The effect of thermal vibrations of crystal lattice on the energy distributions of fast ionized recoils

Surface Scmnce 95 (1980) L289-L292 © North-Holland Publishing Company

SURFACE SCIENCE LETTERS THE E F F E C T OF THERMAL VIBRATIONS OF CRYSTAL LATTICE ON THE ENERGY DISTRIBUTIONS OF FAST IONIZED RECOILS A.M. BORISOV, A.I. DODONOV, E.S. MASHKOVA and V.A. MOLCHANOV Instttute o] Nuclear Physws, Moscow State Umversity, 117234 Moscow, USSR

Received 28 November 1979; accepted for pubhcation 24 March 1980

The effect of target temperature on the energy distribution of fast ionized recoils produced during 30 keV Ar ion bombardment of the Cu(110) face has been studied experimentally. Both the shape of the distribution and the energy position of the distribution maximum have been found to vary with rising temperature. The results obtained are discussed in terms of the vibrating isolated atomic row model.

It is known (see, for example, refs. [ 1,2]) that an ordered arrangement of crystal atoms may strongly affect the energy distributions o f fast recoils ejected from a target during bombardment with accelerated ions. It might-be expected on the basis o f the general principles of atomic particle interaction with crystals that thermal vibrations o f crystal atoms will affect the energy distributions. This assumption was verified experimentally. Both the (110) face of copper crystal and the polycrystalline copper sample were taken as the targets. The target temperature was varied within 1 5 0 - 9 5 0 ° C . The targets were irradiated by 30 keV energy argon ions. The observation angle (read from the primary ion incidence direction) was 40 °, the ejection angle ~ (read from the target surface) was 23 ° - see fig. 1. In the course o f the experiment the ejected recoil energy distributions were measured. It is known [ 1,2] that in the case

Fig. 1. Scheme of the experiment. L289

L290

4 4I Bortsov et al ,/1' tle~ t oj thermal vd~rattons o] crystal lattice'

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of a single-crystal target, the dastnbutlons are either cupolas (when the ejection angles are not too small) or narrow peaks (under blocking condmons) In the present work attention is paid to the cupola-shaped energy dlstribunons A t y p t c a l example of such dtstrlbutaon is presented xn fig. 2 (T = 185°(') The same figure also shows the energy distributions for a number of target temperatures up to 930°( ` It has been found that for a smgle-crystalhne target (in contrast to a polycrystalhne target), both the posatlon o f the dastrlbutlon maximum and the d l s m b u n o n half-width (FWHM) depend strongly on the target temperature. The dependencies are presented in figs. 3 and 4 It can be seen from fig 3 that as the target tempera-

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Exg. 3. Experimental and calculated dependencies of the energy distribution FWHM (l't0 on target temperature Fig 4 Experimental and calculated dependencies of the p o s m o n of the distribution m a x n n u m on target temperature. The dashed lane is the recod energy calculated in the uncorrelated binary collision approximation

.4 M. Borisov et al. /Effect of thermal vibrations of crystal lattice

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ture increases, the FWHM decreases and exhibits a plateau at temperatures of 8 0 0 900°C. It is interesting to note that the FWHM values corresponding to the plateau coincide, wxthln the experimental accuracy, with the FWHM values for polycrystalline copper. The experiment also shows that, as the target temperature increases, the distribution maximum shifts towards lower energies and at high target temperatures the position of the distribution maximum becomes actually the same as the position of the maximum for polycrystalline copper (see fig. 4). Thus, at high temperatures, the energy distributions of the ejected recoils proves to be practically the same for both single- and polycrystalline targets. The studied process was analyzed in terms of the model of an isolated atomic row. In the calculations, the single-crystal target was approximated by a threeatomic fragment of the (110) Cu close-packed atomic row. The axis of the fragment was assumed to lie in the primary Ion incidence plane (see fig. 1). The composite interaction potential used earlier by many authors (cf. ref. [4]) was applied A / r: . V(r) = t CBM e x p ( - r / a B M ) ,

r <~ R c , r >~ R e ,

The parameters of the potentials were [5] A = 466 e V A 2, CBM = 22.5 X 103 eV, anM = 0.196 A for Cu-Cu and A = 351 e V A 2, CBM = 16.9 X 103 eV, aBM = 0.196 A for Ar-Cu, the conjunction point Rc = 0.392 A. The effect of thermal lattice vibrations was taken into account by assuming the displacements p± of the atoms in the primary ion Incidence plane only. The distribution of the displacement probabilities was assumed to be of the Gaussian form with the variance o~± = h 2 T/MkO D± ,

where h is the Planck constant, M the atomic mass, k the Boltzmann constant, and 0D± the surface Debye temperature for copper [6]. The variance of Oa: was taken to be 2o~±. The ions were assumed to be incident onto the middle atom of the fragment. Hence, the atom to the left of that which must be ejected redistributes the primary ion beam, whereas the atom to the right redistributes the flux of the ejected recoils. The energy distributions of the recoils were numerically calculated for a set of static configurations of the fragment atoms. The ejected recotl distributions for each target temperature were constructed to be a superposition of the static energy distributions with due regard for their probabilities. The calculations have shown that the energy distribution shape is an asymmetric cupola: the slope of the lowenergy side of the distribution was found to be much steeper than that of the highenergy side. The analysis of the collision partner trajectories has shown that the low-energy side of the distribution is due to the large thermal displacements, whereas the high-energy side is determined by small thermal displacements. The

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A, M Bortsov et al / Lffect of thermal vtbratzons of crystal latnce

calculations have also shown that as the target temperature increases, the slope of tile low-energy side of the energy distribution becomes much steeper while the distribution maximum shifts towards lower energies. The calculated temperature dependences of both the FWHM and the position of the distribution maximum are presented in figs. 3 and 4 respectively. It can be seen from the figures that despite the quantitative differences, the calculations correctly represent the character of the measured temperature dependencies

References [1] L.L. Balashova, A M Bonsov, E.S Mashkova and V A Molchanov, Surface Scl 77 (1978) L643. [2] L.L. Balashova, A M. Bonsov, E S Mashkova and V A. Molchanov, Surface ScL 80 (1979) 573. [3] J. Lmdhard, Mat. Fys Medd Danske Vldenskab Selskab 34 (1965) No 14 [4] I.M. Torrens, Interatomlc Potentmls (Academic Press, New York, 1972) [5] M.T Robinson and O S Oen, Phys Rev. 132 (1963) 2385 [6] B. Poelsema, L.K. Verhey and A.L Boers, Surface Scl. 64 (1977) 554