Scattering and recoiling mapping of the Kr-Pt(111) and Ne-Ni(111) systems by SARIS∗

The technique of angle resolved mapping of scattering and recoiling imaging spectra (SARIS) combined with computer simulations is demonstrated to be a valuable tool for characterization of atomic collision events on surfaces. The energy distributions of scattered Kr and Ne and fast recoiled Pt and Ni atoms from Pt(111) and Ni(111) surfaces were measured as a function of exit angle. The use of a large area microchannel plate (MCP) detector and time-of-flight (TOF) techniques decreases the collection time and increases the number of detected trajectories above that of other designs. Classical ion trajectory simulations using the three-dimensional scattering and recoiling imaging code (SARIC) are used to simulate the kinematics of the scattering and recoiling particles. It is shown that SARIS mapping allows one to probe the kinematics of both scattered and recoiled particles, the probability for their occurrence in specific trajectories, and the atomic layers from which the particles originate. [DOI: 10.1380/ejssnt.2004.93]


I. INTRODUCTION
Ion beams impinging on solid surfaces have been extensively investigated for applications to materials processing, fabrication techniques, and analysis of solid structures. Low energy ion scattering spectrometry with timeof-flight (TOF) detection has been used extensively to study the composition and structure of surfaces. Recently developed large solid angle detection instruments for scattering and recoiling imaging spectrometry (SARIS) [1,2] provide spatial-and time-resolved, element-specific images from surfaces that directly expose the threedimensional anisotropy of keV scattered and recoiled atoms. The technique has been used for structural information, compositional analysis of surfaces, and ion fraction mapping [3][4][5][6].
It is known that the ordered arrangement of atoms may strongly affect the energy and spatial distribution of recoils ejected from targets under ion bombardment. In keV ion bombardment the majority of the sputtered atoms have energies of only a few eV. These abundant low-energy atoms can arise from several atomic layers and can overshadow the features of high-energy recoiled particles from first few surface layers. Most angle-resolved secondary particle spectrometric studies have focused on the properties of particles sputtered from the surface with kinetic energies less than ∼200 eV. To our knowledge, only a few angular resolved experimental studies have been performed on the ejection of high-energy particles [7][8][9][10][11][12][13][14][15][16]. Computer simulations of ion-surface collision processes have undergone extensive development in the past two decades. These simulations are a complementary source of information that provides valuable insight into the microscopic collision details. The recently developed scattering and recoiling imaging code (SARIC) [17,18] is a classical ion trajectory program that simulates two-dimensional scattering and recoiling patterns and provides quantitative interpretations of ion scattering and recoiling images from SARIS.
The purpose of this paper is to introduce high-precision angle-resolved mapping of scattered and recoiled particles with a large area detector, combined with computer simulations, as a quantitative tool for characterization of scattering and recoiling events on surfaces. In contrast to analysis of scattering features, there have been very few studies [13,14,[19][20][21] focused on the relationship between the kinetic energies of recoiled particles and the emission angles, which, in the azimuthal distribution of these particles, reflects the geometric structure of the surface. Herein we present experimental and simulated results of Kr + incident on Pt(111) and Ne + incident on Ni(111) surfaces for the angle-resolved mapping of recoiled particles with a large area detector, combined with computer simulations as a quantitative tool for characterization of scattering and recoiling events on surfaces. Most of the details of the experimental/simulation techniques have been published elsewhere [16].

II. METHODS
The experiments were performed in an ultra high vacuum chamber with a base pressure ∼ 5 × 10 −10 Torr. All measurements were made with the sample at room temperature in a SARIS spectrometer that has been described elsewhere [1][2][3][4][5]16]. Briefly, a pulsed ion beam [22] scatters and recoils atoms from the surface. The velocities of the keV ejected atoms and ions are analyzed by measuring their flight times from the sample to a rectangular position sensitive MCP detector [23] with a sensitive area of 3.5 × 4.5 cm 2 . The detector is gated so that it can be activated in windows of ∼ 4 µs duration that are appropriate for collection of specific scattered or recoiled atoms. The velocities (energies) of scattered and recoiled particles are analyzed by measuring their flight times from the sample to the MCP using a multiple-stop time-to-digital FIG. 1: Geometry of the SARIS experiment and SARIC calculation. α -incidence angle, ξ -angle between incident beam and plane of MCP, β -variable emission angle, θp = α + βpscattering/recoiling angle varying between θmin and θmax and corresponding to pixel p on the MCP, and h = 13 cm -distance to the detector (at the position of the normal at θ0) which is used for the SARIC calculation.
converter. The detection efficiencies of neutrals and ions is comparable in this energy range.
The Pt and Ni single crystals in the form of 1 × 9 mm disks were polished within 0.5 • of the [111] direction and cleaned by repeated cycles of 3 keV Ar + sputtering and annealing. The surfaces were considered clean and well ordered when no impurity features were observed in the SARIS images and the LEED images exhibited sharp (1× 1) patterns. The pulsed, mass-selected ion beam has a duoplasmatron ion source [22] that produces beam spot sizes down to 1 mm 2 with energies variable over the range 3-25 keV and a final energy spread of < 50 eV. A two step pulsing system produces pulsed beam widths < 30 ns and an average pulsed beam current of 10-100 pA. The 64 ×64 pixel MCP is mounted on a triple-axis goniometer [24] so that it can be positioned at different angles relative to the sample surface. Details of the angular notations are shown in Fig. 1.
Ion trajectory simulations from the SARIC [17,18] program were used to calculate the angle-resolved energy distributions of scattered atoms and recoils. It describes the interactions between atoms and follows the trajectories of all scattered and recoiled atoms in threedimensions, thereby capturing both in-and out-of-plane single and multiple collision events. Surface Debye temperatures, as estimated by Jackson [25], were used to generate the three-dimensional thermal vibrations of atoms around their equilibrium positions as in our previous work [26].

A. Contour plots of angular distributions for
Kr + →Pt (111) Experimental two-dimensional contour plots of the scattering and recoiling intensities as a function of the scattering and recoiling angles and flight times for 10 keV Kr + scattering from Pt(111) are shown in Fig. 2 as extracted from SARIS frame analysis. A horizontal cut through the figure gives an energy distribution at a fixed emission angle and a vertical cut gives an angular distribution at fixed energy (or fixed TOF). Figure 2(a) presents the experimental angular distribution of scattered Kr particles, while Fig. 2(b) consists of the distribution of recoiled Pt particles. Here we use the term 'particles' to represent scattered and recoiled atoms plus ions. The main features can be separated into scattering (s 1 − s 4 ) and recoiling (r 1 − r 3 ) traces. As will be shown later, s 1 and r 1 can be described as quasi-single scattering and recoiling collision events, while s 2 − s 3 and r 2 − r 3 include two or more large-angle collision events. s 4 is a small quasi-single scattering contribution from the 83 Kr isotope. Angle versus TOF scattering and recoiling mapping distributions were also obtained from the simulations. The calculated contour plot distributions of the scattered and recoiled particles can also be separated into three scattering (s 1 −s 3 ) and four recoiling (r 1 −r 4 ) traces as shown in Figs. 2(c)(d).

B. Separation of collision sequences and fractional yields
Classical kinematical analysis is particularly useful in studying the details of the scattering and recoiling events since the observed particles leave the surface as a result of individual primary impacts, the associated cascades are not complex, and the ejected atoms are mainly from the first layer. The well known kinematical description of collisions [2,27,28] provides information about the final energies and scattering angles of interacting particles. The energies of scattered and recoiled atoms in an elastic collision can be determined from the conservation of energy and momentum as and with and where E 0 is the energy of the incident ion with mass M 1 , M 2 is the mass of a target atom which is initially at rest, θ i,j are the partial scattering or recoiling angles, and f S,R is the fraction of energy transferred during the scattering or recoiling event. For in-plane geometry, where θ is the angle between the direction of the incident beam and the direction of the outgoing particle, α is the angle of incidence, and β is the emission angle. When the scattering/recoiling plane is not normal to the target surface, the partial angle is determined by where α i is the partial incident angle, β i is the partial emission angle, and φ i is the partial azimuthal angle. It is easy to see that for particles experiencing out-of-plane collisions, i,j θ i,j > θ. When the energy and mass of the analyzed particles are known, the energy E of the particles is connected with the time-of-flight T OF p corresponding to pixel p on the MCP and the measured flight time (T M ) by the relation where M is the particle mass, l p is the flight length, i.e. the distance between the target and pixel p on detector (see Fig. 1), T 0 is the time it takes the particle to travel between the pulsing aperture and the sample, and ∆ is the fixed electronics delay.  1) and (2). The definitions of the experimental and SARIC traces (r 1 − r 4 , s 1 − s 3 ) are the same as in Figs. 2(a-d). The experimental and calculated peak positions are very close to those of the theoretical binary collision curves that include a maximum of two collisions. The relevant processes are shown schematically in Fig. 2. Curves SS and DR correspond to processes s 1 and r 1 , respectively, defining positions for the energies of particles after a single collision. If several large impact parameter, or "Quasi-single" collisions, with angles ∼ 1 • − 2.5 • are included for incoming and outgoing particles, improved agreement between the SARIS/SARIC results can be obtained. The rest of the higher energy traces in Fig. 2 cannot result from a single binary collision event; at least two binary collisions are necessary to produce these traces. A more detailed understanding of such high energy events can be achieved if the actual trajectories of the scattered and recoiled particles are determined. Such trajectories have been extracted from the SARIC simulations. Inplane collisions can be defined as a double scattering process (DS) from atoms lying in a single row corresponding to trace s 3 . For recoil, a possible collision sequence is the following: a primary ion recoils a Pt atom which scatters off a second Pt atom in the same surface row (curve FR 2 or trace r 3 ). Curve FR 3 corresponds to a collision sequence in which Kr scatters parallel to the surface and then recoils a Pt atom. For out-of-plane collisions including atoms from two parallel rows, one can observe only fixed zig-zag collisional events. From comparison of SARIS and SARIC results with curves from Eqs. (1) and (2), we find that only two angles are possible in zig-zag collisions, i.e. ∼ 20 • (for ZS) and ∼ 22 • (for FR 1 ). These angles do not belong to any specific crystallographic directions and are most likely related to the nature of the screening function for a given collision pair. SARIS experimental images are accurately reproduced by SARIC simulations after including correction factors such as detection efficiency and detector position [3,16]. Features at t < 0.5 µsec correspond to scattered Ne atoms while those at t > 0.5 µsec correspond to recoiled Ni atoms. A typical quasi-single collision recoiling trace is observed for the In order to obtain further information on recoil spot formation, we have considered the depth from which Ni atoms are recoiled when 20 keV Ne atoms are incident on Ni(111) along the [121] azimuth. Additional simulations were performed in order to determine whether or not this preferential ejection direction depends on the subsurface layers. The contributions of the recoil yield from different layers were calculated from SARIC for the same exit angles and targets consisting of 1, 2, 3, and 4 atomic layers. Figure 4 shows the resulting angular-TOF distributions of the recoil fractions from the first (4a), second (4b), third (4c), and fourth (4d) atomic layers. Figure 5 shows the resulting angular yields obtained by integrating the contour plots at Fig. 4 for each atomic layer. The insert in Fig. 5 shows a bar graph of the total integrated yield from each atomic layer.
From Figs. 4 and 5, it is clear that the first three atomic layers contribute most of the recoiled atoms and that the contributions of each of these three layers are very different. The first atomic layer ( Fig. 4(a)) yields ∼22 % of the recoils and exhibits a 'typical' kinematical trace of recoiled atoms (similar to that observed for Kr-Pt(111) [16]) with traces of quasi-direct recoil and fast-recoils. As distinct from the Kr-Pt(111) system (Fig. 2), here the fast recoil traces represent a very small fraction of the scattered atoms. They can be observed on the left side  Fig. 4 and normalized to total yield. Insert -bar graph of total integrated yield from each atomic layer.
of Fig. 4(a) by using a logarithmic scale. The second atomic layer (Fig. 4(b)) yields ∼40% of the recoils in a highly focused recoil spot. The direction of the maximum near 32 • (Fig. 5) cannot be related to any low-index crys-tallographic vectors between the 2nd and 1st layers. This observation again confirms that the position of the 'recoil spot' is only related to the 'atomic lens' formed by atoms of the first atomic layer. The third atomic layer (Fig. 4(c)) yields ∼33% of the recoils, although the recoil distribution is diffuse and exhibits no focused recoil spots. This indicates that atoms recoiled from the third atomic layer are scattered by first and second layer atoms, thereby obliterating any focused recoiled patterns.

IV. DISCUSSION
Our results show that angular distributions of scattering and recoiling particles can be the simplified by using a kinematical description obtained from TOF versus angular traces. A combination of SARIS experiments and SARIC simulations provides a sensitive probe, which can yield, within experimental error, a conclusive description of the three-dimensional collision behavior of energetic atoms scattered from the outermost atomic layers of a surface. SARIS and SARIC provide a quantitative separation of the observed multipeak features in the scattering and recoiling spectra and accurate analysis of the collision sequences. An important result of this work is that the most intense recoiling features are due to atoms recoiled from the first two to three atomic layers. The 'recoil spots' are the results of preferential ejection of secondlayer atoms along the open directions, or 'atomic lens', where atoms can either recoil directly into the atomic lens or it can scatter from a neighboring and aligned into the atomic lens.
Much research has focused on studying the scattering features in experimental spectra. For example, experimental energy spectra have been analyzed in terms of "quasi-single" peaks and "quasi-double" shoulders [27]. Generally, better agreement between experiments and simulations can be achieved if the full three-dimensional nature of the collision is recognized. For example, computer simulations have been used to identify peaks due to "planar" and "zig-zag" collision sequences [26,[30][31][32]. These results support our conclusion about the kinematic nature of separation and description of the observed peaks and traces in Figs. 2 and 3.

V. CONCLUSIONS
This study demonstrates that angle-resolved SARIS mapping combined with computer simulations is a valu-able tool for characterization of scattering and recoiling events on a surface. The measurements allow identification of direct and indirect, i.e. multiple collision, scattering and recoiling particles in the energy distributions. Use of a large area MCP detector and TOF techniques decreases the collection time and increases the number of detected recoils above that of other designs. The scattering and recoiling contour map dependencies provide the kinematics of scattering and recoiling particles, their probability of being detected, and the probability for their occurrence in specific trajectories.