First-principles study of the BiMO4 antisite defect in the Bi12MO20 (M = Si, Ge, Ti) sillenite compounds

Abstract

Structural, electronic and optical properties of the antisite BiMO4 defect in Bi12MO20 sillenites (BMO, M=Si, Ge, Ti) were investigated using density functional theory. The defect is studied in neutral, positively and negatively charged states. It is demonstrated that within the neutral defect the Bi 6s(2) lone pair is broken and the valence state of the Bi is 4+ (6s(1)). Within the charged defects, the Bi 6s orbital is found to be either full (Bi(3+): 6s(2)) or empty (Bi(5+): 6s(0)). All three charged states introduce energy bands within the BMO gap. By analyzing possible transitions between them we deduced a simple model of functioning of the BiMO4 defect that is able to explain the photochromic and photorefractive effect in sillenites and that reproduces almost all known experimental facts.

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First-principles study of the BiMO4 antisite defect in the Bi12MO20 (M=Si, Ge, Ti) sillenite
compounds
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2013 J. Phys.: Condens. Matter 25 495505
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IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 25 (2013) 495505 (9pp) doi:10.1088/0953-8984/25/49/495505
First-principles study of the BiMO4
antisite defect in the Bi12MO20 (M =Si,
Ge, Ti) sillenite compounds
A F Lima and M V Lalic
Departamento de F´
ısica, Universidade Federal de Sergipe, PO Box 353, 49100-000, S˜
ao Crist´
ov˜
ao, SE,
Brazil
E-mail: mlalic@ufs.br
Received 16 May 2013, in final form 11 October 2013
Published 8 November 2013
Online at stacks.iop.org/JPhysCM/25/495505
Abstract
Structural, electronic and optical properties of the antisite BiMO4defect in Bi12MO20
sillenites (BMO, M =Si, Ge, Ti) were investigated using density functional theory. The defect
is studied in neutral, positively and negatively charged states. It is demonstrated that within the
neutral defect the Bi 6s2lone pair is broken and the valence state of the Bi is 4+ (6s1). Within
the charged defects, the Bi 6s orbital is found to be either full (Bi3+: 6s2) or empty (Bi5+:
6s0). All three charged states introduce energy bands within the BMO gap. By analyzing
possible transitions between them we deduced a simple model of functioning of the BiMO4
defect that is able to explain the photochromic and photorefractive effect in sillenites and that
reproduces almost all known experimental facts.
(Some figures may appear in colour only in the online journal)
1. Introduction
The sillenite crystals with chemical formula Bi12MO20
(BMO, M =Ti, Ge, Si) attract significant scientific
attention mostly because of their pronounced photorefractive
(PR) effect that is used in many applications such as multi-
wavelength holography [1], real-time holographic surface
imaging [2,3], optical information processing [4] and in
various metrological problems [5]. Besides, the sillenites also
exhibit pronounced optical activity and Faraday rotation, very
useful properties for development of fiber optic current sen-
sors [6,7] and a variety of photocatalytic applications [8,9].
A simple optical recording in PR materials requires
the presence of photoconductive centers, usually defects or
impurities, which provide additional energy levels within the
band gap. They serve as traps for electrons which, under
coherent illumination, migrate from bright to dark regions of
crystal space, changing electrical and optical properties of the
perfect compound [10]. Characterization of these levels and
comprehension of their origin are necessary tasks for efficient
manipulation and technological application of PR materials.
The nominally pure sillenites possess a complex
structure of intrinsic defects [11–15], a fact proven by
observation of the PR effect in undoped materials [16–18].
Summarizing [11–15], the majority of them involve wrong
population of the M site (with nominal valence 4+) which
can be partially (I) occupied by the Bi3+ion tetrahedrally
coordinated by the O ions (BiMO4), (II) occupied by the
Bi3+ion coordinated with three O ions (BiMO3) and with
the Bi 6s2lone pair pointing in the direction of the fourth
absent O, or (III) vacant (VO4). The BiMO4and BiMO3defect
centers are commonly known as antisite Bi defects (BiM) in
sillenites.
Even though is possible that all three types of defect
coexist simultaneously, the PR effect is always justified on
the basis of the BiMO4defect center [16–18]. The latter has
been studied experimentally in two different states of the host
crystal: (1) a bleached state (reached by thermal exposure
or red light illumination of the sample), and (2) a colored
state (realized by blue light illumination of the bleached
sample). The following facts were established. Within the
bleached state the BMOs do not exhibit any absorption from
the near-infrared to ultraviolet range (the band gap in all three
10953-8984/13/495505+09$33.00 c
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J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
Figure 1. Crystal structure of the perfect Bi12MO20 (left) and local structure around the Bi and the M sites (right). Each Bi3+ion is
surrounded by eight O ions, forming a BiO8irregular polyhedron, whereas each M4+ion is coordinated by four O(3) ions arranged in a
perfect MO4tetrahedron.
BMOs is about 3.2 eV) [18], but a narrow shoulder is detected
at approximately 3 eV near the absorption edge [10]. The fact
that magnetic circular dichroism (MCD) measurements do not
register this shoulder means that it is provoked by diamagnetic
defect [10]. Within the colored state of the BMOs [19] the
optical absorption measurements register a very intense and
broad shoulder in the visible and near-infrared region [10,20].
The MCD and optically detected magnetic resonance
(ODMR) studies correlate this shoulder with the paramagnetic
defect [10,13].
In order to explain these experimental facts various
theoretical models have been proposed, some of them being
very complex and invoking the presence of other kind of
defect in sillenites. Considering solely the structure of the
BiMO4defect, however, only two of them are essentially
different. Both rely on stability of the Bi 6s2lone pair and
suppose that in the electrically neutral state the BiMO4defect
consists of the Bi in its 3+ valence state, with diamagnetic
electron configuration 6s2, and of a hole situated in oxygen
neighborhood. The first model, proposed by Oberschmid [20]
and substantiated by Schirmer et al [21] and Briat et al [10],
supposes that a hole is localized on one of the four
neighboring O2−ions, forming a bound polaron. In this case,
a deformation of the perfect O tetrahedron around the Bi by
elongation of one of the Bi–O bonds is expected, a fact which
is not experimentally observed [13]. The second theoretical
model, proposed by Reyher et al [11], supposes that a hole is
spread equally on all four neighboring O atoms, preserving
a perfect tetrahedral symmetry of the BiMO4defect. The
recent EPR study [13] favors exactly this model, discarding
the possibility of small polaron formation. Both models agree
that in the BMO’s bleached state the BiMO4defect should be
neutral with the Bi ion in diamagnetic configuration 6s2. Blue
light illumination excites one of the Bi 6s electrons into the
conduction band, transforming the host into the colored state
in which the Bi ion appears in paramagnetic configuration 6s1
and the excited electron is captured by other defects.
In this paper we suggest a substantially different model
for the BiMO4defect, based on density functional theory
(DFT) calculations. In the proposed model the Bi ion
within the neutral defect should be in the paramagnetic 6s1
configuration, with a valence state of approximately 4+ (Bi0
M).
This defect is present in the colored state of the host, and
acts simultaneously as electron donor and acceptor. Red
light illumination charges or discharges the Bi 6s1states,
creating the Bi−
M(with the Bi in the 6s2configuration) or
the Bi+
Mdefect (with the Bi in the 6s0configuration). The
bleached state of the BMOs should contain these two kinds
of diamagnetic defect. The blue (or more energetic) light
illumination excites electrons or holes from these defects,
creating again the paramagnetic Bi0
Mdefect and transforming
the host into the colored state. In the rest of the paper
we will detail the theoretical foundation of this model and
demonstrate that it is able to explain most of the established
experimental facts.
2. Computational procedure
2.1. Simulation of isolated intrinsic defect and structural
relaxation
The BMO’s crystal structure is body-centered cubic, with
space group I23 (no 197) [22]. The primitive unit cell contains
1 f.u. (33 atoms) without having a center of inversion. It
contains three nonequivalent O atoms, one at the position 24f
(O(1)), and two at the position 8c (O(2) and O(3)). The M4+
ion occupies 2a site, being bonded with four O(3) atoms. The
local structure can be viewed as a regular tetrahedron with
the M4+at its center and O2−at its vertices. The Bi3+ions
occupy the 24f site, being surrounded by eight O atoms that
form a distorted BiO8polyhedron [32]. Within the unit cell the
MO4tetrahedra are located at the body-centered and corner
sites. Connection between the BiO8polyhedron and the MO4
tetrahedron is established via the O(3) ion (figure 1).
The BiMO4defect center was simulated using the
primitive unit cell of the perfect Bi12TiO20 (BTO) crystal,
whose lattice parameter has been computationally relaxed
2

J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
in our recent work (a=10.322 ˚
A) [23]. The BTO (and
not the Bi12GeO20 (BGO) or Bi12 SiO20 (BSO)) unit cell
was chosen because the calculated gap agrees best with the
experimental value [18]. Within this unit cell the central Ti4+
ion has been replaced by the Bi3+ion generating the neutral
antisite defect Bi0
Ti. The defective periodic system BTO:Bi0
Ti
is then generated by infinite repetition of this unit cell, which
actually does not contain the Ti ions and simulates all three
BMO:Bi0
Mcompounds. We estimated that this unit cell is large
enough to prevent significant interaction between defects and
to correctly simulate their neighborhoods (see the discussion
at the end of section 4). The antisite defect is also studied in
two ionization states: positively charged Bi+
Mis simulated by
removing one electron from the unit cell of the BMO:Bi0
M
and negatively charged Bi−
Mby adding one electron to it.
In both cases a charge compensating homogeneous jellium
background charge is assumed to preserve overall neutrality.
For all three differently charged defective systems all
atomic positions inside respective unit cells were relaxed by
moving the atoms according to forces which act on them
(damped Newton scheme) [24]. The process was repeated
until these forces became less than 2.0 mRyd/a.u. During
relaxation the symmetry constraints of the space group have
been obeyed because of strong experimental evidence that the
M site experiences a perfect tetrahedral crystal field [13].
2.2. Calculations of electronic structure and optical response
All calculations were carried out using a full potential
linear augmented plane wave (FP-LAPW) method [25] based
on DFT [26] and implemented in the WIEN2k computer
code [27]. The electronic wavefunctions, charge density and
crystal potential were expanded in terms of partial waves
inside the non-overlapping atomic spheres centered at each
nuclear position (with radii RMT) and in terms of the plane
waves in the rest of the space (interstitial). The choices for the
Bi and O RMTs were 2.3 and 1.4 a.u. respectively. The partial
waves were expanded up to lmax =10, while the number of
plane waves was limited by the cut-off at Kmax =7.0/RMT(O).
As a basis, the augmented plane waves were used. The charge
density was Fourier expanded up to Gmax =14. A mesh of
seven k-points in the irreducible part of the Brillouin zone
was used. The Bi 5d, 6s, 6p and the O 2s, 2p electronic
states were considered as valence ones and treated within
the scalar-relativistic approach, whereas the core states were
relaxed in a fully relativistic manner.
Exchange and correlation effects were treated in a
twofold manner. The relaxation of atomic positions has
been performed using the generalized gradient approxima-
tion with Perdew–Burke–Ernzerhof parameterization (GGA-
PBE) [28]. While this functional is very useful in calculating
structural and other properties related to total energies, it
severely underestimates the band gaps of most semicon-
ductors and insulators. Thus, electronic bands and optical
response have been calculated using the semi-local modified
Becke–Johnson (mBJ) functional recently proposed by Tran
and Blaha [29]. This functional has been shown to reproduce
better the band gaps, electronic and optical properties
for a variety of semiconductors and insulators [30–32].
The spin–orbit coupling has been taken into account just
for heavy Bi atoms via a second variation procedure,
using scalar-relativistic eigenfunctions as a basis. Electronic
structure was calculated up to an energy of 4.0 Ryd. The
self-consistent calculations of all three defective systems were
performed on the same level of precision and successfully
converged within the energy precision of 10−5Ryd.
The linear optical properties were determined by the
WIEN2k optical package [33], which calculates the imaginary
part of the complex dielectric tensor ε2, directly proportional
to the optical absorption spectrum, on the basis of the
following formula [34]:
ε2(αβ)(ω) =4π2e2
m2ω2X
i,fZBZ
2dk
(2π)3|hϕfk|Pβ|ϕiki|
× |hϕfk|Pα|ϕik i|δ[Ef(k)−Ei(k)−¯
hω].(1)
Formula (1) is valid within the frame of the random phase
approximation and does not account for electron polarization
effects. It therefore cannot describe excitonic effects, but in
the case of sillenites there are no experimental proofs of
their importance. Instead, it describes electric dipole allowed
transitions from populated Kohn–Sham states |ϕikiof energy
Ei(k)to empty Kohn–Sham states |ϕfkiof energy Ef(k)
with the same wavevector k(ωis the frequency of incident
radiation, mthe electron mass, Pthe momentum operator, and
αand βstand for the projections x,yor z). ε2was computed
in the energy range from 0 to 3 Ryd (0–40 eV), taking into
account electronic transitions from −1.2 to 2.0 Ryd. The
number of empty states considered was approximately 254,
for all three defective systems. A mesh of 45 k-points in the
irreducible wedge of the first Brillouin zone was used. Owing
to their cubic symmetry, the sillenite’s dielectric tensor is
diagonal, with ε2xx =ε2yy =ε2zz =ε2, and thus reduced to
scalar function ε2(ω).
3. Results and discussion
3.1. Electronic structure of defective systems
Resulting total and partial densities of electronic states (TDOS
and PDOS) of the three BMO:Bi0,1+,1−
Mdefective systems are
presented in figure 2, together with the TDOS of the perfect
BTO (calculated recently by our group [32]), which is shown
for comparison.
For the perfect BTO the calculated gap was 0.243 Ryd
(3.3 eV), very close to the experimental value of 3.2 eV [18].
The peak at the very top of the valence band (marked by
letter A) is predominantly composed of the 2p states of the
O(3) and the Bi 6s states. The peak at the very bottom of
the conduction band (marked by B) is dominated by the Bi
6p states hybridized with the 2p states of the O atoms [32].
For the defective systems, figure 2reveals two principal
differences relative to the perfect one: (1) significant change
of intensity, form and composition of the TDOS at the top of
the valence band, and (2) formation of one extra band, situated
within the fundamental gap and composed of the hybridized
BiM6s and O(3) 2p states.
3

J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
Figure 2. Top: calculated TDOS of the perfect BTO (a) and the BMO containing the neutral (b), positively (c) and negatively (d) charged
antisite BiMdefect. The letters A and B denote the peaks at the valence band top and conduction band bottom, respectively. The letters C, C0
and C00 denote bands within the gap introduced by the antisite defect. The dashed line indicates the Fermi energy. Bottom: calculated PDOS
of the three defective BMO crystals. A band due to the antisite Bi defect is composed of a mixture of the BiM6s and the O(3) 2p states.
The first difference can be related to the relaxation of
atomic positions in defective systems. In perfect BMOs the
shortest bonds are the M–O(3) ones, so the occupied O(3)
states have high energy and dominate the very top of the
valence band [32]. In defective systems the BiM–O(3) bonds
are significantly elongated (see table 1), and the Bi–O(1)
bonds become the shortest ones (since the neighborhood
around the regular Bi sites in defective systems does not
change much we did not find it necessary to represent a
table with the Bi–O interatomic distances; this table for the
pure BMOs can be consulted in [32]). As a consequence, the
dominant orbital character of the valence band top in defective
systems changes from the O(3) to the O(1) 2p states, while the
TDOS intensity increases because there are more O(1) than
O(3) atoms within the BMO unit cell.
Table 1. Calculated equilibrium distances between the Biq
Mdefects
and their nearest and next-nearest (NN and NNN) neighboring
O atoms, as well as between the Biq
Mand the nearest regular Bi ions.
The same distances in the pure BTO are shown in the last line, taken
from [23].
Distances ( ˚
A)
NN O atoms
O(3)
NNN O atoms
O(2b) Biq
M–Bi
Bi0
M2.112 3.901 3.925
Bi+
M2.026 3.988 3.980
Bi−
M2.200 3.645 3.836
Ti 1.842 3.443 3.913
The second difference is a fundamental one, resulting in
formation of a new permitted energy band within the gap.
In all three defective systems this band can admit up to two
4

J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
Figure 3. Valence electron density of the BiMO4defect projected onto the (111) crystal plane. In the left picture the black frame
emphasizes the TiO4cluster within the perfect BTO: the Ti ion is in the center, and its three neighboring O atoms have density projections
around it (they are actually slightly above the plane). The fourth O is exactly below the Ti and therefore not seen. The three pictures on the
right refer to the differently charged BiMdefects and demonstrate deterioration of the BiM6s2lone pair. The sketch below these pictures
illustrates the form of the 6s2electronic cloud, facilitating the visualization of its projection onto the plane formed by the Bi and three
neighboring O atoms.
electrons, but its actual occupation and energy depend on the
charge state of the defect.
The neutral defect (figure 2(b)) forms a deep, half-
occupied band, placed in the middle of the gap. Since this
band has the dominant Bi 6s character (figure 2(e)), it can
be concluded that the Bi releases one electron from its 6s2
lone pair to satisfy bonding with all four neighboring O(3)
ions. Thus, four of the five valence electrons of the Bi (6s26p3
in free-atom configuration) are used to form the tetrahedral
covalent bonds with the neighbors, while the fifth electron
remains within the BiMatomic sphere. This fact can be
interpreted as if the Bi ion within the Bi0
Mdefect exhibits
approximately the 6s1configuration, being in the valence
state 4+. It introduces both donor and acceptor states into the
BMO’s gap.
The positively charged Bi+
Mdefect forms an acceptor
band (figure 2(c)). Since it has predominantly the Bi
6s character (figure 2(g)), this result indicates that one electron
has been removed from the Bi 6s orbital, leaving the Bi
without any valence electrons. This situation describes the
5+ valence state of the Bi (6s0configuration). It is physically
realized when the Bi 6s1electron is excited to the conduction
band by, for example, an optical absorption process.
The negatively charged Bi−
Mdefect introduces a donor
band within the BMO gap (figure 2(d)). Again, the fact that the
band exhibits predominant Bi 6s character (figure 2(i)) leads
to the conclusion that one extra electron is accommodated into
the Bi 6s2orbital, recuperating the Bi 6s2lone pair. Thus,
the formal valence of the Bi ion within the Bi−
Mdefect is
3+ (6s2configuration). This defect is realized when the neutral
Bi0
Mdefect captures an electron from somewhere, either by
excitation from the valence band top or by de-excitation from
the conduction band bottom. In the first case the 2p electron
is transferred to the Bi from the O(3) surrounding it, while
in the second case the additional electron is captured from
other regions of the crystal (possibly originating from other
defects).
Contrary to existing models, our theoretical results
predict vulnerability of the Bi 6s2lone pair within the BiMO4
defect. Our calculations clearly indicate that within the Bi0
M
defect the Bi uses one of its 6s electrons to satisfy the missing
(fourth) bond with neighboring O atoms without producing
an electron hole but, instead, changing its valence state from
3+ to 4+. The results of simulation of the charged defects
additionally support ‘vulnerability’ of the Bi 6s2states (in
the sense of their facility to be occupied or unoccupied).
Namely, the charged defects were simulated by addition or
subtraction of one electron in the reference of the whole unit
cell of the BMO. During the calculations this electron (or
hole) was redistributed in the manner that leads to convergent
solution of the Kohn–Sham equations. As a result, the extra
(or missing) electron is always localized within the BiM–O(3)
bonds, i.e. by filling (or emptying) the 6s orbital of the Bi ion.
This fact is illustrated in figure 3.
3.2. Energetic and structural characteristics of the BiMO4
defect
In order to check if all three Biq
Mdefects are physically
realizable and to estimate their relative stabilities, we need
to calculate their formation energies. In the present study
the reference pure system is the BTO (see discussion in
the section 2.1), and thus we are able to discuss only
defect formation energies in this compound: Biq
Ti. The
results, however, could be somewhat generalized for the
antisite defects in the other two sillenites (BGO and BSO),
considering the fact that the Ge and Si ions have the same
valence state (4+) and the same surroundings as the Ti ions in
the BTO. Formation energies of the Biq
Ti defects are calculated
on the basis of the following formula [35,36]:
Ef(BTO:Biq
Ti)=ET(BTO:Biq
Ti)−ET(BTO)+µTi
−µBi +q(EVBM +EF+1V(q))(2)
where the first two terms on the right-hand side represent
the total energies of the perfect and defect-containing BTO
5

J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
Figure 4. Formation energies of the Biq
Ti defects as functions of
Fermi energy (calculated from the top of the valence band).
cells, the third and fourth terms are chemical potentials
of the atoms which are removed (Ti) and added (Bi) to
form the defective system, and the fifth term is the electron
chemical potential. In the last term qis the charge state of
the defect (−1,0,+1), EVBM is the energy of the valence
band maximum (VBM) of the perfect BTO system, EFis
the Fermi energy counted with respect to the EVBM, and
1Vis the difference between average electrostatic potentials
in the perfect and defective unit cells (needed to provide
the same reference level for EVBM in different systems).
The µTi and µBi are estimated from their upper bounds,
i.e. they are calculated as energies per atom for bulk hexagonal
close packed metallic Ti and orthorhombic metallic Bi.
All terms in equation (2) are computed using the TB-mBJ
exchange–correlation potential.
The formation energy of the Bi0
Ti defect was calculated to
be +6.42 eV, while the formation energies of the Bi+
Ti and Bi−
Ti
defects were determined as 13.23 eV +EFand 8.35 eV −EF
respectively. From these results it is possible to analyze the
relative stabilities of the charged defects compared to the
neutral one, as shown in figure 4.
From figure 4one can conclude that the neutral defect is
the most stable one over the range of Fermi energies from
0 to 2 eV, while the negative defect becomes energetically
favorable for Fermi energies between 2 and 3.3 eV. The
positively charged defect is the most difficult to realize over
the whole range of possible Fermi energies.
Table 1summarizes the calculated inter-ionic distances
between differently charged antisite Bi defects and their
nearest and next-nearest (NN and NNN) neighboring O atoms,
as well as the distances between Biq
Mand their nearest Bi ions.
For comparison the same distances are listed for the Ti ion in
the perfect BTO. The Ti has the four O(3) ions as the first
and the four O(2b) atoms as the second NNs. This ordering
is preserved for the Bi0
Mand Bi−
Mdefects, but not for the Bi+
M
defect, for which the second neighborhood consists of the 12
Bi atoms at the distance of 3.980 ˚
A, while four O(2b) appear
at the distance of 3.988 ˚
A as the third neighbors.
Table 1exhibits some useful pieces of information
about the structural properties of three defective BMO
systems. First, it shows that all defects induce considerable
expansion of their first and second coordination spheres as
compared with the perfect system. Second, it expresses a
clear dependence of interatomic distances on the charge state
of the defects. If the neutral defect Bi0
Mis considered as
a referent system for comparison, then the Bi+
Mproduces
smaller expansion of its first and larger expansion of its
second coordination sphere. On the other hand, the Bi−
Mdefect
induces larger expansion of its first and smaller expansion of
its second coordination sphere. The Biq
M–Bi distances exhibit
the same trend as the Biq
M–O(2b) ones.
All these characteristics can be understood on the basis
of electronic configurations of three Biq
Mdefects deduced
from electronic structure calculations presented in section 3.1.
Within the neutral Bi0
Mdefect the Bi appears in the formal
valence state 4+. It repulses the NN and the NNN O atoms
for two reasons: (1) the ionic radius of the Bi is much larger
than the M, and (2) the presence of a spatially extended
6s1negative cloud additionally repels the negative oxygen
ions. Within the negatively charged Bi−
Mdefect, the Bi is
in the formal valence state 3+. A spatially extended 6s2
electron cloud is more negative, thus the Bi3+repels the
NN O atoms farther away than the Bi4+. At the same time,
the Bi3+repels the NNN O(2b) atoms less than the Bi4+
due to a weaker electrostatic interaction with the neighboring
Bi3+ions at the regular crystallographic sites (the Bi3+–Bi3+
electrostatic repulsion is weaker than the Bi4+–Bi3+one).
The O(2b) atoms, being the NNs of the regular Bi3+, are
simply dragged together with the regular Bi3+since they
are bound much more strongly to it. Within the positively
charged Bi+
Mdefect the valence state of the Bi is 5+. Owing
to the lack of the 6s negative electron cloud the Bi5+–O(3)
bonds are shorter in comparison with the neutral defect. At the
same time, the Bi5+–Bi3+electrostatic repulsion is stronger
than the Bi3+–Bi3+repulsion, and the Bi5+–O(2b) bonds are
considerably longer than in the case of the neutral defect.
3.3. Optical absorption spectra of defective systems
The presence of antisite defects causes changes in the
absorption spectrum of the BMOs, and these changes are
most pronounced near the optical absorption edge of the
perfect system. Figure 5shows the calculated imaginary part
of the dielectric function ε2of the three BMO:Biq
Mdefective
systems, as well as of the perfect BTO, as a function of
incident radiation energy in the range of 1.5–4.0 eV.
As can be seen from figure 5, the perfect material starts to
absorb the photons at the energy of 3.3 eV, while the spectra
of all defective systems are characterized by prominent peaks
below this energy. These peaks can be interpreted in terms
of electronic structures presented in figure 2. The peaks I, I0
and I00 in the BMO:Bi0
Mspectrum are formed by electronic
transitions from band A to band C and from band C to
band B. Taking into account the distance between atoms and
predominant orbital character of the bands A, B and C, these
structures are mainly determined by transitions from the O(3)
2p to the BiM6s, from the O(3) 2p to the BiM6p-, and from
the Bi 6s to the O(3) 2p and the BiM6p states. All these
6

J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
Figure 5. Imaginary part of dielectric function of the perfect BTO
(red line) and the BMO containing an antisite Bi defect in three
different charge states (black lines) as a function of incident
radiation energy. The prominent structures on the spectra are
denoted by roman numbers I–VI.
transitions transform the Bi electronic configuration from 6s1
to 6s2(Bi3+ion) and 6s0(Bi5+ion), creating the Bi−
Mand the
Bi+
Mantisite defects. The optical spectrum of BMO:Bi+
Malso
exhibits three prominent peaks (III, III0and III00) below the
absorption threshold of the perfect BTO. These structures are
due to electronic transitions from the top of the valence band
A to the unoccupied band C0within the gap. The electronic
transitions involved are those between the O(3) 2p and the
Bi 6s states. The optical spectrum of the BMO:Bi−
Mdefect
exhibits only one peak, numbered as V, below the absorption
edge of the pure BTO. It is formed by electron transfer from
band C00 (occupied Bi 6s and O(3) 2p states) to band B
(unoccupied O(3) 2p and the Bi 6p states).
Figure 5also demonstrates that optical absorption above
the 3.3 eV is more intense in defective systems than in the
perfect BMOs. This characteristic is emphasized by peaks II
(figure 5(a)), IV (figure 5(b)) and VI (figure 5(c)). It can be
related to the existence of the higher DOS at the top of the
valence band of defective systems (figures 2(b)–(d)) compared
to the perfect BTO (figure 2(a)). This occurs because the
O(1) 2p states become dominant at the valence band top of
the defective systems (as discussed in section 3.1), increasing
the probability of optical transition between the Bi and O(1)
within the regular BiO8polyhedron.
4. Model of the BiMO4defect
On the basis of results presented in section 3.3, it is possible
to construct a model of the functioning of the antisite BiMO4
defect that is able to explain the photochromic and PR effect in
sillenites and that agrees with most of the basic experimental
facts established so far. Deduction of the model can be
assisted by a schematic representation of energy bands within
the BMO gap originated from the Biq
Mdefects, as shown
in figure 6. The scheme is constructed on the basis of the
electronic structure presented in figures 2(b)–(d).
Figure 6. Schematic representation of energy bands formed by
antisite defects Biq
Min the BMOs. The arrows indicate possible
processes that ionize the Bi0
Mdefect center leading to the formation
of a donor (Bi−
M) or acceptor (Bi+
M) band.
The neutral Bi0
Mis the defect that exists in the BMOs
which are not subjected to any treatment, i.e. in their so-called
colored state. This defect is paramagnetic (Bi4+: 6s1), a fact
that agrees with MCD and ODMR experiments realized in
the colored state [10,13]. It creates a semi-populated deep
energy band in the middle of the gap, whose center is at
approximately 1.65 eV counted from the valence band top.
Under appropriate illumination (or other kind of excitation)
that provides at least this amount of energy, one electron can
be released from this center to the conduction band, giving
rise to the positively charged Bi+
Mdefect, or one electron can
be captured by it, forming the negatively charged Bi−
Mdefect
(figure 6). In the first case an acceptor band is created, 0.97 eV
below the conduction band bottom. In the second case, a donor
band is formed 0.36 eV above the valence band top. The
longer an energy excitation lasts, the higher is the probability
of creating the donor and acceptor bands. After some time
of continuous excitation, the deep band should be completely
erased and the crystal transformed into another state, in which
just the Bi−
Mand Bi+
Mdefects exist. Both are diamagnetic
defects, with the Bi ion configuration 6s2and 6s0respectively.
The new state of crystal is optically (or thermally) treated,
bleached state. The predicted transformation from colored to
bleached state agrees with the experimental findings that red
light (1.65–2.0 eV) illumination or short thermal annealing
(10–20 min at ∼500 C) transforms the BMO from colored
to bleached state, in which diamagnetic defects prevail
[10,19]. The reverse transformation, from bleached to colored
state, can be performed either by excitation of an electron
from the valence band top to the acceptor band (∼2.33 eV)
or by excitation from the donor band to the conduction band
bottom (∼2.97 eV). In both cases, the Bi+
Mand the Bi−
Mdefects
are discharged, the donor and acceptor bands erased and the
paramagnetic deep band restored in the center of the gap. This
process is also in agreement with experimental findings that
blue (2.50–2.85 eV) [19] or violet (2.85–3.25 eV) [10] light
illumination transforms the BMO from bleached to colored
state.
7

J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
The presented model emphasizes the importance of the
BiMO4defect for explanation of the PR effect in sillenites.
Under coherent illumination of the crystal this defect acts
as a donor and acceptor of the electrons at the same time
(Bi0
M), providing the traps for electrons (Bi+
M) and holes
(Bi−
M) throughout the lattice, fulfilling in this way essential
conditions required for optical recording via space–charge
modulation [16–18].
Considering the optical absorption process caused by
antisite defects, the presented model predicts the following
features.
In the bleached state, optical absorption of the BMO’s
below gap energy should be composed of superposition of
the Bi+
Mand the Bi−
Mε2spectra shown in figure 5. This
superposition results in peaks centered at approximately
2.50, 2.75 and 3.00 eV. The experiment, however, observes
just the shoulder at the energy of ∼3 eV [10]. There
are two possible reasons for this disagreement: (1) optical
calculations overestimated the transition probability from the
O(3) 2p to the BiM6s states (those which generate peaks
at 2.5 and 2.75 eV), resulting in higher absorption intensity
than measured; (2) owing to the relatively small supercell size
and approximate treatment of exchange–correlation effects in
our calculations the energy of the acceptor band is slightly
underestimated; if this band were positioned ∼0.5 eV higher
in energy, the peak at 2.5 eV would be centered on 3 eV while
other peaks would be immersed into the host absorption.
In the colored state, the BMO’s optical absorption edge
should be influenced only by neutral defects and absorption
described by the ε2spectrum of the Bi0
M(figure 5). In the
literature, however, the optical absorption spectrum of the
BMOs at room temperature is sometimes presented [20], in
which case it should be composed of a superposition of all
three spectra shown in figure 5(since all three differently
charged defects should coexist in the host). In both cases our
theoretical model predicts formation of a broad shoulder in the
optical absorption spectrum of the BMO, as shown in figure 7,
which explains the coloration of the material provoked by
proper illumination (photochromism). It also demonstrates
good qualitative agreement with experimental results.
It is worth mentioning that several experimental studies
of doped sillenites have discussed the change of valence
state of the impurities after illumination and its influence on
the photoconductivity and photochromicity of the material.
Montenegro et al [37] and Carvalho et al [38] studied optical
absorption of nominally pure BTO doped with V atoms.
They suggested that some of the tetrahedral sites occupied by
Bi4+defects may be substituted by either V3+or V5+ions.
A similar conclusion is also drawn from works of Marquet
et al [19] and McCullough et al [39], who investigated the
optical absorption of BGO doped with Cr. Our theoretical
study clearly substantiates their suggestions.
Finally, let us briefly discuss the reliability of the
calculations presented in this paper. It is a fact that the size
of the supercell used to simulate antisite defects was not
very large (this is especially valid for consideration of the
charged defects). This size is, however, sufficient to constrain
the geometric influence of the defects within the supercell, as
can be seen from the following facts.
Figure 7. Calculated optical absorption spectra of the BMO in the
colored state (green line) and in the state in which all three Biq
M
defects coexist (black line). They are compared to measured
absorption spectra of nominally undoped BTO (red curve, [21]) and
BGO (blue curve, [10]). The theoretical spectra are calculated in the
energy range 0–3 eV, simulating measurements which were made
up to this energy.
(1) Analysis of interatomic distances has shown that the
lattice deformation is localized nearby the defect. Table 1
demonstrates that the distances between the defect and
its neighboring O atoms are changed very much, which
is not the case with distances between the defect and its
third-neighboring Bi. The distances between the defect
and the atoms situated farther away (not shown in the
paper due to economy of space) are quite similar to the
distances in the pure compound, for all three kinds of
defect considered.
(2) Electronic bands of the defects, introduced within the
band gap, are narrow. The thicknesses of the neutral and
the charged defects’ bands are similar (figure 2). This fact
indicates very small overlap between the wavefunction of
the defect and its periodic images in other supercells.
(3) According to the distribution of the valence charge
density, shown in figure 3, an extra or a missing electron
charge (within the charged defects) is concentrated nearby
the defect, populating or emptying the 6s states of the Bi.
The supercell size used in the present study is also
sufficient to significantly reduce the magnitude of the
Coulomb interaction between the charged defect and its
periodic images. This effect can be estimated by calculating
the first term of the Makov–Payne correction to the energy of
the ionic crystals [40] (written in SI units):
EMP
corr =1
4πε0εr
q2α
2L(3)
where q= ±e(charges), α=3.64 (Madelung constant for
bcc lattice), L=10.322 ˚
A (supercell lattice constant) and
εr≈50 (static dielectric constants of the BTO, BSO and
BGO are 48, 56 and 47 respectively [41]). The result obtained
is Ecorr =50 meV. Thus, even though the supercell is not
large, due to the high dielectric constant of the sillenites the
Coulomb interaction between defects is strongly screened
and, consequently, errors in calculated total energies and
positions of the Kohn–Sham bands within the gap are small.
8

J. Phys.: Condens. Matter 25 (2013) 495505 A F Lima and M V Lalic
5. Conclusions
In this paper we performed a thorough theoretical study of
the antisite BiMO4defect in the Bi12MO20 (M =Si, Ge,
Ti; BMO) sillenite compounds, which is formed by wrong
occupation of the M4+sites by the Bi3+ions (BiM). As a
tool we used the first-principles FP-(L)APW method, based
on DFT and implemented in the WIEN2k computer code. We
discussed the structural, electronic and optical properties of
the BiMdefect in its neutral (Bi0
M), negative (Bi−
M) and positive
(Bi+
M) charge state.
The results of our study demonstrate that within the
neutral defect (Bi0
M) the Bi 6s2lone pair is broken and the
Bi electron configuration is 6s1. By capturing or emitting
one electron, the Bi assumes 6s2or 6s0configurations
respectively, forming the Bi−
Mand Bi+
Mcharged defects. All
three Biq
Mdefects introduce bands inside the BMO gap: the
Bi0
Ma half-occupied deep band, the Bi−
Ma donor band and the
Bi+
Man acceptor band. By analyzing the interplay of possible
transitions between them we deduced a model of functioning
of the BiMdefect in sillenites which is substantially different
from the existing ones. In brief, our model predicts that
the Bi0
Mdefect should be dominant in the colored state
of the BMOs and should act simultaneously as a donor
and an acceptor. Under proper excitation it can create traps
for electrons (Bi+
M) and holes (Bi−
M) throughout the lattice,
transforming the host into the bleached state and fulfilling
the basic conditions required for optical recording via
space–charge modulation. The model explains the domination
of paramagnetic defects in the colored and diamagnetic
defects in the bleached state, and accurately reproduces
conditions that are necessary to transform the colored state
into the bleached one and vice versa. Additionally, it correctly
predicts the formation of the broad and intense shoulder below
the optical absorption edge of the BMOs, explaining their
coloration under appropriate illumination.
Acknowledgments
The authors acknowledge the CNPq, CAPES and FAPITEC
(Brazilian funding agencies) for financial help. We also thank
Professor J Frejlich for fruitful discussions.
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