Investigation of the geometric and electronic structures of ErSi (2-x) with the density functional theory and comparison with STM images

Article abstract of DOI:10.1016/j.susc.2005.07.036

Study of ErSi_(2-x) surfaces system is submitted at one controversy in reason of the STM images bias voltage dependence. In this article, we have investigated by means of calculations issued of the density functional theory (DFT), atomic surface

Full text of DOI:10.1016/j.susc.2005.07.036

Surface Science 595 (2005) 40–48
www.elsevier.com/locate/susc
Investigation of the geometric and electronic structures of
ErSi(2ꢀx) with the density functional theory and
comparison with STM images
*
E. Duverger ,F. Palmino,E. Ehret,J.-C. Labrune
Universit de Franche Comt, Institut FEMTO-ST Dpt CREST, CNRS UMR 6174, 4 place Tharradin, BP 71427,
25211 Montbeliard Cedex, France
Received 14 March 2005; accepted for publication 27 July 2005
Available online 18 August 2005
Abstract
Study of ErSi(2ꢀx) surfaces system is submitted at one controversy in reason of the STM images bias voltage depen-
dence. In this article,we have investigated by means of calculations issued of the density functional theory (DFT),
atomic surface density for 2D and 3D epitaxial erbium silicide on Si(111). DOS (density of state) in front of the surface,
calculated with Wien2k,permits to simulate scanning tunneling microscopy (STM) images in function of the bias volt-
age and to discriminate the different surface arrangements. The calculations confirm the model of structure accepted
and give some new elements in order to close the controversy on the question.
ꢀ 2005 Elsevier B.V. All rights reserved.
Keywords: Erbium; Silicon surface; STM; Wien2k simulation; Interface; Density functional theory
1. Introduction
formation [1–3]. Some rare earth (RE) silicides
have attracted a considerable attention as model
candidates for heteroepitaxial growth on Si(111)
due to their low lattice mismatch with Si(111),
their formation at low temperature and their low
Schottky-barrier on n-type silicon [4–9]. Their un-
usual properties make them attractive for potential
electronic applications [10–16]. Among the RE sil-
Thin films epitaxy of metal silicide on silicon
substrates have been subject to numerous investi-
gations in order to clarify the mechanisms that con-
trol the interface reconstruction and the surface
*
Corresponding author. Tel.: +33 3 81 99 46 88; fax: +33 3
icides,ErSi
have been intensively studied by
(2ꢀx)
81 99 46 10.
different techniques sensitive to the surface. The
ErSi2 disilicide is formed for a submonolayer range
E-mail address: eric.duverger@pu-pm.univ-fcomte.fr (E.
Duverger).
0039-6028/$ - see front matter ꢀ 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2005.07.036

E. Duverger et al. / Surface Science 595 (2005) 40–48
41
Fig. 1. ErSi2 structure. In the side view,the smaller circles
Fig. 2. ErSi1.7 structure. In the side view,the smaller circles
indicate atoms lying below cut plane. The top view (substrate
deleted) represents the p(1 · 1) structure unit cell limited by
large black lines.
indicate atoms lying below cut plane. The top view (substrate
pffiffiffi pffiffiffi
deleted) represents the
ð
3 Â 3ÞR30ꢁ structure unit cell
generated by the vacancies.
close the controversy,surface superstructures are
simulated to obtain the theoretical local density
of states (LDOS) above the surface. Via the Ters-
off–Hamann formulation,we correlate theoretical
results to experimental STM data and give a justi-
fication of the modulation observed in function of
tip-sample bias voltage.
Er deposition on the Si(111) substrate. Its atomic
arrangement can be viewed as a hexagonal erbium
plane sandwiched between the Si substrate and a
buckled Si top layer that closely resembles to the
termination of the unreconstructed Si(111) sur-
face. This top layer is rotated by 180ꢁ with the sub-
strate bilayers (Fig. 1). This structure exhibits a
p(1 · 1) reconstruction.
At higher erbium coverage,the 3D ErSi
sili-
2. Theoretical method
1.7
cide is formed. It crystallizes in a hexagonal phase
of AlB2 type,formed by an alternative stacking of
hexagonal erbium and graphite-like Si plane along
the [111] direction [3,9,17,18]. The ErSi1.7 silicide
is considered as a 2 ML ErSi1.7 slab that involves
a single defected Si plane sandwiched by two hex-
agonal erbium planes [6,19,20]. The outermost Si
atoms called S1 are located right above the Si
vacancies (Fig. 2). The existence of these vacancies
modifies the number of unpaired electrons or dan-
gling bonds. As a result,peculiar,but regular
atomic arrangements occur between the atomic
layers and the surface in order to stabilize the
structure [3,5,9,18].
Self-consistent calculations of total energy and
electronic structure in polarized spin were carried
out using the Wien2k code [22]. They are based
on the scalar relativistic full-potential (FP) aug-
mented plane wave plus local orbitals method
(APW + lo). This is a very accurate and efficient
scheme to solve the Kohn–Sham equations of den-
sity functional theory (DFT). In this case,the ex-
change and correlation effects are treated for
example,by the generalized gradient approxima-
tion (GGA) that often leads to better energetic
and equilibrium structure than the local density
approximation (LDA). Electronic density is ob-
tained by summing over all occupied Kohn–Sham
orbitals and plays a key role in this formalism. A
muffin tin radius of 2.0 and 2.35 a.u. has been
used,respectively for Si and Er. The energy cut-
off was set to 80 eV. The required precision in total
energy was achieved by using a large plane wave
(PW) cut-off. In the linear APW (LAPW) method,
The surface periodicity observed by scanning
tunneling microscopy (STM) is bias voltage depen-
pffiffi pffiffiffi
dent and both ð 3 Â 3ÞR30ꢁ and p(1 · 1) recon-
structions can be observed [18,21]. Relations
between the bias dependence modulations of
STM images and local density of states (LDOS)
of these structures are not well established. To

42
E. Duverger et al. / Surface Science 595 (2005) 40–48
the relevant convergence parameter is RKmax. It is
defined by the product of the smallest atomic
sphere radius times the largest reciprocal lattice
vector of the PW basis. We have used RKmax = 6.5
for the structure. The k mesh was generated in the
irreducible wedge of the Brillouin zone limited
to 60 points. The ErSi2 and ErSi1.7 surfaces were
modeled as a periodic slabs supercell with a vac-
uum region of 25 Bohrs. Constant-current STM
topography was simulated by calculating local
density of states in the vacuum in function of en-
ergy. We have evaluated isosurfaces of constant
density and determined the corrugation of these
isosurfaces following the Tersoff–Hamann scheme.
We have combined this theory for tunneling be-
tween a real surface and a model probe tip with
our ab initio calculations. When the tip is replaced
by a point probe,the tip wave functions are com-
pletely localized. The tunneling current becomes
proportional to the density of state in the cases
of small voltage and small temperature; the tunnel-
ing current matrix becomes an identity matrix
(case of STM images in atomic resolution) [23].
Typically,the isosurfaces are determined at an
average distance of the surface. In our case,we
STM images were acquired in the constant-current
mode with bias voltage applied to the sample.
4. Results and discussion
4.1. The ErSi2 surface
The 2D Er silicide surface reveals a sixfold hex-
agonal rotational symmetry and the LEED pattern
a p(1 · 1) reconstruction. High-resolution STM
images can be achieved and relevant filled state
of the 2D silicide is displayed (Fig. 3). Periodicity
measured in plane corresponds to the p(1 · 1) unit
cell of hexagonal Si(111) or epitaxial ErSi(0001)
atomic planes.
All protrusions are imaged with an equal inten-
sity. All the sites are undeniably structurally equiv-
alent. No bias voltage dependence is observed in
the few tens of mV range where the atomic resolu-
tion can be obtained. In order to interpret high-res-
olution STM images,we have used the Wien2k
code. This code permits to discriminate contribu-
tion due to each atoms and the importance of elec-
tronic structure effects. We obtain data about
density of state near the Fermi level that contribute
˚
have taken a distance of 2.5 A,from the core of
the outermost atoms.
3. Experimental procedure
Experiments were performed in a two-chamber
ultra-high vacuum system (under a pressure below
3 · 10ꢀ10 mbar) equipped with an Omicron STM
and LEED/AES facilities. The Si(111) substrate
(1–3 X cm resistivity) is carefully degassed and
cleaned in situ by series of rapid heating up
to 1200 ꢁC under a pressure lower than 5 ·
10ꢀ10 mbar,and subsequently slowly cooled down
in order to obtain the (7 · 7) reconstruction. Er
deposition was performed using an e-beam evapo-
rator onto the Si(111) substrates at about
0.1 ML minꢀ1. One monolayer is referred to the
Si(111) ideal surface atomic density (7.8 ·
10ꢀ14 atom cmꢀ2). Er was deposited onto the sub-
strate at room temperature (RT) and subsequently
annealed at 500 ꢁC. Both LEED and STM obser-
vations were made at room temperature,and the
Fig. 3. STM image of the p(1 · 1) periodicity on the ErSi2
surface for a sample bias voltage of Vs = ꢀ10 mV, It = 0.4 nA,
size = 5 · 5 nm2.

E. Duverger et al. / Surface Science 595 (2005) 40–48
43
Fig. 4. ErSi2 electronic density of state for Si adatoms. The pz
orbital contribution at the density of state is near the Fermi
level.
Fig. 5. ErSi2 electronic density of state for Si adatoms. Image
to the tunneling current. Integrals of the electronic
density around the different atoms (Fig. 4) show
that in the ErSi2 case,electronic structure at the
top of the valence band is due to Si pz state. The
absence of gap means a semi metallic behavior.
The great spatial extension of the pz orbitals in
the ErSi2 structure gives a homogeneous inte-
grated density of state in function of the energy.
All the Si atoms of the bilayer have the same elec-
tronic structure. We retrieve the same results about
the density of state that those already published
with the APW method [24]. Some light discrepan-
cies exist with some other works due to differences
between the set of parameters and the theoretical
˚
simulated with a bias voltage of ꢀ10 mV at 2.5 A of the surface,
size = 4.6 · 4.8 nm2.
method (LMTO + tight binding,Hu ckel) used
¨
during the ab initio calculation [6,20]. The simu-
lated STM images present the same p(1 · 1) peri-
odicity (Fig. 5) for any bias voltages that the
experimental STM images.
4.2. The ErSi1.7 surface
Fig. 6. High-resolution STM image on the 3 D ErSi1.7 showing
For Er deposition at coverage over 1 ML,flat
a p(1 · 1) periodicity for a sample bias voltage of Vs = ꢀ37 mV,
It = 2.2 nA,size = 5 · 5 nm2. The LEED pattern corresponding
pffiffiffi pffiffiffi
3D islands with hexagonal symmetry are displayed
pffiffi pffiffi
to this surface is a ð 3 Â 3ÞR30ꢁ.
in large scale STM image. The ð 3 Â 3ÞR30ꢁ
LEED pattern is found and is explained in the lit-
erature by the presence of ordered vacancies in the
Si graphite-like planes of the 3D silicide [18]. High-
resolution STM images of the filled states reveal a
bias voltage dependence as shown in Figs. 6 and 7.
Fig. 6 displays an atomic STM image of the filled
states for the 3D ErSi1.7 silicide surface taken with

44
E. Duverger et al. / Surface Science 595 (2005) 40–48
are derived from dangling bonds of the layer
surface.
In order to simulate the ErSi1.7 structure,we
have used the same set of parameters in the
Wien2k code that for ErSi2. We retrieve some
similitude between the two structures. The density
of states,as for the ErSi structure,is not null at
2
the Fermi level for the silicon atoms in the S1
and S3 sites. We are confronted again at a semi
metallic behavior with a modulation of the density
of states in function of the energy for the silicon
adatoms in S1 and S3 (Figs. 8 and 9). The two
Fig. 7. High-resolution STM image on the 3D ErSi1.7 showing
pffiffiffi pffiffiffi
a ð 3 Â 3ÞR30ꢁ modulation with a bias voltage of Vs =
ꢀ160 mV, It = 0.4 nA,size = 5 · 5 nm2. The LEED pattern
pffiffi pffiffi
corresponding to this surface is a ð 3 Â 3ÞR30ꢁ.
a bias voltage of Vs = ꢀ37 mV and tunneling cur-
rent of It = 2.2 nA. The image shows a p(1 · 1)
reconstruction similar with that presented in
Fig. 3 for the 2D silicide.
˚
The measured in-plane periodicity of 3.84 A,
closely corresponds to the p(1 · 1) unit cell of hex-
agonal Si(111) or epitaxial ErSi2(0001) atomic
Fig. 8. ErSi1.7 electronic density of state for Si adatoms in
position S1 (spin up (a) and spin down (b)) above the vacancy.
planes [6,19,20,24]. At lower bias voltage
pffiffiffi pffiffi
(Fig. 7),an additional ð 3 Â 3ÞR30ꢁ modulation
appears clearly on the filled state STM images
[4,9,18,21].
pffiffiffi
The 3 modulation is generally quite small but
it can be enhanced at particular tunneling condi-
tions as those selected in Fig. 7 (Vs = ꢀ160 mV,
It = 0.4 nA). Similarity between the STM images
of the filled states for the 2D and 3D silicides im-
plies closely related surface terminations. It is
apparent from previous works that the states
which provide the major contribution to the tun-
neling current are located near the hole pocket at
C0(C) for the 3D silicide (2D silicide) in the IBZ
(irreducible Brillouin zone) [18]. According to
band structure calculations,the electronic states
near C0(C) have the same physical origin and are
due to surface state with Si 3 pz character that
Fig. 9. ErSi1.7 electronic density of state for Si adatoms in
position S3 (spin up (c) and spin down (d)) at the center of the
structure.

E. Duverger et al. / Surface Science 595 (2005) 40–48
45
surface positions are not equivalent. The sites S3
(Fig. 2) for the silicon atoms on the diagonal of
the atomic cell,present a density of state more
important that the atoms on sites S1. Our results
qualitatively agreed with the results published by
Allan et al. on the ErSi1.7 DOS. The discrepancies
are due to the LMTO plus tight binding method
used in their simulation [20]. The peaks are more
localized in energy,near the Fermi level between
(Ef + 1.0 eV) and (Ef ꢀ 1.0 eV) due to the pz
contribution.
It is admitted that the ErSi1.7 surface is termi-
nated by a buckled Si plane with atomic positions
very close to the position of the Si atoms on an
ideal Si(111) p(1 · 1) surface. However,two differ-
ent assumptions have been made in order to ex-
plain the STM modulation of the surface in
function of the bias voltage. For one group,the
pffiffi pffiffiffi
ð 3 Â 3ÞR30ꢁ reconstruction is due to a relaxa-
˚
tion around 0.2 and 0.3 A of the upper Si atoms
toward either T4 or H3 sites in function of the bias
voltage [20,21]. For the second group,the recon-
pffiffi pffiffiffi
struction ð 3 Â 3ÞR30ꢁ is explained in terms of
a small additional buckling of the topmost Si layer
because of the underlying vacancy periodicity in
the bulk silicide [18]. In this case,the corrugation
of the STM images will be due to a spectroscopic
effect. Our simulations permit to isolate the differ-
ent parameters and determine their contribution.
In the aim to maintain the optimization of the
structure already described,we have chosen to fix
the atoms positions [18,21]. The density of states
obtained in simulation gives the contribution of
the different valence electrons. Using the local
integrated density of states,following the Tersoff–
Hamann model,we have simulated the constant-
current STM topography. The isosurfaces are
Fig. 10. ErSi1.7 electronic density of state for Si adatoms.
Image simulated with a sample bias voltage of +1.0 V (a),0.3 V
˚
(b),0.07 V (c), ꢀ0.07 V (d), ꢀ0.3 V (e), ꢀ1.0 V (f) at 2.5 A of
pffiffiffi pffiffiffi
the surface. The lattice ð 3 Â 3ÞR30ꢁ centered on Si vacancy
is superimposed on the images.
˚
determined at an average distance of 2.5 A from
+0.3 V (Fig. 10(b))) show a p(1 · 1) lattice modu-
pffiffiffi pffiffi
the core of the outermost atoms,on a surface of
lated by the ð 3 Â 3Þ. The bright spots are sepa-
pffiffi pffiffiffi
2
˚
˚
46 · 48 A and for different sample bias voltages
rated by 6.7 A (i.e.
3 Â 3R30ꢁ) as already
(+1.0,+0.3,+0.07,
ꢀ0.07, ꢀ0.3,and ꢀ1.0 V)
described experimentally [9,21]. When the bias volt-
age is diminished (+0.07 V, Fig. 10(c)),we observe
only the p(1 · 1) lattice with a distance between
(Fig. 10). The bias voltages are taken to permit a
comparison with the experimental results already
published [18,21].
˚
spots equal at 3.84 A. For the bias voltage of
In comparing the different images in Fig. 10,we
can identify an apparent modification of the period-
icity in function of the bias voltage. The images sim-
ulated at positive voltage (+1.0 V (Fig. 10(a)),
ꢀ0.3 V,the Si(111) p(1 · 1) surface is slightly mod-
pffiffiffi pffiffi
ulated by a ð 3 Â 3Þ. The corrugation disappears
again for the others voltages (ꢀ0.07,and ꢀ1.0 V).
pffiffiffi pffiffi
This behavior shows that the ð 3 Â 3ÞR30ꢁ

46
E. Duverger et al. / Surface Science 595 (2005) 40–48
periodicity observed in Fig. 10 is due to a real elec-
tronic effect of the surface. A relaxation of the
upper Si atoms in function of the bias voltage is
impossible since in ab initio calculation the position
of the different atoms is fixed. The assumption con-
sidering the relaxation effect cannot explain the
theoretical results. The second group explains the
corrugation of the STM image in terms of a small
additional buckling of the topmost Si layer because
of the underlying vacancy periodicity in bulk sili-
sity of state in function of the atoms position
and of the energy is induced by the lattice recon-
struction. The brutal variation in the density of
states produces a modulation of the tunneling cur-
rent on the theoretical STM images. The intensity
of the modulation is bias voltage dependent
(Fig. 10). This comportment can be explained by
the two geometric nonequivalent sites in surface,
one over the vacancy (S1) and the second inside
the cell (S3). The maximum in the intensity is pro-
vided by the two silicon atoms (site S3) present on
the diagonal of the structure cell (Fig. 2) for the
negative bias voltages and by the four silicon
atoms (site S1) for the high positive bias voltages.
In the case of positive bias voltages,it is due to the
additional buckling between the Si atoms on the
sites S1 and the vacancies. When the bias voltage
is diminished,the contribution of occupied states
centered on the atom S3 increases,competes with
the contribution of the atoms in the positions S1
and corrugates the intensity distribution. This
phenomenon is linked to the modulation of the
electronic density,which becomes too weak for
certain energy [9,21]. It induces the same effect
for the theoretical STM images (Fig. 10(c),(d)
cide. A contour map sketched along the direction
pffiffi pffiffi
½121ꢂ of the 3 Â 3R30ꢁ reconstruction permits
ꢀ
to understand the importance of the vacancy peri-
odicity on the structure (Fig. 11). We observe that
under the Si adatoms present on the S1 sites,vacan-
cies are characterized by an absence of density of
state. A charge transfer exists between the silicon
adatoms of the bilayer and the Er–Si bulk structure.
The Er atoms stabilize the ErSi1.7 and permit with
the vacancies lattice to reduce the number of dan-
gling bonds of the topmost Si layer. We verify the
assumption formulated by Magaud et al. [24].
The theoretical results obtained at high positive
voltages on the images STM simulated confirm
experimental results already obtained (Fig. 10(a)
and (b)) [18]. We retrieve the empty states localized
on the surface due to the interactions between the
Si atoms in the position S1 and the lattice of
vacancies. The modulation of the electronic den-
and (f)).
pffiffiffi
The modulation 3 is always present but some-
times masked by the weak variation of the states
density as the algorithm treatment shows on the
STM simulated images (Fig. 12). This modulation
is inferior at 5% of the integrated intensity and de-
pends of the local density of states and of the bias
voltage. In order to have a better analysis of the
ErSi1.7 images simulated in function of the bias
voltages,we have modified the contrast of the
spot bright for the bias voltages. Usually,the
intensity on an image is a linear function of
the pixel value. With the use of an exponential
function proportional to the pixel value,we can
magnify this intensity. An example is shown in
Fig. 12. The algorithm treatment on the initial
image Fig. 10(d) permits to exhibit the modulation
pffiffi pffiffi
ð 3 Â 3Þ on the p(1 · 1) surface. The obtained
data permit to confirm the experimental STM
results and the assumption proposed. The corruga-
tion obtained experimentally is related to a spec-
troscopic effect and not due to a topographic
displacement of the atoms.
Fig. 11. ErSi1.7 contour map of the electronic density of state
ꢀ
along the direction ½121ꢂ. The arrows indicate the Si adatoms
˚
on sites S1 (distance between each site 6.7 A),the black circles
correspond to the Si vacancies. A charge transfer exists between
the silicon adatoms of the bilayer and the Er–Si bulk structure.

E. Duverger et al. / Surface Science 595 (2005) 40–48
47
calculated and integrated near the Fermi level,per-
mits to show a strong dependence of the observed
pffiffiffi pffiffi
ð 3 Â 3ÞR30ꢁ modulation with the bias voltage.
For the 2D and 3D erbium silicide,a Si buckled
layer terminates the surface. For the 3D erbium
silicide,the small modulation with the periodicity
pffiffiffi pffiffi
ð 3 Â 3ÞR30ꢁ induced by the vacancies is ob-
served and explained in function of the spectro-
scopic voltage and not in function of the atoms
displacements.
Acknowledgments
The authors wish to thank Dr. Koitzsch of the
Institute of Physic,University of Neufchaˆtel,for
the help on the AlB2 structure of the erbium
disilicide.
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