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Surface analysis of crystals by surface channeling
898
SIJRFACE ANALYSIS
Nuclear Instruments and Methods in Physics Research 333 fI988) 8Q8-QM North-Holland, Amsterdam
OF CRYSTALS
BY SURFACE
~
R. FFANDZELTER Sekfion l’hysik, Universifcif Miinchen, Amalienstrmse 34, R-8000 Miinchen 40, FRG M. SCHUSTER
In surface channeling, fast ions are incident at a grazing angle u@on B crystal surface aIung a fow index surface direction. Surface charmeled ions are used as versatile probes for surface analysis. The atomic structure of crystal surfaces, especialfy surface reconstructions and positions of adsorbed atoms, can be analyzed by ions channeled at the crystal surface in combination with
appropriate detection reactions. We review the application of ion surface channeling to surface structure analysis. The principles of surface channeling are outlined. Several detection reactions, such as backscattering, nuclear reactions, X-ray emission, Auger electron emission, forwardscattering, light emission and secondary electron emission, are discussed with respect to surface channeling. Finally, some recent experiments are given as examples: (2 X l}-~~~~l~~}, steps on Ni o,6Fe0,4(l10) and (2 x 2)In,/Si(lOO).
1. PrineipIes of surface channeling
Fast ions incident upon a crystalline target are steered by the repulsive potential of the atomic rows if they are aligned with a low index lattice direction. This effect, well known as axial channeling in the bulk, is also observed at smooth crystal surfaces [l-15], when the ions are incident at a grazing angle upon the crystal surface along a low index surface direction. Let us denote by + the angle between the ion beam and the surface, B the lateral angle between the ion beam and the low index surface direction and J/ = ($’ + 02)1/2 the corresponding angle of incidence towards the low index surface direction (fig. 1). Surface channeling, i.e. axial channeling in the surface near region, occurs under the following conditions of ion incidence [l]: it is required (1) that the transverse energy E, = E sin2+ (E is the energy of the incident ion) is larger than the surface potential to allow the ions to penetrate into the
CrystalSurface
Fig. 1. IWationship between the a&es of incidence and a low index surface direction [ hkl].
~168-~g3~/8~/$~3.5~ 0 Elsevier Science Publishers B.V. (North-Roland Physics Publis~g Division)
crystal, (2) that li, is sm&er than the critical angle of axial channeling fltr,I’f] and (3) that + is small enough that planar channeling cannot develop [K-20]. In fig. 2, the different regimes of ion motion for grazing ion incidence upon a crystal surface are shown for 150 keV H’ incident upon Ni(l10) alcmg [ITO]. The regime of surface channeling is indicated by the cross-hatched area. Some authors [Zl] even discuss h~er~hanne~ng at the surface, but it would be restricted to a small regime (black). At small angles +, the ions suffer specular reflection at the very surface with small energy loss only (heavy dotted). At even smaller values of 9, there is the regime of skipping motion, where the reflected projectiles are drawn back to the surface by their image charge (light dotted) [23]. In the regimes of surface ~h~neling, skipping motion and h~erch~n~ing, the ion motion is bound to the surface. The regime of surface channeling partially interferes with the regimes of planar channeling (hatched) [la]. Besides the planar channels indicated in the diagram, there exist further regimes of high index planar channeling, which are out of the range of fig. 2. The blank areas describe transition regimes and random scattering. In surface channeling, sometimes also called semich~neling, the scattering of the ions is caused by successive correlated collisions with numerous atoms along the low index surface direction. Thus, surface channeling can be described by the concept of Lindhard’s continuum row potentials analogous to axial channeling in the bulk [16,24]. Therefore, at grazing incidence along the low index direction, the ions are strongly steered by the repulsive potential of the atomic rows. This diminishes the ion flux density close to the
R. Pfandzelter, M. Schuster / Surface analysis of crystals
899
incidence. The half width taken at the half minimum of the yield (hwhm) is designated as 01,2. A first order approximation for the angle +i,z = (+2 + 8&z)1/2 can be taken from Lindhard [16]:
# J___ 2ZlZ2e2
l/2
=
E&,/q
0
[ii01
Q-+ specular reflaciion
a
skipping motion
0
random scaftering and lransifion zones
Fig. 2. Regimes of motion for fast ions angles upon a crystal surface. The values calculated for 150 keV Hf incident upon based on Thomas-Fermi-Molibre and on tials.
incident at grazing of this diagram are Ni(ll0) along [ITO], image charge poten-
atomic rows and enhances it between them. Thus, the average impact parameter of the channeled ions to the atoms in the rows is large. Since the probability of elastic or inelastic reactions grows smaller with larger impact parameters between the incoming ions and the target atoms, the reaction yield decreases if the ions are incident parallel to the low index direction. If the lateral angle of incidence 0 between the ion beam and the low index direction is increased, the steering effect weakens and the ion flux becomes more homogeneous. As result, the average impact parameter decreases and the reaction yield increases. For even larger angles 8, the yield reaches the value which is obtained in a random distribution of impact parameters like at an amorphous target surface. In the regime of surface channeling, the absolute ion flux density is strongly enhanced within the topmost atomic layers [25,26]. The projectiles penetrate through the surface and undergo axial channeling in the surface region with their main translational momentum parallel to the low index surface direction. Thus, surface channeled ions selectively excite the atoms in the surface region. This causes an inherent surface sensitivity of all methods in combination with surface channeling. In surface analysis by surface channeling, the angle + is kept constant and the reaction yield is measured as a function of the lateral angle 0. The angular yield profiles are usually normalized to the yield at random
’
where 2, and Z, are the atomic numbers of the ion and the target atom, respectively. E is the energy of the incident ion and dIhkr, the interatomic distance in the [hkl] row. If Z,, Z,, E and C#Jare fixed by the experimental conditions, 81,2 is a measure of the interatomic distance dLhklI in the steering rows. Thus, measurements of +1,2 for ion incidence along different low index surface directions provide a straightforward analysis of the arrangement of the atoms in the topmost substrate layer. Moreover, the inhomogeneous flux of the channeled projectiles will help to localize adsorbate atoms on the crystal surface. The yield of a close-encounter process between the ion and the adsorbed atom is enhanced, if the adsorbates are placed between the atomic rows, and diminished, if they are placed in or near the rows. In other words, the minimum and maximum of the yield profile, respectively, deliver a straightforward determination of the lateral adsorbate position. The distance of the adsorbate atom normal to the surface can be obtained by comparison of the shape of the measured yield profile with a computer simulation.
2. Detection reactions Fast ions interact with a crystal surface in a series of elastic and inelastic collisions (fig. 3). Generally, those interactions which require small impact parameters between the ion and target atom are most suited to obtain strongly modulated angular yield profiles, of course, at the expense of small cross sections. Backscattering is an example for a close-encounter process. It is elementspecific and applicable to a wide variety of projectile species and energies, and target atoms, especially to heavy adsorbates on a light substrate. The yield of the substrate is obtained from the edge height in the backscattering spectrum, whereas heavy adsorbates appear as isolated high energetic peaks in a nearly background free region. Backscattering of 250 keV He+ was applied by Varelas and coworkers to study the adsorption sites of Xe on Si(ll1) [27]. A method related to measuring the backscattered projectiles would be the detection of sputtered target atoms and molecules. To the authors’ knowledge, this has not been applied in surface channeling experiments till now. XIII. SURFACE
ANALYSIS
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R. Pfandzelter, M. Schuster / Surface analysis of crystals
X&y
Auger Electron Emission
Emission
NUCIW Reaction
ef
Secondary Emission
f
eBackscattering
Electron
Forwardscattering
Fig. 3. Schematic illustration of detection reactions used in surface channeling experiments.
Nuclear reactions are close-encounter processes, too. They are of particular interest to light elements, where other means fail. The reactions are element-specific and the highly energetic reaction products can be detected free of background. A disadvantage is the relatively high energy required for nuclear reactions. Varelas and coworkers used the reactions 160(d,p)170 and 12C(d,p)‘3C induc ed by surface channeled 1.2 MeV deuterons to determine the position of adsorbed CO on Ni(ll0) [28]. Deuterium on Ni(ll0) was localized by Sailer and Varelas by means of the reaction ’ H( 3He,p)4He induced by surface channeled 580 keV. 3He+ [29]. The emission of characteristic X-rays resulting from the inner-shell ionization of target atoms or projectiles occurs at larger impact parameters than backscattering and nuclear reactions. Therefore, the channeling dips become shallower [25,30,31]. Detection of X-rays is suited especially for heavier elements (highly energetic transitions), because of the higher fluorescence yield and the possibility to detect energetic X-rays by Si(Li)detectors, which allow the exploitation of large acceptance angles. The detected X-rays are element-specific. Apart from line overlap due to insufficient resolution, no background problems exist. Harbinson and coworkers examined the oxygen position in a WO, layer on W(110) by means of W-M- and O-K-radiation induced by surface channeled 150-275 keV H+ [32]. Backscattering, nuclear reactions and X-rays are not inherently surface sensitive probes. Their applicability to surface analysis is given by the flux peaking of the incident ions in the channels and semichannels of the surface near region (cf. section 1). The surface sensitivity can be enhanced further by the detection of Auger electrons due to their short mean free path. Since Auger
electron emission and X-ray emission are complementary element-specific reactions based on inner-shell ionization, the impact parameter dependence is the same. For low 2 elements, the Auger yield surpasses the fluorescence yield by far. For high Z elements, the ion induced Auger electron analysis can switch over from K-lines to L- or M-lines and, thus, achieve appropriate ionization cross sections and fluorescence yields. The major disadvantage of the analysis of Auger electrons induced by surface channeled ions is the high background due to secondary electrons. Therefore and because of the finite source size at glancing ion incidence, a good electron spectrometer, e.g. a double pass cylindrical mirror analyzer, is favourable. By the above-mentioned method, several surface analysis were made: (2 X l)-O/Ni(llO) [25,26,33], streaked-(2 X 1)-H/ Ni(ll0) [34], (2 X 2)-In/Si(lOO) [35] (cf. section 3). In some cases, reactions with high yields are indispensable. Forwardscattering of projectiles is such a reaction. Compared to backscattering, it occurs at larger impact parameters. The scattered projectiles can be measured as a function of their scattering angle, energy and charge state. An element-specific detection, however, is not possible. The number of forwardscattered ions is easily monitored by a Faraday-cup or counted by a solid state detector. Generally, in surface channeling large impact parameter reactions cannot be interpreted as straightforward. Computer simulations are necessary to discuss the experimental results. Nizhnaya and coworkers studied the ionization degree of scattered Ne+, grazingly incident with 3 keV upon N,/Ni(lOO) [36]. Thereby, they could find out the position and orientation of the adsorbed N, molecules. A variant of forwardscattering measurements is the observation of light emission by excited scattered projectiles. The light intensity and polarization. exhibit a strong dependence on the surface crystallography and coverage [37]. The major advantage of this method is the experimental simplification: the whole detection system is positioned outside the scattering chamber. Graser and Varelas could determine the oxygen position on (2 X 1)-O/Ni,,, Fe,,,(llO) [38,39] and the mean step distance on clean Ni0,6Feo,4(110) [40] (cf. section 3) by measuring the He+ - 468.6 nm light emission from surface channeled 200 keV He+ [39,40]. A reaction, where the description by impact parameters of single atoms is insufficient, is the emission of secondary electrons. The yield of this reaction is determined by the valence electron density and the ion flux distribution. The secondary electron emission scales with the electronic energy loss and gives rather high yields at grazing ion incidence. Winter could confirm the saw-tooth substrate structure of (2 X I)-O/Ni(llO) found in ref. [26] by secondary electron emission induced by surface channeled 75-200 keV H+ and He+
[411.
R. Pfandzelter,
3. Examples of surface channeling studies
P’l
L
3.1. (2X1)-O/Ni(llO)
The structures of clean (1 X 1)-Ni(ll0) and (2 X l)-O/Ni(llO) were examined by surface channeling of 150 keV H+. The yields of the H+ induced Auger electrons of nickel and oxygen were measured simultaneously as a function of the lateral angle of incidence 0 with $I = 1.0 o [26,33]. For clean Ni(llO), the yield profiles of the Ni Law Auger electrons for Ht incidence along [OOl] and [liO] exhibit a 81,2, according to the bulk distances (figs. 4 and 5a). At an oxygen coverage of 0.5 ML, resulting in a (2 x l)-LEED pattern [42], the 01/Z of the yield profile along [liO] is diminished compared to the clean surface (fig. 4). For the corresponding $~i,~s is valid: J/1,2(0/Ni(l10) : $l,z(Ni(llO)) = 1: fi. According to eq. (1) the interatomic distance in the [liO] rows must have become twice the bulk value. Along [OOl], however, the oxygen coverage does not change the yield profile. This indicates a (2 x 1) reconstruction ([26] and refs. therein). A (2 x 1) reconstruction is exhibited by both the missing row model (fig. 5c) and the saw-tooth model (fig. 5b). A comparison of the measured yield profiles with computer simulations favours the saw-tooth reconstruction. Hence, the surface structures of the nickel substrate atoms could be determined as follows: the clean surface is not reconstructed; the 0.5 ML
t
Yield of Ni L,VV Auger
Electrons
r
simulation
experiment
F
A Ni (110) clean
-
Ni (110)
0
---
saw-tooth
OlNi
(110)
clean
1.0
n
-
-Go
-do
-2”
[ii01
2”
901
M. Schuster / Surface analysis of crystals
40
6O o+
Fig. 4. Yields of Ni LsW Auger electrons induced by 150 keV Hf versus angle 0 towards [ITO] for clean Ni(ll0) and oxygen covered (2 X l)-O/Ni(llO). The lines are the result of computer simulations. + = 1.0 ‘, T = 300 K.
[ii01
0 yiEve,0
[OOll
DJll (a) Ni (1lO)clean
(b) Saw-Tooth
Model
Nickel
0
Oxygen
too11 (c) Missing Row Model
Fig. 5. Top views of (a) unreconstructed (1 x l)-Ni(llO), (b) reconstructed saw-tooth (2 x l)-O/Ni(llO) and (c) reconstructed missing row (2 x I)-O/Ni(llO). Below the top views are the profiles of the surface region parallel to the [OOl] direction. oxygen covered surface has a (2 x 1) saw-tooth reconstruction [26,33,41,43-451. The only investigation which is in explicit contradiction to the saw-tooth model is ref. [46]. This study, which is based on quasi-single ion scattering (low energy alkali impact collision ion spectroscopy), claims the missing row model. Calculations of one of the authors (M.S.) exhibit however that at the very ion trajectories, which should be significantly different for the missing row and the saw-tooth model, multiple scattering cannot be neglected. This discards the arguments of ref. [46] supporting the missing row model. In the surface channeling studies [26,33,41] a relaxation, as found by ref. [44,47] has not been taken into account, because surface channeling is not sensitive to a relaxation normal to the surface. To localize the adsorbed oxygen, the oxygen KL 23L 23 Auger electron yield profiles were measured (fig. 6). The strongly enhanced minimum yield of the 0 KL,,L,, Auger electrons for H’ incidence along [liO], compared with that along [OOl], shows that the oxygen atoms are situated between the Ni[liO] rows, shadowed by the Ni[OOl] rows. Thus, the oxygen atoms can be localized in the long bridge position between the nickel atoms in the topmost [OOl] rows of the reconstructed surface. By comparison of the experimental results with computer simulations, the distance of the oxygen atoms above the topmost nickel layer is found to be 25 pm (fig. 6). 3.2. Steps on Nio~,Fe,,,(llO) The presence of atomic steps on real crystal surfaces is known to influence many surface properties like XIII. SURFACE ANALYSIS
902
R. Pfandzelter, M. Schuster / Surface analysis of ctystafs
t Yield of 0 KL&,
Yield of He+Radiation
Auger Electrons
0 experiment
simulation ...._t h= 0 pm --h=lZ.Spm -h=25 pm
t -.-
t
simulation
experiment
h=37.!ipm h=!Sl fern
L,
a)
I,I,j
-60
-40
L
-2~
0
I,[,
20
z!l, b)
1
40
60-60-4~
a 1,
-2O
II
0
[tiol
MO1
1,
2O
P
)I
6”
0 -+
Fig. 8. (a) Yield of He+-468.6 nm radiation versus angle 8 towards [liO] for (1) 200 keV He+, cp=l.O” and for (2) 75 keV He+, C$= 1.63O scattered at clean (1 x l)Ni,,,Fee,,(llO), E, = 61 eV, rmin= 0.065 nm. (a) Experiment, (b) computer sim~ations carried out for a step distance s = 75 lattice constants (75 X 0.25 nm). T = 450 K. After 1401.
Fig. 6. Yield of 0 KLz3Lz3 Auger electrons induced by 150 keV H+ versus angle B towards [liO] for oxygen covered (2 x I)-O/Ni(llO). The lines are the result of computer simulations carried out for different oxygen distances h to the topmost nickel layer of a saw-tooth reconstructed surface. .#~=1.0~, T=3OOK.
adsorption kinetics and catalytic activity. Figs. 7a and b show how surface channeling can be applied to determine the mean distance s between atomic steps. Ions incident at a grazing angle along the [liO] direction of a fcc(ll0) surface, are focused by atomic rows 1 onto row 2 of the second layer and reflected mainly into the direction normal to the surface. On their way out, the ions can be trapped by the atomic row 3 of an upward step and reflected into the bulk. In a stepped surface, the trajectory inclination defines an escape length L (fig. 7b). If the transverse energy E, = E sin2# and, therefore,
Fig. 7. Illustration of the influence of a step on the trajectories of ions incident at a grazing angle along the [liO] direction of a fcc(310) surface towards a row 2 of the second layer; (a) perspective view, (b) side view; trajectories for different ion energies E and angles of incidence q’~at constant r,,, i.e. constant transverse energy E, = E.sin*#~. t is the escape length, s the step distance. Tire scale in the direction of the atomic rows is reduced. After [40].
the value
‘;oie of nearest
approach
are kept
Thus, the mean step distance s can be determined by measuring the yield of the scattered projectiles for different escape lengths L, i.e. for different E. Hereby, the transverse energy E, , i.e. r,, has to be kept constant by adjusting the angle of incidence # ([2], p. 115). By this method, clean Ni~,~Fe~.~(llO) was examined with He+ incident along [liO] [40]. The light emission of the scattered excited He+ ions when emerging from the surface was measured [37]. In fig. 8a, the measured yield profiles as a function of the lateral angle 6 for (1) E=200 keV, +=l.O” and (2) E==75 keV, #=1.63” are plotted. In case (2), the escape length is short enough that many ions, which are focused onto row 2 and reflected, can leave the surface without encountering a step. Therefore, a yield rn~~ at 6 = O” results. In case (l), the escape length is longer. IIere, the ions reflected at row 2 are trapped by the steps. The maximum at B = 0” disappears. By comparison with computer simulations (fig. 8b), a mean step distance s of 75 lattice constants (75 x 0.25 nm) is found. constant,
the escape length is: L - a.
3.3. (2 X2)-h
/ Si(lO0)
Surface analysis by surface channeling is also applicable to semiconductor surfaces. As an example, the
903
R. Pfandzelter, M. Schuster / Surface analysis of crystals t YieldofSiL,,VVAugerElectrons iI>
Si (100) clean
experiment
‘I v it
0
]
experiment
I
In&i (100)
0
Silicon
ls1Lay.r 0
Silicon
Fig. 10. Top view of the reconstructed asymmetric model of (2 x l)-Si(100). -40
-20
[Oil]
20
Qd
dimer
40
Fig. 9. Yield profiles of Si L,,W Auger electrons induced by 75 keV H+ versus angle towards [Oil] measured at (a) clean (2 x l)-Si(lO0) and (b) indium covered (2 x 2)-In/Si(lOO). + = 0.9O, T= 300 K.
arrangement of the silicon atoms at clean and indium covered Si(lO0) was investigated [35]. The yield of the Si L2sW Auger electrons induced by surface channeled 75 keV H+ was measured as a function of the lateral angle of incidence to the [Oil] direction with $I = 0.9 O. For clean (2 x l)-Si(lOO), the measured yield profile of 1.6 o + 0.1” (fig. 9a). This value is in good has a Q agreement with the theoretical value of 1.65 o [17], if a dimer-type reconstruction [48] is supposed (fig. 10). For comparison, the unreconstructed (1 X l)-Si(100) would deliver a Q2 of 2.1”. When the (2 x l)-Si(100) surface is covered with 0.5 ML of indium at T = 300 K, indium is found to form a two-dimensional layer (Stranski-Krastanov mechanism) on the surface with a (2 x2)-In-structure [49]. The measured yield profile for (2 x 2)-In/Si(lOO) has a e 1,2 of 1.6” + 0.1” (fig. 9b). This is the same value as for the clean surface. Thus, the arrangement of the silicon atoms in the surface does not change along the [Oil] rows when indium is deposited on the clean surface. In particular, the Si dimers are preserved in spite of the indium coverage [49,50].
4. Conclusions Surface channeling of fast ions has proved to be a versatile method to analyze the atomic structure of
crystal surfaces. In combination with appropriate detection reactions, it is possible to study all combinations of substrates and adsorbates. Surface channeling is sensitive to both the long range order (substrate structure) and the short range order (adsorbate position) of the surface structure. To a large degree, the obtained information is complementary to that provided by other surface sensitive techniques. The authors are most grateful to Dr. C. Varelas. The findings reviewed in this paper were obtained in cooperation with Dr. C. Varelas, Dr. W. Graser and Dr. H. Winter. Thanks are also gratefully extended to R. Schwab, who made the illustrations. This work was funded by the German Federal Minister for Research and Technology (BMFT) under the contract number 03SIlLMU4.
References [l] R. Sizmann and C. Varelas, Nucl. Instr. and Meth. 132 (1976) 633. [2] C. Varelas, in: Structure and Dynamics of Surfaces I, eds. W. Schommers and P. von Blanckenbagen (Springer, Berlin, 1986) p. 111. [3] A.D. Marwick, M.W. Thompson, B.W. Farmery and G.S. Harbinson, Radiat. Eff. 15 (1972) 195. [4] H.J. Pabst, Radiat._Eff. 31 (1977) 197. [5] M.W. Thompson and H.J. Pabst, Radiat. Eff. 37 (1978) 105. [6] K. Morita, Radiat. Eff. 52 (1980) 235. [7] E.P.Tb.M. Suurmeijer and A.L. Boers, Surf. Sci. 43 (1973) 309. [8] M. Hou and C. Varelas, Appl. Phys. A33 (1984) 121. XIII. SURFACE ANALYSIS
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154.Schuster / Surface analysis of crystals
[9] Y. Yamamura and W. Takeuchi, Radiat. Eff. 61 (1982) 241. [lo] ES. Mashkova and V.B. Flerov, Phys. Chem. Mech. Surf. 3 (1985) 1018. (111 V.I. Shulga, Radiat. Eff. 100 (1986) 71. [12] V.I. Shulga, Radiat. Eff. 26 (1975) 61. [13] E.S. Mashkova and V.B. Fleurov, Radiat. Eff. 80 (1984) 227. 1141 AI. Dodonov, Sh.N. Garin, E.S. Ma&ova and V.A. Molchanov, Surf. Sci. Lett. 140 (1984) L244. [15] K. Kimura, A. Nishimura and M. Mannami, Surf. Sci. 183 (1987) L313. [16] J. Lindhard, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 34 (1965) no. 14. [17] C. Varelas and R. Sizmann, Radiat. Eff. 16 (1972) 211. [18] U. Bill, R. Sizmann, C. Varelas and K.E. Rehm, Radiat. Eff. 27 (1975) 59. 1191 C. Varelas, K. Goltz and R. Sizmann, Surf. Sci. 80 (1979) 524. [ZO] C. Varelas and R. Sizmarm, Surf. Sci. 71 (1978) 51. [21] I.N. Evdokimov, R. Webb, D.G. Armour and D.S. Karpuzov, Radiat. Eff. 42 (1979) 83. [22] D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129 (The critical angle for specular reflection at the surface potential is deduced from the critical angle for planar channeling.). [23] Y.H. Ohtsuki, K. Koyama and Y. Yamamura, Phys. Rev. B20 (1979) 5044. [24] R. Siiann and C. Varelas, in: Advances in Solid State Physics 17, ed. J. Treusch (Vieweg, Brauschweig, 1977) p. 261. [25] M. Schuster and C. Varelas, Nucl. Instr. and Meth. B9 (1985) 145. [26] M. Schuster and C. Varelas, Surf. Sci. 134 (1983) 195. [27] C. Varelas, H. Preissler and F. StGlzle, private communication. [28] C. Varelas, H.D. Carstanjen and R. Sizmann, Phys. Lett. 77A (1980) 469.
[29] E. Sailer and C. Varelas, Nucl. Instr. and Meth. B2 (1984) 326. 1301 D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [31] M. Schuster, thesis, Universitlt Miinchen, 1985. [32] G.S. Harbinson, B.W. Farmery, H.J. Pabst and M.W. Thompson, Radiat. Eff. 27 (1975) 97. [33] M. Schuster and C. Varelas, Nucl. Instr. and Meth. B2 (1984) 299. 1341 R. Pfandzelter and C. Varelas, submitted to Surf. Sci.. [35] R. Pfandzelter, to be published. [36] S.L. Nizlmaya, E.S. Parilis and V.K. Verleger, Radiat. Eff. 62 (1982) 173. [37] W. Graser and C. Varelas, Phys. Scripta T6 (1983) 153. 1381 W. Graser and C. Varelas, in: Proc. European Conf. on Nuclear Physics Methods in Materials Research, eds. K. Bethge, H. Baumann, H. Jex and F. Rauch (Vieweg, Braunschweig, 1980) p. 371. 991 W. Graser, thesis, Universitlt ~nchen (1983). 1401 W. Graser and C. Varelas, Surf. Sci. 157 (1985) 74. [41] H. Winter, thesis, Universitlt Mlinchen (1986). [42] P.R. Norton, P.E. Binder and T.E. Jackman, Surf. Sci. 175 (1986) 313. [43] A.M. Barb, G. Bim-dg, 11. Rohrer, Ch. Gerber, E. Stoll, A. Baratoff and F. Salvan, Phys. Rev. Lett. 52 (1984) 1304. [44] K. Baberschke, U. Dobler, L. Wenzel, D. Arvanitis, A. Baratoff and K.H. Rieder, Phys. Rev. B33 (1986) 5910. [45] W. Schmitt, K.-P. K%mper and G. Glintherodt, Surf. Sci. 189/190 (1987) 741. [46] H. Niehus and G. Comsa, Surf. Sci. 151 (1985) L171. [47] J.F. Van der Veen, R.G. Smeenk, R.M. Tromp and F.W. Saris, Surf. Sci. 79 (1979) 212. 1481 M.T. Yin and M.L. Cohen, Phys. Rev. B24 (1981) 2303. [49] J. Knall, J.-E. Sundgren, G.V. Hansson and J.E. Greene, Surf. Sci. 166 (1986) 512. [50] D.H. Rich, A. Samsavar, T. Miller, H.F. Lin and T.-C. Chiang, Phys. Rev. Lett. 58 (1987) 579.
SIJRFACE ANALYSIS
Nuclear Instruments and Methods in Physics Research 333 fI988) 8Q8-QM North-Holland, Amsterdam
OF CRYSTALS
BY SURFACE
~
R. FFANDZELTER Sekfion l’hysik, Universifcif Miinchen, Amalienstrmse 34, R-8000 Miinchen 40, FRG M. SCHUSTER
In surface channeling, fast ions are incident at a grazing angle u@on B crystal surface aIung a fow index surface direction. Surface charmeled ions are used as versatile probes for surface analysis. The atomic structure of crystal surfaces, especialfy surface reconstructions and positions of adsorbed atoms, can be analyzed by ions channeled at the crystal surface in combination with
appropriate detection reactions. We review the application of ion surface channeling to surface structure analysis. The principles of surface channeling are outlined. Several detection reactions, such as backscattering, nuclear reactions, X-ray emission, Auger electron emission, forwardscattering, light emission and secondary electron emission, are discussed with respect to surface channeling. Finally, some recent experiments are given as examples: (2 X l}-~~~~l~~}, steps on Ni o,6Fe0,4(l10) and (2 x 2)In,/Si(lOO).
1. PrineipIes of surface channeling
Fast ions incident upon a crystalline target are steered by the repulsive potential of the atomic rows if they are aligned with a low index lattice direction. This effect, well known as axial channeling in the bulk, is also observed at smooth crystal surfaces [l-15], when the ions are incident at a grazing angle upon the crystal surface along a low index surface direction. Let us denote by + the angle between the ion beam and the surface, B the lateral angle between the ion beam and the low index surface direction and J/ = ($’ + 02)1/2 the corresponding angle of incidence towards the low index surface direction (fig. 1). Surface channeling, i.e. axial channeling in the surface near region, occurs under the following conditions of ion incidence [l]: it is required (1) that the transverse energy E, = E sin2+ (E is the energy of the incident ion) is larger than the surface potential to allow the ions to penetrate into the
CrystalSurface
Fig. 1. IWationship between the a&es of incidence and a low index surface direction [ hkl].
~168-~g3~/8~/$~3.5~ 0 Elsevier Science Publishers B.V. (North-Roland Physics Publis~g Division)
crystal, (2) that li, is sm&er than the critical angle of axial channeling fltr,I’f] and (3) that + is small enough that planar channeling cannot develop [K-20]. In fig. 2, the different regimes of ion motion for grazing ion incidence upon a crystal surface are shown for 150 keV H’ incident upon Ni(l10) alcmg [ITO]. The regime of surface channeling is indicated by the cross-hatched area. Some authors [Zl] even discuss h~er~hanne~ng at the surface, but it would be restricted to a small regime (black). At small angles +, the ions suffer specular reflection at the very surface with small energy loss only (heavy dotted). At even smaller values of 9, there is the regime of skipping motion, where the reflected projectiles are drawn back to the surface by their image charge (light dotted) [23]. In the regimes of surface ~h~neling, skipping motion and h~erch~n~ing, the ion motion is bound to the surface. The regime of surface channeling partially interferes with the regimes of planar channeling (hatched) [la]. Besides the planar channels indicated in the diagram, there exist further regimes of high index planar channeling, which are out of the range of fig. 2. The blank areas describe transition regimes and random scattering. In surface channeling, sometimes also called semich~neling, the scattering of the ions is caused by successive correlated collisions with numerous atoms along the low index surface direction. Thus, surface channeling can be described by the concept of Lindhard’s continuum row potentials analogous to axial channeling in the bulk [16,24]. Therefore, at grazing incidence along the low index direction, the ions are strongly steered by the repulsive potential of the atomic rows. This diminishes the ion flux density close to the
R. Pfandzelter, M. Schuster / Surface analysis of crystals
899
incidence. The half width taken at the half minimum of the yield (hwhm) is designated as 01,2. A first order approximation for the angle +i,z = (+2 + 8&z)1/2 can be taken from Lindhard [16]:
# J___ 2ZlZ2e2
l/2
=
E&,/q
0
[ii01
Q-+ specular reflaciion
a
skipping motion
0
random scaftering and lransifion zones
Fig. 2. Regimes of motion for fast ions angles upon a crystal surface. The values calculated for 150 keV Hf incident upon based on Thomas-Fermi-Molibre and on tials.
incident at grazing of this diagram are Ni(ll0) along [ITO], image charge poten-
atomic rows and enhances it between them. Thus, the average impact parameter of the channeled ions to the atoms in the rows is large. Since the probability of elastic or inelastic reactions grows smaller with larger impact parameters between the incoming ions and the target atoms, the reaction yield decreases if the ions are incident parallel to the low index direction. If the lateral angle of incidence 0 between the ion beam and the low index direction is increased, the steering effect weakens and the ion flux becomes more homogeneous. As result, the average impact parameter decreases and the reaction yield increases. For even larger angles 8, the yield reaches the value which is obtained in a random distribution of impact parameters like at an amorphous target surface. In the regime of surface channeling, the absolute ion flux density is strongly enhanced within the topmost atomic layers [25,26]. The projectiles penetrate through the surface and undergo axial channeling in the surface region with their main translational momentum parallel to the low index surface direction. Thus, surface channeled ions selectively excite the atoms in the surface region. This causes an inherent surface sensitivity of all methods in combination with surface channeling. In surface analysis by surface channeling, the angle + is kept constant and the reaction yield is measured as a function of the lateral angle 0. The angular yield profiles are usually normalized to the yield at random
’
where 2, and Z, are the atomic numbers of the ion and the target atom, respectively. E is the energy of the incident ion and dIhkr, the interatomic distance in the [hkl] row. If Z,, Z,, E and C#Jare fixed by the experimental conditions, 81,2 is a measure of the interatomic distance dLhklI in the steering rows. Thus, measurements of +1,2 for ion incidence along different low index surface directions provide a straightforward analysis of the arrangement of the atoms in the topmost substrate layer. Moreover, the inhomogeneous flux of the channeled projectiles will help to localize adsorbate atoms on the crystal surface. The yield of a close-encounter process between the ion and the adsorbed atom is enhanced, if the adsorbates are placed between the atomic rows, and diminished, if they are placed in or near the rows. In other words, the minimum and maximum of the yield profile, respectively, deliver a straightforward determination of the lateral adsorbate position. The distance of the adsorbate atom normal to the surface can be obtained by comparison of the shape of the measured yield profile with a computer simulation.
2. Detection reactions Fast ions interact with a crystal surface in a series of elastic and inelastic collisions (fig. 3). Generally, those interactions which require small impact parameters between the ion and target atom are most suited to obtain strongly modulated angular yield profiles, of course, at the expense of small cross sections. Backscattering is an example for a close-encounter process. It is elementspecific and applicable to a wide variety of projectile species and energies, and target atoms, especially to heavy adsorbates on a light substrate. The yield of the substrate is obtained from the edge height in the backscattering spectrum, whereas heavy adsorbates appear as isolated high energetic peaks in a nearly background free region. Backscattering of 250 keV He+ was applied by Varelas and coworkers to study the adsorption sites of Xe on Si(ll1) [27]. A method related to measuring the backscattered projectiles would be the detection of sputtered target atoms and molecules. To the authors’ knowledge, this has not been applied in surface channeling experiments till now. XIII. SURFACE
ANALYSIS
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R. Pfandzelter, M. Schuster / Surface analysis of crystals
X&y
Auger Electron Emission
Emission
NUCIW Reaction
ef
Secondary Emission
f
eBackscattering
Electron
Forwardscattering
Fig. 3. Schematic illustration of detection reactions used in surface channeling experiments.
Nuclear reactions are close-encounter processes, too. They are of particular interest to light elements, where other means fail. The reactions are element-specific and the highly energetic reaction products can be detected free of background. A disadvantage is the relatively high energy required for nuclear reactions. Varelas and coworkers used the reactions 160(d,p)170 and 12C(d,p)‘3C induc ed by surface channeled 1.2 MeV deuterons to determine the position of adsorbed CO on Ni(ll0) [28]. Deuterium on Ni(ll0) was localized by Sailer and Varelas by means of the reaction ’ H( 3He,p)4He induced by surface channeled 580 keV. 3He+ [29]. The emission of characteristic X-rays resulting from the inner-shell ionization of target atoms or projectiles occurs at larger impact parameters than backscattering and nuclear reactions. Therefore, the channeling dips become shallower [25,30,31]. Detection of X-rays is suited especially for heavier elements (highly energetic transitions), because of the higher fluorescence yield and the possibility to detect energetic X-rays by Si(Li)detectors, which allow the exploitation of large acceptance angles. The detected X-rays are element-specific. Apart from line overlap due to insufficient resolution, no background problems exist. Harbinson and coworkers examined the oxygen position in a WO, layer on W(110) by means of W-M- and O-K-radiation induced by surface channeled 150-275 keV H+ [32]. Backscattering, nuclear reactions and X-rays are not inherently surface sensitive probes. Their applicability to surface analysis is given by the flux peaking of the incident ions in the channels and semichannels of the surface near region (cf. section 1). The surface sensitivity can be enhanced further by the detection of Auger electrons due to their short mean free path. Since Auger
electron emission and X-ray emission are complementary element-specific reactions based on inner-shell ionization, the impact parameter dependence is the same. For low 2 elements, the Auger yield surpasses the fluorescence yield by far. For high Z elements, the ion induced Auger electron analysis can switch over from K-lines to L- or M-lines and, thus, achieve appropriate ionization cross sections and fluorescence yields. The major disadvantage of the analysis of Auger electrons induced by surface channeled ions is the high background due to secondary electrons. Therefore and because of the finite source size at glancing ion incidence, a good electron spectrometer, e.g. a double pass cylindrical mirror analyzer, is favourable. By the above-mentioned method, several surface analysis were made: (2 X l)-O/Ni(llO) [25,26,33], streaked-(2 X 1)-H/ Ni(ll0) [34], (2 X 2)-In/Si(lOO) [35] (cf. section 3). In some cases, reactions with high yields are indispensable. Forwardscattering of projectiles is such a reaction. Compared to backscattering, it occurs at larger impact parameters. The scattered projectiles can be measured as a function of their scattering angle, energy and charge state. An element-specific detection, however, is not possible. The number of forwardscattered ions is easily monitored by a Faraday-cup or counted by a solid state detector. Generally, in surface channeling large impact parameter reactions cannot be interpreted as straightforward. Computer simulations are necessary to discuss the experimental results. Nizhnaya and coworkers studied the ionization degree of scattered Ne+, grazingly incident with 3 keV upon N,/Ni(lOO) [36]. Thereby, they could find out the position and orientation of the adsorbed N, molecules. A variant of forwardscattering measurements is the observation of light emission by excited scattered projectiles. The light intensity and polarization. exhibit a strong dependence on the surface crystallography and coverage [37]. The major advantage of this method is the experimental simplification: the whole detection system is positioned outside the scattering chamber. Graser and Varelas could determine the oxygen position on (2 X 1)-O/Ni,,, Fe,,,(llO) [38,39] and the mean step distance on clean Ni0,6Feo,4(110) [40] (cf. section 3) by measuring the He+ - 468.6 nm light emission from surface channeled 200 keV He+ [39,40]. A reaction, where the description by impact parameters of single atoms is insufficient, is the emission of secondary electrons. The yield of this reaction is determined by the valence electron density and the ion flux distribution. The secondary electron emission scales with the electronic energy loss and gives rather high yields at grazing ion incidence. Winter could confirm the saw-tooth substrate structure of (2 X I)-O/Ni(llO) found in ref. [26] by secondary electron emission induced by surface channeled 75-200 keV H+ and He+
[411.
R. Pfandzelter,
3. Examples of surface channeling studies
P’l
L
3.1. (2X1)-O/Ni(llO)
The structures of clean (1 X 1)-Ni(ll0) and (2 X l)-O/Ni(llO) were examined by surface channeling of 150 keV H+. The yields of the H+ induced Auger electrons of nickel and oxygen were measured simultaneously as a function of the lateral angle of incidence 0 with $I = 1.0 o [26,33]. For clean Ni(llO), the yield profiles of the Ni Law Auger electrons for Ht incidence along [OOl] and [liO] exhibit a 81,2, according to the bulk distances (figs. 4 and 5a). At an oxygen coverage of 0.5 ML, resulting in a (2 x l)-LEED pattern [42], the 01/Z of the yield profile along [liO] is diminished compared to the clean surface (fig. 4). For the corresponding $~i,~s is valid: J/1,2(0/Ni(l10) : $l,z(Ni(llO)) = 1: fi. According to eq. (1) the interatomic distance in the [liO] rows must have become twice the bulk value. Along [OOl], however, the oxygen coverage does not change the yield profile. This indicates a (2 x 1) reconstruction ([26] and refs. therein). A (2 x 1) reconstruction is exhibited by both the missing row model (fig. 5c) and the saw-tooth model (fig. 5b). A comparison of the measured yield profiles with computer simulations favours the saw-tooth reconstruction. Hence, the surface structures of the nickel substrate atoms could be determined as follows: the clean surface is not reconstructed; the 0.5 ML
t
Yield of Ni L,VV Auger
Electrons
r
simulation
experiment
F
A Ni (110) clean
-
Ni (110)
0
---
saw-tooth
OlNi
(110)
clean
1.0
n
-
-Go
-do
-2”
[ii01
2”
901
M. Schuster / Surface analysis of crystals
40
6O o+
Fig. 4. Yields of Ni LsW Auger electrons induced by 150 keV Hf versus angle 0 towards [ITO] for clean Ni(ll0) and oxygen covered (2 X l)-O/Ni(llO). The lines are the result of computer simulations. + = 1.0 ‘, T = 300 K.
[ii01
0 yiEve,0
[OOll
DJll (a) Ni (1lO)clean
(b) Saw-Tooth
Model
Nickel
0
Oxygen
too11 (c) Missing Row Model
Fig. 5. Top views of (a) unreconstructed (1 x l)-Ni(llO), (b) reconstructed saw-tooth (2 x l)-O/Ni(llO) and (c) reconstructed missing row (2 x I)-O/Ni(llO). Below the top views are the profiles of the surface region parallel to the [OOl] direction. oxygen covered surface has a (2 x 1) saw-tooth reconstruction [26,33,41,43-451. The only investigation which is in explicit contradiction to the saw-tooth model is ref. [46]. This study, which is based on quasi-single ion scattering (low energy alkali impact collision ion spectroscopy), claims the missing row model. Calculations of one of the authors (M.S.) exhibit however that at the very ion trajectories, which should be significantly different for the missing row and the saw-tooth model, multiple scattering cannot be neglected. This discards the arguments of ref. [46] supporting the missing row model. In the surface channeling studies [26,33,41] a relaxation, as found by ref. [44,47] has not been taken into account, because surface channeling is not sensitive to a relaxation normal to the surface. To localize the adsorbed oxygen, the oxygen KL 23L 23 Auger electron yield profiles were measured (fig. 6). The strongly enhanced minimum yield of the 0 KL,,L,, Auger electrons for H’ incidence along [liO], compared with that along [OOl], shows that the oxygen atoms are situated between the Ni[liO] rows, shadowed by the Ni[OOl] rows. Thus, the oxygen atoms can be localized in the long bridge position between the nickel atoms in the topmost [OOl] rows of the reconstructed surface. By comparison of the experimental results with computer simulations, the distance of the oxygen atoms above the topmost nickel layer is found to be 25 pm (fig. 6). 3.2. Steps on Nio~,Fe,,,(llO) The presence of atomic steps on real crystal surfaces is known to influence many surface properties like XIII. SURFACE ANALYSIS
902
R. Pfandzelter, M. Schuster / Surface analysis of ctystafs
t Yield of 0 KL&,
Yield of He+Radiation
Auger Electrons
0 experiment
simulation ...._t h= 0 pm --h=lZ.Spm -h=25 pm
t -.-
t
simulation
experiment
h=37.!ipm h=!Sl fern
L,
a)
I,I,j
-60
-40
L
-2~
0
I,[,
20
z!l, b)
1
40
60-60-4~
a 1,
-2O
II
0
[tiol
MO1
1,
2O
P
)I
6”
0 -+
Fig. 8. (a) Yield of He+-468.6 nm radiation versus angle 8 towards [liO] for (1) 200 keV He+, cp=l.O” and for (2) 75 keV He+, C$= 1.63O scattered at clean (1 x l)Ni,,,Fee,,(llO), E, = 61 eV, rmin= 0.065 nm. (a) Experiment, (b) computer sim~ations carried out for a step distance s = 75 lattice constants (75 X 0.25 nm). T = 450 K. After 1401.
Fig. 6. Yield of 0 KLz3Lz3 Auger electrons induced by 150 keV H+ versus angle B towards [liO] for oxygen covered (2 x I)-O/Ni(llO). The lines are the result of computer simulations carried out for different oxygen distances h to the topmost nickel layer of a saw-tooth reconstructed surface. .#~=1.0~, T=3OOK.
adsorption kinetics and catalytic activity. Figs. 7a and b show how surface channeling can be applied to determine the mean distance s between atomic steps. Ions incident at a grazing angle along the [liO] direction of a fcc(ll0) surface, are focused by atomic rows 1 onto row 2 of the second layer and reflected mainly into the direction normal to the surface. On their way out, the ions can be trapped by the atomic row 3 of an upward step and reflected into the bulk. In a stepped surface, the trajectory inclination defines an escape length L (fig. 7b). If the transverse energy E, = E sin2# and, therefore,
Fig. 7. Illustration of the influence of a step on the trajectories of ions incident at a grazing angle along the [liO] direction of a fcc(310) surface towards a row 2 of the second layer; (a) perspective view, (b) side view; trajectories for different ion energies E and angles of incidence q’~at constant r,,, i.e. constant transverse energy E, = E.sin*#~. t is the escape length, s the step distance. Tire scale in the direction of the atomic rows is reduced. After [40].
the value
‘;oie of nearest
approach
are kept
Thus, the mean step distance s can be determined by measuring the yield of the scattered projectiles for different escape lengths L, i.e. for different E. Hereby, the transverse energy E, , i.e. r,, has to be kept constant by adjusting the angle of incidence # ([2], p. 115). By this method, clean Ni~,~Fe~.~(llO) was examined with He+ incident along [liO] [40]. The light emission of the scattered excited He+ ions when emerging from the surface was measured [37]. In fig. 8a, the measured yield profiles as a function of the lateral angle 6 for (1) E=200 keV, +=l.O” and (2) E==75 keV, #=1.63” are plotted. In case (2), the escape length is short enough that many ions, which are focused onto row 2 and reflected, can leave the surface without encountering a step. Therefore, a yield rn~~ at 6 = O” results. In case (l), the escape length is longer. IIere, the ions reflected at row 2 are trapped by the steps. The maximum at B = 0” disappears. By comparison with computer simulations (fig. 8b), a mean step distance s of 75 lattice constants (75 x 0.25 nm) is found. constant,
the escape length is: L - a.
3.3. (2 X2)-h
/ Si(lO0)
Surface analysis by surface channeling is also applicable to semiconductor surfaces. As an example, the
903
R. Pfandzelter, M. Schuster / Surface analysis of crystals t YieldofSiL,,VVAugerElectrons iI>
Si (100) clean
experiment
‘I v it
0
]
experiment
I
In&i (100)
0
Silicon
ls1Lay.r 0
Silicon
Fig. 10. Top view of the reconstructed asymmetric model of (2 x l)-Si(100). -40
-20
[Oil]
20
Qd
dimer
40
Fig. 9. Yield profiles of Si L,,W Auger electrons induced by 75 keV H+ versus angle towards [Oil] measured at (a) clean (2 x l)-Si(lO0) and (b) indium covered (2 x 2)-In/Si(lOO). + = 0.9O, T= 300 K.
arrangement of the silicon atoms at clean and indium covered Si(lO0) was investigated [35]. The yield of the Si L2sW Auger electrons induced by surface channeled 75 keV H+ was measured as a function of the lateral angle of incidence to the [Oil] direction with $I = 0.9 O. For clean (2 x l)-Si(lOO), the measured yield profile of 1.6 o + 0.1” (fig. 9a). This value is in good has a Q agreement with the theoretical value of 1.65 o [17], if a dimer-type reconstruction [48] is supposed (fig. 10). For comparison, the unreconstructed (1 X l)-Si(100) would deliver a Q2 of 2.1”. When the (2 x l)-Si(100) surface is covered with 0.5 ML of indium at T = 300 K, indium is found to form a two-dimensional layer (Stranski-Krastanov mechanism) on the surface with a (2 x2)-In-structure [49]. The measured yield profile for (2 x 2)-In/Si(lOO) has a e 1,2 of 1.6” + 0.1” (fig. 9b). This is the same value as for the clean surface. Thus, the arrangement of the silicon atoms in the surface does not change along the [Oil] rows when indium is deposited on the clean surface. In particular, the Si dimers are preserved in spite of the indium coverage [49,50].
4. Conclusions Surface channeling of fast ions has proved to be a versatile method to analyze the atomic structure of
crystal surfaces. In combination with appropriate detection reactions, it is possible to study all combinations of substrates and adsorbates. Surface channeling is sensitive to both the long range order (substrate structure) and the short range order (adsorbate position) of the surface structure. To a large degree, the obtained information is complementary to that provided by other surface sensitive techniques. The authors are most grateful to Dr. C. Varelas. The findings reviewed in this paper were obtained in cooperation with Dr. C. Varelas, Dr. W. Graser and Dr. H. Winter. Thanks are also gratefully extended to R. Schwab, who made the illustrations. This work was funded by the German Federal Minister for Research and Technology (BMFT) under the contract number 03SIlLMU4.
References [l] R. Sizmann and C. Varelas, Nucl. Instr. and Meth. 132 (1976) 633. [2] C. Varelas, in: Structure and Dynamics of Surfaces I, eds. W. Schommers and P. von Blanckenbagen (Springer, Berlin, 1986) p. 111. [3] A.D. Marwick, M.W. Thompson, B.W. Farmery and G.S. Harbinson, Radiat. Eff. 15 (1972) 195. [4] H.J. Pabst, Radiat._Eff. 31 (1977) 197. [5] M.W. Thompson and H.J. Pabst, Radiat. Eff. 37 (1978) 105. [6] K. Morita, Radiat. Eff. 52 (1980) 235. [7] E.P.Tb.M. Suurmeijer and A.L. Boers, Surf. Sci. 43 (1973) 309. [8] M. Hou and C. Varelas, Appl. Phys. A33 (1984) 121. XIII. SURFACE ANALYSIS
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154.Schuster / Surface analysis of crystals
[9] Y. Yamamura and W. Takeuchi, Radiat. Eff. 61 (1982) 241. [lo] ES. Mashkova and V.B. Flerov, Phys. Chem. Mech. Surf. 3 (1985) 1018. (111 V.I. Shulga, Radiat. Eff. 100 (1986) 71. [12] V.I. Shulga, Radiat. Eff. 26 (1975) 61. [13] E.S. Mashkova and V.B. Fleurov, Radiat. Eff. 80 (1984) 227. 1141 AI. Dodonov, Sh.N. Garin, E.S. Ma&ova and V.A. Molchanov, Surf. Sci. Lett. 140 (1984) L244. [15] K. Kimura, A. Nishimura and M. Mannami, Surf. Sci. 183 (1987) L313. [16] J. Lindhard, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 34 (1965) no. 14. [17] C. Varelas and R. Sizmann, Radiat. Eff. 16 (1972) 211. [18] U. Bill, R. Sizmann, C. Varelas and K.E. Rehm, Radiat. Eff. 27 (1975) 59. 1191 C. Varelas, K. Goltz and R. Sizmann, Surf. Sci. 80 (1979) 524. [ZO] C. Varelas and R. Sizmarm, Surf. Sci. 71 (1978) 51. [21] I.N. Evdokimov, R. Webb, D.G. Armour and D.S. Karpuzov, Radiat. Eff. 42 (1979) 83. [22] D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129 (The critical angle for specular reflection at the surface potential is deduced from the critical angle for planar channeling.). [23] Y.H. Ohtsuki, K. Koyama and Y. Yamamura, Phys. Rev. B20 (1979) 5044. [24] R. Siiann and C. Varelas, in: Advances in Solid State Physics 17, ed. J. Treusch (Vieweg, Brauschweig, 1977) p. 261. [25] M. Schuster and C. Varelas, Nucl. Instr. and Meth. B9 (1985) 145. [26] M. Schuster and C. Varelas, Surf. Sci. 134 (1983) 195. [27] C. Varelas, H. Preissler and F. StGlzle, private communication. [28] C. Varelas, H.D. Carstanjen and R. Sizmann, Phys. Lett. 77A (1980) 469.
[29] E. Sailer and C. Varelas, Nucl. Instr. and Meth. B2 (1984) 326. 1301 D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [31] M. Schuster, thesis, Universitlt Miinchen, 1985. [32] G.S. Harbinson, B.W. Farmery, H.J. Pabst and M.W. Thompson, Radiat. Eff. 27 (1975) 97. [33] M. Schuster and C. Varelas, Nucl. Instr. and Meth. B2 (1984) 299. 1341 R. Pfandzelter and C. Varelas, submitted to Surf. Sci.. [35] R. Pfandzelter, to be published. [36] S.L. Nizlmaya, E.S. Parilis and V.K. Verleger, Radiat. Eff. 62 (1982) 173. [37] W. Graser and C. Varelas, Phys. Scripta T6 (1983) 153. 1381 W. Graser and C. Varelas, in: Proc. European Conf. on Nuclear Physics Methods in Materials Research, eds. K. Bethge, H. Baumann, H. Jex and F. Rauch (Vieweg, Braunschweig, 1980) p. 371. 991 W. Graser, thesis, Universitlt ~nchen (1983). 1401 W. Graser and C. Varelas, Surf. Sci. 157 (1985) 74. [41] H. Winter, thesis, Universitlt Mlinchen (1986). [42] P.R. Norton, P.E. Binder and T.E. Jackman, Surf. Sci. 175 (1986) 313. [43] A.M. Barb, G. Bim-dg, 11. Rohrer, Ch. Gerber, E. Stoll, A. Baratoff and F. Salvan, Phys. Rev. Lett. 52 (1984) 1304. [44] K. Baberschke, U. Dobler, L. Wenzel, D. Arvanitis, A. Baratoff and K.H. Rieder, Phys. Rev. B33 (1986) 5910. [45] W. Schmitt, K.-P. K%mper and G. Glintherodt, Surf. Sci. 189/190 (1987) 741. [46] H. Niehus and G. Comsa, Surf. Sci. 151 (1985) L171. [47] J.F. Van der Veen, R.G. Smeenk, R.M. Tromp and F.W. Saris, Surf. Sci. 79 (1979) 212. 1481 M.T. Yin and M.L. Cohen, Phys. Rev. B24 (1981) 2303. [49] J. Knall, J.-E. Sundgren, G.V. Hansson and J.E. Greene, Surf. Sci. 166 (1986) 512. [50] D.H. Rich, A. Samsavar, T. Miller, H.F. Lin and T.-C. Chiang, Phys. Rev. Lett. 58 (1987) 579.