Crystallography Reports, Vol. 50, Suppl. 1, 2005, pp. S124–S129. Original Russian Text Copyright © 2005 by Avetisov, Mel’kov, Zinov’ev, Zharikov.
CRYSTAL GROWTH
Growth of Nonstoichiometric PbTe Crystals by the Vertical Bridgman Method Using the Axial-Vibration Control Technique I. Kh. Avetisov, A. Yu. Mel’kov, A. Yu. Zinov’ev, and E. V. Zharikov Mendeleev University of Chemical Technology, Miusskaya pl. 9, Moscow, 125190 Russia e-mail:
[email protected] Received December 28, 2004
Abstract—A modification of the vertical Bridgman method with the excitation of low-frequency axial vibrations in the melt (axial-vibration control technique) is developed to grow crystals of volatile chemical compounds. It is shown that the use of the axial-vibration control technique in the growth of PbTe crystals makes it possible to obtain a more uniform distribution of the excess (nonstoichiometric) component over the crystal length. As a result of the intense melt mixing, equilibrium between the vapor phase, the melt, and the growing crystal is fixed so rapidly that it becomes possible to change the nonstoichiometry of a growing crystal by changing the vapor pressure. The composition of the congruently melting lead telluride, determined by comparing the nonstoichiometries of the initial charge and the crystal grown, was found to correspond to (2.8 ± 0.3) × 10–4 mol excess Te/mol PbTe. © 2005 Pleiades Publishing, Inc.
INTRODUCTION The problem of the effective control of heat and mass transfer during the growth of crystals from melt is a subject of intense study. This problem is especially urgent for the Bridgman method, which is characterized by a low efficiency of heat and mass transfer in the liquid phase. In recent years, many attempts have been made to develop effective techniques of growth from melt with the application of a rotating magnetic field, precessing ampoule (CVS technology), ultrasound irradiation of melts, shaking of crystals, and many other methods [1–4]. Methods based on the use of the axial-vibration control (AVC) technique have proven to be the most developed ones, both theoretically and practically. In particular, as shown by numerous model experiments, excitation of axial low-frequency vibrations in a melt, either by introducing an inert vibrating body into the melt in the classical vertical Bridgman method or by applying vibrations directly to the growing crystal in the contactless modification of the Bridgman method [5–10], makes it possible to change significantly the hydrodynamics of fluxes in the melt. The result is changes in the characteristics of the diffusion layer, the curvature of the crystallization front, and some other factors, which significantly affect the characteristics of the crystals grown [5–7]. For example, the use of the AVC technique in [8] made it possible to reduce the density of growth dislocations from 103 to 1 cm–2 during the growth of sodium nitrate crystals. The main difficulty in the implementation of a particular technique of melt activation is the absence of a differential approach to melts differing in viscosity, temperature, volatility, and chemical reactivity.
Experiments with the introduction of axial vibrations into a melt were carried out in an open system [11]. In the configuration of the vertical Bridgman method, low-frequency vibrations were introduced into the melt using a disk mounted on a rod, which, in turn, was subjected to mechanical vibrations using a low-frequency loudspeaker. In this study, we attempted to extend the possibility of using the AVC technique for the crystal growth with controlling both the gas and vapor atmospheres at high (up to 106 Pa) and low (down to 10–1 Pa) pressures. We chose lead telluride as a model material to check the setup operation. Lead telluride is a narrow-gap semiconductor. There are many data in the literature on the growth of lead telluride crystals from both melt and vapor phase; thus, this compound can be considered a well-studied one [12, 13]. In contrast to NaNO3, which can be grown in an open system in air, PbTe is grown in closed or quasi-closed systems. Taking into account the necessity of controlling the nonstoichiometry of crystals grown, the process should be performed at a controlled vapor pressure of one of the components, determined from the pi–T projection of the phase diagram of the Pb–Te system. EXPERIMENTAL Construction of the Growth Setup The schematic of the setup for crystal growth by the AVC technique is shown in Fig. 1. The setup is controlled by a personal computer and an LTC crate (ZAO L-Card [14]). The heating unit of the system is a resistance furnace with seven energy-independent zones. The maxi-
1063-7745/05/5001-S0124$26.00 © 2005 Pleiades Publishing, Inc.
GROWTH OF NONSTOICHIOMETRIC PbTe CRYSTALS Lowfrequency amplifier
LPT port
Vibrator
Sound board
ëOM port
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Amplitude sensor
Controller PC
Thermocouples
Digital input output
Current leads
Analog-todigital converter Digitalto-analog converter Mobile telephone
Furnace
Crate
Amplifier Stepper motor controller
Motion mechanism
Fig. 1. Schematic of the setup for crystal growth by the vertical Bridgman method with the introduction of low-frequency vibrations into the melt.
mum operating temperature of the furnace is 1300 K; the error in maintaining temperature is ±0.1 K. The mechanism of motion of the growth ampoule, located in the bottom part of the heating unit, is controlled by a stepper motor. A unit step of the motor corresponds to a displacement of the ampoule by 0.2 µm. Estimation showed that, at a velocity of ampoule motion of 2 mm/h, the maximum deviation of the growth rate from the average value does not exceed 2%. The unit for the excitation of low-frequency vibrations (Fig. 2) is a system of external permanent magnets 4, providing a free suspension of the internal permanent magnet 12 and the electromagnet 15. The internal permanent magnet 12 is placed in a hermetic Teflon housing. The electromagnet 15 provides vibrations of the magnet 12 with a specified frequency and amplitude. A rod 6 with a disk 8 on the end is attached to the Teflon housing of the magnet 12. During the crystal growth, the disk 8 is immersed in the melt 9. The rod with the disk is positioned axially with respect to the growth ampoule 7. The ampoule 7, the rod 6, and the disk 8 are removable and can be made of different materials (corundum, boron nitride, platinum, and so on). For the growth of lead telluride, we used elements made of quartz glass. The electromagnetic vibrator can be shifted vertically to position the disk 8 with respect to the crystallization front. The frequency and amplitude of vibrations is controlled using a specially developed software. An output signal is generated by a sound board with a sampling rate of 40 kHz and amplified by a low-frequency amplifier. The vibration-amplitude feedback is performed using an electromagnetic sensor mounted on CRYSTALLOGRAPHY REPORTS
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the vibrator rod. The computer software can give information about the current operating parameters of the setup and about an emergency situation by sending an SMS message. To this end, a Nokia 6110 mobile telephone was used with a standard Nokia Data Suite 3 interface. The gas atmosphere in the growth ampoule should be inert to avoid oxidation of lead telluride. Evacuation of the ampoule makes it impossible to control the vapor phase during the crystal growth. The saturation vapor pressure of PbTe molecules at the melting temperature is about 7 × 103 Pa. Hence, when the growth ampoule is evacuated, the material rapidly evaporates and crystallizes in the cold part of the ampoule. Evaporation is enhanced significantly when the vibrating rod is introduced into the melt. Since the rod is colder than the ampoule walls because of the radial gradient, a significant fraction of resublimating lead telluride is condensed on the rod and, finally, jams it. During the experiments, we found that the introduction of argon with a partial pressure of about 8 × 104 Pa into the growth ampoule makes it possible to reduce significantly the evaporation rate of PbTe, as a result of which no more than 5% of PbTe is transferred to the cold part of the ampoule during the growth. In the preliminary experiments, carried out without applying vibrations, the optimal velocity of vertical ampoule motion was determined to be 2 mm/h at a diameter of the growing crystal of 13 mm. The external temperature gradient in the crystallization zone was 50 K/cm. To compare the results obtained in the conventional and AVC processes, the same conditions were used to grow crystals using the AVC technique. 2005
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AVETISOV et al.
Charge Synthesis 1 2 5 3 13 4 15 12
3
In the second stage, the polycrystalline compound obtained was subjected to annealing under controlled partial Te vapor pressure. The Te vapor pressure was chosen on the basis of the known p Te2 –T–X diagram for lead telluride [15]. After the annealing, the ampoule with the compound was quenched and the nonstoichiometry of the compound was determined by the technique described below. Measurement of the Characteristics of the Crystals
5 2 5 6 5
3 7 9 8 10
11 14
Fig. 2. Schematic of the growth system with the introduction of axial low-frequency vibrations into the melt in an evacuated ampoule: (1) vacuum valve; (2) tooth-seal housing; (3) tooth-seal nut; (4) external permanent magnet; (5) rubber ring; (6) vibrator rod; (7) growth ampoule; (8) vibrator disk; (9) melt; (10) crystal; (11) ampoule-displacement rod; (12) internal permanent magnet; (13) glass tube; (14) resistance furnace; and (15) electromagnet.
The synthesis of nonstoichiometric lead telluride charge was performed in two stages. In the first stage, elementary tellurium (Extra grade, 99.999) and lead (high-purity C-000 grade) were melted in an evacuated graphitized quartz ampoule. The melt was homogenized at 1230 K for 6 h. To achieve completeness of the reaction, tellurium was taken in excess of 0.1 mol % with respect to the stoichiometric composition. After the synthesis, the polycrystalline ingot was ground to powder with an average grain size of 20 µm and the excess tellurium was removed by low-temperature distillation in a vacuum.
To determine the concentration of the excess component (the nonstoichiometry) in lead telluride, the method of extraction was used [16]. The essence of this method is as follows: upon annealing in an evacuated ampoule in a two-zone furnace, on the basis of the detailed analysis of the pi–T–xi phase diagram of the corresponding chemical compound, the conditions are determined at which the excess component is resublimated to the colder part of the ampoule. The temperature of the PbTe compound is 700 ± 10 K and the vapor pressure of Te2 molecules is 10–7 Pa, which corresponds to a temperature of the colder part of the ampoule of 520 K. In this case, by the end of the annealing, the residual concentration of excess tellurium in the compound (whose temperature is higher) coincides with the stoichiometric composition within the measurement error (10–7 mol of excess component per PbTe mol) [17]. The amounts of tellurium and lead in the condensate were determined photocolorimetrically [18]. The detection limit of this method is 1 µg of Te(Pb) in a test sample. With allowance for this limit and the real weights of nonstoichiometric lead telluride (from 0.5 to 2 g), the detection limit of excess Te was 2 × 10–6 mol of excess component per PbTe mol. The type, concentration, and mobility of free charge carriers were determined by measuring the dc-current Hall effect in a dc magnetic field [19]. The dislocation density in the crystals grown was determined in the (100) plane by the etch-pit method, using an etchant of the following composition: KOH : H2O2 : C3H5(OH)3 (glycerin) : H2O = 10 : 0.5 : 1 : 10 [20].
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T Tmax m = 1197 K
Tmcong
1 Fig. 3. Lead telluride crystal grown by the vertical Bridgman method with the introduction of axial low-frequency vibrations into the melt.
–2
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2
4
6 x
Fig. 4. (1) Solidus and (2) liquidus lines in the T–x projection of the phase diagram of the Pb–Te system near the maximum melting temperature of the PbTe compound (x is the excess-component concentration: 10–4 mol excess Te(Pb)/mol PbTe).
RESULTS AND DISCUSSION The PbTe crystals grown were boules 40-mm-long in the cylindrical part (Fig. 3). The bottom (conical) part of the crystals was ~10-mm-long. To carry out measurements, the crystals were cleaved in the cleavage planes into three parts: bottom (conical), middle, and top. Table 1 contains the electrical parameters of the crystals, calculated from the Hall measurements. Analysis of the data obtained showed that the top part of all crystals has a tendency towards a decrease in the concentration of holes, which are majority carriers in the case of the incorporation of excess tellurium into lead telluride [21, 22]. At the same time, the mobility of majority carriers is the highest in the middle part for all crystals. The difference between the total concentration of excess Te (determined by the direct physicochemical method) and the concentration of free charge carriers was used to calculate the concentration of neutral defects (Table 2). When lead telluride is used as an IRphotosensitive material, the concentration of electrically neutral defects, which can be recombination or attachment centers, determines the kinetic characteristics of the photoconductivity. Comparison of the total defect concentration with the concentration of ionized defects (Table 2) shows that, as a result of an increase in the vibration amplitude, the difference in these concentrations decreases in all parts of the crystals. This fact indicates that ionized defects become dominant and make the largest contribution to the total defect concentration. Specifically, this situation is characteristic of the high-temperature equilibrium at the boundary of the homogeneity range of PbTe from the side of excess Te [15, 21]. Therefore, an increase in the vibration amplitude makes the chemical potentials of the components in different (solid, melt, vapor) phases closer to their equilibrium values.
0
2
Thus, the results obtained can be analyzed on the basis of the equilibrium T–x projection of the phase diagram of the Pb–Te system. At a vibration amplitude of 100 µm, when the nonstoichiometric Te concentration is almost constant along the entire crystal length, crystals were grown from charges with different excess Te concentrations. Suggesting that the mass transfer through the vapor phase during the crystal growth is suppressed by the inert-gas pressure (PAr = 105 Pa), we assumed that, in the initial stage of crystallization, the melt composition Table 1. Electrical characteristics of the PbTe crystals Part of the A, µm crystal
XTe in the charge
Top Middle Bottom Top Middle Bottom Top Middle Bottom Top Middle Bottom
1.2 × 10–4 –1.7 × 1018* 1.5 × 1018 1.1 × 1018 –4 1.2 × 10 2.9 × 1018 1.5 × 1018 1.8 × 1018 1.2 × 10–4 4.3 × 1018 1.7 × 1018 1.1 × 1018 –4 1.2 × 10 3.4 × 1018 2.2 × 1018 2.9 × 1018
0
36
50
100
* n-type conductivity. 2005
p(n), cm–3
m, V cm–1 s–1 550 820 740 530 750 730 440 950 900 350 620 590
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Table 2. Concentrations of charged and neutral point defects in PbTe crystals grown at a vibration frequency of 50 Hz and different vibration amplitudes A, µm 0
36
50
100
50
Part of the crystal Top
XTe in the charge
XTe
Xion
|Xneutr/Xion|
10–4 mol excess Te/mol PbTe 1.2
rel. units
–0.57*
Middle
0.40
0.51
–0.11
0.21
Bottom
2.00
0.37
1.63
4.40
0.94
0.98
–0.04
0.04
Middle
2.00
0.51
1.49
2.96
Bottom
2.30
0.61
1.69
2.79
Top
Top
1.2
0.40
1.45
–1.05
0.72
Middle
1.47
0.57
0.90
1.57
Bottom
1.97
0.37
1.60
4.31
1.29
1.15
0.14
0.13
Middle
1.34
0.74
0.60
0.81
Bottom
1.78
0.98
0.80
0.82
Top
Top
1.2
1.2
4.4
0.35
Middle
0.44
Bottom 50
Xneutr
Middle
3.4
3.36
0.49
2.87
5.86
3.2
0.91
2.29
2.52
* n-type conductivity.
corresponds to that of the initial nonstoichiometric charge. In Fig. 4, these points correspond to the liquidus composition. The solidus composition was determined from the analysis of the nonstoichiometry of the crystals grown. Since we could not exactly determine the temperatures at which the crystallization occurred, relative values of temperature are plotted on the ordinate axis. Analysis of the results showed that the congruent melting point of lead telluride corresponds to an excess of Te of about (2.8 ± 0.3) × 10–4 mol excess Te/mol PbTe. The use of a charge of such composition allowed us to grow crystals with a much lower dislocation density (Table 3). It was shown previously [23] that, at a fixed vibration frequency, a change in the vibration amplitude in the AVC technique makes it possible to change the crystallization-front shape from convex to concave, with an almost planar front at the optimal point. In this case, the density of growth dislocations in sodium nitrate crystals decreased by several orders of magnitude. As can be seen from Table 3, for the PbTe crystals grown from a charge with an excess Te concentration of 1.2 × 10–4 mol Te/mol PbTe, with an increase in the vibration amplitude to 100 µm, the dislocation density significantly increases. At the same time, the nonstoichiometry distribution becomes uniform over the crys-
tal length. This behavior can be explained by the change in the curvature of the crystallization front from convex to concave with an increase in the vibration amplitude. The excess Te concentration in the initial charge affects the dislocation density much stronger (Table 3). A decrease in the excess Te concentration, i.e., the use of a charge with a composition close to stoichiometric, leads to a significant increase in the dislocation density. Vice versa, the use of a charge with nonstoichiometry close to the congruent-melting point makes it possible to grow crystals with a very low dislocation density. Table 3. Dislocation density in PbTe crystals grown from charges with different nonstoichiometry at a vibration frequency of 50 Hz and different vibration amplitudes Dislocation density, cm–2
A, µm
XTe, mol excess Te/mol PbTe
top
0 36 50 100 50 50
1.2 × 1.2 × 10–4 1.2 × 10–4 1.2 × 10–4 6.2 × 10–5 3.4 × 10–4
3× 3 × 105 3 × 105 1 × 106 2 × 106 7 × 104
10–4
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middle
bottom
1.5 × 2 × 105 3 × 105 2.5 × 105 2.5 × 105 3 × 105 1.5 × 106 1 × 106 6 2 × 10 2 × 106 7 × 104 7 × 104 105
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CONCLUSIONS The use of axial vibrations of the solid immersed into a melt as a tool for controlling the heat and mass transfer in the melt during the crystal growth by the Bridgman method gives grounds to suggest that, under certain conditions, the physicochemical parameters of the crystallization process approach the equilibrium values. This circumstance allowed us to determine for the first time the composition of congruently melting lead telluride: (2.8 ± 0.3) × 10–4 mol excess Te/mol PbTe. The introduction of axial vibrations into a melt makes it possible to obtain a uniform nonstoichiometry over the length of a growing crystal. The structural quality of the lead telluride crystals obtained by the Bridgman method depends much more strongly on the nonstoichiometry of the initial charge than on the processes of heat and mass transfer in the melt.
9. 10. 11. 12. 13. 14. 15. 16.
17. 18.
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Translated by Yu. Sin’kov
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