Process for producing single-crystal silicon

Abstract

A method for producing a silicon single crystal, comprising a step of growing a silicon single crystal by applying a horizontal magnetic field while pulling the silicon single crystal from a silicon melt in a quartz glass crucible, wherein a flow of the silicon melt flowing from the silicon single crystal to a side wall of the quartz glass crucible is present at a surface of the silicon melt, and a value calculated from an expression of a radius of a silicon single crystal [mm] divided by a radius of the crucible [mm] multiplied by the number of revolutions of the silicon single crystal [rpm] multiplied by the magnetic field strength [Tesla] divided by a distance from a surface of the silicon melt to a lower end of a shielding plate [mm] is 0.0190 or less, so that a flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible is 0.16 m / s or less.

Description

TECHNICAL BACKGROUNDField of the invention

[0001] The present invention relates to a method for producing a silicon single crystal, and more particularly, to a method for producing a silicon single crystal capable of reducing an oxygen concentration, improving the uniformity of the oxygen concentration in a direction of a crystal growth axis, and further improving the uniformity of the oxygen concentration in a substrate plane perpendicular to the crystal growth plane. Description of related technology

[0002] A silicon substrate obtained by a conventional Czochralski process (CZ process) and having a relatively high oxygen concentration (≥ 1.0 × 10 18 atoms / cm 3 ) was mainly used for the getter effect, but in a complementary metal oxide semiconductor (CMOS) image sensor, an oxygen-poor substrate (<1.0 × 1018 atoms / cm 3 ) is needed to reduce white error.

[0003] The silicon substrate is made from a silicon single crystal. The Czochralski process (CZ process) is widely used to produce a silicon single crystal, pulling a silicon single crystal and simultaneously growing the single crystal from a silicon melt in a quartz glass crucible.

[0004] In the method for producing the silicon single crystal, a method for adjusting an oxygen concentration in the silicon single crystal using a magnetic field application method for controlling convection as disclosed in JP S58-50953 B2, JP 2000-264784 A, or JP H04-31386 A, a method for controlling a flow rate of inert gas or a furnace pressure or for controlling the rotation of a quartz glass crucible as disclosed in JP H09-142990 A, or a method for controlling the rotation of a silicon single crystal as disclosed in JP 2005-145724 A are known.

[0005] However, even though the method for adjusting the oxygen concentration in the silicon single crystal is used, the oxygen concentration is higher in the latter half of a straight body portion of the silicon single crystal. Thus, the uniformity of the oxygen concentration in the direction of the crystal growth axis cannot be improved.

[0006] Specifically, the oxygen concentration in the silicon single crystal is determined as follows: the silicon melt reacts with the quartz component in the quartz glass crucible to dissolve one side wall of the quartz glass crucible, causing oxygen to be incorporated into the silicon melt. Thus, if oxygen is incorporated into the silicon single crystal before the oxygen incorporated into the silicon melt diffuses into the silicon melt or is released outside the melt, the oxygen concentration in the silicon single crystal increases.

[0007] Accordingly, it is necessary to control the flow (convection) in the silicon melt so that the oxygen incorporated into the silicon melt diffuses or is released before the oxygen is incorporated into the silicon single crystal.

[0008] Regarding controlling the flow in the silicon melt, in a state where the amount of the silicon melt in the quartz glass crucible is large, the flow (convection) in the silicon melt can be controlled by using the above-described method for adjusting the oxygen concentration in the silicon single crystal.

[0009] However, in a state where the amount of silicon melt in the quartz glass crucible is small, that is, in the second half of pulling a straight body portion of the silicon single crystal, the flow in the silicon melt cannot be controlled. The oxygen concentration in the later or second half (in the later or second half of pulling) of the straight body portion of the silicon single crystal increases. Therefore, uniformity of the oxygen concentration in the direction of the crystal growth axis of the silicon single crystal cannot be achieved.

[0010] To solve such problems, JP H04-31386 A proposes to reduce a magnetic field strength or flux density from 0.3 Tesla to 0.2 Tesla, 0.1 Tesla and 0.05 Tesla when the silicon single crystal is pulled, that is, while the amount of silicon melt contained in the quartz glass crucible decreases.

[0011] However, when the magnetic field strength or flux density is reduced from 0.3 Tesla to 0.2 Tesla, 0.1 Tesla and 0.05 Tesla and a magnetic field becomes weak, technical problems arise such that the fluctuation of the oxygen concentration in the substrate plane perpendicular to the crystal growth axis increases and the uniformity of the oxygen concentration in the surface plane is thus inhibited.

[0012] CZ devices and methods in which magnetic fields are used are known from US 2008 / 0 302 294 A1 and DE 691 15 131 T2.

[0013] In order to solve such problems, the inventors of the present invention have made extensive studies to reduce the oxygen concentration and to realize the uniformity of the oxygen concentration in the substrate plane perpendicular to the crystal growth axis and the uniformity of the oxygen concentration in the direction of the crystal growth axis.

[0014] In these studies, the inventors of the present invention paid attention to the flow on the surface of the silicon melt. The inventors found that the oxygen concentration can be reduced and that the oxygen concentration can be uniform in the direction of the crystal growth axis when the flow rate of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible is a specific flow rate or lower. As a result, the inventors have completed the present invention. PRESENTATION OF THE INVENTION

[0015] An object of the present invention is to provide a method for producing a silicon single crystal capable of reducing the oxygen concentration, realizing uniformity of the oxygen concentration in a direction of a crystal growth axis, and realizing uniformity of the oxygen concentration in a substrate plane perpendicular to the crystal growth axis.

[0016] A method for producing a silicon single crystal comprises a step of growing a silicon single crystal by pulling it from a silicon melt in a quartz glass crucible under application of a horizontal magnetic field, wherein a flow of the silicon melt flowing from the silicon single crystal to a side wall of the quartz glass crucible is present at a surface of the silicon melt, and a flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible is 0.16 m / s or less.

[0017] In the present embodiment, the flow rate of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible was set to 0.16 m / s or less during the pulling of the silicon single crystal. Under the above condition, the oxygen concentration in the silicon single crystal can be reduced, and uniformity of the oxygen concentration in the direction of the crystal growth axis and uniformity of the oxygen concentration in a substrate plane perpendicular to the crystal growth axis can be achieved.

[0018] An example of the flow of the silicon melt on the surface of the silicon melt includes a flow flowing from the silicon single crystal to the side wall of the quartz glass crucible, flowing downward in contact with (along) the side wall of the quartz glass crucible, and then rising from a bottom surface of the quartz glass crucible.

[0019] When the silicon melt flows into contact with the sidewall of the quartz crucible, the silicon is chemically active at a melting point. Thus, the silicon melt reacts with a quartz component in the quartz crucible, dissolving the sidewall of the quartz crucible. As a result, oxygen (O) is incorporated into the silicon melt.

[0020] Then, if the oxygen has been incorporated into the silicon single crystal before the oxygen has been released or diffused from the silicon melt, the oxygen concentration in the silicon single crystal increases.

[0021] This means that as the flow from the silicon single crystal to the sidewall of the quartz glass crucible increases, the flow rising from the bottom surface of the quartz glass crucible also increases. As a result, the extent of oxygen incorporation into the silicon single crystal can increase before the oxygen is released from the silicon melt and diffuses into the silicon melt.

[0022] In particular, when the flow rate of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible exceeds 0.16 m / s, the flow of the silicon melt rising from the bottom surface of the quartz glass crucible also becomes faster, and before the oxygen is released from the silicon melt and diffuses into the silicon melt, the oxygen may be incorporated into the silicon single crystal. Therefore, a flow rate exceeding 0.16 m / s is not preferred.

[0023] It is desirable that the center of the horizontal magnetic field in the silicon melt is positioned 60 mm below the surface of the melt, and that a magnetic field strength or flux density during the pulling of the silicon single crystal is at least 0.2 Tesla.

[0024] When the magnetic field strength or flux density is less than 0.2 Tesla, it is difficult to control the flow of the silicon melt. Especially when the magnetic field is weak, the fluctuation of the oxygen concentration in the substrate plane perpendicular to the crystal growth axis increases, and uniformity of the oxygen concentration in the surface plane cannot be achieved. Therefore, a weak magnetic field is not preferred.

[0025] When the magnetic field strength exceeds 0.4 Tesla, the flow velocity of the silicon melt flowing from the silicon single crystal to the sidewall of the quartz glass crucible becomes 0.16 m / s or higher. And the melt with high oxygen concentration reaches the crystal. Ultimately, a magnetic field stronger than 0.4 Tesla is not preferred. Therefore, the magnetic field strength is preferably in the range of 0.2 Tesla to 0.4 Tesla.

[0026] In addition, the center of the magnetic field is preferably positioned within 60 mm below the surface of the melt, and more preferably within 20 mm below the surface of the melt.

[0027] In addition, it is desirable that the center of the horizontal magnetic field is positioned below a central portion of the silicon single crystal, during pulling a straight body portion of the silicon single crystal, a solidification ratio is 0.4 or less, the magnetic field strength is at least 0.3 Tesla, the magnetic field strength gradually decreases when the solidification ratio is in a range of more than 0.4 to 0.6, and the magnetic field strength is set to 0.2 Tesla when the solidification ratio is more than 0.6.

[0028] Since the magnetic field strength is at least 0.3 Tesla while the straight body portion of the silicon single crystal is pulled with the solidification ratio of 0.4 or less, the flow in the silicon melt can be controlled, the oxygen concentration can be reduced, the uniformity of the oxygen concentration in the direction of the crystal growth axis of the silicon single crystal can be achieved, the fluctuation in the oxygen concentration in the substrate plane perpendicular to the crystal growth axis can be suppressed, and therefore the uniformity of the oxygen concentration in the substrate plane can be achieved.

[0029] Regarding the solidification, which varies between 0.4 and 0.6, the magnetic field strength is gradually reduced, and in particular, the magnetic field strength is set to 0.2 Tesla after the solidification ratio exceeds 0.6.

[0030] As a result, the oxygen concentration can be reduced and the uniformity of the oxygen concentration in the direction of the crystal growth axis of the silicon single crystal can be improved. Furthermore, the fluctuation or variation of the oxygen concentration in the substrate plane perpendicular to the crystal growth axis can be controlled, and the uniformity of the oxygen concentration in the substrate plane can be improved.

[0031] According to the invention, it is provided that a value calculated from an expression of (radius [mm] of a silicon single crystal / radius [mm] of the crucible) × number of revolutions [rpm] of the silicon single crystal × (magnetic field strength [Tesla] / (distance from the surface of the silicon melt to the lower end of the shielding plate) [mm]) is 0.0190 or less.

[0032] When the value obtained from the expression (radius [mm] of a silicon single crystal / radius [mm] of the crucible) × number of revolutions [rpm] of the silicon single crystal × (magnetic field strength [Tesla] / (distance from the surface of the silicon melt to the lower end of the shielding plate)) is 0.0190 or less, the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the crucible can be set to 0.16 m / s or less.

[0033] As a result, as described above, the oxygen concentration in the silicon single crystal can be reduced, and the uniformity of the oxygen concentration in the direction of the crystal growth axis and the uniformity of the oxygen concentration in the substrate plane perpendicular to the crystal growth axis can be improved.

[0034] A method for producing a silicon single crystal includes a step of growing a silicon single crystal by applying a horizontal magnetic field while pulling the silicon single crystal from a silicon melt in a quartz glass crucible, wherein a radius of the silicon single crystal, a radius of the crucible, a number of revolutions of the silicon single crystal, a magnetic field intensity or flux density, and a distance from a surface of the silicon melt to a lower end of a shielding plate are adjusted such that a value calculated from an expression of radius [mm] of the silicon single crystal / radius [mm] of the crucible × number of revolutions [rpm] of the silicon single crystal × magnetic field intensity or flux density [Tesla] / (distance from the surface of the silicon melt to the lower end of the shielding plate) [mm] is 0.190 or less.

[0035] By setting the value calculated from the expression of the radius [mm] of the silicon single crystal / radius [mm] of the crucible × the number of revolutions [rpm] of the silicon single crystal × the magnetic field strength [Tesla] / (distance from the surface of the silicon melt to the bottom of the shielding plate) [mm] to 0.190 or less, the flow rate of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible can be 0.16 m / s or less during the pulling of the silicon single crystal. As a result, the oxygen concentration in the silicon single crystal can be reduced, and the uniformity of the oxygen concentration in the direction of the crystal growth axis and the uniformity of the oxygen concentration in the substrate plane perpendicular to the crystal growth axis can be improved.

[0036] Furthermore, without measuring the flow velocity of the silicon melt, whether the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is 0.16 m / s or less can be determined by the value calculated from the expression of the radius of the silicon single crystal / radius of the crucible × rotational speed of the silicon single crystal × magnetic field strength / (distance from a surface of the silicon melt to a lower end of a shielding plate).

[0037] According to the present invention, it is possible to implement a method for producing a silicon single crystal capable of reducing an oxygen concentration, improving the uniformity of the oxygen concentration in a direction of a crystal growth axis, and improving the uniformity of the oxygen concentration in a substrate plane perpendicular to the crystal growth axis. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a schematic view illustrating a flow of silicon melt; Fig. Fig. 2 is a schematic view showing a flow of the silicon melt in a state where the silicon melt in a quartz glass crucible is different from the state in Fig. 1 is reduced; Fig. 3 is a schematic view illustrating another flow of the silicon melt; Fig. 4(a) and Fig. 4(b) are schematic views each illustrating a flow of a silicon melt when a magnetic field strength or flux density is 0.1 Tesla, where Fig. 4(a) a plan view and Fig. 4(b) is a cross-sectional view; Fig. 5(a) and Fig.5(b) are schematic views each illustrating a flow of the silicon melt when a magnetic field strength is 0.2 Tesla, where Fig. 5(a) a plan view and Fig. 5(b) is a cross-sectional view; Fig. 6(a) and Fig. 6(b) are schematic views each illustrating a flow of the silicon melt when a magnetic field strength is 0.3 Tesla, where Fig. 6(a) a plan view and Fig. 6(b) is a cross-sectional view; Fig. 7 is a schematic configuration view of a silicon single crystal pulling apparatus; Fig. Fig. 8 is a view showing changes in magnetic field strengths in Experiments 1 to 4; the Fig. 9(a) to 9(c) are views each illustrating a direction and a flow velocity of a flow on a surface of the silicon melt. Fig.9(a) is a view showing a time when a solidification ratio is 0.25 in Experiment 1 (magnetic field strength of 0.3 Tesla). Fig. Figure 9(b) is a view showing a time when the solidification ratio is 0.6 in Experiment 1 (magnetic field strength of 0.3 Tesla). Fig. 9(c) is a view showing a time when a solidification ratio is 0.6 in Experiment 2 (magnetic field strength of 0.2 Tesla); Fig. Fig. 10 is a view illustrating relationships between solidification ratios and oxygen concentrations in Experiments 1 to 4; Fig. 11 is a view illustrating relationships between solidification ratios and variations in oxygen concentrations in a direction of a crystal growth axis of a silicon single crystal in Experiments 1 to 4; the Fig. 12(a) and Fig.12(b) are views illustrating a relationship between a magnetic field strength and a fluctuation in oxygen concentration in a substrate plane perpendicular to the crystal growth axis in Experiment 2. Fig. 12(a) is a view showing measurement points. Fig. 12(b) is a view illustrating variations in oxygen concentrations in the substrate plane at each measurement point; Fig. 13 is a view showing changes in magnetic field strengths in Experiments 5 and 6; Fig. 14 is a view showing relationships between solidification ratios and variations in resistance in a direction of a crystal growth axis of a silicon single crystal in Experiments 5 and 6; and Fig. Figure 15 is a view showing relationships between positions of centers of magnetic fields and oxygen concentrations in Experiments 1 and 16 to 20. DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0038] According to the invention, a method for producing a silicon single crystal comprises a step of growing a silicon single crystal by applying a horizontal magnetic field while pulling the silicon single crystal from the silicon melt in a quartz glass crucible, wherein a flow of the silicon melt flowing from the silicon single crystal to a side wall of the quartz glass crucible is present on a surface of the silicon melt, and a flow of the silicon melt from the silicon single crystal to the side wall of the quartz glass crucible is set to 0.16 m / s or less.

[0039] In particular, the method has a feature that the flow rate of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is set to 0.16 m / s or less during pulling of the silicon single crystal.

[0040] The silicon melt in the quartz glass crucible is affected by the magnetic field strength or flux density, a magnetic field center position, a flow rate of inert gas or a furnace pressure, the number of revolutions of the quartz glass crucible, the number of revolutions of the silicon single crystal, and the like, and changes in the flow (convection) of the silicon melt in the quartz glass crucible occur.

[0041] Fig. 1 is a view showing an example of a flow of a silicon melt M in a quartz glass crucible. The reason why a flow velocity of the silicon melt M flowing from a silicon single crystal to the side wall of the quartz glass crucible is set to 0.16 m / s or less is determined based on the Fig. 1 described.

[0042] Fig.1 illustrates a result of simulating the flow of the silicon melt under a condition such that drawing is performed at a solidification ratio of 0.25 in Experiment 1, which will be described later. Fig. Figure 1 illustrates the flow of the silicon melt in a state where a magnetic field of 0.3 Tesla is applied in a horizontal direction, and the center of the horizontal magnetic field is located in the silicon melt at a position 20 mm below the free surface in a central portion of the silicon single crystal. Furthermore, B in Fig. 1 indicates that the direction of the magnetic flux is from the back of the paper surface to the front.

[0043] The silicon melt M in a quartz glass crucible 1 exhibits different flows.

[0044] For example, as shown by the arrow X1 in Fig.1, in the silicon melt a flow from top to bottom in contact with (along) a side wall 1a of the quartz glass crucible.

[0045] When the silicon melt flows into contact with (along) the sidewall 1a of the quartz glass crucible, silicon is chemically active at the melting point, and thus the silicon melt M reacts with a quartz component in the quartz glass crucible 1, dissolving the sidewall 1a of the quartz glass crucible 1. As a result, oxygen (O) is incorporated into the silicon melt.

[0046] The silicon melt M containing the oxygen rises from the bottom surface (the bottom surface of a central portion of the crucible) of the crucible below a silicon single crystal C, as indicated by the arrow X2.

[0047] Thereafter, the flow flows (meanders) outward in a radial direction of the crucible as indicated by arrow X3, the flow returns to a position below the silicon single crystal C as indicated by arrow X4, and then the flow flows from the silicon single crystal to the side wall of the crucible as indicated by arrow X5.

[0048] As described above, the side wall 1a of the quartz glass crucible 1 is dissolved, and the silicon melt M into which the oxygen (O) has been incorporated, as the silicon melt M containing a great deal of the oxygen, meanders outward in the radial direction of the crucible as it rises from the bottom surface of the quartz glass crucible 1 below the silicon single crystal C, and then reaches the free surface.

[0049] As a result, oxygen incorporated into the silicon melt 1 diffuses, the oxygen concentration in the silicon melt 1 decreases, the incorporation of oxygen into the silicon single crystal C is prevented, and thus the oxygen concentration in the silicon single crystal C is reduced.

[0050] Next, Fig. 2 shows the flow of the silicon melt M into the quartz glass crucible 1 in a state in which the silicon melt M in the quartz glass crucible 1 is reduced after the progress of pulling the silicon single crystal C compared to the state in Fig. 1. Fig. Figure 2 illustrates a result of a simulation of the flow of the silicon melt in which the drawing is carried out with the solidification ratio of 0.6 in Experiment 1 to be described below.

[0051] As in Fig.As shown in Figure 2, when the pulling of the silicon single crystal C progresses and the silicon melt in the quartz glass crucible 1 decreases, the flow, which meanders strongly outwards in the radial direction of the crucible, as shown in Fig. 1 is suppressed. Thus, a flow X2 originating from the bottom surface (the bottom surface of the central portion of the crucible) of the crucible below the silicon single crystal C becomes strong, that is, the flow velocity becomes faster.

[0052] As described above, when the silicon melt rises from the bottom surface of the crucible without meandering toward the lower end of the silicon single crystal C, the oxygen is incorporated into the silicon single crystal C before the oxygen is diffused from the silicon melt into which the oxygen is incorporated or released from the silicon melt.

[0053] This means that a large amount of oxygen O is contained in the silicon melt, rising from the bottom surface of the crucible below the silicon single crystal. When oxygen is incorporated into the silicon single crystal, the oxygen concentration cannot be reduced, and the uniformity of the oxygen concentration along the crystal growth axis is prevented.

[0054] At this time, in a case where the flow velocity X2 of the flow from the bottom surface of the crucible below the silicon single crystal is low, a flow velocity X5 of the silicon melt flowing from the silicon single crystal C to the side wall 1a of the crucible also becomes low.

[0055] In other words, in a case where the flow velocity of the flow X5 of the silicon melt flowing from the silicon single crystal to the side wall of the crucible 1a is low, the flow velocity of the flow X2 rising from a bottom surface 1b of the crucible below the silicon single crystal C is also low.

[0056] In a case where the flow velocity of the flow X2 rising from the bottom surface 1b of the crucible below the silicon single crystal C as shown in Fig.1, it takes a certain amount of time for the flow X2 to reach the silicon single crystal C from the side wall 1a of the crucible via the bottom surface of the crucible. In another case, the flow X2 ascends from the bottom surface of the crucible, then meanders outward in the radial direction of the crucible and is then incorporated into the silicon single crystal via just below the surface of the melt. Thus, the oxygen diffuses into the silicon melt. As a result, the oxygen concentration can be reduced, and the uniformity of the oxygen concentration in the direction of the crystal growth axis and the uniformity of the oxygen concentration in the substrate plane perpendicular to the crystal growth axis can be improved.

[0057] In particular, in a case where the flow velocity X5 of the silicon melt flowing from the silicon single crystal C to the side wall 1a of the crucible is 0.16 m / s or less, the oxygen concentration can be further reduced, and the fluctuation of the oxygen concentration in the direction of the crystal growth axis can be suppressed.

[0058] Furthermore, as in Fig. 3, an example of the flow of the silicon melt in the quartz glass crucible 1 also includes a flow Y1 flowing upwards from below in contact with (along) the side wall 1a of the quartz glass crucible.

[0059] Furthermore, in this case, the silicon melt reacts with the quartz component in the quartz glass crucible, and the side wall 1a of the quartz glass crucible is dissolved. As a result, oxygen is incorporated into the silicon melt.

[0060] The silicon melt flows along the side wall of the quartz glass crucible 1 and reaches the free surface. A flow Y2 is then formed, which flows from the side wall of the quartz glass crucible 1 to the silicon single crystal.

[0061] The silicon melt flow Y2 has high diffusion rates of the incorporated oxygen into the silicon melt and the release of the incorporated oxygen from the silicon melt. The silicon melt with a low oxygen concentration flows into the silicon single crystal. Only an outer peripheral portion of the silicon single crystal has a low concentration, and the in-plane distribution is thus deteriorated. Therefore, the formation of such a flow is not preferred.

[0062] Furthermore, the Fig. In the case shown in Figure 3, the flow X2 rising from the bottom surface 1b of the crucible below the silicon single crystal C is formed.

[0063] This means that the silicon melt flowing from the side wall of the quartz glass crucible to the silicon single crystal has a low oxygen concentration, and the silicon melt rising from the bottom surface of the crucible below the silicon single crystal C has a high oxygen concentration due to less diffusion and release of oxygen.

[0064] As a result, since the central portion of the silicon single crystal has a high oxygen concentration, whereas the outer peripheral portion of the silicon single crystal has a low oxygen concentration, the in-plane distribution deteriorates, and the uniformity of the oxygen concentration in the surface plane perpendicular to the crystal growth axis is prevented.

[0065] It is therefore desirable that the flow Y2 in the flow present at the surface of the silicon melt M flowing from the side wall of the crucible to the silicon single crystal does not reach the silicon single crystal.

[0066] The flow of the silicon melt in the quartz glass crucible is also influenced by the magnetic field strength or flux density. In particular, as the pulling of the silicon single crystal progresses and the silicon melt in the quartz glass crucible decreases, the flow is strongly influenced by the magnetic field strength or flux density, and the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is thereby altered.

[0067] This means that even in a case where the flow rate of the inert gas or the furnace pressure, the number of revolutions of the quartz glass crucible and the number of revolutions of the silicon single crystal are kept constant, the flow of the silicon melt in the quartz glass crucible changes accordingly due to a strength of the magnetic field strength.

[0068] For example, the Fig. 4(a) and Fig. 4(b) shows a flow of the silicon melt when a magnetic field of 0.1 Tesla is applied in a horizontal direction.

[0069] The Fig. 4(a) and Fig. 4(b) each illustrates a result of simulation of the flow of the silicon melt under a condition where drawing is carried out with the solidification ratio of 0.6 in Experiment 1 to be described later. Fig. 4(a) and Fig.4(b) each illustrates the flow of the silicon melt in a state where the magnetic field of 0.1 Tesla is applied in the horizontal direction and the center of the horizontal magnetic field is located at a position 20 mm below the free surface in the central portion of the silicon single crystal in the silicon melt.

[0070] Furthermore, the point of the symbol “◯” of B in Fig. 4(b) indicates that a direction of magnetic flux is directed from the back of the paper to the front.

[0071] Furthermore, the arrow symbol from B indicates the direction of the magnetic flux. Fig. 4(b) is the same view as in Fig. 3.

[0072] As in the Fig. 4(a) and Fig.As shown in Figure 4(b), when a magnetic field of 0.1 Tesla is used, the flow Y2 of the silicon melt is generated, flowing from the side wall of the crucible toward the silicon single crystal. The generation of such a flow is not preferred.

[0073] Since the flow X2 flowing from the bottom surface of the crucible below the silicon single crystal C becomes strong, the silicon melt with the incorporated oxygen further flows to the bottom end of the silicon single crystal and a large amount of oxygen is undesirably incorporated into the silicon single crystal.

[0074] Furthermore, the Fig. 5(a) and Fig. 5(b) each represents a case where the magnetic field strength or flux density varies from 0.1 Tesla to 0.2 Tesla in the Fig. 4(a) and Fig. 4(b) shown state.

[0075] As in the Fig. 5(a) and Fig.As shown in Figure 5(b), the oxygen-containing silicon melt meanders outward in the radial direction of the crucible (flow X3) and rises. As a result, the oxygen diffuses in the silicon melt, and the oxygen concentration can be reduced.

[0076] Furthermore, the Fig. 6(a) and Fig. 6(b) each show a case where the magnetic field strength ranges from 0.1 Tesla to 0.3 Tesla in the Fig. 4(a) and Fig. 4(b) shown state.

[0077] As in the Fig. 6(a) and Fig. As shown in Figure 6(b), the oxygen-containing silicon melt meanders outward in the radial direction of the crucible (flow X3) and rises. As a result, the oxygen diffuses in the silicon melt, and the oxygen concentration can be reduced.

[0078] Therefore, it is preferable that the magnetic field strength during pulling the silicon single crystal is at least 0.2 Tesla, and that the magnetic field strength is controlled such that the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is present on the surface of the silicon melt.

[0079] Further, in a case where a flow directed toward the silicon single crystal from the side wall of the crucible is present as a flow on the surface of the silicon melt, the melt directed toward the silicon single crystal from the side wall of the crucible is preferably controlled such that the flow does not reach the silicon single crystal.

[0080] In particular, it is preferable that the magnetic field strength is at least 0.3 Tesla when the straight body portion of the silicon single crystal is pulled with a sufficient amount of silicon melt in the quartz glass crucible at the solidification ratio of 0.4 or less.

[0081] Since a sufficient amount of silicon melt is present in the quartz glass crucible, the flow is generated which strongly meanders outwards in the radial direction of the crucible, as shown in Fig. 1. As a result, oxygen in the silicon melt diffuses strongly and is released from the silicon melt, and the oxygen concentration in the silicon single crystal can thus be reduced.

[0082] Furthermore, it is desirable that the magnetic field strength is gradually reduced when the solidification ratio is in the range of 0.4 to 0.6, and the magnetic field strength is 0.2 Tesla when the solidification ratio exceeds 0.6.

[0083] Along with the reduction of the silicon melt in the quartz glass crucible, when the magnetic field strength is gradually reduced and adjusted to 0.2 Tesla, at and after the solidification ratio of 0.6, the oxygen-containing silicon melt meanders strongly outward in the radial direction of the crucible and rises from the bottom surface of the crucible below the silicon single crystal, as shown in the Fig. 5(a) and Fig. 5(b). As a result, oxygen diffuses in the silicon melt, and the oxygen concentration can be reduced and the environment in Fig. 5(b) is similar to that in Fig.1, and subsequently the oxygen concentration becomes uniform in the direction of the crystal growth axis.

[0084] Furthermore, the condition that there is a flow of the silicon melt from the silicon single crystal to the side wall of the crucible and the flow rate of the silicon melt from the silicon single crystal to the side wall of the crucible is 0.16 m / sec or less is affected by the magnetic field strength, the control of the flow rate of the inert gas or the furnace pressure, the control of the number of revolutions of the quartz glass crucible, the control of the number of revolutions of the silicon single crystal, and the like.

[0085] The flow velocity of the silicon melt can be measured using a tracer or the like. However, when such a measurement is performed, the crystal being pulled at the moment cannot be used as the product, and the measurement requires time and effort. Therefore, the flow velocity of the silicon melt is predicted by simulation; however, this requires a large amount of calculation time, under the condition that a three-dimensional convection analysis is required for this, as is the case with a transverse magnetic field.

[0086] Then, the inventors of the present invention investigated a relational expression for easily determining a condition for setting the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the crucible to 0.16 m / s or less.

[0087] When the value obtained from the expression radius of the silicon single crystal / radius of the crucible × number of revolutions of the silicon single crystal × magnetic field strength / (distance from the surface of the silicon melt to the bottom of the shielding plate) is 0.0190 or less, it is concretely determined by three-dimensional simulation that the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the crucible can be 0.16 m / s or less.

[0088] The reason is that the value is calculated from the expression radius of the silicon single crystal / radius of the crucible × rotation speed of the silicon single crystal × magnetic field strength / (distance from the surface of the silicon melt to the bottom of the shielding plate), as follows.

[0089] A driving force of the flow flowing from the silicon single crystal to the side wall of the crucible is related to the radius of the silicon single crystal and the crucible, the rotational speed of the silicon single crystal, and the magnetic field strength.

[0090] Since a larger radius of the crucible is addressed to weaken the driving force of the flow from the silicon single crystal to the side wall of the crucible, the radius of the silicon single crystal is divided by the radius of the crucible.

[0091] Furthermore, traditionally, only the driving force is considered. However, since the ease of controlling the oxygen concentration in the melt varies depending on the distance from the surface of the silicon melt to the bottom of the shielding plate, the distance must also be considered. For example, if the distance is too narrow, controlling the oxygen concentration by the magnetic field strength becomes difficult due to the strong influence of the atmosphere in the furnace (the flow rate of Ar gas or the furnace pressure). Conversely, if the distance is wide, controlling the driving force is effective due to the strong influence of convection on the melt.

[0092] Since the influence of the number of crucible revolutions on convection is considered small, the number of crucible revolutions is not included in the relationship expression. However, if the number of crucible revolutions is reduced, a crystal with a lower oxygen concentration can be obtained. Thus, the number of crucible revolutions is preferably 1 rpm or less. Attempts 1 to 4

[0093] A silicon single crystal was treated with a Fig. 7 shown typical pulling device, under the conditions shown in Table 1 and Fig.8. The flow rate of the silicon melt flowing from the silicon single crystal to the side wall of a crucible during pulling, the oxygen concentration and its fluctuations in the direction of the crystal growth axis of the silicon single crystal, and the fluctuations in the oxygen concentration in a substrate plane perpendicular to the crystal growth axis were measured.

[0094] First, the Fig.7 will be described. The apparatus 10 includes a cylindrical chamber (chamber) 11, a crucible 12 provided in the chamber 11, and a carbon heater 13 that heats raw silicon loaded onto the crucible 12. The crucible 12 is formed of a quartz glass crucible 12a on the inside thereof and a graphite crucible 12b on the outside thereof. Further, in the chamber 11, a heat insulation tube 14 is provided on the outer periphery of the carbon heater 13. The heat insulation tube 14 is formed in a cylindrical shape, and a heat insulation plate 15 extending inward from the heat insulation tube 14 is provided at an upper portion of the heat insulation tube 14. Furthermore, a radiation shield (shielding plate) 16 is provided so that unnecessary radiant heat generated by the coal heater 13 is not applied to a silicon single crystal C which is currently being grown (pulled).

[0095] The radiation shield (shield plate) 16 is provided with openings 16a and 16b, which are provided at the upper portion and the lower portion of the radiation shield 16, respectively, above and near the crucible 12, so as to surround the periphery of the silicon single crystal C. A tapered surface 16c is formed such that an area of the opening gradually decreases from an upper portion to a lower portion of the tapered surface 16c. By providing the radiation shield 16, an inert gas (Ar gas) G for purging, which is supplied from above to inside the crucible 12, flows to the outside of the crucible 12 through a gap between the radiation shield 16 and a surface of the silicon melt M, and is finally discharged to the outside of the chamber 11.

[0096] A gap between a lower end of the radiation shield 16 and the surface of the silicon melt M is called a gap.

[0097] A magnetic field generator 17 is also provided outside the chamber 11 to apply a horizontal magnetic field. The magnetic field generated by the magnetic field generator 17 is arranged such that the center of the horizontal magnetic field in the silicon melt is positioned below a free surface at the central portion of the silicon single crystal.

[0098] The magnetic field generator 17 is further controlled to generate a magnetic field with a strength of at least 0.2 Tesla while the silicon single crystal is being pulled.

[0099] Although not shown, a pulling mechanism for pulling the silicon single crystal C is provided above the chamber 11. The pulling mechanism includes a winding mechanism driven by a motor and a pulling rope 18 to be wound by the winding mechanism. Then, a second seed crystal P is attached to one end of a tip of the rope 18, and the rope is pulled up, thereby growing the silicon single crystal C.

[0100] Although not shown, the silicon single crystal manufacturing apparatus 10 further includes a motor for rotating the crucible 12, a lifting device for controlling the height of the crucible 12, and a control device for controlling the motor and the lifting device. The apparatus 10 is configured to grow a silicon single crystal C while rotating the crucible 12 and lifting the crucible 12.

[0101] Further, although not shown, a gas supply port 11a is provided at an upper portion of the chamber 11 and supplies inert gas (Ar gas) for purging into the chamber 11. Further, a plurality of exhaust ports 11b are provided at a bottom surface of the chamber 11, and a discharge pump (not shown) as a discharge unit is connected to the exhaust port.

[0102] The inert gas (Ar gas) G for purging, which is supplied from the gas intake port into the chamber 11, flows to the outside of the crucible 12 by the exhaust pump through the gap between the radiation shield 16 and the surface of the silicon melt M, and is finally discharged to the outside of the chamber 11.

[0103] Here, the gap in Table 1 represents a gap dimension between the radiation shield 16 and the surface of the silicon melt M, SR represents the number of revolutions of the crystal, CR represents the number of revolutions of the crucible, the Ar flow rate represents a flow rate of the inert gas (Ar gas) for purging supplied into the chamber 11, and the furnace pressure represents a pressure in the chamber 11.

[0104] Furthermore, the magnetic field strength was measured under the Fig. 8, and the center of the magnetic field was at a position 20 mm below the surface of the silicon melt M.

[0105] In Experiment 1, a silicon single crystal was grown with a magnetic field strength of 0.3 Tesla.

[0106] In Experiment 2, a silicon single crystal was pulled with a magnetic field strength of 0.3 Tesla until the solidification ratio reached 0.4, the magnetic field strength was gradually decreased until the solidification ratio reached 0.7, and then the magnetic field strength was adjusted to 0.15 Tesla.

[0107] In Experiment 3, a silicon single crystal was pulled with a magnetic field strength of 0.3 Tesla until the solidification ratio reached 0.4, the magnetic field strength was gradually decreased until the solidification ratio reached 0.6, and then the magnetic field strength was adjusted to 0.2 Tesla.

[0108] In Experiment 4, a silicon single crystal was grown with a magnetic field strength of 0.3 Tesla, the magnetic field strength was gradually decreased until the solidification ratio reached 0.2, and then the magnetic field strength was adjusted to 0.2 Tesla. Table 1 parameter Attempt 1 Attempt 2 Attempt 3 Attempt 4 Gap (mm) 40 40 40 40 SR (rpm) 9 9 9 9 CR (rpm) 0,5 0,5 0,1 0,1 Ar flow rate (L / min) 100 100 100 100 Furnace pressure (Torr) 50 50 50 50 magnetic field strength or flux density (Tesla) 0,3 0,3->0,15 0,3->0,2 0,3->0,2 Magnetic field position (mm) -20 -20 -20 -20

[0109] The Fig. 9(a) to 9(c) respectively illustrate a direction and a flow velocity of the silicon melt flow during pulling in each of Experiments 1 to 4.

[0110] Fig. Figure 9(a) illustrates the direction and flow velocity of the silicon melt flow during drawing at the solidification ratio of 0.25 (0.3 Tesla: cf. Fig. 8) in Experiment 1.

[0111] Fig. Figure 9(b) illustrates the direction and flow velocity of the silicon melt flow during drawing at a solidification ratio of 0.6 (0.3 Tesla: cf. Fig. 8) in Experiment 1.

[0112] Fig. Figure 9(c) illustrates the direction and flow velocity of the silicon melt flow during drawing at a solidification ratio of 0.6 (0.2 Tesla: cf. Fig. 8) in experiment 3.

[0113] As in Fig. As shown in Figure 9(a), a maximum value of the flow velocity during drawing at the solidification ratio of 0.25 (0.3 Tesla) is in a range of 0.20 to 0.24 m / s.

[0114] Furthermore, as in Fig. 9(b), a maximum value of the flow velocity during drawing at the solidification ratio of 0.6 (0.3 Tesla) in a range of 0.20 to 0.24 m / sec.

[0115] In contrast, as in Fig. As shown in Figure 9(c), the maximum value of the flow velocity during drawing at the solidification ratio of 0.6 (0.2 Tesla) was in a range of 0.12 to 0.16 m / s.

[0116] Then, as the pulling of the silicon single crystal progresses and the silicon melt in the quartz glass crucible decreases, the maximum value of the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible can be adjusted to 0.16 m / s or less by reducing the magnetic field strength.

[0117] Furthermore, the oxygen concentration in the pulled silicon single crystal was measured using a Fourier transform infrared spectroscopy (FT-IR) method. The results are shown in Fig. 10 shown.

[0118] In Experiment 1, the oxygen concentration increases when the solidification ratio exceeds 0.6, whereas in Experiments 2, 3 and 4, the oxygen concentration does not increase when the solidification ratio exceeds 0.6, or even when the oxygen concentration increases and the oxygen concentration is lower than 1.0 × 10 18 atoms / cm3 is.

[0119] This means that as a result of applying the magnetic field of 0.3 Tesla, if the solidification ratio is more than 0.6, as in Fig. As shown in Figure 9(b), the flow velocity at the surface of the silicon melt was fast.

[0120] Accordingly, the flow that strongly meanders outward in the radial direction of the crucible does not occur, and the flow rises from the bottom surface of the crucible below the silicon single crystal, building up oxygen in the silicon single crystal. The result takes into account that the oxygen concentration increases when the solidification ratio is higher than 0.6.

[0121] Furthermore, a fluctuation ΔOi of the oxygen concentration in the direction of the crystal growth phase of the pulled silicon single crystal was measured. The measurement was performed using Fourier transform infrared spectroscopy (FT-IR) at points with an interval distance of 5 mm in the radial direction. The results are shown in Fig. 11 shown.

[0122] The fluctuation ΔOi of the oxygen concentration was calculated from an equation as follows: ΔOi=(maximum value−minimum value of the measuring points) / minimum value×100[%].

[0123] In Experiment 2, the fluctuation of oxygen concentration occurs at a solidification ratio of more than 0.7, whereas in Experiments 1, 3 and 4, no significant fluctuation of oxygen concentration was observed.

[0124] It is believed that the convection of the silicon melt becomes unstable and the fluctuation of the oxygen concentration increases due to the application of the magnetic field strength of 0.2 Tesla or less (0.15 Tesla) at the solidification ratio of more than 0.7.

[0125] Fig. Figure 12(b) illustrates a variation of the oxygen concentration in the substrate plane at the measured magnetic field strength of the Fig. 12(a) in Experiment 2.

[0126] In other words, in Experiment 2, the fluctuations of oxygen concentrations in the substrate planes cut from the silicon single crystals at the solidification ratio of 0.52 (Sample No. 1), at the solidification ratio of 0.59 (Sample No. 2), at the solidification ratio of 0.67 (Sample No. 3), and at the solidification ratio of 0.75 (Sample No. 4) were measured. The measurement was performed using the Fourier transform infrared spectroscopy (FT-IR) method at points with an interval distance of 5 mm in a radial direction. The results are shown in Fig. 12(b) illustrates this.

[0127] As can be seen from the drawings, the fluctuation of the in-plane oxygen concentration can be reduced by setting the magnetic field strength to 0.2 Tesla. Experiments 5 and 6

[0128] In experiments 5 and 6, as in Fig.As shown in Figure 13, the silicon single crystal was grown under varying magnetic field strengths. The growing conditions were as follows: In Experiment 5, the magnetic field strength was set to 0.3 Tesla, and the magnetic field strength was gradually decreased at and after the solidification ratio of 0.4, and the magnetic field strength was set to 0.2 Tesla at and after the solidification ratio of 0.6. The other conditions were the same as those of Experiment 1.

[0129] In Experiment 6, the magnetic field strength was set to 0.2 Tesla, and the magnetic field strength was gradually increased until the solidification ratio reached 0.2. Then, the magnetic field strength was gradually decreased at and after the solidification ratio reached 0.4, and the magnetic field strength was gradually decreased at and after the solidification ratio reached 0.6. The other conditions were the same as those of Experiment 1.

[0130] Then, a variation in the resistance in the substrate plane, which was pulled from the silicon single crystal, was measured. The measurement was carried out using the 4-probe measurement method at points with an interval of 5 mm in a radial direction of the silicon substrate. The results are shown in Fig. 14 shown.

[0131] Again Fig. As can be seen from Figure 14, the in-plane fluctuation in resistance is kept small by setting the magnetic field strength to 0.2 Tesla. Attempts 7 to 15

[0132] A relational expression was investigated to easily find a condition for the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible, and for the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the crucible to be 0.16 m / s or less. The flow velocity in Table 2 is a value obtained from the simulation.

[0133] That is, using the condition shown in Table 2, it was confirmed that the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible exists, and the flow velocity of the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible can be 0.16 m / s or less when a value obtained from an expression of radius of a silicon single crystal / radius of the crucible × rotational speed of the silicon single crystal × magnetic field strength / distance to the lower end of the shielding plate is 0.0190 or less.

[0134] There is a case where the flow velocity can also be 0.16 m / s or less, but this is not preferred because excellent in-plane uniformity of oxygen concentration cannot be obtained. Table 2 Radius of the crystal cry [mm] radius of the crucible cru [mm] Rotational speed of the crystal SR [rpm] Magnetic field strength [Tesla] Distance from the surface of the melt to the lower end of the shielding plate gap [mm] Result calculated from the expression Flow velocity [m / sec] Rating [< 0.0190) Attempt 7 155 394 9 0,3 55 0,01931 0,195 Bad Attempt 8 155 394 9 0,2 55 0,01287 0,142 Good Attempt 9 105 296 20 0,3 30 0,0709 0,188 Bad Attempt 10 105 296 12 0,2 50 0,01703 0,141 Good Attempt 11 155 394 8 0,3 20 0,04721 0,251 Bad Attempt 12 155 394 8 0,2 20 0,03147 0,249 Bad Attempt 13 155 394 9 0,3 40 0,02655 0,233 Bad Attempt 14 155 394 9 0,2 40 0,01770 0,152 Good Attempt 15 155 394 9 0,15 40 0,01328 0,148 mediocre

[0135] As described above, when the value obtained from the expression radius of the silicon single crystal / radius of the crucible × rotational speed of the silicon single crystal × magnetic field strength / (distance from the surface of the silicon melt to the lower end of the shielding plate) is 0.0190 or less, the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is 0.16 m / sec or less.

[0136] Consequently, it is possible to determine whether the flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is 0.16 m / s or less with the value calculated from the expression radius of the silicon single crystal / radius of the crucible × rotational speed of the silicon single crystal × magnetic field strength / (distance from the surface of the silicon melt to the bottom end of the shielding plate) without measuring the flow velocity of the silicon melt. Attempts 1 and 16 to 20

[0137] As shown in Table 3, the silicon single crystal was grown under the condition of Experiment 1, where the center of the magnetic field was located 20 mm below the melt surface, and the oxygen concentration was measured at a solidification ratio of 0.25. The measurement was performed using a Fourier transform infrared spectroscopy (FT-IR) method. The results are shown in Fig. 15 shown.

[0138] The silicon single crystal was pulled, and the oxygen concentration at the solidification ratio of 0.25 was measured under the same conditions as those of Experiment 1, except that the position of the center of the magnetic field was varied as shown in Table 3 (Experiments 16 to 20). The results are shown in Fig. 15 shown. Table 3 Attempt 1 Attempt 16 Attempt 17 Attempt 18 Attempt 19 Attempt 20 Gap (mm) 40 40 40 40 40 40 SR (rpm) 9 9 9 9 9 9 CR (rpm) 0,5 0,5 0,5 0,5 0,5 0,5 Ar flow rate (L / min) 100 100 100 100 100 100 Furnace pressure (Torr) 50 50 50 50 50 50 Magnetic field strength (T) 0,3 0,3 0,3 0,3 0,3 0,3 Magnetic field position (mm) -20 +50 0 -60 -70 -100 Oxygen concentration (×10 18 atoms / cm 3 ) 0,78 1,01 0,80 0,89 1,03 1,18

[0139] As from Fig.15, it is found that in a case where the center of the magnetic field in the silicon melt is within 60 mm below the surface of the melt (Experiments 17 and 18), the oxygen concentration is as low as less than 1.0 × 10 18 atoms / cm 3 . List of reference symbols 1 quartz glass crucible 1a Side wall of the quartz glass crucible C Silicon single crystal M silicon melt X1 Flow of the silicon melt flowing from top to bottom in contact with the side wall 1a of the quartz glass crucible X2 Flow of the silicon melt rising from the bottom surface 1b of the crucible below the silicon single crystal C X3 Flow of the silicon melt flowing outwards in the radial direction of the crucible X4 Flow of the silicon melt, which flows inwards in the radial direction of the crucible and returns below the silicon single crystal X5 Flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible at the surface of the silicon melt.

Claims

[1] A method for producing a silicon single crystal, comprising a step of growing a silicon single crystal by applying a horizontal magnetic field while pulling the silicon single crystal from a silicon melt in a quartz glass crucible, wherein a flow of the silicon melt flowing from the silicon single crystal to a side wall of the quartz glass crucible is present at a surface of the silicon melt, and a value calculated from an expression of a radius of a silicon single crystal [mm] divided by a radius of the crucible [mm] multiplied by the number of revolutions of the silicon single crystal [rpm] multiplied by the magnetic field strength [Tesla] divided by a distance from a surface of the silicon melt to a lower end of a shielding plate [mm] is 0.0190 or less, so that a flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible is 0.16 m / s or less. [2] The method for producing a silicon single crystal according to claim 1, wherein a center of the horizontal magnetic field in the silicon melt is positioned within 60 mm below a surface of the melt, and a magnetic field strength during pulling is at least 0.2 Tesla. [3] A method for producing a silicon single crystal according to claim 2, wherein the center of the horizontal magnetic field is positioned below a center of the silicon single crystal, and the magnetic field strength during the pulling of a straight section of the crystal at a solidification ratio of 0.4 or less is at least 0.3 Tesla, and the magnetic field strength is gradually reduced at the solidification ratio of 0.4 and thereafter until the solidification ratio reaches 0.6, and then the magnetic field strength is set to 0.2 Tesla at a solidification ratio of more than 0.6 and thereafter.

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