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Surface layer relaxation on Mo(111) measured by low energy alkali ion scattering
123
Surface Science 175 (1986) 123-140 North-Holland, Amsterdam
SURFACE LAYER RELAXATION ON Mo(ll1) MEASURED BY LOW ENERGY ALKALI ION SCATTERING S.H. OVERBURY Ouk Ridge National Laboratory, Oak Ridge, TN 37831, USA Received
4 December
1985; accepted
for publication
8 April 1986
The surface of clean Mo(ll1) has been studied using Li+ ion scattering at 1000 eV. The dependence of single scattering intensity was measured as a function of incident polar angle in the [121] and the [2ii] azimuths for various total scattering angles. Very pronounced intensity cut-offs are ohserved and are readily assignable to shadowing and blocking effects in scattering from first, second or third layer atoms. After taking certain precautions to avoid interference from deeper layers, the measured positions of the features yield the first-second layer spacing which is found to be strongly contracted by (18 i 2)% compared to the bulk spacing. The method also indicates that the second-third layer spacing is possibly expanded (4+4)%, but this result is uncertain due to possible contributions from deeper layers which make this value an upper limit of the layer spacing. The physical implications of these results and the uncertainties in the technique are discussed.
1. Introduction There has been considerable research interest in determining the structure of metal surfaces. Many metal surfaces are reconstructed, but even those surfaces which do not reconstruct exhibit relaxations of the spacings of the outermost layers. The characterization of these multi-layer relaxations has improved rapidly in the last five years as a result of developments in both experimental and theoretical techniques. Various experimental techniques have been applied to measure surface relaxations although probably the two most frequently applied are low energy electron diffraction (LEED) and medium or high energy ion scattering. These techniques have developed to the point that first, second and occasionally third interlayer spacings are determined [l-9]. Theoretical efforts have been aimed at predicting and explaining both the sign and magnitude of the relaxations and the depth over which the relaxations occur [lo-121. The most actively studied systems are the low index faces of fee metals, especially the (110) face [2-6,11,12]. Jona, Marcus and coworkers [1,8] have studied systematic variations for several faces of Fe, a bee metal. Recently high index surfaces of both fee and bee metals have been examined and in 0039-6028/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
124
S. H. Overbury / Surface layer relaxation on Mo(lI1)
some cases relaxations parallel to the surface exist, as well as perpendicular relaxations [ 1,7]. Certain trends have emerged as a result of both the experimental and theoretical efforts. It is usual for surface relaxation to occur. There is generally a contraction of the first interlayer spacing and a damped oscillatory relaxation of the deeper interlayer spacings. The extent of the contraction of the first layer tends to increase with increasing “roughness” i.e., there is a tendency for larger relaxations on the more open surfaces. Less clear, however is the dependence of the period of the oscillatory relaxations upon the layer stacking sequence. On most low index faces which have been examined, e.g., the Al(110) [4] and Cu(ll0) [2,3], the oscillations change signs at each interlayer spacing reflecting the two-layer stacking sequence. In open surface such as the bee (111) and high index surfaces there are more layers in the stacking sequence and the oscillatory pattern may change. For example, the Fe(210) surface shows a contraction of both the first two interlayer spacings [l] and it has been predicted that Na(ll1) may also show a contraction of the first two interlayer spacings [lo]. However, there are limited data on such surfaces, which may be partly due to the difficulty of the LEED analysis of surfaces with small interlayer spacings [8]. This work describes efforts to use low energy alkali ion scattering to determine surface relaxations on Mo(ll1). Striking features in the angle of incidence dependence are observed which can be readily interpreted and which with certain precautions yield information about the surface layer spacings. In the second section, the essential details are presented regarding the sample preparation and the capabilities and accuracy of the experimental equipment. In the third section, the methods are given by which the angle of incidence dependences are obtained and is followed by detailed interpretation of the observed features. In the fourth section, the procedures are given for determining the layer spacings and the resulting values are discussed in terms of their physical meaning and the accuracy of the technique.
2. Experimental The ion scattering measurements were made on an apparatus described and used previously [13,14]. The electrostatic analyzer (ESA) was modified from previous work by using new apertures which gave it an energy resolution AE/E = 2.0%, and an acceptance half angle to 1.5”. All measurements were done with 1000 eV Li+ ions which were mass analyzed and collimated with maximum divergence of k 0.5 O. Beam currents were typically 30 to 40 pA. The procedures used for accurately determining the polar angle of incidence, 4, defined with respect to the plane of the surface, are described in detail elsewhere [13]. Using these methods, the angles of incidence are believed to be
S. H. Overbury / Surface layer relaxation on Mo(l I I)
125
accurate to within f0.5”. The MO crystal was mounted on a stage which allowed rotation of greater than 165O about the surface normal, allowing various surface crystallographic axes to be rotated into the plane of scattering. The azimuthal angle was repositionable to within 0.5O, and the crystallographic orientation is known to within about 2.0”. The surface normal was within about lo of the scattering plane for all azimuths and the polar angle of incidence, #, was corrected for slight azimuthal variations (5 + O.S”) due to deviations of the surface normal from the actual axis of the azimuthal rotation, The laboratory scattering angle, 8, is defined as the angle between incident direction and final direction of the scattered ions, and the accuracy of this angle is important in this experiment. This angle is determined by the rotation of the ESA and the placement of the sample. The rotation of the ESA is reproducibly set to within 0.5” and calibrated at 0” by optical alignment with the beam line. Determining the proper sample placement along the axis of the beam line is also critical to the accuracy of 19.The sample could be accurately and reproducibly placed at a position determined by optical alignment. However, the uncertainty in the relationship between this position and the actual scattering angle may be responsible for systematic error in 8 of f 1”. The MO single crystal was an elliptical disk (12 mm X 8 mm X 0.5 mm thick) which was mechanically polished using a sequence of SIC and alumina powder down to 1 pm size. The surface normal was oriented to (111) to within 0.25O. The crystal was mounted on MO wires 0.25 mm thick with W/Re thermocouples spring loaded to the back. In the ultra-high vacuum system (ambient pressure 5 1.5 X 10T8 Pa), the sample could be heated up to 1400°C and the sample temperature was routinely monitored both with the thermocouple and with an optical pyrometer. The surface structure and composition were characterized by display LEED and Auger electron spectroscopy performed using the retarding field analyzer of the LEED system. The Mo(ll1) was heated extensively in oxygen to remove carbon impurities ubiquitous to MO. Oxygen and sulfur impurities were readily removed by Ar+ sputtering. In spite of sputtering and repeated oxygen treatments at various temperatures up to 1500 K, there remained a residual peak in the Auger spectrum at about 274 eV and with always about the same intensity. This feature in the Auger spectrum of the “clean” surface is believed to be due to bulk carbon. This conclusion derives from studies of the ethylene exposed surface using AES and Li+ ion . scattering. The ethylene saturated surface (lo-20 L at 400 to 475 K) yields a C Auger peak with peak-to-peak intensity which is 6 to 8 times greater and has a different shape than the residual peak. The intensity of the C peak for the ethylene saturated surface is equivalent to about 9 x lOi cm- 2 (based on a calibration curve generated previously for a Mo(001) surface). The excess carbon due to the ethylene exposure is easily removed with oxygen leaving essentially the same residual C Auger peak. Li+ ion scattering at grazing incidence from the surface exposed to ethylene at
126
S.H. Overbuty / Surface layer relaxation on Mo(lI1)
< 475 K reveals a broad peak near the C single scattering energy. This peak disappears upon annealing to 760 K for 60 s even though the C Auger peak does not decrease. Annealing to 1300 K in vacuum causes substantial decrease in the C Auger peak. These results are consistent with both surface and subsurface forms of carbon the latter giving rise to the residual C Auger peak. In view of the Auger peak shape change, and the redistribution of the carbon, it is difficult to assign a concentration from the residual peak associated with the “clean” surface. Typical Li+ exposures used to record a 1c/dependence were less than 3 x lOI3 cm-‘. Between each measurement the surface was treated to an anneal in 0, to remove carbon impurities, Ar+ sputtering to remove oxygen and any traces of imbedded Li, and finally a 60 s anneal at 1500 K to remove sputter damage. The principle effect of the build-up of impurities or damage during ion scattering measurements was a reduction of the Sll intensity (defined below) relative to the background and to the other peaks in the $ dependence. This reduction is unimportant to the major conclusions. 3. Determination
and interpretation of the rC,dependence
The clean surface exhibited a (1 X 1) LEED pattern as expected for an unreconstructed surface. This is in agreement with the findings of Ferrante and Barton [15] and of Lambert et al. [16]. This structure was therefore assumed and no evidence from the ion scattering contradicted this basic conclusion. A diagram of the geometry of this very open surface is shown in fig. 1. The azimuthal orientation of the Mo(ll1) surface was determined from the ion scattering itself. A 1000 eV Li+ ion beam was brought incident at a grazing incidence angle of 10”. The intensity of the Li+ single scattering peak was then monitored as a function of the azimuthal rotation of the crystal at fixed polar angle. Very sharp drops in intensity were observed at intervals of 60” reflecting the six-fold symmetry of the first layer. The occurrence of these dips is readily interpreted on the basis of shadowing by surface chains. The angle of incidence of 10” is below the critical cut-off angle for (li0) chains with interatom spacing of aa,, but is just above the critical angle for the (121) chains of spacing ~%a,. The dips in intensity therefore correspond to alignment of the scattering plane along a (li0) azimuth. The Mo(ll1) surface is actually three-fold symmetric since the second layer atoms break the six-fold symmetry of the first layer. Therefore, scattering from below the first layer atoms should reflect a reduced symmetry and there are expected to be differences between an angle of incidence dependence along the [121] compared to the [2ii] azimuth. These differences were readily apparent in the I/ dependence (to be discussed below) and allowed complete determination of crystal orientation relative to the scattering plane.
S.H. Overbury / Surface layer relaxation on Mo(l1 I)
127
Mo(ttt)
SURFACE
0=
1st
l
=
AND
4th
2nd
LAYER
3rd
LAYER
LAYERS
(b)
Fig. 1. The Mo(ll1) surface as a cut-away view along representative of the features the edge of the shadow cast the [2ii] azimuth is shown
is shown and indexed (a) as viewed down the surface normal and (b) the [121] azimuth and (c) along the [Zii] azimuth. A trajectory S21 in the [l?l] is shown in (b) and is characterized by incidence at by a first layer atom. A trajectory representative of the feature B21 in in (c) and is characterized by exiting along the edge of the blocking cone cast by a first layer atom.
The Li+ energy distribution was characterized by a large sharp peak somewhat below the kinematical single scattering energy. ‘This “single scattering” peak varied with scattering angle approximately as predicted for kinematical single scattering, but obvious deviations were observed indicating multiple scattering and inelastic loss effects were occurring. Under certain conditions an additional, smaller peak appeared at energies below the main peak due to subsurface multiple scattering trajectories, which occurred only for certain conditions of angle of incidence and of scattering angle. These observations are consistent with previous measurements of Li+ scattering from Mo(100) except that strong focusing, such as occurs near the (100) azimuth of Mo(OOl), was not expected or observed on Mo(ll1). The measurement of principle interest to this work is the dependence of intensity of the single scattering peak upon polar angle of incidence 4. These
S.H. Overbwy / Surface layer relaxation on Mo(I 11)
8, ,
c/ \\
J
1
L .
d
,
[4?4]
AZIMUTH
Li+E
Mo(l44)
i = 4000eV
00
j
i I
I
I
I
I
I
I
I
I
I
I
1
Fig. 2. Typical angle of incidence dependence of the Li’ single scattering is shown for various laboratory scattering angles 19 along the [l?l] azimuth. The data are normalized to unit intensity near the peak of either the Sll feature or the S21 feature. The solid curves guide the eye through the data.
S. H. Overbwy
C’
c
/ Surface layer relaxation on Mo(l .I1)
129
SI1 I
B3j
*
+ 842
+...
L
.t
-I
I
[2ii]
AZIMUTH
Li+--c MdVO Ei = ~oooev
a. I
”
0
40
20
30
40
50
-1
60
I
I
I
I
I
70
80
90
(00
(10
1
Fig. 3. The same as in fig, 2 except along the [2ii] azimuth. The breaks in the curves near 15” result from a change in the analyzer energy. Angles of incidence greater than 90” refer to the supplement of the angle of incidence along the [%l] azimuth.
130
S. H. Overbury / Surface layer relaxation on Mo(ll1)
dependences were obtained by fixing the total laboratory angle, 8, and varying the angle of incidence (and therefore also the exit angle). The peak height (count rate at the peak in the energy ~st~bution) was used as a measure of intensity. Under ideal single scattering conditions, the energy of the peak will not shift with Ic, as long as 0 is constant. In fact, small deviations in the peak position were observed necessitating adjustment of the pass energy of the ESA to remain on the peak. At the most grazing angles of incidence, the peak was at a slightly lower energy (A E/E = 0.01) than for higher values of $J_Typical dependences obtained in this way are shown in figs. 2 and 3 for various scattering angles and for the ]l?l] and the [2ii] azimuths respectively. The scattered intensity exhibits considerable structure as a function of 4. Both azimuths show a peak near 10” for every scattering angle. Otherwise, the two azimuths differ completely. These differences in two azimuths which are 60” apart reflects that the surface is three-fold not six-fold symmetric, and similarly proves that the features at high \tt involve scattering from below the first layer MO atoms. Qualitative measurements made in the [i‘l2] azimuth, which is 120” from the [2ii] azimuth, confirmed the same 4 dependence for both. The structure present in the 4 dependence of figs. 2 and 3 is similar to that first observed and described by Niehus and Comsa 117,181. The structure can be interpreted on the basis of atom shadowing and blocking. The shadowing features occur as a result of the incidence conditions. They correspond to a sharp increase in intensity as 4 is increased, and occur always at nearly the same value of il/ independent of the laboratory scattering angle r?. The blocking features occur as a result of exit conditions. They correspond to an abrupt decrease in intensity as 4 is increased and occur at nearly the same exit angle which under the present experimental conditions is 8 - 4. Their location in the + dependences shown in figs. 2 and 3 varies with 0 in such a way that 8 - J, is almost constant. The shadowing and blocking edges are labeled S and B respectively in figs. 2 and 3. The edges are also accompanied by an intensity peak due to flux peaking at the edge of the shadow cone or blocking cone. The scattering mechanisms responsible for each shadowing and blocking feature can be readily determined by considering the atomic geometry in each azimuth, as shown in figs. lb and lc. When the ions are incident at very grazing angles, II, <. lo”, all surface atoms are in the shadow cone of a preceding atom, so scattering into large scattering angles cannot occur. As \ii is increased, a critical angle is reached when a surface atom emerges from the shadow cone of the preceding atom. The intensity increases abruptly and is additionally enhanced by flux peaking at the shadow cone edge. The intensity increase is a result of (un)shadowing of first layer atoms by first layer atoms (Sll). Considering the [121] azimuth (fig. lb), it can be seen that as IE/ is increased, angles will be reached where the second layer MO atoms will emerge
S. H. Overbuty
/ Surface layer relaxation on Mo(l II)
131
from the shadow cone of first layer atoms giving rise to the feature S21 (shadowing of second layer atoms by first layer atoms). Similarly at still higher angles, the third layer atoms become visible giving rise to S31 (fig. 2). The ability to observe scattering from first, second, or third layer atoms depends upon the path of the exiting ions not being blocked. As 4 is increased (at constant f9), an exit angle will be reached in which particles scattered from second layer atoms will be blocked by first layer atoms (B21). At very grazing exit angles, scattering from first layer atoms will be blocked by an adjacent first layer atom giving rise to Bll. The features Sll, S21, S31, and B21 are all observed in the [l?!l] azimuth as seen in fig. 2. The Bll feature was not sought because of experimental difficulties in working at grazing exit angles. Consideration of the geometry of the [2il] azimuth leads to prediction of features Sll, S21, B21, B31, and Bll which are seen (except Bll) in the + dependence shown in fig. 3. As stated above, the shadowing and blocking features occur at nearly constant value of + and 8 - 4, respectively as 8 is varied. There are, however, small systematic deviations from this trend. The source of this deviation is that different impact parameters are required for scattering into different scattering angles. It is the impact point, displaced from the center of the atom by the impact parameter, which must emerge from the shadow cone to result in scattering into the detector. The extent of the deviations can be calculated as will be shown in the next section. The interpretation of the features given above is complicated by scattering from deeper layers. Shadowing or blocking involving the first and second layer may occur simultaneously with similar interference between second and third layers and between third and fourth layers, etc. The possible presence of these deeper layer contributions is indicated in figs. 2 and 3 in labeling some features, for instance indicating S21 + S32 + . . . The extent to which these deeper layers actually contribute is difficult to predict. At low energies used in this experiment, it is difficult for ions to penetrate without multiple scattering, and in addition inelastic losses become important for ions which penetrate below the second or third layer. The more deeply penetrating ions are therefore removed by the energy discrimination of the ESA. In some cases discrimination against scattering from deeper layers is achieved because of incidence conditions. In the [ljl] azimuth, the S21 feature is observed at angles of incidence much less than the S31 feature. At the angle where S21 is observed, the third layer atoms are well within the shadow cone of the first layer atoms. The third layer therefore does not contribute until larger angles of incidence where the onset is clearly marked by the occurrence of S31. It is possible that ions may reach the third layer (or deeper) by multiple scattering trajectories and scatter into the detector, but these mechanisms contribute to the uniform background intensity and should not yield an abrupt increase in intensity near the S21 edge. Similarly, near S21 the fourth
132
S.H. Overbury / Surface layer relaxation on Mo(I 11)
layer atoms are in the shadow cone of second layer atoms, and so on for deeper layers. Therefore, the conclusion is that the feature at S21 arises from scattering from only the second layer for all scattering angles. A similar argument with respect to exit angles can be advanced to conclude that the B21 feature observed in the [2il] azimuth is a result of scattering from only the second layer for all scattering angles. It is also possible to discriminate against scattering from deeper layers by choosing both angle of incidence and exit angle properly. This is equivalent to the “double alignment” conditions used in medium energy ion scattering [6]. This discrimination is achieved in some cases, as can be seen from examining the 0 dependence. As 8 is decreased, the blocking features shift towards lower + and eventually reach the angle associated with a shadowing feature. It is interesting to consider what happens when these features become coincident. Qualitatively, in the [2ii] azimuth (fig. 3) B31 merges with S21 at 8 near 90” with a large increase in intensity of the merged feature. As 8 is decreased below this, the S21 feature remains while the B31 feature vanishes. The feature B31, which originates from single scattering from third layer atoms, cannot exist at J, below S21, because at these angles scattering from third layer atoms is shadowed by second layer atoms. The intensity of the S21 feature as a function of e is shown in fig. 4. The ratio of the intensity at the peak of the S21 feature to the intensity at tc/= 30” is used since this ratio eliminates the t3 dependence of the single scattering cross section. The intensity maximum at t9 = 94” is the result of scattering from third layer atoms with flux peaking at the edge of both the shadow cone and the blocking cone. The intensity at larger 0 (2 100”) is due to scattering from first, second, and third layer atoms (and possibly deeper) with shadow cone flux peaking on both second and third layer atoms. The intensity at lower 0 (5 SO’) is due to scattering only from first and second layer atoms with shadow cone flux peaking on the second layer atom. Discrimination against scattering from the third or deeper layers is therefore achieved at 8 = 70”. Analogous behavior is observed in the [lzl] azimuth when B21 passes through S31. In this case B21 remains but S31 is eliminated when 8 decreases below about 90”. S31 cannot exist at Ic/ larger than B21, because at these exit angles scattering from third layer atoms is blocked by second layer atoms. This intensity of the S31 feature (as a ratio) is also given in fig. 4. It shows a peak at 8 = 98” due to flux peaking both in shadowing and in blocking, but at 0 = 80”, the ratio drops to below unity reflecting the disappearance of the peak. The widths of the experimentally measured shadowing and blocking edges are broadened by thermal vibrations, multiple scattering and instrumental effects. It is therefore difficult to define precisely a critical angle to the broadened, experimentally measured edge. Various approaches, based on
S. H. Overbuty
I 5
/ Surface layer relaxation on Mo(I I I)
I
I
I
I S21
+ S32
133
I
I
+ 831
Lit-Mo(i!i) E; = (OOOeV
2
3
3
ItPEAK)
UPEAK) I (46’=)
I(30°)
2
0
I
I
I
I
I
I
I
50
60
70
80
90
100
110
,0
8(deg)
Fig. 4. The ratio of the peak-to-background intensities is plotted for the S21 feature observed in the (2fi] azimuth and for the S31 feature observed in the [121] azimuth as a function of laboratory scattering angle 0. Ratios less than unity correspond to disappearance of the peak. The principle contributing scattering mechanisms are’indicated. The curves are drawn to guide the eye through the data. Table 1 Position s) and angles
eCd%)
widths b, of shadowing
and
blocking
features
at various
laboratory
scattering
[121] azimuth s31
s21
B21
Position
Width
Position
Width
Position
Width
110 105 80 60
22.3
2.1
53.1 53.9
4.7 4.2
70.8
3.9
21.6 20.5
2.1 2.1
44.4
5.7
e(de)
[2ii]
azimuth
s21
110 105 90 80 70 65
B31
B21
Position
Width
Position
Width
Position
Width
39.2 39.4 38.7 34.9 36.2 35.5
4.0 4.1 4.0 2.8 3.4 3.0
56.8 51.9 41 .o
5.0 5.3 4.0
87.4 82.9 69.1
2.5 2.8 3.0
49.9
2.6
a) Angle of incidence in degrees where intensity is 90% of maximum. b, Angle in degrees between points at 90% and 20% of maximum.
S. H. Overbuy / Surface layer relaxation on Mo(lI1)
134
different calculations or assumptions, have been suggested. Niehus and Comsa [17,18] use the angle where the edge reaches half-height. Aono [19] has stated that the value corresponding to 70% of the maximum intensity is approximately equal to the critical angle. Overbury and Huntley [13] used computer simulation to conclude that for scattering from Mo(001) the angle, $90, corresponding to 90% of the maximum intensity is appropriate. This value is probably an upper limit of #, for shadowing edges. In the present work the point G9e from the measured 4 dependence will be used as the experimental value of the critical angle. This is done for both shadowing and blocking features. The edges could usually be well approximated by a straight line between the 20% and 90% of maximum intensity, so the width of the peak is defined as the angle between these two points. The values of GgO and the widths for the observed edges (except Sll) are listed in table 1.
4. Determination
of the inter-layer spacings
The position of the shadowing and blocking edges are determined by the structure of the surface and in particular by the inter-layer spacings. The features S21 and B21 depend upon the first-second layer spacing, d,,, and the features S31 and B31 depend upon the first-third layer spacing, d,,. If there are no lateral shifts in the position of the surface atoms, it is possible to use the position of the features to determine these layer spacings. The positions of the shadowing features were calculated as follows. The size of the shadow cone was determined using tables of the laboratory scattering angle and time integral as a function of impact parameter. These tables were calculated for Li on MO using a Thomas-Fermi-Moliere scattering potential has been previously with a screening length of a = 0.90~~. This potential determined to give good agreement with experimental data for Li+ scattering from MO [13]. The routine used to calculate these values was checked against the tables of Robinson [20]. Using the shadow cone size, the critical angles were calculated as a function of inter-layer spacing using the geometry of the unreconstructed Mo(ll1) surface. This was done taking into account the impact parameter of the scattering for the total laboratory scattering angle of interest. The resulting critical angles are appropriate for non-vibrating atoms if there is no blocking along the exit path. Calculated values of the shadowing critical angle are shown in fig. Sa as a function of the layer spacing at various scattering angles for one of the S21 features. The inter-layer spacings are expressed in terms of the fractional expansion, 6,J, defined by
d,, =
(1 + 6;,)(j- i)(i’3,‘6)~,,
S. H. Overbury / Surface layer relaxation on Mo(l II)
40
-
26
+c
(8-‘#),
c
135
-I
24
(deg)
(deq)
32 -0.3
-0.2
-0.4
0
Fig. 5. The computed values of the critical entrance or exit angles are shown for the features S21 and B21 observed in the [Zii] azimuth. The critical angles are computed as a function of the fractional expansion of the first-second layer spacing for various different laboratory scattering angles 8. The points indicate the experimentally measured cut-off angles for each scattering angle.
where dij is the spacing between the ith and jth layer. Here a, = 3.15 A is the MO bulk lattice constant. The bulk spacing between adjacent (111) planes is (fi/6)a0. The position of the blocking critical angles were calculated using MARLOWE (version 12.0) [21] by calculating total scattering angles from a static lattice as a function of initial impact parameter along a surface [121] or [21x] chain. Scattering from first, second, or third layers could be distinguished and the minimum exit angles, as a function of the impact parameter, correspond to blocking critical angles. The blocking critical exit angle, (8 - I/J)~, is shown as a function of the interlayer spacing in fig. 5b for one of the B21 features. The experimentally measured values of the cut-off angles, &,, (or 13- Gg,, for blocking), are shown as points on the calculated curves in fig. 5. Each measurement of the position of the shadowing or blocking features provides a value for the spacing of either the first-second or the first-third layer spacing. These values are summarized in table 2. The values consistently indicate a contraction of both spacings. However, before extracting the most probable layer spacing it is necessary to consider these data in view of certain experimental difficulties and of possible interferences of deeper layers. The accuracy in measuring the angle of incidence in this experiment is believed to be better than 5 0.5 O. The uncertainty in determining exit angles is larger however because the exit angles are obtained from 8 - + requiring knowledge of 8 which also has a random error of k 0.5”. The errors given for S,, and S,, (table 2) were determined assuming this random error for # and 8.
136
S.H. Overbury / Surface layer relaxation on Mo(l I I)
Table 2 First and second layer expansion obtained from shadowing and blocking features at various laboratory scattering angles
e(deg)
[l?l] azimuth
s13
s12 s21
B21
s31
110 105 80 60
- 0.17 f 0.05
- 0.225 + 0.04
- 0.075 + 0.02 - 0.06 +_0.02
-0.15*0.05 -0.18iO.05
- 0.30 f 0.04
0 (deg)
[2ii] azimuth 6 12
110 105 90 80 70 65
6 13
s21
B21
B31
-0.16 kO.03 - 0.135 f 0.03 - 0.125 + 0.03 - 0.305 * 0.03 -0.185f0.03 -0.20 *0.03
-0.22 i-0.08 - 0.255 k 0.08 - 0.325 f 0.08
-0.135*0.03 - 0.125 f 0.03
-0.315ztO.08
As stated in the section 2, significant systematic error (&- 1”) in 8 is also possible. Because of this systematic error and the large random error, the values obtained from blocking features are inherently less reliable than those obtained for shadowing features, and it is justified to discard them. It is also important to consider the effects of scattering from deeper layers. As discussed above, the S21 feature observed in [2ii] is strongly affected by the presence of third layer scattering at 8 = 90” where it merges with B31 and there is a third layer contribution at all higher scattering angles. Therefore, the values at 6 >=90” should be discarded. The third layer contribution is predicted to be fully blocked at 8 = 70” corresponding to the minimum of the curve at B = 80” is believed to be too large in fig. 4. The value of S,, obtained (negative) because of residual effects of B31 and is thus discarded. It is concluded on this basis to use only the two values from 0 = 70” and 8 = 65” obtained for this shadowing feature. As discussed in the previous section, the shadowing feature S21 observed in [121] is not expected to include contributions from third or deeper layers at any scattering angle. All three data points from this feature should be valid. Averaging these five data points from both shadowing features leads to a value of a,* = -0.177 &-0.018 as the best value for the contraction of the first layer. Re-examining the values which were discarded, it can be seen that the data together yield a for e = 1100, 105” and 90” (S21 in the [2ii] azimuth)
S. H. Overbuty / Surface layer relaxation on Mo(l I I)
137
systematically lower concentration of a,, = 0.14 f 0.02. This is expected since contributions from deeper layers are expected to reduce the apparent contraction. Also, the widths of these edges (table 1) are broadened relative to those where only first-second layer spacing is contributing (e = 65” and 70”). This is consistent with two different layer spacings contributing at two slightly different values of +!J,thereby broadening the edges for the higher scattering angles. The value obtained at 6 = 80” is six standard deviations away from the best value. The low cut-off angle giving rise to this value was verified repeatedly and is believed to be due to residual effects of the B31 feature passing through S21 and this angle. The position of this feature has been found to be strongly affected by the presence of adsorbates. Finally the blocking features B21 from both azimuths average together to give a value of S,, = -0.273 + 0.046 compared to the values of -0.177 obtained from the shadowing features. A systematic error of only 1.1” in the scattering angle could account for this difference. The values of S31 and B31 give information about the d,,. The two data points from S31 yield the best value of S,, = -0.067 + 0.02 (table 2). If the values obtained for B31 are corrected for an error of ll” in the scattering angle, they yield a value of ai3 = -0.085 which agrees within errors. Both S31 and B31 suffer from the possibility of interference from deeper layer spacings especially to second-fourth layer spacing. Probably the only way to completely eliminate these contributions is to measure these S31 and B31 edges at a total scattering angle of 145” (normal exit angle for S31 and normal entrance angle for B31) where contributions from fourth layer scattering is removed. It was not possible with the present apparatus to work at this scattering angle. Assuming that the second-fourth layer spacing, and deeper layer spacings approach the bulk value, the obtained value of ai3 may be regarded as a lower limit for the actual contraction. The second-third layer spacings, d,,, can be derived from the measured values of a,, and S,,, since a,, = 26,, - S,,. These results yield a value of S,, = 0.043 + 0.044, statistically a nearly insignificant expansion. This number may be affected to an unknown extent by the interference of scattering from deeper layers. The probable sign of this systematic error is such that the actual value of a,, is equal to or less than 0.043. Summarizing, the data indicate a contraction of the first layer (d,,) of 18% and that the second layer (dz3) is not more than about 4% expanded. These values are physically reasonable. The bee (111) face is so open and the layer spacings so short that this apparently large contraction does not result in a large change in bond lengths. The relaxed, first layer atoms have three (second layer) neighbors at 0.850a, and one (fourth layer) atom at 0.827~1,. These bond distances are contracted 1.8% and 4.5% compared to the unrelaxed distance, (G/2) a, = 0.866a,. The distance to third layer atoms in 0.97%~~ which is contracted 2.2% from the unrelaxed distance l.Oa,. For comparison
138
S. H. Overbury / Surface layer relaxation on Mo(lI1)
the bond length in MO dimer [22] is 1.94 A (= 0.616~) which is contracted 29% relative to bulk MO. There have been few other studies of bee (111) surface relaxation. Shih et al. [8] used LEED to study Fe(ll1) and found a first layer contraction of 15.4% with respect to bulk. A later refinement found a contraction of 16.9% in agreement with the present results. The later study also found a contraction in the second interlayer spacing, d,,, of 9.8%. This contraction is in agreement with the predictions of Barnett et al. [lo] for Na(ll1) but differs with the present results for Mo(ll1). Clarke [9] has studied the Mo(ll1) surface and has stated that this surface shows contraction in the first layer in addition to changes in the stacking order. However, apparently no details of these results have been published. The presence of stacking faults should show up as additional features in the 1c,dependence which were not observed. There remain three points of discussion which bear on the accuracy of these layer spacings. The first is that of identifying the 90% point of the edge, #So, as the critical angle. Using the 70% point as suggested by Aono [19] would predict still larger contractions both from shadowing and blocking features yielding a,, = -0.236 and 6,s = -0.120, and thus a,, = -0.004. The contraction of the first layer is then very large while the second layer expansion is reduced to zero. Clearly the difficulty of assigning a critical angle to the measured \c/ dependence is a serious uncertainty in the accuracy of the technique. The second point is the contribution of non-chain-like scattering. Niehus and Comsa [17] have shown that these out-of-plane contributions are greatest when the surface chains are close, and they give rise to additional peaks in the I/J dependence. The (1%) chains on Mo(ll1) are quite close ($@a, apart) but additional peaks are not observed. Considering the surface geometry, it is difficult to see how the possible out-of-plane trajectories could give rise to intensity peaking at the same angles as the observed features S21, B21, etc. It is concluded that although the non-chain-like scattering is present in the background, it does not interfere with the positions of the shadowing and blocking edges. Finally, there remains the possibility of lateral displacements of surface atoms, that is, displacements parallel to the surface. Such displacements would invalidate the determination of the surface layer relaxation. However, no evidence for such displacements exists. The (1 X 1) LEED pattern implies that if there are displacements in the first layer, all atoms must be shifted the same direction and magnitude. The possibility of “small” displacements seems unlikely but cannot be completely eliminated. A large shift such as a stacking reordering is inconsistent with the ion scattering data. 5. Conclusions The angle of incidence dependence of Li+ scattering has been obtained and interpreted. The observed features
from clean Mo(ll1) are readily explained
S. H. Overbuty
/ Surface layer relaxation on Mo(1 II)
139
as shadowing and blocking features coupled with flux peaking at the edges of the shadowing and blocking cones. All observed features are fully consistent with the Mo(ll1) surface being unreconstructed. The position of the features yield surface layer spacings, but considerable care must be taken to assure that conditions are chosen to eliminate contributions from deeper layers. The first-second layer spacing is contracted about 18% while the second-third layer spacing is possibly expanded, but less than 4%. A limitation in the precision of the technique is the difficulty of assigning a critical angle to the broadened, experimentally observable edge and more theoretical and experimental work is needed to clarify this point. The most attractive feature of the technique for determining layer spacings is the simplicity of the analysis.
Acknowledgements The author wishes to thank P.C. Stair for supplying the MO single crystal rod and Benjamin M. DeKoven for cutting, orienting and polishing the Mo(ll1) wafer. Research sponsored by the Division of Chemical Sciences, Office of Basic Energy Sciences, US Department of Energy under contract DE-AC05-840R2-2400 with the Martin Marietta Energy Systems, Inc.
References [l] J. Sokolov, F. Jona and P.M. Marcus, Solid State Commun. 49 (1984) 307, and references therein. [2] D.L. Adams, H.B. Nielsen, J.N. Andersen, I. Stensgaard, R. Feidenhans’l and J.E. Sorensen, Phys. Rev. Letters 49 (1982) 669. [3] H.L. Davis and J.R. Noonan, Surface Sci. 126 (1983) 245. [4] J.N. Andersen, H.B. Nielsen, L. Petersen and D.L. Adams, J. Phys. C (Solid State Phys.) 17 (1984) 173. [5] J.R. Noonan and H.L. Davis, Phys. Rev. B29 (1984) 4349. [6] J.F. van der Veen, R.G. Smeenk, R.M. Tromp and F.W. Saris, Surface Sci. 79 (1979) 212. [7] D.L. Adams, W.T. Moore and K.A.R. Mitchell, Surface Sci. 149 (1985) 407. [8] H.D. Shih, F. Jona, D.W. Jepsen and P.M. Marcus, Surface Sci. 104 (1981) 39; J. Sokolov, F. Jona and P.M. Marcus, Bull. Am. Phys. Sot. 30 (1985) 459. [9] L.J. Clarke, in: Proc. 7th Intern. Vacuum Congr./3rd Intern. Conf. on Solid Surfaces, Vienna, 1977, A-2725 (abstract). [lo] R.N. Bamett, U. Landman and C.L. Cleveland, Phys. Rev. B28 (1983) 1685. [ll] C.L. Fu, S. Oh&hi, E. Wimmer and A.J. Freeman, Phys. Rev. Letters 53 (1984) 675. (12) K.M. Ho and K.P. Bohren, Phys. Rev. B32 (1985) 3446. [13] S.H. Overbury and D.R. Huntley, Phys. Rev. B32 (1985) 6278. (141 S.H. Overbury, P.C. Stair, J. Vacuum Sci. Technol. Al (1983) 1055. [15] J. Ferrante and G.C. Barton, NASA Technical Note D-4735, Washington, DC, 1968. [16] R.M. Lambert, J.W. Linnett and J.A. Schwarz, Surface Sci. 27 (1971) 572. [17] H. Niehus and G. Comsa, Surface Sci. 140 (1984) 18. [18] H. Niehus and G. Comsa, Surface Sci. 152,053 (1985) 93.
140
S. H. Overbuty / Surface layer relaxation on Mo(l I I)
1191 M. Aono, Nucl. Instr. Methods B2 (1984) 374. [20] M.T. Robinson, Tables of Classical Scattering Integrals, US Atomic Energy Commission Report ORNL-4556 (1970). [21] M.T. Robinson, in: Sputtering by Particle Bombardment I, Vol. 47 of Topics in Applied Physics, Ed. R. Behrisch (Springer, Berlin, 1981) pp. 73-144. [22] J.B. Hopkins, P.R.R. Langridge-Smith, M.D. Morse and R.E. Smalley, J. Chem. Phys. 78 (1983) 1627.
Surface Science 175 (1986) 123-140 North-Holland, Amsterdam
SURFACE LAYER RELAXATION ON Mo(ll1) MEASURED BY LOW ENERGY ALKALI ION SCATTERING S.H. OVERBURY Ouk Ridge National Laboratory, Oak Ridge, TN 37831, USA Received
4 December
1985; accepted
for publication
8 April 1986
The surface of clean Mo(ll1) has been studied using Li+ ion scattering at 1000 eV. The dependence of single scattering intensity was measured as a function of incident polar angle in the [121] and the [2ii] azimuths for various total scattering angles. Very pronounced intensity cut-offs are ohserved and are readily assignable to shadowing and blocking effects in scattering from first, second or third layer atoms. After taking certain precautions to avoid interference from deeper layers, the measured positions of the features yield the first-second layer spacing which is found to be strongly contracted by (18 i 2)% compared to the bulk spacing. The method also indicates that the second-third layer spacing is possibly expanded (4+4)%, but this result is uncertain due to possible contributions from deeper layers which make this value an upper limit of the layer spacing. The physical implications of these results and the uncertainties in the technique are discussed.
1. Introduction There has been considerable research interest in determining the structure of metal surfaces. Many metal surfaces are reconstructed, but even those surfaces which do not reconstruct exhibit relaxations of the spacings of the outermost layers. The characterization of these multi-layer relaxations has improved rapidly in the last five years as a result of developments in both experimental and theoretical techniques. Various experimental techniques have been applied to measure surface relaxations although probably the two most frequently applied are low energy electron diffraction (LEED) and medium or high energy ion scattering. These techniques have developed to the point that first, second and occasionally third interlayer spacings are determined [l-9]. Theoretical efforts have been aimed at predicting and explaining both the sign and magnitude of the relaxations and the depth over which the relaxations occur [lo-121. The most actively studied systems are the low index faces of fee metals, especially the (110) face [2-6,11,12]. Jona, Marcus and coworkers [1,8] have studied systematic variations for several faces of Fe, a bee metal. Recently high index surfaces of both fee and bee metals have been examined and in 0039-6028/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
124
S. H. Overbury / Surface layer relaxation on Mo(lI1)
some cases relaxations parallel to the surface exist, as well as perpendicular relaxations [ 1,7]. Certain trends have emerged as a result of both the experimental and theoretical efforts. It is usual for surface relaxation to occur. There is generally a contraction of the first interlayer spacing and a damped oscillatory relaxation of the deeper interlayer spacings. The extent of the contraction of the first layer tends to increase with increasing “roughness” i.e., there is a tendency for larger relaxations on the more open surfaces. Less clear, however is the dependence of the period of the oscillatory relaxations upon the layer stacking sequence. On most low index faces which have been examined, e.g., the Al(110) [4] and Cu(ll0) [2,3], the oscillations change signs at each interlayer spacing reflecting the two-layer stacking sequence. In open surface such as the bee (111) and high index surfaces there are more layers in the stacking sequence and the oscillatory pattern may change. For example, the Fe(210) surface shows a contraction of both the first two interlayer spacings [l] and it has been predicted that Na(ll1) may also show a contraction of the first two interlayer spacings [lo]. However, there are limited data on such surfaces, which may be partly due to the difficulty of the LEED analysis of surfaces with small interlayer spacings [8]. This work describes efforts to use low energy alkali ion scattering to determine surface relaxations on Mo(ll1). Striking features in the angle of incidence dependence are observed which can be readily interpreted and which with certain precautions yield information about the surface layer spacings. In the second section, the essential details are presented regarding the sample preparation and the capabilities and accuracy of the experimental equipment. In the third section, the methods are given by which the angle of incidence dependences are obtained and is followed by detailed interpretation of the observed features. In the fourth section, the procedures are given for determining the layer spacings and the resulting values are discussed in terms of their physical meaning and the accuracy of the technique.
2. Experimental The ion scattering measurements were made on an apparatus described and used previously [13,14]. The electrostatic analyzer (ESA) was modified from previous work by using new apertures which gave it an energy resolution AE/E = 2.0%, and an acceptance half angle to 1.5”. All measurements were done with 1000 eV Li+ ions which were mass analyzed and collimated with maximum divergence of k 0.5 O. Beam currents were typically 30 to 40 pA. The procedures used for accurately determining the polar angle of incidence, 4, defined with respect to the plane of the surface, are described in detail elsewhere [13]. Using these methods, the angles of incidence are believed to be
S. H. Overbury / Surface layer relaxation on Mo(l I I)
125
accurate to within f0.5”. The MO crystal was mounted on a stage which allowed rotation of greater than 165O about the surface normal, allowing various surface crystallographic axes to be rotated into the plane of scattering. The azimuthal angle was repositionable to within 0.5O, and the crystallographic orientation is known to within about 2.0”. The surface normal was within about lo of the scattering plane for all azimuths and the polar angle of incidence, #, was corrected for slight azimuthal variations (5 + O.S”) due to deviations of the surface normal from the actual axis of the azimuthal rotation, The laboratory scattering angle, 8, is defined as the angle between incident direction and final direction of the scattered ions, and the accuracy of this angle is important in this experiment. This angle is determined by the rotation of the ESA and the placement of the sample. The rotation of the ESA is reproducibly set to within 0.5” and calibrated at 0” by optical alignment with the beam line. Determining the proper sample placement along the axis of the beam line is also critical to the accuracy of 19.The sample could be accurately and reproducibly placed at a position determined by optical alignment. However, the uncertainty in the relationship between this position and the actual scattering angle may be responsible for systematic error in 8 of f 1”. The MO single crystal was an elliptical disk (12 mm X 8 mm X 0.5 mm thick) which was mechanically polished using a sequence of SIC and alumina powder down to 1 pm size. The surface normal was oriented to (111) to within 0.25O. The crystal was mounted on MO wires 0.25 mm thick with W/Re thermocouples spring loaded to the back. In the ultra-high vacuum system (ambient pressure 5 1.5 X 10T8 Pa), the sample could be heated up to 1400°C and the sample temperature was routinely monitored both with the thermocouple and with an optical pyrometer. The surface structure and composition were characterized by display LEED and Auger electron spectroscopy performed using the retarding field analyzer of the LEED system. The Mo(ll1) was heated extensively in oxygen to remove carbon impurities ubiquitous to MO. Oxygen and sulfur impurities were readily removed by Ar+ sputtering. In spite of sputtering and repeated oxygen treatments at various temperatures up to 1500 K, there remained a residual peak in the Auger spectrum at about 274 eV and with always about the same intensity. This feature in the Auger spectrum of the “clean” surface is believed to be due to bulk carbon. This conclusion derives from studies of the ethylene exposed surface using AES and Li+ ion . scattering. The ethylene saturated surface (lo-20 L at 400 to 475 K) yields a C Auger peak with peak-to-peak intensity which is 6 to 8 times greater and has a different shape than the residual peak. The intensity of the C peak for the ethylene saturated surface is equivalent to about 9 x lOi cm- 2 (based on a calibration curve generated previously for a Mo(001) surface). The excess carbon due to the ethylene exposure is easily removed with oxygen leaving essentially the same residual C Auger peak. Li+ ion scattering at grazing incidence from the surface exposed to ethylene at
126
S.H. Overbuty / Surface layer relaxation on Mo(lI1)
< 475 K reveals a broad peak near the C single scattering energy. This peak disappears upon annealing to 760 K for 60 s even though the C Auger peak does not decrease. Annealing to 1300 K in vacuum causes substantial decrease in the C Auger peak. These results are consistent with both surface and subsurface forms of carbon the latter giving rise to the residual C Auger peak. In view of the Auger peak shape change, and the redistribution of the carbon, it is difficult to assign a concentration from the residual peak associated with the “clean” surface. Typical Li+ exposures used to record a 1c/dependence were less than 3 x lOI3 cm-‘. Between each measurement the surface was treated to an anneal in 0, to remove carbon impurities, Ar+ sputtering to remove oxygen and any traces of imbedded Li, and finally a 60 s anneal at 1500 K to remove sputter damage. The principle effect of the build-up of impurities or damage during ion scattering measurements was a reduction of the Sll intensity (defined below) relative to the background and to the other peaks in the $ dependence. This reduction is unimportant to the major conclusions. 3. Determination
and interpretation of the rC,dependence
The clean surface exhibited a (1 X 1) LEED pattern as expected for an unreconstructed surface. This is in agreement with the findings of Ferrante and Barton [15] and of Lambert et al. [16]. This structure was therefore assumed and no evidence from the ion scattering contradicted this basic conclusion. A diagram of the geometry of this very open surface is shown in fig. 1. The azimuthal orientation of the Mo(ll1) surface was determined from the ion scattering itself. A 1000 eV Li+ ion beam was brought incident at a grazing incidence angle of 10”. The intensity of the Li+ single scattering peak was then monitored as a function of the azimuthal rotation of the crystal at fixed polar angle. Very sharp drops in intensity were observed at intervals of 60” reflecting the six-fold symmetry of the first layer. The occurrence of these dips is readily interpreted on the basis of shadowing by surface chains. The angle of incidence of 10” is below the critical cut-off angle for (li0) chains with interatom spacing of aa,, but is just above the critical angle for the (121) chains of spacing ~%a,. The dips in intensity therefore correspond to alignment of the scattering plane along a (li0) azimuth. The Mo(ll1) surface is actually three-fold symmetric since the second layer atoms break the six-fold symmetry of the first layer. Therefore, scattering from below the first layer atoms should reflect a reduced symmetry and there are expected to be differences between an angle of incidence dependence along the [121] compared to the [2ii] azimuth. These differences were readily apparent in the I/ dependence (to be discussed below) and allowed complete determination of crystal orientation relative to the scattering plane.
S.H. Overbury / Surface layer relaxation on Mo(l1 I)
127
Mo(ttt)
SURFACE
0=
1st
l
=
AND
4th
2nd
LAYER
3rd
LAYER
LAYERS
(b)
Fig. 1. The Mo(ll1) surface as a cut-away view along representative of the features the edge of the shadow cast the [2ii] azimuth is shown
is shown and indexed (a) as viewed down the surface normal and (b) the [121] azimuth and (c) along the [Zii] azimuth. A trajectory S21 in the [l?l] is shown in (b) and is characterized by incidence at by a first layer atom. A trajectory representative of the feature B21 in in (c) and is characterized by exiting along the edge of the blocking cone cast by a first layer atom.
The Li+ energy distribution was characterized by a large sharp peak somewhat below the kinematical single scattering energy. ‘This “single scattering” peak varied with scattering angle approximately as predicted for kinematical single scattering, but obvious deviations were observed indicating multiple scattering and inelastic loss effects were occurring. Under certain conditions an additional, smaller peak appeared at energies below the main peak due to subsurface multiple scattering trajectories, which occurred only for certain conditions of angle of incidence and of scattering angle. These observations are consistent with previous measurements of Li+ scattering from Mo(100) except that strong focusing, such as occurs near the (100) azimuth of Mo(OOl), was not expected or observed on Mo(ll1). The measurement of principle interest to this work is the dependence of intensity of the single scattering peak upon polar angle of incidence 4. These
S.H. Overbwy / Surface layer relaxation on Mo(I 11)
8, ,
c/ \\
J
1
L .
d
,
[4?4]
AZIMUTH
Li+E
Mo(l44)
i = 4000eV
00
j
i I
I
I
I
I
I
I
I
I
I
I
1
Fig. 2. Typical angle of incidence dependence of the Li’ single scattering is shown for various laboratory scattering angles 19 along the [l?l] azimuth. The data are normalized to unit intensity near the peak of either the Sll feature or the S21 feature. The solid curves guide the eye through the data.
S. H. Overbwy
C’
c
/ Surface layer relaxation on Mo(l .I1)
129
SI1 I
B3j
*
+ 842
+...
L
.t
-I
I
[2ii]
AZIMUTH
Li+--c MdVO Ei = ~oooev
a. I
”
0
40
20
30
40
50
-1
60
I
I
I
I
I
70
80
90
(00
(10
1
Fig. 3. The same as in fig, 2 except along the [2ii] azimuth. The breaks in the curves near 15” result from a change in the analyzer energy. Angles of incidence greater than 90” refer to the supplement of the angle of incidence along the [%l] azimuth.
130
S. H. Overbury / Surface layer relaxation on Mo(ll1)
dependences were obtained by fixing the total laboratory angle, 8, and varying the angle of incidence (and therefore also the exit angle). The peak height (count rate at the peak in the energy ~st~bution) was used as a measure of intensity. Under ideal single scattering conditions, the energy of the peak will not shift with Ic, as long as 0 is constant. In fact, small deviations in the peak position were observed necessitating adjustment of the pass energy of the ESA to remain on the peak. At the most grazing angles of incidence, the peak was at a slightly lower energy (A E/E = 0.01) than for higher values of $J_Typical dependences obtained in this way are shown in figs. 2 and 3 for various scattering angles and for the ]l?l] and the [2ii] azimuths respectively. The scattered intensity exhibits considerable structure as a function of 4. Both azimuths show a peak near 10” for every scattering angle. Otherwise, the two azimuths differ completely. These differences in two azimuths which are 60” apart reflects that the surface is three-fold not six-fold symmetric, and similarly proves that the features at high \tt involve scattering from below the first layer MO atoms. Qualitative measurements made in the [i‘l2] azimuth, which is 120” from the [2ii] azimuth, confirmed the same 4 dependence for both. The structure present in the 4 dependence of figs. 2 and 3 is similar to that first observed and described by Niehus and Comsa 117,181. The structure can be interpreted on the basis of atom shadowing and blocking. The shadowing features occur as a result of the incidence conditions. They correspond to a sharp increase in intensity as 4 is increased, and occur always at nearly the same value of il/ independent of the laboratory scattering angle r?. The blocking features occur as a result of exit conditions. They correspond to an abrupt decrease in intensity as 4 is increased and occur at nearly the same exit angle which under the present experimental conditions is 8 - 4. Their location in the + dependences shown in figs. 2 and 3 varies with 0 in such a way that 8 - J, is almost constant. The shadowing and blocking edges are labeled S and B respectively in figs. 2 and 3. The edges are also accompanied by an intensity peak due to flux peaking at the edge of the shadow cone or blocking cone. The scattering mechanisms responsible for each shadowing and blocking feature can be readily determined by considering the atomic geometry in each azimuth, as shown in figs. lb and lc. When the ions are incident at very grazing angles, II, <. lo”, all surface atoms are in the shadow cone of a preceding atom, so scattering into large scattering angles cannot occur. As \ii is increased, a critical angle is reached when a surface atom emerges from the shadow cone of the preceding atom. The intensity increases abruptly and is additionally enhanced by flux peaking at the shadow cone edge. The intensity increase is a result of (un)shadowing of first layer atoms by first layer atoms (Sll). Considering the [121] azimuth (fig. lb), it can be seen that as IE/ is increased, angles will be reached where the second layer MO atoms will emerge
S. H. Overbuty
/ Surface layer relaxation on Mo(l II)
131
from the shadow cone of first layer atoms giving rise to the feature S21 (shadowing of second layer atoms by first layer atoms). Similarly at still higher angles, the third layer atoms become visible giving rise to S31 (fig. 2). The ability to observe scattering from first, second, or third layer atoms depends upon the path of the exiting ions not being blocked. As 4 is increased (at constant f9), an exit angle will be reached in which particles scattered from second layer atoms will be blocked by first layer atoms (B21). At very grazing exit angles, scattering from first layer atoms will be blocked by an adjacent first layer atom giving rise to Bll. The features Sll, S21, S31, and B21 are all observed in the [l?!l] azimuth as seen in fig. 2. The Bll feature was not sought because of experimental difficulties in working at grazing exit angles. Consideration of the geometry of the [2il] azimuth leads to prediction of features Sll, S21, B21, B31, and Bll which are seen (except Bll) in the + dependence shown in fig. 3. As stated above, the shadowing and blocking features occur at nearly constant value of + and 8 - 4, respectively as 8 is varied. There are, however, small systematic deviations from this trend. The source of this deviation is that different impact parameters are required for scattering into different scattering angles. It is the impact point, displaced from the center of the atom by the impact parameter, which must emerge from the shadow cone to result in scattering into the detector. The extent of the deviations can be calculated as will be shown in the next section. The interpretation of the features given above is complicated by scattering from deeper layers. Shadowing or blocking involving the first and second layer may occur simultaneously with similar interference between second and third layers and between third and fourth layers, etc. The possible presence of these deeper layer contributions is indicated in figs. 2 and 3 in labeling some features, for instance indicating S21 + S32 + . . . The extent to which these deeper layers actually contribute is difficult to predict. At low energies used in this experiment, it is difficult for ions to penetrate without multiple scattering, and in addition inelastic losses become important for ions which penetrate below the second or third layer. The more deeply penetrating ions are therefore removed by the energy discrimination of the ESA. In some cases discrimination against scattering from deeper layers is achieved because of incidence conditions. In the [ljl] azimuth, the S21 feature is observed at angles of incidence much less than the S31 feature. At the angle where S21 is observed, the third layer atoms are well within the shadow cone of the first layer atoms. The third layer therefore does not contribute until larger angles of incidence where the onset is clearly marked by the occurrence of S31. It is possible that ions may reach the third layer (or deeper) by multiple scattering trajectories and scatter into the detector, but these mechanisms contribute to the uniform background intensity and should not yield an abrupt increase in intensity near the S21 edge. Similarly, near S21 the fourth
132
S.H. Overbury / Surface layer relaxation on Mo(I 11)
layer atoms are in the shadow cone of second layer atoms, and so on for deeper layers. Therefore, the conclusion is that the feature at S21 arises from scattering from only the second layer for all scattering angles. A similar argument with respect to exit angles can be advanced to conclude that the B21 feature observed in the [2il] azimuth is a result of scattering from only the second layer for all scattering angles. It is also possible to discriminate against scattering from deeper layers by choosing both angle of incidence and exit angle properly. This is equivalent to the “double alignment” conditions used in medium energy ion scattering [6]. This discrimination is achieved in some cases, as can be seen from examining the 0 dependence. As 8 is decreased, the blocking features shift towards lower + and eventually reach the angle associated with a shadowing feature. It is interesting to consider what happens when these features become coincident. Qualitatively, in the [2ii] azimuth (fig. 3) B31 merges with S21 at 8 near 90” with a large increase in intensity of the merged feature. As 8 is decreased below this, the S21 feature remains while the B31 feature vanishes. The feature B31, which originates from single scattering from third layer atoms, cannot exist at J, below S21, because at these angles scattering from third layer atoms is shadowed by second layer atoms. The intensity of the S21 feature as a function of e is shown in fig. 4. The ratio of the intensity at the peak of the S21 feature to the intensity at tc/= 30” is used since this ratio eliminates the t3 dependence of the single scattering cross section. The intensity maximum at t9 = 94” is the result of scattering from third layer atoms with flux peaking at the edge of both the shadow cone and the blocking cone. The intensity at larger 0 (2 100”) is due to scattering from first, second, and third layer atoms (and possibly deeper) with shadow cone flux peaking on both second and third layer atoms. The intensity at lower 0 (5 SO’) is due to scattering only from first and second layer atoms with shadow cone flux peaking on the second layer atom. Discrimination against scattering from the third or deeper layers is therefore achieved at 8 = 70”. Analogous behavior is observed in the [lzl] azimuth when B21 passes through S31. In this case B21 remains but S31 is eliminated when 8 decreases below about 90”. S31 cannot exist at Ic/ larger than B21, because at these exit angles scattering from third layer atoms is blocked by second layer atoms. This intensity of the S31 feature (as a ratio) is also given in fig. 4. It shows a peak at 8 = 98” due to flux peaking both in shadowing and in blocking, but at 0 = 80”, the ratio drops to below unity reflecting the disappearance of the peak. The widths of the experimentally measured shadowing and blocking edges are broadened by thermal vibrations, multiple scattering and instrumental effects. It is therefore difficult to define precisely a critical angle to the broadened, experimentally measured edge. Various approaches, based on
S. H. Overbuty
I 5
/ Surface layer relaxation on Mo(I I I)
I
I
I
I S21
+ S32
133
I
I
+ 831
Lit-Mo(i!i) E; = (OOOeV
2
3
3
ItPEAK)
UPEAK) I (46’=)
I(30°)
2
0
I
I
I
I
I
I
I
50
60
70
80
90
100
110
,0
8(deg)
Fig. 4. The ratio of the peak-to-background intensities is plotted for the S21 feature observed in the (2fi] azimuth and for the S31 feature observed in the [121] azimuth as a function of laboratory scattering angle 0. Ratios less than unity correspond to disappearance of the peak. The principle contributing scattering mechanisms are’indicated. The curves are drawn to guide the eye through the data. Table 1 Position s) and angles
eCd%)
widths b, of shadowing
and
blocking
features
at various
laboratory
scattering
[121] azimuth s31
s21
B21
Position
Width
Position
Width
Position
Width
110 105 80 60
22.3
2.1
53.1 53.9
4.7 4.2
70.8
3.9
21.6 20.5
2.1 2.1
44.4
5.7
e(de)
[2ii]
azimuth
s21
110 105 90 80 70 65
B31
B21
Position
Width
Position
Width
Position
Width
39.2 39.4 38.7 34.9 36.2 35.5
4.0 4.1 4.0 2.8 3.4 3.0
56.8 51.9 41 .o
5.0 5.3 4.0
87.4 82.9 69.1
2.5 2.8 3.0
49.9
2.6
a) Angle of incidence in degrees where intensity is 90% of maximum. b, Angle in degrees between points at 90% and 20% of maximum.
S. H. Overbuy / Surface layer relaxation on Mo(lI1)
134
different calculations or assumptions, have been suggested. Niehus and Comsa [17,18] use the angle where the edge reaches half-height. Aono [19] has stated that the value corresponding to 70% of the maximum intensity is approximately equal to the critical angle. Overbury and Huntley [13] used computer simulation to conclude that for scattering from Mo(001) the angle, $90, corresponding to 90% of the maximum intensity is appropriate. This value is probably an upper limit of #, for shadowing edges. In the present work the point G9e from the measured 4 dependence will be used as the experimental value of the critical angle. This is done for both shadowing and blocking features. The edges could usually be well approximated by a straight line between the 20% and 90% of maximum intensity, so the width of the peak is defined as the angle between these two points. The values of GgO and the widths for the observed edges (except Sll) are listed in table 1.
4. Determination
of the inter-layer spacings
The position of the shadowing and blocking edges are determined by the structure of the surface and in particular by the inter-layer spacings. The features S21 and B21 depend upon the first-second layer spacing, d,,, and the features S31 and B31 depend upon the first-third layer spacing, d,,. If there are no lateral shifts in the position of the surface atoms, it is possible to use the position of the features to determine these layer spacings. The positions of the shadowing features were calculated as follows. The size of the shadow cone was determined using tables of the laboratory scattering angle and time integral as a function of impact parameter. These tables were calculated for Li on MO using a Thomas-Fermi-Moliere scattering potential has been previously with a screening length of a = 0.90~~. This potential determined to give good agreement with experimental data for Li+ scattering from MO [13]. The routine used to calculate these values was checked against the tables of Robinson [20]. Using the shadow cone size, the critical angles were calculated as a function of inter-layer spacing using the geometry of the unreconstructed Mo(ll1) surface. This was done taking into account the impact parameter of the scattering for the total laboratory scattering angle of interest. The resulting critical angles are appropriate for non-vibrating atoms if there is no blocking along the exit path. Calculated values of the shadowing critical angle are shown in fig. Sa as a function of the layer spacing at various scattering angles for one of the S21 features. The inter-layer spacings are expressed in terms of the fractional expansion, 6,J, defined by
d,, =
(1 + 6;,)(j- i)(i’3,‘6)~,,
S. H. Overbury / Surface layer relaxation on Mo(l II)
40
-
26
+c
(8-‘#),
c
135
-I
24
(deg)
(deq)
32 -0.3
-0.2
-0.4
0
Fig. 5. The computed values of the critical entrance or exit angles are shown for the features S21 and B21 observed in the [Zii] azimuth. The critical angles are computed as a function of the fractional expansion of the first-second layer spacing for various different laboratory scattering angles 8. The points indicate the experimentally measured cut-off angles for each scattering angle.
where dij is the spacing between the ith and jth layer. Here a, = 3.15 A is the MO bulk lattice constant. The bulk spacing between adjacent (111) planes is (fi/6)a0. The position of the blocking critical angles were calculated using MARLOWE (version 12.0) [21] by calculating total scattering angles from a static lattice as a function of initial impact parameter along a surface [121] or [21x] chain. Scattering from first, second, or third layers could be distinguished and the minimum exit angles, as a function of the impact parameter, correspond to blocking critical angles. The blocking critical exit angle, (8 - I/J)~, is shown as a function of the interlayer spacing in fig. 5b for one of the B21 features. The experimentally measured values of the cut-off angles, &,, (or 13- Gg,, for blocking), are shown as points on the calculated curves in fig. 5. Each measurement of the position of the shadowing or blocking features provides a value for the spacing of either the first-second or the first-third layer spacing. These values are summarized in table 2. The values consistently indicate a contraction of both spacings. However, before extracting the most probable layer spacing it is necessary to consider these data in view of certain experimental difficulties and of possible interferences of deeper layers. The accuracy in measuring the angle of incidence in this experiment is believed to be better than 5 0.5 O. The uncertainty in determining exit angles is larger however because the exit angles are obtained from 8 - + requiring knowledge of 8 which also has a random error of k 0.5”. The errors given for S,, and S,, (table 2) were determined assuming this random error for # and 8.
136
S.H. Overbury / Surface layer relaxation on Mo(l I I)
Table 2 First and second layer expansion obtained from shadowing and blocking features at various laboratory scattering angles
e(deg)
[l?l] azimuth
s13
s12 s21
B21
s31
110 105 80 60
- 0.17 f 0.05
- 0.225 + 0.04
- 0.075 + 0.02 - 0.06 +_0.02
-0.15*0.05 -0.18iO.05
- 0.30 f 0.04
0 (deg)
[2ii] azimuth 6 12
110 105 90 80 70 65
6 13
s21
B21
B31
-0.16 kO.03 - 0.135 f 0.03 - 0.125 + 0.03 - 0.305 * 0.03 -0.185f0.03 -0.20 *0.03
-0.22 i-0.08 - 0.255 k 0.08 - 0.325 f 0.08
-0.135*0.03 - 0.125 f 0.03
-0.315ztO.08
As stated in the section 2, significant systematic error (&- 1”) in 8 is also possible. Because of this systematic error and the large random error, the values obtained from blocking features are inherently less reliable than those obtained for shadowing features, and it is justified to discard them. It is also important to consider the effects of scattering from deeper layers. As discussed above, the S21 feature observed in [2ii] is strongly affected by the presence of third layer scattering at 8 = 90” where it merges with B31 and there is a third layer contribution at all higher scattering angles. Therefore, the values at 6 >=90” should be discarded. The third layer contribution is predicted to be fully blocked at 8 = 70” corresponding to the minimum of the curve at B = 80” is believed to be too large in fig. 4. The value of S,, obtained (negative) because of residual effects of B31 and is thus discarded. It is concluded on this basis to use only the two values from 0 = 70” and 8 = 65” obtained for this shadowing feature. As discussed in the previous section, the shadowing feature S21 observed in [121] is not expected to include contributions from third or deeper layers at any scattering angle. All three data points from this feature should be valid. Averaging these five data points from both shadowing features leads to a value of a,* = -0.177 &-0.018 as the best value for the contraction of the first layer. Re-examining the values which were discarded, it can be seen that the data together yield a for e = 1100, 105” and 90” (S21 in the [2ii] azimuth)
S. H. Overbuty / Surface layer relaxation on Mo(l I I)
137
systematically lower concentration of a,, = 0.14 f 0.02. This is expected since contributions from deeper layers are expected to reduce the apparent contraction. Also, the widths of these edges (table 1) are broadened relative to those where only first-second layer spacing is contributing (e = 65” and 70”). This is consistent with two different layer spacings contributing at two slightly different values of +!J,thereby broadening the edges for the higher scattering angles. The value obtained at 6 = 80” is six standard deviations away from the best value. The low cut-off angle giving rise to this value was verified repeatedly and is believed to be due to residual effects of the B31 feature passing through S21 and this angle. The position of this feature has been found to be strongly affected by the presence of adsorbates. Finally the blocking features B21 from both azimuths average together to give a value of S,, = -0.273 + 0.046 compared to the values of -0.177 obtained from the shadowing features. A systematic error of only 1.1” in the scattering angle could account for this difference. The values of S31 and B31 give information about the d,,. The two data points from S31 yield the best value of S,, = -0.067 + 0.02 (table 2). If the values obtained for B31 are corrected for an error of ll” in the scattering angle, they yield a value of ai3 = -0.085 which agrees within errors. Both S31 and B31 suffer from the possibility of interference from deeper layer spacings especially to second-fourth layer spacing. Probably the only way to completely eliminate these contributions is to measure these S31 and B31 edges at a total scattering angle of 145” (normal exit angle for S31 and normal entrance angle for B31) where contributions from fourth layer scattering is removed. It was not possible with the present apparatus to work at this scattering angle. Assuming that the second-fourth layer spacing, and deeper layer spacings approach the bulk value, the obtained value of ai3 may be regarded as a lower limit for the actual contraction. The second-third layer spacings, d,,, can be derived from the measured values of a,, and S,,, since a,, = 26,, - S,,. These results yield a value of S,, = 0.043 + 0.044, statistically a nearly insignificant expansion. This number may be affected to an unknown extent by the interference of scattering from deeper layers. The probable sign of this systematic error is such that the actual value of a,, is equal to or less than 0.043. Summarizing, the data indicate a contraction of the first layer (d,,) of 18% and that the second layer (dz3) is not more than about 4% expanded. These values are physically reasonable. The bee (111) face is so open and the layer spacings so short that this apparently large contraction does not result in a large change in bond lengths. The relaxed, first layer atoms have three (second layer) neighbors at 0.850a, and one (fourth layer) atom at 0.827~1,. These bond distances are contracted 1.8% and 4.5% compared to the unrelaxed distance, (G/2) a, = 0.866a,. The distance to third layer atoms in 0.97%~~ which is contracted 2.2% from the unrelaxed distance l.Oa,. For comparison
138
S. H. Overbury / Surface layer relaxation on Mo(lI1)
the bond length in MO dimer [22] is 1.94 A (= 0.616~) which is contracted 29% relative to bulk MO. There have been few other studies of bee (111) surface relaxation. Shih et al. [8] used LEED to study Fe(ll1) and found a first layer contraction of 15.4% with respect to bulk. A later refinement found a contraction of 16.9% in agreement with the present results. The later study also found a contraction in the second interlayer spacing, d,,, of 9.8%. This contraction is in agreement with the predictions of Barnett et al. [lo] for Na(ll1) but differs with the present results for Mo(ll1). Clarke [9] has studied the Mo(ll1) surface and has stated that this surface shows contraction in the first layer in addition to changes in the stacking order. However, apparently no details of these results have been published. The presence of stacking faults should show up as additional features in the 1c,dependence which were not observed. There remain three points of discussion which bear on the accuracy of these layer spacings. The first is that of identifying the 90% point of the edge, #So, as the critical angle. Using the 70% point as suggested by Aono [19] would predict still larger contractions both from shadowing and blocking features yielding a,, = -0.236 and 6,s = -0.120, and thus a,, = -0.004. The contraction of the first layer is then very large while the second layer expansion is reduced to zero. Clearly the difficulty of assigning a critical angle to the measured \c/ dependence is a serious uncertainty in the accuracy of the technique. The second point is the contribution of non-chain-like scattering. Niehus and Comsa [17] have shown that these out-of-plane contributions are greatest when the surface chains are close, and they give rise to additional peaks in the I/J dependence. The (1%) chains on Mo(ll1) are quite close ($@a, apart) but additional peaks are not observed. Considering the surface geometry, it is difficult to see how the possible out-of-plane trajectories could give rise to intensity peaking at the same angles as the observed features S21, B21, etc. It is concluded that although the non-chain-like scattering is present in the background, it does not interfere with the positions of the shadowing and blocking edges. Finally, there remains the possibility of lateral displacements of surface atoms, that is, displacements parallel to the surface. Such displacements would invalidate the determination of the surface layer relaxation. However, no evidence for such displacements exists. The (1 X 1) LEED pattern implies that if there are displacements in the first layer, all atoms must be shifted the same direction and magnitude. The possibility of “small” displacements seems unlikely but cannot be completely eliminated. A large shift such as a stacking reordering is inconsistent with the ion scattering data. 5. Conclusions The angle of incidence dependence of Li+ scattering has been obtained and interpreted. The observed features
from clean Mo(ll1) are readily explained
S. H. Overbuty
/ Surface layer relaxation on Mo(1 II)
139
as shadowing and blocking features coupled with flux peaking at the edges of the shadowing and blocking cones. All observed features are fully consistent with the Mo(ll1) surface being unreconstructed. The position of the features yield surface layer spacings, but considerable care must be taken to assure that conditions are chosen to eliminate contributions from deeper layers. The first-second layer spacing is contracted about 18% while the second-third layer spacing is possibly expanded, but less than 4%. A limitation in the precision of the technique is the difficulty of assigning a critical angle to the broadened, experimentally observable edge and more theoretical and experimental work is needed to clarify this point. The most attractive feature of the technique for determining layer spacings is the simplicity of the analysis.
Acknowledgements The author wishes to thank P.C. Stair for supplying the MO single crystal rod and Benjamin M. DeKoven for cutting, orienting and polishing the Mo(ll1) wafer. Research sponsored by the Division of Chemical Sciences, Office of Basic Energy Sciences, US Department of Energy under contract DE-AC05-840R2-2400 with the Martin Marietta Energy Systems, Inc.
References [l] J. Sokolov, F. Jona and P.M. Marcus, Solid State Commun. 49 (1984) 307, and references therein. [2] D.L. Adams, H.B. Nielsen, J.N. Andersen, I. Stensgaard, R. Feidenhans’l and J.E. Sorensen, Phys. Rev. Letters 49 (1982) 669. [3] H.L. Davis and J.R. Noonan, Surface Sci. 126 (1983) 245. [4] J.N. Andersen, H.B. Nielsen, L. Petersen and D.L. Adams, J. Phys. C (Solid State Phys.) 17 (1984) 173. [5] J.R. Noonan and H.L. Davis, Phys. Rev. B29 (1984) 4349. [6] J.F. van der Veen, R.G. Smeenk, R.M. Tromp and F.W. Saris, Surface Sci. 79 (1979) 212. [7] D.L. Adams, W.T. Moore and K.A.R. Mitchell, Surface Sci. 149 (1985) 407. [8] H.D. Shih, F. Jona, D.W. Jepsen and P.M. Marcus, Surface Sci. 104 (1981) 39; J. Sokolov, F. Jona and P.M. Marcus, Bull. Am. Phys. Sot. 30 (1985) 459. [9] L.J. Clarke, in: Proc. 7th Intern. Vacuum Congr./3rd Intern. Conf. on Solid Surfaces, Vienna, 1977, A-2725 (abstract). [lo] R.N. Bamett, U. Landman and C.L. Cleveland, Phys. Rev. B28 (1983) 1685. [ll] C.L. Fu, S. Oh&hi, E. Wimmer and A.J. Freeman, Phys. Rev. Letters 53 (1984) 675. (12) K.M. Ho and K.P. Bohren, Phys. Rev. B32 (1985) 3446. [13] S.H. Overbury and D.R. Huntley, Phys. Rev. B32 (1985) 6278. (141 S.H. Overbury, P.C. Stair, J. Vacuum Sci. Technol. Al (1983) 1055. [15] J. Ferrante and G.C. Barton, NASA Technical Note D-4735, Washington, DC, 1968. [16] R.M. Lambert, J.W. Linnett and J.A. Schwarz, Surface Sci. 27 (1971) 572. [17] H. Niehus and G. Comsa, Surface Sci. 140 (1984) 18. [18] H. Niehus and G. Comsa, Surface Sci. 152,053 (1985) 93.
140
S. H. Overbuty / Surface layer relaxation on Mo(l I I)
1191 M. Aono, Nucl. Instr. Methods B2 (1984) 374. [20] M.T. Robinson, Tables of Classical Scattering Integrals, US Atomic Energy Commission Report ORNL-4556 (1970). [21] M.T. Robinson, in: Sputtering by Particle Bombardment I, Vol. 47 of Topics in Applied Physics, Ed. R. Behrisch (Springer, Berlin, 1981) pp. 73-144. [22] J.B. Hopkins, P.R.R. Langridge-Smith, M.D. Morse and R.E. Smalley, J. Chem. Phys. 78 (1983) 1627.