Computational Materials Science 73 (2013) 9–14
Contents lists available at SciVerse ScienceDirect
Computational Materials Science
journal homepage: www.elsevier.com/locate/commatsci
First principles studies of the self trapped hole and the fluorine
adsorption on the SrF2(1 1 1) surface
Ran Jia a,b, Zhijun Yi c,⇑, Chunsheng Liu b, Hongting Shi d, Hongxing Zhang a, Roberts I. Eglitis e
a
Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, 130023 Changchun, PR China
Department Chemie, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany
c
Department of Physics, China University of Mining and Technology, 221116 Xuzhou, PR China
d
School of Science, Beijing Institute of Technology, 100081 Beijing, PR China
e
Institute of Solid State Physics, University of Latvia, 8 Kengaraga Str., Riga LV1067, Latvia
b
a r t i c l e
i n f o
Article history:
Received 30 October 2012
Received in revised form 5 February 2013
Accepted 7 February 2013
Keywords:
DFT-B3PW
Strontium fluoride
Fluorine adsorption
H-center
Electronic structure
Surface effect
Band structure
a b s t r a c t
By using density functional theory (DFT) with hybrid exchange potentials, namely DFT-B3PW, the ground
states of self trapped hole and adsorbed fluorine atom on the strontium fluoride (1 1 1) surface are investigated. The self trapped hole at an interstitial anion site is denoted by H-center. In both the H-center and
fluorine adsorption cases, the strong relaxations due to the surface effects are observed. In the H-center
case, the unpaired electron distributes almost equally over two H-center atoms. This equivalent distribution of the unpaired electron is totally different from that of the bulk H-center [J. Phys. Chem. A 114 (2010)
8444]. The other case with an adsorbed fluorine atom lying outside the slab has a more polarized charge
distribution with respect to the H-center case. The surface effects and the polarizations of H centers can
be well explained with the calculated electric fields on the surfaces. A new b-hole band located 2.80 eV
above the top of valence band (VB) is observed in the case of fluorine adsorption, and a new
b-hole band located 4.26 eV above the VB is also observed in the H-center case. Specifically, the b-hole
bands are primarily composed of pz-orbitals, which are localized on the defect points.
Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
The strontium fluoride (SrF2) appears in nature as a mineral
fluorite and is of special interest due to its wide use and high technological potential. SrF2 is an ionic large-gap insulator with Fm3m
structure and has the lattice constant a = 5.799 Å in experiments
[1]. Its direct band gap at the C point between the conduction band
(CB) and valence band (VB) calculated from our previous study [2]
also with B3PW method is 11.31 eV. The experimental value is
11.25 eV [3]. In chip manufacturing, the new photolithographic
technology is based on 157 nm system. The whole class of the
alkaline earth fluorides are important materials for the latest photolithographic systems due to their high transparencies to deep
ultraviolet (UV) light and their isotropic optical properties. SrF2
can be used as laser-working-media, scintillation material,
superionic conductor, etc. [4–8]. In scientific research, SrF2 is a convenient model system for the studies of the magneto-optical
properties of impurity paramagnetic ions [9]. The perfect single
SrF2 crystal is extremely transparent in the infrared and ultraviolet
spectral regions, but residual absorption, related to linear
absorption due to defects, can result in a degradation of optical
quality and lead to damage in high power applications. For further
⇑ Corresponding author. Tel.: +86 516 83591530.
E-mail address: [email protected] (Z. Yi).
0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.commatsci.2013.02.009
applications of SrF2, it is important to clarify exactly the absorption
mechanisms and the dynamics of intrinsic transient defect
formation. In the last few decades, a number of experimental and
theoretical papers treated the varied defects and impurities in
SrF2 crystals [10–19].
In this work, we focus on the ground states of the H-center and
the fluorine absorption on the SrF2(1 1 1) surface. An H-center is
named for a hole trapped at an interstitial anion site. An H-center
in the SrF2 crystal has already been investigated experimentally in
the 70s of the last century by Beaumont et al. [20], Hayes [21]. The
whole H center is neutral with respect to the lattice. Note that
another common defect, namely Vk center, in the alkaline-earth
fluorides is similar to the H center, but positively charged with
respect to the lattice. Although one can observe many phenomena
directly by experiments, the understanding and interpretation for
such phenomena are complex. Fortunately, with the improvement
in computer power and the development of efficient algorithms for
electronic structure calculations, it is possible to perform sufficiently extensive ab initio simulations of surface adsorption processes with high accuracy.
The SrF2(1 1 1) surface is highly stable in comparison with the
(1 1 0) and (1 0 0) terminated surfaces [22,23]. An H-center is a
two (fluorine) atomic defect center in SrF2 crystal. One atom in
the H-center is called substitutional fluorine (H1 atom) which substitutes a fluorine atom at the lattice point, and the other one is
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R. Jia et al. / Computational Materials Science 73 (2013) 9–14
called interstitial fluorine (H2 atom) which locates at the interstitial site. H-centers can be formed by irradiating an alkaline earth
fluoride crystals doped with heavier trivalent rare-earth ions
(Re3+) with 50 kV X-rays at 4 K [20]. In undoped alkaline earth fluorides one needs heavy irradiation with about 1 MeV electrons to
produce H centers at 77 K [21]. In addition, experiments have
shown that the hole is located on the H2 atom and that H2 atom
as well as the nearest H1 atom give a [1 1 1] oriented molecular
ion [21,1]. Each SrF2(1 1 1) layer has three sublayers forming a fluorine–metal–fluorine (F–M–F) layer structure. We perform our
investigations for the surface H-center and fluorine adsorption in
a slab system containing four layers with 3 3 supercells. Actually,
there are 109 atoms in our simulation systems since an H-center
includes two fluorine atoms. In fact, a fluorine adsorption at the
SrF2(1 1 1) surface can also be treated as an H-center, since the
charge redistribution between the adsorbed fluorine atom and
the F anion on the surface leads to a self trapped hole on the adsorbed fluorine atom. Nevertheless, in order to make a distinction
with the usual surface H-centers, we still call this case a fluorine
adsorption. The geometry properties and electronic structures of
an surface H-center and a fluorine adsorption are presented in this
work.
The paper is organized as follows: Section 2 introduces the calculational method and reports all required parameters in our simulations. The main simulation results about the geometrical
relaxations and the electronic structures will be presented and discussed in Section 3. A short summary can be found in the last
section.
In order to simulate the system with a surface H-center, we
build a 108-atom (1 1 1) slab including four F–Sr–F layers. Each
layer unit cell is magnified up to a 3 3 2D supercell containing
27 atoms. After the interstitial fluorine atom (i.e., the H2 atom in
the H-center or the adsorbed fluorine atom) is added, the atomic
configuration of the surrounding atoms is re-optimized via a
search for the total energy minimum as a function of the atomic
displacements from the regular lattice sites. Again, two fluorine
atoms in an H-center are labeled as H1 and H2 in the present work,
respectively. H1 denotes the substitutional fluorine atom and H2 is
the interstitial fluorine atom. The effective charges of the atoms
and overlap populations between nearest neighbors are obtained
using the standard Mulliken analysis.
3. Results and discussion
3.1. Geometrical properties
The H-center has two different arrangements in an arbitrary F–
Sr–F layer, as shown in Fig. 1. The formation energy of an investigated defect system is computed by subtracting the total energy of
the optimized 108-atom (1 1 1) perfect slab and the energy of an
isolated fluorine atom from the total energy of the optimized
109-atom (1 1 1) slab containing an corresponding defect, as shown
in the following formula:
ðnþ1Þ
Eform ¼ EH
ð1Þ
ðnÞ
EF Eperfect
ð1Þ
2. Calculation methods
It has been shown that the hybrid B3PW functional achieves
remarkably accurate electronic and geometrical structures for
alkaline earth fluorides [22,23,2,24], as well as for ABO3 perovskites [25–27]. In our former works dealing with F and M centers,
oxygen-vacancy dipoles and hydrogen impurities [22,23,2,24], reliable band gaps for these defect systems have been obtained by
using the B3PW method. Therefore, the first-principles DFTB3PW method is employed to investigate the surface H-center
and fluorine adsorption in this work. Here all numerical calculations are performed using the CRYSTAL06 computer code [28].
CRYSTAL06 employs the Gaussian-type functions (GTFs) localized
at atoms as the basis sets for an expansion of the crystalline orbitals. In order to employ the linear combination of atomic orbitals
(LCAOs)-GFT method, it is desirable to use optimized basis sets
(BSs). In our calculations for fluorine atoms, we apply the basis
set named 7_311 which is developed by Nada et al. [29]. For Sr
atoms, the Hay–Wadt small-core effective core pseudopotential
(ECP) is employed [30,26]. The small-core ECP replaces only inner
core orbitals, the orbitals for subvalence electrons and for valence
electrons are calculated self-consistently. The basis sets are transferable, therefore, once some chemical constituents are determined, they may be applied successfully in calculations for a
variety of chemical substances.
The reciprocal space integration is performed by sampling the
two-dimensional Brillouin zone of the 109-atom supercell with
6 6 Pack–Monkhorst net [31]. The thresholds N (i.e., the calculation of integrals with an accuracy of 10N) in our calculations were
chosen as a compromise between the accuracy of calculations and
the necessary computational time for large supercells. They are 7,
7, 7, 7 and 14 for the Coulomb overlap, the Coulomb penetration,
the exchange overlap, the first-exchange pseudo-overlap and the
second-exchange pseudo-overlap, respectively [32]. For the lattice
constant a of SrF2, we use the theoretical optimized value of
5.845 Å from the Ref. [2].
ð1Þ
ðnþ1Þ
where EF stands for the energy of an isolated fluorine atom. EH
ðnÞ
and Eperfect represent the total energies of the slab with and without
an H-center (or an adsorbed fluorine atom), respectively. Via the
above formula, the calculated adsorption energy is 0.55 eV. The
negative Eform corresponds to stable adsorption. A trend of Hcenters near the surface is observed in our simulation studies.
According to our calculations, the fluorine adsorption and the first
arrangement of the H-center on the top layer are more stable than
other deeper-layer H-center systems. Furthermore, the energetically favorable case in the research scope of this work is the fluorine
adsorption. In other words, the total energy (or formation energy) of
the adsorption system is the lowest. Therefore, we mainly focus on
the investigation of the fluorine adsorption and the first arrangement of the H-center on the top (1 1 1) layer. In the following discuss, if there is no other particularly statement, H-center denotes
the first arrangement of the H-center on the top surface layer to
simplify our description.
The defect lengths of H-center (i.e., distance between H1 and H2
atoms) in the CaF2, SrF2 and BaF2 bulk systems are consistent by
1.98 Å [35,33]. The values of the adsorption and the H-center on
SrF2(1 1 1) surface in the present work are 1.99 and 1.96 Å, respectively, thus being very close to the value in the bulk H-center system. There is only little surface effect on the surface cases. The
position analysis shows that the surface H-center has a remarkable
outward relaxation towards the vacuum. The H1 atom in the surface H-center shifts outwards by 4.385% of a0 with respect to its
position of the unrelaxed slab. Even though other F atoms in the
top sublayer of the surface move inwards like for the perfect alkaline-earth fluoride (1 1 1) surface case caused by the surface effect,
the H2 atom locates above the lower fluorine sublayer of the top
layer. The H1 atom in the adsorption case moves inwards by
0.536% of a0. Considering almost the complete H-center in this
adsorption case is outside of the surface, it is reasonable to consider reverse penetration as a possible explanation.
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R. Jia et al. / Computational Materials Science 73 (2013) 9–14
Fig. 1. A SrF2(1 1 1) layer constituted three sublayers, which are two fluorine sublayers (red spheres) and one strontium sublayer (green spheres), with an adsorbed fluorine
atom (blue sphere) and two different arrangements of the surface H-centers. (For interpretation of the references to color in this figure legend, the reader is referred to the
web version of this article.)
3.2. Electronic properties
Table 1 presents the effective charges and spins of the H1 and
H2 atoms in both adsorption and H-center systems. The H1 and
H2 charges in SrF2 bulk [33] are 0.621 and 0.339e, respectively.
According to our previous calculations, the total charge of the Hcenter is not distributed equally between two fluorine atoms of
an H-center, and the hole is mainly located on the H2 atom (i.e.,
the interstitial fluorine). However, for the surface H-center, the
effective charges of H1 and H2 are vrey close, the hole is equally
located on the H1 and H2 atoms. Due to the surface effect, the total
charge of the surface H-center (0.973e) is less than that of the
bulk H-center [33] (0.985e) by 0.012e, and the electrons belonging to the fluorine atoms near the surface tend to move inwards
[2]. The charge difference between the surface and the bulk H1
atoms is 0.137e, thus being more pronounced than that of the other
surface atoms, that implicates a stronger surface effect on the Hcenter. The first derivatives of the electrostatic potential of the
fluorine adsorption and the surface H-center in z-direction are
shown in the middle panel of Figs. 2 and 3. In fact, they are the
z-components of the inverse electric field strength (Ez). The distribution of the electric field at the perfect fluorine site in vacuum
is changed just a bit through the influence of its defect neighbor.
This electric field points from internal to external of the surface.
As we know, an electron moves always along the opposite direction of the electric field. Obviously, the electrons on the H-center
should move inwards, i.e., the electrons should move from the
H1 atom to the H2 atom. This just explains why the charge distribution of the surface H-center is more balanced than in the other
case. The electronic field on the defect position is changed strongly,
and the field strength is increased. Further analysis of the effective
charges demonstrates that this electron transfer is mainly caused
by the pz-electrons in the outer orbital shells. For the H-centers
in the deeper layers, the charge distributions between two fluorine
atoms are similar to the bulk H-center case.
For the adsorption case, the electron distribution between H1
(fluorine at the substitution site) and H2 (adsorbed fluorine) in
the surface H-center is even more unbalanced than within the bulk
H-center system. Whereas the total charge at the adsorption site
(0.969e) is very close to the value of the surface H-center
(0.973e), being also smaller than the bulk H-center charge. Notice
that the top atom at the adsorption site is the H2 atom instead of
H1, which differs from the adsorption case, and there is no other
charged atom in the vacuum influencing on the H2 atom. The
polarization of the electron distribution of the fluorine adsorption
can also be explained by the fact that some electrons belonging to
the H1 atom move outwards to the H2 atom in the vacuum due to
the electric field in the surface region. This causes a strong polarized H-center. Also the change of the surface electric field at the
adsorption position reduces the surface effect since the effective
charge on the H2 atom is still smaller than the perfect surface
fluorine.
The localizations of the unpaired electron at the H-centers are
clearly shown via the spin density maps in Figs. 2 and 3. In the surface H-center system, the spin polarization of the neighbor atoms
almost disappear and the spin densities on the H1 and H2 atoms
are similar. Statistically, the unpaired electron is equally located
on the fluorine atoms of the surface H-center. However, the spin
density map for the fluorine adsorption system is different and
demonstrates a more distinct spin polarization on the H2 atom.
Additionally, the spin density of the H-center looks like a spindle-shaped pattern, which indicates that the unpaired electron
mainly consists of p-orbitals. Further analysis of the direction of
spindle axis (^z-direction) indicates that the projected pz-orbitals
form the hole. As mentioned before, the total charge of the surface
H-center is less than that of the bulk H-center. However, the total
spins (+0.999e and +0.996e for the fluorine adsorption and the surface H-center, respectively) are by around 1.53% and 1.83% larger
than the bulk H-center spin (+0.981e) [33], implicating a strong
spin polarization.
3.3. Band structure and density of states
In order to understand the impact of a self trapped hole on the
surface on the optical properties of SrF2 crystal, the band structures
of the fluorine adsorption and the surface H-center on the SrF2(1 1 1)
surface are studied in this section. The exhibition of an optical
absorption for SrF2 with H-centers is about 4.03 eV [20]. Our calculated results for the defect levels, displayed in Fig. 4, allow us to explain qualitatively this experimental observed optical absorption. In
the one-electron approximation scheme, the experimental observed optical absorption could be due to an electron transfer from
the H-center ground state, to the empty band at
zb-spin induced by the hole localized on the H-center (see Fig. 4).
Table 1
The defect length (i.e., the distance between the H1 and H2 atoms) on the SrF2(1 1 1) surface, the effective charges (Q (e)) and spins on the H1 and H2 atoms. Atomic relaxations of
the H1 atoms are labeled as Z% a (a percentage of the lattice constant: 5.845 Å). DQ labels the change in the effective charge compared to perfect SrF2 crystal (QSr = +1.909e,
QF = 0.954e) [2]. Spin labels present the spin difference of the electrons (i.e., na–nb) in unit (e).
H1
Adsorption
H-center
H2
Defect length (Å)
Z% a0
Q (e)
DQ (e)
Spin (e)
Q (e)
DQ (e)
Spin (e)
1.99
1.96
0.536
+4.385
0.763
0.529
+0.191
+0.425
+0.232
+0.464
0.206
0.444
+0.748
+0.510
+0.767
+0.532
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R. Jia et al. / Computational Materials Science 73 (2013) 9–14
Fig. 2. Electrostatic potential (upper), its first derivative in z-direction (middle) and
spin density (lower) contours in the YZ-plane of the SrF2(1 1 1) surface with a
adsorbed fluorine atom from side view. The electrostatic potential map is plotted
from 0.10 a.u. to 0.50 a.u. with a linear spacing of 0.02 a.u. And its first derivative
in z-direction is mapped between 0.20 a.u. and 0.05 a.u. with a linear spacing of
0.01 a.u. The spin density map shows the contours from 0.1e/bohr3 to +0.7e/bohr3
with a linear spacing of 0.025e/bohr3.
According to our previous work [33], the corresponding
calculated value is 3.01 eV for the SrF2 bulk H-center system, which
is reasonable, however, it is underestimated with respect to
the experimental result. The recent scheme based on the
Bethe–Salpeter equation in many body perturbation theory give a
Fig. 3. Electrostatic potential (upper), its first derivative in z-direction (middle) and
spin density (lower) contours in the YZ-plane of the SrF2(1 1 1) surface with the
surface H-center from side view. The mapping parameters are same as Fig. 2.
much better description of certain excited state properties as
pointed out in our previous work [2,34]. For the H-center system,
as discussed above, there is an unpaired electron localized on the
H-center. The presence of the unpaired electron is also revealed
by the band structure of the defective system as shown in Fig. 4.
The a-defect band lies in the gap, but very closes to the top of VB.
The empty level induced by a hole localized on the H-center appears
R. Jia et al. / Computational Materials Science 73 (2013) 9–14
13
adsorbed fluorine atom, which is outside the surface. Therefore,
the surface effect on this hole is more pronounced than the other
one inside the surface.
The densities of states (DOSs) are also calculated. The total and
projected DOS of the fluorine adsorption system and the surface Hcenter on the SrF2(1 1 1) surface are displayed in Fig. 5. The H1 and
H2 p-orbitals form the b-hole band in the bulk H-center systems,
and the H2 makes the major contribution [33].
Unlike the SrF2 bulk, the projected p-orbitals in px-, py- and
pz-directions of the hole on the surface are not equivalent for the
formation of b-hole band. According to the DOS calculations for
the fluorine surface adsorption and the surface H-center systems,
the b-hole band mainly consists of pz-orbitals of the holes, as we
can see in Fig. 5. As discussed above, the spin patterns in Figs. 2
and 3 look like spindles with a ^z-axis direction (vertical to the surface), which corresponds to a typical p-shape electron cloud. Our
DOS calculations are in agreement with the previous spin density
discussion. In Fig. 5, the H1 peak is much smaller than the H2 peak
for the fluorine adsorption, however, the H1 peak is similar to the
H2 peak in the surface H-center case, also being in agreement with
the earlier statements about the locations of the holes in the fluorine adsorption and the surface H-center systems, respectively.
4. Conclusions
By using the first-principles approach within the hybrid DFTB3PW scheme, the fluorine adsorption and surface H-center on
the SrF2(1 1 1) surface have been calculated. Several surface H-cen-
Fig. 4. Calculated B3PW band structures for the 109-atom supercell modeling the
fluorine adsorption (upper panel) and the H-center (lower panel) on the SrF2(1 1 1)
surface. a and b denote the up- and down-spin bands, respectively. Fermi energy is
shifted to 0 eV.
in the b-spin band structure above the VB. Due to the selection rules,
the electron transition from the a-occupied band to the b-unoccupied band is forbidden. Therefore, the optical absorption could be
explained by an electron transfer from the b-VB top to the b-empty
level, induced by a hole localized on the H-center.
The optical band gaps of the adsorption case and the surface
H-center system can be found in Table 2. The calculated band gaps
at the C point for both cases are less than that of the bulk H-center
system (11.19 eV) [33], and this is similar to the phenomenon of
the surface effect narrowing the band gap of perfect SrF2 crystal
[2]. The b-defect level for the fluorine adsorption system is
4.26 eV above the VB, magnified by 1.25 eV (approx 41.5%) with respect to the band gap of the bulk H-center system. For the surface
H-center, the defect level is higher than the top of VB by 2.80 eV,
which is less than the corresponding values for the bulk H-center
system by 0.21 eV. Moreover, it is less than the gap in the adsorption case by 1.46 eV (in other words, around 52.1%). Whereas the
band gap in the fluorine adsorption system almost does not
change, and this indicates a marked hole-level movement towards
CB. In the fluorine adsorption system, the hole is located on the
Table 2
Direct optical band gaps (eV) (C ? C) for the fluorine adsorption and surface
H-center systems on the SrF2(1 1 1) surface.
Gaps
VB ? H
VB ? CB
Adsorption
H-center
a
b
a
b
–
10.95
4.26
10.95
–
10.94
2.80
10.95
Fig. 5. The total and projected DOS for the fluorine adsorption (upper panel) and
the H-center (lower panel) on the SrF2(1 1 1) surface. a and b denote the up- and
down-spin states, respectively. Fermi energy is shifted to 0 eV.
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R. Jia et al. / Computational Materials Science 73 (2013) 9–14
ter configurations and one fluorine adsorption are studied. we find
that the adsorption case and the first arrangement of the surface Hcenter represent the energetically favorable configurations for the
simulated surface systems, suggesting a trend of the H-centers
locations, which are close to the surface. The surface effect on
the defect length is not pronounced. According to our calculations,
the hole in the adsorption system is mainly localized on the adsorbed fluorine. That is in agreement with the result of the bulk
H-center. Whereas for the surface H-center with first arrangement,
the effective charges of the H1 and H2 atoms are very close. This
phenomenon can be explained with the help of the electrostatic
potential and its first derivative. The spin density study shows that
an unpaired electron with a spindle-shaped electron cloud, implicates a pz unpaired electron, localized around the defects.
The band structures of our investigated systems indicate that
there is a defect level in each case induced by the self trapped hole
in the gap between VB and CB in the b-spin band map, however, in
the a-spin band structure, the defect level is very close to the top of
VB. According to our calculations, the b-hole bands located 4.26 eV
and 2.80 eV above the top of VB for the fluorine adsorption and the
surface H-center, respectively. This gap in the fluorine adsorption
system is much larger than the corresponding value in the bulk
H-center case.
The analysis of the DOS calculations clearly reveals that the
b-hole band is primarily composed of pz-orbitals localized on the
holes, as a result of the broken symmetry of p-orbitals, thus being
in agreement with the previous spin discussion. The DOS investigations dealing with other atoms suggest that the disappearing
defect levels in the a-band gap results from the occupied a-defect
level also consisting mainly of the fluorine p-orbitals.
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