Surface Science 606 (2012) 919–923

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Atomic structure of two-dimensional binary surface alloys:
Si(111)-√21 × √21 superstructure
Y. Fukaya a,⁎, I. Matsuda b, M. Hashimoto a, K. Kubo c, T. Hirahara c, S. Yamazaki c, W.H. Choi d, H.W. Yeom d,
S. Hasegawa c, A. Kawasuso a, A. Ichimiya aaAdvanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan
ISSP, University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan
Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japand
Department of Physics and Center for Atomic Wires and Layers, Pohang University of Science and Technology, Pohang 790-784, Republic of Koreabca r t i c l e

i n f oArticle history:
Received 24 May 2011
Accepted 6 February 2012
Available online 19 February 2012
Keywords:
Two-dimensional alloys
SiliconGold
Silver
Surface structure
Reﬂection high-energy positron diffraction(RHEPD)
Photoemission spectroscopy (PES)a b s t r a c t
The atomic structures of Au and Ag co-adsorption-induced √21 × √21 superstructure on a Si(111) surface,i.e., (Si(111)-√21 × √21-(Au, Ag)), where the Si(111)-5 × 2-Au surface is used as a substrate, have been investigated using reﬂection high-energy positron diffraction (RHEPD) and photoemission spectroscopy. Fromcore-level spectra, we determined the chemical environments of Ag and Au atoms present in the Si(111)√21 × √21-(Au, Ag) surface. From the rocking curve and pattern analyses of RHEPD, we found that the atomic
coordinates of the Au and Ag atoms were approximately the same as those of the Au and Ag atoms in otherSi(111)-√21 × √21 surfaces with different stoichiometries. On the basis of the core-level and RHEPD results,
we revealed the atomic structure of the Si(111)-√21 × √21-(Au, Ag) surface.
© 2012 Elsevier B.V. All rights reserved.

1. Introduction
The Si(111)-√3 × √3-Ag surface, which is formed by the adsorption of one monolayer (ML) of Ag atoms on a Si(111)-7 × 7 surface,has been extensively studied as a prototype of a two-dimensional metallic system fabricated on a semiconductor surface [1,2]. In suchcases, the coverage, ρ, of 1 ML is deﬁned as 7.83 × 10 14 cm − 2. The adsorption of noble metal atoms (e.g., Cu, Ag, and Au) on the Si(111)√3 × √3-Ag surface leads to the formation of √21 × √21 superstructures. In addition, the surface electrical conductivity sharply increases
with increasing coverage of the adsorbed noble metal atoms [1,2].
When the Si(111)-√21 × √21 superstructure covers the whole surface, the surface electrical conductivity is maximized. At an additional
coverage of 0.14 ML, the conductivity is approximately four times
greater than that of a bare Si(111)-√3 × √3-Ag surface [1,2]. Thisdrastic increase in electrical conductivity originates from the dopingof electrons into the Si(111)-√3 × √3-Ag surface since the Fermi circleof the two-dimensional free-electron-like surface state on this surface
is dependent upon the amount of noble metal atoms deposited [3].

⁎ 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.
doi:10.1016/j.susc.2012.02.006

Recently, we investigated, by means of reﬂection high-energy positron diffraction (RHEPD), the structure of the Si(111)-√21 × √21 surface with ρAg = 1.14 ML and ρAu = 0.00 ML, and ρAg = 1.00 ML andρAu = 0.14 ML, where the Si(111)-√3 × √3-Ag surface is used as a substrate [4,5]. Although various structural models were proposed bydifferent surface techniques [6–12], we found that the atomic structures for the Si(111)-√21 × √21 family are almost identical, save forthe marginal difference in adatom heights.
Since the number of valence electrons per atom (e/a) of Ag or Au is
equal to 1, formation of the √21 × √21 phase is achieved when the
total metal coverage is 1.14 ML and e/a is constant. Such one-to-one
correspondence between the crystal periodicity and e/a is known toexist in electron compounds in a bulk binary system [13–16]. Therefore, the Ag- and Au-induced Si(111)-√21 × √21 superstructure isconsidered to be a promising candidate as a two-dimensional electron compound, and it has recently been modeled semi-empirically[17]. If the Si(111)-√21 × √21 superstructures can be categorized aselectron compounds, then Si(111)-√21 × √21 superstructures fabricated with different Ag and Au atom stoichiometries will likely havethe same structure. In fact, the adsorption of Ag atoms (ρAg = 0.74 ML)on the Si(111)-5 × 2-Au surface (ρAu = 0.4 ML) also results in √21×
√21 periodicity [Si(111)-√21 × √21-(Au, Ag) surface] in the diffraction
pattern [17,18]. In a previous paper [18], we analyzed the proﬁles of
the rocking curves and the intensity distribution in the diffraction

pattern by substituting the Au atoms with Ag atoms, i.e., all the atoms
were assumed to be Ag atoms. Thus, the distinguishing adsorption
sites of the Ag and Au atoms in the √21 × √21 structure still remainunresolved. In this paper, we ﬁnd, from core-level photoemission measurements, that Ag and Au atoms individually occupy single chemicalsites in the √21× √21-structure. We also re-examine possible structuralmodels by using the RHEPD analysis. The √21× √21-phase, preparedwith a different composition of Ag and Au, shows an atomic structure
similar to that previously observed, and it can be considered as a regularalloy-type two-dimensional electron compound.

a)Au 5d Valence bandnormal emission

21

21-(Au,Ag)Ag 4d

2. Experimental procedure

He I
6

3. Results and discussion
Fig. 1(a) shows Ag 4d and Au 5d spectra for the Si(111)-√3 × √3-Ag
and Si(111)-√21 × √21-(Au, Ag) surfaces. The Ag 4d spectrum for theSi(111)-√3 × √3-Ag surface has two peaks at a binding energy ofaround 6 eV. The spectrum is similar to that observed in a previous
study [20]. As regards the Si(111)-√21 × √21-(Au, Ag) surface, there
are two components: Au 5d and Ag 4d, as shown in Fig. 1(a). This clearly
indicates that the Si(111)-√21 × √21-(Au, Ag) surface includes both Ag
and Au atoms.
Fig. 1(b) shows the Ag 3d spectra for the Si(111)-√21 × √21-(Au, Ag)
and Si(111)-√3 × √3-Ag surfaces, and Fig. 1(c) shows the Au 4f spectrum for the Si(111)-√21 × √21-(Au, Ag) surface. The Ag 3d spectrum
for the Si(111)-√21 × √21-(Au, Ag) surface is very similar to that for
the Si(111)-√3 × √3-Ag surface, as shown in Fig. 1(b). Since the Ag
atoms in the Si(111)-√3 × √3-Ag surface are located at the same sites
on the surface, those in the Si(111)-√21 × √21-(Au, Ag) surface likely
take rather identical chemical environment. In fact, each peak can beﬁtted by a single Voigt function with a spin–orbit splitting of 6.0 eV, as
illustrated by the solid lines in Fig. 1(b). In the ﬁtting procedure, thefull width at half maximum of the Lorentzian function was ﬁxed at
0.27 eV, as determined in a previous photoemission experiment [21],and that of the Gaussian function was set as a ﬁtting parameter. The
Gaussian widths for the Si(111)-√21× √21-(Au, Ag) and Si(111)√3 × √3-Ag surfaces were determined to be 0.37 and 0.44 eV, respectively. With regard to the Au 4f spectrum (Fig. 1(c)), we can identify

3-Ag

2

EF

Binding Energy (eV)Intensity (arb. units)

Substrates were cut from a mirror-polished n-type Si(111) wafer
with a resistivity of 1–10 Ω·cm. In order to prepare clean 7 × 7 surfaces, the substrates were annealed at 400 °C for several hours andheated several times at 1200 °C for a few seconds under ultra-highvacuum (UHV) conditions. Then, 0.40 ± 0.08 ML of Au atoms was deposited onto the Si(111)-7 × 7 surfaces at 600 °C to form a 5 × 2-Au
surface. Finally, 0.74 ± 0.10 ML of Ag atoms was deposited onto theSi(111)-5 × 2-Au surface at 460 °C. The deposition rates of Ag and
Au atoms were calibrated by the formations of Si(111)-√3 × √3-Ag
and Si(111)-β-√3 × √3-Au surfaces, respectively. After the substratetemperature was decreased to room temperature, well-ordered
Si(111)-√21 × √21-(Au, Ag) surfaces were observed.
The experiments were carried out in two different UHV chambers.
The RHEPD measurements were conducted using a highly parallel
and well-focused positron beam generated from a 22Na positronsource and electromagnetic lens system [19]. The positron beamenergy was set at 10 keV. The diffraction patterns were magniﬁedwith a microchannel plate and a phosphor screen, and recordedwith a charge-coupled-device camera. For the rocking curve measurements, the glancing angle of the incident positron beam wasaltered by rotating the sample from 0.3° to 6.0°, in steps of 0.1°.
Core-level photoemission spectra were recorded with linearly polarized synchrotron radiation on beamline BL-8A1 at Pohang Light
Source (Korea). The well-ordered Si(111)-√21 × √21-(Au, Ag) surfaces were characterized by low-energy electron diffraction (or reﬂection high-energy electron diffraction) in the core-level measurements.

43

Normalized Intensity (arb. units)

Y. Fukaya et al. / Surface Science 606 (2012) 919–923

Intensity (arb. units)

920

b)

21

3

8

21-(Au,Ag)

3-Ag
8

4

0

-4

Relative Binding Energy (eV)

c)

21

Ag 3d

hν=500 eV

Au 4f

21-(Au,Ag)4hν=500 eV
0Relative Binding Energy (eV)Fig. 1. Core-level spectra of (a) Ag 4d for the Si(111)-√3 × √3-Ag surface and Au 5d for
the Si(111)-√21 × √21-(Au, Ag) surface, (b) Ag 3d for the Si(111)-√3 × √3-Ag andSi(111)-√21 × √21-(Au, Ag) surfaces, and (c) Au 4f for the Si(111)-√21 × √21-(Au,Ag) surface. The Ag 4d, Ag 3d, and Au 4f spectra were obtained with a He Iα source
and at a photon energy (hν) of 500 eV, respectively. In (b), the open circles and solidlines denote the experimental and ﬁtted curves, respectively.

two peaks with a spin–orbit splitting of about 3.7 eV [22]. Similarly,
each peak in the Au 4f spectrum can be reproduced by a single Voigt
function. A single Au 4f peak with the spin–orbit splitting in the spectrum indicates that the chemical environment of all Au atoms in theSi(111)-√21 × √21-(Au, Ag) surface is the same.
The bottom curve in Fig. 2 shows the RHEPD rocking curve for theSi(111)-√21 × √21-(Au, Ag) surface at room temperature under aone-beam condition [18]. Under this condition, the RHEPD intensity
is very sensitive to the surface-normal components of atomic positions [23]. The rocking curve for the Si(111)-√21 × √21-(Au, Ag) surface mainly consists of intense total reﬂection [24,25] and (111)
Bragg reﬂection. A comparison between the rocking curves for theSi(111)-√21 × √21-(Au, Ag) and other Si(111)-√21 × √21 surfaces
with a different stoichiometry [4,5] shows that the shapes of thesecurves are similar to each other. This result suggests that there is asimilarity in the stacking of Ag and Au atoms in the other Si(111)√21 × √21 and the Si(111)-√21 × √21-(Au, Ag) surfaces.
Analyses of the rocking curves at various azimuths were carriedout by simulating possible structural models using dynamical diffraction theory [26]. In the atomic model of Fig. 3, for coverage of
ρAg = 0.74 ML (ρAu = 0.4 ML), there are 24 atomic sites and 15 Ag(9 Au) atoms in the √21 × √21 unit cell. Since this results in a million
possible Ag and Au combinations, the possible structure models are
narrowed down based upon the photoemission results that wererecorded before the RHEPD analyses. The adsorption sites for Ag
and Au atoms are considered as follows: three adatoms, nine atoms
bonded to the adatoms, nine nearest neighbor atoms to the atoms
bonded to the adatoms, and the remaining three atoms forming asmall triangle (Fig. 3). In fact, there are four different adsorption
sites for Ag and Au atoms. On the other hand, the core-level results(Fig. 1) indicate that both the Ag and Au atoms individually have similar chemical environments. To relate the adsorption sites to thechemical environments in the surface structure, Fig. 3 depicts theatomic structural model with chemical bonds (shown as lines inFig. 3). Subsequently, the metal atoms can be classiﬁed into two

Y. Fukaya et al. / Surface Science 606 (2012) 919–923

222
111

333

444

TR

RHEPD intensity (arb. units)

: exp
: cal
(0 0)

(1/3 1/3)(2/3 2/3)

one-bea m

0

1

2

3

4

5

6

Glancing angle (deg)Fig. 2. (Bottom) RHEPD rocking curves of the specular spots for the Si(111)-√21 × √21(Au, Ag) surface at room temperature under the one-beam condition (7.5° away
 direction). (Upper) RHEPD rocking curves of the (0 0), (1/3 1/3), andfrom the [112](2/3 2/3) spots for the Si(111)-√21 × √21-(Au, Ag) surface at room temperature. The direction. The circles indicate the experiincident azimuth corresponds to the [112]mental curves [18]. The solid lines show the calculated curves obtained using the optimum parameters. TR stands for the total reﬂection region.

groups, one that forms a bond with the Si atoms and the other that
forms bonds with the Si and the other metal atoms. The chemical environment of an atom is essentially determined by the difference between the electronegativities of the bonding atoms. The
electronegativities (χ) of Ag and Si atoms are both 1.9, while that of
Au atoms is 2.4 [27]. Therefore, Ag atoms within the Ag\Ag andAg\Si bonds possess similar chemical characteristics but those within the Au\Ag bond are distinctive. Thus, from stoichiometric considerations based on the chemical properties, the ﬁfteen Ag atoms in theunit cell will likely be distributed as three adatoms, nine atoms thatform bonds with the adatoms, and three atoms that compose asmall triangle. The Ag atoms are shown as red circles in Fig. 3. On
the other hand, the nine Au atoms seem to only occupy the nine
Au\Si bonding sites in the cell, as shown by purple circles in Fig. 3.
These assignments naturally explain the single-peak (the single
chemical environment) of the Ag 3d and Au 4f spectra (Fig. 1). In
the following discussion, structural arguments are made based on
this model.

Ag

921

In the calculations performed, the thermal vibrational amplitudesof the Ag and Au atoms, and the Si atoms were assumed to be 0.14 Å
and 0.07 Å, respectively [4]. The absorption potentials for the Ag andAu layers, and the Si layer due to electronic excitations (such as
single-electron and plasmons) were taken to be 0 eV and 1.70 eV, respectively [4,28]. The atomic coordinates in the binary layer, which
was composed of the Ag and Au atoms, were set at the inequivalent
triangle (IET) conﬁgurations produced by the ﬁrst-principles calculations [29]. The adatom heights of the Ag atoms were altered so as toprovide a ﬁt between the calculated and measured curves. The goodness of ﬁt was justiﬁed using the reliability (R)-factor [30].
Fig. 4 shows the R-factor as a function of the adatom heightfrom the top layer of the underlying IET structure. The value of theR-factor has a large dependence on the adatom height. From the minimum R-factor, we obtained the optimum adatom height as 0.51 Åfrom the top layer of the IET structure. The solid line (bottom) in
Fig. 2 shows the curve calculated using the optimum adatom height.
It should be noted that under the one-beam condition the calculated
rocking curve does not vary according to the atomic species composed within the IET structure because the number densities of the
Ag and Au atoms in the plane remain constant. The calculated curve
is in good agreement with the measured one (R = 1.7%). The optimum adatom height of 0.51 Å is similar to that in a previous study
concerning the Si(111)-√21 × √21 surface with different stoichiometries of Au and Ag atoms [4,5]. Compared with recent ﬁrst-principles
calculation results [11,12], the tendency for the immersion of anadatom into the IET structure is consistent with our result. However,
the adatom height obtained in this study is slightly higher than theﬁrst-principles calculations.
In order to investigate the atomic conﬁgurations in the plane, wemeasured the RHEPD rocking curves at symmetric azimuths. The
open circles (upper) in Fig. 2 show the RHEPD rocking curves for direction
the Si(111)-√21 × √21-(Au, Ag) surface along the [ 112][18]. Compared with the previous study on the Si(111)-√21 × √21
surface with different stoichiometries of Au and Ag atoms [4,5], we
can see that the shapes of the curves for the Si(111)-√21 × √21-(Au, direction are very similar. Again, this reAg) surface along the [112]sult suggests that there is a similarity in atomic coordinates for the
Ag and Au atoms on the other Si(111)-√21 × √21 and Si(111)-√21 ×√21-(Au, Ag) surfaces.
 direction in order
We calculated the rocking curves along the [112]to determine the atomic conﬁgurations in the plane. The adatom heightof the Ag atoms from the top layer of the underlying IET structure wastaken to be 0.51 Å, as determined above. In the rocking curve analyses,
three different adsorption sites were taken into consideration, namely,

3.0

Si
2.5

R (%)

Au

2.0

Fig. 3. Ball and stick model of the Si(111)-√21 × √21 superstructure. Large andmedium-sized red circles indicate the Ag adatoms and the Ag atoms bonded to theadatoms, respectively. Purple circles show the Au atoms and small black circles denote
the Si atoms. Gray lines show the Ag\Ag and Ag\Si bonds. Purple and black lines indicate the Au\Si and Si\Si bonds, respectively. The parallelogram denotes the √21 × √21
unit cell.

1.5
0.2

0.4

0.6

0.8

Adatom height (Å)
Fig. 4. R-factor between the experimental and calculated rocking curves under the onebeam condition as a function of the adatom height. The origin of the adatom height corresponds to the top layer of the underlying IET structure.

Y. Fukaya et al. / Surface Science 606 (2012) 919–923

at the center of the large triangle, the center of the small triangle, andthe center of the Si trimer. As mentioned above, the nine atoms bonded
to the adatoms are occupied with Ag atoms (denoted as medium-sized
red circles in Fig. 3). As listed in Table 1, when all the adatoms sit at thecenter of the large triangle in the IET structure, the value of R shows aminimum and the measured curves can be well reproduced by calculation, as shown in Fig. 2 (R = 2.8%). We also calculated the rocking curves
when nine Au atoms were bonded to the adatoms. As a result, we foundthat, in this condition, the differences in the calculated rocking curves
for the (0 0), (1/3 1/3), and (2/3 2/3) spots between the atomic species
composed of the IET structure are very small. Furthermore, we also
found that in this condition, the rocking curves for the (0 0), (1/3 1/3),and (2/3 2/3) spots are not sensitive to the atomic conﬁgurations at
the center of the large triangle. In order to conﬁrm the in-plane atomic
conﬁgurations of adatoms and Au atoms in the IET structure, we investigated the line proﬁle of the intensity distribution in the fractionalorder Laue zone.
The open circles in Fig. 5 show the experimental proﬁle of the
1/7th Laue zone for the Si(111)-√21 × √21-(Au, Ag) surface at room
temperature [18]. In the measured line proﬁle, the peak height of the(20/21 17/21) spot is greater than that of the (13/21 10/21) spot. The
relation between the peak heights is important for the determinationof the adsorption sites of the adatoms [4,5]. The intensity distribution
in the 1/7th Laue zone for the Si(111)-√21× √21-(Au, Ag) surface isalso approximately the same as those from the other Si(111)-√21 ×√21 surfaces with different stoichiometries [4,5].
From previous STM observations [16], the atomic conﬁguration ofadatoms possesses three-fold rotational symmetry. Thus, there are
two possible atomic conﬁgurations in which the three adatoms canoccupy the center of the large triangles in the IET structure, i.e., thethree adatoms either surround the Si trimer or the small triangle in
the IET structure. The solid lines (a) and (b) in Fig. 5 represent theline proﬁles calculated using the structural models with two different
atomic conﬁgurations. We also calculated the line proﬁles using thestructural models where the nine atoms bonded to the adatoms areoccupied by Au atoms, as shown by the solid lines (c) and (d) in
Fig. 5. Only the line proﬁle calculated using the structural model ofFig. 3 is able to reproduce the observed relationship between peakheights of the (20/21 17/21) and (13/21 10/21) spots. The observed
feature cannot be explained by considering other adsorption sites
and atomic species, as shown in Fig. 5. Consequently, we found thatthe surface structure of Si(111)-√21 × √21-(Au, Ag) was very close
to that of the other Si(111)-√21 × √21 structures with different stoichiometries of Au and Ag atoms.
Based on the present structural model of the Si(111)-√21 × √21(Au, Ag) surface, the bond length between an Ag adatom and the underlying Ag atoms is estimated to be 2.33 Å. The bond length is much
shorter than that expected from the atomic radius (2.88 Å). Considering the ionic bonding, the bond length is 2.00–2.56 Å, which is ingood agreement with the present value. Therefore, the bond length
between the Ag adatom and the underlying Ag atoms in the present
model can be explained by considering the ionic bonding that ispresent in the system.
The topmost layer of the Si(111)-√21× √21-(Au, Ag) surface iscomposed of the alloys of Au and Ag atoms. Moreover, the Au and Ag

Table 1
R-factors between experimental RHEPD rocking curves and calculated rocking curves
for the (0 0), (1/3 1/3), and (2/3 2/3) spots for three adatoms in the unit cell that are
individually located at various adsorption sites (center of the large triangle, center ofthe small triangle, and center of the Si trimer in the IET structure).
Structural model
Large triangle
Small triangle
Si trimer
R-factor (%)

1
3
0
0
2.84

2
2
1
0
3.52

3
2
0
1
3.28

4
1
2
0
4.56

5
1
1
1
3.29

6
1
0
2
3.54

7
0
3
0
6.72

8
0
2
1
5.12

9
0
1
2
4.00

10
0
0
3
3.43

__
__
(20/21 17/21)(20/21 17/21)____(13/21 10/21)(13/21 10/21)

RHEPD intensity (arb. unitss)

922

(d)

(c)
(b)

(a)

exp
-5 -4 -3 -2 -1

0

1

2

3

4

5

k// (Å-1)
Fig. 5. (Bottom) Line proﬁle of the intensity distribution in the 1/7th Laue zone of the
RHEPD pattern measured for the Si(111)-√21 × √21-(Au, Ag) surface [18]. (Upper) Calculated line proﬁles using the structural models where (a) the adatoms surround the Sitrimer and the Ag atoms are bonded to the adatoms, (b) the adatoms surround thesmall triangle and the Ag atoms are bonded to the adatoms, (c) the adatoms surroundthe Si trimer and the Au atoms are bonded to the adatoms, and (d) the adatoms
surround the small triangle and the Au atoms are bonded to the adatoms.

atoms within the topmost layer show solid solubility. In this system,
therefore, the number of valence electrons per atom plays an importantrole in the formation of the Si(111)-√21 × √21 superstructure. As a result, the Ag- and Au-induced √21 × √21 system is consistent with
two-dimensional electron compounds. In most cases of bulk binary systems, each atom composed of the alloys is randomly situated at thelattice sites. In other words, with regard to each atom, there is no periodicity in its unit cell. Hence, from the RHEPD analyses using the corelevel results, it is inferred that the Si(111)-√21× √21-(Au, Ag) surface
is the regular alloy phase.
4. Summary
In summary, we investigated the two-dimensional √21 × √21 phasecomposed of Au and Ag atoms, fabricated on a Si(111)-5 × 2-Au surface.
The atomic positions of the Au and Ag atoms in the Si(111)-√21× √21(Au, Ag) surface are very similar to those in the Si(111)-√21× √21 surfaces having different stoichiometries of Au and Ag atoms.
Acknowledgments
Useful comments on this paper provided by F. Nakamura and H.
Narita are gratefully acknowledged. WHC and HWY are supported
by CRi program of MEST, Korea. The present work was partly supported by Grant-in-Aid for Young Scientists (B) 22740205 from JSPS.
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