Helium diffraction from (2 × n) structures on Si(001)

Vacuum/volume 38/numbers 4/5/pages 287 to 289/1988

0042-207X/88S3.00+.00 Pergamon Pressplc

Printed in Great Britain

Helium d i f f r a c t i o n f r o m (2 Si(001) D M R o h l f i n g , J Ellis, B J H i n c h * , W A l l i s o n

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n) structures on

a n d R F W i l l i s , Cavendish Laboratory (PCS),

Madingley Road, Cambridge CB3 0HE, UK

Results of hefium diffraction from S i ( 0 0 1 ) - ( 2 x n), n ~ 10 are presented. The (2 x n) unit cells are shown to contain missing dimer defects alongside dimerized surface atoms. The experimental distribution of scattered intensity is compared with current models of the silicon dimer geometry and it is shown that all the main features in the observed spectra can be explained with a symmetric dimer configuration.

1. Introduction

2. Results and discussion

The Si(001) surface has eluded a detailed structural analysis despite many experimental and theoretical studies. One factor that contributes to the difficulty lies in the diversity of the structures reported on this surface. These include (2 x I), c(4 x 2), p(2 x 2) and (2 x n), 7 < n < 11 periodicities (refs 1-8 and references therein). All the higher order structures are believed to arise from arrangements of a basic (2 x 1) surface dimer; however, the structure of the basic dimer itself has not yet been resolved. Some experiments 1'8 and theories 9'~° favour an asymmetric dimer, while others 11 suggest the stable configuration should be a symmetric structure. In recent scanning tunnelling microscopy (STM) studies ~ on Si(001) the observation of both symmetric and asymmetric dimers on a surface having predominantly (2x 1) symmetry, but containing a significant fraction of disordered missing dimer defects has been reported. They also note a relationship between t'ae degree of dimer asymmetry and the proximity to a defect. It is possible to order the defects into arrangements with (2 x n) periodicity and it is interesting to ask if the (2 x 1) dimers within tlhe (2 x n) unit cell are arranged symmetrically, asymmetrically or whether there is a mixture of both types. In this paper we present results of helium diffraction from (2 x n) structures on Si(001) and compare the intensity distribution with predictions given by current structural models for symmetric and asymmetric dimer configurations. Some of the experimental details, especially the methods of surface preparation, have already been presented 6. In the results discussed below, the energy of the helium beam was 63 meV and the instrumental angular resolution 0.4 ° F W H M . For the diffraction intensities in the scattering plane, the beam was incident along the (11) direction while the out-of-plane intensities were obtained by tilting the crystal about the (11 ) direction. Thus, the exact angle of incidence varies somewhat during a scan lhrough the out-of-plane diffraction peaks.

The interpretation of (2 × n) diffraction patterns in terms of ordered missing dimers 4'5'6 was stimulated by Pandey's theoretical conjecture that additional surface dangling bonds could be eliminated by removing a dimer in the outermost layer and allowing the four atoms in the second layer to reconstruct so as to form two additional dimer bonds. The reduction in surface energy resulting from the loss of a dangling bond outweighs the increase due to lattice strain. Helium atom diffraction is sensitive to the distribution of surface charge, so ordered missing dimers on Si(001) can be detected from interference effects between scattering off the top surface layer and the exposed parts of the second layer. The scattering geometry and the variation of diffraction intensity are shown schematically in Figure 1. As the angle of incidence is varied, for a fixed beam energy, the emerging beams [Figure 1(a)] interfere alternately constructively, giving a large specular signal, and destructively giving a reduced specular intensity [Figure l(b)]. The weak and strong specular beams are accompanied by the appearance and disappearance of superlattice spots from the n periodicity in the (2 x n) structure. This behaviour can be observed in the experimental data (Figure 2) where the alternation of superlattice intensity (I,) and specular intensity (I0) is emphasized by plotting (I,/Io) against the change in perpendicular wave vector. The arrows at the top of this figure indicate where peaks are expected for a surface with missing dimer defects. Thus, Figure 2 is a clear demonstration of the existence of missing dimers in the (2 x n) structure. Although the effect of missing dimer defects is clearly visible in the data, they only occupy a small fraction of the area of the unit cell. One would therefore expect the overall distribution of scattered intensity to be dominated by the shape of the individual (2 x 1) surface dimers. Figure 3 demonstrates this point. The experimental data [Figure 3(a)] shows the diffraction intensities in the scattering plane at an angle ofincidence of 48.2 °. Most ofthe intense peaks arise from a (2 x 1) mesh, and are indexed as such on the diagram, while the superlattice contributes the weak satellites around the integer order beams (notably specular). Figure 4(a)

"Present address: MPI fiir Str6mungsforschung, D-3400, Federal Rep Germany.

287

D M Rohlfing et al: Helium diffraction from (2 x n) structures on Si(001 )

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Figure 1. (a) The geometry for the bilayer scattering showing the incoming beams at an angle O~with respect to the surface normal, and the scattered beams emerging at an angle Of from both the upper and lower layers. (b) The variation of the observed specular beam intensity as the emerging beams interfere constructively (c) where specular is strong and no superlattice peaks are observed or destructively (d) where the specular intensity is weaker and superlattice peaks are observed.

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Figure 3. (a) Measured in-plane diffraction pattern for a helium beam of wave vector 11.3 A - i and incident angle 48.2 ° scattered from a Si(001) surface cooled to 150 K. The position of each beam of the two calculated diffraction patterns has been aligned with the measured data thus clarifying the peak indices. The calculations have been performed for the same scattering conditions and the symmetric dimer results (b) have been averaged over the two unique symmetric domain configurations whilst the asymmetric dimer results (c) have been averaged over the four unique asymmetric dimer configurations.

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Figure 2. The ratio of mean superlattice beam intensity to specular intensity for a (2 x n) superlattice structure as a function of Ak,, the change in perpendicular wave vector. Open squares and dashed curve are for a 28 meV beam while filled circles and full curve are for a 63 meV beam, Typical experimental uncertainties are indicated by the vertical bars. The curves are drawn simply to guide the eye. Arrows indicate the expected peak positions for a surface with missing dimer defects.

shows the diffraction intensities n o r m a l to the scattering plane. Again, the superlattice satellites a r o u n d integer order peaks play a m i n o r role in the overall intensity distribution. Thus, trends in the overall intensity distribution can be used as a p r o b e of the local (2 x 1) geometry. The experimental results are c o m p a r e d with predictions from h a r d wall surface models of symmetric a n d asymmetric (2 x 1) dimers in the lower panels of Figure 3 a n d Figure 4. F o r the c o m p a r i s o n s we have chosen the symmetric structure due to A p p e l b a u m a n d H a m a n n ~2 while for the asymmetric dimer we have used the configuration predicted by Yin a n d C o h e n 1°. The charge densities were calculated using the modified a t o m i c charge superposition ( M A C S ) scheme suggested by Sakai, H a m a n n and Cardillo ~3. W e find this m e t h o d gives significantly better agreement with the experimental results t h a n simple atomic charge superposition (SACS) since some a c c o u n t is taken of the 288

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Figure 4. (a) Out-of-plane diffraction pattern for a helium beam of wave vector 11.3 ,~.- 1 incident at an angle of ~ 48.2 ° as in Figure 3 measured by variation of the sample tilt about the (11) crystal direction. (b) and (c) are the calculated results averaged over the unique dimer configurations for the symmetric and asymmetric dimer models respectively. The peak positions of the calculated results have been aligned with the measured data and indexed accordingly.

D M Rohlfing et al: Helium diffraction from (2 x n) structures on Si(O01 )

charge in the partially filled dangling bonds. For the asymmetric dimer there are three 'modified' atom types: bulk, lower dimer atom and upper dimer atom. The 'atomic' parameters used for each type are those suggested in ref 13. For the symmetric dimer there are only two atom types in the MACS calculation since the dimer atoms are now equivalent. In this latter case no first principle calculations were available so the parameters used for the dimer atoms were simply the arithmetic mean of those available for an asymmetric dimer. The hard wall surfaces that result from this procedure are free from adjustable parameters in the sense that the individual atomic characteristics are derived directly from LAPW calculations of the surface 13. Diffraction intensities were calculated from the hard wall models using a 2-D Eikonal approximation ~4, which should give a reasonably accurate description of the intensities for the scattering geometry used in the experiment 15. In the calculations, the diffracted intensities were averaged over the two or four unique domain configurations allowed for the symmetric and asymmetric dimers respectively. The principal features in the in-plane data [Figure 3(a)] are the strong peaks for G = 0 1 , 00, 02. Notice also that the half order features are always smaller than nearby integer order peaks. Both these trends are mirrored in the calculations on a symmetric dimer model [Figure 3(b)] but not by those using the asymmetric dimer geometry [(Figure 3(c)]. The out-of-plane data is more complex [Figure 4(a)]. There are two main groups of peaks in the experimental data, the first around specular + 10° tilt and the second group at larger angles of emergence, around 20 ° tilt. A comparison of these features with the calculations [Figure 4(b,c)] is not as satisfactory as for the inplane case; however, the intensity near specular looks similar to the symmetric dimer pattern [Figure 4(b)] while the intensity away from specular is well reproduced by the pattern of peaks in the asymmetric dimer calculation [Figure 4(c)]. The obvious interpretation of these comparisons is that the 112x n) surface structure contains both asymmetric and symmetric dimers. Such a conclusion is supported by the STM observations 3 of both dimer types on a disordered surface. However, we believe ~hat this obvious interpretation may not be the correct one. First, there is no simple linear combination of the two types of calculated pattern that would give quantitative agreement with both in-plane and out-of-plane scattering data. Second, the primary feature in the observed data that suggests asymmetric

dimers, namely the large angle peaks out-of-plane [Figure 4(a)], has a natural alternative explanation in terms of scattering from the missing dimer defects. The charge distribution at the edges of the missing dimer defects should give rise to strong rainbow scattering. It is easy to estimate where such a rainbow should occur from the geometry of the Si(001 ) surface. In the out-of-plane conditions a rainbow would be predicted near 20° tilt, precisely where the additional intensity is observed. The same phenomenon explains the group of peaks in the in-plane data [Figure 3(a)] lying between 50° and 60 °. In conclusion, the experimental results show that the (2 × n) structures on Si(001) contain an ordered arrangement of missing dimer defects with the remaining surface atoms dimerized in a local (2 × 1) geometry. The distribution of scattered intensity shows features that could be explained by both symmetric and asymmetric dimers. However, the symmetric dimer model gives better overall agreement with the data, and this model, combined with considerations of rainbow scattering from the m!ssing dimer defects, gives a description of all the important features in the experimental data. A quantitative comparison of experiment with detailed models of the surface will require further calculations of the surface charge densities and more sophisticated calculations of the scattering dynamics.

References

i W S Yang, F Jona and P M Marcus, Phys Rev B, 28, 2049 (1983). 2 M J Cardillo and G E Becket, Phys Rev Lett, 40, 1148 (1978); Phys Rev B, 21, 1497 (1980). 3 R J Hamers, R M Tromp and J E Demuth, Phys Rev B, 34, 5343 (1986). 4 T Aruga and Y Murata, Phys Rev B, 34, 5654 (1986). s j A Martin, D E Savage, W Moritz and M G Lagally, Phys Rev Lett, 56, 1936 (1986). 6 D M Rohlfing, J Ellis, B J Hinch, W Allison and R F Willis, Proc ICSOS 2 (edited by F J van der Veen and M A van Hove), p 575. Springer Series in Surface Science (1987). v T Tabata, T Aruga and Y Murata, SurfSci, 179, L63 (1987). s B W Holland, C B Duke and A Paton, SurfSci, 140, L269 (t984). 9 D J Chadi, Phys Rev Lett, 43, 43 (1979). 10 M T Yin and M L Cohen, Phys Rev B, 24, 2303 (1981). 11 K C Pandey, Proc Int Confon Physics of Seraiconductors (edited by D J Chadi and W A Harrison), p 55. Springer, Berlin (1985). 12 j A Appelbaum and D R Hamann, SurfSci, 74, 21 (1978). 13 A Sakai, M J Cardillo and D R Hamann, Phys Rev B, 33, 5774 (1986). 14 B Salanon and G Armand, SurfSci, 112, 78 (1981). 1~ D M Rohlfing, PhD thesis, University of Cambridge (1987).

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