Macrosegregation of Impurities in Directionally Solidified Silicon

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~7.1 9 10 5 Pa (0.7 atm), which was maintained until the end of each experiment. The high-purity argon was injected to minimize the formation of gaseous SiO by chemical reaction between the silicon melt and quartz tube. To stabilize the solidification system thermally, after pouring the melt into the quartz mold, the furnace was maintained for 45 minutes at a temperature of 1773 K (1500 °C), controlled by a type-B thermocouple (Pt- 6 pct Rh / Pt-30 pct Rh) positioned between the zircon shell and the graphite susceptor and fixed at the furnace (Figure 1(b)). This thermocouple was inserted into a completely sealed alumina sheath for protection against the furnace environment. After stabilization, the mold began to move down, out of the graphite susceptor, at a controlled velocity. On leaving the susceptor, the mold crossed a graphite baffle designed to separate the hot and cold zones of the furnace. The cold zone was formed by a water-cooled serpentine. In one of the experiments, two type-B thermocouples sheathed by closed end quartz tubes (inner diameter 5.2 mm, outer diameter 6.7 mm) were located parallel to the quartz mold tube, adjacent to the tube outer surface (Figure 1(b)). These thermocouples, which moved down with the mold, were connected to a data acquisition system to convert the electric signals into temperature, enabling the calculation of a temperature gradient at the tube outer surface. This gradient was considered as a good estimate of the temperature gradient within the mold. The measured temperature gradient (G) varied between 10 and 20 K cm –1 in the temperature range between 1573 K (1300 °C) and 1687 K (1414 °C), at the mold velocity of 10 lm seconds –1 . The current experiments were designed to assess the effect of the withdrawal velocity of the mold from the furnace (5 £ V £ 110 lm seconds –1 ), which is related directly to the solidification velocity, on the macrosegregation of impurities in the directionally solidified Si ingots. III. PREPARATION AND CHEMICAL ANALYSES OF SAMPLES After solidification and cooling to room temperature, each Si cylindrical ingot (length 0.25 m, diameter 0.034 m) was stripped out of the quartz mold and sectioned transversally in at most 10 slices of approximately equal thickness. These slices were then sectioned longitudinally, giving rise to two halves: one for chemical analysis and the other for microstructural and macrostructural examination. The half for chemical analysis (~100 g) was shattered, and enough pieces were collected to create three samples of 3 g. Each sample was dissolved in a solution consisting of 5-mL HNO 3 (65 pct P.A.) and 15-mL HF (48 pct P.A.) and then analyzed by inductively coupled plasma atomic emission spectroscopy (ICP) in a Shimadzu ICPS-7500 system. The average of the concentration values for the three samples, representing about 5 pct of the whole slice mass, was adopted as the slice composition. A quantification limit (QL) was estimated for each impurity by analyzing a series of standard solutions with decreasing concentrations. In the series, the measured concentration of each impurity decreased to an approximately constant value, no longer changing significantly for solutions of lower concentrations. This constant value was actually the blank concentration with a superimposed background noise. The QL given in Table II was defined as three times this constant concentration value. The standard deviation of the blank concentration was used also to calculate the quantification limit recommended by the International Union of Pure and Applied Chemistry, [38] but this limit was always lower than the QL presented in Table II, which was finally adopted in an attempt to improve the quantification methodology carried out in the current work. As will be shown subsequently, in some of the ingots, most slices have concentration values for some impurities that are below their QL. When for a given impurity, the ingot had at least 90 pct of its slices with concentrations above the QL, these values were used to calculate an average concentration (C av ) for the impurity. The C av value is compared with the composition of the starting MG-Si (C 0 ) in Table II, showing reasonable agreement for most impurities. When there is segregation of impurities within one slice (e.g., lateral segregation [39] ), an important source of discrepancy between C av and C 0 could be the small portion of the slice (5 pct of the slice mass) being analyzed. Another source might be the limited number of slices with concentrations above the QL for certain impurities. For example, in the case of V, Ni, and Zr, slices from only one ingot (V = 110 lm seconds –1 ) were taken into account to calculate C av . To calculate C av for Al, all the four ingots obtained in the experiments were considered. Nevertheless, a large discrepancy is still observed between C av and C 0 . A possible explanation is the oxidation of Al during melting in the melting chamber of the Bridgman furnace (Figure 1(a)), decreasing the average Al content from C 0 (in the MG-Si) to C av in the ingots. This preferential oxidation of Al, which is sometimes used to remove it from molten Si by oxygen injection, [40] can occur in the contact between the melt and a top slag naturally formed from the SiO 2 and other oxides already present in the MG-Si used as the starting material. Another source of oxidation is the wall of the quartz crucible located in the furnace melting chamber. For thermodynamic reasons, this oxidation should be even more intense for Na and Ca; furthermore, these elements are volatile and could evaporate both in the melting and solidification chambers of the furnace, possibly affecting their macrosegregation in the ingots. Therefore, these two elements were not analyzed along the resulting ingots. The glow discharge mass spectrometry technique (GDMS) was used also for chemical analysis of an area approximately 18 mm 2 on the surface of slices cut from the bottom of some of the ingots, near the center of their transversal section. Note that the GDMS analyses give METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 42A, JULY 2011—1873
the composition of a relatively small area at the center of the slices. IV. MICROSTRUCTURES AND MACROSTRUCTURES OF SILICON INGOTS The macrostructure of all Si ingots generally consisted of columnar grains. In Figure 2(a), the ingot grown at V =5lm seconds –1 shows columnar grains oriented approximately parallel to the withdrawal direction from the bottom to the top. Because columnar grains are elongated approximately parallel to the heat flux direction, the orientation of these grains indicates that heat extraction occurred mainly in the axial direction at the center of the ingot, but radial extraction becomes increasingly important closer to the mold wall. An examination of the microstructures revealed precipitated particles at the top of all ingots. In the ingot grown at 5 lm seconds –1 , a continuous layer of precipitates indicates severe macrosegregation of impurities to the top (Figure 2(b)). In the remaining ingots (V > 5 lm seconds –1 ), however, there were fewer precipitates at the top, appearing isolated or forming strings. The ingots grown at 5 and 10 lm seconds –1 show precipitates only at the top, whereas for 110 and 20 lm seconds –1 , precipitates were viewed throughout the ingot (bottom, middle, and top). For a mold velocity of 110 lm seconds –1 , for example, Figure 2(c) shows a string of precipitates in a slice cut from the middle of the ingot. A microprobe analysis by energy dispersive spectroscopy of the precipitates indicated different compositions, which consisted of a combination of the following elements: Si, Fe, Al, Ti, Cr, Ni, Cu, Zr, and P. V. STABILITY OF THE SOLID–LIQUID INTERFACE Dendrites or cells were not viewed in the samples observed at the optical or scanning electron (SEM) microscopes. Nevertheless, it is not possible to conclude that the morphology of the solid–liquid interface during solidification was planar. In high-purity metals, the microsegregation and the amount of precipitates formed in interdendritic regions might be insufficient to reveal a dendritic or cellular microstructure by chemical etching or by the backscattered electron contrast of a SEM. For example, Liu et al. [41] observed faceted dendrites in high-purity Si droplets solidified in contact with a Cu chill plate because the dendritic structure became visible by the surface relief formed on the solidified droplet. C¸ iftja [42] concluded that the presence of precipitates rich in Al, Fe, or made of SiC is an indication that the planar solid–liquid interface broke down during solidification, giving rise to a cellular structure. This conclusion was based on the assumption that during solidification, some precipitates that were present already in the molten Si were pushed in between the cells, becoming an evidence of the cell existence. Even when precipitates do not form in the liquid ahead of the solid–liquid interface, these might form during solidification in between the cells as a result of microsegregation, also becoming an evidence of the cells. In the current work, as mentioned in Section IV, precipitates were observed throughout the ingots grown at V = 20 or 110 lm seconds –1 and could indicate a nonplanar solid–liquid interface in these solidification conditions. Kuroda and Saitoh [32] reported that ingots grown from MG-Si at V ‡ 17 lm seconds –1 and a temperature gradient of ~20 K cm –1 in a Czochralski furnace had a cellular structure throughout the ingot. The presence of cells was indicated strongly by a wavelike pattern of local electric resistance across the samples, indicating a local variation of composition. The wavelength of this pattern was of the same order of magnitude as a typical spacing between cells. Chalmers [43] discussed the possibility of precipitation of particles in the liquid adjacent to a planar solid–liquid interface. Therefore, the existence of precipitates alone might not be irrefutable evidence of the cell presence. Because of the low segregation coefficient of most impurities, Chalmers [43] suggested that the liquid adjacent to the interface would eventually be enriched with these impurities, and some precipitates would form. In the context of eutectic solidification, Mollard and Flemings [44] showed that a planar solid–liquid interface could be maintained during the solidification of a twophase solid. Similarly, solidification conditions might exist to maintain a planar interface during solidification of the MG-Si even with the formation of precipitates at this interface. The stability of the solid–liquid interface in the current work experiments was examined by the application of the constitutional supercooling criterion (CSC). This criterion establishes that a planar solid– liquid interface is stable when [45] G ¼ @T @ n @T L int @ n ½7Š int where G is the temperature gradient at the liquid adjacent to the interface; T is the liquid temperature; n is the normal direction to the interface; and T L is the liquidus temperature. The two derivatives in Eq. [7] are calculated at the position of the interface, on the liquid side. For a multicomponent alloy solidifying with a planar solid–liquid interface, when interactions between diffusion coefficients in the liquid and diffusion in the solid are both neglected, the Stefan or jump condition of species conservation can be written at the interface independently for each element [46,47] @ C li @ n ¼ ð C li C si Þ V ½8Š D li where C li and C si are the concentration fields of element i in the liquid and solid, respectively, and D li is the diffusion coefficient of element i in the liquid. In this equation, C li and C si on the right-hand side are calculated at the interface, on the liquid and solid sides, respectively. Accordingly, the derivative of C li on the left-hand side is also calculated at the interface, on the liquid side and in the normal direction. 1874—VOLUME 42A, JULY 2011 METALLURGICAL AND MATERIALS TRANSACTIONS A
Page 1 and 2: Macrosegregation of Impurities in D
Page 3: The macrosegregation in directional
Page 7 and 8: Table III. Slope of Liquidus Line o
Page 9 and 10: conservation to the mixed liquid ou
Page 11 and 12: Fig. 5—Continued. 1880—VOLUME 4
Page 13 and 14: VIII. MECHANISMS OF MASS TRANSFER I
Page 15 and 16: values for V = 110 and 20 lm second
Page 17: 27. H.E. Bridgers and E.D. Kolb: J.

Macrosegregation of Impurities in Directionally Solidified Silicon

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