Computational study of low energy ion surface hyperchanneling

Surface Science 581 (2005) 1–8 www.elsevier.com/locate/susc

Computational study of low energy ion surface hyperchanneling Z.L. Fang a, W.M. Lau b, J.W. Rabalais a

c

c,*

Department of Physics and Photonics Research Center, Xiamen University, Xiamen 361005, PR China b Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China Department of Chemistry and Physics, Lamar University, P.O. Box 10022, Beaumont, TX 77710, USA Received 6 October 2004; accepted for publication 28 January 2005 Available online 10 March 2005

Abstract Classical ion trajectory simulations using the scattering and recoiling imaging code (SARIC) have been applied to study the low energy ion surface hyperchanneling phenomenon. It was found that the ion-surface interaction geometry, projectile type, surface chemisorbed hydrogen, and phonon amplitudes had a profound effect on the scattered ion trajectories. It is possible to determine the surface Debye temperature through analysis of the scattering yields and angular distributions. The simulations will find application in delineation of classical ion trajectories for specific as well as generic ion surface interactions.
2005 Elsevier B.V. All rights reserved. Keywords: Ion–solid interactions; Channeling; Scattering; Platinum; Computer simulations; Low index single crystal surfaces

1. Introduction The guided motion of ions by a planar potential along a planar channel in a crystal is known as ÔchannelingÕ. Channeling commonly occurs in the open space between two parallel planes of atoms on a surface or along an axial channel with a continuous cylindrical potential, i.e. the open space *

Corresponding author. Tel.: +1 409 880 7904; fax: +1 409 880 8270. E-mail address: [email protected] (J.W. Rabalais).

between several adjacent rows of atoms. The channelling phenomenon was first discovered in computer simulations by observing the enhancement of the penetration range of ions that were aligned along the principal azimuthal directions of crystals. It was experimentally verified in high-energy ion scattering experiments [1]. When ions approach a crystal surface with a very small incident angle, string scattering or surface planar/axial channeling can occur, depending on the incident azimuthal angle relative to the surface channels. An increase in the incident polar

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2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.01.057

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angle can result in the steering of the projectiles into troughs formed by atomic rows in subsurface layers. This is also known as subsurface channeling. Surface channeling is often mixed with subsurface channeling due to the efficient penetration of ions into subsurface or bulk channels. The particles moving in a potential valley also tend to escape into the empty top of the semichannel and thus are easier to dechannel. The use of ions in the MeV range as a probe simplifies the bulk channeling observation due to the very small scattering cross-sections (< ˚ 2) for such high energy ions. However, for 10
8 A surface channeling, a very small incident angle has to be employed in order to prevent the penetration of the fast projectiles into subsurface layers. The stringent requirements of crystal or film quality, beam divergence, and accurate goniometer make it very difficult to realize fast ion surface channeling. To the best of our knowledge, only a few reports on fast or medium-energy ion surface channeling [2–4] exist. In comparison, low energy ion scattering in the keV range has a large scattering cross-section ˚ 2), which confines the incident ions predom(1 A inately to the 1st-atomic layer. Accordingly, a relatively large incident angle can be used. This has the advantage of reducing the requirement of a sample with a large uniform surface area due to the relatively small projected area of the incoming ion beam on the surface. Moreover, the allowed incident Lindhard critical angle [5] is larger in low-energy ion scattering than those in mediumand high-energy ion scattering. These features simplify the sample preparation and reduce the instrumental requirements. Classical ion trajectory simulations arc important, for example, in studies of the scattering patterns of ions on surfaces, penetration depths and concentration profiles of ions in materials, and understanding the neutralization of ions scattered along different trajectories. Low energy ion surface channeling has been realized [6] and successfully used to study the surface structure and thermal vibrations for Ir(1 1 0), Pb(1 1 0), and alloy Au3Pd(1 1 3) surfaces by Heiland and coworkers [7]. Focusing of 4 keV He+ ions on semichannel planes in the Pt{1 1 1}-(1 · 1) surface has been ob-

served using scattering and recoiling imaging spectrometry (SARIS) by Rabalais and coworkers [8]. The nature of the ion trajectory has been shown [9] to be crucial in the neutralization of hydrogen anions on FCC surfaces. Surface channeled ions can wander into different surface channels without violating the channeling conditions. The steering of a highly collimated incident ion beam onto one single set of surface channels is called surface hyperchanneling [10, 11]. The conditions for surface hyperchanneling include (1) surface channeling conditions and (2) transverse energy of incident ions referenced to the atomic rows (semichannel axis) smaller than the Lindhard ‘‘string’’ potential [5] of one atomic row. In the present work, the Scattering and Recoiling Imaging Code (SARIC) was used to study the effects of the mass of the projectile ion, ion-surface interaction geometry, thermal vibrations, and surface chemisorption on the ion trajectories, channeling, and the energy distribution of the scattered ions. Details of the SARIC code have been described elsewhere [12]. In order to acquire the layer-to-layer critical incident angles, we performed backscattering (BS) versus incident angle a scans along selected low-index azimuths [13]. Low-energy ion-surface hyperchanneling phenomena were investigated by detailed simulations of ion trajectories tracing the incoming and outgoing paths and energy distributions of the scattered ions. Studies on the effects of thermal vibration and surface chemisorption on surface hyperchanneling were also included.

2. Results and discussion Multiple scattering (MS) normally dominates in grazing incidence ion-surface interactions. Generally, the trajectories are in the forms of (i) random scattering from the surface (surface planar channeling); (ii) string scattering from single atomic rows; (iii) straight trajectories or zigzag walks in the potential valley of one single surface channel (surface hyperchanneling); (iv) zigzag walks into different surface channels without violating

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channeling conditions (surface axial channeling); and (v) subsurface channeling. 2.1. Effect of ion-surface interaction geometry on ion trajectories Fig. 1 shows a set of ion trajectories for 4 keV Ne+ ions impinging on the Pt(1 1 1) surface along the [1 1 0] direction which is assigned as the azimuthal angle d = 0. When the incident angle a and exit angle b equal 5 along the [1 1 0] direction, most of the incoming ions are directly scattered by the 1st-layer atomic-row atoms (so called ‘‘string scattering’’) with only a few of them being able

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to enter the surface channel as shown in Fig. 1(a). Increasing the incident and exit angle to 8.5 results in hyperchanneling as shown in Fig. 1(b). Most of the incoming ions are spatially confined into the surface channel with none of them penetrating into the second layer. From both the side-view and the topview, it can be observed that most of the ions possess oscillatory paths between the two atomic rows of the surface channel for a long distance before leaving the surface. Considering the non-specular case (a = b), it was found that only about one-half of the incident ions were hyperchanneled with considerably shorter ion trajectories. From LindhardÕs theory

Fig. 1. SARIC simulations of 4 keV Ne+ ion trajectories on the Pt(1 1 1)-(1 · 1) surface for (a) a = b = 5, d = 0; (b) a = b = 8.5, d = 0; (c) a = b = 8.5, d = 2.5; (d) a = 12, b = 10, d = 6; (e) a = 15, b = 12, d = 0. The solid ‘‘balls’’ represent the surface atoms and the solid lines represent the ion trajectories.

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[5], as long as the deviation angle Dd between beam azimuthal angle and surface channel axis is less than the Lindhard critical angle, hyperchanneling will persist. This has been observed as shown in Fig. 1(c). When Dd = 2.5, most of the ions can perform hyperchanneling. Further increases of the incident angle result in a transition of the scattering phenomenon from surface hyperchanneling to surface planar channeling. The incoming ions can wander from one semichannel to another without violation of the surface planar channeling conditions. This becomes evident in Fig. 1(d) when the incident angle is 12, exit angle 10, and azimuthal angle 6, i.e. Dd = 6. From the top-view, it is clear that the ions are not confined into any single surface channel but are diverted into different surface channels. When the incident angle a is increased to 15 and exit angle b to 12 for ion scattering along the [1 1 0] azimuth, most of the incoming ions penetrate into the subsurface and are scattered by the second atomic layer (subsurface channeling) as shown in Fig. 1(e). Some of them perform quasidouble or multiple scattering from the 1st atomic layer. The above observations are consistent with a three-dimensional equipotential valley above the surface channel that is formed by the repulsive potential of the three rows of atoms lining the [1 1 0] semichannel [10,11]. Here we define the x-direction along the semichannel axis, the z-direction along the surface normal, and y-direction perpendicular to the x–z plane. The scattering phenomenon is determined by the incoming ion energy, interaction geometry, and interaction potential. Briefly, when the incident angle is too small, the transverse component of ion energy Ez is not large enough to overcome the repulsive potential barrier V 1z (here ‘‘1’’ indicates the repulsive potential contributed from the 1st-layer atoms) and therefore the ions cannot enter the potential valley, resulting in string scattering (Fig. 1(a)). Only under appropriate conditions with suitable Ez and Ey (i.e. suitable incident polar angle and azimuthal angle), incoming ions can enter the potential valley and describe zigzag trajectories inside one single semichannel before leaving the surface, i.e. surface hyperchanneling (Fig. 1(b)). When the incident angle is increased further, the contribution of the repulsive

potential V 2z from the 2nd-layer atoms becomes more effective and the 2nd-layer atoms become visible to the incoming ions (Fig. 1(e)). Considering the azimuthal deviation angle Dd for an appropriate incident angle, when Dd is small, i.e. Ey < Vy, the interaction potential is continuous and hyperchanneling conditions maintain (Fig. 1(c)). When Dd is high, the incoming ions actually feel the discrete repulsive potential and dechannelling occurs (Fig. 1(d)). 2.2. Projectile effect on ion trajectories Studies of the projectile effect on the ion trajectories showed that with the same incident energy and target atoms, it is more difficult to observe the hyperchanneling phenomena for lighter projectiles. For example, in Fig. 2(a) and (b), 4 keV Ar+ is able to hyperchannel with incident and exit angles in the range of 7–10.5. In comparison, when 4 keV Ne+ was used as shown in Fig. 2(c) and (d), the incident angle for hyperchanneling was within the narrower range of 7.5–9.5. It was very difficult to establish hyperchanneling conditions for 4 keV He+ ions. This apparent feature can be understood by observing the shadow cone shown in Fig. 2(e), (f) and (g). The shadow cone radius can be expressed as R = d sin ac, where d is the interatomic spacing and ac the Lindhard critical angle. With the trend in the radii being RHe < RNe < RAr, the minimum critical angle for hyperNe Ar channeling varies as aHe c < ac < ac . The weaker shadowing effect for a smaller shadow cone size results in an increase in the corrugations of the interaction potential and the probability of dechanneling of incoming ions. 2.3. Energy distributions The energy distribution of 4 keV Ar+ scattered from the Pt(1 1 1)-(1 · 1) surface along the [1 1 0] direction with a scattering angle of 18 is shown in Fig. 3. In the case of specular reflection, hyperchanneling ions experience a series of small-angle multiple scattering collisions from the sample surface and thus suffer little energy loss and a narrow energy spread as compared with large-angle single scattering. For an incident angle a = 13 and exit

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Fig. 2. SARIC simulations of 4 keV ion trajectories on the Pt(1 1 1)-(1 · 1) surface for (a) Ar+, a = b = 10.5; (b) Ar+, a = b = 7; (c) Ne+, a = b = 9.5; (d) Ne+, a = b = 7.5; and molecular dynamics (MD) simulations of shadow cones of 4 keV ions scattering from Pt for (e) He+, (f) Ne+, and (g) Ar+, respectively.

angle b = 5, the multiple-scattering peak is sharp with little energy loss and the scattering cross section is very low. The energy position of the quasisingle scattering peak and the corresponding FWHM were found to be lower and broader than those of the hyperchanneling peak. Through manipulation of these characteristics, hyperchanneling could be employed to generate a pulsed

neutral beam, which is an attractive probe for analyzing insulating materials. 2.4. Hydrogen effect on hyperchanneling Hyperchanneling ions were found to be very sensitive to the chemisorbed hydrogen. The adsorption site of hydrogen atoms on Pt is located

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ms

Relative Intensity

4 keV Ar - Pt(111)-(1x1) o Scattering Angle θ = 18 o o α = 13 , β = 5 ; x200 o o α= 9 , β =9

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"ss" / single scattering "ds" / double scattering "ms" / multiplescattering

3500

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ds

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Energy (eV) Fig. 3. SARIC simulations of energy spectra of 4 keV Ar+ scattered from the Pt(1 1 1)-(1 · 1) surface along the [1 1 0] direction with a scattering angle of 18, (a) a = b = 9; (b) a = 13 and b = 5. In the figure, ‘‘ss’’, ‘‘ds’’, and ‘‘ms’’ stand for the energy position of quasi-single scattering, double scattering, and multiple scattering, respectively.

˚ [14]. above the surface at a height of 0.9 A Although the shadowing and blocking effect of H on the trajectories of projectiles and outgoing particles is minor, the energy loss of incident ions to H is not negligible. By a simple calculation, 4 keV Ar is deflected by a surface H with a scattering angle as large as 1.44 (h < hmax = arcsin(l), l = MH/ MAr) and an energy loss of 5% of E0 in single scattering. In a set of trajectory simulations (Fig. 4(a)) with a = 9, b = 9, and d = 0, most of the incoming ions were deflected by hydrogen atoms instead of entering the potential trough of the surface channels and performing hyperchanneling. The energy distribution of hyperchanneled ions changed drastically (Fig. 4(b)) and the scattering yield was very low for this specular scattering geometry. The scattering peak was broadened with a long tail extending to the low energy part because most of the hyperchanneled ions performed multiple scattering from both H and Pt atoms. 2.5. Thermal effects on hyperchanneling Fig. 5(a) depicts the effect of phonon amplitude on the hyperchanneling yield. It should be noted that the exit angle b was taken to be higher than that of specular reflection in order to observe the effect of phonon induced dechanneling of the ions.

Fig. 4. (a) Effect of surface hydrogen on ‘‘hyperchanneling’’ ion trajectories; (b) Energy spectra of 4 keV Ar+ scattered from the Pt(1 1 1)-(1 · 1) and Pt(1 1 1)-(1 · 1)-H surface along [1 1 0] with a = 9 and b = 9. In the figure, the solid-circle line is from the Pt(1 1 1)-(1 · 1) surface and the open-circle line from the Pt(1 1 1)-(1 · 1)-H surface.

When the phonon amplitude is small, the scattering yield along the direction is predicted to be low. When the rms phonon amplitude was taken ˚ , most of the ions performed hyperchannelas 0 A ing and escaped from the surface with an exit angle b in the range of 8.5–10 as shown in Fig. 5(b). No hyperchanneled ions could be observed at an exit angle of 13. It should be noted that even at 0 K, the zero point motion of the lattice will have an effect on the scattering trajectories. Therefore this calculation provides only an approximation to the true behavior at very low temperatures. ˚ reIncreasing the rms phonon amplitude to 0.05 A sulted in peak broadening to the range of 7.5– 10.5. Only a very small fraction of ions were scattered to an exit angle of 13. A further increase ˚ resulted in peak in rms phonon amplitude to 0.1 A broadening to the range of 6.9–11.3. More ions could be observed at b = 13 than at lower phonon amplitudes. As a result, the systematic increase in the scattering yield along the 0 azimuth with an increase in rms phonon amplitude indicates that an increasing amount of ions are being

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β = 9.1°

0.00 (0K) 0.05 (298K) 0.10 (1192K)

-18

-12

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6

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18

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0.00 (0K) 0.05 (298K) 0.10 (1192K)

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β = 13°

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Fig. 5. SARIC simulations of 4 keV Ar+ ions scattered from the Pt(1 1 1)-(1 · 1) surface at different surface temperatures: (a) azimuthal angle d scans with an incident angle of 9 and exit angle of 13; (b) exit angle b scans with a fixed incident angle of 9 and azimuthal angle of 0. The equivalent temperature was estimated by assuming the surface Debye temperature of Pt to be 94 K.

dechanneled due to the increase of potential corrugation induced by the thermal motion of the target atoms (Fig. 5(a)). Based on the equation hDl2 i ¼ 3 h2 T o = ð4p2 mkh2D Þ, where Dl is the rms phonon amplitude corresponding to temperature To, m is the atomic mass, and hD is the Debye temperature, the gradual increase in scattering yield (Fig. 5(a)) and the change of angular distribution of the outgoing atoms (Fig. 5(b)) can be used to estimate the surface Debye temperature.

Acknowledgments This work was supported in part by the R.A. Welch Foundation under Grant No. E-656 and the National Science Foundation under award number CHE-0303708. It was also partially supported by the Chinese University of Hong Kong and by the Research Grant Council Grant Nos. CUHK/1/97C and CUHK4315/98E.

References 3. Summary In summary, the SARIC code has been used to study low energy ion surface hyperchanneling. It was found that the ion-surface interaction geometry, projectile type, and surface chemisorbed hydrogen had a profound effect on the scattered ion trajectories and energy distributions. It was shown that the scattering yields and angular distributions are very sensitive to the phonon amplitudes. Using these scattering yields and angular distributions, it is possible to determine the surface Debye temperature. This may prove to be a useful technique for obtaining a simple estimate of the surface Debye temperature of crystals.

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