Crystal growth and electrical properties of β-CdP2 single crystals

Article abstract of DOI:10.1007/s10789-005-0233-7

Optically homogeneous single crystals of tetragonal cadmium diphosphide (β-CdP₂) are prepared by vapor-phase growth, and their electrical conductivity, dielectric permittivity, and loss tangent are measured during slow heating from 78 to 400 K

Full text of DOI:10.1007/s10789-005-0233-7

Inorganic Materials, Vol. 41, No. 9, 2005, pp. 901–905. Translated from Neorganicheskie Materialy, Vol. 41, No. 9, 2005, pp. 1031–1036.
Original Russian Text Copyright © 2005 by Trukhan, Soshnikov, Marenkin, Haliakevich.
Crystal Growth and Electrical Properties
of b-CdP2 Single Crystals
V. M. Trukhan*, L. E. Soshnikov*, S. F. Marenkin**, and T. V. Haliakevich*
* Institute of Solid-State and Semiconductor Physics, Belarussian Academy of Sciences,
ul. Brovki 17, Minsk, 220072 Belarus
** Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences,
Leninskii pr. 31, Moscow, 119991 Russia
e-mail: truhan@ifttp.bas-net.by
Received March 22, 2005
Abstract—Optically homogeneous single crystals of tetragonal cadmium diphosphide (β-CdP2) are prepared
by vapor-phase growth, and their electrical conductivity, dielectric permittivity, and loss tangent are measured
during slow heating from 78 to 400 K in the [001] and [100] directions at frequencies of 102, 103, 104, and
106 Hz. The permittivity of the crystals increases with temperature. The electrical properties of β-CdP2 are
shown to be anisotropic.
INTRODUCTION
and HNO3 for 5 min and in concentrated HNO3 for
10−16 h, followed by rinsing in bidistilled water and
drying.
The mixture was sealed in the ampule under vac-
uum, and the ampule was introduced into a horizontal
two-zone resistance furnace. The temperature was
maintained by an RIF-101 temperature controller. The
thermal conditions suitable for β-CdP2 synthesis are
summarized in the table.
CdP2, a II–V semiconductor, crystallizes in tetrago-
nal symmetry (sp. gr. P41212 = D44 , Z = 8) [1] with lat-
tice parameters a = 5.2768(7) Å and c = 19.753(3) Å.
The band gap of CdP2 is Eg = 2.03 eV [2]. Cadmium
diphosphide crystals offer a large thermooptical coeffi-
cient, large Verdet constant which is a linear function of
magnetic induction, and high optical activity which
varies linearly with temperature [3]. Cadmium diphos-
phide is used in the fabrication of optical and thermal
sensors, pulse stretchers and intensity stabilizers for
solid-state lasers, and input polarizing prisms for thin-
film waveguides [4, 5].
The above properties and applications of β-CdP2
crystals have been the subject of many studies, whereas
their dielectric properties have not yet been investigated
in sufficient detail, and available data are often contra-
dictory.
In this paper, we report the growth of optically
homogeneous β-CdP2 crystals and their conductivity
and dielectric properties as functions of frequency in
the range 78–400 K in the [001] and [100] directions.
EXPERIMENTAL
β-CdP2 was synthesized from V5 phosphorus and
KD-000 cadmium additionally purified by zone melt-
ing. A stoichiometric mixture of Cd and P was loaded
into a silica ampule precleaned in several steps. First,
the ampule was etched in a 1 : 20 mixture of HF and
H2O, rinsed in bidistilled water, dried, and fire-pol-
ished. Next, the ampule was etched in a mixture of HF
Fig. 1. Single crystals of tetragonal cadmium diphosphide.
0020-1685/05/4109-0901 © 2005 Pleiades Publishing, Inc.

902
TRUKHAN et al.
(a)
1
2
600
500
400
300
200
100
1—100 Hz
2—1 kHz
3—10 kHz
4—1 MHz
3
4
0
106
105
104
103
102
150
1.5
(b)
1.2
0.9
0.6
0.3
0
200
250
T, K
3
4
2
1
100
150
200
250
300
350
400
T, K
Fig. 2. Temperature dependences of (a) dielectric permittivity and (b) loss tangent in the [001] direction for β-CdP single crystals
2
at different frequencies.
The temperature of the evaporation zone in the first the crystallization zone in the first two steps of CdP2
and second steps of synthesis ensured active reaction
between the cadmium melt and phosphorus vapor.
Increasing the temperature of the evaporation zone to
above the limits indicated in the table might cause
explosion because of the rapid heat release in the first
step (exothermic reaction) and the high phosphorus
vapor pressure in the second step. The temperature of
synthesis ensured annealing of nucleation centers. In
the third step, the reaction product was transported to
the crystallization zone. The synthesized material was
used as the charge for vapor-phase growth of β-CdP2.
To grow β-CdP2 single crystals, one must ensure
critical supercooling in the conical part of the ampule
and a sufficient rate of CdP2 transport from the evapo-
ration zone to the crystallization one.
CdP2 synthesis conditions
Critical supercooling for CdP2 nucleation was found
to be 3–8 K. The temperature of the crystallization zone
was 980–1010 K. To control the nucleation process and
restrict the growth duration to a reasonable level, we
produced low supersaturation in large-diameter
(18−20 mm) ampules. The growth rate then remained
rather high. The ampule was translated toward the crys-
Step
Tevaporation zone, K
Tcrystallization zone, K
τ, h
I
635–690
735–790
940–1020
1070–1100
1070–1100
900–990
2–3
2–3
II
III
80–120
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CRYSTAL GROWTH AND ELECTRICAL PROPERTIES
903
1
1500
1200
900
(a)
1—100 Hz
2—1 kHz
3—10 kHz
4—1 MHz
2
3
600
4
300
0
4
106
4
105
(b)
104
3
2
1
0
103
102
3
2
1
150
200
250
T, K
100
150
200
250
300
350
400
T, K
Fig. 3. Temperature dependences of (a) dielectric permittivity and (b) loss tangent in the [100] direction for β-CdP single crystals
2
at different frequencies.
tallization zone (steeper temperature gradient) at a rate
of 0.6–0.8 mm/h, approximately equal to the growth
rate, which ensured a constant temperature in the evap-
oration zone and stable growth conditions throughout
the growth run.
In electrical measurements, we used 0.9- to 1.1-mm-
thick single-crystal plates, which were oriented on the
DRON-3 with an accuracy of 0.5°. Dielectric permit-
tivity ε', loss tangent tanδ , and electrical conductivity
σ were measured along and across the c axis at frequen-
cies of 102, 103, 104, and 106 Hz by a digital LCR meter
during heating from 78 to 400 K at a constant rate of
1−2 K/min. Ohmic contacts to the sample faces were
made with Aquadag (ꢀ0.1-mm layer) after lapping.
The sample was sandwiched between polished brass
electrodes and introduced into a liquid-nitrogen cry-
ostat. The accuracy in dielectric measurements was
0.1% or better. The temperature was controlled with an
accuracy of 0.1–0.2 K.
Thus, we found an optimal combination of the
growth temperature, critical supercooling, and ampule
translation rate, which ensured stable growth of β-CdP2
single crystals.
As a result, we obtained bulk single-crystal boules
up to 20 mm in diameter at the back end and 40–50 mm
in length (Fig. 1).
X-ray diffraction characterization (DRON-3 powder
diffractometer, CuKα radiation) showed that the crys-
tals were single-phase and homogeneous.
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TRUKHAN et al.
RESULTS AND DISCUSSION
Figures 2b and 3b show the temperature depen-
dences of tanδ for β-CdP2 single crystals. The curves
Figure 2a shows the temperature dependences of
dielectric permittivity in the [001] direction for β-CdP2
single crystals. The permittivity of β-CdP2 increases
with increasing temperature and decreases with
increasing frequency. The low-temperature permittivity
is 10 to 12 (depending on the sample), which is compa-
rable to the values extracted from optical measurements
[6]. At a frequency of 100 Hz, ε' varies little in the range
show a maximum in tanδ in the temperature range of
the steep rise in permittivity. The 0.1- and 1-kHz
curves show a second peak at 190–210 K (Fig. 2b),
suggesting that several polarization mechanisms may
be operative.
Figure 4 displays the Arrhenius plots of conductiv-
ity in the [100] and [001] directions for single-crystal
78–140 K and rises steeply to about 102 at higher tem- cadmium diphosphide. The conductivity of β-CdP2 var-
ies widely, from 10–9 to 10–2 S/cm, in accordance with
earlier results [6]. The curves show a well-defined tran-
sition from low-temperature, impurity conduction to
high-temperature, intrinsic conduction. In the tempera-
ture range of impurity depletion, the concentration of
majority carriers is essentially constant, and the varia-
tion in conductivity is dominated by that in carrier
mobility. The conductivity of β-CdP2 depends signifi-
peratures. At higher frequencies, the rise in ε' begins at
higher temperatures. The temperature dependences of
[100] permittivity for β-CdP2 single crystals are dis-
played in Fig. 3a. With increasing temperature, the per-
mittivity along [100] rises more rapidly than that along
[001], which means that β-CdP2 has an anisotropic tem-
perature coefficient of permittivity. The ε' along [100]
exceeds that along [001] by a factor of 1.3 in the range
78–150 K and by a factor of 2.5 at higher temperatures. cantly on frequency, which may be interpreted as evi-
(a)
–6
–9
1—100 Hz
2—1 kHz
3—10 kHz
4—1 MHz
1
2
3
–12
–15
–18
4
–21
–6
1
(b)
2
3
–9
–12
–15
–18
–21
4
2
4
6
8
10
12
103/T, K–1
Fig. 4. Arrhenius plots of conductivity along (a) [001] and (b) [100] for β-CdP single crystals at different frequencies.
2
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CRYSTAL GROWTH AND ELECTRICAL PROPERTIES
905
relaxation in β-CdP2. The same is evidenced by the
temperature dependence of the peak-loss frequency
(Figs. 2, 3, insets). The temperature effects on the
dielectric properties of β-CdP2 can be interpreted in
terms of several models [7, 8]. The model proposed by
Zhukovskii et al. [7] describes the temperature-depen-
dent permittivity of defect-rich semiconductors in
terms of hopping transport. Electron exchange between
neighboring neutral defects leads to the formation of
dipoles, thereby increasing polarization. We believe
that the present experimental results are best described
by the isolated defect model [8].
ε''
90
60
30
4
3
2
1
CONCLUSIONS
Optically homogeneous single crystals of tetragonal
cadmium diphosphide were prepared by vapor-phase
growth, and their electrical conductivity, dielectric per-
mittivity, and loss tangent were measured between 78
and 400 K. The electrical properties of β-CdP2 were
shown to be anisotropic.
0
100
200
300
400
ε'
Fig. 5. Davidson–Cole diagrams for single-crystal β-CdP
in the [001] direction at frequencies of (1) 100 Hz,
(2) 1 kHz, (3) 10 kHz, and (4) 1 MHz.
2
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ε''
300
200
100
0
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ε'
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INORGANIC MATERIALS Vol. 41 No. 9 2005