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Argon ion double scattering from polycrystalline copper
Surface Science 76 (1978) L590-L598 0 North-Holland Publishing Company
LETTER TO THE EDITOR ARGON ION DOUBLE SCATTERING FROM POLYCRYSTALLINE COPPER
L.L. ~ALASHOVA, E.S. MASHKOVA and V.A. MOLCHANOV ~ns~~~~e of l&&ear l%ysics, ~os&ow State University, 117 234 Moscow B-234, i_J&S’R Received 1 February 1978; manuscript received in fiiai form IO May 1978
It has been found that under certain conditions the high-energy side of the polycrystalscattered ion energy distribution may exhibit a distinct and intense peak similar to the doublescattering peak observable for single-crystalline targets.
The various directional effects are known to arise (see, for example, refs. [ 1,2]) in atomic particle-crystal ~teractions. In particular, the energy distribution of ions scattered from a single crystal is known to exhibit, under certain conditions, a characteristic double peak [3]. The position of the peak on the energy scale, as well as its intensity, are functions, of, in particular, the crystal target orientation relative to both the .primary ion beam and the observation direction. Numerous theoretical and experimental studies of this effect, which has been called the double-scattering effect have shown (see the review [4]) that the main features of the effect may be explained by examining just two successive collisions of the scattered ion with the target atoms in the crystal lattice. The aim of the present work is to examine the conditions of distinct appearance of the double-scattering effect for polycrystalline targets and to trace its main features. Though the double-scattering effect is a structural effect and the polycrystal consists of r~domly oriented grains, it is probable that the double-scattering effect fails to completely disappear when the non-monotonic angular dependences are averaged over all orientations of the grains. This is similar to the situation in electron diffraction from molecules and the X-ray structural analysis of polycrystals. It should be noted that the problem of averaging the diffraction effects from various distributions of scattering centers was analysed in detail by Debye [ 5 $1. It will also be noted that the first undoubted evidence for the double-scattering effect from polycrystalline targets was obtained already at Bell Telephone Laboratories [7,8] see also ref. [9]. Conventional experimental techniques were used. The ion beam was directed to a polycrystahine copper target at angle a! to its surface - fig. 1. The ions scattered through angle 0 relative to the primary beam direction were analyzed with a 0.5% resolution electrostatic analyzer. The experimental equipment was described earlier I”590
L.L. Balashova et al. /Argon
ion double scattering from copper
L591
Fig. 1. Scheme of the angles.
(see p. 153 in ref. [lo] and p. 221 in ref. [4]). The only special feature of the present experiment was the necessity of obtaining the results characteristic for nontextured polycrystals. In fact, it is known (see, for example, ref. [ll]), that as a result of the ion bombardment the surface of a polycrystal may be enriched with crystalline grains with predominant alignment relative to the bombarding ion beam direction. This fact is due to the strong and non-monotonic dependence of the single crystal sputtering yield on the bombardment direction [ 1 ,121. As a result, the target surface crystal grains oriented definitely relative to the bombardment direction are much less sputtered than other grains, a fact that gives rise to the enrichment of the irradiated surface with the grains of predominant orientation. This effect was eliminated during the experiment by azimuthally rotating the target. Approximately 30-40 scattered ion energy distributions were measured for every combination of the sliding (incidence) and scattering angles and the primary ion energy. Since the obtained data failed to reveal any dependence on the
Fig. 2. Histogram: the number (n) of the distributions shows the energy distribution.
versus (hz/hl).
The upper right part
L592
L.L. Balashova et al. /Argon
ion double scattering from copper
Fig. 3. The averaged energy distribution. The dashed lines show the boundaries characterizing the maximum uncertainty in the behaviour of the averaged curve relative to the experimental points.
azimuthal angle of target rotation, it could be concluded that some differences in thf observed energy distributions were due to various accidental factors, including the apparatus instability. For this reason, in the processing of the experimental data we used the conventional technique when analyzing the independent values. A certain parameter characterizing the main features of the energy distribution shape of the scattered ions was selected and then the histograms of the distribution numbers with given value of the selected parameters were plotted. As will be seen below (see figs. 4-6) the obtained distributions are in general the two-peaked curves whose low-energy peak is standard in the polycrystahine targets whereas the high-energy peak is similar to the double-scattering peak observable for the single-crystal targets. The high-energy peak (or shoulder) to low-energy peak height ratio hz/hl was selected as the parameter characterizing the energy distribution shape. A typical histogram is shown in fig. 2. The distributions corresponding to the histogram maximum were arithmetically averaged and it was those averaged distributions that were taken as the energy distributions of the scattered ions corresponding to the studied combination of the scattering angles and the primary ion energy. Fig. 3 presents the results of the averaging for (Y= 15”, 0 = 30” and Eo = 17.5 keV and
L.L. Balashova et al. /Argon
Fig. 4. See the text.
ion double scattering from copper
Fig. 5. See the text.
L593
Fig. 6. See the text.
shows the boundaries characterizing the maximal uncertainty in the behaviour of the averaged curve relative to the experimental points. Figs. 4-6 present the results of measurements of the energy distributions of the polycrystal-scattered ions. It can be seen, first of all, that for each combination of the sliding and scattering angles there is a certain primary ion energy range for which the energy distributions of the scattered ions exhibit a clear two-peaked structure. For example, such ranges are 17-30 keV for Q = 10” and 0 = 20°, 12.5-30 keV for QC = 12” and 0 = 24’, and IO-25 keV for (Y= 15” and B = 30”. It can also be seen that the height of the high-energy peak may be very significant and, under certain conditions, comparable with the height of the low-energy peak. In particular, at Q = IO”, 0 = 20” and the 17.5-2.5 keV primary ion energies, the height of the high-energy peak exceeds 90% of the single peak height. The primary ion energy dependence of the relative height of the high-energy peak for each fixed combination of the angles is of the following form. As the primary ion energy decreases, the relative height increases, reaches its maximum and then decreases. A distinct double scattering peak is observed at neither low nor
L594
L.L. Balashova et al. /Argon
?Q
L?u
30
40
ion double scattering from copper
fO
Fig. 7. The primary energy dependence of the double-to-single peak height ratio. Fig. 8. See the text.
high primary ion energies. At both low and high primary ion energies only a shoulder can be seen in the high-energy side of the distribution. The general pattern of the h2/hl behaviour with changing primary ion energies is illustrated in fig. 7, which also presents the data for the single-crystalline target - see fig. 8. It can be easily seen when comparing the data for single crystals with those for polycrystals, that the general mode of the energy dependences is qualitatively the same in the two cases, though the absolute values of hz/h, are much higher for the single-crystal target at the same sliding and scattering angles. The comparison between the scattered ion energy distributions for the single-crystalline and polycrystalline targets (figs. 5 and 8) shows that the high-energy peaks for the single-crystalline target are more pronounced. Thus, the above described experiments have shown that experimental conditions may be selected under which the effect similar to the double-scattering effect characteristic of the single-crystalline scatterers can be clearly observed for polycrys-
L.L. Balashovaet al. /Argon ion double scattering from copper
I‘595
Fig. 9. The scheme of the double scattering. Shown below are the calculations for 01= 12” and 0 = 24”.
talline targets. It has also been established that the general character of the dependence of the effect on both primary ion energy and the scattering angles is qualitatively the same as that of the conventional double-scattering effect. We will discuss now the results of the experimental study of the regularities in the ion scattering by polycrystalline targets. The above traced analogy to the conventional double-scattering effect makes it possible to try and interpret the experimental data in terms of the same simple models of the,scattering process that proved to be productive when analyzing the double-scattering for single crystalline targets (see the review [4]). Attention will be paid, in particular, to the conclusions about the scattering regularities that may be drawn on the assumption of ion scattering by only two target atoms spaced a distance d apart, which equals the mean interatomic spacing in the polycrystalline target. Consider the planar problem in the small-angle approximation. The inversesquared approximation of the Firsov potential [4] will be taken as the ion-atom interaction potential. Inelastic energy losses will be neglected. At a given sliding angle a! and a total scattering angle 0 (see fig. 9) the impact parameters of the first (PI) and second (P2) collisions are interrelated as Pz =P,
+aye, -a)
L.596
L.L. Balashova et al. /Argon
ion double scattering from copper
where d is the interatomic spacing. Since for the chosen interaction impact parameter is related to the scattering angle as 3.05z,z* @-f/Z + z;/2)2/3 where A is the constant 1 f
(0
_e,)l/2
lo-l6
eV
potential,
the
cm2)
in V(R) = A/R’, the above expression takes the form
1 -$
1
=
c(e1
-4,
where C= (2Ed2/nA)q
0 = 13~t 02,
In general, this equation has three solutions (see the lower part of fig. 9). Thus, three values of the scattering ion energy corresponding to three scattered ion trajectories in the two-atom field are possible for every fixed combination of cr and 8. In particular, an ion may be strongly scattered by either the first or the second atom and only a little scattered by another atom. In these cases the scattered ion energy is naturally close to the energy of the ion singly scattered through the given angle 0. The third possibility is what is usually called double scattering, i.e. the ion is scattered through the angle 0 in two successive collisions at comparable angles in the first and second collisions. The scattered ion energy in this case appreciably exceeds the energy of the single scattered ion. It will be seen that either one or two solutions may exist under certain conditions instead of three solutions. In the case of symmetrical scattering, i.e. when 8r = e2 = (Y= e/2, a solution corresponding to the double scattering always exists in practice. As for the solutions corresponding to the quasi-single scattering, it was shown in ref. [4] that a limiting energy existed (at given scattering angle) below which the “single” scattering cannot be realized. Though the above treatment is purely kinematic and, hence, fails to yield information on the intensity of the single and double scattering, the disappearance of the quasi-single scattering at some limiting energy of the primary ions means actually that the relative intensity of the double-scattering peak at such an energy approaches infinity. The experiment shows, however (see fig. 7), that the increase in the relative height of the double peak with decreasing the primary ion energy is observed only up to a certain value of the energy (depending particularly on the sliding and scattering angles), after which the relative height of the double peak starts decreasing. The origin of such energy dependence will be understood only on the basis of concrete estimates in terms of the above described model. Consider, for example, the cases corresponding to the primary ion energies of 10 and 25 keV - see fig. 10. One can see that two peaks, namely, a quasi-single peak (corresponding actually to two trajectories of the scattered ion - either to small 0r and large e2 = 0 - 0, or to large 8, and small e2 = e - e,) and a double peak (corresponding to 0 r = e2 = 8/2) should be observed in both cases for a strictly symmetrical scatter-
L.L. Balashova et al. /Argon
ion double scattering from copper
L.591
Fig. 10. The calculations for 01 = IS’, 0 = 30”. The dashed line characterizes the spread of the sliding angles due to both angular spread of primary ions and thermal vibrations of target atoms.
ing ((u = 1So, 0 = 30”). If, however, the scattering is not quite symmetrical (due, for example, to the finite angular divergence of the primary ion beam, to the thermal vibrations of the crystal lattice atoms, etc.), the situation proves to be essentially different for the primary ion energies of 25 and 10 keV. The dashed line in fig. 10 shows the boundaries of y = c(0, - a) due to the variations in the sliding angles corresponding to Aa * 1.5” (i.e. to the spread of the angles in the primary ion beam). It can be seen that such a spread for 25 keV results in but a small spread of the angles t?i and e2 and, hence, in but a slight broadening of the peaks in the energy distribution of the scattered ions. As to the 10 keV ions, the +1.5” variations in the sliding angles result in a significant alteration of the scattering kinematics, namely, the solution which corresponds to the double-scattering event (i.e. to 8i - e2 - e/2) disappears. If 1y= e/2 - 1.5”, the scattering is actually realized by only the first atom (in this case 8i is large and e2 is small). If cu= e/2 t 1.5’ the scattering is actually realized by only the second atom (in this case f3i is small and, hence, Ba = 0 - 8i is large) *. Since the primary ion beam contains ions with different directions of velocity * The physical cause of such scattering kinematics for non-symmetrical scattering geometry is the ion flux redistribution as a result of ion interactions with the scattering centers. When both the sliding angle and the primary ion energy Eo are small enough, the shadow behind the first scattering atom screens the small impact parameters of the second atom responsible for the large-angle ion scattering by the second atom. As a result, only the ions scattered strongly by only the first atom (0 1 is large and 82 is small) enter the analyzer. When the primary ion sliding angle is large and the ion energy is low enough the ions scattered by the first atom in the direction of the second atom cannot enter the analyzer after being scattered by the second atom since in this case the analyzer is inside the shadow (blocking) cone behind the second atom - see also fig. 10 in ref. (131. As a result only the ions scattered practically by only the second atom can enter the analyzer (0, is large and 0 r is small).
L598
L.L. Balashova et al. /Argon
ion double scattering from copper
vectors, the conditions giving rise to two-peaked energy distributions of the scattered ions are satisfied for a portion of the ions, whereas the conditions for other ions are such that but a single peak is observable. It is the circumstance that should result, for a definite energy range, in a decrease of the relative probability of the double scattering with the primary ion energy decreasing. The increase in the relative intensity of the double peak with decreasing primary ion energy could be naturally explained by the energy dependence of the doublescattering cross-section. In the first approximation the double-scattering intensity is proportional to the product of the cross-sections of ion scattering on the first atom towards the second atom and on the second atom towards the analyzer divided by the cross-section of ion scattering on a single atom towards the analyzer. Assuming that the scattering is symmetrical and that the ion-atom interaction can be described by the inverse-square potential, we obtain a formula
(see, for example, ref. [4]). The above simple treatment shows that the correlation of the successive collisions of the scattered ions for but two atoms permits the main features of the observable double-scattering effect to be explained. The authors are deeply indebted to Professor Carl J. Altstetter for the informative discussions of some results.
References [l] M. Kaminsky, Atomic and Ionic Impact Phenomena on Metal Surfaces (Springer, Berlin, 1965). [2] J.W. Mayer, L. Eriksson and J.A. Davies, Ion Implantation in Semiconductors (Academic Press, New York, 1970). [3] ES. Mashkova, V.A. Molchanov, E.S. Parilis and N.Yu. Turaev, Phys. Letters 18 (1965) 7. [4] E.S. Mashkova and V.A. Molchanov, Radiation Effects 23 (1974) 215. [S] P. Debye, Collected Papers (Interscience, New York, 1954). [6] P. Debye, Struktur der Materie, Vier Vortrage (Leipzig, 1933). [7] D.J. Ball, T.M. Buck, D. MacNair and G.H. Wheatley, Surface Sci. 30 (1972) 69. [8] S.P. Sharma and T.M. Buck, .I. Vacuum Sci. Technol. 12 (1975) 468. [9] L.L. Balashova, E.S. Mashkova and V.A. Molchanov, Phys. Letters 61A (1977) 193. [lo] E.S. Mashkova and V.A. Molchanov, Radiation Effects 16 (1972) 143. [ll] V.A. Molchanov and V.G. Tel’kovsky,Izv. Akad. Nauk SSSR, Ser. Phys. 24 (1962) 1359. [ 121 R. Behrisch, Ergebn. Exakt. Naturwissensch. 35 (1964) 295. [13] E.S. Mashkova and V.A. Molchanov, Radiation Effects 25 (1975) 193.
LETTER TO THE EDITOR ARGON ION DOUBLE SCATTERING FROM POLYCRYSTALLINE COPPER
L.L. ~ALASHOVA, E.S. MASHKOVA and V.A. MOLCHANOV ~ns~~~~e of l&&ear l%ysics, ~os&ow State University, 117 234 Moscow B-234, i_J&S’R Received 1 February 1978; manuscript received in fiiai form IO May 1978
It has been found that under certain conditions the high-energy side of the polycrystalscattered ion energy distribution may exhibit a distinct and intense peak similar to the doublescattering peak observable for single-crystalline targets.
The various directional effects are known to arise (see, for example, refs. [ 1,2]) in atomic particle-crystal ~teractions. In particular, the energy distribution of ions scattered from a single crystal is known to exhibit, under certain conditions, a characteristic double peak [3]. The position of the peak on the energy scale, as well as its intensity, are functions, of, in particular, the crystal target orientation relative to both the .primary ion beam and the observation direction. Numerous theoretical and experimental studies of this effect, which has been called the double-scattering effect have shown (see the review [4]) that the main features of the effect may be explained by examining just two successive collisions of the scattered ion with the target atoms in the crystal lattice. The aim of the present work is to examine the conditions of distinct appearance of the double-scattering effect for polycrystalline targets and to trace its main features. Though the double-scattering effect is a structural effect and the polycrystal consists of r~domly oriented grains, it is probable that the double-scattering effect fails to completely disappear when the non-monotonic angular dependences are averaged over all orientations of the grains. This is similar to the situation in electron diffraction from molecules and the X-ray structural analysis of polycrystals. It should be noted that the problem of averaging the diffraction effects from various distributions of scattering centers was analysed in detail by Debye [ 5 $1. It will also be noted that the first undoubted evidence for the double-scattering effect from polycrystalline targets was obtained already at Bell Telephone Laboratories [7,8] see also ref. [9]. Conventional experimental techniques were used. The ion beam was directed to a polycrystahine copper target at angle a! to its surface - fig. 1. The ions scattered through angle 0 relative to the primary beam direction were analyzed with a 0.5% resolution electrostatic analyzer. The experimental equipment was described earlier I”590
L.L. Balashova et al. /Argon
ion double scattering from copper
L591
Fig. 1. Scheme of the angles.
(see p. 153 in ref. [lo] and p. 221 in ref. [4]). The only special feature of the present experiment was the necessity of obtaining the results characteristic for nontextured polycrystals. In fact, it is known (see, for example, ref. [ll]), that as a result of the ion bombardment the surface of a polycrystal may be enriched with crystalline grains with predominant alignment relative to the bombarding ion beam direction. This fact is due to the strong and non-monotonic dependence of the single crystal sputtering yield on the bombardment direction [ 1 ,121. As a result, the target surface crystal grains oriented definitely relative to the bombardment direction are much less sputtered than other grains, a fact that gives rise to the enrichment of the irradiated surface with the grains of predominant orientation. This effect was eliminated during the experiment by azimuthally rotating the target. Approximately 30-40 scattered ion energy distributions were measured for every combination of the sliding (incidence) and scattering angles and the primary ion energy. Since the obtained data failed to reveal any dependence on the
Fig. 2. Histogram: the number (n) of the distributions shows the energy distribution.
versus (hz/hl).
The upper right part
L592
L.L. Balashova et al. /Argon
ion double scattering from copper
Fig. 3. The averaged energy distribution. The dashed lines show the boundaries characterizing the maximum uncertainty in the behaviour of the averaged curve relative to the experimental points.
azimuthal angle of target rotation, it could be concluded that some differences in thf observed energy distributions were due to various accidental factors, including the apparatus instability. For this reason, in the processing of the experimental data we used the conventional technique when analyzing the independent values. A certain parameter characterizing the main features of the energy distribution shape of the scattered ions was selected and then the histograms of the distribution numbers with given value of the selected parameters were plotted. As will be seen below (see figs. 4-6) the obtained distributions are in general the two-peaked curves whose low-energy peak is standard in the polycrystahine targets whereas the high-energy peak is similar to the double-scattering peak observable for the single-crystal targets. The high-energy peak (or shoulder) to low-energy peak height ratio hz/hl was selected as the parameter characterizing the energy distribution shape. A typical histogram is shown in fig. 2. The distributions corresponding to the histogram maximum were arithmetically averaged and it was those averaged distributions that were taken as the energy distributions of the scattered ions corresponding to the studied combination of the scattering angles and the primary ion energy. Fig. 3 presents the results of the averaging for (Y= 15”, 0 = 30” and Eo = 17.5 keV and
L.L. Balashova et al. /Argon
Fig. 4. See the text.
ion double scattering from copper
Fig. 5. See the text.
L593
Fig. 6. See the text.
shows the boundaries characterizing the maximal uncertainty in the behaviour of the averaged curve relative to the experimental points. Figs. 4-6 present the results of measurements of the energy distributions of the polycrystal-scattered ions. It can be seen, first of all, that for each combination of the sliding and scattering angles there is a certain primary ion energy range for which the energy distributions of the scattered ions exhibit a clear two-peaked structure. For example, such ranges are 17-30 keV for Q = 10” and 0 = 20°, 12.5-30 keV for QC = 12” and 0 = 24’, and IO-25 keV for (Y= 15” and B = 30”. It can also be seen that the height of the high-energy peak may be very significant and, under certain conditions, comparable with the height of the low-energy peak. In particular, at Q = IO”, 0 = 20” and the 17.5-2.5 keV primary ion energies, the height of the high-energy peak exceeds 90% of the single peak height. The primary ion energy dependence of the relative height of the high-energy peak for each fixed combination of the angles is of the following form. As the primary ion energy decreases, the relative height increases, reaches its maximum and then decreases. A distinct double scattering peak is observed at neither low nor
L594
L.L. Balashova et al. /Argon
?Q
L?u
30
40
ion double scattering from copper
fO
Fig. 7. The primary energy dependence of the double-to-single peak height ratio. Fig. 8. See the text.
high primary ion energies. At both low and high primary ion energies only a shoulder can be seen in the high-energy side of the distribution. The general pattern of the h2/hl behaviour with changing primary ion energies is illustrated in fig. 7, which also presents the data for the single-crystalline target - see fig. 8. It can be easily seen when comparing the data for single crystals with those for polycrystals, that the general mode of the energy dependences is qualitatively the same in the two cases, though the absolute values of hz/h, are much higher for the single-crystal target at the same sliding and scattering angles. The comparison between the scattered ion energy distributions for the single-crystalline and polycrystalline targets (figs. 5 and 8) shows that the high-energy peaks for the single-crystalline target are more pronounced. Thus, the above described experiments have shown that experimental conditions may be selected under which the effect similar to the double-scattering effect characteristic of the single-crystalline scatterers can be clearly observed for polycrys-
L.L. Balashovaet al. /Argon ion double scattering from copper
I‘595
Fig. 9. The scheme of the double scattering. Shown below are the calculations for 01= 12” and 0 = 24”.
talline targets. It has also been established that the general character of the dependence of the effect on both primary ion energy and the scattering angles is qualitatively the same as that of the conventional double-scattering effect. We will discuss now the results of the experimental study of the regularities in the ion scattering by polycrystalline targets. The above traced analogy to the conventional double-scattering effect makes it possible to try and interpret the experimental data in terms of the same simple models of the,scattering process that proved to be productive when analyzing the double-scattering for single crystalline targets (see the review [4]). Attention will be paid, in particular, to the conclusions about the scattering regularities that may be drawn on the assumption of ion scattering by only two target atoms spaced a distance d apart, which equals the mean interatomic spacing in the polycrystalline target. Consider the planar problem in the small-angle approximation. The inversesquared approximation of the Firsov potential [4] will be taken as the ion-atom interaction potential. Inelastic energy losses will be neglected. At a given sliding angle a! and a total scattering angle 0 (see fig. 9) the impact parameters of the first (PI) and second (P2) collisions are interrelated as Pz =P,
+aye, -a)
L.596
L.L. Balashova et al. /Argon
ion double scattering from copper
where d is the interatomic spacing. Since for the chosen interaction impact parameter is related to the scattering angle as 3.05z,z* @-f/Z + z;/2)2/3 where A is the constant 1 f
(0
_e,)l/2
lo-l6
eV
potential,
the
cm2)
in V(R) = A/R’, the above expression takes the form
1 -$
1
=
c(e1
-4,
where C= (2Ed2/nA)q
0 = 13~t 02,
In general, this equation has three solutions (see the lower part of fig. 9). Thus, three values of the scattering ion energy corresponding to three scattered ion trajectories in the two-atom field are possible for every fixed combination of cr and 8. In particular, an ion may be strongly scattered by either the first or the second atom and only a little scattered by another atom. In these cases the scattered ion energy is naturally close to the energy of the ion singly scattered through the given angle 0. The third possibility is what is usually called double scattering, i.e. the ion is scattered through the angle 0 in two successive collisions at comparable angles in the first and second collisions. The scattered ion energy in this case appreciably exceeds the energy of the single scattered ion. It will be seen that either one or two solutions may exist under certain conditions instead of three solutions. In the case of symmetrical scattering, i.e. when 8r = e2 = (Y= e/2, a solution corresponding to the double scattering always exists in practice. As for the solutions corresponding to the quasi-single scattering, it was shown in ref. [4] that a limiting energy existed (at given scattering angle) below which the “single” scattering cannot be realized. Though the above treatment is purely kinematic and, hence, fails to yield information on the intensity of the single and double scattering, the disappearance of the quasi-single scattering at some limiting energy of the primary ions means actually that the relative intensity of the double-scattering peak at such an energy approaches infinity. The experiment shows, however (see fig. 7), that the increase in the relative height of the double peak with decreasing the primary ion energy is observed only up to a certain value of the energy (depending particularly on the sliding and scattering angles), after which the relative height of the double peak starts decreasing. The origin of such energy dependence will be understood only on the basis of concrete estimates in terms of the above described model. Consider, for example, the cases corresponding to the primary ion energies of 10 and 25 keV - see fig. 10. One can see that two peaks, namely, a quasi-single peak (corresponding actually to two trajectories of the scattered ion - either to small 0r and large e2 = 0 - 0, or to large 8, and small e2 = e - e,) and a double peak (corresponding to 0 r = e2 = 8/2) should be observed in both cases for a strictly symmetrical scatter-
L.L. Balashova et al. /Argon
ion double scattering from copper
L.591
Fig. 10. The calculations for 01 = IS’, 0 = 30”. The dashed line characterizes the spread of the sliding angles due to both angular spread of primary ions and thermal vibrations of target atoms.
ing ((u = 1So, 0 = 30”). If, however, the scattering is not quite symmetrical (due, for example, to the finite angular divergence of the primary ion beam, to the thermal vibrations of the crystal lattice atoms, etc.), the situation proves to be essentially different for the primary ion energies of 25 and 10 keV. The dashed line in fig. 10 shows the boundaries of y = c(0, - a) due to the variations in the sliding angles corresponding to Aa * 1.5” (i.e. to the spread of the angles in the primary ion beam). It can be seen that such a spread for 25 keV results in but a small spread of the angles t?i and e2 and, hence, in but a slight broadening of the peaks in the energy distribution of the scattered ions. As to the 10 keV ions, the +1.5” variations in the sliding angles result in a significant alteration of the scattering kinematics, namely, the solution which corresponds to the double-scattering event (i.e. to 8i - e2 - e/2) disappears. If 1y= e/2 - 1.5”, the scattering is actually realized by only the first atom (in this case 8i is large and e2 is small). If cu= e/2 t 1.5’ the scattering is actually realized by only the second atom (in this case f3i is small and, hence, Ba = 0 - 8i is large) *. Since the primary ion beam contains ions with different directions of velocity * The physical cause of such scattering kinematics for non-symmetrical scattering geometry is the ion flux redistribution as a result of ion interactions with the scattering centers. When both the sliding angle and the primary ion energy Eo are small enough, the shadow behind the first scattering atom screens the small impact parameters of the second atom responsible for the large-angle ion scattering by the second atom. As a result, only the ions scattered strongly by only the first atom (0 1 is large and 82 is small) enter the analyzer. When the primary ion sliding angle is large and the ion energy is low enough the ions scattered by the first atom in the direction of the second atom cannot enter the analyzer after being scattered by the second atom since in this case the analyzer is inside the shadow (blocking) cone behind the second atom - see also fig. 10 in ref. (131. As a result only the ions scattered practically by only the second atom can enter the analyzer (0, is large and 0 r is small).
L598
L.L. Balashova et al. /Argon
ion double scattering from copper
vectors, the conditions giving rise to two-peaked energy distributions of the scattered ions are satisfied for a portion of the ions, whereas the conditions for other ions are such that but a single peak is observable. It is the circumstance that should result, for a definite energy range, in a decrease of the relative probability of the double scattering with the primary ion energy decreasing. The increase in the relative intensity of the double peak with decreasing primary ion energy could be naturally explained by the energy dependence of the doublescattering cross-section. In the first approximation the double-scattering intensity is proportional to the product of the cross-sections of ion scattering on the first atom towards the second atom and on the second atom towards the analyzer divided by the cross-section of ion scattering on a single atom towards the analyzer. Assuming that the scattering is symmetrical and that the ion-atom interaction can be described by the inverse-square potential, we obtain a formula
(see, for example, ref. [4]). The above simple treatment shows that the correlation of the successive collisions of the scattered ions for but two atoms permits the main features of the observable double-scattering effect to be explained. The authors are deeply indebted to Professor Carl J. Altstetter for the informative discussions of some results.
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