Unipolar injection currents in Bi₄Ge₃O₁₂ crystals
Current-voltage characteristics of bismuth orthogermanate (Bi₄Ge₃O₁₂) single crystals have been measured at different temperatures under conditions of unipolar injection of charge carriers. It has been found that conduction is characterized by the existence of two channels of the percolation. The te...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2003
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| Цитувати: | Unipolar injection currents in Bi₄Ge₃O₁₂ crystals / T.M. Bochkova, S.N. Plyaka, G.Ch. Sokolyanskii // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 461-464. — Бібліогр.: 23 назв. — англ. |
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irk-123456789-1180752017-05-29T03:05:05Z Unipolar injection currents in Bi₄Ge₃O₁₂ crystals Bochkova, T.M. Plyaka, S.N. Sokolyanskii, G.Ch. Current-voltage characteristics of bismuth orthogermanate (Bi₄Ge₃O₁₂) single crystals have been measured at different temperatures under conditions of unipolar injection of charge carriers. It has been found that conduction is characterized by the existence of two channels of the percolation. The temperature dependencies of the conductivity, mobility and concentration of the electrons and holes are considered. The obtained results are discussed in terms of hopping transport model of charge carriers in doped heavily compensated semiconductors. 2003 Article Unipolar injection currents in Bi₄Ge₃O₁₂ crystals / T.M. Bochkova, S.N. Plyaka, G.Ch. Sokolyanskii // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 461-464. — Бібліогр.: 23 назв. — англ. 1560-8034 PACS: 72.20 Iv http://dspace.nbuv.gov.ua/handle/123456789/118075 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Current-voltage characteristics of bismuth orthogermanate (Bi₄Ge₃O₁₂) single crystals have been measured at different temperatures under conditions of unipolar injection of charge carriers. It has been found that conduction is characterized by the existence of two channels of the percolation. The temperature dependencies of the conductivity, mobility and concentration of the electrons and holes are considered. The obtained results are discussed in terms of hopping transport model of charge carriers in doped heavily compensated semiconductors. |
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Bochkova, T.M. Plyaka, S.N. Sokolyanskii, G.Ch. |
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Bochkova, T.M. Plyaka, S.N. Sokolyanskii, G.Ch. Unipolar injection currents in Bi₄Ge₃O₁₂ crystals Semiconductor Physics Quantum Electronics & Optoelectronics |
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Bochkova, T.M. Plyaka, S.N. Sokolyanskii, G.Ch. |
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Bochkova, T.M. |
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Unipolar injection currents in Bi₄Ge₃O₁₂ crystals |
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Unipolar injection currents in Bi₄Ge₃O₁₂ crystals |
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Unipolar injection currents in Bi₄Ge₃O₁₂ crystals |
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Unipolar injection currents in Bi₄Ge₃O₁₂ crystals |
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Unipolar injection currents in Bi₄Ge₃O₁₂ crystals |
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unipolar injection currents in bi₄ge₃o₁₂ crystals |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2003 |
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http://dspace.nbuv.gov.ua/handle/123456789/118075 |
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Unipolar injection currents in Bi₄Ge₃O₁₂ crystals / T.M. Bochkova, S.N. Plyaka, G.Ch. Sokolyanskii // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 461-464. — Бібліогр.: 23 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT bochkovatm unipolarinjectioncurrentsinbi4ge3o12crystals AT plyakasn unipolarinjectioncurrentsinbi4ge3o12crystals AT sokolyanskiigch unipolarinjectioncurrentsinbi4ge3o12crystals |
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2025-07-08T13:19:22Z |
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2025-07-08T13:19:22Z |
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1837084981567946752 |
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461© 2003, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2003. V. 6, N 4. P. 461-464.
PACS: 72.20 Iv
Unipolar injection currents in Bi4Ge3O12 crystals
T.M. Bochkova, S.N. Plyaka, G.Ch. Sokolyanskii
Dniepropetrovsk National University, 13, Naukova str., 49050 Dniepropetrovsk, Ukraine
Phone: +380 (562) 465597; E-mail: tbochkova@ff.dsu.dp.ua
Abstract. Current-voltage characteristics of bismuth orthogermanate (Bi4Ge3O12) single crys-
tals have been measured at different temperatures under conditions of unipolar injection of
charge carriers. It has been found that conduction is characterized by the existence of two
channels of the percolation. The temperature dependencies of the conductivity, mobility and
concentration of the electrons and holes are considered. The obtained results are discussed in
terms of hopping transport model of charge carriers in doped heavily compensated semicon-
ductors.
Keywords: hopping conductivity, current-voltage relations, bismuth orthogermanate.
Paper received 08.09.03; accepted for publication 11.12.03.
1. Introduction
Crystalline bismuth orthogermanate, (Bi4Ge3O12, named
as BGO) was initially synthesized and studied as an
electrooptical material, then it was considered as per-
spective laser host for rare-earth elements and now it is
one of the most effective scintillators for the detection of
ionizing radiations. At present time BGO is widely used
in high-energy physics and computer tomography. Ac-
cording to priority directions of BGO technical applica-
tions, the most attention of the scientists was concentrated
on the study of its structure and growth procedures, opti-
cal and scintillation performances [1, 2]. At the same time
in literature there are not enough data about local centers
in a crystal lattice of BGO, phenomena of charge trans-
port and mechanisms of a recombination. There are dif-
ferent opinions in respect of a luminescence mechanism:
some authors suppose exciton nature [3�5], other ones
presume the recombination mechanism of the lumines-
cence [3, 6, 7]. Physical properties of BGO caused by
processes of charge transfer (photoconductivity,
photochromism, emissive recombination) were consid-
ered only from conduction band model positions [8]. And
current-voltage characteristics of BGO samples measured
at room temperature were ohmic [9]. But thermal depo-
larization investigation have shown that in BGO simul-
taneous formation of homo- and heterocharge takes place
due to the accumulation of carriers on the spatially and
in energy separated energy levels [10]. It is agreed with
the data of our work [11], where the investigations of the
conductivity of BGO have been carried out in wide tem-
perature, field and frequency ranges. Results have shown
that BGO crystals one can consider as partially compen-
sated semiconductors. The transport of charge carriers is
realized by hopping from one localized state to another.
Gradual transition from pair jumps near Fermi level to
multiple jumps with frequency is shifted to higher tem-
peratures. It points out the existence of quasicontinuous
distribution of localized states in the forbidden band.
Current-voltage characteristics of BGO studied in [11]
were typical for space-charge-limited currents (SCLC)
and had a series of features, viz.: the field hysteresis of
the direct and reverse currents with increase of tempera-
ture not only decreases but also changes a sign; the tem-
perature dependence of concentration of the equilibrium
charge carriers, calculated from I�V relations transits
through a maximum. It had allowed to assume presence
of double injection of charge carriers from electrodes into
the samples.
This paper is the natural continuation of the work
[11]. We present the results of the study of current-volt-
age relations in BGO single crystals in a mode of unipo-
lar injection.
2. Experimental
Studied BGO single crystals of a good optical quality
were grown by Czochralski technique from high-purity
Bi2O3 and GeO2 oxides. The material and quality of the
contacts are of great importance. In the work [9] the care-
ful examination of I�V characteristics of BGO samples
at room temperature was carried out both in the dark and
462
SQO, 6(4), 2003
T.M. Bochkova et al.: Unipolar injection currents in Bi
4
Ge
3
O
12
crystals
under light exposure. The semitransparent Al, Cr elec-
trodes thermally sputtered and transparent high frequency
sputtered In2O3 + 9%SnO2 electrodes were used for meas-
urements [9]. In our work we used liquid In-Ga electrodes.
It was found that all considered metals at room tempera-
ture form neutral type of contacts with BGO.
Asymmetrical contacts were used for measurements
of I�V characteristics in the unipolar injection mode. As
injection electrode was In-Ga one. On the other side of
the sample the thin layer of silicate glass Na2SiO3 was
put between the electrode and the crystal. The conductiv-
ity of such glasses has ionic nature and is a few orders of
magnitude higher than the conductivity of the investi-
gated samples. Application of this layer allows to elimi-
nate the double injection.
I�V relations were studied in (102�104 V/cm) range of
electric fields at temperatures 25�400ºÑ. Measurements
of a current have carried out for steady-state achieved
after application of voltage during 5 minutes. Low val-
ues of the currents were measured with electrometer BK2-
16. Q-meter BM-311G was used for measurements of the
conductivity at frequency of 20 MHz. The influence of
space charge was avoided by employing a preliminary
annealing of the samples with shorted electrodes at 4000Ñ
during 2 hours.
3. Results and discussions
Results of measurements of I�V relations in BGO under
conditions of unipolar injection of electrons and holes
are shown in Figs 1, 2. In both cases in an explored inter-
val of voltages up to temperatures ~100°Ñ I�V relations
are ohmic and values of the currents are low, that agree
well with data of [9]. Above 100°Ñ the regions of linear,
quadratic and steep rise of currents are observed on the
I�V curves. It is typical for space-charge limited currents
in dielectrics with traps [12].
Values of a specific conductivity (σn and σp), concen-
trations of equilibrium carriers of charge (n0 and p0) and
effective mobility (µn and µp) are presented in Fig. 3.
Comparison of these data and values of analogous
parameters obtained by us earlier for the case of double
injection [11] allows to note that absolute values of con-
ductivity in all three cases are rather close. Invariable
there is also an activation character of temperature de-
pendence of conductivity (Fig. 3a). Up to ~200°Ñ tem-
perature dependencies of electronic and hole conductiv-
ity coincide, the activation energy ∆Åσ = 0.9 eV, Above
200°Ñ the hole conductivity is predominant and the acti-
vation energy of holes rises up to 1.32 eV. These values
of the activation energy are less than half of a forbidden
gap width in BGO (4.5 eV [1, 2]), i.e. charge transport is
realized with the participation of local centers.
The effective mobilities (µn and µp) of charge carriers
up to ~200°Ñ also practically coincide in magnitude
(Fig. 3b). Above this temperature the effective mobility
of holes rises more quickly. The activation energy of elec-
trons and holes ∆ŵ in the first region is 1.11eV, in the
second region, for holes, ∆ŵ = 1.72eV. Lack of the co-
incidence of the activation energies of the conductivity
and mobility (in our case ∆Åσ > ∆ŵ) testifies about the
distribution of the traps in energy in the forbidden band.
In particular, at Gaussian distribution of the density of
localized states N(E), the activation energy of mobility
∆ŵ = Åt + δ/2kT, where Åt � energy of maximum, δ �
parameter of Gaussian distribution of the traps [13]. In
the injection process the quasi-Fermi level, shifting
through Gaussian dumbbell, can lie lower or higher Åt,
but only in a case δ = 0 (a monoenergetic level)
∆Åσ = ∆ŵ = Åt.
0.0
�12
�11
�10
�9
�8
�7
�6
�5
0.5 1.0 1.5 2.0 2.5 3.0 3.5
1
2
3
4
567
lg , VU
lg
,
A
I
Fig. 1. Current-voltage characteristics of Bi4Ge3O12 crystals meas-
ured in a mode of unipolar injection of electrons: 1 � 100°Ñ, 2 �
150°Ñ, 3 � 200°Ñ, 4 � 250°Ñ, 5 � 300°Ñ, 6 � 350°Ñ, 7 � 400°Ñ.
Fig. 2. Current-voltage characteristics of Bi4Ge3O12 crystals meas-
ured in a mode of unipolar injection of holes: 1 � 100°Ñ, 2 �
150°Ñ, 3 � 200°Ñ, 4 � 250°Ñ, 5 � 300°Ñ.
lg , VU
0.0
�12
�11
�10
�9
�8
�7
�6
�5
0.5 1.0 1.5 2.0 2.5 3.0 3.5
lg
,
A
I
1
2
3
45
T.M. Bochkova et al.: Unipolar injection currents in Bi
4
Ge
3
O
12
crystals
463SQO, 6(4), 2003
The temperature dependencies of the experimentally
obtained eqiulibrium concentrations of electrons n0 and
holes p0 are presented in Fig. 3c. Using known relations
( )kTEσσσ ∆−= exp0 , ( )kTEµµµ ∆−= exp0 ,
( )kTEnn n∆−= exp0
and taking into consideration the equality σ = enµ, one
obtains ∆Ån = ∆ŵ � ∆Åσ.
Actually, with increase of temperature the concentra-
tion as electrons, and holes decreases exponentially with
the positive activation energy making 0.19�0.21 eV both
for electrons and holes in the temperature range up to
~250°Ñ. At the further rise in temperature the hole con-
centration falls more sharply with the activation energy
0.40 eV. The values obtained are agreed with experi-
mental values ∆ŵ � ∆Åσ, which are equal 0.21 eV and
0.38 eV for electrons and holes in corresponding tem-
perature ranges.
On the basis of the experimental results one can con-
clude that in BGO crystals charge carriers are simulta-
neously both electrons and holes. Values of mobility and
conductivity for electrons and holes are close. Activation
rise of mobility with temperature for both types of carri-
ers and its low values confirm hopping mechanism of the
conduction. Such processes and high values of the acti-
vation energy ∆Åσ for electrons and holes are typical for
hopping conduction involving impurity centers and ∆Åσ
is governed by the position of quasi-Fermi level relatively
the percolation level [14]. This mechanism of the con-
duction is widespread enough for strongly compensated
semiconductors with a wide band gap [15, 16]. Its activa-
tion temperature dependence is usually connected with
the �smearing out� of discrete impurity levels involved
into �hopping� due to the presence of charged impuri-
ties, random distribution of which creates a large-scale
fluctuations of electrostatic potential of a crystal lattice.
Though we have investigated the nominally pure crys-
tals, the existence of the proper defects in BGO grown by
Czochralski method, have been established by many au-
thors. So, wide bands in the optical absorption spectra
observed after an irradiation with UV-light or X-ray were
connected with the color centers forming from the de-
fects-precursors. [17,18]. The investigations of the local
centers in the crystals, carried out by methods of ther-
mally stimulated luminescence and photoconductivity
[17, 19], thermally stimulated exoelectronic emission [20]
and thermal depolarization [10] have confirmed the ex-
istence of the wide energetic spectrum of local states in
Bi4Ge3O12.
Values of the concentration of traps Nt obtained by us
from voltage-current curves for electrons as well as val-
ues of the concentration of the equilibrium carriers of
charge (n0, p0) are close (~1012 cm�3) and are obviously
understated in comparison with really existing in the
crystal the concentration of uncontrolled impurities and
other electrically active defects. It takes place because at
temperatures of experiment hopping of charge carriers
may occur inside clusters of finite sizes, i.e. infinite clus-
ter for percolation of charge is not formed yet. The accu-
mulation of charge at the ends of the clusters leads to
peculiar migration polarization of the sample. Thus,
moving of the charge carriers inside of clusters of differ-
ent sizes may give a contribution into dielectric permit-
tivity and conductivity of semiconductors [21] and the
estimation of concentration of electrons and holes n(p)
shall be more correct, if we use values of ac-conductivity
and dielectric permittivity measured at high frequency,
when more considerable amount of charge carriers takes
part in the transfer.
The existence of clusters of different sizes in BGO
crystals was experimentally found in [11] from tempera-
ture dependences of ac-conductivity at different frequen-
cies. The estimation of the chain length of jumps per-
formed according to [22], have shown that at 20�180°Ñ
jumps of charge carriers near quasi-Fermi level occur
inside of the pair centers, at higher temperatures the trans-
port of charge is realized by multiple jumps. And, the
increase of frequency leads to rise of σ~ due to decrease
of cluster sizes.
Measurements of dielectric permittivity and conduc-
tivity were performed at 20 MHz and have shown that
they vary in this temperature range a little: ε = 66�73,
σ~ = (2�6)⋅10�4Ohm�1cm�1. Computed values n and ð are
given in the table.
Using obtained values of the concentration of elec-
trons and holes, it is possible to estimate also concentra-
tion of the basic impurities (proper defects). It is known
that value of hopping conductivity and its activation en-
ergy depend on an impurity concentration and a degree
of compensation of donors and acceptors (K = Nd/Na). In
�12
�6
10.5
11.0
11.5
12.0
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
�10
�4
�8
�2
�6
�6
2
1/ , 10 KT × �3 �1
�
1
2
�
3
�
1
lg
,
O
m
c
m
s
lg
,
m
/V
c
m
c
lg
,
m
n
c
0
1
1
1
2
a
b
c
2
2
Fig. 3. Temperature dependences of conductivity (à), mobility
(â) and concentration (ñ) of charge carriers in Bi4Ge3O12 crys-
tals: 1 � electrons; 2 � holes.
464
SQO, 6(4), 2003
T.M. Bochkova et al.: Unipolar injection currents in Bi
4
Ge
3
O
12
crystals
case of strong compensation (Ê → 1) following expres-
sion was obtained in [14, 23] :
⋅−
+−=
kTK)(
Ne
aN
d
d
3/1
3/1
0
3/10
1
exp
εε
ασσ ,
where α � the coefficient dependent on a degree of com-
pensation, à � Bohr radius. Considering temperature
dependence of conductivity and taking into account, that
at strong compensation concentration of the free charge
carriers n = Nd � Na, we shall find:
2/1
2/3
0 n
e
E
Nd ⋅
=
εεσ
.
Values of Nd, Na, calculated for electrons and holes
are presented in the table. Apparently, values of a degree
of compensation K are close to 1, i.e. Bi4Ge3O12 crystal
really is strongly compensated semiconductor. That fact,
that on the direct current both electrons and holes are
mobile, and also distinctions in values of Nd and Na for
electrons and holes at temperatures above 200°Ñ demon-
strated presence of two channels of percolation of the
charge, parted recombination barriers. Therefore, the
cause of described above the exponential decrease of con-
centration of equilibrium charge carriers may be their
mutual recombination through barriers. Obviously, that
feather study of a nature of local centers and electron-
hole processes in Bi4Ge3O12 is necessary as for the solu-
tion of a problem of growth of the perfect crystals, under-
standing of regularities of the radiation defect formation
and mechanisms of luminescence, and for development
of the modern model of conduction in wide band semi-
conductors of complex oxides.
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Table. The calculated parameters of hopping conductivity in
Bi4Ge3O12.
t°C The electrons
n, cm�3 Nd, cm�3 Na, cm�3 K
200 5.21⋅1017 7.273⋅1019 7.221⋅1019 0.993
250 3.38⋅1016 1.853⋅1019 1.850⋅1019 0.996
300 2.86⋅1015 6.978⋅1018 6.951⋅1018 0.998
The holes
p, cm�3 Na, cm�3 Nd, cm�3 K
200 5.63⋅1017 7.561⋅1019 7.508⋅1019 0.993
250 3.12⋅1015 9.998⋅1018 9.995⋅1018 0.999
300 2.80⋅1014 3.879⋅1018 3.8787⋅1018 0.999
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