Electronic properties of alkali submonolayers on a metal substrate

Surface Science 55 (1976) 246-258 0 North-Holland Publishing Company

ELECTRONIC

PROPERTIES

OF ALKALI SUBMONOLAYERS

ON A METAL SUBSTRATE K.F. WOJCIECHOWSKI* International

Cen tre for Theoretical Physics, Trieste, Italy

Received 29 August 1975 The electronic properties of alkali submonolayers on a metal substrate are investigated on the example of the Cs-W system. Using Lang’s jelhum model for the substrate adsorbate system, the charge density profiles in the submonolayers as a function of coverage were determined. The profiles were used, in local density approximation, to determine the distance from the metal substrate at which the density of an electron gas is the same as in the bulk adsorbate, and the distance at which the extra adatom acquires an additional bound state. The transition probability of valence electron of adatom to the metal-adsorbate system was also estimated as a function of coverage. The results obtained in the framework of the jellium model, as well as those following from the virtual impurity bound states picture, point.out that in a very low coverage range the submonolayer consists of adions forming surface dipoles together with their screening charges, and in a near-monolayer coverage range the transition of the submonolayer to the metallic state is to be expected.

1. Introduction In recent years the theory of chemisorption on metals has been widely developed [l-5]. In particular, quite a number of paper have been devoted to the theoretical [3-51 and experimental [6-91 investigations of alkali adsorption. The theoretical papers have dealt mainly with the so-called zero adsorption, for zero coverage. The adsorption of many atoms is, of course, a more complicated problem from the theoretical point of view, but it is so far the most favourable case’for experimental investigations. There are, however, papers containing successful theoretical results in the case of many alkali atoms adsorption on metals [ 10,111. In these papers the influence of the charge density in a submonolayer on the work function was examined. There is a lack, however, of theoretical investigations of the behaviour of an adsorbed layer with complete coverage. In this paper we shall present some approximate considerations which enable us to give a qualitative explanation of adsorbed alkali layers properties within the

* Permanent address: Institute of Experimental Physics, University of Wroclaw, Ul. Cybulskiego 36, Wroclaw, Poland.

K.F. WojciechowskilElectronicproperties ofalkdi ~brnono~a~~~ on metal

247

*Jr

Thai--_-___-WoQ& -_---...-__

___A---=-

_A-

%I 2

E.

%a (a)

a

[PI 4I-

i

Fig. 1. (a) The dependence of the experimentally determined lattice constant a density R. (b) The same for the lattice constant P of alkali metals.

on

the electron

248

K.F. WojciechowskifElectronic

properties of alkali submonolayers

on metal

cp[eVI’ 5-

4-

3-

::

10

20

30

40

50

60

70

80

n=rci36.u.

(a)

2.5 -

(b) Fig. 2. (a) The dependence of the experimental work function upon the electron density n. (b) The same for the work function q of alkali metals.

within the framework of the jellium model. The main physical quantity in this model is the density n of conduction electrons and other quantities depending essentially on n [ 121. In figs. la-3a we present the experimental values of lattice constant a, work function cpand cohesive energy E, versus electron density n for a number of metals. From the figures it follows that for the entire metallic range of n, one can observe only some gross dependence of a, cpand Es on n. On the other hand, however, we can conclude from these figures that for alkali metals the depen-

RR Wojciee~owsk~~E~ectr~n~c properties of alkali submonduyers on metal

249

ES

eV

It

atom [

r

8 n

x1tF3a.u.

(b) Fig. 3. (a) The dependence of the experimentally determined sublimation energy Es on the electron density n. (b) The same for the sublimation energy Es of atkali metals.

dence of a, ~1and Es on n is distinct and regular (figs. lb-3b). This conclusion is the starting point of the present paper, where we shall consider the electronic properties of alkali submonolayers in the framework of the jellium model and using the sugges-

250

K.F. WojciechowskilElectronic

properties of alkali submonolayers

on metal

tion of March [ 131 that the above-mentioned properties depend strongly on the electron density profile near the metal surface.

2. Uniform-background

models

The present treatment is based on the theory of the inhomogeneous electron gas [ 141. The electronic properties of alkali submonolayers on a metal substrate will be considered in a framework of jellium models used by Lang and Kohn [ 1.51. Thus the metal substrate is represented by the model in which the positive charges are replaced by a uniform background of density &(‘)

=nM,

ZdO,

= 0,

z > 0,

(1)

where $I denotes the bulk density in the metal and the plane z = 0 passes through the centres of the external layer of metal ions. In order to study the electron properties of alkali submonolayers on a metal substrate, we adopt the model used by Lang [lo]. In this model the ionic charge of the adsorbate layer is replaced by a homogeneous positive slab of thickness 22, and of density ntd(0), adjoining the substrate background (fig. 4). Thus the total positive background is n+(z, 0) = n,M,

z GO,

=n+Ad(e)=en*,

O
= 0,

z>2z,,

(2)

where 0 denotes the coverage of the metal surface (0 = 1 for monolayer), nA the bulk density of alkali metal, and z. the distance of the centres of adatoms from the substrate surface.

0

Fig. 4. Schematic layer (en,).

representation

of positive background

2z0

7.

of metal substrate (no)

and adsorbed

251

K.F. Wojciechowski/Electronicproperties of alkalisubmonolayers on metal

a(n)

(4

4

6

v(n)

-o-‘_‘_‘_

._._._

‘1.

9

Cs

Rb

K

I

1

1

I

I

I

I

1

2

3

4

5

6

7

5.5

‘\

‘\,

‘.

I

8

9

Na

I

I

n I lo-‘trti21r

change of work function p of tungsten (100) plane covered by Na [ 171, K [ 181, and Cs [ 191 (full lines), and the change of lattice constant a (0) and tvork function up(0) of bulk alkali metals versus adatom concentration n.

The

Such a choice of the slab representing the adlayer follows from the experimental observation of work function variations with the coverage. Fig. 5 contains the experimental curves of work function variation with the surface concentration n, ofalkaliadatoms(Na [17],K [18],Cs [19]) on the (100) plane of tungsten. In the same figure the curves are also given representing the variation of work function cp and lattice constant a of alkali metals on bulk electron density n (compare figs. 1b and 2b) transformed into surface concentration n, by the relation n, = na. It is seen from fig. 5 that the work function of an alkali monolayer on metal is very close to the work function of the bulk alkali metal. Now we shall focus our attention on the adsorption of Cs on tungsten; therefore, ny = 56.2 X 10e3 a.u. [16], which corresponds to rs = 1.62 and nCs = 1.33 X 10e3 a.u. [16]. For z. we accept the value z. = 2.4 A, which is approximately the sum of the ionic radii of W6+ and Cs+. The method of self-consistent calculation of n(z) and n(z, 0) is the same as that adopted by Lang and Kohn [ 151. Namely, it reduces to numerical solution of the following set of equations (atomic units are used):

J/k(z)=+ck2 -kc) J/k(z), u&L”; a3 = 9 [n(Z)] - 47r J dz’ J d2” [n(Z”) - n+(Z”)] Z

Z’

+ /.l,,(n(Z))

(3b)

252

K.F. WojciechowskilElectronic

properties of alkali submonolayers

on metal

kF

n(Z) = ?- jlr2 0

(kc - k2) [$&)I 2dk,

(34

where $k(z) = sin [kz + y(k)], asymptotically

for z + -m, and y(k) is the phase shift,

@[n(z)1 = 47r sz

_m

[n(z) -

n+(z)1dz - ik; + I-+&+,&

and

with l/3

0.458 0.44 EXC= - - r,(n) - 7.8 ’ r,(n)

n-113.

For the denotation of symbols see ref. [ 151. Since we have calculated only the tail (for z > 0) of the electron profile n(z), we have neglected the Friedel oscillations, which are not so important in the case being considered.

3. Electron density profdes The computed tail of the electron number distributions n(k), zo, z) (z > 0) for 8 =0,0.5 and 1, and for z. = 2.4 A are presented in fig. 6. The density profile n(z, zo, 0 ) for z > 0 can be approximated by the numerically fitted function n(z, zo, 0)

= 0.462 ny exp (-2.23~) tenCsexp

[-$

(y)L]

_ forz
= 0.462 ny exp (-2.23~)

+BnCsexp[

-y

(y)2]

(4) forz>zO.

An analytic form of n(z, zo, 0 ), determined by (4) enables us to obtain further information on the electronic structure of an adlayer. Namely, let us consider now what happens when an extra adatom enters the region where the conduction electrons

K.F. Wojciechowski/Electronic

2

properties of alkali submonolayers

3

4

5

z(A)

on metal

253

6

Fig. 6. Self-consistent electron density distributions n(z, ~9) for bare-substrate model (tungsten, 0 = 0) and for model of substrate with a half monolayer (0 = 0.5) and with a full monolayer of adsorbed Cs atoms.

spill out from the metal covered by adsorbate. Using a local density approximation, we can estimate from the equality n(zfi 20, e) = n,CS,

(5)

where n(zC ~0, 8 ) is g iven by (4) with z = Zi, the distance Zi(e) from the metal surface at which the density of the electron gas is the same as in bulk alkali metal. The distance Zi as a function of 0 is given in fig. 7. On the other hand, it has been shown by Meyer et al. [20], that when an ion such as Cs+ is inserted into a free-electron gas of sufficiently low density, a new bound state of s character is formed. The authors have calculated the critical densities n, at which atoms acquire an additional bound state. March and collaborators [21] have used the values of n, to calculate the distance zc at which a proton brought up to a metal surface acquires a bound state. Using the analytic form (4) for the density profile n(z, zo, 0) we have estimated the distance z,(0) for the system considered here, using the equality n(z,,zo,

0) = n,.

(6)

The result is shown in fig. 7 (dashed line) where the function Az = zc -zi is also given. As is seen from this figure, z,(0) is an increasmg function of 0. This increase, however, is not very rapid and thus, in practice, a bound state cannot be formed for

254

ofalkali submonoluyers on metal

K.F. Wojciechowski/E~ectronic properties

5 I

7

I’

&

,I’

w-cs ,I

4-

I6 ,I ‘/ z,

0

I

/

I

I

I

1

0.2

0.4

0.6

0.8

8

1

Fig. 7, The distance Zi from the metal substrate surface at which the density of the electron gas is the same as in the bulk adsorbate, and the distance zc at which the extra adatom acquires an additional bound state versus coverage 8; A = z,(@) -z&e).

the case of the system W-Cs, for which the calculated [22] transition probability of valence electron of adatom to the metal is still high (- 0.80) even for a quite large distance (z = 5 a). On the other hand, we observe from fig. 7 that z$,e) distinctly increases starting from 8 - 0.6. These two facts may be interpreted in the following manner. For low coverages the valence electrons of adatoms are fully transferred into the metal, and the adions form the surface dipoles together with their screening charges. For greater coverages the adions are embedded in electron gas of increasing density, and for coverage equal to about 0.8, the submonolayer of alkali adsorbate attains properties of bulk alkali metal. Now let us estimate how the transition probability (per unit of time) o of electron from adatom to the adsorbate layer changes with coverage. To do this we begin by calculating the energy shift AE of the ionization level of the adatom in the presence of an adlayer:

AE(t3,d) = (nsl

r_;‘(s)

‘ns),

where Ins) denotes an atomic s-like wave function

K.F. WojciechowskilElectronic

properties of alkali submonolayers

on metal

255

Ins) = rr(~n)~” (1 - ar) exp (-ur),

(8)

with a = 0.99 A-’ for Cs. Here k;’ denotes the screening length, which in the framework of a local density approximation can be computed from the relation k,l@)

= 0.91 .-l/6(,

= 20, e) A,

(9)

but only for 0 > 0.5. For 8 = 0 we have used in (9) the bulk density of tungsten. was shown [23] that AE(B, d) =(3.6/d)

(1 -k;‘/2d)eV,

It

(10)

where d is the effective distance between the ion core and the polarization charge which it induces. Using formula (9) we have from (10) (taking d = ri, ‘i being the ionic radius of Cs+): AE(B = 0) = 1.82 eV,

uqe

= 0.2) = 1 .SO eV,

aE(e = O.S)= 1.51 eV,

aE(B = 1) = 1.63 eV.

(11)

The width I’, for a single Cs atom adsorbed on tungsten (0 = 0) was calculated by Gadzuk [22] ;

r, =

(w + EFw - Jcs + AE)l12

2Z,e4q2

X (l--

d3exp (-24zd)

wtEFw

an(2m)1/2

4/a2d2 + S/a4d4),

where Z eff is the effective adion charge number; % is the work function, E,, the Fermi energy of tungsten and J,, the ionization energy of the Cs atom. The transition probability w is related to the width r by: w = r/h.

(13)

To estimate o for an adatom under the submonolayer, rcs-w tie)=r,=x

+&w(e) [

ZCP zC&W

%J +EFW (PCs-w@)

t EF,&w@) ‘pw+EFw

we compute the ratio u(e):

-Jcs

t E~,c,_w(@

- Jcs + M(e) +AE(O)

1

(14)

1’2 .

Taking gfiWcs = 1, Z2&-w = 0.8 [24], \ocs = 1.8 1 eV, Jcs = 3.86 eV and EFW = 18.99 eV (according to quantities given in ref. [ 161 for tungsten), it follows from (14) that r(0) is a decreasing function of 0 for 0 < 0.4, and an increasing function of t9 for 0 > 0.4. Thus (see also fig. 7), for low coverage range one expects to observe the desorption of ions, and after that, with increase of coverage, the number of desorbed atoms increases. This conclusion agrees with experiments on the surface ionization [25,26] and with the classical Saha-Langmuir relation. The energetic

256

K.F WojciechowskilElectronic properties of alkali submonolayers on metal

Fig. 8. Energy level diagrams for Cs-W system, which represent the shift of energy levels of Cs as it interacts with the clean surface (0 = 0) and with the surface covered by cesium layers (0 = 0.2, f3 = 0.5,0 = 1). Values of 9, A and Jo are given in eV.

situation of an extra adatom adsorbed on a cesium layer, as computed above, is illustrated in fig. 8. From this diagram and from results concerning zc given in fig. 7 it follows that for coverages, say, between -0.3 and 0.5, the quasi-bound states at adatoms may be formed. Therefore, one can expect that for very low coverages the submonolayer of alkali atoms on metal of high electron density is built up from ions, for intermediate coverages the layer consists of atoms, and near to a full monolayer one expects metallic character. Therefore, for the adsorption system considered here we may expect something like a transition of the adsorbed layer form the non-fully-metallic state to the metallic one. It is to be noted here that the concept of metallization of the alkali submonolayers for high coverage was suggested by many authors [27-29,10,8] and recently has been applied by March and collaborators [30] to the H2 adsorption on the (111) platinum plane. This suggestion finds additional confirmation in the experimentally observed variations of work function with coverage. Namely, from fig. 5 it follows that the run of the experimentally observed work function dependence on coverage, starting from high coverages to the coverages at which the work

K.F

Wojciechowski/Electronic

properties of alkali submonolayers

on metal

251

function achieves its minimum, is nearly the same as the dependence of bulk alkali work functions on electron density. On the other hand, accepting the above concept that for coverages greater than about 0.8 the adlayer has properties similar to bulk alkali metals, one can predict, on the basis of curve a(n) in fig. 5, that the mean distance R between Cs adions in a monolayer will be smaller than in bulk cesium due to the fact that the electron density in the vicinity of the adion position (z = zu) is slightly greater than in bulk cesium, as can be seen from fig. 6. This conclusion is confirmed by experiment [9,3 1,321. In particular, Fedorus and Naumovets [3 1] have found that R in a cesium monolayer equals 4.7 A, while R for bulk cesium is 5.25 A.

4. Final remarks The jellium model approximation is, of course, inadequate for a fully quantitative description of the above-mentioned kind of transition of alkali submonolayers on metals. Nevertheless, the rapid increase of z,(e) for coverages greater than 0.5 indicates that the electronic configuration in the adlayer changes distinctly at about half monolayer coverage. Starting from this fact, one can divide the whole range of coverage into two intervals: (i) low coverage range (LCR) (0 < 19< 0.5) and (ii) near monolayer coverage range (NMCR) (0.5 5 0 < 1). The work function changes induced by alkali adsorption has been examined by Lang [lo] and, more recently, by Muscat and Newns [ 111. In the latter paper it was shown that for LCR both the induced dipole and dipolarization effect of these dipoles with increasing 8 play an essential role. Thus, in the first approximation, the frequently used depolarizing model gives a good explanation of the initial decrease of cp(B)(cf. refs. [33] and [7-91). When the coverage reaches such a value that the conducting electrons in the submonolayer (NMCR) can be treated as nearly free, the increase of work function results from the increase of density of electrons in the adsorbed layer with a coverage. This effect is similar to the work function increase with increasing electronic density in bulk alkali metals (cf. figs. 2b and 5). Similarly, in LCR we can explain the experimentally observed decrease of adsorption heat 4 by mutual addipole-addipole interaction. Indeed, taking into account the energy of interaction between adions and its screening charges and the change of interaction energy between surface dipoles, when an extra adatom is added we find quite good agreement between calculated q(0) and that determined experimentally for LCR.

Acknowledgements I am grateful to Professor N.H. March, Dr. J.W. Gadzuk and Dr. N.D. Lang for helpful discussions and for critical reading of the manuscript. I also wish to express

258

K.F. WojciechowskifEiectronicproperties of alkalisubmonolayers on metal

my tahnks to Professors Abdus Salam and P. Budini as well as the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste.

References [I] J.R. Schrieffer, J. Sci. Technol. 9 (1972) 561. [ 21 T.B. Grimley, Theory of Chemisorption (to be pub~shed). [3] J.W. Gadzuk, in: Surface Physics of Crystalline Materials, Ed. J.M. Blakely (Academic Press, New York, 1975). [4] J.R. Schrieffer, lectures at the Winter College on Surface Science, ICTP, Trieste, 1974. 1.51 N.D. Lang, in: Solid State Physics, Vol. 28, Eds. H. Ehrenreich, F. Seitz and D. Turnbull (Academic Press, New York, 1973). [6] R. Comer, lectures at the Winter College on Surface Science, ICTP, Trieste, 1974. [7] C.J. Todd and T.N. Rhodin, Surface Sci. 42 (1974) 109. [8] 2. Sidorski, Acta Univ. Wrat. No. 254 (1975) (in Polish). [9] V.K. Medvedev and A.J. Yakivtchuk, The Structure and Electron-Adsorption Properties of Alkali Layers on (Ill)-Face of Tungsten Monocrystal (Acad. Sci. Ukrainian SSR, Kiev, 1975) (in Russian). [lo] N.D. Lang, Phys. Rev. B4 (1971) 4234. [ 1i] J.P. Muscat and D.M. Newns, J. Phys. C7 (1974) 2630. [ 121 W. Jones and N.H. March, Theoretical Solid State Physics, Vol. 2 prey-Interscien~, London, 1973). [ 131 N.H. March, private communication. [ 14) P. Hohenberg and W. Kohn, Phys. Rev. B136 (1964) 864. [15] N.D. Lang and W. Kohn, Phys. Rev. Bl (1970) 4555. [ 161 J.R. Smith, Phys. Rev. 181 (1969) 522. [ 17) E.V. Klimenko and V.K. Medvedev, Solid State Phys. (USSR) 10 (1968) 1986. [18] R. Blaszczyszyn, M. Blaszczyszyn and R. Meclewski, Surface Sci. 51 (1975) 396. I191 Yu. Vedula, Yu. Konoplev, V. Medvedev, A. Naumovets, T. Smereka and A. Fedorus, Third Intern. Conf. on Thermionic Electrical Power Conservation, Jiilich, 1972. [20] A. Meyer, C.W. Nestor and W.H. Young, Proc. Phys. Sot. (London) 92 (1967) 446. [21] J.S. Brown and N.H. March, Phys. Letters 47A (1974) 489. [22 j J.W. Gadzuk, Surface Sci. 6 (1967) 133; 6 (1967) 159; M. Remy, J. Chem. Phys. 53 (1970) 2487. 1231 F.K. Wojciechows~, Surface Sci. 36 (1973) 689. (241 J.W. Gadzuk, in: The Structure and Chemistry of Solid Surfaces, Ed. GA. Somorjai (Wiley, New York, 1969). (2.51 A.T. Forrester, J. Chem. Phys. 42 (1965) 972. [26] N.I. Ionov, Progr. Surface Sci. 1 (1972) 344 [27] AU. MacRae, K. Mtiller, J.J. Lander, J. Morrison and J.C. Philips, Phys. Rev. Letters 22 (1969) 1048. f28J 2. Sidorski and K.F. Woj~ie~howski, Acta Phys. Polon. A40 (1971) 661. [29] Z. Sidorski, Acta Phys. Polon. A42 (1972) 437. [30] R.C. Brown, P.J. Dobson and N.H. March, Phys. Letters, in press. [31] A.C. Fedorus and A.G. Naumovets, Surface Sci. 21 (1970) 426. [32] S. Andersson and U. Jostell, Solid State Commun. 13 (1973) 829. [33] S. Andersson and U. Jostell, Surface Sci. 46 (1974) 62.5.