Surface Science 606 (2012) 1918–1921

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Structural analysis of Si(111)-√21 × √21-(Ag, Cs) surface by reﬂection high-energy
positron diffraction
Y. Fukaya a,⁎, I. Matsuda b, R. Yukawa b, A. Kawasuso aab

Advanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, JapanISSP, University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8581, Japana r t i c l ei n f oArticle history:
Received 23 December 2011
Accepted 31 July 2012
Available online 4 August 2012
Keywords:Surface structure
SiliconSilverCesium
Reﬂection high-energy positron diffraction(RHEPD)a b s t r a c t
We have investigated the Si(111)-√21 × √21-(Ag, Cs) superstructure using reﬂection high-energy positron
diffraction. Rocking curve analysis based on the dynamical diffraction theory reveals that Cs atoms are locatedat a height of 3.04 Å above the underlying √3 × √3-Ag structure and that they form a triangular structure witha side length of 10.12 Å. The structure of the Si(111)-√21 × √21-(Ag, Cs) surface is signiﬁcantly different fromthose of the Si(111)-√21 × √21-Ag and Si(111)-√21 × √21-(Ag, Au) surfaces, probably because of the different electronic structures of the alkali and noble metal atoms.
© 2012 Elsevier B.V. All rights reserved.

1. Introduction
Extensive studies have been carried out on the surface of Si(111)√3 × √3-Ag, as a typical two-dimensional metal system [1,2]. Adsorption of small amounts of noble (Cu, Ag, and Au) or alkali (Na, K, andCs) metal atoms on this surface results in the formation of √21 × √21
superstructures with a sharp increase in the surface electrical conductivity [1,2]. From the metallurgical point of view, √21× √21 superstructures have attracted attention as two-dimensional electron compoundalloys [3,4]. Recently, Matsuda et al. investigated the interaction energy
among adatoms in the √21× √21 superstructures by considering themas electron compounds [5,6]. They demonstrated that the interaction
among the adatoms can be explained in terms of the pseudopotential
model [5].
The atomic coordinates of √21 × √21 superstructures have beenstudied both experimentally [7–13] and theoretically [14–16]. In thecases of Si(111)-√21 × √21-Ag and Si(111)-√21× √21-(Ag, Au), we
found that three adatoms are situated at the centers of large Ag triangles
surrounding the Si trimers in a unit cell [12,13]. Although the electronic
states of alkali-metal-induced Si(111)-√21× √21 surfaces resemble
those of noble-metal-induced Si(111)-√21× √21 surfaces [17], theirstructures are considered to be different, as seen in scanning tunnelingmicroscopy (STM) observations [18]. In this study, we measured therocking curves for the Si(111)-√21× √21-(Ag, Cs) surface by reﬂection⁎ Corresponding author. Tel.: +81 27 346 9330; fax: +81 27 346 9432.
E-mail address: fukaya.yuki99@jaea.go.jp (Y. Fukaya).
0039-6028/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.susc.2012.07.039

high-energy positron diffraction (RHEPD) and determined the structureof the surface. We also discussed the difference between the noble- andalkali-metal-induced √21× √21 superstructures.

2. Experimental procedure
Substrates (10 × 5 × 0.5 mm 3) were cut from a mirror-polishedn-type Si(111) wafer with a resistivity of 1–10 Ω cm. These substrates were transferred into an ultra-high vacuum (UHV) chamberwith a base pressure less than 3 × 10 −8 Pa. After degassing at 670 K
for 3 h, by ﬂashing at 1470 K for a few seconds, clean 7 × 7 structures
were formed on these substrate surfaces. Subsequently, by depositing
one monolayer (ML) of Ag atoms on the 7 × 7 structures at 740 K(1 ML = 7.83 × 10 14 cm −2), √3 × √3-Ag structures were formed.
Finally, after the deposition of 0.14 ± 0.01 ML of Cs atoms at 160 K,well-ordered Si(111)-√21 × √21-(Ag, Cs) surfaces were formed. The
deposition rate of Cs atoms was calibrated by the formations of
6 × 6-(Ag, Cs) and √21 × √21-(Ag, Cs) surfaces [8].
RHEPD measurements were carried out using a highly parallel andfocused positron beam generated from a 22Na positron source andelectromagnetic lenses. The positron beam energy was 10 keV. The
diffraction patterns were observed using a microchannel plate witha phosphor screen and a charge-coupled-device camera. For rocking
curve measurements, the glancing angle (θ) of the incident positron
beam was changed from 0.3° to 6.0° in steps of 0.1° by rotating thesample. The details of experimental setup were described elsewhere[19].

Y. Fukaya et al. / Surface Science 606 (2012) 1918–1921

3. Results and discussion
The open circles in Fig. 1 represent the RHEPD rocking curve of theSi(111)-√21 × √21-(Ag, Cs) surface at 140 K. The azimuth of the inci direction (the so-calleddent beam is 7.5° with respect to the [112]one-beam condition [20]). Under this condition, the RHEPD intensityof a specular spot mainly depends on atomic positions perpendicular
to the surface. In the total reﬂection region [21], two distinct dip
structures appear, one at around 1.2° and the other at around 2.2°.
These dip structures are quite different from those observed forthe Si(111)-√21 × √21-Ag and Si(111)-√21 × √21-(Ag, Au) surfaces,
which show strong total reﬂections and (111) Bragg reﬂections[12,13]. The above result indicates that the height of the Cs atoms isrelatively higher than the underlying Ag layer.
To determine the height of the Cs atoms from the underlying Aglayer, we compare the experimental and calculated rocking curves
on the basis of the dynamical diffraction theory [22]. For the calculations, we assume the thermal vibration amplitudes for the Ag and55
55
4.0

0.0

12

3

456555111
1.00TRRHEPD intensity (arb. units)

2.0444(a)3.0333Specular intensity (arb. units)

had (Å)Cs, and Si atoms to be 1.09 × 10 −1 and 5.62 × 10 −2 Å, respectively[12,13]. The absorption potentials due to the electronic excitations(single-electron and plasmon) for the Ag and Cs and Si layers weretaken to be 0 and 1.70 eV, respectively [12,13,23]. The underlying
layers were assumed to have the inequivalent triangle (IET) structure.
The black lines in Fig. 1 show the calculated RHEPD rocking curves forCs atoms at different heights (had) from the underlying Ag layer (alsosee Fig. 3(a)). A dip appears at θ = 1.6° for had = 2 Å, two dips appearat θ = 1.2° and 2.1° for had = 3 Å, and three dips appear at θ = 0.8°,1.5°, and 2.2° for had = 4 Å. The appearance of multiple dips for increasing values of had is due to the interference between the positron
beams reﬂected from the adatom and the underlying Ag layers [24].
Fig. 1(b) shows the reliability factor (R) as a function of had. Thereare two local minima of R at had = 1.20 and 3.04 Å. The value of1.20 Å should be an artiﬁcial coincidence because the dip structuresin the curves calculated using had = 1.20 Å do not reproduce those(θ = 1.2° and 2.2°) in the measured curve, as shown in Fig. 1(a). In
considering the dip structures and the minimum value of R, we
obtained at had = 3.04 ± 0.26 Å. As shown by the red line inFig. 1(a), when had = 3.04 Å, the calculations best reproduced the experimental results. This height of the Cs atoms from the underlying
Ag layer was much greater than those of the Ag and Au atoms onthe Si(111)-√21 × √21-Ag and Si(111)-√21 × √21-(Ag, Au) surfaces(0.53–0.59 Å) [12,13].
Fig. 2(a) shows the RHEPD rocking curves of the (0 0), (1/3 1/3),and (2/3 2/3) spots from the Si(111)-√21 × √21-(Ag, Cs) surface in direction at 140 K. It should be noted that since the surface
the [112]
is composed of the double domains of the √21 × √21(R ± 10.89°)

222

44
44

33
33

TR

2222111(a)

1919: exp (140 K): cal (d Cs-Cs = 10.2 Å)(0 0)(1/3 1/3)

7(2/3 2/3)

Glancing angle (deg)(b)901234561012

Glancing angle (deg)(b) 7.0

86.5
65R (%)

R (%)

7430

1234

Cs height, had (Å)
Fig. 1. (a) RHEPD rocking curves of the specular spot from the Si(111)-√21 × √21-(Ag,Cs) surface under the one-beam condition. The incident azimuth of the positron beam direction. The open circles denote the experimental
is 7.5° with respect to the [112]
curve at 140 K. The black solid lines indicate the calculated curves for various heights(had) of the Cs atoms from the underlying Ag layer. The red solid line indicates thecurve calculated using the optimum adatom height. TR stands for total reﬂection region. (b) Reliability factor (R) between the experimental and calculated rocking curves
under the one-beam condition as a function of had.

6.0
5.5
5.0
4.5

0

2

4

6

8

Cs-Cs distance, dCs-Cs (Å)
Fig. 2. (a) RHEPD rocking curves of the (00), (1/3 1/3), and (2/3 2/3) spots from the direction at 140 K. The open circles
Si(111)-√21 × √21-(Ag, Cs) surface in the [112]and solid lines denote the experimental curves and the calculated curves determinedusing the optimum dCs–Cs, respectively. (b) Reliability factor (R) between the experimental and calculated rocking curves as a function of dCs–Cs.

1920

Y. Fukaya et al. / Surface Science 606 (2012) 1918–1921

structures [8], the (1/3 1/3) and (2/3 2/3) spots from the double domains are overlapped. To determine the in-plane adsorption sites of dithe Cs atoms, we calculated the RHEPD rocking curves in the [112]rection on the basis of the dynamical diffraction theory, taking into
account the double domains. The STM observations [11] revealed
that the Cs atoms arrange themselves in triangular structures on theunderlying √3 × √3-Ag structure. Thus, in the calculations, the side
length (dCs–Cs) and adsorption sites are assumed to be ﬁtting parameters (also see Fig. 3(a)). Fig. 2(b) shows the reliability factor R determined for the rocking curves of the (0 0), (1/3 1/3), and (2/3 2/3)
spots for various values of dCs–Cs when the center of the Cs triangle coincides with the center of the Si trimer. Minimum value of R is
obtained at dCs–Cs = 10.12 ± 1.72 Å. It is interesting to note that two
local minima appear at dCs–Cs = 2.2 and 4.1 Å. In considering theionic radius (1.67–1.88 Å) of Cs atoms and the repulsive force
among the ions, dCs–Cs = 2.2 and 4.1 Å are physically unacceptable.
Even though the rocking curve is reproduced, it should be an artiﬁcialcoincidence. The variation of R as a function of dCs–Cs was nearly thesame (within ±0.2%) for different positions of the Cs triangles.
Thus, the optimum value of dCs–Cs is determined to be 10.12 Å. Although the exact Cs adsorption site is not determined in the aboveﬁtting procedure, since the Cs atoms are at a notable height fromthe underlying Ag layer (had = 3.04 Å), the Cs atoms are probably located above the Ag atoms and not at the centers of the Ag triangles
and Si trimers.
Fig. 3(a) and (b) show the schematics of the Si(111)-√21×√21-(Ag,Cs) and Si(111)-√21×√21-Ag (or Si(111)-√21×√21-(Ag, Au)) surfaces, respectively. In the former surface, Cs adatoms are almost homogeneously distributed while maintaining a triangular lattice with dCs–Cs =10.12 Å. In the latter surfaces, Ag or Au adatoms form small triangularislands around the Si trimers with dAg–Ag or dAu–Au =6.16 Å. Why does
the above difference appear despite the fact that adatoms are in themonovalent state and have the same √21 ×√21 periodicity?
Geometrically, the minimum adatom coverage required for√21 × √21 periodicity is 1/21 ML. However, experimentally, no√21 × √21 periodicities are observed when the coverage is less than
3/21 (= 1/7) ML. This implies that when the adatom coverage isless than 3/21 (=1/7) ML, (i) adatoms are not inﬂuenced by
self-ordering processes and can move freely and/or (ii) the adatoms
are mutually and locally bound to form complexes, and such local
complexes are randomly distributed.
The Si(111)-√21× √21-Ag (or Si(111)-√21× √21-(Ag, Au)) surface
might be explained as the second case mentioned above [25]. When theadatom coverage is low, the Ag or Au adatoms form triangle islands spatially and randomly. With an increase in the adatom coverage, eventually, a √21× √21 periodicity, as shown in Fig. 3(b), is established. Sucha change is probably due to the cohesive nature of the Ag and Auatoms. The noble metals have s–d hybridized orbitals and hence thecohesive nature is more prominent in the Ag and Au atoms. On the contrary, the Si(111)-√21 × √21-(Ag, Cs) surface might be explained as theﬁrst case since the dCs–Cs value (=10.12 Å) is close to the maximum
adatom distance (10.16 Å) when 1/7 ML of adatoms is homogeneously
distributed and arranged in a triangular lattice. Probably, Cs atoms arehighly mobile when the coverage is low. With an increase in the coverage, each Cs atom is affected by the potentials due to the other atoms
and eventually an ordered structure is formed. Even so, because of
their weak cohesive nature, Cs atoms do not tend to agglomerate andremain as far as possible from one another. The above difference between noble and alkali metals seems to originate from their electron
conﬁgurations of the s–d hybridized orbitals or nearly pure s orbitals.
Such a scenario might be modeled by considering two-dimensional
Friedel oscillations [5].

4. Summary
On the Si(111)-√21×√21-(Ag, Cs) surface, Cs atoms are located at aheight of 3.04±0.26 Å from the underlying √3×√3-Ag layer and arrange themselves in a triangular structure with a side length of 10.12 Åin the lateral direction. The structure of the Si(111)-√21×√21-(Ag, Cs)
surface is signiﬁcantly different from that of the Si(111)-√21×√21-Agand Si(111)-√21×√21-(Ag, Au) surfaces, although √21×√21 periodicity is observed in all cases. This difference is because of the different electronic structures associated with alkali and noble metals.

Fig. 3. Schematic of the structures of (a) Si(111)-√21 × √21-(Ag, Cs) and (b) Si(111)-√21 × √21-Ag and -(Ag, Au) surfaces. Large, medium, and small circles indicate the Cs, Ag (Au),and Si atoms, respectively. A √21 × √21 unit cell is denoted by the parallelogram.

Y. Fukaya et al. / Surface Science 606 (2012) 1918–1921Acknowledgment
The present research was partly supported by Grant-in-Aid forYoung Scientists (B) 22740205 from JSPS.
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