Article pubs.acs.org/crystal
Crystal Growth of BixSb1−x Solid Solutions with an Ultrasound Presence in Two Orthogonal Directions G. N. Kozhemyakin* Laboratory of Crystal Growth, Shubnikov Institute of Crystallography of Federal Scientific Research Centre “Crystallography and Photonics” of Russian Academy of Sciences, Pr. Lenina, 59, 119333 Moscow, Russia ABSTRACT: A modified Stepanov method of crystal growth with the application of ultrasound in two orthogonal directions was developed to reduce the component inhomogeneity. Ultrasonic waves at frequencies of 2.5 and 5 MHz were introduced into the melt parallel and perpendicular to the pulling axes of the grown crystals. BixSb1−x solid solution crystals were grown with a square and round cross section. The crystals grown with a square cross section had a smaller Sb inhomogeneity than the crystals with round cross section. They were grown in the presence of ultrasound simultaneously in two orthogonal directions in the melt and increased pulling rate. We explain the effect of two orthogonal standing waves to eliminate convection in the melt under the solid−liquid interface inside of a graphite die due to complex oscillation of the melt particles. The component inhomogeneity was measured before and after melt crystallization in a Czochralski crucible by a radioactive analysis method. The component inhomogeneity after melt crystallization increased to ±17% with the increase of the mass component difference (In, Sn, Sb, and Bi) from 1 to 85 amu and the melt overheating above the melting point to 100 °C. diameter up to 450 mm.26,27 For this target a super conductive cusp type magnet was developed which had a weight of about 10 t. However, this method does not allow complete elimination of the striations in dislocation free Si single crystals that is the obstacle for nanoelectronics development. Additionally, a magnetic field acts on all volumes of the melt which creates technical and economic difficulties for Si single crystal growth with a diameter larger than 450 mm as an increase of magnet dimensions and electricity consumption are required. An alternative approach is the application of ultrasound for the decrease or elimination of the striations in the crystal growth by the Czochralski method and liquid-phase epitaxial growth.28−32 It is worthwhile to note that ultrasound in two orthogonal directions more effectively reduces the inhomogeneity in the single crystals.33 Unlike gravitation and magnetic field, ultrasound can influence the melt part under the solid− liquid (S/L) interface due to the formatting of the ultrasonic standing wave channel. As a result the melt mixes up out of the ultrasonic standing waves channel. It is necessary for the growth of the doped crystals and solid solutions with a large concentration of the components. It is plausible that the different atomic mass components also can influence their inhomogeneity in the melt and crystal. Therefore, studying of component behavior in a crystallization process and the influence of an ultrasonic field to distribution components has fundamental and practical interest.
1. INTRODUCTION The composition inhomogeneity is a major problem in the growth of solid solution crystals by crystallization methods. It is especially important for the crystals having the components with considerably different distribution coefficients. Such materials are BixSb1−x, GexSi1−x, GaxIn1−xSb solid solutions. They have prospective applications for quantum electronics, photonics, thermoelectricity, and X-ray monochromators.1−9 The component inhomogeneity in these crystals essentially influences their electrophysical properties.10 Therefore, different types of inhomogeneity in these solid solutions and the reason for their formation are carefully studied.11−13 Theoretically and experimentally it was shown that convection is the main reason for the appearance of component inhomogeneity in the cross section of a crystal.14,15 The methods of the component inhomogeneity elimination were developed with the use of gravitation and magnetic and ultrasonic fields.15−20 Crystal growth for the conditions of low and high gravitation with the acceleration of gravity g at 10−4g to 3g confirmed the influence of convection on inhomogeneity formation and allowed dampened conditions to develop for the crystal growth.19,20 However, these methods are very expensive and apply only for fundamental studies. Magnetic and electromagnetic fields are used for the stabilization of convective flow in the crystal growth process by different designs.21−27 The potential virtue of magnetic field influence is that it can be tailored to provide controlled transport of convective flow in the melts having electrical conductivity. This distinctive feature of the magnetic field provides the ability to suppress silicon melt convection and to control oxygen concentration in pulled Si single crystals with a © XXXX American Chemical Society
Received: May 26, 2016 Revised: September 16, 2016
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DOI: 10.1021/acs.cgd.6b00799 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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used for the growth of BixSb1−x crystals with the Sb concentration from 11 atom % to 16 atom %. The dies had 8 × 8 mm2 square internal openings and 9 mm diameter round openings. These graphite edge-definers were fixed to a fused silica ring, which was fused to a fused silica waveguide with a 8 mm diameter and 105 mm length (Figure 1). Ultrasonic waves at a frequency of 5 MHz were introduced in the melt volume inside of the graphite die from a piezo transducer fixed to the opposite end of this waveguide. Ultrasonic waves at a frequency of 2.5 MHz were introduced into the melt parallel to the pulling axis from a piezo transducer though a fused silica waveguide with 15 mm diameter and 300 mm length fused to the bottom of the fused silica crucible. The crucible had 45 mm ID and 35 mm height. The pulled crystals were cut parallel to the growth axis using an electrical discharge machine. The cut surfaces of the crystals were ground abrasive with 40 μm Al2O3, polished 1−2 μm Cr2O3, and a soap solution. The Sb distribution in BixSb1−x crystals was studied by X-ray fluorescence analysis in a Nanolab-2100 electronic microscope, which allowed a scan of the surface of the sample crystal with an electronic beam of 100 Å in diameter.
In the present study, we present the results of the influence of different atomic mass components on the distribution for a crystallization process and the ultrasound effect in two orthogonal directions on the decrease of component inhomogeneity in BixSb1−x solid solutions crystals grown by the Stepanov method.
2. EXPERIMENTAL SECTION A Czochralski pulling apparatus was used for the melt crystallization and to grow BixSb1−x solid solutions crystals by Czochralski and Stepanov methods. The melts masses for the investigations of the component distribution in the Czochralski crucible were 1600 g. The crucible material was fused silica with 70 mm inside diameter and 50 mm height and was not rotated. Bismuth (Bi), antimony (Sb), indium (In), tin (Sn), and tellurium (Te) of high purity (6N) were used as the source materials. The component distribution in the melts before and after their crystallization was measured by a radioactive analysis method. Sb124, In114, Sn113, and Te125 radioactive isotopes were used as dopant materials. The concentrations of these radioactive isotopes in the melts were less than 10−3 wt %. The samples of the melts and solid phases had a mass of 0.4 g. These samples were dissolved in HNO3/HCl = 2:3 solution with 5 cm3 volume in the glass crucibles with 35 mm inside diameter and 30 mm height. The melting and crystallization process of these materials were executed at 0.4 atm in high purity Ar atmosphere. A Nokia 800-channel impulse analyzer and a Ge−Li detector were used for the measurement of the radioactive isotope concentration. A number of radioactive impulses for the measurement of the samples were more than 100 000. Therefore, the measurement error of the radioactive isotope concentration did not exceed ±1%. BixSb1−x single crystal with 11 atom % Sb was pulled with orientation of the (111) parallel to the growth axis using a solid Sb feed by the Czochralski method.4 The melt mass was 1600 g. A singlecrystal seed with a 10 mm diameter, which had Sb concentration close to the grown crystal, was used for growing the crystal. The pulling and rotation rates of the crystal with 15 mm diameter were 0.04 mm/min and 60 rpm, respectively. The crucible material was fused silica and it rotated by 8 rpm in the opposite direction. This single crystal was pulled at 0.4 atm in high-purity He. This crystal was grown for comparison of the component inhomogeneity in the crystals pulled by the Czochralski and Stepanov methods. The melt mass was 160 g for the crystals growth by the Stepanov method (Figure 1). The pulling rate of BixSb1−x crystals was from 0.1 mm/min to 0.33 mm/min. The crystals were pulled without rotation at 0.4 atm pressure in high purity Ar atmosphere. Graphite dies were
3. RESULTS AND DISCUSSION 3.1. Melt Crystallization. It is known that the atomic mass difference of the components causes liquation in a melt. Almost a double atomic mass difference of Bi (208.98 amu) and Sb (121.76 amu) can influence the component inhomogeneity in the melts and after their crystallization. Therefore, we experimentally investigated the component distribution in the metallic melts before and after their crystallization using radioactive isotopes, which can ensure the concentration measurement with a high precision. The influence of an atomic mass difference of the components was investigated in the component systems: In−In114, Sb−Sb124, Sn− Sn113, Bi−Sb124, In−Sb−In114, and In−Sb−Te125. The atomic mass difference in these systems was from 1 to 85 amu. The melts were overheated above the melting point by 5, 70, and 100 °C, and a steady state was established at these temperatures for 1 h before the crystallization. Thereafter, five quartz ampules simultaneously were lowered into the melts to 10 mm depth, were filled of the melt, and were lifted (Figure 2a). These samples defined the component concentration in the melt cross section. The melt samples along the melts depth were made by means of the double ampules, which opened for the melts filling and closed in the melts (Figure 2b). Such ampules allowed preventing the penetration of other melt parts during lifting. Further, the melts were crystallized after the ampules were lifted above the melt surface. The component concentration difference in certain places of the melts before and after their crystallization is shown in Figure 3. The increase of the melt overheating above 5−70 °C increased the component inhomogeneity in the melts less than ±2%. The maximal inhomogeneity ±7% of the components was observed in the Bi−Sb melt for 100 °C overheating. This increase of the component inhomogeneity with the rise of the melt overheating above 70 °C is the result of intensive mixing due to an appearance of nonstationary convection. Taking into consideration these results, the melts were overheated less than 50 °C before the crystal growth in our experiments. Five samples of the top and bottom surfaces of every melt crystallized were cut for the measurement of the radioactive isotopes concentration (Figure 2a). Thus, radioactive isotopes inhomogeneity was determined for 10 measurements of every component in these systems. As is clearly seen in Figure 3, the radioactive isotopes inhomogeneity rose from ±2.5% to ±17% with the increase of the atomic mass difference of the
Figure 1. Schematic arrangement of the apparatus pulling BixSb1−x solid solutions crystals by the Stepanov method. B
DOI: 10.1021/acs.cgd.6b00799 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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known that Sb distribution coefficient in BixSb1−x crystals is higher than 1, and for these Sb concentrations it has values near 2.6−3.34 As a result, the Sb composition must decrease to the bulk end during the crystal growth. Besides, the melt depth must decrease in the graphite die for the crystal pulling. Therefore, we used the solid feed for the elimination of these technological difficulties in the crystal growth. Cylindrical bulks of the feeds had cross sections and compositions identical to the pulled crystals. Four BixSb1−x polycrystals were pulled with the ultrasound effect by this method. The schemes of the samples arrangement in the crystals, growth rate, ultrasound direction, and Sb inhomogeneity are shown in Table 1. BixSb1−x single crystal N1 grown by the Czochralski method (Figure 4a) had the lowest Sb inhomogeneity 8%. BixSb1−x polycrystal N2 (Figure 4b1,b2) with square cross section was grown at a maximal pulling rate 0.33 mm/min and ultrasound introduction into the melt simultaneously in two orthogonal directions at frequencies of 2.5 and 5 MHz. This crystal had Sb inhomogeneity 13.5%. It is necessary to note that vertical ultrasonic waves (VUS) at a frequency of 2.5 MHz did not completely act on this crystal cross section (Figure 4b2). Therefore, the crystal region pulled without the presence of VUS had large Sb inhomogeneity of 16% (Table 1). A similar changing of the Sb distribution was observed in the BixSb1−x polycrystal N3 (Figure 4c1,c2). However, Sb inhomogeneity near 11% in this crystal was less due to a smaller pulling rate of 0.2 mm/min. On the other hand, Sb inhomogeneity in BixSb1−x polycrystal N4 (Table 1, Figure 4d1,d2) with a round cross section was larger than in the crystal N3 with a square cross section for the same pulling rate. It is obvious the increase of Sb inhomogeneity in the crystal N4 is the result of the standing waves’ absence in the horizontal direction under the S/L interface. For the present case, the round opening in the graphite die did not provide the transfer and reflection of ultrasonic waves in that horizontal direction that is necessary for standing waves formation. BixSb1−x polycrystal N5 (Table 1, Figure 4e1,e2) with a round cross section was pulled for the introduction of ultrasound into the melt across the die only in one direction parallel to the S/L interface and had maximal Sb inhomogeneity of 21%. These results have an important advantage for BixSb1−x polycrystals with a square cross section in comparison with BixSb1−x single crystal growth by the Czochralski method with a minimal pulling rate equal 0.04 mm/min. The effect of ultrasound in two orthogonal directions for BixSb1−x crystals allowed us to increase the pulling rate by a factor of 5 and 8 at a rising of the Sb inhomogeneity by 38% and 70%, respectively. On the other hand, the Sb inhomogeneity increased by 106% with the increase of the pulling rate by a factor of 5 for the crystal grown with a round cross section. Additionally, an increase of Sb inhomogeneity by 260% was observed in the crystal with a round cross section pulled with an ultrasound presence only parallel to the S/L interface and pulling rate larger by a factor of 2.5. As we can note that the introduction of ultrasound simultaneously in two orthogonal directions into the melt under the S/L interface has an advantage for the component inhomogeneity decrease with the pulling rate increase of BixSb1−x crystals. Nevertheless, we want to underscore that better results were reached using the die with a square cross section inside opening and plane-parallel walls, which were perpendicular to the horizontal direction of ultrasonic waves.
Figure 2. Schematic drawing of the crucible with the ampules and samples of the melt before and after crystallization.
Figure 3. Dependence of component inhomogeneity on atomic mass differences.
components after the melt crystallization. Such a component inhomogeneity increase during the crystallization may be the result of many reasons, including the difference of physical− chemical properties, and the influence of external fields as gravitational, temperature, magnetic, and other. It is obvious that the component inhomogeneity can decrease using the presence of an external field to the crystal growth. Therefore, we applied an ultrasonic field for the inhomogeneity component decrease in the BixSb1−x crystal growth by the Stepanov method. 3.2. Crystal Growth by the Stepanov Method. BixSb1−x solid solutions crystals with Sb concentration from 11 atom % to 16 atom % were pulled by a modified Stepanov method. It is C
DOI: 10.1021/acs.cgd.6b00799 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Table 1. Schemes of the Samples Arrangement in the Crystals, Growth Rate, Ultrasound Direction, and Sb Inhomogeneity
Such an opening provides standing waves formation into the melt in the direction parallel to the S/L interface. Vertical standing waves in this method form between the crucible bottom with a fused waveguide and the S/L interface of the pulled crystal.35 Horizontal and vertical standing waves stimulate more complete oscillations of the dopant and melt particles and thus suppress convective flow under the S/L interface (Figure 5). Such oscillations are in the knots of standing waves and prevent pass melt flow through these waves.
These particles oscillations have a configuration shown in Figure 5b and were considered in ref 33.
4. CONCLUSIONS Experimental measurements of the component inhomogeneity before and after the melt crystallization were studied by a radioactive analysis method. It was found that overheating the melts by 5, 70, and 100 °C and a steady state established for 1 h changed the component inhomogeneity from ±1% to ±7%. The melt overheating above 70 °C promotes transfer of D
DOI: 10.1021/acs.cgd.6b00799 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Figure 4. Sb inhomogeneity in the cross section of pulled BixSb1−x crystals: (a) Bi0.885Sb0.115 single crystal by the Czochralski technique and Stepanov technique with horizontal (HUS) and vertical (VUS) ultrasound direction; (b1, b2) Bi89Sb0.11 crystal 2; (c1, c2) Bi0.88Sb0.12 crystal 3; (d1, d2) Bi0.853Sb0.147 crystal 4; (e1, e2) Bi0.842Sb0.158 crystal 5.
Figure 5. Schematic representation of ultrasonic standing waves forming in vertical (VSW) and horizontal (HSW) directions inside the graphite die (a) and melt particles oscillations (b).
stationary convection to nonstationary convection increasing the speed flow and as a result increases the components inhomogeneity. The composition inhomogeneity after the melt crystallization increased from ±2% to ±17% with the increase of the component mass difference from 1 to 85 amu. This inhomogeneity in the crystallization process may be the result of the physical−chemical properties difference of the components and the influence of external fields as gravitational, temperature, magnetic, etc. The influence of ultrasound in two orthogonal directions at frequencies of 2.5 and 5 MHz on Sb inhomogeneity in BixSb1−x crystals pulled by the Stepanov method was studied. The crystals were grown with square and round cross sections using graphite die. The lowest Sb inhomogeneity was observed in the polycrystals with square cross section. They were grown with the introduction into the melt of ultrasonic waves at frequencies different by a factor of 2, in the two directions simultaneously parallel and perpendicular to the pulling axis. Additionally, the pulling rate increase by a factor of 5 and 8 increased Sb inhomogeneity in these crystals by 38% and 70%, respectively, in comparison to Sb inhomogeneity in a BixSb1−x
single crystal. Nevertheless, BixSb1−x crystal pulled with a round cross section and the pulling rate increase by a factor of 5 had a larger Sb inhomogeneity near 106%. The largest Sb inhomogeneity increase to 260% was found in Bi xSb1−x polycrystal with a round cross section grown with an ultrasound presence in one direction parallel to the S/L interface. Therefore, the introduction of ultrasound into the melt in two orthogonal directions and frequencies different by a factor of 2 allowed an increase of the pulling rate of square cross section crystals with a smaller increase in inhomogeneity, compared to round cross section crystals. We attribute this result to the effect of two orthogonal standing waves on convection suppression in the melt under the S/L interface inside the graphite die due to complex oscillation of the melt particles.
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AUTHOR INFORMATION
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DOI: 10.1021/acs.cgd.6b00799 Cryst. Growth Des. XXXX, XXX, XXX−XXX
Crystal Growth & Design
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Notes
(32) Kozhemyakin, G. N.; Zolkina, L. V.; Inatomi, Y. Cryst. Growth Des. 2006, 6, 2412−2416. (33) Kozhemyakin, G. N. J. Cryst. Growth 2012, 360, 35−37. (34) Zemskov, V. S.; Belaya, A. D.; Kozhemyakin, G. N.; Lyuttsau, V. G.; Kostyukova, E. P. J. Cryst. Growth 1985, 71, 243−245. (35) Kozhemyakin, G. N. Ultrasonics 2014, 54, 731−736.
The author declares no competing financial interest.
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ACKNOWLEDGMENTS The author would like to thank Dr. A. Churilov for helpful discussions.
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REFERENCES
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DOI: 10.1021/acs.cgd.6b00799 Cryst. Growth Des. XXXX, XXX, XXX−XXX
