Structure analysis of an alkali metal adsorbed Si(001)(2 × 1) surface by tensor LEED

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Structure analysis of an alkali metal adsorbed Si( OOl)(2 x 1) surface by tensor LEED T. Urano,

S. Hongo

and

T. Kanaji

Faculty of Engineering, Kobe Unir~ersity,Rokko, Nada, Kobe 657, Japan Received

1 September

1992; accepted

for publication

19 November

1992

The structures of the alkali metal (K, Cs) adsorbed Si(OO1)(2 X 1) surface have been studied by tensor LEED. A reliability factor (R factor) analysis has been carried out for models having different sites for the alkali atoms, that is, a pedestal site model (so called Levine’s model), a cave site model and a double-layer model. Although the difference between the numerical values of R is small for these models. the smallest R factor is obtained for the double-layer model with a symmetric dimer model for the topmost Si atoms.

1. Introduction The structure of alkali atom adsorbed Si(OOlx2 X 1) surfaces has been studied by several researchers. One of them is Levine who developed a model in which alkali atoms form linear chains on dimer rows of the topmost Si atoms (pedestal site or quasi-hexagonal hollow site H in fig. 1) with half a monolayer coverage (19= 0.5) [l]. Another model is the one in which alkali atoms sit on the valley in between dimer chains (cave site or valley bridge site, C site) as proposed by Asencio et al. on the bases of an analysis of the angular dependence of Auger electron yield (6 = 0.5) [2]. However, Abukawa and Kono proposed a model in which alkali atoms sit on both H and C sites (double-layer model, 0 = 1.0) by the analysis of X-ray photoelectron diffraction (XPD) and angle-resolved (AR) UPS [3]. Theoretically, Morikawa et al. find the double-layer model to be the optimal structure. Their conclusions are based on first-principles molecular dynamics using the norm-conserving pseudopotential [4]. Zhang et al. also obtained a similar result for Na on a Si(OO1) (2 X 1) surface by first principles total-energy calculations [5]. In a LEED analysis Wei et al. indicate that the H-site adsorbed model by Levine is best for the 0039-6028/93/$06.00

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Science

Publishers

structure of Na on Si(OO1) with a saturation coverage 0 = 0.5 [6]. However, they also indicated that although the coverage was inconsistent, the R factor of the double-layer model was as good as that of the H site model. We have investigated the structures of K adsorbed on a Si(OO1) surface

r

H site rCsite

top

view

side

view

Fig. 1 Schematic diagram of two adsorption sites, pedestal quasi-hexagonal hollow site (HI and cave site (0.

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or

T. Urano et al. /Analysis of an alkali metal adsorbed Si(OOlJ(2 x I) surface

with the saturation coverage at room temperature and have demonstrated that the double-layer model is optimum by conventional dynamical LEED analysis [7]. Tensor LEED is a perturbation method for calculating LEED Z-I’ curves in which an initial reference structure is distorted. At the first stage in a tensor LEED calculation, changes in the t matrix of the atom produced by displacing from their reference positions are calculated as well as the diffraction intensity for the reference structure. At the second stage an automated search is performed for the optimum R factor structure. If the atom& displacements are not so large (less than 0.4 A), this is a very efficient and time-saving method [8]. In this paper we investigate the structure of the K and Cs adsorbed Si(OOlX2 X 1) surfaces by tensor LEED in order to verify that the doublelayer model is indeed the optimum one and to obtain a more precise structure.

295

Cs-

NOO(47eV)

at rocfn temp.

Deposition

time

(min)

Fig. 2. The peak-to-peak amplitude of the CsNOO(47 eV) Auger signal as a function of deposition time at room temper ature.

case of Cs on Si(OO1) the (20) and (+, 1) beams are not clear, these beams have been excluded from the analysis.

3. Tensor LEED analysis 2. Experiment The experiments were carried out in a standard ultra-high vacuum system with a conventional four-grid LEED-AES system. The procedure of sample preparation and alkali atom deposition is presented in a previous paper [7]. The peak-to-peak amplitude of the CsNOO(47 eV) AES signal as a function of deposition time at room temperature is shown in fig. 2. The figure shows that the amplitude of the Cs Auger signal saturates at about 10 min as for the case of K [7]. LEED Z-V curves were measured with a system using a conventional TV camera and a microcomputer constructed in our laboratory. As the surface having a saturation coverage of alkali atoms also indicates the (2 x 1) structure with two domains, symmetrical beams, e.g. (lo), , (01) and (Oi), show the same Z--I/ curves. Firstly the normal incidence of an electron beam was confirmed by comparing Z-I/ curves between the symmetrical beams with each other. Next Z-V curves of three integral order beams, (101, (11) and (20), and four half-order beams, (4, 01, (i, 11, (+, 0) and (+, 1) were measured. Because in the

Tensor LEED analyses are carried out by using a set of computer programs constructed by Rous et al. [91. They have been partly modified to adapt to the computer used and to the symmetric dimer model in which the atomic distortion is restricted and the intensity of symmetrical beams is averaged.

Table 1 Example of optimum R values obtained for K/Si(OOl) Double layer model

Single layer model

H-C site

H site

C site

Initial

0.351

0.379

0.352

1st step 2nd step 3rd step 4th step

0.335 0.311 0.297 0.295

0.374 0.360 0.319 0.312

0.336 0.336 0.330 0.315

Simultaneous

0.305

0.348

0.338

The bottom shows the simultaneous distortion of atomic positions up to the 4th layer of the Si substrate. The center shows the results in which the atomic positions are distorted sequentially, including the upper layer of the Si substrate. The initial structures are the optimum structures obtained by conventional LEED analysis.

T. Urano et al. /Analysis

296

of an alkali metal adsorbed Si(OO1)(2 x I) surface

R = 0.29

K / S i (001)

2x1

(312 I)

ca,c

(312 0)

’ “&

rmo.27

h

;=0.32

(l/2 I)

t-=0.34

1

I.5

r=od2

I.3 I.3 1.3 I.3

(a)

Energy

(eV)

lb) Fig. 3. (a) Best-fit

parameters

of atomic

distortions

in, and (b) comparison the K/ Si(OOlx2

I-V curves with experimental

curves for

R =0.26 r=o.38

w

(312 0)

Cs/Si(OOl)2xl

of theoretical

$XP ,iv2I)*

Lo.37

.

I rao.21

(l/2 0)

,A,

I r=O.22

(I I)

(1 0)

0

(a)

‘r-=0.32

*

100 Energy

I 200 (eV)

(b) Fig. 4. (1) Best-fit

parameters

of atomic

distortions

in, and (b) comparison of theoretical the Cs/Si(OOlX2 x 1) surface.

I-V curves with experimental

curves

for

T. Urano et al. / Analysis of an alkali metal adsorbed Si(OO1)(2x 1) surface

A set of phase shifts is calculated by using Pendry’s program [lo] and the core state wave functions tabulated by Herman and Skillman [ll]. It is assumed that an alkali atom has a single conduction electron, the rest being core electrons, and that a Si atom has four conduction electrons and ten core electrons. Four phase shifts were included in the calculation of Z-v curves. The inner potential was set to 10 eV. We use two types of R factor, i.e. Pendry’s R factor (R,,)[12] and Zanazzi-Yona’s R factor ( RZY) [131. In our experience R, is a good criterion for structures a little bit far from the true structure, whereas R,, is a better criterion for structures near the true structure. Thus we used R,, in the final stages in our determination of the optimum structure. We started from the various reference structures and performed two types of searches: one search involving the simultaneous distortion of atomic positions up to the 4th layer of the Si substrate and another search in which the atomic positions were distorted sequentially, including the upper layer. For example, results of optimum R values obtained for K/%(001) are tabulated in table 1. In this case the reference structures are the optimum structures obtained by conventional LEED analyses. Although many local optimum structures appear and there is little difference among the R values for these structures, for both K/ Si(OO1) and Cs/ Si(OO1) the double-layer model yields the minimum R value. The best-fit parameters for the atomic positions and the experimental and theoretical I-lr curves are shown in figs. 3 and 4 for the cases of K/Si and Cs/Si, respectively.

297

One of them is the distance of the two alkali layers. We found about 0.5 A for both K and Cs,, which is to be compared with the value of 1.1 A found in the experimental [3] and theoretical [4] studies. Another difference regards the magnitude of the displacements in the 3rd and 4th substrate layers. Our values are rather larger. When we judged by eye in a sequential distortion from the upper layer mentioned above, the peaks, dips and shoulders in Z-l’ curves are reproduced only if the displacements are in the topmost 2-3 layers. However, the complete Z-v curve and in particular the relative peak heights do not match very well. We believe that one problem in our analysis is the number of phase shifts included in the calculation. We used four phase shifts to save computing time, which may be too small a number. Another problem is the reliability factor. We used Pendry’s R factor. This is very sensitive to the position of peaks and dips, but less sensitive to the relative intensity. Fig. 4 shows for the (10) beam that although the position of the peaks is reproduced, the similarity of the complete profile is not so good. It may be necessary to combine another R factor which is more sensitive to the relative intensity with Pendry’s R factor.

5. Summary The structures of alkali atoms (K and Cs) adsorbed on the Si(OOlX2 x 1) surface have been studied by tensor LEED analysis. Three models, that is, a pedestal site model (H site), a cave site model (C site) and a double-layer model (H-C site) were considered. The H-C site model is the optimum one in both cases.

4. Discussion For both K/Si(OOl) and Cs/Si(OOl) the H-C site adsorbed double-layer model indicates the smallest R value. The directions of the displacements from bulk positions in the optimum structure are the same as those presented in another experimental study of Na on Si(OO1)[6] and theoretical study of K on Si(OO1) [4]. However, the magnitudes of the displacements are different.

Acknowledgements The authors would like to thank Professor M.A. Van Hove of the Lawrence Berkeley Laboratory, University of California, and Dr. A. Wander of Cambridge University for their offer of a set of tensor LEED programs and their useful suggestions.

298

T. Urano et al. /Analysis

of an alkali metal adsorbed Si(Wl)(2

References [l] J.D. Levine, Surf. Sci. 34 (1973) 90. [2] M.C. Asencio, E.G. Michel, J. Alvarez, C. Ocal, R. Miranda and S. Ferrer, Surf. Sci. 211/212 (1989) 31. [3] T. Abukawa and S. Kono, Phys. Rev. B 37 (1988) 9097. [4] Y. Morikawa, K. Kobayashi, K. Terakura and S. Blogel, Phys. Rev. B 44 (1991) 3459. [5] B.L. Zhang, C.T. Chan and K.M. Ho, Phys. Rev. B 44 (1991) 8210. [6] C.M. Wei, H. Haung, S.Y. Tong, G.S. Glander and M.B. Webb, Phys. Rev. B 42 (1990) 11287.

x 1) surface

[7] T. Urano, K. Sakaue, K. Nagano, S. Hongo and T. Kanaji, J. Cryst. Growth 115 (1991) 411. [B] P.J. Rous and J.B. Pendry, Surf. Sci. 219 (1989) 355; 373. [9] P.J. Rous, M.A. Van Hove and G.A. Somorjai, Surf. Sci. 226 (1990) 15; A. Wander, M.A. Van Hove and G.A. Somorjai, Phys. Rev. Lctt. 67 (1991) 626. [lo] J.B. Pendry, in: Low Energy Electron Diffraction (Academic Press, London, 1974). [ll] F. Herman and S. Skillman, in: Atomic Structure Calculations (Prentice Hall, Englewood Cliffs, NJ, 1963). [12] J.B. Pendry, J. Phys. C 13 (1980) 937. [13] E. Zanazzi and F. Jona, Surf. Sci. 62 (1977) 61.