 °K (4.89 x 10" 6 ohm cm), whereas those for iron and nickel films are of the same order of magnitude as the bulk resistivities t h a t are 8.71 x 10 - 6 ohm cm for iron and 6.05 x 10 - 6 ohm cm for nickel. The large residual resistivities of tungsten films are due to the low mobility of tungsten atoms over tungsten surfaces which leads to relatively small crystallites.

E 5b

r. > u 2 "5 2 1

500 Film thickness (Ä) F I G . 43. Residual resistivities calculated according to equation (III)-(3) for metal films deposited on Pyrex kept at the temperatures indicated. Before measuring the resistance, the films were annealed for 16 hrs at 296 °K (iron and nickel) or 373 °K (tungsten). x , W 283 °K; + , Fe 77 °K; T , Fe 273 °K; # , Ni 77 °K.

We have found t h a t crystallites in tungsten films condensed on Pyrex kept at 293 °K have diameters of about 40 Ä; Anderson, Baker and Sanders (1962) observed crystallite sizes of the same order of magnitude. The specific surface area of tungsten films (300-500 cm 2 mg _ 1 ) points to columnar crystallites with a diameter of 40 to 60 Ä, which is in good agreement with the estimates from electron micrographs. As shown above, iron and nickel films contain larger metal particles. The small crystallite size in tungsten films affects the conduction electrons in two ways: where the metal crystallites are grown together, a large density of grain boundaries scattering conduction electrons is present and, where the crystallites have free surfaces, the dimensions of flat planes in the surface are too small to give rise to specular reflection. The small

THE INFLUENCE OF ADSORPTION ON METAL FILMS

409

crystallite size in tungsten films hence easily accounts for the high residual resistivity. As was observed by many authors for a large number of metals, the residual resistivity of iron and nickel films decreases with increasing film thickness. The explanation for the decrease in resistivity based on the assumption of parallel-sided films and scattering of conduction electrons at the film surface was dealt with in section I I . D . l (Figure 23). I t is difficult to accept this explanation for the data of Figure 41. The surface areas of the films are approximately proportional to the volume of the deposited metal (Figure 39). This implies t h a t the specific surface area of the films and, consequently, the probability t h a t conduction electrons strike a metal surface does not decrease as the film thickness grows. I t is moreover, argued in other Chapters t h a t metal crystallites in vapour deposited films generally have a large fraction of close-packed crystallographic planes in their surfaces. Specular reflection of the conduction electrons must therefore be expected for metal films deposited and kept in ultrahigh vacuum. We hence ascribe the decrease in residual resistivity displayed in Figure 43 to an increase in the crystallite size with growing film thickness, a process known to occur from direct electron microscopic observation. The smaller size of iron particles in films deposited onto Pyrex kept below 200 °K is reflected in the higher residual resistivity of iron films in Figure 43. Since the reflection of conduction electrons at metal surfaces is of paramount importance for the explanation of the effects of adsorption on the electrical conductance of metal films, we here consider briefly the evidence obtained by others. Often metal films are evaporated at high residual gas pressures and transported through the air to an apparatus where the resistance is measured at varying temperatures. Since nearly all metals rapidly chemisorb oxygen, owing to which the specular reflection is destroyed, these experiments cannot give reliable information. However, gold is highly resistant to oxidation even at high temperatures (Clark, Dickinson and Mair, 1959; Gonzalez and Parravano, 1956; Hondros and Gladman, 1968). Experiments with gold films therefore can give reasonably reliable information about the reflection of conduction electrons at metal surfaces even when the films are deposited at high residual gas pressures and exposed to atmospheric air before the measurement of their resistance. Gold films deposited on bismuth oxide adhere strongly to the substrate and can be annealed at high temperature without breaking up into isolated crystallites. Since annealing removes the grain boundaries, the resistivity of annealed thin gold films can approximate t h a t of bulk gold provided the reflection of the conduction electrons at the film

410

J . W. GEUS

surface is specular. Gilham, Preston and Williams (1955) were the first to observe that gold films deposited on bismuth oxide and annealed at 200 to 450 °C display resistivities of the same order of magnitude as bulk gold. Since films with thicknesses of the order of 100 Ä displayed the resistivity of bulk gold for which the mean free path at 273 °K is 406 Ä, the reflection of the conduction electrons at the film surface must be largely specular. Whilst Gilham, Preston and Williams worked with sputtered gold films, Ennos (1957) obtained analogous results with vapour deposited gold films. This author found the resistivity of 60 Äthick gold films to approach the bulk value after annealing at 350 °C. Chopra, Bobb and Francombe (1963) and Chopra and Bobb (1964) established specular reflection at the surfaces of epitaxial gold films on mica. At the substrate temperature required for epitaxy, 270-300 °C, the gold films were continuous only at a thickness of 300 Ä. Films deposited on substrates t h a t were not heated displayed higher resistivities; evidently, this is due to the small crystallite size in these films, which brings about much grain boundary scattering. Lucas (1964) carried out a very enlightening experiment in depositing gold atoms on to specular reflecting gold films. The gold films were prepared by deposition of a 60 to 100 Ä-thick gold layer onto bismuth oxide; after annealing for a few minutes at 350 °C in air the films displayed specular reflection of conduction electrons as was evident from their low resistivities. When gold atoms were desposited on to the gold films, the resistance varied as represented in Figure 44. The resistance of the specular reflecting films traverses a maximum during the deposition of gold atoms, whereas t h a t of the sputtered unannealed film decreases steadily. The change in the resistance of the specularly reflecting films closely resembles the behaviour predicted in section U.E.3 (Figure 36). Deposition of gold atoms leads first to a coverage with isolated atoms t h a t migrate over the surface to form small clusters. The isolated adatoms and the small clusters scatter conduction electrons colliding with the surface of the film. On further deposition of gold, the clusters grow to dimensions t h a t afford again specular reflection of conduction electrons, and rapidly capture the arriving gold atoms; since the thickness of the metallic layer grows also, the resistance drops below the original value. The sputtered unannealed film contains crystallites of about 30 Ä (Gilham, Preston and Williams, 1955). The size of the surfaces of these particles is too small for specular reflection. Deposition of gold atoms leads to preferential growth of favourably oriented crystallites after the atomically rough parts of the surface have been filled in. Owing to this, the surface reflects conduction electrons more specularly as the deposition of gold goes on. Together

THE INFLUENCE OF ADSORPTION ON METAL FILMS

411

with the growth of the thickness of the gold layer this brings about a relatively rapid fall in the film resistance.

+10

o

5

a:

0

-10 0

10

20

30

40

50

Average thickness of superimposed gold (Ä) F I G . 44. Change in the resistance (R) of gold films on further deposition of gold atoms at room temperature. Films I and I I were prepared by vapour deposition; films I I I and IV by sputtering. Film IV was not annealed. Films I, I I , I I I were specular, film IV nonspecular. (Reproduced with permission from Lucas (1964). Appl. Phys. Letters 4, 73.)

Learn and Spriggs (1963) deposited tin and lead on to quartz substrates at pressures of the order of 10 - 7 torr. These authors could account very well for the effect of residual gas molecules by measuring the film resistances during the deposition and varying the rate of evaporation. The decrease in the mobility of metal atoms by reaction with residual gas molecules is clearly evident from their results. From an analysis of the film conductance versus time (thickness) plot during the deposition, they could show t h a t the reflection of conduction electrons at the surfaces of lead and tin films is specular when the substrate was kept at 300 °K. At 255 °K, where only lead was deposited, the rate of deposition must be below a critical value to obtain plots t h a t point unambiguously to specularly reflecting surfaces. At lower substrate temperatures, the mobility of lead and tin atoms is too small to prevent, in continuous films, formation of relatively small crystallites t h a t merge when the thickness is increased. The increase in crystallite size and hence the decrease in grain

412

J. W. GEUS

boundary scattering during the growth of the continuous metal film means t h a t Learn and Spriggs' analysis cannot be used for films deposited on substrates kept below about 250 °K. Owing to reaction with residual gas molecules, a strong decrease in the rate of deposition cannot be used to compensate for the slower grain boundary migration at lower temperatures. Nevertheless the results of Learn and Sprigg prove t h a t specular reflection at metal surfaces is not restricted to gold surfaces. Recently much work has been done on silver and aluminium films. Though these films were transported through the air to cryostats where the resistance was measured, the surface in contact with the substrate was not necessarily contaminated by impurity atoms. Larson and Boiko (1964) deposited silver on to mica kept at 270 to 300 °C, which resulted in single crystal films. Analysis of the resistivities at 4.2 °K of films with thicknesses from 640 to 13,000 Ä points to metal surfaces exhibiting about 50% specular reflection. Tanner and Larson (1968) investigated silver films deposited on to heated rocksalt and mica. Since the grain boundary density will be different for the two substrates, the resistivities of the films does not follow the Fuchs-Sondheimer relations. Nevertheless, a reflection parameter between 0.25 and 0.5 could be extracted from the experimental data. Since silver surfaces rapidly adsorb a monolayer of oxygen on contact with molecular oxygen, the outer surface of the above silver films will scatter conduction electrons, whereas the surface contacting the substrate will display a large extent of specular reflection. Though Lucas (1965) has demonstrated t h a t for differently reflecting top and bottom surfaces the Fuchs-Sondheimer treatment must be modified, the above values for the reflection parameter are consistent with a specularly and a diffusely reflecting surface at the bottom and top of the film, respectively. Analogous results were obtained on aluminium films. Von Bassewitz and Mitchell (1969) deposited aluminium at pressures of the order of 2 x 10 - 6 torr (of mainly water vapour) on to potassium bromide substrates and found for epitaxial films reflection parameters t h a t were substantially larger than those for poly crystalline films. Since the epitaxial films were condensed on substrates kept at 380 °C, reaction of the surface contacting the substrate with residual water is not likely. The bottom surface of epitaxial films consequently will display specular reflection in contrast with the top surface t h a t is completely covered with adsorbed oxygen after exposure to air. Polycrystalline films, on the other hand, were condensed on substrates kept at room temperature and which are likely to be covered with adsorbed water. Von Bassewitz and Mitchell's results therefore again show t h a t reflection of conduction electrons at clean metal surfaces is specular, whereas reaction of the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

413

surface with gas molecules leads to scattering of conduction electrons. Mayadas (1968) working with aluminium films deposited in ultrahigh vacuum on to unheated glass substrates demonstrated that the grain size affects the resistivities of the films more strongly than boundary scattering. Later Mayadas, Feder and Rosenberg (1969) deposited aluminium on glass kept at 200 °C and found the crystallite size to increase with the thickness of the film (the average grain diameter was about equal to the film thickness). Mayadas, Shatzkes and Janak (1969) finally developed a model that accounts for both boundary scattering and increase in crystallite size with increasing film thickness. They showed that even when the reflection at the surface is completely specular, the growing grain size causes the residual resistivity to decrease with the film thickness. From the evidence on the resistivities of thin metal films we can conclude that the surfaces of metal films that do not contain very small metal crystallites reflect conduction electrons specularly provided they are not covered by chemisorbed foreign atoms. The latter condition will be described more precisely in the next section dealing with the effects of adsorption on the electrical conductance of metal films. From the above discussion of the structure of vapour deposited metal films, it is apparent that the structure appreciably deviates from that of the model film in Figure 26. We now shall investigate whether the general mechanisms by which adsorption may affect the electrical conductance and which were discussed in section II.E must be extended. As indicated in Figure 45, three different film structures can be expected. First of all, adsorption may change the structure of the film. One possible reason for a change in the structure is liberation of the heat of adsorption. As discussed earlier, metal particles on non-metallic substrates become mobile at rather high temperatures only. Thermal effects therefore are not likely to influence the structure of island-type films, unless the metal particles are very small. On the other hand, continuous films may be broken up into isolated metal particles by heating. In continuous films, grain boundaries can be annealed and metal crystallites can sinter together eliminating the gap between them. Since metal films evaporated on to substrates kept at low temperatures are far from equilibrium, their resistance continuously decreases after deposition. The decrease in the resistance which is due to annealing of grain boundaries can be accelerated appreciably by liberation of heat of adsorption. Films to be used in studies on the effect of adsorption on the electrical conductance must therefore previously be sintered at temperatures well above the deposition temperature and the temperatures at which the adsorption is carried out. The resistance of presintered films is very

414

J . W. GEUS

stable, and the heat of adsorption is dissipated quickly by metal films, which have a high electrical and thermal conductivity. Interaction with an adsorbate may also change the bonding energy of metal crystallites to non-metallic substrates. This can happen with water as an adsorbate. As discussed in Chapter 3 water can decrease the interaction of gold and silver particles with non-metallic substrates so far t h a t considerable coalescence of metal particles occurs.

F I G . 45. Models of vapour deposited metal films. a. Film with island structure. b . Continuous film with little surface roughness. c. Highly porous metal films.

Adsorption decreases the surface energy of metal particles, which can lead to a change in the stresses in the film. Parker and Krinsky (1963) studied the electrical resistance versus strain characteristics of thin evaporated metal films and observed a strain-sensitivity coefficient t h a t was smaller for continuous metal films than the corresponding value for the bulk metal. Ehrlich (1961c) argued on the basis of bulk strain-sensitivity coefficients t h a t effects of adsorption on the stress on metal films are likely to be too small to give rise to appreciable effects on the film resistance. We hence do not consider this mechanism further. More attention must be given to the possibility t h a t the charge transport occurs to a marked extent via electrons directly crossing the gaps between neighbouring metal particles. For island-type films this, besides charge transport through the substrate, is the only admitted

THE INFLUENCE OF ADSORPTION ON METAL FILMS

415

possibility. Tunnelling of electrons across gaps can also markedly contribute to the charge transport in continuous films consisting of metal crystallite connected over small surface areas only and separated by narrow gaps. Since adsorption influences the work function of metals, the potential barrier between neighbouring metal particles is changed. For films in which transport of electrons across gaps is important, adsorption will strongly affect the electrical conductance. As discussed above, many authors assume t h a t electrons are transported between metal particles in island films via the substrate. If this is correct, the conductance should not be influenced by adsorption on the surfaces of the particles. B . EFFECT OF ADSORPTION ON ELECTRICAL RESISTANCE

1. Island-type Films The effects which adsorption exerts on the resistance of metal films consisting of isolated metal particles can give information about both the mechanism of charge transport in these films and the effect of the crystallite size on the chemisorptive properties of metals. As said above, transport of electrons through the substrate is not affected by the work function of the metal particles; adsorption hence influences only the resistance of those films in which electrons directly cross the gaps between the particles. Moreover, a change in the potential barrier between two metal particles cannot change the activation energy associated with interaction of Coulombic fields surrounding small isolated metal particles t h a t governs the tunnelling of electrons. Consequently the temperature coefficient of resistance should not change when the work function of the metal crystallites is varied by adsorption. The effect of adsorption on the resistance of island-type metal films is determined by the effect on the work function. Since island-type films can consist of very small metal particles (dimensions about 30 Ä), it is possible to study the effect on the work function of these particles. Comparison with the change in the work function of large particles in thick metal films may show differences in adsorptive properties with the size of metal particles. Offret (1961) carefully studied the change in the resistance of very thin metal films evaporated in ultrahigh vacuum. I n Figure 46 Offret's measurements on the effect of hydrogen on the resistance of platinum films are represented. At the three temperatures used, the resistance starts to increase, but at 77 and 20 °K it subsequently drops below the original value. Admission of helium to a film kept at 293 and 77 °K did not affect the resistance, whereas at 20 °K the resistance falls precisely as on adsorption of hydrogen at 20 °K, except for the slight initial

416

J. W. GEUS

increase in the resistance. That adsorption of hydrogen affects the electrical resistance of island-type platinum films demonstrates t h a t electrons are transported through the vacuum separating the metal particles. The change in the resistance is determined by the effect of adsorption on the Admission of hydrogen Pumping

X

^

10

2

9

υ c ΙΛ

-20* K

%—«» Ό) 8

o

7

0

50

100 150 Time (min)

FIG. 46. Effect of hydrogen adsorption on the electrical resistance (ohms) of a platinum film with an average thickness of about 15 A. (After Offret (1961).)

work function; this is confirmed by a comparison with the effect adsorption of hydrogen has on the work function of thick continuous platinum films. I n Figure 47 we represent the change in the work function of a thick platinum film kept at 77 °K by hydrogen adsorption as measured by Mignolet (1957). The first stage with a work function increase is due to chemisorption of hydrogen. At room temperature Mignolet found only an increase in the work function of 0.15 eV by hydrogen adsorption. These increases in the work function agree with the rise in the resistance of the platinum film kept at 293 °K, as well as the temporary rise in the resistance at 77 °K. At 20 °K the hydrogen t h a t increases the work function is chemisorbed. However, subsequently a physically adsorbed layer of hydrogen molecules is presumably taken up, a conclusion reached by noting the corresponding decrease in resistance caused by helium adsorption. As must be expected for physical adsorption, the decrease in resistance is almost completely reversible as can be seen from Figure 46. The fact that the slow irreversible decrease in resistance at 77 °K is absent at 20 °K points to the decrease in work function being caused by an activated process which is too slow at

THE INFLUENCE OF ADSORPTION ON METAL FILMS

417

20 °K to proceed to a marked extent. Sachtler and Dorgelo (1960) ascribed the slow process to dissolution of hydrogen in platinum. They could suppress the dissolution of hydrogen by lowering the temperature of the platinum to 63 °K. 0-2 0-1 0 •©I

"si

-0-1 1-5 x10' 3 torr

-0-2 -0-3 0

5

— 10 15 time (min)

20

25

FIG. 47. Mignolet's results for the change in the work function (Δ93) of a thick platinum film kept at 77 °K due to adsorption of hydrogen. The hydrogen was leaked to the film at gradually increasing pressures, the final pressure being ~ 10~3 torr. (After Mignolet, 1957.)

Offret also determined the temperature coefficient of the resistance of platinum films between 77 and 90 °K as a function of the hydrogen coverage. She established t h a t the temperature coefficient decreased together with the resistance as the hydrogen coverage increased. This points to thermionic emission dominating the charge transport in Offret's films. On ageing, the platinum films used by Offret increased both their resistance and their temperature coefficient of resistance, which indicates t h a t the distances between the metal particles grew by particle migration over the surface and coalescence. Concomitantly, the effect of hydrogen adsorption strongly decreased. Though at larger interparticle distances thermionic emission should dominate, the smaller effect of hydrogen adsorption may point to electron transport through the substrate being more important for larger particles at larger mutual distances. As well as on platinum, Offret also studied adsorption of hydrogen on nickel, tungsten, molybdenum and tantalum films. The resistance of molybdenum and tantalum films increased on hydrogen adsorption at

418

J . W. GEUS

both 293° and 77 °K. The resistances of nickel and tungsten films kept at 293 °K rose also on hydrogen adsorption, but at 77 °K t h a t of nickel after an initial rise decreased irreversibly, and t h a t of tungsten fell partly reversibly. Whereas the work function of thick nickel and tungsten films at 77 °K remains above the value for the clean film on hydrogen adsorption, t h a t of small nickel and tungsten particles evidently does not. If Offret's measurements are correct, this should imply t h a t the effect of hydrogen adsorption on the work function of nickel and tungsten depends on the size of the metal particles. Confirmation and extension of the above results should be very interesting. The results Offret obtained for oxygen on very thin platinum films suggest the same sort of difference for small and large platinum particles reacting with oxygen. Adsorption of oxygen onto thick platinum films increases the work function by 1.0 to 1.2 eV, as measured by Oatly (1939), Giner and Lange (1953) and Heyne and Tompkins (1966). Offret on the other hand observed both at 293° and 77 °K after a small temporary rise a strong decrease in the resistance of platinum films t h a t was reversible to a small extent only. Hansen and Littmann (1963) measured the effect of adsorption of xenon both on the work function and the resistance of zirconium films of varying thickness. Whereas xenon adsorption decreases only the work function of thick films and did not affect the resistance, very thin films displayed a decrease in the work function as well as in the resistance. This again demonstrates t h a t the charge transport in island-type films occurs at least partly through the vacuum. Fehlner (1966a, b ; 1967) investigated the effect sorption of oxygen has on the resistance of island-type nickel, titanium and zirconium films; interaction of these metals with oxygen is not restricted to a monolayer. This author observed the resistance to change during admission of oxygen as indicated in Figure 48. The initial flat part of the resistance versus time curve is brought about by adsorption exclusively on top of the metal particles. I n this stage the work function of the metal surfaces at the gaps is not affected. When adsorption of oxygen has decreased the sticking coefficient of the outer surface, oxygen molecules can penetrate into the gaps. Oxygen adsorption on the gap surfaces raises the potential barrier between metal particles and hence the resistance. There is L E E D evidence t h a t points to adsorption of oxygen on metal surfaces proceeding in patches, the area of which grows during exposure to oxygen (Geus, 1970). Owing to this, the proportion of low work function area at the gaps steadily decreases. When the patches meet, the total metal surface assumes rather rapidly the work function corresponding to full coverage and the resistance increases abruptly.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

419

Sorption of oxygen beyond a monolayer, which proceeds more slowly than adsorption of the first monolayer, raises the resistance further as can be seen in Figure 48. This indicates t h a t at the surface the metal is converted into a non-conducting compound, the thickness of which increases on continued exposure to oxygen. The growing non-conducting layer on the metal particles increases the distances between the metallic-conducting parts of the metal crystallites and, hence, the resistance. The results obtained by de Boer and Kraak (1937) on islandtype molybdenum films show rapid adsorption of a monolayer of oxygen

Adsorption on outer surface

Penetration into gaps

Monolayer coverage

Oxidation beyond monolayer

F I G . 48. Change in the resistance of an island-type titanium film on interaction with oxygen at 6 x 1 0 - 8 torr and 26 °C. (Reproduced with permission from Fehlner (1966b). "Proceedings of the 1965 Transactions of the Third International Vacuum Congress" Vol. 2, Pergamon Press, Oxford, p . 691.)

at 88 °K, oxidation beyond a monolayer at room temperature, and physical adsorption of oxygen over the sorbed layer at 88 °K (Geus, 1970). From the above discussion, it is apparent t h a t the effects of adsorption on the resistance of island-type metal films can be accounted for very well. The experimental data give interesting information about the nature of both adsorbed species and the conduction process in such films. Island-type films of metals with low melting points deposited on glass in ultrahigh vacuum are very unstable and the results of Offret

420

J. W. GEUS

and Fehlner with very thin copper, gold and aluminium films are therefore not easy to interpret. I t might be interesting to deposit island-type films of low melting metals onto substrates like bismuth oxide which bond metal atoms more strongly than well-baked glass. 2. Continuous Films As discussed above adsorption can influence the electrical conductance of continuous metal films in three ways, by changing: (a) The reflection of conduction electrons at metal surfaces. (b) The conductivity of one or more atomic layers of the metal surface; and (c) The transport of electrons through gaps separating the metal particles in porous films. We here assume t h a t the metal films used are presintered sufficiently to prevent migration of grain boundaries or sintering of metal particles by liberation of the heat of adsorption. Since the above three mechanisms will generally be operative together, it is difficult to disentangle the effect of each mechanism. We therefore shall discuss first cases where either mechanism (a) or mechanism (b) is dominating. Thereafter we can consider cases where two or three of the above mechanisms are acting. To deal properly with the effects on the electrical conductance we first must discuss experiments with adsorbates t h a t affect the conductance in a simple way. When gases can be adsorbed in several states which influence the conductance differently, involved arguments are required to separate the different effects on the conductance properly and the change in the proportions of different adsorbed species. Though carbon monoxide is known to be bonded to metal surfaces in more than one adsorbed state, its effect on the conductance of metals is rather simple. The evidence for the above mechanisms will hence be developed by using data for adsorption of carbon monoxide. Interaction of metal surfaces with oxygen is somewhat more complicated, as oxygen can affect also the subsurface layers of metals. Nevertheless, the effect of oxygen sorption on the electrical conductance can be explained in a reasonably straightforward way. Next results for hydrogen adsorption t h a t are more difficult to account for will be presented, after which transport of molecules through narrow pores in evaporated films will be discussed. Finally, reaction with nitrogen and with more complex molecules will be reviewed. a. Adsorption of Carbon Monoxide and Oxygen. As mentioned above, evaporated tungsten films have a large residual resistivity which means

THE INFLUENCE OF ADSORPTION ON METAL FILMS

421

that the mean free path of conduction electrons in tungsten films is relatively short. Consequently, the effects of adsorption on the resistivity of the metal surface layer will predominate. When adsorption causes the metal surface layer to acquire a resistivity large compared with that of the metal itself, adsorption will change the geometric factor of the metallic conducting phase. In Figure 49 the change in conductance of an evaporated tungsten film as a function of the carbon monoxide coverage is represented. After 101A molecules CO cm" 2 2

3

4

5

FIG. 49. Effect of adsorption of carbon monoxide on the electrical conductance (λ) of an evaporated tungsten film. Gas admitted at 273 °K, conductance measured at 273 °K ( Δ ) and 77 °K (A). (Reproduced with permission from Geus, Koks and Zwietering (1963). J.Catal. 2, 274.)

an initial less steep decrease, the conductance fell approximately linearly with coverage until about 3 x 1014 carbon monoxide molecules cm- 2 were taken up. Subsequently, the conductance decreased more slowly. At 77 °K the tungsten film adsorbed considerably more carbon monoxide than at 273 °K and without a further decrease in conductance. Obviously, carbon monoxide is adsorbed in one or more states

422

J. W. GEUS

decreasing the conductance and in one or more states t h a t do not affect the conductance. When the straight part of the conductance versus coverage plot is extrapolated, a coverage of 3.7 x 1014 molecules c m - 2 of the state(s) decreasing the conductance is obtained. This is in fair agreement with the results of Brennan and Hayes (1965) who observed a very high heat of adsorption steeply decreasing from 125 to about 80 kcal mole - 1 at a coverage of 1 x 1014 molecules cm - 2 . At higher coverages the heat of adsorption decreased linearly from 80 to about 65 kcal mole - 1 at a coverage of 4.1 x 1014 molecules cm - 2 , after which the heat of adsorption sharply decreased. The states t h a t do not change the conductance are populated at 273 °K much less than at 77 °K. From Figure 49 it can be seen t h a t the relative decrease in conductance does not vary markedly with the temperature. In view of the high residual resistivity of tungsten films, this must be expected. Since at 273 °K the scattering by thermal vibrations is only about one tenth of the scattering by lattice defects, the mean free path of the conduction electrons is at 273 °K also about one tenth smaller than t h a t at 77 °K. This implies t h a t the ratio of the collisions with the metal surfaces and those with lattice waves only slightly depends on the temperature. Consequently, if adsorption influences the reflection conditions of conduction electrons at the tungsten surface, this will affect the conductance slightly more at 77 °K than at 273 °K. This can also be rationalized from the fact t h a t a change in the reflection of conduction electrons at the metal surface increases the temperature-independent part of the resistance only. As a result, the increase in the resistance does not depend on the temperature, whereas the relative change in resistance does as, owing to phonon scattering, the total resistance increases with temperature. The geometric factor of the metallic conducting phase does not depend on the temperature, if thermal expansions are neglected. A change in the geometric factor of the conducting phase hence gives rise to a relative change in the conductance t h a t is independent of temperature. I n agreement with the above, the relative decrease in conductance in Figure 49 is slightly larger at 77 °K than at 273 °K. I n Table 4 the effects of carbon monoxide adsorption on the geometric factor and the residual resistivity of tungsten films are given. From the data in this table it can be seen t h a t both the reflection of the conduction electrons and the geometric factor is influenced. That the specular reflection of the conduction electrons is decreased shows t h a t at least a fraction of the metal crystallites have facets in their surface large enough to afford specular reflection. Moreover, it demonstrates

THE INFLUENCE OF ADSORPTION ON METAL FILMS

423

that after adsorption the potential energy on these facets has a periodicity larger than that of the original surface. TABLE 4

Effect of Carbon Monoxide Adsorption on the Geometric Factor G, and Residual Resistivity pR, of Evaporated Tungsten Films G (cm-1)

Film

No.

after

G

V o/

before 5

PR (ohm cm)

f—\

(%)

5

after

27

3.45 X 10

3.28 X 10

5.2

3.30 X 10"

29

3.84

3.62

6.1

4.66

„

„

„

(^\

\ *V

before 5

3.22 X 10" 4.53

„

(%)

5

2.4 2.8

If we assume the film surface to contain {110} and {100} planes only, having atomic densities of 1.4 x 1015 and 1.0 X 1015 cm - 2 , the number of carbon monoxide molecules adsorbed with an effect on the conductance (about 3.7 x 1014 cm - 2 ) is too small to cover all the metal surface atoms even for the most probable two-site adsorption (Gomer, 1967). Since a fraction of the metal atoms does not adsorb carbon monoxide molecules in a way t h a t decreases the conductance, a surface periodicity larger than t h a t of the original surface is reasonable. According to equation (II)-(46a) of section I I , the change in geometric factor is equal to (1—/>0//>s) (dt/t 0 ). We shall discuss the implications of the experimental values for this quantity after a discussion of the effect of oxygen sorption on the conductance of tungsten films. Figure 50 shows the effect sorption of oxygen has on the conductance of an evaporated tungsten film. To prevent local sorption beyond a monolayer, oxygen was admitted at 77 °K and, after equilibrium had been established, the film was heated up to 273 °K. As for carbon monoxide, the relative decrease in conductance does not depend on the measuring temperature. Up to a coverage of about 5 χ 1014 oxygen molecules cm - 2 , the decrease in conductance observed at 77 °K was maintained on heating up to 273 °K and recooling. At higher coverages, the conductance did not change on admission of oxygen at 77 °K. On heating up to 273 °K the physically adsorbed oxygen was partly desorbed and slowly readsorbed. During this slow uptake the conductance decreased; the decrease was maintained on recooling to 77 °K. I n agreement with other evidence, a monolayer of oxygen is adsorbed at 77 °K. At temperatures above about 150 °K, oxygen is sorbed beyond a monolayer in an activated process (Lanyon and Trapnell, 1954).

424

J. W. GEUS

Figure 50 demonstrates that the effect on the conductance per oxygen molecule is smaller on sorption beyond a monolayer. In Table 5 the effects of oxygen sorption on the geometric factor and the residual resistivity of tungsten films are collected. TABLE 5

Effect of Oxygen Sorption on the Geometric Factor G, and Residual Resistivity />R, of Evaporated Tungsten Films G (cm- 1 )

Film No. after

pR (ohm cm)

before

(%)

after

before

(%)

24

0.432 X 105

0.384 X 105

12.5

2.24 X 10~5

2.27 X 10- 5 —1.3

25

1.22

„

1.07

„

14.0

3.48

„

3.45

„

0.9

28

2.71

„

2.40

„

12.9

3.62

„

3.60

„

0.6

109

3.40

„

3.07

„

10.75 3.75

„

3.76

„

—0.3

10u molecules 0 2 cm"2 2 4 6 \ Λ

\ \

S° "5

X

s

« \

-10

■

^

FIG. 50. Effect of oxygen sorption on the conductance (λ) of an evaporated tungsten film (No. 28). Oxygen was admitted at 77 °K. The conductance was measured at 77 °K before (Δ) and after (A) equilibrating at 273 °K, and also at 273 °K ( x). (Reproduced with permission from Geus, Koks and Zwietering (1963). J. Catal. 2, 274.)

THE INFLUENCE OF ADSORPTION ON METAL FILMS

425

I t appears t h a t the residual resistivity does not change beyond the experimental error, since small positive and negative effects are observed. This is in remarkable contrast with the effect of carbon monoxide adsorption. That the reflection of the conduction electrons is not affected by adsorption of a monolayer of oxygen, which influences the metal structure as appears from the effect on the geometric factor, points to a surface structure with a spacing t h a t is equal to t h a t of the original metal surface. This explanation is supported by L E E D data. Germer and May (1966) observed t h a t the L E E D pattern of a tungsten (110) plane returned to t h a t characteristic for the clean surface after sufficiently extensive interaction with oxygen. On exposure to oxygen at temperatures below about 600 °K, Anderson and Danforth (1965) did not find a L E E D pattern for (100) tungsten t h a t deviated from t h a t of the clean surface. The author could rationalize the total complex of data for the interaction of oxygen with molybdenum and tungsten, by supposing t h a t the oxygen adatoms are bonded on top of the metal surface atoms t h a t are presumably slightly lifted (Geus, 1970). I n view of the above, it can be assumed t h a t the tungsten surface layer is rendered non-conducting on adsorption of a monolayer of oxygen. Hence ps^>Po a n ( i ^ e relative change in the geometric factor is according to equation (II)-(46a) and Table 5 - d t / t 0 = 0.107 to 0.14 Since one layer of tungsten corresponds to a thickness of about 2.5 A, the data of Table 5 suggest t 0 = 23 to 18 A. I n view of the possibility t h a t contact resistances between the particles may determine the film resistance, we here only state t h a t these values are not unreasonable in view of the diameter of the metal crystallites, which is about 50 A. A value for t 0 of about 20 A leads for carbon monoxide adsorption to (1 — PQIPS) dt = 1.0 to 1.2 A. If pa^>Po> this should imply t h a t about one half of the metal surface atoms are rendered non-conducting on adsorption of carbon monoxide. I n view of the effect on the reflection of the conduction electrons this is reasonable. If, on the other hand, the surface layer is converted into a state with p8 = (2 to 2.5)/>0, a complete atomic layer is involved, which cannot be excluded either. (In the determination of the geometric factor, we neglect the change in temperature dependence brought about by the thin layer with resistivity />s.) Comparison with results on iron films, however, will modify this interpretation. As shown in Figure 39 iron films can be prepared with strongly different porosities by depositing on to substrates kept at 77 and 273°K. Measurements on iron films of different porosities are therefore very

426

J. W. GEUS

suitable to investigate the effect of adsorption on the conductance of metal films with different structures. Figure 51 represents a measurement of the effect of carbon monoxide adsorption on the conductance of an iron film deposited on glass kept at 77 °K. From this figure it appears that the effect of carbon monoxide on the conductance of iron films differs in two respects from that on the conductance of tungsten films: the coverage of carbon monoxide adsorbed in a state that decreases the conductance is appreciably smaller 10 u molecules CO cm"2 2

4

6

-5 o

-10

-15 FIG. 51. Effect of carbon monoxide adsorption on the electrical conductance (λ) of an iron film (No. 21) deposited on glass kept at 77 °K. Carbon monoxide admitted at 273 °K; conductance determined at 273 °K before (O) and after ( # ) cooling to 77 °K and rewarming to 273 °K, and at 77 °K ( x ) . (After Geus and Koks, unpublished.)

in iron films and the relative change in conductance depends strongly on the temperature. That a change in the reflection of conduction electrons at the metal surfaces causes the relative decrease in conductance to be strongly temperature dependent follows from the relatively low residual resistivity of iron films. At 273 °K the mean free path is a factor of 1.5 larger than at 77 °K for the film of Figure 51. Iron films deposited on glass kept at 273 °K behave in the same way on adsorption of carbon

THE INFLUENCE OF ADSORPTION ON METAL FILMS

427

monoxide. This can be seen in Figure 52 where the change in conductance of an iron film deposited on glass kept at 273 °K is represented. Owing to the large crystallite size in the film deposited on glass kept at 273 °K, the effects on the conductance are smaller. Figure 53 shows the effect on the geometric factor and residual resistivity of the film of Figure 52. It appears that the geometric factor slightly decreases, whereas the residual resistivity strongly rises during adsorption. The small decrease 0

rcr^

2

1

101A molecules CO cm"2 U 6 ΓΊ 1

8

1

10

r

FIG. 52. Effect of carbon monoxide adsorption on the electrical conductance (λ) of an iron film (No. 25) deposited on glass kept at 273 °K. Carbon monoxide admitted at 273 °K; conductance determined at 273 °K before (O) and after ( · ) cooling to 77 °K and rewarming to 273 °K, and at 77 °K ( x ) . (After Geus and Koks, unpublished.)

in the geometric factor is presumably due to a slight additional sintering brought about by cycling the film temperature from 77 °K to 273 °K. As can be seen from Table 6 where data for six iron films are collected, the behaviour of Figure 53 is displayed by all iron films. This implies that only the reflection of electrons at the film surface is influenced by adsorption of carbon monoxide, whereas the resistivity of the surface layer remains unaffected. As remarked above, carbon monoxide is adsorbed on iron in a state leading to scattering of the conduction electrons at the iron surfaces and a state that does not influence the conductance. The total amount of carbon monoxide taken up is rather low if compared with the number of iron surface atoms. A final coverage of about 7.5 x 1014 carbon monoxide molecules cm -2 is obtained at 273 °K, while the atomic densities in iron (110), (100), and (211) surfaces are respectively 1.7 x , 1.2 x and

428

101A Molecules CO cm-2 FIG. 53. Effect of carbon monoxide adsorption on the residual resistivity (pR) and geometric factor (G) of the iron film (No. 25), the change in conductance of which is represented in Figure 52. Before cooling to 77 °K, · , A; after cooling to 77 °K, O» Δ · (After Geus and Koks, unpublished.) TABLE 6

Effect of Carbon Monoxide Adsorption on the Geometric Factor G, and Residual Resistivity p R . of Evaporated Iron Films

Film No>>

(b)

G (cm-1) after

1

before

(%)

(ohm cm)

after

before

\ PRO/

(%)

10.45 X 10- 6

8.74 X 10-e

— 2.2

11.2!

„

8.0e

„

39.1

„

-7.5

13.8

„

10.7

„

29.0

14.8

„

-0.7

7.18

„

6.70

„

7.2

„

9.3

„

-1.1

4.74

„

4.45

„

6.5

„

33.4

„

+ 0.0

9.6e

„

9.3X

„

3.7

4.2 X 10*

4.2 X 10*

19

8.8

„

9.0

„

21

17.2

„

18.6

20

14.7

„

25

9.2

28

33.4

8

PR

0.0

19.6

(a) films No. 8, 19 and 21 deposited on glass kept at 77 °K; films 20, 25 and 28 on glass kept at 273 °K. (b) films deposited on glass kept at 77 °K are more susceptible to sintering by thermal cycling than those deposited on glass kept at 273 °K.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

429

1.0 x 1015 cm - 2 . The total coverage therefore roughly corresponds to about one carbon monoxide molecule per two iron surface atoms. The amount adsorbed with an effect on the specular reflection of conduction electrons is only 3.1 to 3.7 x 1014 molecules cm - 2 ; films deposited on glass at 273 °K show larger values than those deposited at 77 °K. I n Figure 54 a configuration leading to a total coverage of 4.2 x 1014 carbon monoxide molecules c m - 2 is represented. As can be seen from this figure, adsorption of more carbon monoxide leads to strong interaction between the adsorbed molecules. Owing to this, the spacing of either the

F I G . 54. Configuration of carbon monoxide molecules adsorbed on a (110) surface of iron. Each set of differently shadowed molecules corresponds to an array with a coverage of 2.1 x 1014 molecules c m - 2 ; the combined coverage is 4.2 x 1014 molecules c m - 2 . The use of two metal atoms per adsorbed CO is assumed.

first adsorbed carbon monoxide molecules or of the iron atoms displaced in bonding these molecules is larger than the spacing of the original (110) surface. The wavelength of the conduction electrons is evidently so small t h a t the surface represented in Figure 54 gives rise to scattering of the conduction electrons. Mutual repulsion of adsorbed carbon monoxide molecules even at much larger mutual distances than their van der Waals diameter is suggested by the decrease in the heat of adsorption. In Figure 55 measurements of Brennan and Hayes are given. I t can be seen t h a t the heat of adsorption steadily decreases until about 4 x 1015 carbon monoxide molecules c m - 2 are adsorbed. The amount of carbon monoxide taken up with a high heat of adsorption corresponds

430

J . W. GEUS

rather well with the amount adsorbed with a decrease in specular reflection. We tentatively suggest t h a t the configuration of one of the equally shadowed molecules in Figure 55 is gradually filled up with the other one; repulsive interactions between the configurations lead to the continuous decrease in the heat of adsorption. Repulsive interactions between admolecules operating over some atomic diameters seem to be quite usual in view of the many ordered L E E D patterns of covered metal surfaces showing spacings larger than t h a t of the uncovered

T

50

o E ν

I 30

> · ^ ! · Θ · Θ• Q

©

- -r^^·-·—

Q.

8

*§ 20 o

S 10

x

0

1

J

2

3

1A

L

A

10 molecules CO cm"

5

6

2

F I G . 55. Heat of adsorption of carbon monoxide on evaporated iron films. (Reproduced with permission from Brennan and Hayes (1965). Phil. Trans. R. Soc. A258, 347.)

metal surface. The larger amount of carbon monoxide taken up by films deposited on glass at 273 °K is presumably due to the larger fraction of most densely packed {110} planes in the surface of these films, while the films deposited at 77 °K have more {100} planes, as well as others of lower density. The difference in the effect of carbon monoxide on the conductance of tungsten and iron films is remarkable. Whereas the geometric factor of tungsten films is mainly affected, iron films show only a decrease in specular reflection. The most reasonable explanation for this difference is, we believe, a differing fraction of atomically rough planes in the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

43 1

surfaces of iron and tungsten films. It is likely that tungsten films contain a markedly larger fraction of atomically rough planes. Since the metal atoms in these planes are less densely packed, every atom can bond strongly a carbon monoxide molecule and consequently lose at least partly its metallic conductivity. We therefore suggest that the limited effect carbon monoxide adsorption has on both the geometric factor and the residual resistivity of tungsten films is due to the presence of an appreciable fraction of atomically rough planes in the surface of these films. Bonding of about 4 x 1014carbon monoxide cm-2 molecules by a (110) iron surface in which the metal atoms are surrounded by many neighbouring metal atoms does not decrease the metallic conductivity of the surface layer markedly. The strong next-nearest neighbour interaction between b.c.c. metal atoms may also play a role here. Whereas adsorption of carbon monoxide on iron remains limited, as was apparent above, interaction of iron surfaceswith oxygen proceeds to several monolayers. Brennan, Hayward and Trapnell ( 1960) observed an uptake of about 3.5 oxygen atoms per iron surface atom with a heat of adsorption of 133 kcal mole-l of oxygen. The heat of adsorption is of the same order of magnitude as the heat of formation of bulk oxides (e.g. FeO 130 kcal mole-l of OJ, which shows that a surface oxide is formed with a structure that has some resemblance to that of the bulk oxide. Since it is likely that the conductivity of the surface oxide is lower than that of iron, sorption of oxygen can be expected to affect both the residual resistivity and the geometric factor of iron films. I n Figure 56 the effect of oxygen sorption on the conductance of an iron film deposited on glass kept at 77 OK is represented. It appeares that the interaction is very extensive; at 273 OK about 40 x 1014oxygen molecules cm-2 were taken up. For an average number of iron surface atoms of 1.6 x 1015 cm-2, the oxygen sorption corresponds to an uptake of about 5 monolayers. Up to a coverage of 12 x lOI4 oxygen molecules cm-2 the decrease in the conductance obtained after dosing at 77 OK was maintained after heating up to room temperature. At higher coverages, heating to 273 O K brought about a further decrease in conductance, while at a coverage of about 22 x 1014 oxygen molecules cm-2 oxygen does not penetrate through the adsorbed layer at 77 OK. As appears from Figure 57, oxygen sorption affects both the geometric factor and the residual resistivity of iron films. The fact that Brennan, Hayward and Trapnell (1960) found the heat of sorption to remain constant until 3.4 monolayers of oxygen was taken up, indicates that each dose is sorbed so as to give rise to the same surface structure. As will be dealt with later in the section on the transport of admitted gas

432

J . W. GEUS

101A Molecules 0 2 cm"2

F I G . 56. Effect of oxygen sorption on the electrical conductance (λ) of an iron film (No. 29) deposited on glass kept at 77 °K. Oxygen admitted at 77 °K; conductance measured at 77 °K and, after establishment of equilibrium at 77 °K, at 273 °K. Measured at 77 °K before heating to 273 °K, O; measured at 77 °K after heating to 273 °K, · ; measured at 273 °K, x . (After Geus and Koks, unpublished.)

molecules over the large surface of evaporated films, a region where the surface has taken up about 20 x 1014 oxygen molecules c m - 2 moves gradually inwards towards the bottom of the film. This can be concluded also from Figure 57. If a low oxygen coverage was established on the complete iron surface, after which the coverage increased uniformly over the surface, the residual resistivity should increase to a maximum before the rise of the geometric factor. This is to be expected for a uniform covering of the surface, since the coverage required to destroy the specular reflectivity of a metal surface is appreciably lower than t h a t required to destroy the metallic conductivity of the surface layer. Since in Figure 57 the residual resistivity and the geometric factor increase at an equal rate, the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

433

coverage is very inhomogeneous. After about 20 x 1014 oxygen molecules c m - 2 were adsorbed, the residual resistivity rose more slowly, while the geometric factor still increased steadily. This indicates t h a t after sorption of about 20 x 1014 oxygen molecules cm - 2 , transport of oxygen molecules through the narrow pores in the film starts to keep up with the penetration of oxygen through the adsorbed layer (or alternatively the migration of iron ions through the adsorbed layer) for layer growth to occur.

0

10

20

30

40

10u molecules 0 2 cm"2 F I G . 57. Effect of oxygen sorption on the residual resistivity (pR) and geometric factor (G) of the iron film (No. 29) the decrease in conductance by oxygen sorption of which is represented in Figure 56 (77 °K). (After Geus and Koks, unpublished.)

The change in the residual resistivity and geometric factor of iron films due to oxygen sorption reflects the film structure. This can be concluded from a comparison of Figures 57, 58 and 59. For the film deposited on glass at 273 °K, the reflection of the conduction electrons at the surface was affected before the geometric factor changed. After about 4 x 1014 oxygen molecules c m - 2 were taken up, the geometric factor increased. The difference in behaviour of films deposited on glass kept at 273 ° and 77 °K can be explained from their structure as evident

434

J. W. GEUS

from electron micrographs. The iron films deposited at 77 °K have crystallites with flat tops, whereas those deposited at 273 °K have crysstallites that are more rounded off. When oxygen is sorbed on to the round tops of the metal crystallites of the 273 °K films, only the nature

- o 10
«s

§

JS*

5h S

s

*/·

»/ A - · 4-

o l g > * f t t .«-»i-*-

- * - · "* ■

-*-*-*10 15 20 1A 2 10 molecules 0 2 cm"

25

FIG. 58. Effect of oxygen sorption on the residual resistivity (pR) and geometric factor (G) of an iron film (No. 32) deposited on glass kept at 273 °K. (After Geus and Koks, unpublished.)

Glass kept at 273°K

Glass kept at 77°K FIG. 59. Structure of iron films deposited on glass kept at 273 ° and 77 °K.

of the reflection of the conduction electrons is changed. On penetration of oxygen between the metal crystallites, the electron transport through the film is influenced more strongly by a change of the reflection at the gap surfaces, together with an increase of the geometric factor owing to a decrease in the conductivity of the surface layer.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

435

Unlike the effect of carbon monoxide on the electrical conductance of iron films, the change in conductance of nickel films by carbon monoxide has been studied much more profoundly (Zwietering, Koks and van Heerden, 1959; Suhrmann, Wedler and Heyne, 1959; Suhrmann, Ober and Wedler, 1961; Geus, 1964; Wedler and Fouad, 1964; Cukr, Merta, Adamek and Ponec, 1965). Since nickel atoms, which crystallize in the f.c.c. structure, are much more mobile over terracelike nickel surfaces than metal atoms crystallizing in the b.c.c. structure (see Chapter 3), only nickel films on glass kept at 77 °K have a very large surface area. The investigations on the effect of adsorption on the conductance of nickel are therefore best done with nickel films deposited on glass kept at 77 °K. In Figure 60 the change in conductance of a nickel film by adsorption of carbon monoxide is represented. Carbon monoxide was admitted to the film kept at 273 °K; after equilibrium was established, the conductance was measured. Subsequently the film was cooled down to 77 °K before admitting the next dose. Figure 60 shows that carbon monoxide affects the conductance of nickel analogously to that of iron. The relative 10 u CO molecules cm"2

1 *..

V

_

-1

\

8

— i

1

10

—1

\

o

< <

-2

^

6

— - ^

x

-3

\

\ x

*-—

x

FIG. 60. Effect of carbon monoxide adsorption on the electrical conductance (λ) of a nickel film (No. 34) deposited on glass kept at 77 °K. Carbon monoxide admitted at 273 °K. After establishment of equilibrium, film cooled down to 77 °K and conductance determined at 77 °K ( x ) . Conductance measured at 273 °K before and after cooling to 77 °K (O, Δ ) . (After Geus and Koks, unpublished.)

436

J . W. GEUS

decrease in conductance is at 77 °K appreciably larger than at 273 °K, which points to a change in the reflection of the conduction electrons at the film surface. Moreover, carbon monoxide decreases the conductance up to a coverage of about 5.2 x 1014 molecules cm - 2 , whereafter more gas is taken up without an effect on the conductance. After adsorption of about 8 x 1014 molecules cm - 2 , equilibrium pressures were observed at 273 °K. I n Figure 61 the change in residual resistivity and geometric factor corresponding to the measurements of Figure 61 is given. I t can

3

o o
S

1

o

0 10u CO molecules cm"2 F I G . 61. Change in residual resistivity (pR) and geometric factor (G) of the nickel film the effect of carbon monoxide on the conductance of which was represented in Figure 60.

be seen t h a t the residual resistivity increases strongly, as does the residual resistivity of iron films, on carbon monoxide adsorption; however, in contrast with iron films, the geometric factor has increased too, though to a limited extent only. Edmonds and Pitkethly (1969) obtained L E E D evidence for the configuration of an adsorbed carbon monoxide layer given in Figure 62. They found this surface structure to be present in three equivalent positions on the nickel surface. Owing to boundaries between domains with different orientations, a (111) surface will adsorb a somewhat lower number of carbon monoxide molecules at room temperature than the 6.9 x 1014 molecules c m - 2 indicated in Figure 62. Since the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

437

spacing of the surface structure in Figure 62 is not much larger than t h a t of the (111) plane of nickel itself, the wavelength of the conduction electrons in nickel must be rather small. The amount of carbon monoxide taken up with a decrease in the conductance is about 5.2 x 1014 molecules cm - 2 . This is markedly lower than the coverage corresponding to the structure of Figure 62. Besides the presence of domain boundaries, which lower the coverage, this is due to a marked fraction of higher

FIG. 62. Carbon monoxide on a nickel (111) surface. The configuration is in agreement with a LEED pattern observed by Edmonds and Pitkethly (1969). Coverage 6.9 x 10 14 molecules c m - 2 ; each carbon monoxide molecule is supposed to be bonded to two nickel surface atoms.

index planes in the surface of nickel films deposited on glass kept at 77 °K and sintered at about 300 °K. King (1968) investigated the structure of surfaces of evaporated nickel films by determining desorption spectra of nitrogen taken up at 77 °K. His results point to a marked fraction of (110) or higher index planes. Brennan and Hayes (1965) determined the heat of adsorption of carbon monoxide on nickel films. Figure 63 shows t h a t up to a coverage of about 4 x 1014 molecules cm - 2 , carbon monoxide is adsorbed on nickel with a substantial heat of adsorption. The heat of adsorption does not decrease markedly with growing coverage in contrast to t h a t of carbon monoxide on iron. This suggests a much smaller repulsive interaction between carbon monoxide molecules adsorbed on nickel

438

J. W. GEUS

compared to iron, to which the relative closeness of packing of the adsorbed molecules in Figure 62 points too. The conductance versus coverage plot of Figure 60, moreover, demonstrates that a coverage of about 5 x 1014 molecules c m - 2 on nickel is easily obtained. If a configuration less densely packed than t h a t of Figure 62 was more stable, a fraction of the molecules should be sufficiently mobile to migrate to parts of the surface not yet covered. As long as the total uptake by a nickel 50 E

i

40 '

—"8--'■—°—o_

30 o 20 10 O

10

O I

0

1

1

1 2 3 4 10u CO molecules cm"2

I

I

5

FIG. 63. Heat of adsorption of carbon monoxide on nickel. (Reproduced with permission from Brennan and Hayes (1965). Phil. Trans. R. Soc. A258, 347.)

film is limited, carbon monoxide molecules should migrate from parts of the surface covered initially to parts less easily accessible from the gas phase. As a result, the increase of the residual resistivity should be complete at a considerably lower coverage since, for a homogeneous distribution of adsorbed molecules over the surface, a very low coverage is sufficient to destroy the specular reflection of the conduction electrons. We now must discuss two other differences in the effects of carbon monoxide on the conductance of iron and nickel films. The first is the slight increase in the conductance at 77 °K when the coverage is raised above about 7 x 1014 molecules cm - 2 ; the second is the increase in the geometric factor of nickel films by adsorption of carbon monoxide. The conductance of iron films does not display these phenomena. These effects are both due to nickel carbonyl being formed more easily than iron carbonyl. First, the heat of formation of nickel carbonyl (see Table 3) is larger than t h a t of iron carbonyl. More important, however, is t h a t a nickel atom must react with four carbon monoxide molecules to form

THE INFLUENCE OF ADSORPTION ON METAL FILMS

439

nickel carbonyl, whereas an iron atom must either take up five carbon monoxide molecules or form a polymeric carbonyl, which is kinetically still more difficult. I t consequently can be expected t h a t on surfaces t h a t do not contain close-packed crystallographic planes nickel carbonyl is formed, but this does not proceed on higher index iron planes. Sachtler, Kiliszer and Nieuwenhuys (1968) obtained evidence t h a t at room temperature nickel carbonyl volatilizes from nickel films even at rather low carbon monoxide pressures. From the results of Wedler and Fouad (1964) formation of nickel carbonyl can also be concluded. At 273 °K and pressures of about 8 x 10 - 3 torr these authors measured a total uptake of carbon monoxide of three or four times the amount t h a t is adsorbed with a decrease in conductance: this corresponds to 15 to 20 X 1014 molecules cm - 2 , a number of molecules t h a t cannot be accommodated on an undisturbed metal surface. Whereas adsorption of carbon monoxide on nickel (111) and presumably also on nickel (100) planes affects a fraction of the nickel surface atoms to a limited extent only, and hence does not destroy their metallic conductivity, on (110) all nickel surface atoms are involved in binding carbon monoxide molecules (Park and Farnsworth, 1964b). Owing to this, the metal surface loses its metallic conductivity. Since the fraction of the surface t h a t does not contain close-packed planes is limited, the change in the geometric factor of the metallic conducting film remains small. Consequently, the effect on the reflection of the conduction electrons at close-packed planes predominates, as can be seen from the much larger change in the residual resistivity. When the nickel atoms in the higher index planes bind carbon monoxide molecules, the reaction stops unless the carbon monoxide pressure is raised. At larger pressures formation of gaseous nickel carbonyl can occur. Since the nickel atoms were probably already lifted somewhat from their original positions in the adsorption step, further reaction does not affect the conductance; the reflection at the surface remains diffuse. At low temperatures however, nickel carbonyl is physically adsorbed on the nickel surface. Adsorption of nickel carbonyl decreases the work function of the nickel surface. Owing to the decrease of the potential barrier, transport of electrons across gaps is facilitated and the conductance increases. Since transport of electrons through vacuum comprises a very small fraction of the total charge transport through the film, the effect of a decrease in work function on the conductance is also very small. I t is nevertheless perfectly reproducible, as Wedler and Fouad (1964) noted exactly the same slight increase in conductance as displayed in Figure 60. Interaction of a nickel film with oxygen is very interesting, since the

440

J . W. GEUS

oxygen can be dosed in two ways. The first is admission of molecular oxygen to a film kept at 77 °K, just as was done for iron films. The second is reaction with nitrous oxide. At low pressure nitrous oxide slowly decomposes on nickel surfaces into oxygen t h a t is chemisorbed and nitrogen t h a t is either weakly adsorbed and removed by oxygen, or immediately desorbed. Since at low pressures decomposition of nitrous oxide occurs more slowly than transport into the gaps in the film, it is possible to arrive at a nearly homogeneous distribution of adsorbed oxygen atoms over the film surface.

0

Ρ^^^

- ^ -χ ^

10u CO molecules cm"2 5 10 1

1

15 1

~

F I G . 64. Decrease in conductance (λ) of an evaporated nickel film by reaction with molecular oxygen. Gas admitted at 77 °K. Conductance measured at 77 °K before (O) and after ( · ) heating to 273 °K, and at 273 °K ( x ). (After Geus and Koks, unpublished.)

As can be seen in Figure 64, interaction with molecular oxygen affects the conductance of a nickel film in a way analogous to t h a t for iron. Up to an uptake of about 10 x 1014 molecules cm - 2 , the conductance does not decrease further on heating to 273 °K. At higher coverages a small further decrease was observed after heating to 273 °K. As the most closely packed plane of nickel, the (111), contains 1.86 x 1015 atoms cm - 2 , sorption beyond a monolayer is evident from the total uptake t h a t is about 3 x 1015 oxygen atoms cm - 2 . As Figure 64 shows, the conductance first decreases slowly on admission of molecular oxygen. When a nickel film reacted with nitrous oxide, the conductance decreased as represented in Figure 65. The increase in geometric factor and residual resistivity by reaction with nitrous oxide and molecular oxygen is given in Figure 66.

THE INFLUENCE OF ADSORPTION ON METAL FILMS

441

Iron films deposited on glass at 273 °K and nickel films on glass at 77 °K have rather comparable structures. This follows from the specific surface areas represented in Figure 39, but also from electronmicrographs. Accordingly, the effects of oxygen on the residual resistivity and geometric factor of such iron (Figure 58) and nickel films (Figure 66) are analogous, and the explanations are also similar. Oxygen from nitrous oxide causes both the residual resistivity and the geometric 10 u oxygen atoms cm"2

FIG. 65. Decrease in conductance (λ) of an evaporated nickel film by reaction with nitrous oxide at 273 °K. Conductance measured at 273 °K before (O) and after ( # ) cooling to 77 °K, and at 77 °K ( x ). (After Geus and Koks, unpublished.)

factor of nickel films to increase from the beginning. As said earlier, a low coverage of adsorbed atoms is sufficient to destroy specular reflection of the conduction electrons at the surface. This is apparent from Figure 66, where the residual resistivity reaches a maximum at a coverage of 2 to 4 x 1014 oxygen atoms cm - 2 . Since on reaction with nitrous oxide, oxygen is adsorbed at the contacts between the nickel crystallites from the beginning, where it decreases the conductivity of the surface layer, the geometric factor rises gradually. To render the surface layer badly conducting, a large coverage is required, owing to which the geometric factor rises much more slowly than the residual resistivity.

442

J . W. GEUS

The maximum displayed by the residual resistivity on interaction with nitrous oxide (Figure 66) shows that a nickel surface covered with a monolayer of oxygen scatters conduction electrons less than a surface being more sparsely covered. This points to a decrease in the spacing of the surface structure or a better screening by bound electrons as the coverage gradually grows.

^5 Nifilm #60

o A -A

-

A

o c

5

10 1A

K) 0 2 Molecules c m "

2

F I G . 66. Change in residual resistivity (pR) and geometric factor (G) of nickel films on reaction with nitrous oxide and molecular oxygen. Upper: nitrous oxide, open symbols film No. 61, filled symbols film No. 60. Lower: molecular oxygen, film No. 56. (After Geus and Koks, unpublished.)

We believe t h a t the effects of carbon monoxide adsorption and oxygen sorption on the conductance of tungsten, iron and nickel films demonstrates t h a t the mechanisms brought forward above can readily account for the experimental data. That adsorption affects the nature of the scattering of the conduction electrons and the conductivity of the surface layer of the metal is established beyond doubt, while the importance of emission or tunnelling across gaps between particles is shown by the experiment in Figure 60. The effect of adsorption on the reflection of conduction electrons links up beautifully with the evidence on the resistivities of vapour deposited metal films dealt with previously. Since adsorption of a limited amount of residual gas is able to destroy

THE INFLUENCE OF ADSORPTION ON METAL FILMS

443

the specular reflection of smooth metal surfaces, metal films must be prepared and kept in ultrahigh vacuum if they are to display specular reflection. Only for gold the requirements are less severe, as this metal has a low reactivity. The above results also allow important conclusions to be drawn about the structure of metal surfaces having reacted with carbon monoxide and oxygen. I n section I I . E . l adsorption of carbon monoxide was compared with reaction to bulk carbonyls. I t was argued t h a t the difference in formation of bulk and chemisorption compounds is mainly in the degree to which the intermetallic bonds are weakened. From the effects on the conductance, it has appeared t h a t the conductivity of the surface layer of iron films is not affected at all by adsorption of carbon monoxide, while t h a t of nickel films is markedly affected, and t h a t of tungsten films is appreciably decreased. The decrease in the conductivity of the surface layer for nickel and tungsten appears to be limited. We therefore conclude t h a t the strong effect on the structure of the surface layer as apparent from the decrease in conductivity is due to adsorption on higher index planes in the surface of the films. Since iron films deposited on glass at 77 °K must also contain higher index planes in their surface, we must explain why the conductivity of the surface at rough iron planes is not influenced by carbon monoxide adsorption. Two reasons for this difference can be indicated; a different interaction between nearest and next-nearest neighbours for f.c.c. and b.c.c. lattices, and the tendency to form carbonyls with more than one metal atom per molecule. Since for b.c.c. metals the next-nearest neighbour interaction is stronger than t h a t between nearest-neighbours (Drechsler and Liepack, 1965), it is more difficult to lift b.c.c. metal atoms from their lattice positions than f.c.c. metal atoms. The difference between films of the b.c.c. metals iron and tungsten is due to the relatively low mobility of tungsten atoms over tungsten surfaces. This means t h a t planes where the metal atoms are very badly coordinated are likely to be present in the surface of evaporated tungsten films, whereas with iron films this is less likely to occur. The high residual resistivity of those tungsten films which have a specific surface area not much larger than that of some iron films deposited on glass kept at 77 °K, points to a surface that at least partly scatters conduction electrons. Moreover, Brennan and Hayes (1965) observed a very high heat of adsorption for the first doses of carbon monoxide admitted to a tungsten film, about 120 kcal mole - 1 , against a mean value of about 80 kcal mole" 1 . This points to the presence of some planes where the coordination of metal atoms is very small, owing to which the intermetallic bonding is strongly affected on reaction with carbon monoxide.

444

J. W. GEUS

Bridged and polynuclear metal carbonyls are found only in the columns of the periodic system containing manganese, iron and cobalt, but not in those containing tungsten and nickel. We consequently believe t h a t the tendency to be strongly bonded simultaneously to other metal atoms and to carbon monoxide molecules is smaller for tungsten and nickel than for iron. Higher index planes of iron hence can adsorb carbon monoxide without considerably decreasing their interaction with other metal atoms in contrast to tungsten and nickel. The effect of adsorption of carbon monoxide on the metal structure of close-packed metal planes is apparent also from the effect of adsorption on the electrical conductance. The above evidence shows t h a t the conductivity of the surface layer is not affected, which points to a small effect of adsorption on the intermetallic bonds. Hence adsorption of carbon monoxide on close-packed metal planes does not give rise to a marked perturbation of the metal structure. I n section U.E.3 it was argued t h a t scattering of conduction electrons at metal surfaces can be caused by adsorbed atoms the charge of which is not completely screened by localized electrons, or by metal atoms displaced from their lattice positions in bonding adsorbates. Since the conductivity of the surface layer of close-packed iron and nickel surfaces is not affected, it is likely t h a t the adsorbed carbon monoxide molecules are scattering the conduction electrons. This conclusion is substantiated by an observation of Suhrmann, Ober and Wedler (1961) on the change in conductance of copper films by adsorption of carbon monoxide. Carbon monoxide is weakly adsorbed on copper, decreasing the work function of the metal (Culver, Pritchard and Tompkins, 1959; Pritchard, 1963). At room temperature a marked adsorption of carbon monoxide on copper can be obtained only at relatively high pressures. Despite the weak adsorption of carbon monoxide, Suhrmann, Ober and Wedler observed a very large decrease (more than 20%) in the conductance of copper films by adsorption of carbon monoxide at 90 °K. Since copper has a low melting point, the density of grain boundaries in copper films is likely to be low. As, moreover, the resistivity of bulk copper is relatively small, the conduction electrons can have a long mean free path in films at 90 °K. This leads to frequent collisions of conduction electrons with the copper surface and, hence, to a strong effect of the nature of the reflections at the surface. Suhrmann, Ober and Wedler observed a rather large residual resistivity for their copper films in contrast to the above arguments. This might be due to a contact resistance (largely temperature independent) between the platinum contact foils and the thin (80 Ä thickness) copper film. Nevertheless, the strong effect on the conductance of weakly adsorbed carbon monoxide t h a t will not affect the metal

THE INFLUENCE OF ADSORPTION ON METAL FILMS

445

structure demonstrates that adsorbed molecules can scatter conduction electrons. Interaction of the metals with oxygen perturbs the surface structure. This is demonstrated by interaction of nickel with nitrous oxide which decreases the conductivity of the surface layer even at low oxygen coverages. Consequently, the metal surface atoms bonding oxygen atoms lose their metallic conductivity. Brennan and Graham (1966) measured at 293 °K a heat of sorption for oxygen on nickel and cobalt that is of the same order of magnitude as the heat of formation of the corresponding bulk oxides. At 77 °K these authors observed a lower heat of adsorption, which points to the surface layer obtained at 77 °K having a structure deviating from that obtained at 293 °K. The effect of interaction with oxygen on the conductance does not change when a film upon which oxygen has been adsorbed at 77 °K is heated to 273 °K and recooled, provided the coverage is not too large. The metal surface atoms are hence rendered non-conducting already on reaction at 77 °K. From the above discussion it appears that the effect of adsorption on the electrical conductance can give much information on the structure of the metal surface to which are bonded adsorbate molecules. b. Adsorption of Foreign Metal Atoms. As dealt with above, the effect that self-adsorption of gold atoms has on the conductance of gold films 4

3

~o2

1

0

1 2 3 10 u Cs atoms cm"2

F I G . 67. Effect of cesium adsorption at 333 °K on the conductance (λ) of an evaporated tungsten film. (After Geus, 1964.) S*

446

J . W. GEUS

was studied by Lucas (1964). Geus, Koks and Zwietering (Geus, 1964) investigated the effect of cesium adsorption on the conductance of tungsten films. I t appears t h a t adsorption of cesium strongly increases the conductance of tungsten films. If cesium was adsorbed well dispersed on to specularly reflecting surfaces, a decrease in the conductance should be observed at low coverages. As appears from Figure 67, the conductance rises during adsorption of cesium, though more slowly at lower than at higher coverages. We believe t h a t this is due to a large fraction of diffusely reflecting surfaces in tungsten films. This leads to an increase in conductance analogous to t h a t given in Figure 39 for deposition of gold onto a "non-specular" gold film. c. Adsorption of Hydrogen. The change in conductance of tungsten films by adsorption of hydrogen was studied by Geus, Koks and Zwietering (1963). As represented in Figure 68, the conductance decreases steadily on adsorption of hydrogen, though the decrease is markedly lower than t h a t brought about by an equal amount of carbon monoxide

r\

1

1014 H2 molecules cm' 2 2

1

3

r

A

1

5

1

o

5 -2

[-3h u F I G . 68. Effect of hydrogen adsorption at 273 °K on the conductance (λ) of an evaporated tungsten film. (After Geus, Koks and Zwietering, 1963.)

or oxygen. Since no accurate data were obtained for the change in residual resistivity and geometric factor, it is difficult to account for the results of Figure 68. We therefore shall take up the discussion of effect of hydrogen on the conductance of tungsten films after dealing with the effects on iron and nickel films. The effect of adsorption of hydrogen on the conductance of iron films was studied by Zwietering, Koks and van Heerden (1959), by Suhrmann, Hermann and Wedler (1962) and by Cukr, Merta, Adamek and Ponec (1965). I n Figure 69 the change in conductance caused by adsorption of

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447

hydrogen onto an iron film deposited on glass kept at 273 °K is represented. The conductance appears to traverse a minimum situated at a coverage of about 2.5 x 1014 hydrogen molecules cm - 2 . At coverages of about 5.5 x 1014 hydrogen molecules cm - 2 , the conductance has almost returned to its original value. I n Figure 69 we also give the change in geometric factor and residual resistivity; it appears that the residual resistivity traverses a maximum, whereas the geometric factor does not change markedly beyond the experimental error. From these data, it can be concluded t h a t hydrogen adsorption only affects the reflection of the conduction electrons at the iron surface. 101A H2 molecules cm"2 2 3 4

r^-s,

β

■ ^

\

* - Hβ

\ ^ -1 o

"\

5

-fc#-

-°--§—β—β—i

"N.

- * - β ·

^F=F=*-i-*—i 101A H? molecules cm"2 F I G . 69. Upper: Effect of hydrogen adsorption on the conductance (λ) of an iron film (No. 24) deposited on glass kept at 273 °K. Hydrogen admitted at 273 °K. Conductance measured a t 273 °K before (O) and after ( # ) cooling to 77 °K, and a t 77 °K ( x ) . Lower: Change in residual resistivity (pR) and geometric factor (G) during hydrogen adsorption. Open symbols before cooling to 77 °K, filled symbols after cooling. (After Geus and Koks, unpublished.)

448

J . W. GEUS

Comparison between the effects of hydrogen and carbon monoxide is instructive: adsorption of the latter also does not lead to a decrease in the conductance of the surface of iron. As dealt with in section I I , scattering of conduction electrons by foreign charges strongly depends on the screening of these charges by bound electrons. Since the increase in residual resistivity brought about by adsorption of carbon monoxide (see Figure 53) is appreciably larger than t h a t caused by hydrogen adsorption, adsorbed carbon monoxide is much less well screened than hydrogen, which is a reasonable conclusion. I n section U.E.2 we derived theoretically some residual resistivity versus coverage plots (Figure 36): comparison with Figure 69 shows t h a t the adsorbed hydrogen atoms are mobile and repel each other. The coverage at the conductance minimum is fairly low, about 5 x 1014 hydrogen atoms cm - 2 . In Figure 70 a (110) iron surface is shown covered with 5.6 x 1014 hydrogen atoms cm - 2 . As the spacing of the hydrogen atoms is markedly larger than t h a t of the metal atoms, diffuse reflection of conduction

F I G . 70. Configuration of adsorbed hydrogen atoms on a (110) surface of iron. Coverage 5.6 x 1014 hydrogen atoms c m - 2 .

electrons can be expected. At a coverage of about 12 x 1014 hydrogen atoms cm - 2 , the reflection is again largely specular. This coverage is too small to fill all the sites in a (110) surface (1.7 x 1015 cm" 2 ) completely. These low coverages (relative to a monolayer on (110)) presumably result from the presence in the surface of iron films of a proportion of

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449

planes less closely packed than (110): a similar situation occurs with carbon monoxide. Figure 71 shows the variation of conductance due to hydrogen adsorption on an iron film deposited on to glass kept at 77 °K. (The adsorption of hydrogen atoms at 77 °K, which was carried out after adsorption of 5 x 1014 hydrogen molecules cm - 2 , will be dealt with later.) I t can be seen t h a t the conductance of a film deposited on glass 10 u H2 molecules cm"2

-1

^

-2 ^

5 —r"

-3

< V -5

-8-8—8-

x

\

V

*\

-6

-7h

F I G . 71. Upper: Effect of hydrogen adsorption on the conductance (λ) of an iron film (No. 34) deposited on glass kept at 77 °K. Hydrogen admitted at 273 °K. Conductance measured at 273 °K before (O) and after ( · ) cooling to 77 °K, and at 77 °K ( x ) . At 77 °K more hydrogen was adsorbed by atomization ( + ). Lower: Change in residual resistivity (pR) and geometric factor (G) during hydrogen adsorption. Open symbols before cooling to 77 °K, filled symbols after cooling. (After Geus and Koks, unpublished.)

450

J . W. GEUS

kept at 77 °K, though displaying a minimum on hydrogen adsorption, did not return to the value of the clean film. As can be seen also in Figure 71, the residual resistivity rose strongly, traversed a faint maximum at a coverage of about 2.5 x 1014 hydrogen molecules cm - 2 , but did not strongly decrease as the coverage increased further. The decrease in the geometric factor of the iron film deposited at 77 °K is again due to some sintering induced by cycling the film temperature between 273° and 77 °K. The change in conductance of iron films deposited at 77 °K on adsorption of hydrogen is between t h a t of tungsten films given in Figure 68 and an iron film deposited at 273 °K (Figure 69). We believe t h a t the behaviour of an iron film deposited at 77 °K is influenced by a marked fraction of less closely packed surface planes, to which the data for carbon monoxide, as discussed above, point also. On crystallographic planes like (211) t h a t can be expected to reflect conduction electrons specularly, hydrogen adsorption may lead to a surface structure with an increased spacing. For hydrogen adsorption on the analogous (110) surface of nickel, Germer and MacRae (1962) observed in L E E D diffraction patterns a spacing perpendicular to the rows of atoms t h a t was twice t h a t of the original surface. At higher hydrogen pressures the increased spacing persisted. We believe t h a t on iron planes t h a t have a structure analogous to t h a t of the nickel (110) surface, the spacing of the surface structure remains larger than t h a t of the original surface at higher hydrogen coverages. This causes the reflection of the conduction electrons to be diffuse also at larger hydrogen coverages. As can be seen from Figure 71, the reflection of the conduction electrons on close packed iron surfaces becomes specular again at larger coverages, but the permanent loss of specular reflection at less closely packed surfaces causes the conductance to remain below the value of the clean film. I t is obvious to use analogous arguments in accounting for the effect of hydrogen adsorption on the conductance of tungsten films. Since the fraction of less closely packed planes in the surface of tungsten films is larger, the permanent decrease in specular reflection of conduction electrons dominates, and the conductance does not increase again at high coverages. There are, however, several difficulties with this explanation. The increase in residual resistivity of tungsten films by carbon monoxide adsorption is only about 3 % ; since hydrogen is screened better by bound electrons, scattering by adsorbed hydrogen atoms should be less. Thus, at higher coverages the experimental decrease in conductance of about 3 % is not likely to be due to adsorbed hydrogen affecting the reflection of conduction electrons. Moreover, L E E D experiments do not show surface structures with an enlarged

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451

spacing at high hydrogen coverages on tungsten. For instance the (211) surface of tungsten does not change its L E E D pattern at all during hydrogen adsorption, while Estrup and Anderson (1966) observed for the (100) surface of tungsten a transient structure with enlarged spacing, which disappeared at higher hydrogen coverages. We therefore believe that hydrogen atoms penetrate into the atomically rough planes present in tungsten films; the resulting badly ordered surface hydride will have an appreciable lower conductivity than t h a t of the original surface. Hydrogen adsorption on flat planes will cause a transient scattering of the conduction electrons, t h a t disappears at higher coverages. Superposition of the effects on the conductivity of the surface layer, which dominates for tungsten films, and on the reflection of the conduction electrons, leads to the decreasing slope of the conductance versus coverage curve of Figure 68. The change in conductance of nickel films by adsorption of hydrogen has been much studied. We here refer to papers by Sachtler and Dorgelo (1958), Suhrmann, Mizushima, Hermann and Wedler (1959), Zwietering, Koks and van Heerden (1959), Mizushima (1960), and Ponec and Knor (1960). The experimental results are all in qualitative agreement with Figure 72, where the effect of hydrogen adsorption on the conductance of a nickel film deposited at 77 °K is given. As can be seen from Figure 72, hydrogen adsorption affects the conductance of nickel films in about the same way as t h a t of iron films deposited at 273 °K, which have about the same structure. There is, however, an important quantitative difference which is the very low coverage at which the minimum conductance and the conductance approaching the value of the clean film are observed. In Figure 72 the minimum conductance is found at a coverage of 1 X 1014 hydrogen molecules cm - 2 , which is small if compared with the number of nickel atoms in close-packed planes, which is 1.87 x 1015 c m - 2 for the (111) and 1.61 x 1015 c m - 2 for the (100) plane. The low coverage at the minimum is also found by others. Zwietering, Koks and van Heerden observed the minimum at a coverage of 1.4 x 1014 molecules cm - 2 , and Ponec and Knor at a coverage of 1.5 x 1014 molecules cm - 2 . In section U.E.3 it was shown t h a t there should be a minimum in the conductance at low coverages with an attractive interaction between mobile adsorbed atoms. Since, however, the minimum in conductance is situated at about one half of the coverage at which the conductance of the clean film is approached, this explanation cannot be accepted. By an accurate investigation of the effect of the film structure on the kinetics of hydrogen adsorption Knor and Ponec (1961) could demonstrate t h a t nickel films have an appreciable fraction of their surface with

452

j . w. GEUS

lower accessibility to the gas phase. Adsorption on the outer surface displays the characteristics of mobile adatoms with a repulsive interaction. After covering the outer surface almost completely, hydrogen penetrates into the interior parts of the film surface: each new dose of hydrogen covers a fraction of the surface to a fairly large extent, owing

0

-1

1

V7 \

/

10 u H 2 molecules cm"2 2 3 4 5 6

7

8

\ \ \

o

-2

\

F I G . 72. Effect of hydrogen adsorption the conductance (λ) of a nickel film (No. 46) deposited on glass kept at 77 °K. Hydrogen admitted to film kept at 273 °K. Conductance measured at 273 °K before ( x ) and after ( + ) cooling to 77 °K, and at 77 °K (O)· Conductance also measured at 273 °K after adsorption of atomized hydrogen to the extent of 3.8 x 1014 molecules c m - 2 ( · ) . (After Geus and Koks, unpublished.)

to which the conductance remains at the level observed for the fully covered surface. In the experiment of Figure 72 the hydrogen pressure was below 10~2 torr. When the latter pressure is established over a nickel film, the coverage increases to about 6 x 1014 hydrogen molecules c m - 2 without a strong effect on the conductance. Since the conductance remains below the level observed at a coverage of 3 x 1014 molecules cm - 2 , it is likely t h a t the parts of the nickel surface t h a t are less easily accessible contain a higher proportion of higher index planes. Nickel films deposited at 77 °K and iron films deposited at 273 °K, though having an analogous structure, deviate in the distribution of admitted gases over their internal surface. Whereas on iron films both

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453

carbon monoxide and hydrogen easily establish a uniform low coverage, on nickel carbon monoxide is adsorbed into a densely packed surface configuration and hydrogen attains a uniform low coverage on the more easily accessible parts of the surface only. We believe t h a t the difference in distribution of admitted gases over the surfaces of iron and nickel films is not due to a difference in the structure of these films, though this possibility should be considered seriously. If carbon monoxide was adsorbed into a less densely packed configuration on the outer surface of nickel film, the conductance versus coverage plot should have a strongly curved character, as observed for adsorption of oxygen from nitrous oxide on nickel. We therefore assume t h a t the repulsive interaction between adsorbed carbon monoxide molecules and between adsorbed hydrogen atoms is smaller for nickel than for iron, unless it can be demonstrated t h a t the pores in nickel films deposited at 77 °K are markedly smaller than those in iron films deposited at 273 °K. After being saturated by hydrogen atoms adsorbed from molecular hydrogen, a nickel surface kept at 77 °K can take up about an equal amount of hydrogen atoms from hydrogen atomized on a heated tungsten filament (Hayward, Herley and Tompkins, 1964; Ponec, Knor and Cerny, 1965). As shown in Figure 72, the hydrogen atoms strongly decrease the conductance. We ascribe the big effect on the conductance to the formation of a badly ordered layer of adsorbed hydrogen. This surface hydride has a low conductivity and causes the reflection of the conduction electrons to be diffuse. As indicated in Figure 71, the amount of hydrogen taken up from hydrogen atoms by an iron surface kept at 77 °K and previously saturated from gaseous hydrogen molecules, is much smaller. The effect on the conductance per hydrogen atom taken up from gas atoms is about equal to t h a t caused by adsorption of hydrogen on the clean film. The hydrogen atoms adsorbed over the hydrogen taken up from molecules consequently increases the scattering of conduction electrons at the iron surface. This is due to the perturbation of the surface structure which on close packed planes previously had a periodicity almost equal to t h a t of the clean surface. The different tendency of iron and nickel to form surface hydrides by reaction of the already covered surface with hydrogen atoms at 77 °K, is reflected in the solubility of hydrogen in nickel which is considerably larger than that in iron (Fast, 1965). It, moreover, corroborates the proposed difference in repulsive interaction between hydrogen atoms adsorbed on iron and nickel. Since nickel can accommodate much more hydrogen in its surface than iron, the repulsive interactions between the adatoms must be smaller. The reaction of nickel surfaces with hydrogen gas atoms to give a

454

J . W. GEUS

surface nickel hydride links up very well with those cases where hydrogen is able to dissolve into the metal. Palladium is a very good example of the latter. Suhrmann, Schumicki and Wedler (1964) investigated the change in the conductance of palladium films caused by reaction with hydrogen. At room temperature, hydrogen does not absorb into palladium at low pressures. Consequently, the conductance varies analogously to that of iron and nickel films. At lower temperatures, 195° and 90 °K, palladium hydride is stable even at low hydrogen pressures. Now the conductance decreases with dissolution of hydrogen into the bulk. Consequently, the increase in conductance connected with the restoration of specular reflection is not displayed at 195° and 90 °K. Platinum dissolves a small amount of hydrogen, which strongly increases its conductivity. Suhrmann, Wedler and Gentsch (1958) only observed the conductance of platinum films to increase on treatment with hydrogen. At 295° and 195 °K the effect of the conditions at the surface is completely obscured by the rapid penetration of hydrogen into the bulk and the corresponding increase in the conductance. At 90 °K, however, the adsorbed hydrogen penetrates more slowly into the bulk, owing to which a transient decrease in the conductance can be observed. Sachtler and Dorgelo (1960) could suppress the dissolution of hydrogen into platinum sufficiently by decreasing the film temperature to 63 °K. They observed adsorption on the platinum surface to decrease the film conductance by about 2 - 5 % . Adsorption of hydrogen on titanium is also interesting. As discussed in section U.E.4, the conductivity of ordered titanium hydride is higher than t h a t of pure titanium. Van Heerden and Zwietering (1957) and Wedler and Strothenk (1966) investigated the effect of hydrogen adsorption on the conductance of titanium films. Wedler and Strothenk established t h a t the conductivity of α-titanium hydride is smaller than t h a t of pure titanium, whereas t h a t of y-titanium hydride is larger and grows with increasing hydrogen content (see Figure 38). At room temperature, consequently, the conductance of a titanium film decreases as hydrogen is taken up, until y-titanium hydride is formed (at a titanium/ hydrogen ratio of about 0.06) and the conductance increases again. I n the a region, the conductance falls linearly with the hydrogen content, which makes it possible to separate the effect of the surface conditions from t h a t of dissolution. Wedler and Strothenk found t h a t the extent of the decrease in the conductance traverses a maximum and is negligible at completion of a monolayer of hydrogen. This demonstrates t h a t hydrogen dissolved into the surface of the metal increases both the resistivity of the surface layer and the scattering of the conduction

THE INFLUENCE OF ADSORPTION ON METAL FILMS

455

electrons, until a monolayer is taken up and the reflection is again specular. At 77 °K recrystallization of presumably badly ordered atitanium hydride into y-titanium hydride cannot proceed. Hence, the conductance continues to decrease on sorption of hydrogen until the film is heated up to 273 °K which causes the conductance to increase appreciably. d. Mobility of Adsorbates over Metal Surfaces. As was apparent in the above discussion, the change in the conductance of evaporated metal films during adsorption can reflect the distribution of adsorbed gas molecules over the surface. I t is therefore possible to investigate the mobility of adsorbed molecules or atoms by determining the effect adsorption of these molecules has on the conductance of the film kept at different temperatures. For carbon monoxide interesting information is available. As was evident from Figure 49, where the effect of carbon monoxide adsorption admitted at 273 °K on the conductance of a tungsten film was represented, at 77 °K some gas is taken up without an effect on the conductance. When carbon monoxide is admitted to a film kept at 273 °K, molecules not affecting the conductance are adsorbed after the surface is completely covered with carbon monoxide t h a t decreases the conductance. If the adsorbed molecules are not mobile over the metal surface, it can be expected t h a t carbon monoxide not affecting the conductance is adsorbed in between the more strongly adsorbed gas molecules. This is confirmed experimentally. Geus, Koks and Zwietering (1963) observed the slope of the conductance versus coverage plot as well as the change in conductance at full coverage to decrease with decreasing film temperature. While films kept at 273° and 195 °K displayed the same final decrease in conductance, films kept at 77 °K showed a smaller decrease in conductance. Suhrmann, Mata Arjona and Wedler (1961) admitted carbon monoxide to a film kept at 90 °K; these authors observed a strong decrease in the conductance when a heavily covered film was heated up to room temperature and recooled. The above evidence shows t h a t carbon monoxide which does not decrease the conductance has a restricted mobility at 195 °K and a very low surface mobility at 77 °K. I n evaporated metal films there may be pores so narrow t h a t gas molecules cannot pass through them at a reasonable rate. Surfaces situated at these pores, therefore, can only be covered by adsorbates migrating over the surface. When the adsorbate is not mobile, part of the internal film surface is not covered and the decrease in conductance remains limited. Moderate heating of the film to a temperature where adsorbed molecules are mobile, leads to

456

j . w. GEUS

coverage of the surface at narrow pores and to a corresponding decrease in conductance. I n section III.C.l it was argued t h a t on iron surfaces the carbon monoxide coverage required to destroy specular reflection at the surface is relatively small compared with the density of metal atoms in iron surfaces. If carbon monoxide not affecting the conductance is adsorbed simultaneously with the more strongly bonded molecules, the conductance versus coverage plot will show a much lower slope. As can be seen in Figure 73, where the effect of carbon monoxide adsorption on the conductance of iron films kept at 273° and 77 °K during admission,

0

10u CO molecules cm'2 A 6

2

8

10

G*C -2 -U

N\

X.

\

\

\ \

-6 o -8

<

-10

X

\ \

-12

X

-14 -16 F I G . 73. Change in conductance (λ) of iron films with carbon monoxide adsorption. Films deposited on glass kept at 77 °K. Film No. 8 (O) measured at 77 °K, film No. 21 ( x ) measured at 77 °K after admitting gas at 273 °K. (After Geus and Koks, unpublished.)

is represented, this is experimentally observed. Moreover, the film kept at 77 °K displays a decrease in conductance t h a t is appreciably smaller than t h a t of the film kept at 273 °K. Figure 74 shows t h a t carbon monoxide not affecting the conductance is also immobile on nickel surfaces at 77 °K. Wedler and Fouad (1964) studied the effect of carbon monoxide on the conductance of nickel films with thickness varying from 37 to 244 Ä. Since continuous thin nickel films do not contain narrow pores, Wedler and Fouad's results are very well suited to demonstrate the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

457

effect of the porous structure of thicker nickel films on the change in conductance by carbon monoxide adsorption. For the slope of the conductance versus coverage plots, Wedler and Fouad did not establish an effect of temperature (273° or 77 °K) at which the film was kept during the experiments. This is caused by the larger change in conductance at 77 °K due to the larger mean free path of the conduction electrons being compensated by the simultaneous adsorption of a considerable fraction 10 u CO molecules cm"2

FIG. 74. Change in conductance (λ) of nickel films with carbon monoxide adsorption. Films deposited on glass kept at 77 °K. Film No. 36 (O) measured at 77 °K, film No. 34 ( x ) measured at 77 °K after admitting gas at 273 °K. (After Geus and Koks, unpublished.)

of the carbon monoxide admitted in a state not affecting the conductance. A comparison of the 273 °K plot in Figure 60 and the plot obtained at 77 °K in Figure 74 shows t h a t here also the slopes of the curves are nearly equal. The decrease in conductance at full coverage was, for films with a thickness below 125 Ä, clearly larger on keeping the films at 77 °K than at 273 °K. Penetration into the short pores of thin films evidently proceeds sufficiently rapidly. However, films with thicknesses of about 250 Ä on keeping both at 273° and 77 °K displayed the same decrease in conductance at full coverages. In these films narrow

458

J . W. GEUS

pores must be present into which gas molecules cannot penetrate at 77 °K. Adsorption of hydrogen by tungsten films is also affected by the surface mobility of adsorbed atoms. As shown in Figure 75, the conductance of a film kept at 77 °K decreases more slowly than t h a t of a

F I G . 75. Change in conductance (λ) of evaporated tungsten films with hydrogen adsorption. Films deposited on glass kept at 77 °K. Film (O) measured at 77 °K, films ( · , ▲) measured at 273 °K after gas admission at 273 °K. (Reproduced with permission from Geus, Koks and Zwietering (1963). J. Gatdl. 2, 274.)

film kept at 273 °K. The final decrease, however, is about the same for films at 77° and 273 °K. That hydrogen is not mobile over tungsten surfaces kept at 77 °K is in good agreement with Gomer, Wortman and Lundy's (1957) field-emission work. These authors observed the activation energy for surface migration to decrease as more hydrogen was adsorbed. At the maximum coverage of chemisorbed hydrogen atoms, they found mobility only above 180 °K. Also the mobility of hydrogen atoms adsorbed on iron films can be studied by means of conductance measurements. In Figure 76 measurements are represented for films kept at 77°, 195° and 273 °K. From the shape of the plots it is evident t h a t at 195 °K hydrogen atoms are mobile (compare with Figure 36 of section II), whereas at

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459

101A H2 molecules cm"2 2 3 4 5

*< %

F I G . 76. Change in conductance (λ) of evaporated iron films with hydrogen adsorption. Films deposited on glass kept at 77 °K. Films measured a t 77 °K (O), 195 °K ( x ) , 273 °K ( · ) : gas admitted at measurement temperature. (Reproduced with permission from Zwietering, Koks and van Heerden (1959). J. Phys. Chem. Solids 11,18.)

77 °K they are immobile. The shape of the conductance versus coverage plot measured for a film kept at 77 °K is, however, not as predicted for adsorption of immobile adatoms. We believe t h a t the experimentally observed decrease in conductance is due to the fact t h a t a diatomic molecule is adsorbed. When diatomic molecules are dissociatively adsorbed as atoms of very low mobility, formation of gaps (isolated single adsorption sites) in the adsorbed layer is likely. These gaps are filled only after very long exposures. Before equilibrium pressures of hydrogen can be established, the coverage of the surface must be high. Consequently, the iron surface is covered first with a layer of adatoms containing gaps which leads to scattering of the conduction electrons; finally these gaps are filled in, which requires a relatively small number of hydrogen atoms and increases the conductance appreciably.

460

J . W. GEUS

As can be seen in Figure 77, hydrogen adsorbed on nickel is immobile at 77 °K. This is in good agreement with the result of Brennan and Hayes (1964) who, from a determination of the heat of adsorption of hydrogen on nickel, concluded t h a t adatoms were immobile at 77 °K. 1014 H2 molecules cm"2 20

ΑΌ

-0-2

-OA

F I G . 77. Change in the conductance (λ) of evaporated nickel films with hydrogen adsorption. Films deposited on glass kept at 77 °K. Films measured at 77 °K ( # ) , 273 °K ( O ) ; gas admitted at measurement temperature. (Reproduced with permission from Zwietering, Koks and van Heerden (1959). J. Phys. Chem. Solids 11, 18.)

e. Adsorption of Nitrogen and More Complex Molecules. We shall first discuss the effect on the metal surface of nitrogen adsorption: with this molecule, dissociative adsorption is often slow. Adsorption of nitrogen on tungsten has been studied intensively. By studying the isotope

THE INFLUENCE OF ADSORPTION ON METAL FILMS

461

exchange of adsorbed nitrogen, Madey and Yates (1965) showed that nitrogen strongly bonded on tungsten surfaces is presumably dissociated. Besides strongly adsorbed nitrogen, Ehrlich (1962) established the presence of two more weakly bonded nitrogen species by means of flashfilament experiments. These states are molecular as they do not display isotope exchange (Rigby, 1965). Ehrlich (1962) found that at 115 °K considerably more nitrogen is adsorbed as molecules than at 273 °K. It was mentioned in section II.E.l that in metallic nitrides, nitrogen shares covalent strongly directed bonds with metal atoms. Owing to this, it can be expected that nitrogen atoms will be bonded at metal surfaces on sites where the atom is situated between two metal atoms. It is interesting to investigate whether the metal surface is distorted in adsorption of nitrogen atoms. Moreover, it is interesting to establish the nature of the adsorptive bond of the weakly adsorbed molecular nitrogen. Geus, Koks and Zwietering studied the effect of nitrogen adsorption 1014 N2 molecules cm"2 1

2

F I G . 78. Effect of nitrogen adsorption on the conductance (λ) of an evaporated tungsten film. Films deposited on glass kept at 283 °K. Film No. 34 ( x ) kept at 77 °K during adsorption and measurement, then heated to 273 °K and measured (dotted line). Film No. 33 heated to 273 °K, nitrogen admitted at 273 °K, measured at 77 °K ( # ) , reheated to 273 °K and measured (0)> then next gas dose added. (Reproduced with permission from Geus, Koks and Zwietering (1963). J. Catal. 2, 274.)

462

J . W. GEUS

on the conductance of evaporated tungsten films. I n Figure 78 their results are represented. As can be seen in Figure 78, tungsten after being saturated at 273 °K (uptake about 2 x 1014 molecules cm - 2 ) can adsorb about an equal number of molecules at 77 °K with a small effect only on the conductance. I t is obvious to associate the latter nitrogen with weakly adsorbed molecular nitrogen. Ehrlich (1961a) found t h a t a tungsten filament kept at 115 °K adsorbed atomically and molecularly bonded nitrogen at a ratio of 0.41. When this ratio is applied to the data in Figure 78 for film 34 which adsorbed about 4.5 x 1014 nitrogen molecules cm - 2 , this film appears to have bonded about 2.6 x 1014 nitrogen atoms cm - 2 . In the experiment with film 33, 4 x 1014 nitrogen atoms c m - 2 were adsorbed decreasing the conductance by about 7%. For an adsorption of 2.6 x 1014 atoms c m - 2 a decrease in conductance of about 4.5% is expected, which is in reasonable agreement with the experimentally observed decrease of 4 % . In Figure 78 the additional adsorption at 77 °K on film 33 brought about a small further decrease in conductance. This is demonstrated by calculating the geometric factor of the film from the resistance at 77 °K of the film covered with about 4 x 1014 molecules c m - 2 and t h a t at 273 °K with 2 x 1014 molecules cm - 2 ; a value for the geometric factor is obtained markedly below that of the clean film (see also Figure 79). This shows that at 77 °K the resistance is increased owing to the adsorption of the weakly bonded molecular nitrogen. Evidently the charge on these molecules is not screened completely so t h a t scattering of the conduction electrons results. As mentioned previously a homogeneous coverage of about 10% is sufficient to increase appreciably the diffuse reflection of an originally specular reflecting surface. If the 4 x 1014 nitrogen atoms c m - 2 adsorbed at 273 °K were distributed homogeneously, a marked effect on the scattering by weakly adsorbed molecules is unlikely. We hence believe t h a t nitrogen atoms are adsorbed exclusively on less closely packed planes, leaving the most closely packed (110) plane bare (Ehrlich, 1966). The reflection of conduction electrons against the (110) surface is affected by adsorption of molecular nitrogen at 77 °K. The effect of nitrogen adsorption on the structure of tungsten surfaces is most important. In Figure 79 the change in geometric factor and residual resistivity for film 33 of Figure 78 is represented. I t appears that first the geometric factor increases together with the residual resistivity, whereafter only the residual resistivity rises. Whereas on adsorption of carbon monoxide the geometric factor of tungsten films increased more than the residual resistivity, nitrogen adsorption affects the residual

THE INFLUENCE OF ADSORPTION ON METAL FILMS

463

resistivity more. We believe that the increase in the geometric factor which precedes the increase in residual resistivity is due to preferential adsorption of nitrogen into atomically rough planes which scatter conduction electrons even before adsorption. Since metallic nitrides still have a marked conductivity, the decrease in conductivity of the surface layer remains limited. Subsequently, nitrogen is adsorbed on atomically more smooth planes such as (100). Estrup and Anderson (1967)

1

2 * 101A No molecules cm"2

FIG. 79. Change in residual resistivity (pR) and geometric factor (G) for the experiment with tungsten film 33 represented in Figure 78, for nitrogen adsorption. Open symbols before cooling to 77 °K, filled symbols after cooling.

obtained L E E D evidence t h a t may very well be explained by penetration of nitrogen atoms into this plane, and this would lead to a strong scattering of the conduction electrons at (100) surfaces and hence to a large increase in the residual resistivity. Adsorption of nitrogen on evaporated iron films was studied by Ponec and Knor (1968). Geus and Koks (unpublished) investigated the effect

464

J . W. GEUS

of nitrogen adsorption on the residual resistivity and geometric factor of iron films. In Figure 80 the change in conductance of an evaporated iron film on adsorption of nitrogen is represented. Nitrogen was admitted at 77 °K and, after measuring the conductance, the film was 101A N 2 molecules cm" 2

F I G . 80. Change in conductance (λ) of an iron film (No. 36) with nitrogen adsorption. Film deposited on glass kept at 77 °K. Film measured at 77° K before (O) and after ( · ) heating to 273 °K, and at 273 °K ( x ) . Gas admitted at 77 °K. (After Geus and Koks, unpublished.)

heated to 273 °K. The nitrogen taken up at 77 °K was partly desorbed during heating and then slowly readsorbed at 273 °K. After equilibrium was reached, the film was cooled down to 77 °K, its conductance was measured and the next dose was admitted. Adsorption of nitrogen at 77 °K brought about a decrease in the conductance. At 273 °K the nitrogen adsorbed at 77 °K was transferred into a state that decreased the conductance much more. However, up to coverages of about 1 x 1014 nitrogen molecules c m - 2 at 273 °K and 3.5 x 1014 molecules c m - 2 at 77 °K, admission of a new dose of nitrogen caused the conductance of the film kept at 77 °K to decrease. The above results demonstrate t h a t dissociative adsorption of nitrogen proceeds on iron surfaces considerably more slowly than on tungsten surfaces. Consequently, the weakly bonded molecular state of nitrogen is adsorbed exclusively at 77 °K. Owing to the imperfect screening of the charges of the nitrogen atoms, conduction electrons are scattered by the adsorbed molecules, which results in an increase in the

THE INFLUENCE OF ADSORPTION ON METAL FILMS

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resistance. Since at 77 °K the mean free path of conduction electrons in iron films is rather large, this affects the conductance relatively strongly. Ponec and Knor (1968) found for an iron film kept at 77 °K and hence adsorbing molecular nitrogen only, an increase in resistance of about 3 % . The slight decrease in conductance on approaching saturation of the film must be ascribed to the decrease in work function caused by adsorption of molecular nitrogen t h a t was also measured by these authors. A decrease in the potential barrier between the metal particles increases the transport of electrons across gaps. Suhrmann, Richter and Wedler (1963) studied the effect of nitrogen adsorption at 77 °K on iron and nickel films with varying structures. For films where conduction across gaps between metal particles can be expected, they found a large decrease in resistance at nitrogen pressures of about 2.5 x 10 - 2 torr. The physically adsorbed nitrogen t h a t decreased the work function could be removed by pumping, which caused the resistance to increase again sharply. From the conductance versus coverage plot for nitrogen on tungsten, it was concluded t h a t nitrogen is chemisorbed atomically on less closely packed planes only. This can be inferred also for iron from Figure 80. For a uniform distribution of gas molecules, a low overall coverage is sufficient to cause scattering of conduction electrons at the whole surface; a homogeneous coverage of the iron surface with nitrogen atoms is therefore not compatible with the decrease in conductance displayed on admission of nitrogen to the film cooled to 77 °K. We hence conclude t h a t the nitrogen atoms adsorbed at room temperature are concentrated on the (100) and atomically more rough planes. As nitrogen molecules will be adsorbed on the (110) planes too, they decrease the conductance of this surface. Ponec and Knor's observation t h a t the resistance of a film saturated at 273 °K for 100 min with nitrogen decreased further on cooling down to 78 °K with further nitrogen adsorption, is also in keeping with no adsorption of nitrogen atoms on (110) surfaces. In Figure 81 we plot the change in residual resistivity and geometric factor of the iron film of Figure 80 during nitrogen adsorption. As on carbon monoxide adsorption, the residual resistivity increases only, whereas the geometric factor only shows a small decrease caused by sintering during thermal cycling of the film. Since nitrogen was first adsorbed at 77 °K where it was distributed relatively homogeneously over the internal surface of the film, the effect on the residual resistivity per adsorbed nitrogen atom is large. Whereas for carbon monoxide a coverage of 0.5 x 1014 molecules c m - 2 causes the conductance of an iron film deposited at 77 °K to decrease by 1%, the same coverage of

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J . W. GEUS

adsorbed nitrogen atoms leads to a decrease in conductance of about 2.6%. That a low coverage is sufficient to destroy the specular reflectivity of a surface is apparent from the rapidly decreasing slope of both the residual resistivity and the conductance plots. Figure 65 where the effect of nitrous oxide on the conductance of a nickel film was given, as well as Figure 66 show the same behaviour.

F I G . 81. Effect of nitrogen adsorption on the residual resistivity (pR) and geometric factor (G) of the evaporated iron film (No. 36) used in the experiment of Figure 80.

The small coverage of nitrogen atoms adsorbed at room temperature also indicates t h a t the nitrogen atoms are not adsorbed over the whole surface of the film. A coverage of about 3 x 1014 nitrogen atoms cm - 2 , which is reached in Figure 80, is very small if compared with the density of iron atoms in the surface, which is about 14 x 1014 cm - 2 . The most conclusive evidence t h a t adsorption of atomic nitrogen leaves the (110) planes, that are most abundant, unaffected can be obtained from Ponec and Knor's work. These authors adsorbed hydrogen onto an iron film saturated at 273 °K with nitrogen. In Figure 82 we represent their results. As can be expected, adsorption of hydrogen onto the film the less closely packed planes of which were covered with nitrogen, displayed a

THE INFLUENCE OF ADSORPTION ON METAL FILMS

467

plot analogous to that measured on a clean film but with a slightly lower maximum in resistance. This demonstrates that a large fraction of the iron film still had specularly reflecting surfaces after reacting at 273 °K with nitrogen. As mentioned above, weakly adsorbed molecular nitrogen decreases the specular scattering of conduction electrons. For physically adsorbed

I

0

I

0-2

I

I

I

04 0-6 0-8 relative hydrogen coverage

1 —

10

FIG. 82. Change in resistance (R) of evaporated iron films on hydrogen adsorption at 273 °K. Films presintered at 330 °K. Measurements for a clean film (O) and a film pretreated ( # ) with nitrogen at 273 °K are given. (Reproduced with permission from Ponec and Knor (1968). J. Catal. 10, 73.)

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J . W. GEUS

molecules Suhrmann and coworkers observed also a small decrease in conductance. For the rather thin films Suhrmann and coworkers used, physical adsorption decreases the conductance by about 0.6%. Suhrmann (1957) found the conductance of a nickel film kept at 90 °K to fall by 0.6% on adsorption of xenon; Suhrmann, Busse and Wedler (1965) obtained for a nickel film kept at 77 °K a decrease in the conductance of 0.6% by adsorption of methane. Suhrmann, Krüger and Wedler (1961) studied the effect of adsorption of benzene on the conductance of iron, nickel, copper, zinc, palladium, and silver films kept at 90 °K. I t was found t h a t the conductance decreased by amounts varying from 0.2% for zinc to 6% for nickel and palladium as a monolayer was adsorbed, and to remain constant when more than a monolayer was taken up. The effect per adsorbed benzene molecule gradually decreased as the coverage grew. We believe t h a t the ^-electrons of benzene are responsible for the relatively strong scattering of conduction electrons at the surface. Suhrmann, Busse and Wedler also investigated the effect of methane on the conductance of nickel films kept at 295, 373 and 473 °K. From their results it can be concluded t h a t methane decomposed at these temperatures forming hydrogen and adsorbed hydrocarbon residues; at higher temperatures the hydrogen formed in the decomposition was desorbed. At 295 °K the conductance steadily decreased as more methane was admitted, while pumping strongly slowed down the rate of decrease in conductance. At 473 °K, however, the hydrogen set free was desorbed on pumping and the conductance markedly rose. The effect of the structure of the film on the change in conductance on adsorption is evident from the work of Suhrmann, Kern and Wedler (1963). Whereas Sachtler and Dorgelo (1960) observed the conductance of thick nickel films to decrease on reaction with formic acid, Suhrmann and Wedler (1956) found the conductance to increase slightly. On reaction with formic acid, the nickel surface will have its specular reflectivity for conduction electrons decreased, and presumably also its conductivity. As established by Suhrmann, Kern and Wedler, formic acid decreases the work function of nickel. The combination of the decrease in work function and in conductivity of the nickel surface causes the experimentally observed effects on the conductance to depend strongly on the film structure. Continuous films t h a t do not contain metal particles separated by very narrow gaps and making contact over small surfaces only, always displayed a decrease in the conductance on reaction with formic acid. When nickel films with a thickness of about 100 Ä are sintered at temperatures of about 400 °K, they take up an island structure. Since during adsorption of the first amounts of formic

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469

acid, the work function strongly decreases, transport of electrons between the metal island is facilitated. At higher coverages the nickel particles react over an increased depth with formic acid so that, owing to the larger distances between the metallic nickel particles, the conductance decreases in this stage. The effect of water on the conductance of metal films is difficult to study. First of all, water may strongly decrease the interaction of particles of the more noble metals with non-metallic substrates (Bachmann and Hilbrand, 1966). Owing to this, the metal particles become extremely mobile and coalesce, which can result in a partial break-up of the film and, hence, a large decrease in conductance. For porous films, the result may give rise to an increase in conductance since grain boundaries are eliminated. Besides the possibility of an effect on the film structure, adsorption of water without dissociation decreases the work function of metals. In porous films, electrons crossing over gaps always contribute slightly to charge transport. A decrease in work function, therefore, can markedly raise the conductance of porous films. The effects of a modification in the reflection of electrons at the film surface and in the conductivity of the surface layer on the film conductance can be estimated from a knowledge of the surface area and the residual resistivity of the film. The effect on the conductance due to a change in work function is, however, difficult to estimate. Finally, water is likely to be adsorbed immobile on metal surfaces at low temperatures, where a very inhomogeneous distribution of water molecules over the film surface will be obtained. Suhrmann, Heras, Viscido de Heras and Wedler (1964, 1968) studied the change in the conductance of nickel, iron and copper films on interaction with water. They determined the work function of the outer surface of the film together with the film conductance. On iron and nickel films kept at 77° or 90 °K, water adsorption decreases the conductance. On admission of water vapour the conductance as well as the work function firstly rapidly decreases, after which the work function remains constant and the conductance goes on to fall but at a much slower rate. We ascribe the prolonged decrease in conductance as the film takes up more water, to a slow penetration of water into the interior of the films. On continued admission of water to a film kept at 77° or 90 °K, the outer surface will adsorb several monolayers. Whereas the conductance of nickelfilmsrapidly assumes a constant value after admission of water, that of iron films increases more slowly, which points to a limited dissociation of water on iron even at 77 °K. The decrease in the conductance brought about by adsorbed water molecules that are inhomogeneously distributed over the film surface is of the order of 7%. When an iron or T

470

J . W. GEUS

nickel film covered at 77 °K with water is heated, the conductance decreases slowly after the films have attained a temperature of 273 °K. The films cooled down again to 77 °K after being equilibrated at 273 °K show a decrease in conductance that is appreciably larger than before heating to 273 °K. An iron film covered with more than one monolayer for instance, displayed before heating a decrease in conductance of about 7% and after heating of 19%. Since these authors published the resistances at 77° and 273 °K of three iron films before and after reaction with water at 273 °K, it is possible to calculate the change in residual resistivity and geometric factor. The geometric factor does not change on reaction with water, whereas the residual resistivity increases by about 20%. It appears that on iron surfaces water decomposes to hydroxyl groups and hydrogen atoms at temperatures of 195 °K or higher. For formation of hydrogen direct evidence was obtained; after interaction with water for 38 hr at 273 °K, a hydrogen pressure of 2 x 10 -3 torr was observed. From the effect of pumping on the conductance, the presence of adsorbed hydrogen could be inferred. When the hydrogen coverage is decreased by pumping, the conductance falls as can be seen from Figures 69, 71 and 72. It is interesting to speculate about the adsorption of the hydrogen. The effect of pumping on the conductance demonstrates that some parts of the iron surface are almost completely covered with hydrogen atoms. A large specular reflectivity that decreases on desorption of hydrogen can be obtained only for a surface on which besides hydrogen atoms no other scattering foreign charges are present. This points also to a very limited penetration of water into the pores of the iron film. Part of the hydrogen set free on decomposition of water molecules present on the outer film surface desorbs and part penetrates into the film where it adsorbs on the clean surfaces that are difficult for water molecules to reach. At a hydrogen pressure of about 2 x 10 -3 torr, the iron surface is covered to the extent corresponding to the increasing branch of the conductance versus coverage plot. Analogous effects on conductance due to desorbed hydrogen were observed by Cukr, Merta, Adamek and Ponec (1965). These authors admitted carbon monoxide to an iron film precovered at 273 °K with hydrogen after removing more weakly adsorbed hydrogen by pumping for 30-60 minutes. They observed that the decrease in conductance brought about by displacement of adsorbed hydrogen by the more strongly scattering carbon monoxide was lower when the evolved hydrogen remained in the gas phase above the film. Since carbon monoxide penetrates with a rather sharp boundary into the porous metal film, the internal surfaces are probably still covered with hydrogen atoms only.

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On increasing the hydrogen pressure the gaps in the hydrogen layer are filled, which causes the conductance to rise. From the above it can be concluded that hydroxyl groups are adsorbed on an iron surface having reacted with water. It is very interesting that hydroxyl groups affect the reflection of the conduction electrons at the surface and not the geometric factor; whereas oxygen adatoms also decrease the conductivity of the surface layer of metals, hydroxyl groups only scatter conduction electrons. The evidence for decomposition of water into hydroxyl groups and hydrogen atoms is much less conclusive for nickel. No desorption of hydrogen was found, nor was the effect on the film conductance studied from pumping after water adsorption. Nevertheless it is likely that on nickel, hydroxyl groups and hydrogen atoms are formed by decomposition of adsorbed water. Some interesting data about the effect of adsorbed hydroxyl groups on the conductance can be obtained from a paper by Ponec and Knor (1962). They admitted hydrogen to nickel films covered with oxygen, the reaction producing surface hydroxyl groups. Provided the hydrogen molecules could dissociate, reaction increased the conductance. From their results one may conclude that adsorbed hydroxyl groups only scatter conduction electrons, in agreement with Suhrmann's data for iron films. When the surfaces of iron or nickel films are heavily covered with hydroxyl groups, oxygen atoms, or hydrogen atoms, water molecules may be adsorbed over or into the adsorbed layer. With homogeneous coverages large enough to lead to scattering of conduction electrons, water adsorption will not affect the conductivity of the metal particles in the film. Since adsorption of water without decomposition decreases the work function, charge transport across gaps is increased, and consequently also the conductance of the film. This is the origin of the generally reversible increase in conductance brought about by condensing water vapour on to film with an almost completely covered surface. It is surprising that water appears to react rapidly with clean copper surfaces. Suhrmann and coworkers quoted results of Güllemann, who found the conductance of copper films kept at 77° and 90 °K to increase on hydrogen adsorption and of those kept at 273 °K to decrease. Evidently, physical adsorption of molecular hydrogen decreases the work function of copper and hence increases charge transport across gaps in the films. At 273 °K a very limited activated adsorption of hydrogen atoms leads to scattering of conduction electrons. On admission of water to a copper film kept at 77 °K, the conductance first increases to a small extent, subsequently to decrease strongly. On heating the covered film to 273 °K and recooling the decrease in conductance does not change.

472

J. W. GEUS

From the published resistances at 77 and 273 °K, it can be calculated t h a t for copper the geometric factor increases by 3 to 5 % , and the residual resistivity by 3 to 4 % . If this is correct, it points to copper surfaces dissociating water to oxygen atoms and hydrogen atoms even at 77 °K. The adsorbed oxygen atoms destroy the metallic conductivity of the surface layer, while the hydrogen atoms combine to molecules and desorb. Hence, the reaction of water on copper surfaces is completely different from t h a t on nickel and iron surfaces. The first doses of water decompose on top of the metal crystallites, where the adsorbed oxygen does not affect much the conductance through the film. The evolved hydrogen is physisorbed at the gap surfaces in the film and slightly increases the conductance. When more water is admitted, it covers a larger part of the outer film surface and the oxygen adatoms generated decrease the conductance. The small effect on the conductance at 77 °K of heating a covered copper film to 273 °K is presumably due to the relatively small porosity of copper films. C. EFFECT O FADSORPTIONO NFERROMAGNETIC PROPERTIE S

Investigation of the effect of chemisorption on the saturation magnetization of metal films can provide useful information. I n ferromagnetic materials, the atomic magnetic moments are directed in parallel. There is much evidence t h a t the moments of atoms situated in the surface of metals are also lined up with the magnetic moment of the metal specimen. The effects adsorption can have on the magnetic moment of adsorbing metal atoms are surveyed in Figure 83. The establishment of chemisorptive bonds may or may not lead to decoupling of the moments of the surface atoms from those of the other atoms. If the moments of the surface atoms remain lined up with the magnetic moment of the metal, the change in the moment of surface atoms can be inferred straightforwardly from the effect on the saturation magnetization. If, on the other hand, the moments of the surface atoms are decoupled on adsorption, the effect on the saturation magnetization depends strongly on temperature. At temperatures above about 70 °K, the orientation energy of an isolated atomic moment in a magnetic field of about 104 oe (of the order of 10 - 1 5 erg) is small compared with the thermal energy, which is 1.4 x 10~14 erg at 100 °K and 4.2 x 10~14 at 300 °K. Since the moments of a ferromagnet are coupled, the orientation energy is larger than t h a t of an isolated atomic moment by a factor equal to the number of atoms in the specimen, which generally is extremely large. Decoupling of the moments of the surface atoms consequently decreases the saturation magnetization measured at tern-

THE INFLUENCE OF ADSORPTION ON METAL FILMS

473

peratures above about 100 °K, irrespective of an increase or decrease of the moments. When the decoupled moments do not interact mutually, determination of the magnetization at very low temperatures, e.g. 4.2 °K, shows whether the moments of the surface atoms increase or

no decoupling decoupling

JM>0

e K, JM>0 if temp.>100 if temp.~4eK. JM depends on interaction between decoupled moments

4M=0

AM<0

ΔΜ<0 FIG. 83. Survey of effects of adsorption on the ferromagnetism of adsorbents.

decrease on adsorption. If, however, the decoupled moments interact, they cannot orient their moments at low temperatures in a magnetic field. Interaction between decoupled moments may be antiferromagnetic as in bulk nickel oxide, where the atomic moments are oriented anti-

474

J . W. GEUS

parallel. When the metal surface atoms retain their metallic character when taking part in adsorption, Pauli paramagnetism prevents orientation of all atomic moments in a magnetic field. To endow the collective electrons with wave functions having equal spins, their kinetic energy must be increased much more than the energy connected with orientation of the moments in a magnetic field. On formation of a metal surface hydride, Pauli paramagnetism of decoupled moments is quite conceivable. Two sets of experiments on the effect of adsorption on the saturation magnetization of nickel and iron films are available. Neugebauer (1961) investigated the change in magnetic moment of nickel films evaporated in ultrahigh vacuum on exposure to hydrogen and oxygen. Oxygen decreased the magnetic moment of nickel films measured at room temperature. On reaction with oxygen at low pressures, Neugebauer observed the thickness of the nickel, as calculated per cm 2 of geometric surface area, to decrease by 6 to 12 Ä. Since a decrease in atomic moment of nickel on reaction with oxygen is quite improbable, Neugebauer's results point to decoupling of the moments of the chemisorbing nickel atoms on reaction with oxygen. The effect of hydrogen adsorption on the magnetic moments of nickel films appeared to depend strongly on the size of the nickel crystallites in the film. At mean film thicknesses below about 30 Ä, where the nickel particles were so small t h a t they behave super-paramagnetically (Bean and Livingstone, 1959), the magnetization falls on hydrogen adsorption. The saturation magnetization of thicker nickel films containing larger metal crystallites was, however, not affected by hydrogen adsorption. Geus and Koks (unpublished) determined the thickness of the ferromagnetic layer of iron and nickel films by measuring the rotation of the plane of polarization of linearly polarized light which passed through the films (Figure 84). The apparatus used for estimating the rotation allows the ferromagnetic thickness of iron and nickel films to be determined with an accuracy of about 0.1 Ä for iron and 0.2 A for nickel. I n Figure 85 the rotation of the plane of polarization is represented as a function of the film thickness. The curves in Figure 85 do not pass through the origin because of the surface roughness of the films. Since the transmitting light is strongly absorbed by the metal film, the rotation of the plane of polarization is determined by the thinner parts of the film. As can be seen from Figure 85, the diffraction of the light passing through the film restricts the difference between the weight and optical thickness to a constant value of about 100 A for iron and 150 Ä for nickel above thicknesses of about 150 Ä (iron) and 200 A (nickel).

475

magnetic field

linearly polarized light

rotation of plane of polarization measures [ferromagnetic thickness

metal film FIG. 84. Measurement of the ferromagnetic thickness of metal films by means of the Faraday effect. 4000

3000

a 'S

£. 2000| c o "S 15

1000h

100

200

300

400

500

film thickness (Ä) FIG. 85. Rotation of plane of polarization of light passing through iron (O) and nickel ( # ) films as a function of film thickness determined by X-ray fluorescence.

476

J. W. GEUS

I n Figure 86 the decrease in ferromagnetic thickness by sorption of oxygen for iron and nickel films is indicated. From the data for nickel films it can be seen t h a t the results are highly reproducible. The differing slopes of the experimental curves are due to preferential adsorption of oxygen on top of the crystallites in the first stage of the sorption process. As the oxygen penetrates more between the crystallites where the thickness of the ferromagnetic metal determines the rotation of the plane of polarization, the slope increases. The decrease in ferromagnetic thickness of nickel films by oxygen sorption is 3.8 to 4.3 Ä, which corresponds to an amount of 3.5 to 3.9 x 1015 nickel atoms c m - 2 of which the atomic moments are decoupled. Since a roughness factor of two to three is usual, the decrease is in agreement with Neugebauer's results, who observed a decrease of 6 to 12 A per cm 2 of geometric surface area. From independent sorption measurements it is known that nickel surfaces take up some 2.68 x 1015 oxygen atom cm - 2 . The larger number of nickel atoms affected demonstrates t h a t the nickel surfaces near the gaps t h a t determine the rotation of the plane of polarization are inclined to the light beam, as must be expected. The experimental data suggest an angle of about 40°, which is quite reasonable. The decrease in ferromagnetic thickness for iron is about 10.4 Ä, which corresponds to 8.76 x 1015 iron atoms cm~ 2 decoupled. The fact t h a t iron surfaces take up about 6.42 x 10 ]5 oxygen atoms c m - 2 suggests also for iron an angle of about 40°. The above experimental data point to a reaction of one oxygen atom with one surface nickel or iron atom. A higher oxygen-to-metal atom ratio leads to an unreasonable inclination of the adsorbing surface with respect to the substrate plane. This ratio is not unreasonable for nickel: nickel oxide is the only stable oxide of nickel and does not display marked deviations from the stoichiometric composition. The heat of adsorption of oxygen on nickel at room temperature is roughly equal to the heat of formation of nickel oxide, which also points to a structure of the surface approximating t h a t of nickel oxide. Since for iron a number of stable oxides are known which all display about the same heat of formation per mole of oxygen, the results for iron are more interesting. Iron (II) oxide is not stable at temperatures below about 500 °C, where it tends to disproportionate to magnetite (Fe 3 0 4 ) and metallic iron. Since the mean magnetic moment per iron atom in magnetite is more than one half of t h a t in bulk iron (1.4 and 2.2 Bohr magnetons, respectively), the present experimental data point to formation of iron (II) oxide. The oxygen-to-iron ratio experimentally found is too low to be compatible with iron (III) oxide. That iron (II) oxide is formed on reaction of iron surfaces at room

477

THE INFLUENCE OF ADSORPTION ON METAL FILMS

101Zf O2 molecules cm"2 5

10

15

20

2 -10 o

-20h

-30h

101A 0 2 molecules cm"2

0

u

σ 'S

X

-50

30

20 »

10

1

> , "Ό

0 Qv

-100 ~

\

0

FIG. 86. Decrease in rotation of plane of polarization of light going through iron (lower graph) and nickel (upper graph) films on reaction with oxygen. For iron a maximum oxygen sorption of 3.2 x 1015 oxygen molecules c m - 2 is assumed, and for nickel of 1.7 X 1015 oxygen molecules cm - 2 . These values are based on data for oxygen sorption on iron and nickel films with a known BET surface area. Four separate nickel experiments are shown. The vertical bars indicate ΔΜ to be expected for one layer of metal atoms. (After Geus and Koks, unpublished.) T·

478

J. W. GEUS

temperatures in agreement with L E E D evidence. Pignocco and Pelissier (1967) observed on extensive reaction of oxygen with (110) iron surfaces an epitaxial iron (II) oxide layer, which was confirmed by Moliere and Portele (1969). The latter authors only found an epitaxial spinel lattice on heating the covered iron crystal to about 300 °C. As can be seen in Figure 87, hydrogen adsorption does not affect the ferromagnetic thickness of nickel films, which was also established for iron films. This is in agreement with the findings of Neugebauer for larger nickel crystallites. From the effect of hydrogen on the conductance of iron films deposited at 273 °K and nickel films deposited at 77 °K, it was also apparent t h a t adsorption of hydrogen on surfaces t h a t are not atomically rough to an appreciable extent did not influence the metal structure markedly. On the other hand, there is much evidence that adsorption of hydrogen decreases the ferromagnetism of small supported nickel particles (Selwood, 1962; Geus, Nobel and Zwietering, 1962), as was found also for thin nickel films by Neugebauer. We believe that the profound difference in the effect of hydrogen adsorption on the magnetic moment of small and large nickel particles is again due to the difference in structure of the surface. From the large uptake of atomized hydrogen by nickel films kept at 77 °K, it was apparent t h a t the stability of surface nickel hydride is relatively large. If, hence, expansion of the metal lattice does not require much energy, this can be easily formed. Penetration of hydrogen atoms at steps in nickel surfaces can proceed easily. This leads to formation of a surface nickel hydride that is not ferromagnetic, as can be concluded from the data of Bauer and Schmidbauer (1961). As can be seen in Figure 87, carbon monoxide affects less than one layer of nickel atoms, with a corresponding rotation of 14.5 sec. Since the effects are very small and differ for different films, it is difficult to draw conclusions from the data. The effect of carbon monoxide on the conductance of nickel films showed t h a t about 5 x 1014 carbon monoxide molecules c m - 2 were taken up with a decrease in conductance, which was due to a relatively small increase in geometric factor and a larger effect on the residual resistivity. We believe t h a t the decrease in ferromagnetic thickness is due to nickel atoms being lifted somewhat from the surface at some crystallographic planes; this also results in the increase in the geometric factor. When nickel atoms are lifted from the surface, their moments will be decoupled from those of the underlying nickel. This conclusion is substantiated by the fact t h a t the ferromagnetic thickness of iron films, the geometric factor of which is not affected by carbon monoxide, does not decrease on carbon monoxide adsorption. Nevertheless, it is difficult to

THE INFLUENCE OF ADSORPTION ON METAL FILMS

479

envisage how metal atoms can strongly bond carbon monoxide without changing their atomic moments in the configuration of Figure 30. However, bonding of carbon monoxide in a configuration in which both the carbon and the oxygen atoms contact metal surface atoms cannot be excluded (Gomer, 1967). Work by Bradshaw and Pritchard (1969) demonstrates that infrared evidence obtained on supported nickel particles (Eischens and Pliskin, 1958) should be treated with caution.

FIG. 87. Effect of carbon monoxide and hydrogen adsorption on the ferromagnetic thickness of nickel films. Carbon monoxide: O, average film thickness 105 A; □ , 292 Ä; x , 150 A; V, 230 A. Hydrogen: · , The vertical bar indicates ΔΜ to be expected for ■fa layer of nickel atoms. The dotted extension to the V curve is a measurement after 16 hours. (After Geus and Koks, unpublished.)

Finally, we stress once more that the scatter of the decreases in ferromagnetism in Figure 87 among different films is too large to draw firmly based conclusions. D . EFFECT OF ADSORPTION ON THE HALL COEFFICIENT

In section II.A.2 (Figure 9), the determination of the sign and density of charge carriers by means of the Hall effect was mentioned. From

480

J . W. GEUS

equation (II)-(27) it can be derived t h a t for a magnetic field, H, perpendicular to the film plane the Hall voltage V H is equal to Hi VH = R H - J

(ΠΙ)-(4)

where i is the current through the film and d is the film thickness. From equation (III)-(4) it can be seen t h a t the Hall voltage is determined by the density of the charge carriers and the thickness of the conducting layer. When the mean free path of the charge carriers is of the order of the film thickness and the film surface reflects conduction electrons diffusely, the Hall coefficient, R H , becomes larger than for an infinite conductor. Sondheimer (1950) theoretically calculated this increase in Hall coefficient. With decreasing ratio of film thickness to mean free path, the Hall coefficient increases, but not as rapidly as the resistivity. From the discussion in section II.C it can be expected t h a t the Hall voltage is increased by adsorption on the film surface owing to an increase in the diffuse reflection of the conduction electrons. If the specular reflection of the surface grows at increasing coverage as is found, for instance, for hydrogen and oxygen, the Hall voltage will decrease. Hansen and Littmann (1963) investigated the effect of carbon monoxide on the conductance and Hall voltage of zirconium, nickel and iron films and of oxygen on copper films. I n all the above cases, an increase in Hall coefficient was observed. From the data of section III.C this must be expected as either the conductivity of the surface layer is decreased or the specular reflection of conduction electron is destroyed, or both. For carbon monoxide adsorption on zirconium films, the increases in the Hall voltage and in the resistance were about equal. Since the mean free path of conduction electrons will be short in these films at room temperature, this is reasonable. Bastl (1968, 1970) published some results on the effect of oxygen sorption on the Hall voltage of nickel films and t h a t of hydrogen, oxygen and nitrogen chemisorption on the Hall voltages of molybdenum films. Whereas the results obtained for oxygen on nickel could be explained quite well, Bastl could not account for his results obtained on molybdenum films. I n view of the columnar structure of evaporated metal films and the rather large experimental geometric factor displayed by the analogous tungsten films, we believe t h a t the effective thickness of the films can be rather small. Since, moreover, oxygen on tungsten did not affect the reflection on the conduction electrons, which nitrogen strongly does, we think t h a t Bastl's results can be reasonably well explained. However, the results of Murgulescu and Comsa (1967) who reported a decrease in Hall voltage of copper films on reaction with

THE INFLUENCE OF ADSORPTION ON METAL FILMS

481

oxygen and carbon monoxide, present greater difficulty. This result is in contrast to the findings of Hansen and Littmann discussed above. We here suggest a repetition of the measurements at better vacua, because copper films which have a low surface area can be easily contaminated to a great extent. REFERENCES

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