ISSN 10628738, Bulletin of the Russian Academy of Sciences. Physics, 2016, Vol. 80, No. 2, pp. 109–112. © Allerton Press, Inc., 2016. Original Russian Text © V.N. Samoilov, A.I. Musin, N.G. Ananieva, 2016, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2016, Vol. 80, No. 2, pp. 122–125.
Specific Features of the Angular and Energy Distributions of Overfocused Sputtered Atoms Ejected from the (001) Ni Face V. N. Samoilov, A. I. Musin, and N. G. Ananieva Faculty of Physics, Moscow State University, Moscow, 119991 Russia email:
[email protected] Abstract—Peculiarities of the overfocusing of atoms sputtered from the surface of (001) Ni face are studied with the use of molecular dynamics computer simulations. The multivaluedness of the signal of overfocused atoms with respect to initial azimuthalal angle of ejection ϕ0 is discovered and found to be associated with dif ferent mechanisms of atom scattering. The overfocused atoms form a separate maximum and can be sepa rated from the focused and “proper” atoms in experiments with angle and energy resolution. DOI: 10.3103/S106287381602026X
INTRODUCTION The anisotropy of twodimensional angular distri bution of atoms sputtered from the surfaces of the low index faces of a single crystal when exposed to ion bombardment is a complex effect that reflects the anisotropy of the surface structure of crystals. The pat tern of the angular distribution of sputtered atoms is sensitive to the type of crystal face irradiated by ions [1–3]. In calculations of the ejection of atoms from the surfaces of (001) Ni and (111) Ni faces (in partic ular with energy resolution), emission maxima are found that correspond in angular width and directions of formation to experimentally observed emission maxima (Wehner spots) [4]. Thus, the formation of Wehner spots in a twodimensional angular distribu tion of atoms sputtered from single crystal surfaces can be explained only by the action of the surface mecha nism of focusing. At the stage of emission, there occurs such strong redistribution of ejecting atoms over their angles and energy so that this stage plays an important role in the formation the angular and energy distribu tions of sputtered atoms. A nonmonotonous shift of the maximum of the polarangle distribution of sputtered atoms upon a rise in their energy was discovered and investigated in [4–7]. This effect is the result of competition between two factors: the blocking of emitted atoms toward the nor mal of the surface during their ejection and refraction on the planar potential barrier. This shift of the maxi mum was also observed experimentally in [8]. It has been shown that the main features of the observed energyresolved angular distributions are described by the interaction of the ejected atoms with lenses that consist of two atoms: the nearest neighbors of an ejected atom in the surface plane [5, 7]. In studying the focusing of sputtered atoms, atten tion is concentrated on the mechanisms of focusing with respect to the polar angle of ejection. Few works
have been devoted to studying the azimuthalangle focusing of sputtered atoms. It therefore seemed important to us to investigate the mechanisms respon sible for the anisotropy of the azimuthal distribution of sputtered atoms. For asymmetric (relative to direction 〈010〉) inter vals of azimuthal angle ϕ, the forming of a signal of sputtered atoms when atoms are ejected from a surface proceeds due to “proper” atoms, whose initial angle of ejection ϕ0 falls into the interval of angles ϕ, and to the focusing of “improper” atoms: focused atoms scat tered by the nearest atom of a lens consisting of the two surface atoms nearest to the ejected atom, and overfo cused atoms scattered from the far atom of the lens. For the focused atoms, angles ϕ and ϕ0 lie on the same side of the 〈010〉 direction toward the center of the lens (formed by the two surface atoms nearest to the ejected atom); for the overfocused atoms, ϕ and ϕ0 lie oppo site this direction. The focusing of atoms thus occurs toward the center of the lens consisting of two atoms, while overfocusing proceeds through the center of the lens consisting of two surface atoms. The effect of overfocusing was discovered in [5, 9] and has been investigated in a number of works (e.g., [10]). In this work, peculiarities of the azimuthalangle (ϕ) focusing of atoms sputtered from the surface of the (001) Ni face with resolution in the polar angle and energy were explored. The aim was to study the contribution from overfocused atoms to the formation of the angular and energy distributions of sputtered atoms. The problem of separating overfocused atoms from the total signal of emitted atoms was also investigated. MODEL OF CALCULATION Calculations were performed for the ejection of atoms from the surface of (001) Ni face. The simula tion results obtained using two models of calculation
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Fig. 1. Distribution of sputtered atoms over the initial azi muthal angle ϕ0 and energy E for polar angles of emission ϑ [56.3°, 57.8°] and azimuthal angles ϕ [82.5°, 85.5°]. The focused atoms are shown in the lower part of the fig ure; the overfocused atoms are shown in the top part. In contrast to the 5atom model, there are no overfocused atoms with high energies.
were compared. In model I, the crystal surface was simulated by the 20 surface atoms nearest to the lattice site from which the atom was ejected (a 21atom model). A similar model was used in [11]. In model II, the crystal surface was represented by a minimal frag ment: a ring consisting of the four surface atoms near est to the lattice site from which the atom was ejected (a 5atom model). This model was used in a number of our earlier works (e.g., [10]). Molecular dynamics was used to calculate the ejec tion of atoms. The interaction between an ejected atom and the surface atoms was described by the repulsion potential, while a planar potential barrier was introduced at a sufficiently great distance of the atom from the surface. We used the Born–Mayer potential as a potential of atom–atom interaction: U ( r ) = A exp ( – r/b )
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for interaction of two Ni atoms with parameters A = 23853.96 eV and b = 0.196 Å [12]. The binding energy was 4.435 eV. An atom was knocked out of a site at the surface with energy Е0 at angles ϑ0 (the initial polar angle was counted from the normal to the surface) and ϕ0 (initial azimuthal angle, ϕ0 = 90° corresponded to the 〈010〉 direction toward the center of the lens consisting of the two surface atoms nearest to the ejected atom). Initial energy Е0 varied from 0.5 to 100 eV. The step in Е0 was 0.01 eV. The step in ϕ0 was 0.5°, and the step in 1 – cosϑ0 was 1/450. The initial angular and energy distribution of ejected atoms cosϑ0/ E 02 [13, 14] was used. The distribution of ejected atoms over initial azi muthal angle ϕ0 was thus isotropic. Sputtering was assumed to be due only to atoms of the surface layer. This assumption was quite justified,
since the contribution from surfacelayer atoms to sputtering dominates for targets consisting of medium mass and heavy atoms (88.6% for the ion bombardment of Cu [15], 82% for the ion bombardment of Mo [16]). Some features and the correctness of the model used in this work were also discussed in [5]. During our calculations, we considered the ques tion of how the interaction of ejected atoms with the atoms of a crystal surface in the process of emission influences the observed energyresolved angular dis tribution of sputtered atoms. Our calculations were performed using the Lomonosov supercomputer complex at Moscow State University [17, 18]. The software program for these computations was written in the Fortran 90 language using Intel MPI. RESULTS AND DISCUSSION Multivaluedness of Distribution of Overfocused Atoms over Angle ϕ0 Let us examine more thoroughly the mechanisms of formation of the energyresolved angular distribu tion of ejected atoms. For this purpose, we calculate the initial azimuthal angles at which the sputtered atoms observed within the fixed ranges of the ϑ and ϕ angles and energy E ejected from the surface. Note that the planar potential barrier does not change the azimuthal angle at which the ejected atom moves after scattering by one or several surface atoms (for a sput tered atom). In the differential angular and energy distributions of sputtered atoms, the multivaluedness of signals of the focused and overfocused atoms was detected with respect to angle of ejection ϕ0. Figure 1 presents the dis tribution (over initial azimuthal angle ϕ0 and energy E) of sputtered atoms (ejected from the surface of the (001) Ni face) for polar angles of emission ϑ [56.3°, 57.8°] and azimuthal angles ϕ [82.5°, 85.5°]. The number of sputtered atoms is shown as a logarith mic plot (the scale is on the right). It was found that the overfocused atoms were very sensitive to the selected model, which cannot be said of the focused atoms. In the 21atom model, the highenergy part of the distribution of overfocused atoms observed in the 5atom model is bent toward low values of energy E and angles ϕ0 more close to the direction of the lens center. Multivaluedness thus appears in the distribu tion of overfocused atoms over angle ϕ0, and a zero signal region emerges whose size increases as energy E decreases. The overfocused atoms ejected at different angles ϕ0 are observed in the detector with a narrow angular aperture at energy E ≤ 6 eV. This multivalued ness is shown to be associated with the two different mechanisms of the scattering of overfocused atoms for different angles ϕ0. For the overfocusing of the upper branch atoms, the scattering from the closest atom of the lens is substantial. For the overfocusing of the
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SPECIFIC FEATURES OF THE ANGULAR AND ENERGY DISTRIBUTIONS 1 – cosϑ 0
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Fig. 2. Distribution of sputtered atoms emitted from the (001) Ni face simultaneously over 1 – cosϑ and energy E for interval of azimuthal angles ϕ [76.5°, 79.5°]. The upper ridge is formed mainly by focused atoms; the lower ridge is formed only by overfocused atoms.
lowerbranch atoms, the scattering from the atom located behind the lens is also substantial. The basis of the ϕ0angle multivaluedness of the signal of overfo cused atoms is thus the multiple scattering of the ejected atoms by the surface atoms. Individual Ridges of the Energy and PolarAngle Distribution of Sputtered Atoms for Overfocused and Focused Atoms It was found that in distributions with the simulta neous resolution in energy and polar angle for fixed intervals of the angle ϕ, individual ridges (the maxima of distributions) are clearly distinguished for focused and overfocused atoms (Fig. 2). The upper ridge is formed mainly by the focused atoms; the lower ridge is formed only by the overfocused atoms. The distribu tion maximum of the overfocused atoms is observed in the range of energy and polar angles at which there is no emission for other groups of atoms. The overfo cused atoms form 100% of the observed signal. In the experiments with angle and energy resolution, the sig nal of overfocused atoms alone can thus in principle be separated. Observability of Overfocused Sputtered Atoms The energy distribution of sputtered atoms for fixed intervals of the polar and azimuthal angles (Fig. 3) consists of contributions from focused atoms (left hand maximum) and overfocused atoms (righthand maximum), and a small contribution from “proper” atoms at energies E of 0 to 1.2 eV. The highenergy maximum (see Fig. 2) in the energy distribution of ejected atoms with resolution in the polar and azi muthal angles [19], which is observed at energies E > 20 eV, was formed by focused rather than overfocused atoms.
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Fig. 3. Distributions of (a) all sputtered atoms and (b) only overfocused sputtered atoms over energy E for emission from the (001) Ni face for polar angles of emission ϑ [56.3°, 57.8°] and interval of azimuthal angles ϕ [76.5°, 79.5°].
Similarly, the polarangle distribution of sputtered atoms for the fixed energy and azimuthal angle (Fig. 4) consists of contributions from focused atoms (left hand maximum), overfocused atoms (righthand maximum), and “proper” atoms near the normal to the surface with 1 – cosϑ from 0 to 12/45. The polar angle distribution of sputtered atoms for the same interval of azimuthal angles with no energy resolution Y, arb. unit 12000
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Fig. 4. Distribution of (a) all sputtered atoms and (b) only overfocused sputtered atoms over 1 – cosϑ for emission from the (001) Ni face at E = 3.0 ± 0.1 eV and interval of azimuthal angles ϕ [76.5°, 79.5°].
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has only a single maximum formed by the focused and overfocused atoms. CONCLUSIONS Peculiarities of the azimuthalangle overfocusing of atoms ejected from the surface of the (001) Ni face in formation of the distributions of sputtered atoms with simultaneous resolution in the polar angle and energy were studied by means of molecular dynamics. The mechanisms of formation of the features of these distributions were examined. The differential distributions of sputtered atoms over initial angle ϕ0 and energy E were calculated. The multivaluedness of signals of the focused and overfo cused atoms with respect to angle of ejection ϕ0 was detected in the 21atom model at relatively low values of energy E. It was shown that this multivaluedness was due to two different mechanisms of the scattering of overfocused atoms for different angles ϕ0. In azimuthal direction from the site of ejection toward the center of the lens (consisting of the two nearest atoms of the surface), the difference between distributions calculated using the 5atom and 21atom models was due to the scattering of the ejected atoms by the atom behind the lens, which is present only in the 21atom model. The overfocused atoms in the 21atom model can originate closer to the lens center, due to the scattering of ejected atoms by the atom behind the lens. The ranges of energy E and polar and azimuthal angles of emission ϑ and ϕ were found in which 100% of the signal of sputtered atoms formed was due to ejected atoms overfocused with respect to the lens center. It was found that in the distributions simulta neously resolved in the energy and the polar angle, individual ridges (distribution maxima for the focused and overfocused atoms) were clearly distinguished for the fixed intervals of angles ϕ. It was shown that in the experiments with angle and energy resolution, the sig nal of overfocused sputtered atoms alone can in prin ciple be separated.
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