DE102020210833A1 - Process for the production of a single crystal silicon - Google Patents

Abstract

There is provided a method of manufacturing a silicon single crystal capable of lowering the oxygen concentration, realizing the uniformity of the oxygen concentration in a direction of a crystal growth axis, and realizing the uniformity of the oxygen concentration in a substrate plane perpendicular to the axis. The method for producing a silicon single crystal comprises a growth step of the silicon single crystal with application of a horizontal magnetic field while pulling the silicon single crystal from the silicon melt in a quartz glass crucible, wherein a center of the magnetic field in the melt is below a free surface in a central section of the Crystal is positioned, a magnetic field strength during pulling is at least 2000 Gauss, a flow of the melt flowing from the crystal to a side wall of the crucible is present on a surface of the melt, and a flow velocity of the melt 0.16 m / s or less.

Description

TECHNICAL BACKGROUND

Field of the invention

The present invention relates to a method of manufacturing a silicon single crystal, and more particularly, to a method of manufacturing a silicon single crystal capable of decreasing an oxygen concentration, improving the uniformity of the oxygen concentration in a direction of a crystal growth axis, and also the uniformity to improve the oxygen concentration in a substrate plane perpendicular to the crystal growth plane.

Description of the related art

A silicon substrate obtained by a conventional Czochralski method (CZ method) and having a relatively high oxygen concentration (≥ 1.0 × 10 ¹⁸ atoms / cm ³ ) has been mainly used for the getter effect, but is used in a complementary one Metal oxide semiconductor (CMOS) image sensors ^{require a substrate that is low in oxygen (<1.0 × 10 18} atoms / cm ³ ) in order to reduce a white defect.

The silicon substrate is made of a silicon single crystal. As a method for producing a silicon single crystal, the use of the Czochralski method (CZ method) for pulling a silicon single crystal and at the same time growing the single crystal from a silicon melt in a quartz glass crucible is widely used.

In the method of manufacturing the silicon single crystal, a method of adjusting an oxygen concentration in the silicon single crystal using a magnetic field application method for controlling convection as in FIG JP-B-58-50953 , JP-A-2000-264784 , or the JP-A-04-31386 discloses 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 in FIG JP 9-142990 A or a method of controlling the rotation of a silicon single crystal as disclosed in FIG JP 2005-145724 A disclosed, known.

However, although the method of adjusting an oxygen concentration in the silicon single crystal is used, the oxygen concentration is higher in the latter and second half portions (in the last and second half stages of pulling) 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.

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 a side wall of the quartz glass crucible, and therefore oxygen is built into the silicon melt. Thus, if the oxygen is built into the silicon single crystal before the oxygen built into the silicon melt diffuses into the silicon melt or is released to the outside of the melt, the oxygen concentration in the silicon single crystal increases.

Accordingly, it is necessary to control the flow (convection) in the silicon melt so that the oxygen built into the silicon melt is diffused or released before the oxygen is built into the silicon single crystal.

With regard to 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 to be controlled.

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 the pulling) of the straight body portion of the silicon single crystal increases. Therefore, the uniformity of the oxygen concentration in the direction of the crystal growth axis of the silicon single crystal cannot be achieved.

In order to solve such problems, JP-A-04-31386 proposes reducing a magnetic field strength or flux density from 3000 Gauss to 2000 Gauss, 1000 Gauss and 500 Gauss when the silicon single crystal is pulled, that is, while the The amount of silicon melt contained in the quartz glass crucible is decreased.

However, if the magnetic field strength or flux density is reduced from 3000 Gauss to 2000 Gauss, 1000 Gauss and 500 Gauss and a magnetic field becomes weak, technical problems arise in such a way that the fluctuation of the oxygen concentration in the substrate plane increases perpendicular to the crystal growth axis and the uniformity of the oxygen concentration in the surface plane is thus inhibited.

In order to solve such problems, the present inventors made extensive studies to lower 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.

In these studies, the inventors of the present invention paid attention to the flow on the surface of the silicon melt. The inventors have found that an oxygen concentration can be decreased and further, uniformity of the oxygen concentration in the direction of the crystal growth axis can be achieved 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 less is. As a result, the inventors have completed the present invention.

DISCLOSURE OF THE INVENTION

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

A method for producing a silicon single crystal comprises a growth step of a silicon single crystal by pulling from a silicon melt in a quartz glass crucible while applying 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 at a Surface of the silicon melt exists, and a flow speed 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.

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, an oxygen concentration in the silicon single crystal can be decreased, and uniformity of oxygen concentration in the direction of the crystal growth axis and uniformity of oxygen concentration in a substrate plane perpendicular to the crystal growth axis can be achieved.

An example of the flow of the silicon melt on the surface of the silicon melt includes a flow that flows from the silicon single crystal to the side wall of the quartz glass crucible, flows down in contact with (along) the side wall of the quartz glass crucible, and then rises from a bottom surface of the quartz glass crucible .

When the silicon melt flows in contact with the side wall of the quartz glass crucible, the silicon is chemically active at a melting point, and thus the silicon melt reacts with a quartz component in the quartz glass crucible and thus the side wall of the quartz glass crucible dissolves. As a result, oxygen (O) is built into the silicon melt.

Then, if the oxygen has been incorporated into the silicon single crystal before the oxygen is released from the silicon melt or diffuses, the oxygen concentration in the silicon single crystal increases.

This means that when the flow that flows from the silicon single crystal to the side wall of the quartz glass crucible becomes faster, the flow that rises from the bottom surface of the quartz glass crucible, also gets faster. As a result, the degree of oxygen incorporation into the silicon single crystal may increase before the oxygen is released from the silicon melt and diffuses into the silicon melt.

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 can be built into the silicon single crystal. Therefore, the flow rate of more than 0.16 m / s is not preferable.

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 2000 Gauss.

If the magnetic field strength or flux density is less than 2000 Gauss, it is difficult to control the flow of the silicon melt. In particular, when the magnetic field is a weak magnetic field, a fluctuation in 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 cannot be achieved. Therefore, a weak magnetic field is not preferred.

When the magnetic field strength is more than 4,000 gauss, the flow speed of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible becomes 0.16 m / s or higher. And the melt with high concentration of oxygen reaches the crystal. Ultimately, a stronger magnetic field greater than 4,000 gauss is not preferred. Therefore, the magnetic field strength is preferably in a range from 2000 Gauss to 4000 Gauss.

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

In addition, it is desirable that the center of the horizontal magnetic field is positioned below a central portion of the silicon single crystal, while 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 3000 Gauss 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 2000 gauss when the solidification ratio is more than 0.6.

Since the magnetic field strength is at least 3000 Gauss while pulling the straight body portion of the silicon single crystal with the solidification ratio of 0.4 or less, the flow in the silicon melt can be controlled, the oxygen concentration can be decreased, the uniformity of the oxygen concentration in the 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.

Regarding the solidification varying between 0.4 and 0.6, the magnetic field strength is gradually decreased, and more specifically, the magnetic field strength is set to 2000 gauss after the solidification ratio exceeds 0.6.

As a result, the oxygen concentration can be decreased, the uniformity of the oxygen concentration in the direction of the crystal growth axis of the silicon single crystal can be improved. Further, the fluctuation in 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.

In addition, it is desirable that a value obtained 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 [Gauss] / (Distance to the surface of the silicon melt to the lower end of the shield plate) [mm]) is 190 or less.

If 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 [Gauss] / (distance to the surface of the silicon melt to the lower end of the shield plate) is 190 or less, the flow rate of the flow 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.

As a result, as described above, the oxygen concentration in the silicon single crystal can be decreased, 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.

A method for producing a silicon single crystal comprises a growth step of a silicon single crystal with application of a horizontal magnetic field when 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 strength 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 derived from an expression of the radius [mm] of the silicon single crystal / radius [mm ] of the crucible × number of revolutions [rpm] of the silicon single crystal × magnetic field strength or flux density [Gauss] / (distance from the surface of the silicon melt to the lower end of the shielding plate) [mm] is 190 or less.

By the value obtained from the expression of the radius [mm] of the silicon single crystal / radius [mm] of the crucible × number of revolutions [rpm] of the silicon single crystal × magnetic field strength [Gauss] / (distance from the surface of the silicon melt to the lower End of shield plate) [mm] is set to be 190 or less, the flow rate of silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible may be 0.16 m / s or less during the Silicon single crystal is pulled. As a result, the oxygen concentration in the silicon single crystal can be decreased, 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.

Further, without measuring the flow rate of the silicon melt, it can be determined whether the flow rate of the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is 0.16 m / s or less by the value which can be 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).

According to the present invention, it is possible to implement a method of manufacturing a silicon single crystal capable of lowering an oxygen concentration, improving the uniformity of the oxygen concentration in a direction of a crystal growth axis, and the uniformity of the oxygen concentration in a substrate plane to improve perpendicular to the crystal growth axis.

Figure list

• 1 Fig. 13 is a schematic view illustrating a flow of silicon melt;
• 2 FIG. 13 is a schematic view showing a flow of silicon melt in a state where silicon melt in a quartz glass crucible is opposite to the state in FIG 1 is decreased;
• 3 Fig. 13 is a schematic view illustrating another flow of the silicon melt;
• 4 (a) and 4 (b) are schematic views each showing a flow of silicon melt when a magnetic field strength or flux density is 1000 gauss, wherein 4 (a) a top view and 4 (b) is a cross-sectional view;
• 5 (a) and 5 (b) are schematic views each showing a flow of silicon melt when a magnetic field strength is 2000 gauss, wherein 5 (a) a top view and 5 (b) Fig. 3 is a cross-sectional view;
• 6 (a) and 6 (b) are schematic views each showing a flow of silicon melt when a magnetic field strength is 3000 gauss, wherein 6 (a) a top view and 6 (b) Fig. 3 is a cross-sectional view;
• 7th Fig. 13 is a schematic configuration view of a silicon single crystal pulling device;
• 8th Fig. 13 is a view showing changes in magnetic field strengths in Experiments 1 to 4;
• the 9 (a) to 9 (c) are views each showing a direction and a flow speed of a flow on a surface of the silicon melt. 9 (a) Fig. 13 is a view showing a point of time when a solidification ratio in Experiment 1 is 0.25 (magnetic field strength of 3000 Gauss). 9 (b) Fig. 13 is a view showing a point of time when the solidification ratio in Experiment 1 is 0.6 (magnetic field strength of 3000 Gauss). 9 (c) Fig. 13 is a view showing a point of time when a solidification ratio in Experiment 2 is 0.6 (magnetic field strength of 2000 Gauss);
• 10 Fig. 13 is a view illustrating relationships between solidification ratios and oxygen concentrations in Experiments 1 to 4;
• 11 Fig. 13 is a view illustrating relationships between solidification ratios and fluctuations in oxygen concentrations in a direction of a crystal growth axis of a silicon single crystal in Experiments 1 to 4;
• the 12 (a) and 12 (b) 12 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) Fig. 3 is a view showing measurement points. 12 (b) Fig. 13 is a view illustrating fluctuations in the oxygen concentration in the substrate plane at each measurement point;
• 13th Fig. 3 is a view showing changes in magnetic field strengths in Experiments 5 and 6;
• 14th Fig. 13 is a view showing relationships between solidification ratios and fluctuations in resistance in a direction of a crystal growth axis of a silicon single crystal in Experiments 5 and 6; and
• 15th Fig. 13 is a view showing relationships between positions of centers of magnetic fields and oxygen concentrations in Experiments 1 and 16-20.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

According to the invention, a method for producing a silicon single crystal comprises a growth step of a silicon single crystal with the application of a horizontal magnetic field when 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 flows, exists 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.

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 reduced to 0.16 m / sec. or less is set while pulling the silicon single crystal.

The silicon melt in the quartz glass crucible is influenced by the magnetic field strength, 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 occur in the flow (convection) of the silicon melt in the quartz glass crucible.

1 Fig. 13 is a view showing an example of a flow of silicon melt M. shows in a quartz glass crucible. The reason that a flow rate of 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 based on the 1 described.

1 Fig. 11 illustrates a result of simulation of the flow of 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. 1 Fig. 10 illustrates the flow of silicon melt in a state where a magnetic field of 3000 Gauss is applied in a horizontal direction, and the center of the horizontal magnetic field is in the silicon melt at a position 20 mm below the free one Surface in a central section of the silicon single crystal. Furthermore, B gives in 1 indicates that the direction of magnetic flux is from the back of the paper surface to the front.

The silicon melt M. in a quartz glass crucible 1 has different currents.

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

When the silicon melt is in contact with (along) the side wall 1a of the quartz glass crucible flows, silicon is chemically active at the melting point, and thus the silicon melt reacts M. with a quartz component in the quartz glass crucible 1 and the side wall 1a of the quartz glass crucible 1 thus dissolves. As a result, oxygen (O) is built into the silicon melt.

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. on, as by the arrow X2 indicated.

Thereafter, the flow flows (meanders) outwards in a radial direction of the crucible, as indicated by the arrow X3 indicated, the current is reversing, as indicated by the arrow X4 indicated to a position below the silicon single crystal C. back, and then the current flows, as through the arrow X5 indicated, from the silicon single crystal to the side wall of the crucible.

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

As a result, oxygen built into the silicon melt 1 diffuses, the oxygen concentration in the silicon melt 1 decreases, and the build-up of oxygen into the silicon single crystal C. is suppressed, and thus the oxygen concentration in the silicon single crystal becomes C. decreased.

Next illustrated 2 the flow of silicon melt M. in the quartz glass crucible 1 in a state in which the silicon melt M. in the quartz glass crucible 1 is decreased after the pulling of the silicon single crystal proceeds C. compared to the state in 1 . 2 Fig. 10 illustrates a result of simulating the flow of the silicon melt in which drawing is carried out with the solidification ratio of 0.6 in Experiment 1 to be described below.

As in 2 is shown when pulling the silicon single crystal C. progresses and the silicon melt in the quartz glass crucible 1 reduces the flow, which meanders strongly outward in the radial direction of the crucible, as in 1 shown prevented. Thus becomes a current X2 from the bottom surface (the bottom surface of the central portion of the crucible) of the crucible below the silicon single crystal C. strong, ie the flow speed becomes faster.

As described above, when the molten silicon rises from the bottom surface of the crucible without moving toward the lower end of the silicon single crystal C. to meander, the oxygen in the silicon single crystal C. built in before the oxygen diffuses from the silicon melt into which the oxygen is incorporated or is released from the silicon melt.

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 the oxygen is incorporated into the silicon single crystal, the oxygen concentration cannot be decreased and the uniformity of the oxygen concentration in the direction of the crystal growth axis is prevented.

This is done in a case where the flow velocity of the flow X2 that is low from the bottom surface of the crucible below the silicon single crystal, a flow rate X5 the silicon melt by the silicon single crystal C. to the side wall 1a of the crucible flows, also low.

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

In a case where the flow velocity of the flow X2 from the bottom surface 1b of the crucible below the silicon single crystal C. ascends, as in 1 shown is low, it takes time for the flow X2 the silicon single crystal C. from the side wall 1a of the crucible has reached over the bottom surface of the crucible. In another case the current increases X2 from the bottom surface of the crucible, and then the flow meanders X2 outwards in the radial direction of the crucible and is then built into the silicon single crystal just below the surface of the melt. The oxygen thus diffuses into the silicon melt. As a result, the oxygen concentration can be decreased, 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.

Especially in a case where the flow velocity of the flow X5 the silicon melt by 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 decreased, and the fluctuation in the oxygen concentration in the direction of the crystal growth axis can be suppressed.

Furthermore, as in 3 shown an example of the flow of silicon melt in the quartz glass crucible 1 also a flow Y1 coming into contact with (along) the sidewall from below 1a of the quartz glass crucible flows upwards.

Further, 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 built into the silicon melt.

The silicon melt flows along the side wall of the quartz glass crucible 1 and reaches the free surface. Thereafter, a flow Y2 is formed from the side wall of the quartz glass crucible 1 flows to the silicon single crystal.

The flow Y2 of the silicon melt has high degrees of diffusion of the built-in oxygen into the silicon melt and the release of the built-in 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, it is not preferable to form such a flow.

Furthermore, in the in 3 the case shown is the flow X2 from the bottom surface 1b of the crucible below the silicon single crystal C. rises, formed.

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 that the silicon melt flowing from the bottom surface of the crucible below the silicon single crystal C. rises, has a high oxygen concentration due to less diffusion and release of oxygen.

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.

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

The flow of the silicon melt in the quartz glass crucible is also influenced by the magnetic field strength or flux density. In particular, when the pulling of the silicon single crystal proceeds and the silicon melt in the quartz glass crucible decreases, the flow becomes strong by the magnetic one The field strength or flux density is influenced, and the flow of the silicon melt, which flows from the silicon single crystal to the side wall of the crucible, is changed as a result.

That is, 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 silicon melt in the quartz glass crucible due to a strength of magnetic field strength changed accordingly.

For example, the 4 (a) and 4 (b) each a flow of silicon melt when a magnetic field of 1000 Gauss is applied in a horizontal direction.

The 4 (a) and 4 (b) each illustrate a result of simulating the flow of silicon melt under a condition that drawing is performed with the solidification ratio of 0.6 in Experiment 1 to be described later. The 4 (a) and 4 (b) each illustrate the flow of silicon melt in a state where the magnetic field of 1000 Gauss is applied in the horizontal direction and the center of the horizontal magnetic field is at a position 20 mm below the free surface in the central portion of the silicon single crystal in the silicon melt .

Furthermore, the point of the symbol “o” of B indicates in 4 (b) indicates that a direction of magnetic flux is directed from the back of the paper to the front. Furthermore, the arrow symbol from B indicates the direction of the magnetic flux. 4 (b) is the same view as in 3 .

As in the 4 (a) and 4 (b) As shown, when a magnetic field has 1000 Gauss, the flow Y2 of the silicon melt flowing from the side wall of the crucible to the silicon single crystal is generated. Generating such a flow is not preferred.

As the current X2 from the bottom surface of the crucible below the silicon single crystal C. becomes strong, the silicon melt with the built-in oxygen further flows to the lower end of the silicon single crystal, and a large amount of oxygen is undesirably built into the silicon single crystal.

Furthermore, the 5 (a) and 5 (b) each represents a case in which the magnetic field strength or flux density from 1000 Gauss to 2000 Gauss in the in 4 (a) and 4 (b) shown fluctuates.

As in the 5 (a) and 5 (b) shown, the oxygen-containing silicon melt meanders in the radial direction of the crucible (the flow X3 ) outwards and rises. As a result, the oxygen diffuses in the silicon melt, and the oxygen concentration can be decreased.

Also illustrate the 6 (a) and 6 (b) in each case a case in which the magnetic field strength is from 1000 Gauss to 3000 Gauss in the in the 4 (a) and 4 (b) shown fluctuates.

As in the 6 (a) and 6 (b) shown, the oxygen-containing silicon melt meanders outwards 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 decreased.

Therefore, it is preferable that the magnetic field strength during the pulling of the silicon single crystal is at least 2000 Gauss, 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 opens the surface of the silicon melt is present.

Further, in a case where there is a flow directed toward the silicon single crystal from the side wall of the crucible as a flow on the surface of the silicon melt, the melt directed from the side wall of the crucible toward the silicon single crystal is preferred controlled so that the flow does not reach the silicon single crystal.

In particular, it is preferable that the magnetic field strength is at least 3000 Gauss 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.

Since there is a sufficient amount of the silicon melt in the quartz glass crucible, the flow is generated which meanders greatly outward in the radial direction of the crucible, as in FIG 1 shown. in the As a result, the oxygen in the silicon melt diffuses greatly and is released from the silicon melt, and the oxygen concentration in the silicon single crystal can thus be decreased.

Further, it is desirable that the magnetic field strength is gradually decreased when the solidification ratio is in the range of 0.4 to 0.6, and the magnetic field strength is 2000 gauss when the solidification ratio exceeds 0.6.

Along with the reduction in the silicon melt in the quartz glass crucible, if the magnetic field strength is gradually reduced and set to 2000 Gauss, 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 in the 5 (a) and 5 (b) shown. As a result, the oxygen diffuses in the silicon melt, and the oxygen concentration can be reduced and the environment in 5 (b) becomes similar to that in 1 , and as a result, the oxygen concentration becomes uniform in the direction of the crystal growth axis.

Further, 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 speed of the silicon melt flowing from the silicon single crystal to the side wall of the crucible becomes 0.16 m / sec. or less is influenced 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.

The flow rate of the silicon melt can be measured with a tracer or the like. However, when such measurement is performed, the crystal that is currently being pulled cannot be used as a product, and the measurement takes time and effort. Therefore, the flow velocity of the silicon melt is predicted by means of simulation; however, it takes a large amount of time for calculation on a condition that three-dimensional convection analysis is required therefor as a case of a transverse magnetic field.

Then, the inventors of the present invention studied a relational expression for easily finding a condition for setting the flow rate of the silicon melt flowing from the silicon single crystal to the side wall of the crucible to 0.16 m / s or less.

When the value derived 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 lower end of the shielding plate) is 190 or less, it is concretely represented by three-dimensional Simulation determines 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.

Here, the reason why the value is calculated from the expression radius of silicon single crystal / radius of crucible × rotational speed of silicon single crystal × magnetic field strength / (distance from the surface of the silicon melt to the lower end of the shielding plate) is as follows.

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.

Here, since a larger radius of the crucible is addressed in order 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.

Further, only the driving force is usually considered, but since the ease of controlling the oxygen concentration in the melt changes depending on the distance from the surface of the silicon melt to the lower end of the shielding plate, it is also necessary to consider the distance. For example, if the distance is too narrow, the control of the oxygen concentration by the magnetic field strength becomes difficult due to the strong influence due to the atmosphere in the furnace (a flow rate of Ar gas or the furnace pressure). On the other hand, when the distance is wide, control of the driving force is effective due to the strong influence of convection on the melt.

Since the influence of the number of revolutions of the crucible on the convection is considered to be small, the number of revolutions of the crucible is therefore not included in the relational expression. However, if the number of revolutions of the crucible is decreased, a crystal having a lower oxygen concentration can be obtained. Thus, the number of revolutions of the crucible is preferably 1 rpm or less.

Trials 1 to 4

A silicon single crystal was made with a like in 7th typical pulling device shown, among those in Tables 1 and 8th conditions shown. The flow velocity of the silicon melt flowing from the silicon single crystal to the side wall of a crucible during pulling, the oxygen concentration and fluctuations thereof 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 became measured.

First the in 7th shown pulling device described. The apparatus 10 has a cylindrical chamber (chamber) 11, a crucible 12 provided in the chamber 11, and a coal heater 13 that heats raw silicon loaded on the crucible 12. The crucible 12 is formed from a quartz glass crucible 12a on the inside thereof and a graphite crucible 12b on the outside thereof. Furthermore, a heat insulation tube 14 is provided on the outer circumference of the coal heater 13 in the chamber 11. The heat insulation pipe 14 is formed in a cylindrical shape, and a heat insulation plate 15 that extends inward from the heat insulation pipe 14 is provided on an upper portion of the heat insulation pipe 14. Furthermore, a radiation protection (shielding plate) 16 is provided so that no unnecessary radiant heat, which is generated by the coal heater 13, onto a silicon single crystal C. that is currently growing (being pulled).

The radiation shield (shield plate) 16 is provided with openings 16a and 16b provided at the upper portion and the lower portion of the radiation shield 16 above and in the vicinity of the crucible 12, respectively, around the periphery of the silicon single crystal C. to surround. A conical surface 16c is formed such that an area of the opening gradually decreases from an upper portion to a lower portion of the conical 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 through a gap between the radiation shield 16 and a surface of the silicon melt M. to the outside of the crucible 12 and is ultimately diverted to the outside of the chamber 11.

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

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

The magnetic field generator 17 is further controlled in such a way that it generates a magnetic field with a strength of at least 2000 Gauss while the silicon single crystal is being pulled.

Although not shown, a pulling mechanism for pulling the silicon single crystal is located above the chamber 11 C. intended. The pulling mechanism includes a winding mechanism driven by a motor and a pull 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 becoming the silicon single crystal C. bred.

Further, although not shown, the silicon single crystal manufacturing apparatus 10 includes a motor for rotating the crucible 12, a lifting device for controlling a height position of the crucible 12, and a control device for controlling the motor and the lifting device. The device 10 is designed to be a silicon single crystal C. to grow while rotating the crucible 12 and lifting the crucible 12.

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) into the chamber 11 for purging. Furthermore, a variety of Outlet port 11b is provided on a bottom surface of the chamber 11, and an outlet pump (not shown) as an outlet unit is connected to the outlet port.

The inert gas (Ar gas) G for purging, which is supplied from the gas supply port into the chamber 11, flows to the outside of the crucible 12 through the discharge pump through the gap between the radiation shield 16 and the surface of the silicon melt M. , and is finally diverted to the outside of the chamber 11.

The gap in Table 1 represents a gap dimension between the radiation protection 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 chamber 11.

Furthermore, the magnetic field strength under the in 8th condition shown varied, and the center of the magnetic field was at a position 20 mm below the surface of the silicon melt M. .

In experiment 1, a silicon single crystal was pulled with a magnetic field strength of 3000 Gauss.

In Experiment 2, a silicon single crystal was pulled at a magnetic field strength of 3000 Gauss 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 1500 Gauss .

In Experiment 3, a silicon single crystal was pulled at a magnetic field strength of 3,000 Gauss 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 set to 2,000 Gauss .

In Experiment 4, a silicon single crystal was pulled at a magnetic field strength of 3000 Gauss, the magnetic field strength was gradually decreased until the solidification ratio reached 0.2, and then the magnetic field strength was set to 2000 Gauss. 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 (G) 3000 3000-> 1500 3000-> 2000 3000-> 2000 Magnetic field position (mm) -20 -20 -20 -20

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

9 (a) illustrates the direction and the flow rate of the flow of the silicon melt during the pulling at the solidification ratio of 0.25 (3000 Gauss: cf. 8th ) in experiment 1.

9 (b) illustrates the direction and the flow velocity of the flow of the silicon melt during the drawing at a solidification ratio of 0.6 (3000 Gauss: cf. 8th ) in experiment 1.

9 (c) illustrates the direction and the flow speed of the flow of the silicon melt during the drawing at a solidification ratio of 0.6 (2000 Gauss: cf. 8th ) in experiment 3.

As in 9 (a) As shown, a maximum value of the flow velocity during pulling at the solidification ratio of 0.25 (3000 Gauss) is in a range of 0.20 to 0.24 m / sec.

Furthermore, as in 9 (b) is shown a maximum value of the flow velocity during drawing at the solidification ratio of 0.6 (3000 Gauss) in a range of 0.20 to 0.24 m / sec.

In contrast, as in 9 (c) shown, the maximum value of the flow velocity during drawing at the solidification ratio of 0.6 (2000 Gauss) in a range of 0.12 to 0.16 m / sec.

Then, as the pulling of the silicon single crystal proceeds and the silicon melt in the quartz glass crucible decreases, the maximum value of the flow rate of the silicon melt flowing from the silicon single crystal to the side wall of the quartz glass crucible can be increased to 0.16 m / sec. or less by decreasing the magnetic field strength.

Further, an oxygen concentration in the pulled silicon single crystal was measured by a Fourier transform infrared spectroscopy (FT-IR) method. The results are in 10 shown.

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 / cm ³ .

That is, as a result of applying the magnetic field of 3000 gauss, when the solidification ratio is more than 0.6, as in FIG 9 (b) demonstrated that the flow velocity at the surface of the silicon melt was fast.

Accordingly, the flow which meanders strongly 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 and oxygen is built up in the silicon single crystal. As a result, it is considered that the oxygen concentration increases when the solidification ratio is higher than 0.6.

Furthermore, a fluctuation ΔOi in the oxygen concentration in the direction of the crystal growth phase of the pulled silicon single crystal was measured. The measurement was carried out by means of the Fourier transform infrared spectroscopy method (FT-IR) at points with an interval spacing of 5 mm in the radial direction. The results are in 11 shown.

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

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

It is believed that the convection of the silicon melt becomes unstable and the fluctuation in the oxygen concentration due to the application of the magnetic field strength of 2000 gauss or less (1500 gauss) increases when the solidification ratio is more than 0.7.

12 (b) illustrates a fluctuation in the oxygen concentration in the substrate plane with the measured magnetic field strength of the 12 (a) in experiment 2.

In other words, in Experiment 2, the fluctuations in the oxygen concentrations in the substrate planes cut out from the silicon single crystals obtained at the solidification ratio of 0.52 (sample No. 1) and 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). The measurement was carried out by the Fourier transform infrared spectroscopy method (FT-IR) at points with an interval distance of 5 mm in a radial direction. The results are in 12 (b) illustrated.

As can be seen from the drawings, the fluctuation in the in-plane oxygen concentration can be reduced by setting the magnetic field strength to 2000 Gauss.

Experiment 5 and 6

• In Versuch 5 wurde die magnetische Feldstärke auf 3000 Gauß eingestellt, und die magnetische Feldstärke wurde schrittweise bei und nach dem Erstarrungsverhältnis von 0,4 verringert, und die magnetische Feldstärke wurde auf 2000 Gauß bei und nach dem Erstarrungsverhältnis von 0,6 eingestellt. Die anderen Bedingungen sind die gleichen wie jene des Versuchs 1.

In experiments 5 and 6, as in 13th shown, the silicon single crystal is pulled with fluctuating magnetic field strength. The drawing conditions were as follows:

• In Experiment 5, the magnetic field strength was set to 3000 gauss, 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 2000 gauss at and after the solidification ratio of 0.6. The other conditions are the same as those of Experiment 1.

In Experiment 6, the magnetic field strength was set to 2000 gauss, and the magnetic field strength was gradually increased until the solidification ratio reached 0.2, and then the magnetic field strength was gradually decreased at and after the solidification ratio of 0.4 and the magnetic field strength was gradually decreased at and after the solidification ratio of 0.6. The other conditions are the same as those of Experiment 1.

Then, a fluctuation in resistance in the substrate plane pulled from the pulled silicon single crystal was measured. The measurement was measured by the 4-probe measuring method at points with an interval distance of 5 mm in a radial direction of the silicon substrate. The results are in 14th shown.

Again 14th can be seen, the level-internal fluctuation in resistance is kept small by setting the magnetic field strength to 2000 Gauss.

Attempts 7 to 15

A relational expression to easily find a condition that the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible exists and that the flow speed of the flow of the silicon melt flowing from the silicon single crystal toward the side wall of the crucible flows, 0.16 m / sec. or less has been examined. The flow rate in Table 2 is a value obtained from the simulation.

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 and the flow velocity of the flow of the silicon melt flowing from the silicon single crystal to exist flowing through the side wall of the crucible can be 0.16 m / s or less if a value derived from an expression of the radius of a silicon single crystal / radius of the crucible × speed of the silicon single crystal × magnetic field strength / distance to the lower end of the Shield plate is 190 or less.

There is a case where the flow velocity may be 0.16 m / s or less, but it is not preferable 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] Speed of the crystal SR [rpm] Magnetic field strength [Gauss] 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] Evaluation [<190) Trial 7 155 394 9 3000 55 193.1 0.195 Bad Attempt 8 155 394 9 2000 55 128.7 0.142 Good Attempt 9 105 296 20th 3000 30th 709.5 0.188 Bad Attempt 10 105 296 12th 2000 50 170.3 0.141 Good Attempt 11 255 394 8th 3000 20th 472.1 0.251 Bad Attempt 12 155 394 8th 2000 20th 314.7 0.249 Bad Trial 13 155 394 9 3000 40 265.5 0.233 Bad Attempt 14 155 394 9 2000 40 177.0 0.152 Good Attempt 15 155 394 9 1500 40 132.8 0.148 mediocre

As described above, when the value obtained from the expression radius of silicon single crystal / radius of crucible × rotation speed of silicon single crystal × magnetic field strength / (distance from the surface of the silicon melt to the lower end of the shielding plate) is 190 or less, the flow velocity of the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible, 0.16 m / sec. or less.

As a result, it is possible to determine whether the flow speed of the flow of the silicon melt flowing from the silicon single crystal to the side wall of the crucible is 0.16 m / sec. or less, with the value 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 lower end of the shielding plate) without the flow rate of the Measure silicon melt.

Trials 1 and 16 to 20

As shown in Table 3, the silicon single crystal was pulled under the condition of Experiment 1 in which the center of the magnetic field was at the position 20 mm below the surface of the melt, and the oxygen concentration at the solidification ratio became 0.25 measured. The measurement was carried out by a Fourier transform infrared spectroscopic method (FT-IR). The results are in 15th shown.

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 as shown in Table 3 (Experiments 16 to 20 ) was varied. The results are in 15th 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 (G) 3000 3000 3000 3000 3000 3000 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

How out 15th As can be seen, 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 (Trials 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 silicon melt, from top to bottom in contact with the side wall 1a of the quartz glass crucible flows

X2

Flow of the silicon melt coming from the bottom surface 1b of the crucible below the silicon single crystal C. ascends

X3

Flow of the silicon melt, which flows outward in the radial direction of the crucible

X4

Flow of the silicon melt, which flows inward in the radial direction of the crucible and returns below the silicon single crystal

X5

Flow of the silicon melt, which flows [from] the silicon single crystal to the side wall of the crucible on the surface of the silicon melt.

QUOTES INCLUDED IN THE DESCRIPTION

This list of the documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent literature cited

• JP 58050953 B [0004]
• JP 2000264784 A [0004]
• JP 4031386 A [0004]
• JP 9142990 A [0004]
• JP 2005145724 A [0004]

Claims (5)

A method for producing a silicon single crystal, comprising a growing step of 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 on a surface of the silicon melt, and a flow speed 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. 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 in a range of 60 mm below a surface of the melt, and a magnetic field strength during the pulling is at least 2000 Gauss. 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 drawing of a straight portion of the crystal at a solidification ratio of 0.4 or less is at least 3000 Gauss, and the magnetic field strength at the solidification ratio is gradually decreased from 0.4 and thereafter until the solidification ratio reaches 0.6, and then the magnetic field strength is set to 2000 gauss at a solidification ratio of more than 0.6 and thereafter. Method for producing a silicon single crystal according to Claim 1 , where a value obtained 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 [Gauss] divided by a distance from a surface of the silicon melt to a lower end of a shield plate [mm] is calculated to be 190 or less. A method for producing a silicon single crystal, comprising a growth step of the silicon single crystal with application of a horizontal magnetic field when pulling the silicon single crystal from a silicon melt into a quartz glass crucible, wherein during a pulling step of a silicon single crystal the radius of the silicon single crystal, the radius of the crucible, the number of revolutions of the silicon single crystal, the magnetic field strength and the distance from the surface of the silicon melt to the lower end of the shielding plate are adjusted such that the value obtained from an expression of the radius of the silicon single crystal [mm] divided by the radius of the crucible [mm] multiplied by the number of revolutions of the silicon single crystal [rpm] multiplied by the magnetic field strength [Gauss] divided by the distance from the surface of the silicon melt to the lower end of the shielding plate [mm] is calculated, 190 or less.

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