Sputtering of a cesium-covered copper crystal: A computer simulation

Nuclear Instruments and Methods North-Holland, Amsterdam

SPU~ERING Christiane .Xmraroire

in Physics

Research

OF A CESIU~-COVERER

COUDRAY

and Georges

de Ph.wique des Solrdes Kitiment

29

B15 (1986) 29-33

COPPER CRYSTAL:

A COMPUTER

SIMULATION

SLODZIAN 510. 91405 0rsa.v. France

The sputtering yields, as well as the angular and energy distributions of the sputtered atoms can be modified by a monolayer of .Idsorhed atoms. The magnitude of such effects have been estimated with the help of a computer simulation (MARLOWE) in the Lpecific case of a copper single crystal (100) face covered with a p(2 x 2) monolayer of cesium and bombarded with a 10 keV Ne beam. For three different orientations of this beam, the mean radii of the cascade range and the sputtering yields are calculated with. and ,.vithout. cesium coverage, It has been found that the main effect of cesium coverage lies in the angular distributions of the sputtered particles.

The adsorption of cesium on metallic surfaces is csften used to lower the work function [I]. In SIMS experiments [Z-4] the lowering of the work function is responsible for a very large increase in the ionization J ields of negative secondary ions. At high cesium coverages one may wonder whether changes in the sputtering yield, and in energy and angular distributions could not play an important part. With the help of a computer simulation we have tried to estimate the influence of cesium on the ejection of target atoms. This is a special case of a more general problem concerning sputtering from surfaces covered with adsorhates which has been studied extensively in recent years; see for example (iarrison et al. [5-71 for their work on copper covered with oxygen or nickel with CO.

1. The simulation For this work, the program MARLOWE has been ured. This computer code can take into account a number of regular (or random) solid configurations. The superficial layer of adsorbed atoms has been described in the simulation by considering these atoms as if they were interstitials. Their peculiar geometrical locations outside instead of inside the crystal - require a rewriting of the conditions at the entrance and the exit of the crystal. Likewise, it proves useful to include the possibility for an adsorbed atom to be a reference atom, i.e. to generate the crystal from either a Cu or a Cs atom, and, in the search for the next collision set, to allow parameters to be different inside the crystal, and in the adsorbate region, where the density is lower. A Cs ~(2 x 2) coverage has been assumed on a (100) Cu crystal (see Fig. ID). The distance d between the adsorbate layer and the copper first layer has been

0168-583X/86/%03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

estimated by two ways. First, Gyftopoulos and Levine [8] evaluate the distance between a cesium atom and its nearest neighbouring copper atom as the sum of the copper covalent and of the cesium ionic radius. This leads to a value of 2.42 A for d. A very different approach, based on the jellium model of Lang and Kohn [9], provides d = 2.45 A. The two values are very close to each other, and our choice (the second one) is not significant. Another parameter, the cesium binding energy, must be estimated. A value of 1.84 eV is obtained by assuming that it is the sum of a covalent and of an ionic part (GyftopouIos and Levine [IO]). Besides, two other estimations may be found in a paper of Rasor and Warner [ll]. The first one starts from the classical image forces acting on the valence electron, the ion core and a free electron and provides 1.79 eV. The second one is an extrapolation of experimental results obtained by Houston [ 121 and leads to a value of 1.72 eV. Here again, the three results agree very well with one another; we have chosen the middle value of 1.79 eV. A last problem must be solved: how many interstitials have to be simulated? This problem is of fundamental importance for the computation itself, because it has a direct effect not only on the size of the data blocks, but also on the length of the calculations. Let us recall that after each collision, the procedure which allows one to obtain the next collision partners of a moving particle tests successively n nearest neighbours of the reference atom (for Cu n may be chosen equal to 18) and the whole of the interstitials set. So, too large a set causes prohibitively long computation times. On the other hand, if this set is chosen too small, particles may be sputtered outside the covered region, and the simulation is meaningless. A compromise has to be found, taking into account the size of the collision cascades. The first step of this study concerns this point. I. THEORETICAL ASPECTS

30

C. Coudray, G. Slodzian / Compuler simulation of sputtering

(a)

2. Study of the size of the collision cascades \ Let us first point out the conditions of our simulation. A parallel beam of 10 keV *‘Ne atoms is sent upon the (100) face of a 63Cu perfect crystal, covered, or not, with cesium. This crystal, which may be as large as desired, contains 10 layers. Thermal vibrations are neglected. Three different incident directions have been studied: (1) normal incidence, (2) 45’ in a (010) incidence plane (“transparent” direction), (3) 45’ in a (110) incidence plane (“opaque” direction). For these three directions, the impacts were randomly distributed inside the representative areas shown in fig. 1. Our results are summarized in table 1. In this table, A is defined as a circular area within which 70% of the particles are emitted. Some particles are emitted fairly far from the impact point: P is the percentage of Cu (or Cs) atoms emitted beyond 20a from the impact point (a: crystalline cell edge; a = 3.615 A). In absence of cesium, the dependence of the size of A on the incident direction is very weak. However, this zone, as well as the entire ejection region is narrower for incidence direction (3) than for the two others. When cesium is present, the cascades have similar extents, except for incidence direction (2) which gives rise to a few very long cascades. The longest is due to an incident ion, channeling in a (310) direction just under the copper surface and ejecting first layer Cu atoms along its path. In this cascade, a Cs atom slightly deflects the incoming Ne atom from its original direction, and the next collision, which occurs against a first layer atom, makes use of this small deviation to deviate the Ne atom into the channel. This phenomenon cannot happen for incidence

Table 1 Sizes of the studied

Fig. 1. The representative areas for bare (a) and Cs-covered (/3) Cu. (1) normal incidence; (2) transparent incidence; (3) opaque incidence. conditions (1) or (3). We shall see later (sect. 3.1) one of its other consequences. It should be observed that these very long cascades give rise to an important displacement of the center of emission. From the results concerning the bare copper crystal, we have been led to simulate 600 Cs atoms, set in a circular area of 20a of radius. This is large enough for 98% of the cascades. For the last 28, a special study has been necessary: a first simulation was done, involving the 600 Cs atoms, then the ejection locations of the sputtered particles were noted, and supplementary Cs atoms were added in the vicinity of these locations, in order to be sure that every sputtered copper atom could meet the cesium layer.

3. The main effects of the cesium adsorption For each incidence, N,, instead of 100 impacts have been simulated. The raw results of these runs are given

cascades

Incidence conditions

Cs coverage

N0

Type of ejected atoms

(1) Normal incidence

without Cs with Cs

200 200

cu Cu cs

(2) Transparent incidence

without Cs with Cs

200 100

Cu Cu cs

(3) Opaque incidence

without Cs with Cs

100 100

CU cu cs

N,,: number of studied cascades R: radius of A D: distance of the center of A (center of emission) (3) direction passing by the origin.

to the representative

R/a 8.5 7 6 8 15 6 6 5.5 7

D/a

P

Percentage of very long cascades

0 0 0

13.5 0 0

1 0 0

0 8.5 3

13 37 18.5

0.5 2 1

4.5 1 2.5

0.4 0.5 16

1 2 1

area. This center is located

on the (100) (2) or on the (110)

31

C. Coudray, G. Slodzian / Computer simulation of sputtering Table 2 Number of ejected particles

(for 100 impacts)

Cs coverage

N

N2

NI

1) Normal incidence

without Cs with Cs

103 77

76 59

23 15

3.3 4

0 25

0 0.3

(2) Transparent incidence

without Cs with Cs

62 65

45 50

13 12

3.5 4.2

0 27

0 0.42

( 3)Opaque inci-

without

495

343

90

3.8

0

391

281

80

3.5

124

Incidence (

dence if (N,.,):

Cs

with Cs Number

of ejected Cu (Cs) atoms.

N,

N, ( N2): Number

in table 2. One should keep in mind that these numbers are subject to rather large relative uncertainties because of the small number of simulated impacts.

IN2

G/N

NC\

of Cu atoms ejected from the first (second)

0

0.32 layer.

3. I. Number of ejected atoms When cesium is present, N is reduced by a factor 0.75 for incidences (1) and (3). This reduction does not

n(E)

t

LOAn(E)

Fig. 2. Energy distributions

for opaque

incidence

(a) bare Cu,

(p)

Cs-covered

Cu.

1. THEORETICAL

ASPECTS

32

appear quence well as N&N cesium

C. Coudray, G. Slodzian

/ Computer simulation

for the transparent incidence. This is a conseof the channeling effects already mentioned, as the increased ratio N&N. Besides, the ratio remains constant for every incidence: sputtered and copper atoms undergo the same variations.

of sputtering

n 18)

1

.

60

3.2. Energy distributions The results being very similar for the three incidences, only the opaque incidence histograms are given in fig. 2. They show a small modification of the structures between 0 and 20 eV, the statistics becoming too poor at higher energies to allow any conclusion. Apparently, the presence of Cs prevents the atoms with very low energy - below 2 eV - to escape. In compensation a higher and narrower peak is observed around 5 eV. .

3.3. Angular distributions

. .

Angular distributions are shown in fig. 3 for the opaque incidence, 0 being the angle between the momentum of a sputtered particle and the normal to the surface. They have been evaluated for equal solid angles (each revolving solid angle being limited by the two cones 0 < 0i and 8 < 8,). It may be said that the main modification brought about by the adsorption of cesium concerns the angular distributions. In the absence of cesium there are two maxima at 0 = 0” and 0 = 45”, mainly due to second and to first layer atoms, respectively. The contribution of the inner layers is negligible in any direction (cf. table 2). When cesium is present, the adatoms deflect most of the focused first layer atoms and prevent a fraction of them from escaping. Fig. 3b shows the consequences of these effects: widening of the 0 = 0” structure and disappearing of the 0 = 45” peak. The structures observed for bare Cu are almost entirely flattened, and the distribution becomes near to being a Lambert law one. Although it has poor statistics, the Cs distribution appears to be very similar (cf. fig. 3c). 3.4. Comparison with experiments It could be objected that the conditions of our simulation: - perfectly parallel and monoenergetic incident beam, - the crystal being perfect before each impact, - perfect Cs p(2 X 2) coverage, are rather different from the usual experimental conditions. Besides, the experimental results with and without cesium coverage in similar geometrical conditions are relative to ion emission. In absence of cesium, Bernheim and Slodzian [13] found a ratio Nopaque/Ntransparent of about 5 for Cu+ ions. Ours is larger, 8 f 1, but may be lowered to 6 f 2 when only the particles sputtered

(b)

0..

n 18)

T !

(cl

20

l

. * . l

l l

I

0

20

I

LO L-5'

*.

l

60

. . .

l

7’. l

60

46.

e

Fig. 3. Angular distributions for opaque incidence (a) bare Cu; (b) G-covered Cu: Cu atoms; (c) G-covered Cu: Cs atoms. In (a) and (b) 0 indicates all atoms 0 first layer atoms and X second layer atoms.

around the normal (i.e. for cos 0 > 0.95) are taken into account, in order to match the experimental collection conditions. With cesium, our global ratio is 6 + 1, and a drastic lack of statistics can only provide 8.3 f 4.6 along the normal direction. The experimental value 2.1 [13] cannot directly be accounted for. To a great extent, the difference is probably due to the perturbations of the Cs arrangement produced by the bombardment.

4. Conclusion This study is far from being complete. On the one hand, it would be worthwhile to improve the statistics, and on the other hand to simulate other locations of the Cs atoms and higher coverages. However, within its

33

C. Coudruy, G. Slodzran / Computer simulation of sputtering

lirnitations our model allows us to describe the main effects of a Cs monolayer on the ejection of Cu atoms, and to assert that, except for very special cases, sputtering of copper should be little changed by the adsorption of a cesium monolayer. It should be noted that our computations could be easily extended to monolayers cc,mposed by other types of atoms.

References [l] S.A. Lingren and L. Wallden, Solid State Comm. 25 (1978) 13. [-!I M. Bernheim and G. Slodzian, J. Physique (lett.) 38L (1977) 325. [I] M. Bernheim and G. Slodzian, J. Microsc. Spectrosc. Electron. 6 (1987) 141.

[4] M.L. Yu, Phys. Rev. Lett. 40 (1978) 9. [S] B.J. Garrison, N. Winograd and D.E. Harrison Jr., Phys. Rev. B18 (1978) 6000. [6] N. Winograd, B.J. Garrison. T. Fleisch, W.N. Delgass and D.E. Harrison Jr., J. Vat. Sci. Technol. 16 (1979) 629. 171 B.J. Garrison, N. Winograd and D.E. Harrison Jr., Surf. Sci. 87 (1979) 101. [8] E.P. Gyftopoulos and J.D. Levine, J. Appl. Phys. 33 (1962) 67. [9] N.D. Lang and W. Kohn, Phys. Rev. B7 (1973) 3541. [lo] J.D. Levine and E.P. Gyftopoulos, Surf. Sci. 1 (1964) 171. [ll] N.S. Rasor and C. Warner, J. Appl. Phys. 35 (1964) 2589. [12] J.M. Houston, Adv. Electron. 17 (1962) 147. [13] M. Bernheim and G. Slodzian, Sims 111 Conference, Springer Series in Chemical Physics 19 (1981) 151.

1. THEORETICAL

ASPECTS