Content uploaded by R. V. Gamernyk
Author content
All content in this area was uploaded by R. V. Gamernyk
Content may be subject to copyright.
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 18 (2006) 5323–5331 doi:10.1088/0953-8984/18/23/006
Optical and photoelectric spectroscopy of
photorefractive Sn2P2S6crystals
RVGamernyk
1,YuPGnatenko
2,3,PMBukivskij2,PASkubenko2and
VYuSlivka
1
1Lviv National University, 8 Kyrylo and Mefodiy street, 29005 Lviv, Ukraine
2Institute of Physics of NAS of Ukraine, 46 Prospect Nauky, 03028 Kyiv, Ukraine
E-mail: gnatenko@iop.kiev.ua
Received 19 January 2006
Published 26 May 2006
Online at stacks.iop.org/JPhysCM/18/5323
Abstract
Low-temperature studies of the absorption, photoluminescence, photodiffusion
and photoconductivity spectra of Sn2P2S6crystals were carried out in the wide
spectral range 0.8–3.5 eV. The position of defect energy levels relative to the
crystal energy bands has been determined. It was shown that the photoionization
transitions from the valence band to the level with the energy Ev+1.35 eV
are caused by the presence of the hole metastable state. In the optical and
photoelectric spectra several bands were revealed with energy greater than the
band gap of the crystal (Eg=2.5eV).Itwasestablished that these bands are
caused by the optical transitions between the valence band and upper conduction
bands. It was shown that the electron–hole recombination, caused by the band-
to-band transitions with the participation of the upper conduction subbands, is
fast and corresponds to the nanosecond region. The combined scheme of the
defect energy level and the band-to-band electronic phototransitionsin Sn2P2S6
crystals was constructed. A mechanism for the photorefractive effect in these
crystals is proposed.
1. Introduction
Sn2P2S6crystals are ionic–covalent compounds [1–3]. These crystals attract special attention,
since they are considered promising photorefractivematerials. They combine ferroelectric and
semiconductor properties, which makes it possible to obtain a photorefractive gain factor of
≈30 cm−1andaresponse time of about 10−3s. The spectral range of the photosensitivity of
such crystals spreads from 0.5 to 1.32 µm[5]. However, the mechanism of the photorefractive
effect and the photoinduced changes in Sn2P2S6crystals are still not very clear and require
additional studies. Such studies would help one optimize the photorefractive properties of
3Author to whom any correspondence should be addressed.
0953-8984/06/235323+09$30.00 ©2006 IOP Publishing Ltd Printed in the UK 5323
5324 RVGamernyket al
these crystals and would contribute to their applications. At the present time, the studies of
Sn2P2S6crystals have mainly been devoted to the phase transitions, the phonon spectra and
the peculiarities of photorefractive properties of such crystals depending on the technology of
their growth [2,5–7]. However, the studies of the nature of defect states as well as the position
of their energy levels relative to the crystal energy band are at the first stage of understanding.
Recently several papers have been published [8–11]whichare devoted to studies of electronic
structure of Sn2P2S6crystals. It was shown [4]thatthe energy band spectrum of Sn2P2S6
crystal is characterized by poor curvature of both the bottom of the conduction band and the
top of the valence band, which indicates relatively high effective masses of the charge carriers.
Such crystals have p-type conductivity, which is determined by the Sn vacancies.
In this work, low-temperature studies of the optical (absorption and photoluminescence)
and photoelectric (photoconductivity and photodiffusion current) properties of Sn2P2S6crystals
were carried out. The studies revealed the defect states and determined their nature as well as
the positions of the defect energy levels relative to the crystal energy bands and the type of
the photoionization transitions. The combined scheme of defect energy level and the band-to-
band electronic phototransitions in Sn2P2S6crystals was constructed. The mechanism for the
photorefractive effect in these crystals is presented.
2. Experimental procedures
The non-doped Sn2P2S6crystals were grown by a gas-transport reaction. The parallel-sided
crystal samples were prepared by mechanical treatment and then polished. The absorption,
photoconductivity and photodiffusion current spectra were measured using an MDR-23
monochromator and processed with a computer. The samples were mounted on the cold
finger of a variable temperature liquid-nitrogen cryostat. The accuracy of the measurements
and temperature stabilization by the UTREKS system was 0.01 K. In these measurements, the
light beam incident on the crystal sample was modulated by a mechanical chopper and the
signal was measured using a phase-sensitive lock-in detection system. The spectral resolution
of the system was about 1 cm−1.
The photoconduction and photodiffusion spectra were measured along the [010] crystal
direction. The ring In–Ga–Sn paste electrodes were deposited on polished front and rear
(010) faces of the crystals. These faces were set perpendicular to the direction of incident
monochromatic light propagation. The photodiffusion current (PDC) spectra were measured
using plane-parallel samples whose thickness dsatisfied the condition kd 1, i.e. the light
wasadsorbedonthe natural cleaved faces of the crystals perpendicular to the direction of the
light propagation, and their ohmic resistance was checked. The experimental scheme is shown
in figure 1.
The PDC experiments were carried out using a quartz halogen lamp as the light source.
The diameter of the beam spot was 10–12 mm and the light intensity incident on the crystal
face depended on the light wavelength. The illumination was homogeneous all over the
crystal sample face including the electrodes. The maximum of the light intensity (Imax =
1.08 mkW cm−2)corresponds to the wavelength at 650 nm (1.91 eV). For the wavelengths
λ1=1000 nm (1.24 eV) and λ2=350 nm (3.54 eV) the light intensity corresponds
to 0.639 and 0.146 mkW cm−2,respectively. Due to the nonuniform depth distribution of
excessminority carriers in the crystal, illumination of the samples produces a diffusion current
perpendicular to the crystal surface (since the cross section of the incident light was uniform,
this eliminated carrier diffusion perpendicular to the direction of the light propagation). As a
result of the establishment of equilibrium in an isolated sample, a potential difference is created
between the illuminated and dark surfaces of the crystal, which is responsible for the Dember
Optical and photoelectric spectroscopy of photorefractive Sn2P2S6crystals 5325
Monochromatic
Electrometer
V7-30
light
Figure 1. Experimental scheme for photodiffusion current measurement.
E1E1
Eg
E2E2
IPDC
2
1
IPDC
-
+
Figure 2. Diagram of the polarity of photoionization transitions in the measurement of the
photodiffusion current.
photo-emf. In our measurements, the input resistance of the electrometer was much lower than
the resistance of the samples, so in these experiments we measured a diffusion current close to
the short circuit current. The direction of this current is determined by the direction of light
propagation. The samples were exposed to monochromatic light. The polarity of the PDC
wasdetermined by the polarity of the charge observed at the front (illuminated) surface of the
sample and was opposite to that of the excited carriers. The PDC spectra were normalized
to the same number of incident photons. In the PDC spectra, the positive bands are caused
by photoionization transitions of electrons from impurity or defect levels to the conduction
band, while the negative bands are attributed to the excitation of valence-band electrons to
discrete levels positioned in the crystal band gap (photoionization of holes from impurity
levels to the valence band). A diagram of the polarity of photoionization transitions in the
measurement of the photodiffusion current is shown in figure 2.Thus the PDC method has
the advantage in comparison with the photoconduction (PC) measurements of photoionization
transitions caused by the optical transitions between the defect (donor or acceptor) levels and
the energy crystal bands. It makes it possible to determine not only the energy but also the
type of phototransition (from defect levels to theconduction band or from the valence band to
defect levels). Undoubtedly the measurements of both the PDC spectra and the PC spectra let
us obtain more complete data regarding the photoionization transitions. Therefore in this paper
the PDC and PCmeasurements are used.
5326 RVGamernyket al
Absorption Coefficient k (cm-1)
Photon Energy E (eV)
0
5
10
15
20
25
30
35
40
1,81,6 2,0 2,2 2,4
Figure 3. Absorption spectrum of Sn2P2S6at 295 K.
3. Experimental results and discussion
In figure 3the absorption spectrum of Sn2P2S6crystals is presented at 293 K. It shows that
the absorption edge (for an absorption coefficient equal to 35 cm−1)ispositioned at an energy
about 2.35 eV and the absorption of the crystal in the transparent spectral range is insignificant
(3cm
−1). In figure 3the absorption spectrum of the crystal is shown for the energy range
from 1.55 to 2.35 eV. It should be noted that the absorption measurements of Sn2P2S6crystals
were carried out in a wider spectral range up to λ=1.8µm(≈0.69 eV). For energies smaller
than 1.55 eV the absorption decreases (the absorption coefficient k≈2cm
−1at the energy
0.7 eV) very smoothly. For energies greater than 2.35 eV, the absorption coefficient of Sn2P2S6
crystal is strongly increasing. It is known that for the band-to-band transitions the value of kis
≈105cm−1.Inour case the experimental equipment let us measure an absorption coefficient
less than 40 cm−1.Theabsorption spectrum of Sn2P2S6crystal in the spectral range from 1.6
to 2.2 eV indicates the possibility of the presence of optical photoionization transitions. In
order to study photoionization transitions between the acceptor/donor centres and the energy
bands of the crystal, and to determine the energies and types of the phototransitions, we used
the measurements of the PDC and PC spectra of the investigated crystals. These measurements
let us obtain more complete data regarding the photoionization transitions and enabled us to
distinguish PDC peaks from troughs.
In figure 4the PDC spectrum of Sn2P2S6crystals at 78 K is shown. It should be noted
that the negative PDC spectrum located in the spectral range 1.2–3.7 eV is caused by the
photoionization of electrons from the valence band to the defect energy levels, which are
positioned in the band gap. There are several PDC bands of negative polarity at the energies
1.35, 1.85, 2.12, 2.55 and 3.45 eV, indicated by the arrows in figure 4.Itisalsopossible
that positive PDC bands of small intensity can be present in the spectral range about 1.0 eV.
The inflection shown on the low-energy edge of the 2.27 eV PDC band may be caused by the
transitions to one of the conduction subbands, since the calculations of the band structure of
Sn2P2S6crystals indicate [10]that two conduction subbands have very close energies. Another
mechanism for the appearance of a PDC band at 2.27 eV can be caused by the optical transitions
from the valence band to the donor level (it is possible that this PDC band may be caused
by the optical transitions from the acceptor levels to the conduction band) with the energy
≈Ec−0.29 eV. The negative PDC band at 3.45 eV is caused by the band-to-band transitions
between the valence band and one of the conduction subbands [10].
Optical and photoelectric spectroscopy of photorefractive Sn2P2S6crystals 5327
0
-100
-200
-300
-400
-500
1.0 1.5 2.0 2.5 3.0 3.5 4.0
PDC Intensity (arb. units)
Photon Energy E (eV)
1,35eV
1,85eV
2,12eV
2,55eV
3,45eV
Figure 4. Photodiffusion current spectrum of Sn2P2S6at 78 K.
450
400
350
300
250
200
150
100
50
0
1,0 1,5 2,0 2,5 3,0 3,5
0,70eV
0,87eV
0,98eV
1,34eV
1,66eV
2,12eV
2,27eV
2,48eV
2,70eV
2,97eV
3,45eV
Photoconductivity (arb.units)
Photon Energy E (eV)
Figure 5. Photoconductivity spectrum of Sn2P2S6at 78 K.
It should be noted that the relative intensity of the PDC bands strongly depends on the
method of the preparing of samples. When the crystal sample is heated above the ferroelectric
phase transition temperature (337 K) and then cooled in the dark in short circuit conditions,
the 2.55 eV band is the most intensive in the spectrum. The preliminary illumination of Sn2P2S6
crystals by light with the energy 2.60 eV produces a redistribution of intensitybetween different
PDC bands. In this case, the intensity of the PDC bands at 1.85, 2.12 and 2.27 eV is essentially
increased and the 2.55 eV band is strongly decreased. The heating of the crystal up to 337 K
and the cooling in the dark leads to the reconstruction of the primary spectrum.
The measurements of the PC spectrum of Sn2P2S6crystals let us determine both the
energies of the photoionization transitions and the PDC bands of positive polarity in the region
about 1.0 eV (shown as a wide band in the PDC spectrum) with higher precision. In figure 5
the PC spectrum is presented. As can be seen, the PC bands at 0.70, 0.87, 0.98, 1.34, 1.66,
2.12, 2.27, 2.48, 2.70, 2.97 and 3.45 eV appear in the spectrum. It should be noted that most of
the PC bands with energy higher than 1.00 eV appear in the PDC spectrum too. Thus the PDC
bands at 1.35, 2.12, 2.27, 2.55 and 3.45 eV correspond to the PC bands at 1.34, 2.12, 2.27, 2.48
and 3.45 eV, respectively. Three PC bands are located in the low-energy region at 0.70, 0.87
and 0.98 eV. The PDC bands at 2.70 and 3.00 eV are shown in figure 4as a wide inflection.
5328 RVGamernyket al
It should be noted that the positive PDC band in the 0.8–1.2 eV range has been detected
earlier. It was possible to observe the structure of this band in the PC spectrum because this
spectrum was measured with better spectral resolution ratio since the signal intensity of the
PC spectrum was stronger than that of the PDC spectrum. Therefore in fact we carried out
the measurement of the PC spectrum with the better spectral resolution. The intensity of the
monochromatic light was the same for both measurements. We think that the PC bands at 0.70,
0.87 and 0.98 eV correspond to the optical transitions from deep defect levels positioned in the
band gap of Sn2P2S6crystal to the conduction band.
The appearance of the negative PDC band at 1.35 eV is correlated with the photo-EPR data
obtained in [10]. In that research it was reported that holes are generated in Sn2P2S6crystals
when excited by light with an energy of 1.40 eV. The holes are trapped by the Sn2+ions. In this
case the polaron state can appear in the Sn2P2S6crystal [12], i.e. the holes are trapped by the
metastable states positioned in the bandgap of the crystal. The results of the studiesof PDC and
PC spectra indicate that the metastable state corresponds to the energy level at Ev+1.35 eV.
It should be noted that illumination of Sn2P2S6crystals by light with an energy of 2.0 eV leads
to the disappearance of Sn3+ions in the photo-EPR spectrum. In our opinion, it may be caused
by the photoionization transitions from the valence band to the levels of Sn3+ions and the
formation of Sn2+ions. Since for the Sn2P2S6crystals there are two nonequivalent positions of
Sn2+ions, then it is obvious that the optical transitions at 1.85 and 2.12 eV can be caused by the
acceptor photoionization of such levels. The PDC and PC bands at 2.27 eV are possibly caused
by the optical transitions from the valence band to the level with the energy Ec−0.28 eV, which
is the trap for electrons. This coincides with thedataforthethermoluminescence measurement
of Sn2P2S6crystals [13].
The photoluminescence (PL) spectra including a time-resolved spectrum of Sn2P2S6
crystals were measured at 4.5 K. A nitrogen laser was used for excitation of the spectra.
Figure 6presents PL spectra of Sn2P2S6crystals in the range 2.1–3.5 eV at 4.5 K. It should
be noted that the investigation of the PL spectra of Sn2P2S6crystals under the excitation of a
Hg lamp was carried out earlier [13]inthe spectral range 1.48–2.07 eV, i.e. at energies smaller
than the bandgapofSn
2P2S6.TwowidePLbands at 1.8 and 2.1 eV were revealed [13], which
with no doubts are caused by the optical transitions with the participation of Sn2P2S6defect
levels. It was noted that the increasing of the temperature from 4.5 to 40 K leads to the strong
decreasing of the high-energy PL band intensity. In this work there is no explanation regarding
the nature of PL bands and their temperature dependence. The thermoluminescence spectrum
of Sn2P2S6[13]indicates the presence of carrier traps with energies Ec−0.041 eV and Ec−
0.088 eV. The calculation of the energy bands of Sn2P2S6crystal, presented in [10], indicates
the presence of five conduction subbands positioned above the lower conduction subband in the
energy region of 1.2 eV. Taking into account the energy structure of Sn2P2S6crystals, we think
that the above-mentioned PL bands are caused by the electron–hole recombination between
several conduction subbands from one hand and the top of valence band from the other hand,
i.e. they correspond to the band-to-band transitions. This assumption correlates with the results
of the PDC and PC spectra where the bands at 2.70, 3.00 and 3.45 eV are shown. It should
be noted that the band at 3.00 eV is broadened and appears as a kink. Such a shape does
not exclude the presence of another band at 2.82 eV. As can be seen, there are no significant
differences between the stationary and time-resolved PL spectra (the delay time equals 3.0 ns).
This indicates that the processes of electron–hole recombination in the spectral region above
2.3 eV are fast and take place in the nanosecond time region.
Figure 7presents a combined schemeofdefect energy level and band-to-band electronic
phototransitions in Sn2P2S6crystals. The obtained results indicate that these crystals contain
Sn2+and Sn3+states and metastable (Sn2++h) polaron states. These states are situated in two
Optical and photoelectric spectroscopy of photorefractive Sn2P2S6crystals 5329
700
600
500
400
300
200
100
0
2,0 2,2
2,69eV
2,82eV
3,00eV
3,35eV
2,4 2,6 2,8 3,0 3,2 3,4 3,6
Photoluminescence (arb.units)
Photon Ener
gy
E (eV)
Figure 6. Stationary (solid line) and time-resolved (dotted line) photoluminescence spectra of
Sn2P2S6at 4.5 K.
Figure 7. Scheme of the defect energy levels andelectronic phototransitions of Sn2P2S6crystals.
nonequivalent positions. Besides, there are some (D1–D4)donor states. In this case, the positive
charges of the Sn3+ions are clearly compensated by the presence of these donor states as well
as the shallow donor states revealed in the thermoluminescence. The donor concentration in
the dark should correspond to that of the triply charged Sn ions.
According to the presented results, we propose the following mechanism for the
photorefractive effect in these crystals. It is known that the photorefractive effect is a
phenomenon in which the local index of refraction is changed by the spatial variation
of the light intensity. Nonlinear optical processes including two-wave mixing are typical
characteristics of the photorefractive effect that can be observed in crystals possessing
both electrooptic and photoconductive properties. Sn2P2S6crystals belong to such type of
semiconductors. It should be noted that a refractive grating is created in the photorefractive
crystal as a result of the illumination of the crystal sample surface by two coherent light beams.
In this case an interference pattern is produced on the crystal surface. When Sn2P2S6crystals
are excited by He–Ne laser light (hν=1.96 eV), a photorefractive effect may occur as a
result of photoionization of Sn3+ions with energy 1.85 and 2.12 eV. It should be noted that
5330 RVGamernyket al
when a Sn2P2S6crystal is excited by He–Ne laser light at T=300 K, the Sn3+
2centres
with the photoionization energy 2.12 eV may undergo photoionization as a result of optical
transitions involving the absorption of two longitudinal optical phonons with energy 76 meV
(607 cm−1)[7]. The photoionization transitions with the energies 1.85 and 2.12 eV correspond
to the phototransitions of the electrons from the valence band to the Sn3+states. In this case,
Sn2+ions are formed and free holes are created in the valence band. It should be noted that
EPR measurement of Sn2P2S6[14]supports the identification of holes as the dominating charge
carriers in this crystal. These carriers migrate by diffusion or drift from the regions of high
illumination to the regions of low illumination and then are trapped by the Sn2+centres to
form the positive charged Sn3+centres. Thus, in the regions of the crystal corresponding
to the maximum of the interference pattern, the concentration of Sn3+centres is lower than
that required to compensate for the negatively charged donor centres. In other regions of the
crystal some distance from the maximum of the interference pattern, there is an excess of Sn3+
centres as a result of trapping of holes by Sn2+centres. Consequently, the trapped charges are
distributed in space according to the light intensity distribution of the interference pattern. The
excessofuncompensated donor states near the interference pattern maximum and the excess
of Sn3+centres in the other parts of the crystal lead to the formation of a periodic space charge
field, which modulates the refractive index and thus produces the photorefractive effect [15].
It should be noted that the phase of the space-charge field is shifted in comparison with
the interference pattern. This phase shift can have values between 0 and πdepending on the
transport mechanism of the charge carriers during the formation of the space-charge field [15].
The recording of the grating in the pure diffusion regime leads to a phase shift equal to π/2.
Thus in photorefractive crystals the interference of two coherent beams creates a refractive-
index grating corresponding to the interference pattern but with a shifted spatial phase. This
phase shift leads to an energy transfer between the beams, i.e. the signal beam is amplified at
the expense of the pump beam. This process is called photorefractive two-beam coupling.
In our opinion, the proposed scheme of the defect energy level in Sn2P2S6crystals lets us
understand how the PDC spectra depend on the method of the sample preparation. It should
be noted that Sn2P2S6crystals are characterized by the presence of a domain structure in the
ferroelectric state. Therefore, in this case, the localization of the carriers near the domain
walls [16]ispossible. When the crystal sample is heated above the ferroelectric phase transition
temperature (337 K), the domain structure is damaged. In this case the localized carriers are
free. Since the crystal sample is in the dark and in the regime of short circuit the charged carriers
can migrate into the Sn2P2S6crystals. The transition of Sn2P2S6into the ferroelectric state lets
the charge carriers diffuse and drift in the depolarizing field of the domain structure [16]. The
redistribution of intensity between the different PDC bands and, in particular, the decrease of
the intensity of the bands at 1.85 and 2.12 eV may be caused by the decreasing of concentration
of Sn3+ions as a result of the trapping of free electrons by these ions. In this case, the
2.56 eV band that corresponds to the band-to-band transitions will be most intensive in the
spectrum.
The preliminary illumination of Sn2P2S6crystals using light with energy 2.56 eV leads
to the photogeneration of the free charge carriers both in the valence and in the conduction
bands. The intensity of the PDC bands at 1.85 and 2.12 eV is essentially increased, which
may be caused by the increasing of the concentration of Sn3+ions. Obviously the free holes
are trapped by the Sn2+centres which are recharged into the Sn3+states. Besides, the free
holes may be trapped near Sn2+ions and hole polaron states created. Thus only a portion of
free electrons is able to recombine with the free holes. The other electrons remain free in the
conduction band. This leads to the increasing of dark conductivity. These results are in good
agreement with the photoinduced changes of the dark conductivity. It was established that the
Optical and photoelectric spectroscopy of photorefractive Sn2P2S6crystals 5331
illumination of Sn2P2S6crystals by white light leads to the appearance of photoinduced dark
conductivity [17]. In this case the resistance of the crystal sample is decreased. Besides, it
wasshown that this illumination of Sn2P2S6leads to an increase of the photorefractive gain by
afactor of 6 [14]. In our opinion, this may be caused by the increasing of the effective trap
density as a result of the increasing of the photoinduced Sn3+ions [18].
4. Summary
Complex optical and photoelectric studies of Sn2P2S6crystals in the spectral region 0.8–3.5 eV
were carried out. A detailed analysis of the spectral dependence of PDC and photoconductivity
spectra let us determine some deep impurity levels in the band gap. It was shown that the level
with energy Ev+1.35 eV is caused by the metastable state. The appearance of other levels with
the energies Ev+1.85 eV and Ev+2.12 eV are caused by the acceptor photoionization of Sn3+
ions located in two nonequivalent positions. It was shown that the PDC and photoconductivity
bands at 0.70, 0.87 and 0.98 eV are caused by donor photoionization from the deep impurity
levels to the conduction band. It was established that some PL, PDC and PC bands at energies
greater than the band gap of Sn2P2S6crystals are obviously caused by the band-to-band
transitions with the participation of the valence band and several upper conduction subbands.
It was shown that the electron–hole recombination is fast and takes place in the nanosecond
range. A combined scheme of defect energy level and band-to-band electronic phototransitions
in Sn2P2S6crystals was constructed. The obtained results indicate that there are Sn2+,Sn
3+and
metastable (Sn2++h) states in these crystals. They are situated in two nonequivalentpositions.
Besides, there are some (D1–D2)donor states. It was shown that the charge compensation for
Sn2P2S6crystals is caused by the presence of triply charged Sn ions and some deep and shallow
donor states. The micromechanism of the photorefractive effect based on the obtained results
has been presented. The nature of the electronic processes responsible for the photoinduced
changes of the photoelectric properties of the investigated crystals was established.
References
[1] Carpentier C D and Nitsche R 1974 Mater. Res. Bull. 9401
[2] Odoulov S, Shumelyuk A, Hellwig U, Rupp R, Grabar A and Stoyka I 1996 J. Opt. Soc. Am. B13 2352
[3] Grabar A A, Kedyk I V, Gurzan M I, Stoyka I M, Molnar A A and Vysochanskii Y M 2001 Opt. Commun.
188 187
[4] Enjalbert R, Gaby J, Vysochanskii Y, Ouedraogo A and Saint-Gregoire P 1999 Eur. Phys. J. B8169
[5] Shumelyuk A, Odoulov S, Kip D and Kratzig E 2001 Appl. Phys. B72 707
[6] Kedyulich V M, Slivka A G, Gerzanich E I, Shusta V S and Guranich P P 2001 Ferroel ectrics 254 243
[7] Hlinka J, Gregora I and Vorlicek V 2002 Phys. Rev. B65 0643081
[8] Kuepper E, Schneider B, Caciuc V, Neumann M, Postnikov A V, Ruediger A, Grabar A A and
Vysochanskii Yu M 2003 Phys. Rev. B67 115101
[9] Fenchak V Yu, Kityk I V, Grabar A A and Slivka V Yu 1997 Ferroe l ectrics 192 129
[10] Bercha D M, Grabar A A, Harhalis L Yu, Mitin O B and Bercha A I 1997 Fiz. Tverd. Tela 39 1219
[11] Kityk I V, Fenchak V Yu, Grabar A A and Slivka V Yu 1995 Fiz. Tekh. Poluprov. 29 697
[12] Ruediger A, Odoulov S and Grabar A 2001 Opt. Mater. 18 123
[13] Bravina S L, Morozovsky N V, Kadashchuk A K and Manzhara V S 1997 Fer ro electrics 192 197
[14] Ruediger A, Schirmer O, Odoulov S, Shumelyuk A and Grabar A A 2001 Opt. Mater. 18 123
[15] Petrov M P, Sokolov I A, Stepanov S I and Trofimov G S 1990 J. Appl. Phys. 68 2216
[16] Lupascu D C, Genenko Yu A and Balke N 2006 J. Am. Ceram. Soc. 89 224
[17] Grabar A A 1997 Ferroel ectrics 192 155
[18] Gnatenko Yu P, Borshch A O, Kukhtarev N, Kukhtareva T, Faryna I O, Volkov V I, Bukivskij P M,
Gamernyk R V, Rudenko V I, Paranchych S Yu and Paranchych L D 2003 J. Appl. Phys. 94 4896