PHYSICAL REVIEW B 85, 245438 (2012)

Atomic configuration and phase transition of Pt-induced nanowires on a Ge(001) surface studied
using scanning tunneling microscopy, reflection high-energy positron diffraction, and angle-resolved
photoemission spectroscopy
Izumi Mochizuki,* Yuki Fukaya, and Atsuo Kawasuso
Advanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan

Koichiro Yaji, Ayumi Harasawa, and Iwao Matsuda
Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8581, JapanKen Wada and Toshio Hyodo
Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan(Received 19 January 2012; revised manuscript received 27 March 2012; published 22 June 2012)
The atomic conﬁguration and electronic band structure of Pt-induced nanowires on a Ge(001) surface areinvestigated using scanning tunneling microscopy, reﬂection high-energy positron diffraction, and angle-resolved
photoemission spectroscopy. A previously proposed theoretical model, composed of Ge dimers on the top layer
and buried Pt arrays in the second and fourth layers [Vanpoucke et al., Phys. Rev. B 77, 241308(R) (2008)],
is found to be the fundamental structure of the observed nanowires. At low temperatures (T < 80 K), each Ge
dimer is alternately tilted in the surface normal direction (asymmetric), causing a p(4 × 4) periodicity. At hightemperatures (T > 110 K), each Ge dimer is ﬂat with respect to the horizontal axis (symmetric), giving rise top(4 × 2) periodicity. Upon the above phase transition, the electronic band dispersion related to the Ge dimers in
the deeper energy region shifts to the Fermi level.
DOI: 10.1103/PhysRevB.85.245438

PACS number(s): 61.05.jh, 68.37.Ef, 79.60.Jv

I. INTRODUCTION

Self-assembled nanowires formed on semiconducting crystal surfaces have attracted a great deal of interest as they
can further our fundamental understanding of one-dimensional(1D) properties such as the non-Fermi liquid and the Peierlstype metal-insulator transition.1 From these interests, extensive studies have been performed on surface 1D systems such
as In/Si(111),2–4 Au/Si(553),(557),5 Y/Si(001),6 Au/Ge(001),7
and so on.
Recently, Gürlu et al.8 found that well-ordered and defectless nanowires can be formed on Ge(001) surfaces bydepositing a submonolayer of Pt atoms. They proposed astructural model called “Pt dimer (PD)” model, here, as shownin Fig. 1(a). In this model, the ﬁrst surface layer is covered by
Pt dimers on a β terrace8,31 giving rise to a p(4 × 2) unit cell.
The β terrace is composed of alternating Ge-Ge and Pt-Ge
dimers along nanowires. van Houselt et al.9 reported that thesurface periodicity changes from p(4 × 2) at room temperature
to p(4 × 4) at temperatures below 77 K. They explained
this phase transition as an alternate buckling of topmost
Pt dimers due to the Peierls instability, since the doubling
periodicity is associated with a reduction of the density ofstates near the Fermi level. On the other hand, Vanpoucke
et al.10 suggested the phase transition is not due to the Peierls
instability. On the basis of the results of recent research on
theoretical calculations, two models have been proposed for
the Pt-induced nanowires.11,12 Stekolnikov et al.12,13 suggested
the tetramer-dimer-chain (TDC) model as shown in Fig. 1(b).
In this model, the topmost layer is covered by Ge dimers and
Pt atoms are placed in the second layer. The reconstructedp(4 × 2) unit cell contains 0.25 monolayers (ML) of Pt atoms.
Figure 1(c) shows the nanowire (NW) model proposed by
1098-0121/2012/85(24)/245438(6)Vanpoucke et al.10,11 In this model, the total coverage of Pt
atoms is 0.75 ML and the surface periodicity is a p(4 × 2). The
two Pt arrays in the second layer are bridged by the top Ge
dimers. Pt atoms are also placed in the fourth layer. To explain
the observation of p(4 × 4) periodicity at low temperatures,
Vanpoucke et al. also suggested the existence of a Pt atom atsite A in Fig. 1(c).10 In this case, the Pt coverage is 0.8125 ML.
Despite extensive studies using scanning tunnelingmicroscopy/spectroscopy (STM/S) and ab initio
calculations,8–18 the atomic conﬁguration and the phasetransition mechanism of Pt-induced nanowires on Ge(001)surfaces have not been fully elucidated. There are only alimited number of works of diffraction and photoemission
studies revealing the structural and electronic properties associated with this surface. In this study, we investigated a highlyordered Pt-induced nanowires on Ge(001) surface using STM,
reﬂection high-energy positron diffraction (RHEPD),19–21 andangle-resolved photoemission spectroscopy (ARPES).
II. EXPERIMENTAL SETUPSThe samples used in the STM and RHEPD experiments
were cut from a mirror-polished ﬂat Ge(001) wafer (0◦ OFF,n type, R < 45 cm). Those used in the ARPES experiments
were cut from a vicinal Ge(001) wafer (2◦ OFF, n type, R <0.3 cm) tilted in [110] direction, to realize uniformly oriented
nanowires.22 Clean Ge(001) surfaces were prepared by a few
cycles of sputtering in 800 V Ar+ ion at 670 K for 15 min
and annealing at 850 K for 10 min. Pt atoms were depositedat the rate of 0.01 ML/min at 620 K, to afford a coverage of∼1.2 ML [1 ML is deﬁned as the number of Ge atoms on
the ideal Ge(001) cutting plane (∼6.3 × 1014 atoms/cm2 )].
The amount of deposited Pt atoms was calibrated using the245438-1©2012 American Physical Society

IZUMI MOCHIZUKI et al.

PHYSICAL REVIEW B 85, 245438 (2012)

positron beam energy and the internal potential of a Ge crystal(2.3 eV).24 The ARPES measurements were performed withpolarized ultraviolet light radiation of hν = 24 eV and anangle-resolved electron analyzer (SCIENTA SES-100) at the
BL-18A beamline of the KEK Photon Factory (Institute for
Solid State Physics, University of Tokyo). The angular andenergy resolutions were less than 1◦ and 0.1 eV, respectively.
All the above experiments were conducted under ultra-highvacuum (∼ 10−8 Pa) conditions.
III. RESULTS AND DISCUSSION
A. Results of STM observations

Figure 2(a) shows an STM image obtained at room
temperature. As proposed by Schäfer et al.,15 well-ordered
Pt-induced nanowires are formed on the Ge(001) surface. The
nanowire arrays cover a large area with few defects. The
total area ratio of α and β terraces8 is less than 10%.
The α terrace contains a dense defect of missing dimers related
to Pt atoms sitting in subsurface positions, where the nanowires
are not constructed. As shown in Figs. 2(b) and 2(c), p(4 × 4)
periodicity observed at 50 K changes to p(4 × 2) at 100 K.
The p(4 × 2) periodicity is preserved at room temperature.
Figures 2(e) and 2(f) show the height proﬁles of the nanowires
under the black solid lines in Figs. 2(b) and 2(c). At 50 K,
the two dimers in each unit cell are tilted opposite each other

FIG. 1. Schematic illustrations of Ge(001)-p(4 × 2)-Pt structures
as proposed by (a) PD, (b) TDC, and (c) NW models. The black andgray spheres represent Pt and Ge atoms, respectively. The dottedrectangles represent the p(4 × 2) unit cells. When Pt atoms areinserted at A sites, the periodicity is p(4 × 4) with a Pt coverageof 0.8125 ML. The interlayer and interatomic distances are labeled
by a, b, c , c⊥ , and d.

diffraction patterns of a√
Pt/Si(111)√ surface whose periodicity
changes from 7 × 7 to 3 × 3 as the Pt coverage reaches
0.41 ML.23 The substrate temperature was measured using
infrared radiation thermometers above room temperature andthermocouples for temperatures below room temperature withan error range of ±10 K.
STM images were obtained by using an Omicron VTSTM in the constant current mode with several tunnelingcurrents (I ) and sample bias voltages (VS ). The RHEPD
experiments were performed using a positron beam of 10 keV
generated from a 22 Na source19 at Japan Atomic Energy
Agency (JAEA) and an intense positron beam in the Slow
Positron Facility of the High Energy Accelerator Research
Organization (KEK). The incident azimuth was set at the[11̄0] direction (many-beam condition) or 22.5◦ away fromthe [11̄0] direction (one-beam condition). The glancing angle(θ ) was varied from 0.5◦ to 6◦ . The critical glancing angle fortotal reﬂection is approximately 2.2◦ as calculated from the

FIG. 2. (a) A large-scale STM image of Pt-induced nanowire
arrays at room temperature (I = 0.5 nA, VS = −1.5 V, 150 ×
150 nm2 ). (b) and (c) Close-up STM images at 50 and 100 K,
respectively (I = 0.05 nA, VS = −1.0 V, 7 × 7 nm2 ). The grayboxes denote the unit cells. (d) A close-up STM image at 90 K (I =0.5 nA, VS = −1.5 V, 11 × 11 nm2 ). (e) and (f) Height proﬁles of the
top dimers under the black solid lines in (b) and (c), respectively.

245438-2

ATOMIC CONFIGURATION AND PHASE TRANSITION OF . . .

PHYSICAL REVIEW B 85, 245438 (2012)

in the direction normal to the surface. The height difference
is approximately 0.2 Å. On the other hand, at 100 K, theheight difference vanishes (i.e., each dimer is ﬂat with respect
to the horizontal axis). These two kinds of dimers are called“asymmetric” and “symmetric,” respectively, here. The above
results agree with those reported by van Houselt et al.9
As shown in Fig. 2(d), at an intermediate temperature of
90 K, the p(4 × 2) and p(4 × 4) phases coexist in the same
nanowires. In the p(4 × 4) phase, most of the neighboring
dimers perpendicular to the nanowires are buckled in the same
direction. Boundaries due to the antiphase patches are also seen
(denoted as 4 × 4 ). These boundaries often randomly move inthe longitudinal direction of the nanowire during consecutive
STM scans. The formation and motion of antiphase patches
is less frequent at 50 K than those at 90 K. The formationof these antiphase patches seems to be the phase slipping
assisted by a thermal lattice ﬂuctuation effect. The features arevery similar to those of quasi-1D metallic chains on In/Si(111)
surfaces.25–27
B. RHEPD rocking curves

Since the STM observations described above reveal that the
low-temperature p(4 × 4) phase is responsible for the groundstate of the Pt-induced nanowires on Ge(001) surface, we ﬁrst
determine its structure. Figure 3(a) shows the RHEPD rocking
curve of the specular reﬂection spot at 35 K under the one-beamcondition. Under this diffraction condition, the intensity of thediffraction spot depends mainly on interlayer distances and theatomic densities of the layers.28
As described in the introduction, three structural models
named PD, TDC, and NW are experimentally and theoretically
proposed for the Pt-induced nanowires. The solid and brokenlines plotted in Fig. 3(a) are the rocking curves calculated
assuming the PD model, the TDC model, and the two
NW models, while optimizing the atomic positions so as tominimize the reliability factor (R).20 Under the assumptions of
the PD model and the TDC model, the calculated curves exhibit
dips at θ = 1.7◦ and 1.4◦ , respectively, in the total reﬂection
region, because of the interference effects of the positron waves
reﬂected by the ﬁrst and second surface layers.30 This featuredoes not appear in the experimental curve. The overall shapeof the calculated curves for both models is also not similar
to the experimental data (R = 4.6% and 4.9%). Contrarily,
the calculated curves for the NW models with a Pt coverageof 0.75 and 0.8125 ML are in good agreement with theexperimental curve. Their reliability factors are 1.2%. We also
examined other proposed structural models composed of the
topmost Ge and/or Pt dimers with the Pt coverage ranging
from 0.25 ∼ 1 ML in Refs. 10, 13, and 18. Among all theexamined models, the two above-mentioned NW models withthe topmost Ge dimers exhibit the lowest reliability factors.
Thus, the present results prefer the topmost Ge dimers rather
than the Pt dimers. As for the CO adsorption,29 a theoretical
study suggests that Pt atoms in the second layer may act asadsorption sites.31 The local density of states near the Fermi
level obtained through the STS measurements32 seem to agreewith that theoretically predicted for the topmost Ge dimers.10
Figure 3(b) shows the rocking curve at 25 K in the manybeam condition. Solid and broken lines are the calculated
curves for the NW models with a Pt coverage of 0.75 and

FIG. 3. (a) RHEPD rocking curves measured from Pt-induced
nanowires on the Ge(001) surface under the (a) one-beam condition
at 35 K, (b) many-beam condition at 25 K, (c) one-beam condition atroom temperature, and (d) many-beam condition at room temperature.
The open circles denote experimental data. The solid gray, broken
gray, solid black, and broken black lines are the calculated curves for
the TDC, PD, and (two) NW models with a Pt coverage of 0.75 and0.8125 ML, respectively.

0.8125 ML, respectively. The NW model with a Pt coverage of
0.75 ML is in better agreement with the experimental data (R =1.8%) than is the NW model with a Pt coverage of 0.8125 ML(R = 2.8%). In the latter model, additional Pt atoms occupyingsites A shown in Fig. 1(b) result in the dip at θ = 2.3◦ . Thus,
the fundamental structure of the Pt-induced nanowires may be
explained by the NW model with a Pt coverage of 0.75 ML. The
amount of evaporated Pt (∼1.2 ML) is greater than 0.75 ML.
The excess Pt atoms probably re-evaporate and/or diffuse into
the bulk during the deposition.15,33,34
Table I lists the optimized interlayer and interatomic
distances [see Fig. 1(b)] obtained from the RHEPD
experiments and the theoretical calculation.10 The
experimental values nearly match those predicted theoretically.
The RHEPD result suggests the presence of asymmetric Ge
dimers (a = 0.22 ± 0.10 Å), that is, adjacent Ge dimers arealternately buckled in the direction normal to the surface. The
appearance of the p(4 × 4) periodicity is indeed explainedby the asymmetric Ge dimers. This is consistent with thepreviously mentioned STM observations.
Figures 3(c) and 3(d) show the RHEPD rocking curves
obtained at room temperature under the one-beam and245438-3

IZUMI MOCHIZUKI et al.

PHYSICAL REVIEW B 85, 245438 (2012)

TABLE I. Interlayer and interatomic distances in the Pt-induced
nanowire, as determined from the RHEPD rocking curve analysis.
The labels a, b, c (= c2 + c⊥2 ), and d are denoted in Fig. 1(b).
Experimental errors are written in parentheses. For comparison, thetheoretical values10 are also listed.

Low temperature
High temperature
Theorya (Å)b (Å)c (Å)d (Å)

0.22(±0.10)0.04(±0.09)< 0.030.74(±0.17)0.64(±0.15)0.52

3.4(±0.2)
3.3(±0.2)
3.13

2.9(±0.2)
2.9(±0.2)
2.72

many-beam conditions. Figure 4(a) shows the comparison of
the rocking curves under the one-beam condition at 35 K androom temperature for θ = 1◦ –4◦ . It can be seen from the ﬁgurethat the intensity for the curve obtained at room temperature
is higher than that for the curve obtained at 35 K as θ varies

FIG. 5. (a) A LEED pattern from the Pt-induced nanowires on
the vicinal Ge(001) substrate at room temperature. The energy of theincident beam is 80 eV. The dashed rectangle indicates the reciprocal
unit cell. (b) The surface Brillouin zone of the p(4 × 2) unit cell. The
solid and dashed lines represent the orthogonally rotated domains.
(c) and (d) Second derivatives of ARPES spectra obtained at 65 K
and room temperature, respectively. The photoemission intensity isgreater in the brighter areas in gray scale. The white vertical lines
denote the ¯ and J¯ points. (e) and (f) Enlarged views of the areas
around the J¯ point in (c) and (d), respectively. The solid and open
circles represent the peak positions. EF denotes the Fermi level.

FIG. 4. (a) Comparison of the one-beam RHEPD rocking curves
from Figs. 3(a) and 3(c). The black and gray open circles show
the experimental data at 35 K and room temperature, respectively.
the solid lines are the calculated curves for the NW model with a
Pt coverage of 0.75 ML. (b) The temperature-dependent one-beamspecular spot intensity curve at θ = 2.5◦ for temperature range 50–
200 K. The solid lines indicate the calculated temperature dependence
assuming Debye temperatures of 210 and 130 K. The inset shows thecloseup of the temperature dependence around Tc . The solid curveand solid line indicate the optimum temperature dependence below
and above Tc , respectively.

from 2.3◦ to 3.2◦ . The solid lines in Figs. 3(c) and 4(a) are
the calculated curves for the NW model with a Pt coverageof 0.75 ML after further optimization of the atomic positions.
Consequently, as listed in Table I, at room temperature, thedifference in height of the topmost Ge dimer atoms disappears(a = 0.04 ± 0.09 Å). The rocking curve under the many-beamcondition can also be explained by the symmetric Ge dimers.
Figure 4(b) shows the temperature dependence of the
specular spot intensity for the one-beam condition at θ = 2.5◦in the temperature range 50–200 K. The intensity gradually
increases from 80 to 110 K indicating the progress of the phasetransition, and thereafter, a conventional Debye-Waller-like
temperature dependence is observed within the experimental
errors. From the slopes of the temperature-dependent specularintensity curve, the surface Debye temperatures are determined
to be 210 ± 80 K for the low-temperature p(4 × 4) phaseand 130 ± 40 K for the high-temperature p(4 × 2) phase.
The amplitudes of the surface-normal vibrations20 of the
topmost Ge dimers are 0.06 Å at 50 K and 0.15 Å at 120 K.

245438-4

ATOMIC CONFIGURATION AND PHASE TRANSITION OF . . .

PHYSICAL REVIEW B 85, 245438 (2012)

Between 80 and 110 K, the above temperature dependence issomewhat continuous and would be reproduced by a powerlaw, as shown by the inset in Fig. 4(b). The order parameter21
is proportional to |1 − T /Tc |β with β = 0.36 ± 0.15 andTc = 111 ± 10 K. Although isolated nanowires9 existing at
the domain boundaries alter the critical exponent, consideringlarge enough domain areas of the present samples, such aneffect is probably negligible. The value of the β (0.36) issmaller as compared to that anticipated for the mean-ﬁeld
approximation (β = 0.5). This is probably due to coexistencesand ﬂuctuations of the p(4 × 4), p(4 × 4 ), and p(4 × 2) phases
as observed by STM in Fig. 2(d). In the present results with
the STM observation in Fig. 2, the structural phase transitionis very similar to a new type of phase transition,35 that is, theprecursory order-disorder behavior for the thermal ﬂuctuatingp(4 × 4) phase triggers the displacive transition from thep(4 × 4) phase to the p(4 × 2) phase.

atoms in Fig. 1(c). At 65 K, this dispersion shifts to a deeper
region that is ∼0.2 eV below the Fermi level. Similar behavior
is also seen at the next J¯ point at k = 1.2 Å−1 , though it is
not shown in the diagram. Considering the results of the STM
and RHEPD experiments, the change in the band dispersion
from 65 K to room temperature seems to be explained by thedisplacive transition from asymmetric to symmetric Ge dimers.
The relatively high energetic gain of the asymmetric Ge dimer
as compared to that of the theoretical value (∼ 0.1 eV) on aGe(001) surface38 may indicate a contribution of the greater
charge transfer from the lower atom to the higher atom of theasymmetric dimers.
The observed change of the STM image from p(4 × 2) top(4 × 4) with ﬂuctuating patches is consistent with the formation of charge density waves. The temperature dependenceof the RHEPD intensity could also be interpreted as a Peierls
transition associated with a thermal lattice ﬂuctuation effect.35
However, if a Peierls transition occurs, the width of a nesting
vector at the Fermi level should appear to be |k| = 0.4 Å−1 andnot to be |k| = 0.8 Å−1 as observed at the J¯ points. Therefore,
we consider, the shift of the band dispersion at the J¯ points is
probably due to the displacement of the topmost Ge dimers,
but is not directly related to the Peierls transition. To discuss
the possibility of the Peierls transition, more detailed ARPES
experiments and theoretical calculations need to be performed.

C. Electronic band dispersions by ARPES

Figure 5(a) shows a typical low-energy electron diffraction(LEED) pattern from the Pt-induced vicinal substrate atroom temperature. A double periodicity appears in the [110]direction with little sign of quadruple spots, whereas aquadruple periodicity prevails in the [1̄10] direction. Thesefeatures suggest that most Pt-induced nanowires are alignedin the [110] direction. Thus, the Brillouin zones on the vicinal
Pt/Ge(001) surface are single domains with a periodicity ofp(4 × 2), as shown by solid rectangles in Fig. 5(b).
Figures 5(c) and 5(d) show the ARPES images taken along
the [110] direction at 65 K and room temperature, respectively.
In both images, the Ge bulk band appears at the center of theﬁrst surface Brillouin zone near the Fermi level, with parabolic
dispersion toward the wave vector (k) ∼ 0.2 Å−1 and binding
energy (E) of ∼0.5 eV. Another bulk band dispersion36 isseen from the (k,E) ≈ (0.1 Å−1 , 0.1 eV) to the (k,E) ≈(0.4 Å−1 , 0.8 eV).
The dispersions around the J¯ point within the bulk bandgap, as depicted in Figs. 5(e) and 5(f), are attributed to thesurface state bands. There are the separable peaks denoted byopen and solid circles by the peak-ﬁtting procedure.37 The
dispersions denoted by open circles are nearly the same at
65 K and room temperature. Unfortunately, the origins of thesebands are not known at present. One possible explanation
might be the overlapping of the components of orthogonal
minority domains.
The dispersions denoted by solid circles are probably
related to the nanowires. The theoretical band dispersion for
the NW model with a Pt coverage of 0.75 ML indeed explains
the observed dispersion at room temperature. According
to the theory behind that model,10 the band dispersion can be
attributed to the bonding state between symmetric Ge dimers
and the Pt atoms in the fourth layer as shown by the bottom Pt*

mochizuki.izumi@jaea.go.jp
P. C. Snijders and H. H. Weitering, Rev. Mod. Phys. 82, 307 (2010).
2
J. R. Ahn, J. H. Byun, J. K. Kim, and H. W. Yeom, Phys. Rev. B
75, 033313 (2007).
1

IV. SUMMARY

We investigated the atomic conﬁguration and electronic
structure of the Pt-induced nanowires on a Ge(001) surface
using STM, RHEPD, and ARPES. The structure of Pt-induced
nanowires is very similar to that of a proposed theoretical
NW model with a Pt coverage of 0.75 ML. However, thetopmost Ge dimers are buckled to afford an asymmetricshape at low temperatures, and this explains the periodicityof the p(4 × 4) phase. At high temperatures, the asymmetric
Ge dimers change to a symmetric ﬂat structure. The abovephase transition is explained as a displacive transition. We
found that the shift of the band dispersion at the J¯ points is notdirectly related to a Peierls transition. To conﬁrm the originof the structural phase transition, more precise ARPES-based
experiments are under progress.
ACKNOWLEDGMENTS

Some of the RHEPD experiments and all the ARPES
experiments were carried out at the Slow Positron Facility,
KEK Photon Factory, Japan (PF-PAC Grant No. 2010G652)
and at BL-18A beamline, KEK Photon Factory, Japan (PF-PAC
Grant No. 2010G649), respectively, under the approvals of the
PF Program Advisory Committee. A part of this research was
conducted under the auspices of Joint Development Research
at High Energy Accelerator Research Organization (KEK).

3

C. González, Jiandong Guo, J. Ortega, F. Flores, and H. H.
Weitering, Phys. Rev. Lett. 102, 115501 (2009).
4
S. Hatta, Y. Ohtsubo, T. Aruga, S. Miyamoto, H. Okuyama, H.
Tajiri, and O. Sakata, Phys. Rev. B 84, 245321 (2011).

245438-5

IZUMI MOCHIZUKI et al.
5

PHYSICAL REVIEW B 85, 245438 (2012)

J. N. Crain and F. J. Himpsel, Appl. Phys. A 82, 431 (2006).
C. Blumenstain, J. Schäfer, S. Mietke, S. Meyer, A. Dollinger,
M. Lochner, X. Y. Cui, L. Patthey, R. Matzdorf, and R. Claessen,
Nature Phys. 7, 776 (2011).
7
Changgan Zeng, P. R. C. Kent, Tae-Hwan. Kim, An-Ping Li, andHanno H. Weitering, Nature Mat. 7, 539 (2008).
8
O. Gürlu, O. A. O. Adam, H. J. W. Zandvliet, and B. Poelsema,Appl. Phys. Lett. 83, 4610 (2003).
9
A. van Houselt, T. Gnielka, J. M. J. Aan de Brugh, N. Öncel,
D. Kockmann, R. Heid, K. P. Bohnen, B. Poelsema, and H. J. W.
Zandvliet, Surf. Sci. 602, 1731 (2008).
10
D. E. P. Vanpoucke and G. Brocks, Phys. Rev. B 81, 085410 (2010).
11
D. E. P. Vanpoucke and G. Brocks, Phys. Rev. B 77, 241308(R)(2008).
12
A. A. Stekolnikov, F. Bechstedt, M. Wisniewski, J. Schäfer, and
R. Claessen, Phys. Rev. Lett. 100, 196101 (2008).
13
A. A. Stekolnikov, J. Furthmüller, and F. Bechstedt, Phys. Rev. B
78, 155434 (2008).
14
J. Schäfer, D. Schrupp, M. Preisinger, and R. Claessen, Phys. Rev.
B 74, 041404(R) (2006).
15
J. Schäfer, S. Meyer, C. Blumenstein, K. Roensch, R. Claessen,
S. Mietke, M. Klinke, T. Podlich, R. Matzdorf, A. A. Stekolnikov,
S. Sauer, and F. Bechstedt, New J. Phys. 11, 125011 (2009).
16
M. Fischer, A. van Houselt, D. Kockmann, B. Poelsema, and H. J.
W. Zandvliet, Phys. Rev. B 76, 245429 (2007).
17
U. Schwingenschlögla and C. Schuster, Eur. Phys. J. B 60, 409(2007).
18
U. Schwingenschlögla and C. Schuster, EPL 81, 26001 (2008).
19
A. Kawasuso, T. Ishimoto, M. Maekawa, Y. Fukaya, K. Hayashi,and A. Ichimiya, Rev. Sci. Inst. 75, 4585 (2004).
20
Y. Fukaya, A. Kawasuso, K. Hayashi, and A. Ichimiya, Phys. Rev.
B 70, 245422 (2004).
6

21

Y. Fukaya, A. Kawasuso, and A. Ichimiya, Phys. Rev. B 75, 115424(2007).
22
H. W. Yeom, Y. K. Kim, E. Y. Lee, K.-D. Ryang, and P. G. Kang,
Phys. Rev. Lett. 95, 205504 (2005).
23
P. Morgen, M. Szymonski, J. Onsgaard, B. Jørgensen, and G. Rossi,
Surf. Sci. 197, 347 (1988).
24
G. Radi, Acta Crystallogr., sect. A: Cryst. Phys., Diffr., Theor. Gen.
Crystallogr. 26, 41 (1970).
25
S. J. Park, H. W. Yeom, J. R. Ahn, and I.-W. Lyo, Phys. Rev. Lett.
95, 126102 (2005).
26
J. Guo, G. Lee, and E. W. Plummer, Phys. Rev. Lett. 95, 046102(2005).
27
H. Morikawa, I. Matsuda, and S. Hasegawa, Phys. Rev. B 70,
085412 (2004).
28
A. Ichimiya, Solid State Phenom. 28–29, 143 (1992).
29
N. Oncel, W. J. van Beek, J. Huijben, B. Poelsema, and H. J. W.
Zandvliet, Surf. Sci. 600, 4690 (2006).
30
A. Kawasuso and S. Okada, Phys. Rev. Lett. 81, 2695 (1998).
31
D. E. P. Vanpoucke and G. Brocks, Phys. Rev. B 81, 235434 (2010).
32
H. J. W. Zandvliet, A. van Houselt, and B. Poelsema, J. Phys.:
Condens. Matter 21, 474207 (2009).
33
O. Gürlu, H. J. W. Zandvliet, B. Poelsema, S. Dag, and S. Ciraci,
Phys. Rev. B 70, 085312 (2004).
34
H. J. W. Zandvliet, H. K. Louwsma, P. E. Hegeman, and B.
Poelsema, Phys. Rev. Lett. 75, 3890 (1995).
35
T. Aruga, Surf. Sci. Rep. 61, 283 (2006).
36
K. Nakatsuji, Y. Takagi, F. Komori, H. Kusuhara, and A. Ishii, Phys.
Rev. B 72, 241308(R) (2005).
37
I. Mochizuki, R. Negishi, and Y. Shigeta, J. Appl. Phys. 106, 013709(2009).
38
H. J. W. Zandvliet, D. Terpstra, and A. van Silfhout, J. Phys.:
Condens. Matter 3, 409 (1991).

245438-6