Charge transport in bismuth orthogermanate crystals
Current-voltage relations in bismuth orthogermanate crystals with Ag, Pt, InGa electrodes have been measured in the modes of double and unipolar injection of charge carriers. It has been shown that Bi₄Ge₃O₁₂ is relaxation type semiconductor. The appearance of the regions with negative differentia...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2011
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| Cite this: | Charge transport in bismuth orthogermanate crystals / T.M. Bochkova, S.N. Plyaka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 170-174. — Бібліогр.: 17 назв. — англ. |
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Bochkova, T.M. Plyaka, S.N. 2017-05-26T12:49:26Z 2017-05-26T12:49:26Z 2011 Charge transport in bismuth orthogermanate crystals / T.M. Bochkova, S.N. Plyaka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 170-174. — Бібліогр.: 17 назв. — англ. 1560-8034 PACS 72.20.Ht, -i https://nasplib.isofts.kiev.ua/handle/123456789/117709 Current-voltage relations in bismuth orthogermanate crystals with Ag, Pt, InGa electrodes have been measured in the modes of double and unipolar injection of charge carriers. It has been shown that Bi₄Ge₃O₁₂ is relaxation type semiconductor. The appearance of the regions with negative differential resistance or sublinear rise of the current in characteristics is connected with the injection of the minority charge carriers and recombination processes in the space charge layer. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Charge transport in bismuth orthogermanate crystals Article published earlier |
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charge transport in bismuth orthogermanate crystals |
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Current-voltage relations in bismuth orthogermanate crystals with Ag, Pt, InGa
electrodes have been measured in the modes of double and unipolar injection of
charge carriers. It has been shown that Bi₄Ge₃O₁₂ is relaxation type semiconductor. The
appearance of the regions with negative differential resistance or sublinear rise of the
current in characteristics is connected with the injection of the minority charge
carriers and recombination processes in the space charge layer.
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1560-8034 |
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Charge transport in bismuth orthogermanate crystals / T.M. Bochkova, S.N. Plyaka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 170-174. — Бібліогр.: 17 назв. — англ. |
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| last_indexed |
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1850605140880392192 |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 170-174.
PACS 72.20.Ht, -i
Charge transport in bismuth orthogermanate crystals
T.M. Bochkova, S.N. Plyaka
Dnepropetrovsk National University, 49050, Dnepropetrovsk, Ukraine
Phone:+38 (056) 776-83-18; e-mail: tbochkova@meta.ua
Abstract. Current-voltage relations in bismuth orthogermanate crystals with Ag, Pt, In-
Ga electrodes have been measured in the modes of double and unipolar injection of
charge carriers. It has been shown that Bi4Ge3O12 is relaxation type semiconductor. The
appearance of the regions with negative differential resistance or sublinear rise of the
current in characteristics is connected with the injection of the minority charge
carriers and recombination processes in the space charge layer.
VI −
Keywords: bismuth orthogermanate, current-voltage characteristics, relaxation type
semiconductors.
Manuscript received 10.02.10; accepted for publication 16.03.11; published online 30.06.11.
1. Introduction
Bismuth orthogermanate (Bi4Ge3O12, BGO) single
crystals are used in technology as an effective
scintillation material for registration of high-energy
ionizing radiation in detector systems. These crystals
have considerable advantages over analogs. They are
transparent, colorless, nonhygroscopic. The high γ-
quantum detection efficiency, relatively short decay time
and small afterglow provide a wide application of
Bi4Ge3O12 in high-energy physics and positron computer
tomography [1, 2]. The problem of the improvement of
the resistance to radiation damage for scintillation
crystals is very actual and connected with the production
of high quality crystals. They have not to contain
impurities and structural defects that can be transformed
into color centers or create spatial layers with changed
properties under the influence of external factors,
namely: irradiation, electric fields, temperature changes.
The scientists try to solve this problem, as a rule, by
technological means using chemical and physical
purification of raw materials, the modification of
available crystal growth methods and development of
the new ones [3, 4]. Investigation of the effect of
impurities and radiation defects on the scintillation
characteristics of Bi4Ge3O12 crystals is another main line
[4-7]. But study of their electrical properties is also
sufficiently informative relative to the nature of the local
centers, their energy and spatial distribution, charge
transport mechanisms and recombination processes.
This work is continuation of the dc and ac
conductivity investigations in bismuth orthogermanate
crystals [8-10], in which it has been shown that high-
resistance Bi4Ge3O12 crystals should be considered as
heavily compensated semiconductors. Charge carrier
transport is realized by phonon-assisted quantum
mechanical tunneling of the carriers from one localized
state to another. There is gradual transition from pair
jumps near the Fermi level to multiple hopping that
shifts to higher temperatures with the frequency
increase. Existence of this transition indicates that
distribution of localized states in the forbidden energy
gap is quasi-continuous. It has been also found that in
the direct current both electrons and holes are mobile,
and there are distinctions in values of donor and acceptor
concentrations for electrons and holes at temperatures
above 200 ºC. It allows to suggest the presence of two
channels of charge percolation parted by recombination
barriers.
This paper presents the results of further
investigation of the charge carrier transport in high
quality Bi4Ge3O12 crystals by means of measurements of
the current-voltage characteristics under the conditions
of unipolar and double injection of charge carriers.
2. Experiment
Bismuth orthogermanate single crystals were grown by
Czochralski method from platinum crucibles in air. The
starting materials were “OSCh”-grade Bi2O3 and GeO2
oxides. The double recrystallization technique was used.
The obtained single crystals were colorless, transparent
and contained uncontrolled impurities in amounts up to
10–4 mass% (according to data of the spectral analysis).
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
170
mailto:tbochkova@meta.ua
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 170-174.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
The applied electrodes were of Pt (evaporation in
vacuum), Ag (cathode sputtering) and In-Ga (liquid
eutectic). The thickness of the samples used was about
0.5 mm. The measurements of characteristics VI −
were performed in the electric field 102 to 104 V/cm and
within the temperature range 25 to 400 °С according to
the standard technique described in [10].
3. Results and discussion
Bi4Ge3O12 crystals belongs to wide band-gap
semiconductors. The dark dc conductivity is about
10–14 Ohm–1·cm–1 at room temperature and increases
with heating. The width of the forbidden band obtained
from optical measurements exceeds 4.5 eV [1]. VI −
characteristics measured in a wide temperature range in
the samples of bismuth orthogermanate with Ag, Pt, In-
Ga contacts differ in details, quite possible, due to
different levels of the charge carrier injection, but their
common features allow to consider them in the complex.
The main feature is the existence on the VI −
characteristics observed not only the regions with linear
(I ~ U m, m = 1) and superlinear (I ~ Um, m > 1) rise of
the current but also the regions with sublinear (I ~ U m,
m = 1/2 or 0 < m < 1) dependence of the current and
regions with negative differential resistance (NDR) of n-
type. characteristics of BiVI − 4Ge3O12 sample with Ag
electrodes are shown in Fig. 1.
Two temperature ranges are available on presented
curves. In the former, up to the temperature ∼ 150 ºС,
the ohmic, quadratic regions and regions with the sharp
rise of the current are observed. All the regions are
shifted to lower electric fields with heating. The
presence of the quadratic region testifies to the ohmic
character of the contacts and shows that the
concentration of injected carriers becomes of the same
order of magnitude with the concentration of the
equilibrium carriers. Such behavior of VI −
characteristics is typical for the case of the space charge
limited currents (SCLC).
0,0 0,5 1,0 1,5 2,0 2,5 3,0
-11
-10
-9
-8
-7
-6
-5
m=0.5
m=2
lg
(I
, A
)
lg (U, V)
1
2
3
4
5
m=1
Fig. 1. Current-voltage characteristics of Bi4Ge3O12 crystals
with Ag electrodes: 1 – 100 ºC, 2 – 150 ºC, 3 − 225 ºC, 4 −
250 ºC, 5−300 ºC.
In the second temperature range, at 150-250 ºС,
one can observe the regions with NDR. And at the
temperatures above 250 ºC, we can see the extensive
sublinear regions (m = 1/2), which are again replaced by
the ohmic and superlinear dependences.
Bismuth orthogermanate is a high-resistance
semiconductor with hopping conductivity, therefore it
can belong to semiconductors of the relaxation type [11].
It means that the minority charge carrier lifetime τ0 that
defines the diffusion length of the minority carriers is
less than the dielectric relaxation time τd (maxwellian
time). For classic semiconductors (such as Si, Ge), the
opposite relation τ0 > τd is valid. But for Bi4Ge3O12,
the conductivity of which varies from 10–13 up to
10–10 Ohm–1·cm–1 in the studied temperature range, the
dielectric relaxation time that can be estimated as
τd ~ εε0 /σ is equal ∼101–10–2 s, respectively. It can
considerably exceed the lifetime of minority carriers.
If the injection of the minority carriers of charge
takes place, the restoration of the system into the
equilibrium state is realized by means of the relaxation
and recombination processes. According to [11], in
relaxation type semiconductors quasi-Fermi levels that
describe the nonequilibrium electron and hole
concentrations coincide on the expiry of τ0 due to
recombination of charge carriers long before restoration
of the system to equilibrium by maxwellian relaxation.
So, recombination in the space charge region
(SCR) may be a cause of NDR appearance and sublinear
regions in VI − characteristics. The theory of charge
carrier recombination in SCR of a p-n junction for the
first time was considered by Sah, Noyce and Shockly in
[12] where a model of single energy level uniformly
distributed Shockly-Read-Hall recombination centers
was used for developing the specific dependence of the
recombination current density J on the voltage U
J ~ exp(eU / 2kT). (1)
The modern theory of the recombination processes
in SCR of the semiconductor structures, in which the
electrons and holes are spatially distributed in the
localized centers and have to tunnel through potential
barriers for the recombination, is more complex. In
particular, it is established that the recombination rate
reaches the saturation under the assumption of low
probability of tunneling and only with the rise of this
probability the classic dependence of the recombination
(1) is observed [13].
In bismuth orthogermanate, electrons are dominant
charge carriers at room temperature. It was determined as a
result of investigation of the thermoelectric power [14] and
exoelectron emission [15]. Consider characteristics
of Bi
VI −
4Ge3O12 crystals measured under conditions of
asymmetrical contacts, when one of them is metal and
another is made with the thin layer of dried orthophosphoric
acid between the metal and the crystal. The use of
orthophosphoric acid, that is ionic conductor, allows to
eliminate the double injection. In Figs 2 and 3, the families
171
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 170-174.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
1,0 1,5 2,0 2,5 3,0
-12
-11
-10
-9
-8
-7
-6
-5
lg
(I
, A
)
of characteristics measured under conditions of
unipolar injection of electrons (the metal electrode is
cathode) and holes (the metal electrode is anode) are
presented. The platinum is used as the metal for electrodes
in experimental results shown in these figures.
VI −
In both cases at the temperatures above 100 ºC, one
can see the linear (I ~ U2) and the quadratic regions (I ~ U2)
that is the criterion of the injected space charge appearance
and testifies to the ohmic character of Pt contact. VI −
characteristics allows, in accordance with SCLC formulas,
to calculate values of the specific conductivity, effective
drift mobility, concentration of the equilibrium charge
carriers and dielectric relaxation time τd . The calculated
data to a considerable extent confirm the experimental
results obtained earlier [8-10]. In both cases, the values of
the concentrations and mobilities of charge carriers are
rather close and very small. The conductivity and mobility
have an activation character. All these features are
attributed to the hopping conductivity. In Fig. 4, the
temperature dependences of Bi4Ge3O12 conductivity
calculated from I – V curves are displayed. These are
conductivities σh, σl, computed respectively from the high-
field (appearing above 200 ºC) and low-field ohmic regions
of I – V characteristics inherent to Bi4Ge3O12 crystals with
symmetrical Pt electrodes as well as conductivities σp, σn
computed from I – V characteristics of crystals with
asymmetrical electrodes.
From this figure, one can see that σl, σp, σn
identically increase with the temperature up to ∼150-
175 ºС (activation energy Eσ ∼ 0.5 еV). Above this
temperature, the value of the activation energy is
changed: for σl and σn – Eσ ∼ 0.95 еV; for σh and σp –
Eσ ∼ 0.70 еV. The temperature dependences of the
mobility give the activation energy 0.85 eV for holes and
0.70 eV for electrons (The insert in Fig. 4). Two regions
are also observed in the temperature dependences of
equilibrium concentrations of the charge carriers
(Fig. 5). These concentrations decrease exponentially up
to 175 ºC (En ≈ –0.2 eV, Ep ≈ –0.3 eV) and then, in the
case of the hole injection, the concentration remains at
the constant level, in the case of electron injection, the
concentration increases with the temperature
(En ≈ 0.25 eV). The values of dielectric relaxation time
τd calculated from VI − curves are equal 67 s for
electrons; 19.1 s for holes at 100 ºC and 2.4⋅10–2 s for
electrons; 6.6⋅10–2 s for holes at 250 ºC. The calculation
of the activation energy for the conductivity, mobility
and concentration of the equilibrium charge carriers in
both cases satisfies classic equations
lg (U, V)
1
2
3
4
5
6
7
Fig. 2. Current-voltage characteristics of Bi4Ge3O12 crystals
with injecting Pt electrode that were measured in the mode of
unipolar injection of electrons: 1−75ºC, 2–125ºC, 3−175ºC,
4−200ºC, 5−225ºC, 6−250ºC, 7−300ºC.
1,0 1,5 2,0 2,5 3,0
-11
-10
-9
-8
-7
-6
-5
-4
lg
(I
, A
)
lg (U, V)
1
2
4
5
3
6
7
Fig. 3. Current-voltage characteristics of Bi4Ge3O12 crystals
with injecting Pt electrode that were measured in the mode of
unipolar injection of holes: 1 – 100 ºC, 2 – 125 ºC, 3 –
175 ºC, 4 − 200ºC, 5 − 225 ºC, 6 − 250 ºC, 7 − 300 ºC.
σn = enμn, σp = epμp (2)
in all the temperature ranges.
1,2 1,6 2,0 2,4 2,8 3,2 3,6
-14
-13
-12
-11
-10
-9
-8
1,6 2,0 2,4 2,8
-8
-6
-4
-2
2
4
3
2
lg
(μ
, O
hm
−1
cm
-1
)
1/T, 10-3K-1
lg
(σ
, O
hm
−1
cm
-1
)
1/T, 10-3K-1
1
1
Fig. 4. Temperature dependences of the conductivity and
mobility of charge carriers in Bi4Ge3O12 crystals: 1 – σl; 2 – σn
; 3 – σh ; 4 – σp. In the insert: 1 – holes; 2 – electrons.
172
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 170-174.
1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0
11,8
12,0
12,2
12,4
12,6
12,8
lg
(n
,p
c
m
-3
)
1/T, 10-3K-1
2
1
Fig. 5. Temperature dependences of the charge carrier
concentration in Bi4Ge3O12 crystals: 1 – holes; 2 – electrons.
As it was aforesaid, the investigated nominally pure
Bi4Ge3O12 crystals are heavily compensated
semiconductors. It means that the concentrations of
donors and acceptors are close, and charge carrier
concentration is small. The carriers are in the most deep
energy states created by pairs of nearest impurity
centers. Moreover, the energy bands of the
semiconductor are modulated by large scale potential
caused by fluctuations of the charged impurity
concentration. Screening these impurities by charge
carriers is weak, because the carriers get into the deep
potential wells and Fermi level fall additionally by an
order of magnitude as to the modulation amplitude of the
potential η that increases with decrease of the density of
charge carriers [16]
3/1
0
3/22
c
t
n
Ne
⋅εε
⋅
=η . (3)
Here, Nt is the total concentration of donors and
acceptors, and nc is the average density of charge
carriers.
In Bi4Ge3O12, both electrons and holes are mobile.
The activation energy of charge carrier jumps is counted
from the Fermi level to the percolation one. It is obvious
that for comparatively low temperatures Bi4Ge3O12 is
semiconductor of n-type, the Fermi level is close to the
maximum of density of states corresponding to isolated
donor position. With the increase of temperature, the
equilibrium concentration of the mobile charge carriers
decreases due to recombination, and the hole component
of current, that has its own percolation level, is
considerable. So, the activation energies of the conduction
for electrons and holes are different at high temperatures.
The obtained data enabled us to interpret the
current-voltage characteristics of bismuth
orthogermanate with two symmetrical electrodes as
follows. In the first temperature range (up to 150 ºC),
injection of the majority charge carriers (electrons) is
realized, and SCLC phenomenon is observed. In the
second range (above 150 ºC), injection of the minority
charge carriers (holes) is noticeable and becomes the
dominant mechanism with the further increase of the
temperature. According to [11], after injection of Δp
holes into bismuth orthogermanate, restoration of the
equilibrium law of mass action takes place during the
time of τ0, and as a result – the reduction of the local
concentration of the majority carriers (electrons) is
observed. In the moment of this process finishing, the
product pn satisfies the equation
pn = (n0 + Δn)(p0 + Δp) = ni
2 = p0n0, (4)
where n0, p0, n, p are equilibrium and nonequilibrium
concentrations of electrons and holes, respectively; ni is
the concentration of electrons or holes in an intrinsic
specimen; Δn is the concentration of electrons which are
pulled into the space charge region. The value of Δn
from (4) is
Δn = –n0Δp / (p0+Δp). (5)
If the hole injection level is so high that Δp > p0,
we shall obtain Δn → –n0. It means that mobile electrons
in the space charge region can quite vanish.
Reduction of the local concentration of mobile
electrons leads to the increase of the resistance of
crystal. The layer depleted with electrons is positioned in
close proximity to the anode which injects the holes. It is
expanded into the bulk of semiconductor following the
narrow recombination front. The sublinear dependence
of the current on voltage (I ~ U 1/2) is observed in VI −
curves. The voltage rise increases the space charge in the
depleted layer leading in certain cases to the creation of
NDR region due to the negative gradient in the majority
carrier concentration.
The temperature increase leads to the gradual
decrease of the voltage at which the depleted with
electrons region occupies the interelectrode space
entirely, and the crystal sample becomes spatially
homogeneous again. The sign of the majority carriers of
charge is changed. Now these are holes. This process
corresponds to the second ohmic (high-field) region in
VI − characteristics. With further temperature increase
one can observe the high-field regions of quadratic and
more steep rise of the current, i.e. SCLC phenomenon
but only for the holes. Thus, the existence of regions
with NDR and sublinear rise of the current in VI −
characteristics of bismuth orthogermanate crystals may
be caused by the so-called process “recombination
space-charge injection” [17].
Among other reasons that could result in these
VI − characteristics, there is transformation of the
current controlled by the bulk properties of the sample
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
173
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 170-174.
into the current controlled by the electrode processes
near the blocking contacts. In these cases, the ideal
characteristic I ~ UVI − 1/2 is observed.
However, the existence of the quadratic
dependencies in the same VI − curves testifies about
charge carrier injection from the electrodes into the
sample, and therefore, the contacts are ohmic. Secondly,
from the obtained curves with sublinear regions
one can see that calculations of the resistance for high-
field linear regions give the considerably higher values
then for the low-field ones (Fig. 1). Thirdly, for the
justification of the stated affirmations let us again come
back to Fig. 4. An observed good coincidence of the
values and activation energies for σ
VI −
h and σp, σn and σl
shows that the proposed model is valid.
Conclusions
Thus, bismuth orthogermanate is the semiconductor of
relaxation type, the conduction processes in which are
very different from the ones taking place in the classic
inorganic semiconductors (Si, Ge). Bi4Ge3O12 has such
electrical properties as high resistance, low mobility of
charge carriers, its activation rise with temperature, very
low density of mobile charge carriers, large time of
dielectric relaxation, hopping mechanism of the
conduction, power character of the increase of the
conductivity in alternative field, sublinear VI −
dependences. These features are characteristic rather for
high-resistance organic semiconductor crystals (such as
anthracene, naphthalene) or amorphous semiconductors
(such as chalcogenide glasses). The existence of double
injection into the crystal at the application of usual Ag,
Pt, In-Ga contacts gives an opportunity to study waves
of the space charges of different type (both enriched and
depleted with the charge carriers), to investigate the
recombination mechanisms and control the processes of
heterovalent impurity ion charge exchange in this
practically important material.
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