X.P.S. LINE BROADENING IN SMALL METAL PARTICLES

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X.P.S. LINE BROADENING IN SMALL METAL

PARTICLES

P. Ascarelli, M. Cini, G. Missoni, N. Nisticò

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C2, supplfiment au no 7, Tome 38, Juillet 1977, page C2-125

X.P.S.

LINE BROADENING IN

SMALL

IMETAL PARTICLES

P. ASCARELLI, M. CINI, G. MISSONI and N. N I S T I C ~

Laboratori Ricerche di Base, Snamprogetti S.p.A., Monterotondo (Rome), Italy

R6sum6. - La largeur h mi-hauteur du pic X.P.S. des films discontinus d'or a kt6 mesurCe en fonction de son Bpaisseur et nous avons trouv6 qu'elle augmente avec la diminution de la dimension de la particule.

Nous proposons une explication th6orique de cet effet en termes de reduction du pouvoir d'bcran des electrons sur le potentiel d'6tat final de trou.

Abstract.

-

The X.P.S. line-width of discontinuous gold films is measured as a function of film thickness and is found to increase with decreasing particle's size.

A theoretical explanation of this effect is proposed in terms of the reduced electronic screening of the final state core hole potential.

1. Introduction.

-

The peculiar electronic properties displayed by small metal particles (i.e. 10

A

; 100

A

size) are subject of considerable current interest in surface physics and their detailed characterization is necessary for the improvement of their technological use.

One field where this need is mostly felt is heterogeneous catalysis, since many metallic cata- lysts consist of very small metallic particles (up to 100

A

in size) supported on high surface area insulators like A1203 (alumina) or SiOz (silica).

Among the small size particle's properties one seems to be particularly 'relevant to its catalytic properties, it is the reduced electron ability to screen electrostatic fields [I, 21. A consequence of this fact is a longer interaction range which should affect chemisorption properties especially when electron transfer is involved [3].

Here we report a study of X.P.S. spectra of 4f 5 / 2 , 7/2 Au lines in discontinuous gold films. A

A "

FIG. 1. - Typical X.P.S. spectra of gold films of different thickness evaporated on teflon. Sample (1) ha$ a thickness of about or less than 1 A, sample (2) of about 50 A, and sample (3)

was a piece of bulk gold.

The F.W.H.M. of the lines are reported and are respectively for sample (1) 2.6 (eV), (2) 1.8 (eV), (3) 1.3 (eV). The fluorine line for sample (1) and (2) are also reported, they show the same

F.W.H.M.

broadening of the X.P.S. line with decreasing

The whole set of data is shown on figure 2,

average metallic particle size is observed and

where the full width at half -maximum (F. W .H.M.) explained theoretically in terms of the reduced

of the Au line is reported as a function of film screening of the final state core hole potential. _{thickness. The error bars represent an evaluation of}

2. Experiment.

-

The samples were prepared by evaporating at a pressure of torr films of high purity gold on teflon plates 20 mm long 0.5 mm large.

The thickness was measured by a conventional quartz oscillator and the spectra taken with an A.E.I. E.S. 100 spectrometer operating in a vacuum of the order of torr and using the AlK,X ray line. The Au 4f 5/2, 7/2 and F 1 s lines have been recorded for samples of nominal thicknesses in the range between less than 1

A

to about 100

A.

3. Results.

-

Typical spectra for bulk gold and discontinuous thin films are shown on figure 1.

the experimental uncertainty on such data. It should be noticed that because evaporated thin films usually agglomerate to form isIands thin films up to about 60

A

are discontinuous and not conductive. This means that the sample under X-ray irradiation and consequent electron emission charges up [4]. Since charging, due to secondary electron flux is inhomogeneous over the sample surface it is a source of line broadening. However an evaluation of the maximum line broadening due to charging can easily be made, for instance, by means of a sample where a reticulate of macrosco- pic thick metallic islands are produced by evapprat- ing gold through a metal net with a fine mesh (e.g.

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C2- 126 P. ASCARELLI, M. CINI, G. MISSONI AND N. NISTICO

F W H M ( e v >

100 50 10 ₁

T H I C K N E S S ( i ; )

FIG. 2. - F.W.H.M. as a function of film thickness. The F.W.H.M. of bulk gold and that of bulk gold plus charging (see

text) are indicated with a dotted line. The point dotted line is drawn to indicate the trend of the data.

0.25 mm2 holes separated by 0.1 mm). Each metallic island defined by the dimension of the mesh gives indication of the local electrostatic field at the island position. The dimension of the net holes has been choosen suitably smaller than the electrostatic field inhomogeneity over the sample surface which was independently measured by a fine probe put at different position over the teflon plate. Such a

procedure gives a F.W.H.M. of 1.8 (eV) for Au 4f

line. Besides, the fluorine line does not change its F.W.H.M. in the full range of gold particle dimension tested indicating that there are not variations of surface potential with gold coverage. An other way of overcoming the charging pro- blem was to evaporate gold only on a central part of

the sample about 3 mm2 wide, over which no field

inhomogeneity is detectable. We found that bulk

gold has a 1.3 eV F.W.H.M. which results from the

intrinsic life time broadening and the spectrometer resolution.

From figure 2 it is seen that samples about 70

A

thick which have been tested to be a discontinuous show a F.W.H.M. of 1.8 eV. Hence the increase

from 1.3 eV to 1.8 eV can be considered to be

largely determined by field inhomogeneity due to charging.

Decreasing the nominal thickness from 70

a

to

less than 1

A

we observe an increase in the

F.W.H.M. up to a maximum of 2.6 eV. This is

shown in figure 2. We then conclude that in going

from bulk gold to small gold particles (some

A

in

size) on a teflon substrate, an increase of the F.W.H.M. of about 1 eV takes place, which we believe to be intrinsic and not due to a trivial charging effect [5].

4. Theory.

-

In the following, we demonstrate that a broadening of the observed order of magnitude can be justified in terms of an enhanced final state core hole potential [6]. In the initial state, the

wavefunction of the

N

electron system in the metal

particle is expressed by a determinantal ground

state 10) of a simple free electron hamiltonian Yea.

The creation of a deep hole causes the sudden

switching on of a perturbation hamiltonian X I . The

X.P.S. spectrum is given by a convolution of the

density of states [7] :

with a certain line shape due to lifetime and instrumental broadenings. In terms of the single electron matrix elements of the final state potential V(r) the square of the width of the density of states is given by

where the f a r e Ferrni functions. We shall first take V(r) to be a short range, size independent potential

and look for the size dependence of A. In

section 4.2, instead, we shall look for effects due to the size dependence of V. As we shall see, the latter are by far the most important.

4.1 EFFECTS TO BE EXPECTED FOR A SIZE INDE- PENDENT, SHORT RANGE POTENTIAL. - A very

simple model is obtained if we let Yeo to be the

hamiltonian of free electrons enclosed in a cubic box of side L. The side will be so chosen that the mean density in the box equals the bulk density in the metal. The hole potential V(r) can be represent- ed by a localized potential placed at the center of the cube. It will not be too bad to take the intensity of the potential to be equal to a constant Vo inside a

small cube of side 2 a and zero outside. If Vo = 1

a.u. and a = ~ / K T F , when KTF is the Thomas-Fermi

wavevector, A is predicted to increase with

decreasing particle dimensions and attains a value

of 0.95 atomic units for L = 8

A.

For smaller

values of L, A decreases, essentially because the

short range potential now approximates a constant potential throughout the metal particle, and a constant potential would obviously produce no broadening at all. The limiting value for large L is

found to be about A = 0.62 atomic units. Thus, the

total increase is relatively small and is of the order

of 50 % of the bulk value of A, very much less than

the experimental broadening.

Furthermore, we think it is partly due to an artifact of the model. Due to the sharpness of the boundary conditions, the electron density is forced to pile up too strongly near the centre of the cube, and this unphysical effect could cause much of the

enhancement of A. This point is further clarified by

using a tight binding model for the metal particle. This calculation will not be reported here for saving space, but the result is that no explicit dependence

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X.P.S. LINE BROADENING IN SMALL METAL PARTICLES C2-127

dependence is related to small nonuniformities of the electron distribution.

4.2 EFFECTS DUE TO INCOMPLETE SCREENING.

-

To evaluate the selfconsistent potential due to a

charge

1

e l enbedded in a small metal particle, the

following peculiar features should be considered. First of all, size quantization of the electron energy levels affects the response function of the electron system. In such conditions, the metal particle can be characterized by a finite value of the dielectric

constant [I] whereas the q = 0 limit of the dielectric

function of an uniform electron gas is infinite. Physically this means that a portion of the coulom- bic bare potential is unscreened in the selfconsistent potential.

Further on, the continuity boundary conditions on the electrostatic potential and the electric field, set at a finite distance from the core hole causing the disturbance, also tend to limit the ability of the electron system to screen external perturbations. As a result, the selfconsistent potential due to a core hole in a small metal particle is much more intense than would be in a bulk metal. A theoretical model [2] has recently been proposed by one of the authors, that allows to take into account the size dependence of the dielectric function and the

boundary conditions as well. In figure 3 we present

FIG. 3.

-

Self consistent potcnt~nl V ( R ) - V(R0) due to a point charge placed at the center of spherical gold particles of radius

R a . V ( R ) - V ( R , ) indicated as (2) is for a particle of Ro = 30 (a.u.). V ( R ) - V ( R o ) indicated as (1) is for a particle of R, = 8 (a.u.). The potentials are calculated according to reference [2].

the selfconsistent electrostatic potential due to a point charge placed at the center of a spherical gold

particle (r, = 3) with radius R, = 8 a.u. (1 line) and

R, = 30 a.u. (2 line). The smaller particle contains

20 electrons, the larger one 1000. We see that the potential shape changes dramatically with decreasing size. Our present knowledge of the selfconsistent potential is probably good enough to

allow an accurate evaluation of A, via equation (2).

This would however be unduely time consuming for the present purpose, and we content ourselves, in the following, to obtain a rough estimate of the'

broadening. The electrostatic potential due to the core hole can be roughly approximated at short distances as

Here, 77 denotes the portion of the selfconsistent

potential that is screened in the small particle.

Obviously, 77- 1 in the limit of large particles

(indeed 77

-

1 even for RO

-

60 a.u.) and can be

seen to be about 0.64 if RO = 4.76 a.u. Equation (3)

approximately holds for V(r) in the range of 2.3 a.u. from the core hole. Actually, it is the short range portion of the selfconsistent potential that contributes the most to the width A of the spectrum. To see that, we rewrite equation (2) in terms of the Fourier components of the potential V(r). We get

Since we have seen that the explicit effects of size

quantization are not very important in evaluating A,

we can treat the q, q ' sum in the first line of

equation (4) as if Ro were very large. Then, the

quantity F ( q ) =

C

fK(l

-

fK+q) is readil,~ seen

K

to vanish for q = 0 and to become important

for q - K F / ~ , where KF is the Fermi wave-

vector. Since for large q, F(q) equals the electron number N e I we c a n approximately write

F(q) = Net 0(

1

q ( - KF/2). This will be accurate

enough for an order of magnitude calculation. Theref ore

Here, fl is the volume of the system and we have

introduced an upper cutoff qPs in order to take into

account the finite size of the core-hole pseudopotential. This is particularly important in the case of gold, where the pseudopotential due to the core- hole should be taken to be expecially .small, in order to account for the very small asymmetry of the gold

X.P.S. line shape [8]. Actualy, KF/2 =. 0.32 a.u. and

the width of the pseudopotential of gold in wave-

vector space is also estimated to be [8] about

0.3 a.u. A good description of the experimental

data results if we choose q,, = 0.33 a.u. The short

range part of the potential is given by equation (3). By fourier transforming and inserting into equation (5) we readily obtain

Here, po is the mean electron density of gold,

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C2-128 P. ASCARELLI, M. CINI, G. MISSONI AND N . NISTICO

to be

-

0.26 eV, and this is of the correct order of magnitude. Indeed, our value of q,, was chosen ad

hoc to ensure this. However, with decreasing particle dimensions, 77 also decreases, because the potential is screened less effectively. For N,I = 500

(particle radius Ro

-

23.8 a-u.) we obtain 77

--

0.96

and A = 0.34 eV. For N,1 = 20 (particle radius

-

8.1 a-u.) we get 77

-

0.7 and A

-

0.86eV. For very small particles, A approaches 1 eV. Despite the semiquantitative character of our model, we can conclude that the effects due to imperfect screening are strong enough to easily produce a broadening of the order of the observed one. Therefore, the observed broadening of the X.P.S. line can be regarded to be a property of the metal clusters themselves reflecting the enhance- menTof the final state hole potential. Thus, we feel

that the X.P.S. line broadening can be considered an useful probe of the electronic properties of small particles.

5. Conclusions.

-

Core X.P.S. lines of discontinuous gold films are observed to broaden with reducing metal particle size. Electrostatic potential inhomogeneities on the sample surface (charging) cannot explain the observed trend. On the other hand, a simple calculation shows that a broadening of the observed magnitude is to be expected a priori

as a consequence of the reduced screening of the core hole potential in the final state. Therefore, the width of the X.P.S. line be regarded to be a tool to gain insight in the electronic properties of metal clusters.

References

[I] CINI, M. and ASCARELLI, P., J. Phys. F Metal Phys. 4 (1974) [5] A similar observation was reported by KIM, K. S. and

1998. WINOGRAD, N., Chem. Phys. Lett. 30 (1975) 91.

[2] CINI, M., Surf. Sci. in press. [6] Our results concerning the size dependence of the plasmon

[3] CINI, M., Surf. Sci. 52 (1975) 75. satellites will be presented elsewhere. [4] ASCARELLI, P. and MISSONI, G., in Electron Spectroscopy 5 [7] LANGRETH, D. C., Phys. Rev. B 1 (1970) 471.