The structure of Si(OOl) 2 × 1 surface — Studied by low energy electron diffraction

Surface Science 78 (1978) 459-466 0 North-Holland Publishing Company

THE STRUCTURE

OF Si(OO1) 2 X 1 SURFACE - STUDIED BY LOW ENERGY

ELECTRON DIFFRACTION

*

S.Y. TONG and A.L. MALDONADO Department of Physics and Surface Studies Laboratory, Wisconsin 53201, USA

University of Wisconsin, Milwaukee,

Received 10 March 1978; manuscript received in final form 19 June 1978

Intensity-voltage spectra of low energy electron diffraction are calculated by the quasidynamical method and the results analyzed to determine the validity of new structural models proposed for the Si(OO1)surface.

1. Introduction

Many surface models have been proposed for the structure of Si(OO1) 2 X 1 surface during the past 25 years. These models may be classified into two types: (1) those containing vacancies in one or more surface layers, plus small displacements of surface atomic positions from bulk equilibrium positions, and (2) models which do not have any vacancies but include rather large displacements of surface atomic positions from bulk sites [l-S]. Low energy electron diffraction (LEED) has been used to study the validity of many of the models. From LEED spot patterns of Si(OOl), it has long been observed that a 2 X 1 reconstruction surface exists which exhibits a periodicity twice as large as that of the bulk along one symmetry direction. On a typical reconstruction .surface, equal number of domains of 1 X 2 and 2 X 1 periodicities co-exist. Intensity-voltage IV curves can be used to determine the registries and interlayer spacings of surface planes. LEED IV spectra analysis is a sensitive test [S] of surface structural models because each IV curve contains 3 to 4 major peaks. Usually, 5 to 6 curves (beams) are available for comparison with theory. This means in a typical LEED analysis of surface structure, the positions of 15 or more major peaks are available for matching. This is a large number compared to most other surface techniques where the reliance is on 2 to 3 measured peaks. Due to uncertainties in the theory - particularly to the fact that the surface scattering potential is a quantity difficult to calculate accurately, it is unlikely that a calculation can match all the measured peaks of an experiment. A useful gauge is * Work supported in part by NSF Grant No. DMR 73-02614 and by the Graduate School, University of Wisconsin-Milwaukee. 459

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S. Y. Tong and A.L. Maldonado / Structure of Si(OO1) 2 X I surface

the following: calculated IT/ curves for known surface structures (e.g., Ni(OO1) where there is little surface displacement from the bulk geometry) match between 80%-90% of major measured peak positions. Thus, a discrepancy of lo%-20% is close to the best that can be achieved in current LEED fV spectra analysis. Various reports [2-S] indicate that none of the models proposed before 1977 generated calculated IV curves in satisfactory agreement with experiment. For most of the earlier models, the match in peak positions between theory and experiment was less than 50%. Recently, a new surface model was proposed by Appelbaum and Hamann [I]. This model contains no vacancies and has atomic position displacements that penetrate deep into the semiconductor surface. In this paper, we report results of LEED fV spectra calculations of the Appelbaum-Hamann (AH) model and an optimized surface structure which produced good agreement with experiment.

2. The Si(OO1) surface model and method of calculation The model of Appelbaum and Hamann [l] on the Si(OO1) 2 X 1 surface was determined by rn~~iz~g the elastic surface energy arising from bond stretching and bond bending forces. Surface energies based on the harmonic approximation and on including anharmonic contributions were both considered by them. Keating’s [6] model for the elastic energy of bulk semiconductors was used. Appelbaum and Hamann [l] determined that appreciable displacements from bulk equilibrium sites occur for as deep as five surface layers down. We used their results (both harmonic and anharmonic models) and calculated corresponding LEED IV curves. Comparing with experimental IV curves [7], we then determined an optimized surface structure, which produced improved a~eement with exper~ent. Table 1 tabulates surface interlayer spacings and atomic displacements of our optimized model. A schematic diagram of the model is shown in fig. 1. This model cor-

Table 1 The optimized AH model; displacements for atoms marked l-5 in fig. 1 are listed; displacements for atoms l’-5’ have equal amplitudes but their directions are shown in fig. 1; the atoms are first shifted from bulk positions to new interlayer separations d12 = 1.357, d23 = 1.257, d34 = 1.207 and d45 = dbulk = 1.357 A; an error bar of 0.05 a m.ay be placed on the d-spacings; the arrows are additional displacements from the new surface positions Layer 1 2 3 4 5

x (A)

r (A)

0.695 0.119 0 0 -0.032

0.092 -0.005 -0.130 -0.078 0

S. Y. Tong and A.L. Maldonado /Structure of Si(OO1)2 X I surface

3 f + d3, t

rz i

.P

20 40 60 80 100120140160

Energy (ev)

Fig. 1. Schematic diagram of the optimized AH model. Si(OO1) 2 X 1 projected side view. The arrow on each atom indicates the direction of displacement of the atom. Fig. 2. Leed intensity spectra calculations for Si(OO1) 2 X 1 SF dimer model. The dynamical method (thick line), the quasidynamical method (QDM) thin line. The dimer nearest neighbor distance is 2.35 A and the first interlayer spacing is dl = 1.15 A.

responds to changes of 7%-11% in the interlayer distances between the Znd, ZSrd and 4’h layers from those of the AH harmonic approximation model. The intralayer distances are determined as same as those of the AH harmonic approximation model. We shall not reproduce here the numbers in the AH harmonic and anharmanic models, as they are tabulated in table 2 of ref. [ 11. To calculate LEED fV spectra of structures cont~ning five reconstructed surface layers, we used the quasidynamical method (QDM) [8], This method includes all orders of multiple scattering events between different atomic layers, but only one scattering event from each atom within a given unit cell. The method seems to work rather well for semiconductor surfaces where the scattering factors are only moderately strong. How good is the QDM for a surface such as Si(OOl)? In fig. 2, we show direct comparison between two calculated results of the same Si(OO1) 2 X 1 structure: the dynamical method (thick line) and QDM (thin line) results for the S&her-Farnsworth (SF) surface dimer model [9]. We note that positions of major peaks and valleys agree very well, whereas the numbers of shoulders and split peaks in the two calculations do not match in all cases. Allowances for these mismatches must be made when using QDM results to compare with experiment. From the results of the qu~idyn~ic~ method on the optimized AH model, we

S. Y. Tong and A.L. Maldonado /Structure of Si(OO1)2 X 1 surface

462

Si(OOl) 2x1 Surface SNOOI)2x I Surface 8=0” (I I)Beam AH optimized

0

0

60

Model

120

Energyte

Fig. 3. Comparison of LEED intensity spectra for Si(OO1) 2 X 1 optimized AH model, the (10) beam. (a) Top curve is QDM result. (b) Middle curve is experiment of Debe and Johnson [7]. (c) Lower curve is result of kinematical method (KM). Fig. 4. Comparison of LEED intensity spectra for Si(OO1) 2 X 1, the (11) beam. (a) Top curve is QDM result of the optimized AH model. (b) Lower curve (solid line) is experiment of Debe and Johnson. (c) Broken line is QDM result of the AH harmonic model.

found that the half-order beams (additional beams that appear due to the 2 X 1 and 1 X 2 periodicities) exhibit rather weak multiple scattering contributions. But the integral order beams (beams from the 1 X 1 bulk periodic@) contain strong multiple scattering contributions. An example of this is shown in fig. 3, for the integral order (10) beam, We note that there are important differences between the QDM result and kinematical result.

3. Search for the optimized surface structure We used the quasidynamical method to calculate IV curves for both the AH harmonic and anharmonic models. For both models, we found that agreement with experiment for integral order beams was not satisfactory (see, for example, the broken line in fig. 4 for the (11) beam). We then varied atomic positions in the first five layers away from those of the AH models. By following shifts in peak positions as intralayer and interlayer spacings were changed, we searched over 70 variations. The optimal surface structure we found is listed in table 1. The major im rovedp ments in the calculated ZY curves come from contractions in the 2”d and 3’ inter-

S. Y. Tong and A.L. ~aldo~o

/ S~~~~re of S~~~~~]2 X 1 surface

463

Si(OO1) 2x1 Surface 8=V (l/2 I)Beam

Fig. 5. Comparison of LEED intensity spectra for Si(OO1) 2 X 1, the (l/2 1) beam. (a) Top curve is QDM result of the optimized AH model. (b) Middle curve is experiment of Debe and Johnson. (cl Lower curve is dynamical calculation of the SF dimer model. Fig. 6. Comparison of LEED intensity spectra for Si(OO1) 2 X 1 optimized AH model, the (372 0) beam. (a) Top curve is QDM result. fb) Lower curve is experiment of Debe and John-

Si (001) 2 xl Surface r

Si(OOl) 2x1 -

&P

Surface

w2 oH3eam

Fig. 7. Same as in fii. 6, except for the (20) beam. Fig. 8. Comparison of LEED intensity spectra for Si(OO1) 2 X 1 optimized AH model, the (l/2 0) beam. (a) Top curve is QDM result. (b) Lower curve is experiment of Ignatiev and Jona 171.

464

S. Y, Tong and A.L. Maldonado / Structure of Si(OO1) 2 X I surface

Si (001) 2x 8=O”

I Surface

(3/2

I)Beam

EnergyIeV) Fig. 9. Comparison of LEED intensity spectra for Si(OOl), the (3/2 1) beam. (a) Top curve is QDM result of the optimized AH model. (b) Lower solid curve is experiment of Debe and Johnson. (c) Broken line is QDM result of the model by Poppendick et al. [4].

layer spacings from the AH model. The comparisons between theory and experiment for the optimized structure for all the measured beams [7] at 8 = 0” are shown in figs. 3-9. In fig. 5, the calculated curve for the SF surface dimer model Table 2 Match between theory and experiment for different surface models; the denominator indicates number of peaks counted in each beam; the numerator indicates number of these peaks that match to within 5 eV in energy position Beam

Optimized AH model

(11) (1:) (30) ( 3 1) ($0 (10) (20)

415 313 314 313 213 415 214

Total

21127 18%

SF dimer model

l/5 213 214 l/3 _a 115 l/4 g/24 33%

PNW model

415 2t3 213 213 213 215 214 16127 59%

a Debe and Johnson [ 71 did not measure that (i 0) beam, hence we did not print out the calculated values of this beam at the time we did the SF dimer model.

S. Y. Tong and A.L. ~~ldo~~do

/ Structure

ofSi(OO~j 2 X I surface

465

[9] is also shown. The calculation used an inner potential of 20 eV for the AH and optimized AH models and a value of 10 eV for the SF surface dimer model. The inner potential value in a LEED calculation is an adjustable parameter used to line up the maximum number of peaks between theory and experiment, considering all the beams. An inelastic damping potential of 0.2 hartree (5.44 eV) was used in the quasidynamical method for all the models. For the optimized AH model, the agreement between c~culation and experiment was rather good, with 21 out of 27 major peaks matching to within 5 eV (a 78% match). By comparison, the match for the SF dimer model [9] was only 33%. The breakdown in the matching for individual beams is listed in table 2.

4. A model with~multilayervacancies and atomic displacements Recently, Poppendick et al. [4] prepared a reproducible, reconstructed Si(OO1) surface with a c(4 X 2) unit mesh, Except for the additional beams, the 1l’ data of the common beams were very similar to those of ref. [7]. Poppendick et al. proposed a model with vacancies in the first two surface layers and atomic displacements from bulk positions in the 3’d layer. We calculated 15/ curves for this model by the quasidynamical method. Comparing with experiment [7], a total of 16 out of 27 major peaks match between theory and experiment (a 59% match). A tabulation by individual beams is given in tabIe 2. As an example, the comparison for the (3f2 1) beam is shown in fig. 9. It is not clear whether this poorer agreement is due to the possible existence of two different structures on the Si(OO1) surface, with c(4 X 2) and (2 X 1) unit meshes.

5. Discussion Considering the overall comparison between calculated II’ curves and experimental data for the different surface models of the Si(OO1) 2 X 1 structure, it is apparent that with the optimized AH model the best agreement is obtained. This agreement is particularly good for the half-order beams, where multiple scattering cont~butions are small and hence, the QD&I results are expected to be accurate. The agreement is less detailed for the integral order beams, especially in cases where peaks are split. This could be due to the fact that the quasidynamical method neglects interlayer multipIe scattering contributions and is unable to reproduce the finer details of the data. We plan to carry out full dyn~ic~ c~culations of the optimized AH model. For the experiment, we show here only curves taken by Debe and Johnson [7], to reduce tlse number of curves necessary in each figure-The only exception is the (l/2 0) beam, where the data taken by Ignatiev and Jona [7] are shown. This is because Debe and Johnson did not measure this beam in their experiment. The

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S. Y. Tong and AL Maldonado [Structure of Si(OO1)2 X 1 surface

experimental curves taken by the various groups are very similar in peak positions (see, for example, refs. [4] and [7]), although there are real differences in the relative peak intensities. It would be interesting to investigate whether the surface model of Poppendick et al. [4] can be optimized to give better agreement with experiment. Also, it seems that the question of whether one or two distinct surface structures exist on Si(OO1) should be properly answered - either experimentally, or in comparison with theory.

Acknowledgments We want to thank Drs. J.A. Appelbaum, D.R. Hamann, F. Jona and MB. Webb for many helpful discussions.

References [l] J.A. Appelbaum and D.R. Hamann, Surface Sci. 74 (1978) 21. [Z] F. Jona, H.D. Shih, A. Ignatiev, D.W. Jepsen and P.M. Marcus, J. Phys. Chem. 10 (1977) L67. [3] M-A. Van Hove and K.A. R. Mitchell, Surface Sci., to appear. [4] T.D. Poppendick, T.C. Ngoc and M.B. Webb, to appear; T.D. Poppendick, Ph.D. Thesis, University of Wisconsin (1977) and references therein. [5] S.Y. Tong, Comments on Solid State Physics (1978). [6] P.N. Keathg, Phys. Rev. 145 (1966) 637. [7] A. Ignatiev, F. Jona, M. Debe, D.C. Johnson, S.J. White and D.P. Woodruff, 3. Phys. Chem. 10 (1976) 1109. [ 81 S.Y. Tong, M.A. Van Hove and B.J. Mrstik, in: Proc. 7th Intern. Vacuum Congr. and 3rd Intern. Conf. on Solid Surfaces, Vienna, 1977, Vol. 3, p. 2407. [9] R.E. Schlier and H.E. Farnsworth, Semiconductor Surface P&&s (Univ. of Penn. Press, Philadelphia, 1957) p. 3.