PHYSICAL REVIEW B 88, 205413 (2013)

Structure of silicene on a Ag(111) surface studied by reflection high-energy positron diffraction
Y. Fukaya,1,* I. Mochizuki,2 M. Maekawa,1 K. Wada,2 T. Hyodo,2 I. Matsuda,3 and A. Kawasuso1
12Advanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan
Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
3Institute for Solid State Physics, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan(Received 11 September 2013; published 8 November 2013)
The structure of silicene fabricated on a Ag(111) surface was determined using reflection high-energy positron
diffraction with a linac-based brightness-enhanced intense positron beam. From the rocking curve analysis, thesilicene was verified to have a buckled structure with a spacing of 0.83 Å between the top and the bottom Silayers. The distance between the bottom Si layer in the silicene and the first Ag layer was determined to be2.14 Å. These results agree with the theoretically predicted values from a previous study [Phys. Rev. Lett. 108,155501 (2012)] within an error of ±0.05 Å.
DOI: 10.1103/PhysRevB.88.205413

PACS number(s): 61.46.−w, 61.05.jh, 61.48.Gh

Two-dimensional systems suspended on a crystal surface,such as graphene,1 have attracted increasing attention becauseof the interest in their fundamental properties and their potential applications in the technology of high carrier-mobility
electronic devices. Silicene, which is a two-dimensional sheet
composed of silicon, is an example of an analog of graphene.
Since the first theoretical discussion on the structural andelectronic properties of free-standing silicene,2 the synthesis ofsilicene has been extensively attempted by many researchers.
In particular, various phases of Si layers were reported to form
on a Ag(111) surface; the resulting phase was dependent on
the amount of Si coverage and the substrate temperature.3,4Recently, the synthesis of silicene on a Ag(111) surface, finally,
was successfully performed.5,6 Silicene has also been formed
on a zirconium diboride thin film grown on a Si(111) surface.7
Two-dimensional symmetry of silicene on a Ag(111)
surface, predicted by the theoretical calculations, was verified
by scanning tunneling microscopy observations.5,6 However,a buckled structure due to the strong sp3 -bonding character
predicted by the theories,5,6 as shown in Fig. 1, has not been
confirmed. The buckling feature is in sharp contrast to the caseof graphene, which is a flat sheet. The calculated shape of theDirac cone of the energy dispersion in silicene is modulatedby the magnitude of buckling in the silicene sheet8 as well as
by interactions with the Ag(111) surface.9 Thus, the spacing
between the top and the bottom Si layers in silicene and thatbetween the bottom Si and the top Ag layers are importantfactors in understanding its electronic properties.
In this paper, we determined the detailed structure ofsilicene on a Ag(111) surface using reflection high-energy
positron diffraction (RHEPD) with a brightness-enhanced
intense positron beam. Recently, RHEPD has been shown to
be a powerful tool in determining the structure of the topmost
surface layer.10 When incident on a surface at an angle smaller
than a certain critical angle, positrons are totally reflected at
the first surface layer, owing to the positive potential barriers ofmaterials to positrons. Under the total reflection condition, thepenetration of the positron wave into the crystal is negligibly
small, and hence, the diffraction intensity depends almost
exclusively on the structure and the thermal vibration of
the first surface layer. Since the first observation of RHEPD
using a 22 Na-based positron beam,11 this method has been1098-0121/2013/88(20)/205413(4)applied to the structural analysis of various surface systems.12
Developments incorporating the positron beam at the Slow
Positron Facility of the Institute of Materials Structure Science,KEK,13 which is nearly 100 times more intense than the22Na-based positron beam, has allowed measurements ofgreatly increased precision and, consequently, a more efficient
structural analysis of the topmost surface layer.
The present study, carried out at the Slow Positron Facilityat KEK,13 used a pulsed 50-Hz electron beam from a dedicated
55-MeV linac to produce positrons from pair creation throughbremsstrahlung radiation in a Ta convertor. The positrons werethen injected into 25-μm W foils, moderated to thermal energy,
and a fraction were spontaneously reemitted from the foil
surfaces with an energy of 3 eV due to the negative work
function. The positron convertor/moderator assembly washeld at an electrostatic voltage of 15 kV. The monoenergetic
positrons emitted were, thus, accelerated to 15 keV as
they entered the grounded beamline and were magneticallytransported to the experimental hall. The beam was thenreleased into a nonmagnetic region and was focused with amagnetic lens on a transmission type remoderator (100-nm Wfilm)14,15 electrostatically floated to 10 kV. The remoderated
positrons were reemitted from the other side of the film with abrightness enhanced by about 5 × 105 times over the initial
magnetically guided beam and were further transported tothe grounded RHEPD chamber with an energy of 10 keV.
The final beam intensity at the sample was estimated tobe approximately 1 × 106 slow e+ /s with a beam diameterof 0.5 mm. The diffracted positrons were observed with amicrochannel plate and a charge-coupled device camera. The
reflection high-energy electron diffraction (RHEED) was used
to monitor the Ag thickness and to check the formation of
the silicene through the symmetry of the pattern in situ as insurface experiments with other techniques.
The fabrication procedure of silicene was as follows.5,6 A Si
substrate was cut from an n-type mirror polished Si(111) wafer.
This sample was held at 700 K overnight, then was taken up to1473 K for a few seconds several times in ultrahigh vacuum—aclean 7 × 7 reconstructed structure was, thus, formed on theSi(111) surface. By depositing Ag atoms onto the Si(111)-7 ×
7 surface at 130 K (Ref. 16) and subsequently annealing it byheating up to room temperature, a crystalline Ag(111) thin film

205413-1©2013 American Physical Society

Y. FUKAYA et al.

PHYSICAL REVIEW B 88, 205413 (2013)

111

Specularr intensity (arb. units)

(a)

333

222

: Exp: Cal

Total reflection

0123456

Specular intensity (arb. units)

Glancing angle (deg)FIG. 1. (Color online) Schematic of proposed silicene on aAg(111) surface.5,6 Light- and deep-red circles are the Si atoms,
and the gray circles are the Ag atoms of the substrate. The spacing
between the top (denoted by large light-red circles) and the bottom(denoted by small deep-red circles) Si layers is denoted by . The
distance between the bottom layer of silicene and the underlying firstAg layer is denoted by d. The bond angles are labeled α and β.

with a thickness of 20 monolayers (MLs) was formed. After
depositing 1 ML of Si atoms at 520 K, the formation of a 4 × 4
structure was confirmed by the RHEED pattern obtained where−2
1 ML is defined as 1.38 × 1015 cm√. Weak√ spots showing theformation of a small fraction of 13 × 13 domains werealso observed, indicating that the control within the narrow3
temperature range√during√the deposition was not perfect. The
coverage of the 13 × 13 domains is estimated to be lessthan 5% from the spot intensity √relative√to that of the 4 × 4
domains. Thus, the effect of the 13 × 13 domains on therocking curve for the specular spot is negligibly small.
The critical angle for the total reflection of a positron beamfrom a surface θc is given by θc = arcsin(eV /E)1/2 , where eV
and E are the mean potential energy of the positrons in thecrystal and the kinetic energy of the incident positron beam.10
For a positron beam of E = 10 keV, θc is estimated to be 2.0◦
for Si (eV = 12 eV) and 2.8◦ for Ag (eV = 23 eV).
RHEPD rocking curves of the specular spot were measured
in two different incidence directions. The first was in theone-beam condition where the incident azimuth was 13◦ off
the [112̄] direction. Under this condition, the intensity of thespecular spot depends mainly on the vertical components of
the atomic positions and the number density of atoms in eachlayer for atoms in plane are randomly distributed when viewed
with a small glancing angle along this particular incidence
direction.17 The other was in the many-beam condition wherethe incident azimuth was along the [112̄] direction. Under thiscondition, the intensity of each spot depends on the in-plane
as well as the vertical components of the atomic positions. By
using rocking curve analyses in both conditions, it is possible
to make a reliable determination of the structure. First, thevertical features of the structure can be elucidated by using
the data from the one-beam condition without being hindered

111(b)

333

222: Exp: Cal

Total reflection

01

2

3

4

5

6

Glancing angle (deg)FIG. 2. RHEPD rocking curves for (a) the Ag(111)-1 × 1 surfaceand (b) silicene on a Ag(111) surface in the one-beam condition
at room temperature. Circles are the experimental data. Solid lines
indicate the calculated curves using optimum values for the adjustableparameters. The incident positron energy is 10 keV. The angle range
for total reflection for the Ag crystal is shown by a double-headedarrow.

by the uncertainty in the in-plane location of atoms. Then, thein-plane positions can be found by using the data from themany-beam condition taking into account the information on
the vertical features already known.
After deposition of Ag atoms on the Si(111)-7 × 7 surface,
the formation of the Ag(111)-1 × 1 surface was confirmedfrom observations of the RHEED pattern. Then the interlayer
distance between the first and the second Ag layers wasdetermined by the rocking curve of RHEPD in the one-beamcondition at room temperature. The circles in Fig. 2(a) show theresults obtained, and the solid line shows the best-fit rocking
curve calculated with the dynamical diffraction theory.18 The
thermal vibrational amplitude for the Ag layers was assumed tobe 9.64 × 10−2 Å.19 The absorption potential due to electronic
excitations was taken to be 1.68 eV for Ag layers.20 Theinterlayer distance between the first and the second Ag layers
was varied so as to minimize the difference between themeasured and the calculated rocking curves. The goodnessof fit was judged using a reliability factor R.21 The optimum
interlayer distance was, thus, determined to be 2.34 Å, which

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STRUCTURE OF SILICENE ON A Ag(111) SURFACE . . .

PHYSICAL REVIEW B 88, 205413 (2013)(a)Specular intensity (arb. units)

Total
reflection

111 222 333

Δ= 0 Å(b)Totalreflection

Δ (Å)

d (Å) d = 2.2 Å

1.00.82.80.72.6123

Specular intensity (arb. units): Exp: Cal

Total reflection

0123333456

Glancing angle (deg)111 222(b)333

Total reflectiono()
120
110
100
9080

0

123456

Glancing angle (deg)FIG. 4. (a) RHEPD rocking curve for silicene on a Ag(111)
surface in the many-beam condition at room temperature. Circles
indicate the experimental data. The solid line indicates the calculated
curve using the optimum parameters. (b) Calculated rocking curves
for silicene on a Ag(111) surface in the many-beam condition forvarious values of α with β fixed at 110◦ .

111 222 333

3.00111 222(a)Specular intensity ((arb. units)

is close to that of 2.36 Å in the bulk. Therefore, the first Ag
layer of the Ag(111) thin-film surface was found to have nosignificant relaxations in the lattice.
The circles in Fig. 2(b) show the RHEPD rocking curvefor the 4 × 4 reconstructed structure of silicene on theAg(111) surface measured in the one-beam condition at room
temperature. It is significantly different from the curve before
deposition [Fig. 2(a)]. Using these data, the interlayer distances
and the number density in each layer in the silicene weredetermined. The thermal vibrational amplitude and the absorption potential for silicene were assumed to be 7.84 × 10−2 Å
(Ref. 19) and 0 eV,21 respectively. The rocking curve wascalculated as a function of the distance between the top andthe bottom Si layers  and the distance between the bottom
Si layer and the top Ag layer d (see Fig. 1) and the number
densities of the top and bottom layers of atoms in silicene ρtopand ρbottom , respectively. These parameters were simultaneously varied with the constraint that ρtop + ρbottom = 18 so as
to minimize the factor R. The solid line in Fig. 2(b) is the result;it can be seen that the experimental result is reproduced very
well by the calculation. The optimized values thus obtained are
d = 2.14,  = 0.83 Å, ρtop = 5.9, and ρbottom = 12.1. Thesevalues are in good agreement with the theoretical predictionsof Ref. 5 (d = 2.17,  = 0.78 Å, ρtop = 6, and ρbottom = 12).
The value of  reported in Ref. 6 is slightly smaller thanour result. Thus, it is certain that silicene has some buckled
structure as predicted and does not have a flat structure as ingraphene.
Figures 3(a) and 3(b) show the dependence of the calculated
rocking curves on d and , respectively. The value of  isfixed at 0 Å in (a) and that of d is fixed at 2.2 Å in (b). The
sensitivity to these parameters of both the overall shape andthe peak positions are illustrated in these figures. In Fig. 3(a),it can be seen that the peak positions gradually shift towards
lower angles with increasing d. The same tendency is observedfor  up to 0.6 Å as shown in Fig. 3(b). When the value of 

0.6

2.4

0.4

2.2

0.2

2.00.04 5 0 1 2 3Glancing angle (deg)456FIG. 3. Calculated RHEPD rocking curves for silicene on aAg(111) surface in the one-beam condition (a) for various d’s witha fixed  and (b) for various ’s with a fixed d. Dotted lines are avisual guide.

increases from 0.6 to 0.8 Å, there appears to be a sudden shift
towards higher angles of the peak positions of the 222 and 333
Bragg reflections.
The circles in Fig. 4(a) show the RHEPD rocking curvemeasured in the many-beam condition. Using these data, thein-plane components of the atomic positions were determined.
The rocking curves under this condition were calculated forvarious bond angles α and β (see Fig. 1) within the frameworkof the model given in Ref. 5 and using the values for dand  obtained from the analysis of the rocking curve inthe one-beam condition. Figure 4(b) shows the sensitivityof the curve to the value of α with β fixed at 110◦ . The
width of the peak at 2.5◦ broadens, and the dip at around3.5◦ shifts towards higher angles with increasing α. The sametendency was found for β with α fixed. The values of α andβ were simultaneously varied with the constraint of d = 2.14
and  = 0.83 Å so as to minimize the R factor. The solidline in Fig. 4(a) shows the best-fit result. The optimum bondangles thus determined are α = 112◦ and β = 119◦ , which
are close to those expected from the theoretical calculations.5
This indicates that six Si atoms at on-top sites in the unit cell

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Y. FUKAYA et al.

PHYSICAL REVIEW B 88, 205413 (2013)

TABLE I. Structure parameters for silicene on a Ag(111) surface.
 (Å)d (Å)α (◦ )β (◦ )

0.83
0.78
0.7

2.14
2.17

112
110

119118

confirmed experimentally by this study using RHEPD. The
magnitude of the buckling and the interlayer distance between
the silicene and the underlying Ag layer concur with thosereported previously by theoretical calculations5 within an errorof ±0.05 Å.

are displaced upward. The present study, thus, confirms thatthe 4 × 4 model predicted by the theoretical calculations5,6 isvalid for the atomic configuration of silicene on a Ag(111)
surface. Table I summarizes these results.
The atomic arrangement of silicene on a Ag(111) surface,
theoretically proposed5,6 to have a buckled configuration, was

We thank T. Shirasawa, K. Kawahara, and N. Takagiof the University of Tokyo for useful suggestions on thesample preparation. This research was conducted under thePF Proposal No. 2012G653 and the auspices of the Joint
Development Research at the High Energy Accelerator Research Organization (KEK). The present work was partly
supported by a Grant-in-Aid for Scientific Research, Grant
No. (S) 24221007 and for Young Scientists Grant No. (B)25800182 from JSPS.

*10

1

11

This study
Theory5
Theory6

fukaya.yuki99@jaea.go.jp
A. K. Geim, Science 324, 1530 (2009).
2
K. Takeda and K. Shiraishi, Phys. Rev. B 50, 14916 (1994).
3
H. Jamgotchian, Y. Colignon, N. Hamzaoui, B. Ealet, J. Y. Hoarau,B. Aufray, and J. P. Bibérian, J. Phys.: Condens. Matter 24, 172001(2012).
4
R. Arafune, C.-L. Lin, K. Kawahara, N. Tsukahara, E. Minamitani,
Y. Kim, N. Takagi, and M. Kawai, Surf. Sci. 608, 297 (2013).
5
P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis,
M. C. Asensio, A. Resta, B. Ealet, and G. Le Lay, Phys. Rev. Lett.
108, 155501 (2012).
6
C.-L. Lin, R. Arafune, K. Kawahara, N. Tsukahara, E. Minamitani,Y. Kim, N. Takagi, and M. Kawai, Appl. Phys. Express 5, 045802(2012).
7A. Fleurence, R. Friedlein, T. Ozaki, H. Kawai, Y. Wang, andY. Yamada-Takamura, Phys. Rev. Lett. 108, 245501 (2012).
8S. Cahangirov, M. Topsakal, E. Aktürk, H. Şahin, and S. Ciraci,
Phys. Rev. Lett. 102, 236804 (2009).
9C.-L. Lin, R. Arafune, K. Kawahara, M. Kanno, N. Tsukahara,
E. Minamitani, Y. Kim, M. Kawai, and N. Takagi, Phys. Rev. Lett.
110, 076801 (2013).

A. Ichimiya, Solid State Phenom. 28-29, 143 (1992).
A. Kawasuso and S. Okada, Phys. Rev. Lett. 81, 2695
(1998).
12Y. Fukaya, M. Maekawa, I. Mochizuki, K. Wada, T. Hyodo, andA. Kawasuso, J. Phys.: Conf. Series 443, 012068 (2013).
13
K. Wada, T. Hyodo, A. Yagishita, M. Ikeda, S. Ohsawa,
T. Shidara, K. Michishio, T. Tachibana, Y. Nagashima,
Y. Fukaya, M. Maekawa, and A. Kawasuso, Eur. Phys. J. D 66, 37(2012).
14
A. P. Mills, Jr. and R. J. Wilson, Phys. Rev. A 26, 490 (1982).
15
M. Fujinami, S. Jinno, M. Fukuzumi, T. Kawaguchi, K. Oguma,and T. Akahane, Anal. Sci. 24, 73 (2008).
16
I. Matsuda, T. Ohta, and H. W. Yeom, Phys. Rev. B 65, 085327(2002).
17
A. Ichimiya, Surf. Sci. 192, L893 (1987).
18
A. Ichimiya, Jpn. J. Appl. Phys. 22, 176 (1983).
19
C. Kittel, Introduction to Solid State Physics (Wiley, New York,1995).
20
G. Radi, Acta Crystallogr. A 26, 41 (1970).
21
Y. Fukaya, A. Kawasuso, K. Hayashi, and A. Ichimiya, Phys. Rev.
B 70, 245422 (2004).

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