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THE RELATIONSHIP BETWEEN THE
METASTABLE AND STABLE PHASES OF Pb/Si (111)
F. Grey, R. Feidenhans’L, M. Nielsen, R. Johnson
To cite this version:
F. Grey, R. Feidenhans’L, M. Nielsen, R. Johnson. THE RELATIONSHIP BETWEEN THE
METASTABLE AND STABLE PHASES OF Pb/Si (111). Journal de Physique Colloques, 1989,
50 (C7), pp.C7-181-C7-188. �10.1051/jphyscol:1989718�. �jpa-00229692�
CoLLOQUE D E PHYSIQUE
Colloque C7, suppl6ment au nO1O, Tome 50, octobre 1989
THE RELATIONSHIP BETWEEN THE METASTABLE AND STABLE PHASES OF Pb/Si (111)
F. GREY, R. FEIDENHANS 'L, M. NIELSEN and R. L. JOHNSON"
~ i s d National Laboratory, DK-4000 Roskilde, Denmark
11 Institute for Experimental Physics. University of Hamburg, 0-2000 Hamburg 52, F.R.G.
Le ddpst de Pb sur la surface Si(111)7x7 2 tempdrature ambiante induit une phase mgtastable bidimensionnelle(2d) .A l'aide de la diffusion en surface de rayons X 3 angle d'incidence rasant, nous montrons que cette phase est une structure 7x7 commensurable,mais que la dis- tribution des intensitds des facteurs de structure est trgs diff6rente de ~i(111)7x7. Une bonne interprgtation qualitative de ce &eau de diffusion est que Pb forme un assemblage compact 2d avec 8x8 atomes de Pb par maille 7x7 de Si. Lors d'un recuit de lT6chantillon 3 200°C, la structure m6tastable 7x7 se transforme irr6versiblement en une phase stable qui est incommensurable avec le substrat de Si.Cette phase incommensurable est aussi un empile- ment compact, mais le vecteur de rdseau Pb [ l ,O
1,
au lieu d'8tre paralldle avec Si(
l ,O lcommedans la phase 7x7, est tourn6 30'. Abstract
When Pb is deposited on the Si(111)7x7 surface at room temperature,a metastable two-dimen- sional(2d) phase results. Using grazing incidence synchrotron surface x-ray diffraction, we show that this phase is a commensurate 7x7 structure, but with a very different structure factor intensity distribution from the Si(111)7x7.~ good qualitative interpretation of the diffraction pattern is that Pb forms a 2d close-packed structure, with 8x8 Pb atoms per 7x7 Si unit cell. Upon annealing at 200°C,the metastable 7x7 phase transforms irreversibly into a stable phase that is incommensurate with the Si substrate. This incommensurate phase is also a 2d close-packed structure,but the ~bll,01 lattice vector,instead of being parallel with Sil1,01 as in the 7x7 phase, is rotated 30°.
1. Introduction
Pb grows on S i ( l l 1 ) first a s a 2d layer, then as 3d crystallites (Stranski-Krastanov growth mode). In this article we focus on the dense 2d Pb layer that coexists with the 3d crystallites, and the dependence of its structure on preparation conditions.
In an early LEED study, Estrup and Morrison (1) deposited Pb on Si(111)7X7 a t room temperature, and observed the 7 X 7 pattern to change a s a function of coverage. Gradually there appeared "extra spots"
outside the six main Si spots (the Si(1,O) reflections in LEED notation). The interpretation was that Pb grew a s an incommensurate close-packed layer, with the Pb[l,Ol vector parallel to Si[l,Ol, and with a Pb- Pb separation nearer to 3.50
W
(bulk Pb interatomic distance) than 3.84A
( Si[l,O] basisvector).Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989718
In a more recent study of Pb/Si(lll), Saitoh et a1.(2), observed a similar phenomenon: six reflections could be seen in LEED around the Si(1,O) reflection, the strongest being the one furthest from the origin. The interpretation was that this pattern was due to double diffraction between a 2d close-packed Pb layer and the Si substrate. Saitoh e t al. also pointed out that the Pb-Pb bondlength in this structure might be less than 3.50
A,
tending towards a commensurate relationship Pb-Pb : Si-Si = 7:8 with a Pb-Pb bondlength of 3.36A.
The S i ( l l l ) 7 X 7 might thus play a role in stabilizing this structure.In both the LEED studies just mentioned, it was found that on annealing above about 300" C (or on depositing the same amount of Pb a t 340" C) there resulted a d 3 x d 3 R 3 0 ° strucuture. In both cases, the interpretation was that Pb again formed a 2d close-packed layer, but this time with the Pb[1,0]
lattice-vector rotated 30" relative to the Si[l,Ol. The Pb-Pb bondlength would have to be 3.33
a
in order to achieve lattice matching with the Si substrate. A very similar model has been derived from surface x-ray diffraction measurements of the close-packed &phase of ~ b / G e ( l l l ) d 3 X 4 3 ~ 3 0 " (3).We note that Le Lay et al. have recently proposed a quite different picture (4). They observe no new features on room-temperature deposition of Pb on S i ( l l l ) , only a gradual decay of the 7 x 7 into a
1x1
pattern. After annealing, they also find a d 3 x d 3 R 3 o 0 structure. Based on their quartz microbalance coverage measurements, they deduce a coverage of 1ML (one monolayer [ML] is defined a s one Pb atom per surface S i atom) for this phase, whereas a close-packed structure should have a coverage of 413 ML.
They therefore propose a structure that is essentially a 1 X l mesh of Pb atoms. Subsurface relaxations are invoked to give the observed d 3 X d 3 ~ 3 0 " symmetry.
In this article, we report surface x-ray diffraction measurements which show that the initial room- temperature deposited phase i s in fact a commensurate 7 X 7 structure, whereas the phase obtained upon annealing, or hot deposition, is incommensurate. Both phases are essentially close-packed Pb structures, the Pb[l,O] lattice vector being parallel to Si[l,O] in the 7 x 7 phase, and rotated 30" relative to Si[l,O] in the incommensurate phase.
2. Experimental Method
High purity Si was cut, polished and etched to give a mirror-like surface with a crystallographic misorietation of less than 0.1". The samples were cleaned in the ultra-high-vacuum (UHV) preparation chamber of the Flipper 11 photoemission bearnline in HASYLAB, the Hamburg Synchrotron Radiation Laboratory. Annealing the samples a t 900" C for several hours and slowly cooling resulted in sharp Si(111)7X 7 LEED patterns, and valence band photoemission gave no indication of any contaminant. Pb was deposited from a BN effusion cell a t a rate of 0.2ML/minute. We verified by core-level photoemission that annealing the metastable phase a t 250" C to obtain the stable phase lead to no noticeable change i n the Pb coverage. We note the following features apparent in photographs of the resulting LEED patterns:
a) The pattern after room-temperature deposition did not indicate extra spots, but appeared to be a 7 X 7 pattern with a much altered intensity distribution. The backround was considerably higher than for the clean 7 X 7 surface, and there were weak streaks of intensity along the high-symmetry directions.
b) Annealing a t 250" C resulted in a d 3 ~ d 3 ~ 3 0 " pattern, but the peaks appeared considerably more diffuse than i n the case of annealed ~ b / ~ e ( l l l ) d 3 xd3R30°. As was noted by Le Lay e t al., the fractional order reflections with indices (h,k) are absent if either h or k has an odd numerator.
After preparation, each sample was transferred i n vacuo to a transportable UHV chamber which maintained a pressure of 5.10-l0 mbar during the experiment. The chamber was detached from Flipper
JIand mounted on a Z-axis vertical scattering x-ray diffractometer a t the 32-pole wiggler line W1 in HASYLAB. The x-rays were monochromated by two Si(ll1) crystals. The x-ray wavelength was 1.390
A.
The beam was focused by a gold-coated mirror. The alignment of the crystal for surface diffraction a t grazing angles of incidence has been described in detail elsewhere (5). The grazing angle of incidence was 0.16". A position sensitive detector (PSD) subtending 4" perpendicular to the surface and 0.8" i n the surface plane was used to measure integrated intensities of surface Bragg reflections. The integrated intensities were collected by sample rotation scans (m-scans).
The transportable UHV chamber is equipped for heating and cooling the sample. Heating was achieved in this case by passing current directly through the Si substrate. Temperature was measured by a W/Rh thermocouple making pressure contact with the back of the sample. Three samples were used in this study; two were cold-deposited and heated in-situ in the transportable UHV chamber, the third was hot deposited (substrate a t 250" C). In all three cases, the coverage was estimated a t about 2ML, and Bragg reflections due to bulk Pb crystallites could be measured by x-ray diffraction. The orientation of the crystallites was P b ( l l l ) / / S i ( l l l ) and P b ( l i o ) / / S i ( l i ~ ) , a s reported previously (4). The coexistence of the 3d crystallites indicates that the 2d phase is saturated.
3. Analysis
The high resolution in reciprocal space obtainable with surface x-ray diffraction, compared to standard LEED equipment, leads immediately to the following conclusions:
a) The room-temperature deposited structure is a commensurate 7X 7 phase. The six reflections around each Si(1,O) reflection observed by Saitoh et a1.(2) can be indexed as fractional order reflections of a 7 x 7 strucuture, as can all other observed reflections. The strongest reflection is (8/7,0). Bearing in mind that multiple scattering is negligible for surface x-ray diffraction, we conclude that this diffraction pattern i s not, as Saitoh et al. suggested, the result of double diffraction between an incommensurate Pb layer and the Si substrate. We shall henceforth refer to this phase asPb/Si(lll)7 X 7.
b) The annealed (or hot-deposited) structure is an incommensurate close-packed Pb layer. The Pb(1,O) reciprocal vector of this incommensurate structure is about 2.3% shorter than the (2/3,2/3) reflection of a commensurate d 3 X d 3 ~ 3 0 " structure, corresponding to a Pb lattice with a n average Pb-Pb bondlength of 3.40
A.
The degree of incornmensuration is found to depend sensitively on temperature and coverage.The diffraction peaks from the incommensurate phase a r e considerably broader t h a n for t h e commensurate structure, and overlap the (2/3,2/3) position, which may explain why this structure was mistaken for a commensurate phase in the LEED studies. We shall henceforth refer to this structure a s Pb/Si(l11)R3O0 i.
Having clarified the correct crystallographic notation for the stable and metastable phases, we have made measurements to determine their atomic geometry. A detailed analysis of our results will be presented elsewhere; here we outline the main features.
To determine that this structure is commensurate, we have made high resolution scans of the (8/7,0) peak, using as reference the (1,l) in-plane bulk reflection of Si. We obtain for the position of the peak along the h direction h=1.1427-10.0002 (8/7=1.14286). The width of this peak is, for reference, 12.1.10-3 A-1 radially and 8.7-10-3 A-1 transversally (instrumental resolution 1.5.10-3 a-1 ). This implies spatial coherence lengths on the surface of 700
fi
or more.We have collected 145 fractional-order Bragg intensities of this structure, of which 97 are symmetry non- equivalent. The data come from measurements on two samples. Reproducibility between samples and between symmetry equivalent reflections on each sample was a t the 10% level. After correction for cross- beam area and Lorentz factor we obtain a set of structure factor intensities (see ref. 5 for details).
The main feature of the diffraction pattern is that the intensity is concentrated on the high-symmetry axes joining the integer-order Si reflections, and especially near integer multiples of (817,O). A Patterson function (electron density autocorrelation function) can be constructed directly from the data, without reference to any model (5). This function is a map of the interatomic vectors in the unit cell. A contour plot of this function in the 7 X 7 unit cell is shown in Figure 1.
Figure 1: Patterson function (electron density autocorrelation function) of Pb/Si(lll)7 X 7. Only positive contours are shown. The solid right-angle triangle is the irreducible unit of the Patterson function.
The Patterson function suggests an 8 X 8 mesh of atoms in a 7 X 7 unit cell, An 8 X 8 unrelaxed mesh of Pb atoms is essentially a 1 X 1 structure with a lattice parameter 718 that of the SiE1,Ol vector. Such a structure would have Bragg intensity a t multiples of (8/7,0), in qualitative agreement with the data. With this model a s a starting point we have made a least-squares refinement. We use $,the least-squares residual, a s a measure of goodness of fit of model to data (for a description, see ref. 5 ).
For a n 8 X 8 unrelaxed Pb structure, = 23. If the Pb atoms are allowed to relax while preserving 6rnm symmetry, x2= l1 (10 structural fit parameters plus an overall scale factor). In the resulting relaxation pattern the Pb lattice expands near the centre of the unit cell, adopting a lattice parameter nearer the bulk value. There is a concomitant contraction of the Pb lattice near the corners of the unit cell. Allowing the occupation of the Pb sites to vary as well (10 more parameters) we obtain for a model where the corner atoms have a population of 5 % f 10% and the atoms nearest the corner have a 25%f 10%
population. The other sites are fully populated within errors. In the above fitting procedure, the Pb Debye-Waller factor was held a t its bulk value. Releasing this parameter did not improve t h e fit markedly.
Partial occupancy suggests that there is disorder in the structure near the corners of the unit cell, which is reasonable in view of the relaxation pattern, and consistent with the high backround seen in LEED.
This disorder could explain why i t has not been possible to obtain a satisfactory fit with a single model, even though the model appears qualitatively correct.
We note that a 7 X7 bilayer of Si atoms contributes only about 5% of the intensity of an 8 X 8 Pb layer.
Including Si atoms in order to refine the model cannot, therefore, have much effect. Nevertheless, guided by the dimer-adatom-stacking-fault model for Si(111)7X7, we included i n the model a n unrelaxed stacking faulted Si bilayer and Si dimers (but no Si adatoms) which lead to a slight improvement,x2 = 7.
We emphasize that the measurements reported here are made with perpendicular momentum transfer close to zero (grazing angles of incidence and exit for the x-rays), and therefore we are not sensitive to possible vertical relaxations of the atoms: we measure only the projected surface structure.
Only two symmetry independent reflections can be seen for this phase a t about (0.65,0.65) and (1.95,O);
these reflections can be indexed as Pb(1,O) and Pb(1,l). The Pb(2,O) reflection near (413,413), could not be detected in our measurements. Also, in contrast to ~ b / ~ e ( l l l ) d 3 X d 3 ~ 3 0 " @ ( 3 ) , no diffracted intensity i s measured a t (113,113) or (413,113). These reflections are forbidden for a simple close-packed structure, but occur for a commensurate d 3 structure due to the symmetry breaking of the substrate. As mentioned above, these reflections are also absent in LEED patterns of PblSi(ll1).
.'
c-.'. /
(213.213).(
0,o (1,O 1
Figure 2: Sketch of the reciprocal space of the Pb/Si(lll)R30° i surface
.
The expanded region around the (213,213) position shows the fundamental Pb peak of the incommensurate layer a t (0.65,0.65) i n Si coordinates. The expected positiolis of two satellite peaks, due to domain-wall formation, are indicated.Figure 2 shows a sketch of the reciprocal space of PblSi(lll)R30° i. The continuous line in Figure 3 is a measured radial scan through the Pb(1,O) peak of the incommensurate structure for the hot-deposited s a m p l e , i n d i c a t e d a s s c a n 1 i n F i g u r e 2. T h e G a u s s i a n - f i t t e d p e a k p o s i t i o n i s (0.6515,0.6515)
+
(.0005,.0005). The radial width of the peak is 0.048 A-1, and the transverse width (scan not shown) is 0.057 A-l, the experimental resolution being 1.5.10-3 A-l. This should be compared with the values quoted above for the (8/7,0) reflection, a t approximately the same momentum transfer. The typical spatial coherence of the structure is thus about 130a.
Figure 3: Solid line: measured radial scan
7
-
through the fundamental Pb reflection of-
6 - Pb/Si(lll)R30° i (scan 1 i n Figure 2), t h eU W
V) vertical dashed l i n e i n d i c a t e s t h e com-
z 5 -
-.
V ) W
mensurate (213,2/3) position. Points: measured 5 4 -
0 scan i n Si(1,O) direction through t h e fun-
Y
3 - damental Pb reflection, a shoulder can be seen
L
V) near the expected satellite position (scan 2 i n
B 2 - l -
Figure 2). Both scans are plotted in units of Si(1,O).
r l
5.6 5.8 6 . 0 6 . 2 6.4 6.6 6 . 8 7 . 0 xio-l X IN UNITS OF (1,O)
As Frank and van der Merwe have pointed out (6), the interaction between a periodic potential and a lattice of atoms that has an incommensurate periodicity can produce a domain wall structure. This superstructure leads to extra "satellite" reflections in the diffraction pattern.If the walls are sharp, several of these superstructure reflections will have significant intensity. Pb/Si(lll)7 X7 can be thought of a s an extreme example, where a Pb(ll1) layer is forced to adopt a commensurate superstructure due to the underlying Si(111)7X7. If the wall region is broad, intensity will be concentrated in only a few satellite reflections near the position of the incommensurate peak. If the walls are completely washed out, corresponding to no interaction, only the incommensurate peak remains.
There exists a simple recipe for generating the superstructure reflections in the case of weak interactions (harmonic approximation) (7). In the present case, the characteristic reciprocal lattice vector of the superstructure is expected to be 3 X (213-.6515) =0.0455 in units of Si(1,O). The strongest satellites are expected near the commensurate position (2/3,2/3),as indicated in Figure 2.
A scan along the Si(1,O) direction through the incommensurate peak a t (0.6515,0.6515) is shown in Figure 3 (points). A shoulder c a n clearly be seen n e a r t h e expected s a t e l l i t e position 0.6515 0.0455 = 0.697, corresponding to one of the two satellites indicated in Figure 2. A two-Gaussian fit to this line shape gives a satellite position of 0.690 f 0.005, close to the predictedvalue.
The two satellites indicated in Figure 3 can more clearly be seen in a transverse scan (a-scan) shown in Figure 4. The solid line is a two-Lorentzian fit to the data. The center of the scan i s the point (0.6749,0.6749). The separation of the peaks in angular units is 2.36" , which corresponds to an angle of 61"
+
1" subtended a t the incommensurate (0.6515,0.6515) position. In other words, the satellites are along high-symmetry directions relative to the incommensurate peak.I l I l I
1.4- Figure 4 : Points: Sample rotation scan ( a -
We note finally that the superstructure lattice vector is very close to that for a 2 2 x 2 2 unit cell. The characteristic size of these superstructure domains is thus 85
82.
The spatial coherence length derived from the peak widths is 130A.
The superstructure preserves coherence over only about two domains. This i s why the the superstructure peaks cannot be properly resolved.G i , 2 -
W V) Z
-.
W I- 1.0-
5 0.8- ,IY
0.6-
C C( m
0.4-
!=
M0 . 2
4. Conclusion
scan) through t h e s a t e l l i t e reflections of
) L I ~
Pb/Si(lll)R3t)"i two-Lorentzian fit. (scan The 3 centre in Figure of the 2). scan Solid is line: the point (0.6749,.6749). The separation of t h e satellites corresponds to a subtended angle of 61"+
1" a t the incommensurate position (0.6516,.6515). The satellites are t h u s along high-symmetry directions relative to t h eI I I I I
The stable and metastable dense 2d phase of Pb/Si(lll) discussed here, and the dense 2d phase of P b / G e ( l l l ) (3) are all similar, in that they are essentially close-packed Pb structures with a lattice parameter slightly less than the bulk Pb lattice parameter. On Ge(ll1) the close-packed layer can adapt a
-3 -2 -1 o i 2 3 fundamental Pb peak, as shown in Figure 2.
OUEGA [DEGREES]
commensurate d 3 structure, corresponding to a 1% compression of the Pb layer relative to a bulk P b ( l l 1 ) layer. On S i ( l l l ) , a commensurate d 3 structure would require a 5% compression relative to the bulk lattice parameter. This is apparently too much; the Pb lattice adopts instead a n incommensurate structure, with a mean lattice parameter corresponding to a 2.3% compression relative to a bulk P b ( l l 1 ) layer. We find evidence for superstructure ordering of this incommensurate layer due to domain wall formation, though the superstructure is only coherent over about two domains.
The metastable phase of Pb/Si(lll), obtained by room-temperature adsorption onto the Si(111)7X7 structure, has also a close-packed structure, which is essentially a n 8 x 8 Pb mesh in a 7 X 7 unit cell. Such a n arrangement corresponds to a 4.0% compression, relative to a bulk P b ( l l 1 ) layer. The 7 x 7 super- structure therefore appears unfavourable in comparison with the the stable incommensurate phase.
Ideally the Pb layer should adopt a larger Pb-Pb:Si-Si ratio, but in this case the superstructure domains are effectively pinned a t the commensurate 7X 7 size by the underlying Si(111)7 X7. We find evidence for partial occupancy of Pb atoms near the corner of the 7 X 7 unit cell, presumably reflecting a n attempt to accomodate excess strain. When the underlying Si(111)7X7 is removed by heat treatment, i t becomes favourable for the Pb layer to rotate 30" , since in this orientation the superstructure domains can be larger, reducing the amount of energetically unfavourable dense domain walls. For example, consider a 2.3% compressed Pb layer on a S i ( l l 1 ) l X l surface: the unrotated P b layer would have a n 8x8 superstructure, versus the 22X 22 superstructure for the 30" rotated layer.
The above arguments for the relative stability of the phases are crude. We do not, for example, take into account the ability of the P b layer to accomodate excess strain by relaxations perpendicular to t h e surface. Nevertheless, these arguments seem to provide a good description of our measurements.
We note finally the interesting fact that, although the chemisorption of Pb alone is apparently not enough to remove the stacking faults of the S i ( l l l ) 7 X 7 structure, these faults can be irreversibly removed by a very mild heat treatment (200" C) in the presence of Pb. In contrast, the reversible transformation of clean Si(11117 X 7 + l X l occurs a t 850°C.
We acknowledge useful discussions with J a n Skov Pedersen. We would like to thank the staff a t HASYLAB for their help. This work was supported by the German Federal Ministry for Science and Technology, the Max Planck Society and the Danish National Research Council.
References
1) P. J. Estrup and J. Morrison, Surf. Sci. 2, p465-472 (1964)
2) M. Saitoh, K. Oura, K. Asano, F. Shoji and T. Hanawa Surf. Sci. 154, p394-416 (1985)
3) R. Feidenhans'l, J.S. Pedersen, M. Nielsen, F.Grey, and R.L. Johnson, Surf. Sci. 178, p927-933 (1986) 4) G . Le Lay, J. Peretti, M. Hahnbuecken and W. S. Yang, Surf. Sci. 204, p57-68 (1988)
5) Two excellent and thorough reviews of the surface diffraction technique are in print: I. K. Robinson, to appear in " Handbook of Synchrotron Radiation III" eds. D, Moncton and E. Brown, North Holland (1989); R. Feidenhans'l, Surf. Sci. Rep. 10, no. 3 (1989)
6) F. C. Frank and J. H. van der Merwe, Proc. Roy. Soc. A 198 p205-216 (1949)
7) M. Nielsen, J. Als-Nielsen and J. P. McTague, in "Ordering in two dimensions" p135-141 ed. S.K.
Sinha, North Holland (1980)
