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Angular distributions of fast noble gas atoms and ions after grazing scattering from a Cu(111) surface
Nuclear Instruments and Methods in Physics Research B 182 (2001) 213±217
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Angular distributions of fast noble gas atoms and ions after grazing scattering from a Cu 1 1 1 surface R. Pfandzelter, T. Hecht 1, H. Winter
*
Humboldt-Universitat zu Berlin, Institut fur Physik, Invalidenstrasse 110, 10115 Berlin, Germany
Abstract We report on the scattering of 3 keV He, Ne, Ar, Kr, Xe atoms and singly charged ions from a Cu(1 1 1) surface under grazing angles of incidence. Polar angular distributions of scattered neutral projectiles show a well-de®ned peaked structure in the direction of specular re¯ection with a small FWHM of typically 0.5° at an incidence angle of 1°. The measured distributions are compared with elastic scattering computer simulations and previous studies by Harder et al. [Surf. Sci. 289 (1993) 214]. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 79.20.Rf; 79.20.Ap; 61.85.+p; 68.35.Bs
1. Introduction The scattering of atoms or ions with energies in the keV range impinging under a glancing angle upon a ¯at single crystal surface can be described, to a good approximation, by the concept of ``planar surface channeling'' [1,2]. The projectiles are elastically scattered in an averaged planar surface potential, which is repulsive at small distances and leads to specular re¯ection. In accordance with this concept, measured angular distributions of scattered projectiles show a wellde®ned peak located around the direction of specular re¯ection.
*
Corresponding author. Fax: +49-1-588-01-5710. E-mail address: [email protected] (H. Winter). 1 Present address: In®neon Technologies Dresden GmbH & Co. OHG, Postfach 100940, 01076 Dresden, Germany.
The understanding of small angular shifts of the peak towards sub- or supraspecular re¯ection and, in particular, the ®nite angular widths, however, requires a more thourough modeling. Angular shift and broadening (``angular straggling'') are caused by geometrical, elastic, and inelastic eects. Purely geometrical eects (angular divergence of incident beam, ®nite irradiated area on the target surface, aperture of the detector, etc.) can be minimized by appropriate experimental settings. Eects due to elastic scattering are manifold, comprising the discrete lattice structure of the unreconstructed or reconstructed surface (``surface corrugation''), elastic recoil, thermal vibrations, and the real structure of the single crystal surface (structural defects, surface steps, mosaic structure). Inelastic processes are charge or electron transfer between target and projectile, plasmon and electron±hole pair excitation, or (multiple) scattering at electrons.
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 6 7 8 - 4
214
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
Clearly, the (relative) signi®cance of these effects depends on the experimental parameters (projectile species, target surface, beam energy, etc.), and some of the broadening mechanisms can be reduced by appropriate settings. This has been achieved by the authors [3] for He0 -atoms with energies of a few keV grazingly scattered from Al(1 1 1). Here charge state ¯uctuations are supposed to be widely excluded [4] and elastic eects are reduced due to the small corrugation and smoothness of the close-packed surface. Measured angular distributions of scattered atoms show a peak located at the specular angle with very small width (0.1° FWHM for 0.4° incidence angle), thus approaching the limit of perfect specular re¯ection. Binary-collision computer simulations reproduce the experiments in detail, suggesting that angular broadening is dominantly caused by multiple scattering at thermally displaced surface atoms and conduction band electrons. Related experimental and computational studies by Pfandzelter et al. [5,6] for 25 keV (He -scattering from Fe(1 0 0) show a strong and characteristic in¯uence of structural defects like surface steps or displacements of atoms on peak width and form. This opens the possibility to use grazingly scattered atoms or ions as a probe in structure analysis, but, on the other hand, impedes general conclusions on fundamental aspects of the ion±surface interaction (e.g., charge exchange processes) from measured distributions. In this paper we report on the scattering of 3 keV noble gas atoms and ions from a Cu(1 1 1) surface. Such measurements (for 3 keV Ne -ions) have been previously reported by Harder et al. [7], where slightly subspecular peaks with large widths (about 3° FWHM for incidence angles between 2° and 3°) are observed. In order to rationalize this pronounced angular straggling, a mechanism based on inelastic resonant scattering of ``hot electrons'' has been invoked [7±9]. 2. Experimental A carefully oriented and polished Cu(1 1 1) single crystal surface (miscut angle 60:1°) is prepared in situ by cycles of grazing sputtering with
25 keV Ar -ions and annealing at about 520°C. 3 keV noble gas atoms (ions) are scattered in the forward direction and detected by a channeltron within the plane spanned by the ion beam and the surface normal. The detector is mounted on a stepping-motor-driven manipulator to measure the intensity of scattered projectiles as a function of the polar scattering angle Us with respect to the incoming beam direction (``polar angular distribution''). Precise calibration of Us is rendered possible by positioning the center of the target surface slightly below the beam axis so that a fraction of the beam passes above the target without de¯ection. This gives rise to a reference peak when the detector is positioned on the beam axis [2]. The (macroscopic) incidence angle Uin is inferred with an accuracy of about 0:05° from the smallest scattering angle observed (scattering angles Us < Uin are not possible due to the shadow cast by the target) [10]. The exit angle Uout with respect to the surface plane is Uout Us Uin . In the experiments we use incidence angles Uin 0:5°±3° and an azimuthal angle of a few degrees to the 1 0 1-surface lattice direction (``random azimuthal orientation''). The calculated geometric broadening due to our experimental setup is small (0.06° FWHM). A signi®cant contribution, however, is expected from the mosaic structure of our target crystal. X-ray rocking curves reveal (within a probing depth of some lm) an almost Gaussian distributed orientation of lm crystallites with a FWHM of 0.17°. 3. Results and discussion We ®rst present angular distributions for 3 keV He0 -atoms at dierent Uin (Fig. 1, circles). The distributions are sharp with maxima at the direction of specular re¯ection Uout Uin (the distribution at Uin 3:15° is slightly subspecular). Specular re¯ection is expected, because image charge attraction, which may lead to sub- or supraspecular re¯ection [11] is absent here. The asymmetry in favor of large scattering angles at Uin 0:55° seems to be, at least partly, caused by the cutting o at Uout 0°. The FWHMs increase with Uin (Fig. 3, solid circles) in a way similar to
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
215
Fig. 1. Measured (circles) and simulated (curves) polar angular distributions (normalized) for 3 keV He0 -atoms scattered from Cu(1 1 1) for incidence angles Uin as indicated. Hatched areas mark the residual direct beam. Dashed curves are results of a simulation with a mosaic distribution of 0.2° (FWHM) and a surface Debye temperature of 170 K. For the solid curves surface steps with a mean are included. Note the dierent abscissa scales. distance of 200 A
our previous results for Al(1 1 1) [3] and Fe(1 0 0) [5,6]. However, compared with isoenergetic data for Al(1 1 1), the distributions are broader by 0.2± 0.3°. This is surprising, since the stronger repulsion for Cu(1 1 1) should mitigate eects of the (thermally induced) surface corrugation (note that the vibration amplitudes of surface atoms are expected to be similar [12]). The curves in Fig. 1 are results of classical mechanics computer simulations for sequential elastic binary collisions of 3 keV He0 -atoms with Cu-atoms of a semi-in®nite crystal with unreconstructed (1 1 1)-surface, neglecting inelastic interactions. Previous studies [5] have shown that, beside from the interatomic potential [13], the surface Debye temperature H? normal to the surface and the surface step distributions are relevant parameters. In addition, the mosaic structure of our target crystal is considered here. Dashed curves in Fig. 1 are results for H? 170 K [12] 2 and Gaussian distributed crystallites (0.2° FWHM) with lateral dimensions much larger than the projectile±surface interaction length. Agreement with experimental data is considerably improved when surface steps are incorporated. This, however, is somewhat arbitrary in the present case,
2
We use H? about 10% less than Jackson's value derived from LEED, to take account of the ®nite penetration depth of electrons.
in contrast to, e.g., scattering from Fe(1 0 0), where characteristic features at small scattering angles help to identify heights and distributions of steps [5,6,10]. The solid curves in Fig. 1 are results for alternating monatomic up- and downward steps with geometrically distributed distances around a mean value of 200 A. Broadening due to surface steps is not Gaussian, as is expected for distributions resulting from a large number of small individual de¯ections [14], but more Lorentzian-like, due to sporadic large de¯ections. Incorporation of steps considerably improves the description of experimental distributions, especially at the smallest Uin (Fig. 1). Nevertheless, there remains a discrepancy between simulated and measured FWHMs (Fig. 3, solid circles, solid curve). To ®nd reasons for this discrepancy is speculative, but we doubt whether inelastic contributions are sucient, in view of our previous Al(1 1 1) study [3] (multiple electronic scattering causes a broadening of only about 0.1°). Whereas a tentative implementation of other kinds of structural defects like adatoms or vacancies is not successful either, satisfactory agreement is obtained by increasing the FWHM of the mosaic distribution to 0.3±0.4°. This is not a priori unreasonable, considering that values derived from X-ray diraction refer to bulk rather than surface properties. The assumption that angular straggling in He0 atom scattering from Cu(1 1 1) is essentially
216
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
Fig. 2. Measured (circles) and simulated (curves) polar angular distributions (normalized) for 3 keV He0 , Ne0 , Kr0 , and Xe0 -atoms scattered from Cu(1 1 1) for Uin 1:15° 0:1°. Simulations are performed with parameters from Fig. 1 (solid curves).
determined by the mesoscopic structure of the target surface rather than microscopic interaction processes is corroborated by a comparison with other noble gas projectiles. In Fig. 2, we show angular distributions for 3 keV He0 -, Ne0 -, Kr0 and Xe0 -atoms for Uin 1:15° 0:1°. Despite the largely dierent atomic numbers (the scattering angle roughly scales with the atomic number for screened Coulomb potentials [15]) and momentum (governing elastic recoil), the measured distributions for dierent projectiles are similar. In particular, we do not observe signi®cant dierences in the FWHMs (Fig. 3, symbols). This is supported by our computer simulations (Figs. 2 and 3, curves), where all parameters except the atomic number and mass of the projectile are kept constant. We note that the invariance of angular straggling on projectile species suggests that inelastic eects are of minor importance. Theoretical models on charge transfer in atom±surface interaction show a dependence on velocity and electronic structure of the projectile [16], at least as hidden parameters. For example, inelastic resonant scattering of hot electrons, invoked by Kato et al. [8,9] to rationalize broad angular distributions of 3 keV Ne -ions scattered from Cu(1 1 1) [7], is dependent on a velocity-dependent characteristic projectile±surface distance. Compared with incident noble gas atoms, singly charged ions lead to angular distributions which are broader and slightly shifted to supraspecular directions. This eect (not shown here) is
Fig. 3. FWHM2 of measured (symbols) and simulated (curves) polar angular distributions vs. incidence angle Uin for scattering of 3 keV noble gas atoms from Cu(1 1 1) at room temperature. Simulated values for He0 and Xe0 (solid and dashed curves, repectively) refer to the solid curves from Figs. 1 and 2.
ascribed to image charge attraction [11,17]. In Fig. 4, we compare a polar angular distribution for 3 keV Ne -ions (open circles) with data measured by Harder et al. [7] for the same experimental conditions (Uin 2:0° 0:1°) (solid circles, evaluated from the two-dimensional contour plot in Fig. 2(a) of [7]). The striking dierence in shape and, especially, FWHM is assumed to be due to dierent real structures of the target surfaces with presumably higher defect concentrations in the former studies.
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
217
et al. [7]. We therefore do not ®nd evidence for a broadening mechanism due to inelastic resonant scattering of hot electrons, as invoked by Kato et al. [8,9]. Acknowledgements We thank U. Linke (J ulich) for the preparation of the target crystal and performing X-ray studies. This work was supported by the Deutsche Forschungsgemeinschaft under contract Wi1336 and Sonderforschungsbereich 290. References
Fig. 4. Measured polar angular distributions (normalized) for 3 keV Ne -ions scattered from Cu(1 1 1) from the present work (open circles) and Harder et al. [7] (solid circles), respectively. Uin 2:0° 0:1°.
4. Conclusions Polar angular distributions of scattered projectiles in grazing-angle scattering of 3 keV noble gas atoms and ions consist of a sharp peak with a maximum at or close to the direction of specular re¯ection. In view of our previous studies on Al(1 1 1) [3] and elastic scattering computer simulations, however, the distributions are broader by some 0.1° than expected. It is tentative to invoke the mesoscopic mosaic structure of our target crystal to rationalize this discrepancy, although (small) contributions to angular straggling from inelastic processes cannot be ruled out. The distributions presented here are better de®ned than those reported for similar conditions by Harder
[1] D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [2] B.W. Farmery, A.D. Marwick, M.W. Thompson, in: D.W. Palmer, M.W. Thompson, P.D. Townsend (Eds.), Atomic Collision Phenomena in Solids, North-Holland, Amsterdam, 1970, p. 589. [3] R. Pfandzelter, T. Hecht, H. Winter, Europhys. Lett. 44 (1998) 116. [4] H. Winter, Nucl. Instr. and Meth. B 78 (1993) 38. [5] R. Pfandzelter, Phys. Rev. B 57 (1998) 15496. [6] R. Pfandzelter, T. Igel, H. Winter, Phys. Rev. B 56 (1997) 14948. [7] R. Harder, A. Nesbitt, J.-H. Rechtien, W. Mix, C. R othig, M. Kato, K.J. Snowdon, Surf. Sci. 289 (1993) 214. [8] M. Kato, W. Mix, K.J. Snowdon, Surf. Sci. 294 (1993) 429. [9] M. Kato, K.J. Snowdon, Nucl. Instr. and Meth. B 90 (1994) 80. [10] R. Pfandzelter, T. Igel, H. Winter, Surf. Sci. Lett. 411 (1998) L894. [11] H. Winter, J. Phys.: Condens. Matter 8 (1996) 10149. [12] D.P. Jackson, Surf. Sci. 43 (1974) 431. [13] D.J. O'Connor, J.P. Biersack, Nucl. Instr. and Meth. B 15 (1986) 14. [14] N. Bohr, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 18 (1948) 8. [15] C. Varelas, R. Sizmann, Rad. E. 25 (1975) 163. [16] H. Winter, Comments At. Mol. Phys. 26 (1991) 287. [17] H. Winter, Europhys. Lett. 18 (1992) 207.
www.elsevier.com/locate/nimb
Angular distributions of fast noble gas atoms and ions after grazing scattering from a Cu 1 1 1 surface R. Pfandzelter, T. Hecht 1, H. Winter
*
Humboldt-Universitat zu Berlin, Institut fur Physik, Invalidenstrasse 110, 10115 Berlin, Germany
Abstract We report on the scattering of 3 keV He, Ne, Ar, Kr, Xe atoms and singly charged ions from a Cu(1 1 1) surface under grazing angles of incidence. Polar angular distributions of scattered neutral projectiles show a well-de®ned peaked structure in the direction of specular re¯ection with a small FWHM of typically 0.5° at an incidence angle of 1°. The measured distributions are compared with elastic scattering computer simulations and previous studies by Harder et al. [Surf. Sci. 289 (1993) 214]. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 79.20.Rf; 79.20.Ap; 61.85.+p; 68.35.Bs
1. Introduction The scattering of atoms or ions with energies in the keV range impinging under a glancing angle upon a ¯at single crystal surface can be described, to a good approximation, by the concept of ``planar surface channeling'' [1,2]. The projectiles are elastically scattered in an averaged planar surface potential, which is repulsive at small distances and leads to specular re¯ection. In accordance with this concept, measured angular distributions of scattered projectiles show a wellde®ned peak located around the direction of specular re¯ection.
*
Corresponding author. Fax: +49-1-588-01-5710. E-mail address: [email protected] (H. Winter). 1 Present address: In®neon Technologies Dresden GmbH & Co. OHG, Postfach 100940, 01076 Dresden, Germany.
The understanding of small angular shifts of the peak towards sub- or supraspecular re¯ection and, in particular, the ®nite angular widths, however, requires a more thourough modeling. Angular shift and broadening (``angular straggling'') are caused by geometrical, elastic, and inelastic eects. Purely geometrical eects (angular divergence of incident beam, ®nite irradiated area on the target surface, aperture of the detector, etc.) can be minimized by appropriate experimental settings. Eects due to elastic scattering are manifold, comprising the discrete lattice structure of the unreconstructed or reconstructed surface (``surface corrugation''), elastic recoil, thermal vibrations, and the real structure of the single crystal surface (structural defects, surface steps, mosaic structure). Inelastic processes are charge or electron transfer between target and projectile, plasmon and electron±hole pair excitation, or (multiple) scattering at electrons.
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 6 7 8 - 4
214
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
Clearly, the (relative) signi®cance of these effects depends on the experimental parameters (projectile species, target surface, beam energy, etc.), and some of the broadening mechanisms can be reduced by appropriate settings. This has been achieved by the authors [3] for He0 -atoms with energies of a few keV grazingly scattered from Al(1 1 1). Here charge state ¯uctuations are supposed to be widely excluded [4] and elastic eects are reduced due to the small corrugation and smoothness of the close-packed surface. Measured angular distributions of scattered atoms show a peak located at the specular angle with very small width (0.1° FWHM for 0.4° incidence angle), thus approaching the limit of perfect specular re¯ection. Binary-collision computer simulations reproduce the experiments in detail, suggesting that angular broadening is dominantly caused by multiple scattering at thermally displaced surface atoms and conduction band electrons. Related experimental and computational studies by Pfandzelter et al. [5,6] for 25 keV (He -scattering from Fe(1 0 0) show a strong and characteristic in¯uence of structural defects like surface steps or displacements of atoms on peak width and form. This opens the possibility to use grazingly scattered atoms or ions as a probe in structure analysis, but, on the other hand, impedes general conclusions on fundamental aspects of the ion±surface interaction (e.g., charge exchange processes) from measured distributions. In this paper we report on the scattering of 3 keV noble gas atoms and ions from a Cu(1 1 1) surface. Such measurements (for 3 keV Ne -ions) have been previously reported by Harder et al. [7], where slightly subspecular peaks with large widths (about 3° FWHM for incidence angles between 2° and 3°) are observed. In order to rationalize this pronounced angular straggling, a mechanism based on inelastic resonant scattering of ``hot electrons'' has been invoked [7±9]. 2. Experimental A carefully oriented and polished Cu(1 1 1) single crystal surface (miscut angle 60:1°) is prepared in situ by cycles of grazing sputtering with
25 keV Ar -ions and annealing at about 520°C. 3 keV noble gas atoms (ions) are scattered in the forward direction and detected by a channeltron within the plane spanned by the ion beam and the surface normal. The detector is mounted on a stepping-motor-driven manipulator to measure the intensity of scattered projectiles as a function of the polar scattering angle Us with respect to the incoming beam direction (``polar angular distribution''). Precise calibration of Us is rendered possible by positioning the center of the target surface slightly below the beam axis so that a fraction of the beam passes above the target without de¯ection. This gives rise to a reference peak when the detector is positioned on the beam axis [2]. The (macroscopic) incidence angle Uin is inferred with an accuracy of about 0:05° from the smallest scattering angle observed (scattering angles Us < Uin are not possible due to the shadow cast by the target) [10]. The exit angle Uout with respect to the surface plane is Uout Us Uin . In the experiments we use incidence angles Uin 0:5°±3° and an azimuthal angle of a few degrees to the 1 0 1-surface lattice direction (``random azimuthal orientation''). The calculated geometric broadening due to our experimental setup is small (0.06° FWHM). A signi®cant contribution, however, is expected from the mosaic structure of our target crystal. X-ray rocking curves reveal (within a probing depth of some lm) an almost Gaussian distributed orientation of lm crystallites with a FWHM of 0.17°. 3. Results and discussion We ®rst present angular distributions for 3 keV He0 -atoms at dierent Uin (Fig. 1, circles). The distributions are sharp with maxima at the direction of specular re¯ection Uout Uin (the distribution at Uin 3:15° is slightly subspecular). Specular re¯ection is expected, because image charge attraction, which may lead to sub- or supraspecular re¯ection [11] is absent here. The asymmetry in favor of large scattering angles at Uin 0:55° seems to be, at least partly, caused by the cutting o at Uout 0°. The FWHMs increase with Uin (Fig. 3, solid circles) in a way similar to
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
215
Fig. 1. Measured (circles) and simulated (curves) polar angular distributions (normalized) for 3 keV He0 -atoms scattered from Cu(1 1 1) for incidence angles Uin as indicated. Hatched areas mark the residual direct beam. Dashed curves are results of a simulation with a mosaic distribution of 0.2° (FWHM) and a surface Debye temperature of 170 K. For the solid curves surface steps with a mean are included. Note the dierent abscissa scales. distance of 200 A
our previous results for Al(1 1 1) [3] and Fe(1 0 0) [5,6]. However, compared with isoenergetic data for Al(1 1 1), the distributions are broader by 0.2± 0.3°. This is surprising, since the stronger repulsion for Cu(1 1 1) should mitigate eects of the (thermally induced) surface corrugation (note that the vibration amplitudes of surface atoms are expected to be similar [12]). The curves in Fig. 1 are results of classical mechanics computer simulations for sequential elastic binary collisions of 3 keV He0 -atoms with Cu-atoms of a semi-in®nite crystal with unreconstructed (1 1 1)-surface, neglecting inelastic interactions. Previous studies [5] have shown that, beside from the interatomic potential [13], the surface Debye temperature H? normal to the surface and the surface step distributions are relevant parameters. In addition, the mosaic structure of our target crystal is considered here. Dashed curves in Fig. 1 are results for H? 170 K [12] 2 and Gaussian distributed crystallites (0.2° FWHM) with lateral dimensions much larger than the projectile±surface interaction length. Agreement with experimental data is considerably improved when surface steps are incorporated. This, however, is somewhat arbitrary in the present case,
2
We use H? about 10% less than Jackson's value derived from LEED, to take account of the ®nite penetration depth of electrons.
in contrast to, e.g., scattering from Fe(1 0 0), where characteristic features at small scattering angles help to identify heights and distributions of steps [5,6,10]. The solid curves in Fig. 1 are results for alternating monatomic up- and downward steps with geometrically distributed distances around a mean value of 200 A. Broadening due to surface steps is not Gaussian, as is expected for distributions resulting from a large number of small individual de¯ections [14], but more Lorentzian-like, due to sporadic large de¯ections. Incorporation of steps considerably improves the description of experimental distributions, especially at the smallest Uin (Fig. 1). Nevertheless, there remains a discrepancy between simulated and measured FWHMs (Fig. 3, solid circles, solid curve). To ®nd reasons for this discrepancy is speculative, but we doubt whether inelastic contributions are sucient, in view of our previous Al(1 1 1) study [3] (multiple electronic scattering causes a broadening of only about 0.1°). Whereas a tentative implementation of other kinds of structural defects like adatoms or vacancies is not successful either, satisfactory agreement is obtained by increasing the FWHM of the mosaic distribution to 0.3±0.4°. This is not a priori unreasonable, considering that values derived from X-ray diraction refer to bulk rather than surface properties. The assumption that angular straggling in He0 atom scattering from Cu(1 1 1) is essentially
216
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
Fig. 2. Measured (circles) and simulated (curves) polar angular distributions (normalized) for 3 keV He0 , Ne0 , Kr0 , and Xe0 -atoms scattered from Cu(1 1 1) for Uin 1:15° 0:1°. Simulations are performed with parameters from Fig. 1 (solid curves).
determined by the mesoscopic structure of the target surface rather than microscopic interaction processes is corroborated by a comparison with other noble gas projectiles. In Fig. 2, we show angular distributions for 3 keV He0 -, Ne0 -, Kr0 and Xe0 -atoms for Uin 1:15° 0:1°. Despite the largely dierent atomic numbers (the scattering angle roughly scales with the atomic number for screened Coulomb potentials [15]) and momentum (governing elastic recoil), the measured distributions for dierent projectiles are similar. In particular, we do not observe signi®cant dierences in the FWHMs (Fig. 3, symbols). This is supported by our computer simulations (Figs. 2 and 3, curves), where all parameters except the atomic number and mass of the projectile are kept constant. We note that the invariance of angular straggling on projectile species suggests that inelastic eects are of minor importance. Theoretical models on charge transfer in atom±surface interaction show a dependence on velocity and electronic structure of the projectile [16], at least as hidden parameters. For example, inelastic resonant scattering of hot electrons, invoked by Kato et al. [8,9] to rationalize broad angular distributions of 3 keV Ne -ions scattered from Cu(1 1 1) [7], is dependent on a velocity-dependent characteristic projectile±surface distance. Compared with incident noble gas atoms, singly charged ions lead to angular distributions which are broader and slightly shifted to supraspecular directions. This eect (not shown here) is
Fig. 3. FWHM2 of measured (symbols) and simulated (curves) polar angular distributions vs. incidence angle Uin for scattering of 3 keV noble gas atoms from Cu(1 1 1) at room temperature. Simulated values for He0 and Xe0 (solid and dashed curves, repectively) refer to the solid curves from Figs. 1 and 2.
ascribed to image charge attraction [11,17]. In Fig. 4, we compare a polar angular distribution for 3 keV Ne -ions (open circles) with data measured by Harder et al. [7] for the same experimental conditions (Uin 2:0° 0:1°) (solid circles, evaluated from the two-dimensional contour plot in Fig. 2(a) of [7]). The striking dierence in shape and, especially, FWHM is assumed to be due to dierent real structures of the target surfaces with presumably higher defect concentrations in the former studies.
R. Pfandzelter et al. / Nucl. Instr. and Meth. in Phys. Res. B 182 (2001) 213±217
217
et al. [7]. We therefore do not ®nd evidence for a broadening mechanism due to inelastic resonant scattering of hot electrons, as invoked by Kato et al. [8,9]. Acknowledgements We thank U. Linke (J ulich) for the preparation of the target crystal and performing X-ray studies. This work was supported by the Deutsche Forschungsgemeinschaft under contract Wi1336 and Sonderforschungsbereich 290. References
Fig. 4. Measured polar angular distributions (normalized) for 3 keV Ne -ions scattered from Cu(1 1 1) from the present work (open circles) and Harder et al. [7] (solid circles), respectively. Uin 2:0° 0:1°.
4. Conclusions Polar angular distributions of scattered projectiles in grazing-angle scattering of 3 keV noble gas atoms and ions consist of a sharp peak with a maximum at or close to the direction of specular re¯ection. In view of our previous studies on Al(1 1 1) [3] and elastic scattering computer simulations, however, the distributions are broader by some 0.1° than expected. It is tentative to invoke the mesoscopic mosaic structure of our target crystal to rationalize this discrepancy, although (small) contributions to angular straggling from inelastic processes cannot be ruled out. The distributions presented here are better de®ned than those reported for similar conditions by Harder
[1] D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [2] B.W. Farmery, A.D. Marwick, M.W. Thompson, in: D.W. Palmer, M.W. Thompson, P.D. Townsend (Eds.), Atomic Collision Phenomena in Solids, North-Holland, Amsterdam, 1970, p. 589. [3] R. Pfandzelter, T. Hecht, H. Winter, Europhys. Lett. 44 (1998) 116. [4] H. Winter, Nucl. Instr. and Meth. B 78 (1993) 38. [5] R. Pfandzelter, Phys. Rev. B 57 (1998) 15496. [6] R. Pfandzelter, T. Igel, H. Winter, Phys. Rev. B 56 (1997) 14948. [7] R. Harder, A. Nesbitt, J.-H. Rechtien, W. Mix, C. R othig, M. Kato, K.J. Snowdon, Surf. Sci. 289 (1993) 214. [8] M. Kato, W. Mix, K.J. Snowdon, Surf. Sci. 294 (1993) 429. [9] M. Kato, K.J. Snowdon, Nucl. Instr. and Meth. B 90 (1994) 80. [10] R. Pfandzelter, T. Igel, H. Winter, Surf. Sci. Lett. 411 (1998) L894. [11] H. Winter, J. Phys.: Condens. Matter 8 (1996) 10149. [12] D.P. Jackson, Surf. Sci. 43 (1974) 431. [13] D.J. O'Connor, J.P. Biersack, Nucl. Instr. and Meth. B 15 (1986) 14. [14] N. Bohr, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 18 (1948) 8. [15] C. Varelas, R. Sizmann, Rad. E. 25 (1975) 163. [16] H. Winter, Comments At. Mol. Phys. 26 (1991) 287. [17] H. Winter, Europhys. Lett. 18 (1992) 207.