JP4844429B2 - Method for producing sapphire single crystal - Google Patents

Description

  The present invention relates to a method for producing a sapphire single crystal by crystal growth from a melt of aluminum oxide containing a small amount of titanium oxide.

  Sapphire is a single crystal of aluminum oxide (melting point: about 2050 ° C.) having a hexagonal crystal structure. The sapphire single crystal is used for various applications, for example, as a substrate material such as a GaN film formation substrate for blue LEDs. A sapphire single crystal is an anisotropic material. When a wafer for GaN film formation is cut out from an ingot of a sapphire single crystal, the main surface of the wafer is a plane (c plane) perpendicular to the c-axis <0001> of the sapphire single crystal. It is common to cut out so that.

  Further, since sapphire is an optically uniaxial transparent material, it is also used as an optical material for liquid crystal projector films. When used as an optical material, it is required to be transparent without being colored. Further, due to the polarization characteristics of the sapphire single crystal, a substrate whose main surface is a surface perpendicular to the c-axis (hereinafter referred to as “c-plane substrate”) is mainly used, as in the case of the substrate material.

  When cutting a c-plane substrate from a sapphire single crystal ingot, in order to avoid wasting material as much as possible, the crystal is grown in the c-axis direction to obtain a substantially cylindrical ingot, and this ingot is formed in the c-axis direction (ingot direction). It is desirable to cut perpendicularly to (axial direction). However, it is known that bubble defects tend to occur when crystals are grown in the c-axis direction. If there are bubble defects in the ingot, cracks are likely to occur during processing, and when used as a substrate material or an optical material, their characteristics are likely to be insufficient. As a method for reducing the occurrence of bubble defects, it is known that the growth direction of the sapphire single crystal is shifted by a predetermined angle from the c-axis, or the a-axis or m-axis direction perpendicular to the c-axis (for example, Patent Document 1).

  By the way, as a manufacturing method of a sapphire single crystal, the Czochralski method, Bernoulli method, EFG method, kilopross method, etc. are mentioned. Among these, the Czochralski method can increase the size of a single crystal and relatively easily adjust the temperature gradient, so that a high-quality ingot can be produced. In the Czochralski method, a raw material put in a crucible is melted, a seed crystal made of a sapphire single crystal is brought into contact with the melt, and the single crystal is grown by rotating it.

In the Czochralski method, the growth of a sapphire single crystal is generally performed in an inert gas (for example, nitrogen or argon) or in a vacuum. However, when aluminum oxide, which is a raw material of sapphire single crystal, is heated and melted, a part of the raw material is decomposed to generate oxygen, which may cause bubble defects. In order to remove excess oxygen generated in this way from the melt, a method is known in which hydrogen or carbon monoxide is added to an inert gas to reduce the occurrence of bubble defects (for example, see Patent Document 2). ).
JP 2004-83316 A Japanese Patent No. 2964295

  However, as described above, when the sapphire single crystal is grown in the c-axis direction, bubble defects are likely to occur, and in an inert gas atmosphere to which hydrogen or carbon monoxide is added as in Patent Document 2. Even if crystals were grown, there was room for improvement in the generation of bubble defects.

  In view of the above circumstances, an object of the present invention is to provide a method for producing a sapphire single crystal that can sufficiently reduce generation of bubble defects even when the sapphire single crystal is grown in the c-axis direction.

The present invention provides a method for producing a sapphire single crystal by crystal growth from a raw material melt, containing aluminum oxide and titanium oxide, the ratio of the number of moles M _T of the titanium oxide to moles M _A of aluminum oxide ( (M _T / M _A ) Melting a raw material with 20 × 10 ⁻⁶ or less to obtain a melt, and pulling up the sapphire single crystal from the melt contained in the crucible while rotating the sapphire single crystal A shoulder forming step for forming the shoulder portion of the ingot, and a straight body forming step for forming the straight body portion of the ingot so that the sapphire single crystal is pulled up while rotating and extends below the shoulder portion. And a pulling speed and a rotating speed of the sapphire single crystal are adjusted so that a lower end surface of the straight body portion becomes a horizontal surface in the straight body portion forming step.

  Bubble defects in the sapphire single crystal are considered to be caused by various causes, but the anisotropy of the sapphire single crystal is also considered to be one of the causes. Since the growth rate of crystals varies greatly depending on the growth orientation, it is considered that bubble defects are likely to be taken into a portion where the growth rate is slow. For example, even if the sapphire single crystal is pulled up and grown at a constant speed, the lower end surface of the sapphire single crystal being grown may have a shape that swells toward the melt side. If the lower end surface of the single crystal is not sufficiently horizontal, the crystal growth direction varies. Then, the crystal growth rate also varies, and bubble defects are likely to occur as described above.

  In order to reduce bubble defects caused by the anisotropy of the sapphire single crystal, the present inventors have studied a method for suppressing variations in crystal growth rate due to the growth orientation. As a result of investigation, it was found that bubble defects in the sapphire single crystal can be reduced by growing the sapphire single crystal using a raw material containing a small amount of titanium oxide. The main cause is assumed as follows. That is, since titanium oxide can change charges such as trivalent and tetravalent, a small amount of titanium oxide serves as a buffer of charge imbalance in the single crystal. Therefore, variation in crystal growth rate due to orientation is suppressed by maintaining the charge balance of the crystal during crystal growth. Thereby, it is thought that the bubble defect in a sapphire single crystal is reduced.

  Further, in order to further suppress variation in crystal growth rate, in the present invention, the pulling speed and rotation speed of the sapphire single crystal are adjusted so that the lower end surface of the straight body portion is a horizontal plane in the straight body portion forming step. By adjusting the pulling speed and the rotational speed, the convection state of the melt in the crucible is adjusted, and the temperature distribution at the interface between the straight body portion and the melt is made uniform.

  Since the density of the melt in the crucible differs between the high temperature part and the low temperature part, convection of the melt occurs. In the crucible, the melt is usually heated and expanded on the outside in contact with the inner wall surface of the crucible, and then cooled and contracted on the surface of the melt to sink again downward from the vicinity of the center of the crucible. Natural convection occurs. Natural convection is likely to occur when the rotation speed is low at the stage where the diameter of the single crystal in contact with the melt is small (for example, at the beginning of the shoulder forming step).

  On the other hand, when the single crystal has a large diameter (for example, at the end of the shoulder forming process, the straight body forming process) or when the rotation speed of the single crystal is high, the melt is dragged by the rotation of the single crystal, Due to the centrifugal force, the melt near the surface tends to flow outward. When the diameter of the single crystal and the rotation speed thereof are sufficiently large, the convection of the melt is forced convection that sinks on the inner wall surface side of the crucible and rises near the center of the crucible.

  In the straight body part forming step in the present invention, the melt flows upward from the lower part of the crucible on the center side in the horizontal direction in the crucible toward the lower end of the shoulder part after the shoulder forming step in the crucible. The rotation speed of the sapphire single crystal is adjusted so that convection flowing downward (forced convection) occurs on the side wall surface of the sapphire, and the portion immersed in the melt at the lower end of the shoulder is remelted. It is preferable to provide a remelting step for adjusting the pulling rate of the crystal.

  In the remelting step, forced convection is generated in the melt in the crucible by controlling the rotation speed. In addition to controlling the rotation speed, if the lower end surface of the single crystal swells to the melt side instead of being horizontal in the shoulder formation process by controlling the pulling speed, the lower end surface of the single crystal is remelted. Can be level enough.

  Moreover, it is preferable that a straight body part formation process is equipped with the lower end part formation process which pulls up a sapphire single crystal and forms the lower end part of an ingot, decelerating the rotational speed of a sapphire single crystal. The convection of the melt in the crucible is kept sufficiently constant by gradually decreasing the rotation speed of the single crystal according to the growth stage of the single crystal, that is, according to the remaining amount of the melt in the crucible. The lower end surface of the single crystal becomes sufficiently horizontal.

  In the present invention, the sapphire single crystal can be produced by pulling up the sapphire single crystal in a direction in which the angle formed with the c-axis of the single crystal is within 10 °. A sapphire single crystal ingot that can be used as a c-axis substrate can be manufactured by raising the sapphire single crystal by pulling it up in the above-mentioned range.

  ADVANTAGE OF THE INVENTION According to this invention, even if it is a case where a sapphire single crystal is made to grow in a c-axis direction, the manufacturing method of a sapphire single crystal which can fully reduce generation | occurrence | production of a bubble defect can be provided.

  Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant descriptions are omitted.

  First, the pulling device used in this method will be described with reference to FIG. The pulling device 10 shown in the figure has a high-frequency induction heating furnace 14. This heating furnace 14 is a bottomed container with a fireproof side wall, and the shape of the bottomed container itself is the same as that used for single crystal growth based on the known Czochralski method. A high frequency induction coil 15 is wound around the side surface of the bottom of the heating furnace 14. A crucible 17 (for example, an Ir crucible) is arranged on the bottom surface inside the heating furnace 14.

  The crucible 17 also serves as a high frequency induction heater. Then, when aluminum oxide as a raw material of sapphire single crystal is put into the crucible 17 and high frequency induction is applied to the high frequency induction coil 15, the crucible 17 is heated and an aluminum oxide melt 18 is obtained.

  Further, an opening (not shown) penetrating from the inside of the heating furnace 14 to the outside is provided at the center of the bottom of the heating furnace 14. A crucible support bar 16 is inserted from the outside of the heating furnace 14 through the opening, and the tip of the crucible support bar 16 is connected to the bottom of the crucible 17. By rotating the crucible support rod 16, the crucible 17 can be rotated in the heating furnace 14. A space between the opening and the crucible support rod 16 is sealed with packing or the like.

  Next, a more specific manufacturing method using the pulling device 10 will be described. FIG. 2 is a process diagram showing a process for producing a sapphire single crystal according to this method. The method includes a melting step of melting a raw material containing aluminum oxide and titanium oxide to obtain a melt, a single crystal growing step of raising a single crystal from the melt and growing, and an ingot of the obtained single crystal. And a cooling step for cooling. The single crystal growing step includes a shoulder forming step for forming a shoulder portion of the ingot and a straight body forming step for forming a straight body portion extending below the shoulder portion.

First, a predetermined amount of aluminum oxide and titanium oxide are put into the crucible 17 as raw materials. Preferably the ratio of the number of moles _{M T} of the titanium oxide to moles _{M A} of aluminum oxide _(M T / _{M A)} is ^{5 × 10 -6 ~20 × 10 -6} , 5 × 10 -6 ~18 × 10 ⁻⁶ is more preferable, and 5 × 10 ⁻⁶ to 10 × 10 ⁻⁶ is even more preferable. If the ratio is less than 5 × 10 ⁻⁶ , the effect of adding titanium oxide is insufficient, and bubble defects are likely to occur. On the other hand, if it exceeds 20 × 10 ⁻⁶ , the single crystal is likely to be colored.

In the growth of the titanium sapphire single crystal, a raw material containing about 1 × 10 ⁻² titanium oxide at the ratio is used as the raw material. However, since a single crystal obtained from a raw material to which such titanium oxide is added is colored red, it is not suitable for use as an optical material.

  After sufficiently replacing the air in the heating furnace 14 with an inert gas (for example, nitrogen or argon), the high-frequency induction coil 15 is subjected to high-frequency induction to obtain a raw material melt 18 (melting step).

  Next, from above the crucible 17, the pulling rod 12 with the seed crystal 2 fixed to the lower end is put into the melt 18 from the center of the surface of the melt 18 to perform seeding (see FIG. 1). When the crystal is grown in the c-axis direction of the sapphire single crystal, it is preferable to seed the seed crystal 2 so that the c-axis is perpendicular to the melt surface of the crucible 17. After seeding, the pulling rod 12 is rotated while being rotated to form a substantially columnar single crystal ingot 1 (single crystal growing step).

  The single crystal growing process includes a shoulder part forming process and a straight body part forming process. The shoulder forming step is a step of growing the crystal until the single crystal ingot 1 has a desired diameter by adjusting the heating output of the heater 13. The shoulder 1a of the single crystal ingot 1 is formed through the shoulder forming step (see FIG. 3). The diameter of the single crystal ingot 1 is preferably 50 mm or more. When the diameter is increased to 50 mm or more, it becomes easy to control the convection of the melt 18 in the straight body part forming step. In addition, a large substrate can be cut out from the obtained single crystal ingot 1.

  The straight body portion forming step is a step of forming a straight body portion 1b extending below the shoulder portion 1a. The straight body part forming process includes a remelting process performed in the initial stage and a lower end forming process performed in the final stage. The remelting step is a step of remelting a portion immersed in the melt 18 in the lower end portion of the shoulder portion 1a after the shoulder forming step. By passing through this remelting step, the lower end surface of the shoulder portion 1a can be made sufficiently horizontal, and variations in the crystal growth direction can be reduced when the straight body portion 1b of the single crystal ingot 1 is grown.

  In the remelting process, the melt 18 flows upward from the lower part of the crucible 17 in the horizontal direction toward the lower end of the shoulder 1 a after the shoulder forming process in the crucible 17, and downward on the side wall surface side of the crucible 17. The rotational speed of the lifting rod 12 is adjusted so that forced convection flowing through In addition, the pulling speed of the pulling rod 12 is reduced for a certain period so that the portion immersed in the melt 18 at the lower end of the shoulder 1a after the shoulder forming step is remelted. Even if the convection of the melt 18 is forced convection, the portion immersed in the melt 18 at the lower end of the shoulder 1a is not immediately remelted. Therefore, the pulling speed of the pulling rod 12 can be reduced to reduce the pulling distance. During the interval, the lower end is remelted.

  It should be noted that the lower end surface of the shoulder portion 1a after the shoulder forming step tends to swell toward the melt side, and the swelled portion is immersed in the melt. The lower surface of the sapphire single crystal has such a shape because the sapphire single crystal is easy to transmit radiation because of its high transparency, and the temperature of the crystallized part is higher than the temperature of the melt. Is considered to be low.

  After leveling the lower end surface of the shoulder portion 1a in the remelting step, the straight barrel portion 1b can be grown by increasing the pulling speed while maintaining the rotational speed and maintaining the flow of the melt 18 in forced convection. it can. FIG. 3 shows a state in which the straight body portion 1b of the single crystal ingot 1 is formed, and an arrow B in the figure represents a forced convection flow of the melt 18. On the other hand, FIG. 1 shows a state of an initial stage of the shoulder forming process, and an arrow A in the figure represents a natural convection flow of the melt 18.

  As the straight body portion 1b grows and the amount of the melt 18 in the crucible 17 decreases, it becomes difficult to keep the convection state constant. If the convection of the melt 18 becomes unstable, irregularities are likely to occur on the lower end surface of the single crystal ingot 1, and as a result, bubble defects in the single crystal become prominent or internal stress increases, resulting in the processing. Cause cracking.

  The lower end portion forming step is a step of forming the lower end portion of the single crystal ingot 1 by pulling up the pulling rod 12 while reducing the rotational speed of the pulling rod 12 at the final stage of the straight body portion growing step. In this way, the convection in the crucible 17 can be stabilized by growing while gradually reducing the rotational speed as the melt 18 in the crucible 17 decreases. The end face can be made sufficiently horizontal.

  Next, in the cooling step, the single crystal ingot 1 obtained by the single crystal growth step is separated from the melt 18 and then cooled at a predetermined rate.

  According to such a manufacturing method of the single crystal ingot 1, it is possible to reduce bubble defects caused by the charge imbalance in the crystal by adding a small amount of titanium oxide to the raw material. In addition, by controlling the pulling speed and rotating speed of the pulling rod 12 in the straight body forming step, it is possible to grow the crystal while maintaining the lower end surface of the growing single crystal ingot 1 to be horizontal. . Thereby, bubble defects caused by the anisotropy of the sapphire single crystal can be reduced.

  Moreover, the stress inside the manufactured single crystal ingot 1 can be relieved by growing the crystal so that the lower end surface of the growing single crystal ingot 1 is horizontal. For example, when the lower end surface of the single crystal ingot 1 is swelled downward (melt side), the rotation center side of the single crystal ingot 1 is grown at a lower temperature than the outer peripheral side. On the other hand, when the lower end surface of the single crystal ingot 1 is recessed upward, the rotation center side of the single crystal ingot 1 is grown at a higher temperature than the outer peripheral side. As described above, when there is a temperature difference between the rotation center side and the outer peripheral side of the single crystal ingot 1 during crystal growth, it leads to an increase in internal stress. According to this method, the generation of such stress is alleviated. The occurrence of cracks during processing due to this can be reduced.

  EXAMPLES Hereinafter, although an Example demonstrates this invention, this invention is not limited to these Examples.

Example 1
An iridium crucible having a diameter of 100 mm and a depth of 100 mm was filled with a mixture of 2600 g of aluminum oxide having a purity of 99.99% by mass or more and 20 mg of titanium oxide having a purity of 99.99% by mass or more as a raw material. The ratio of the number of moles _{M T} of the titanium oxide to moles _{M A} of the aluminum oxide of the material _(M T / _{M A)} is 5 × ^{10 -6.} This crucible was placed in a high frequency induction heating furnace. A zirconia cylinder was placed on the outer periphery of the crucible to keep the area around the crucible warm. The crucible was heated by high-frequency induction to melt the raw material in the crucible.

  In producing a sapphire single crystal ingot based on the Czochralski method, the atmosphere in the heating furnace was nitrogen and the pressure was atmospheric pressure. A seed crystal of sapphire was fixed to the tip of a pulling rod, and this seed crystal was put into a raw material melt and seeded. At this time, the seed crystal was seeded so that its c-axis was perpendicular to the melt surface.

  After seeding the seed crystal, first, a shoulder portion of the single crystal ingot was formed (shoulder portion forming step). That is, the pulling rod was rotated at a rotation speed of 1 rotation / minute and pulled up at a pulling speed of 1.5 mm / hour. By adjusting the temperature of the melt, the diameter of the single crystal ingot was expanded to 60 mm to form a shoulder. At this time, the lower end surface of the single crystal ingot was swelled to the melt side.

  Next, a straight body part of the single crystal ingot was formed (straight body part forming step). That is, the rotation speed of the lifting rod was set to 50 rotations / minute and the lifting speed was set to 0.1 mm / hour, and the lifting was continued for 2 hours under these conditions. As a result, the portion immersed in the melt at the lower end portion of the single crystal ingot (the portion swelled on the melt side) was remelted (remelting step).

  Thereafter, the single crystal ingot was pulled up under the conditions of a rotation speed of 50 rotations / minute and a pulling speed of 0.7 mm / hour, and a single crystal was grown in the c-axis direction until the length of the straight body portion reached 80 mm. Then, when the length of the straight body portion was 80 mm, the rotation speed was linearly reduced from 50 rotations / minute to 35 rotations / minute over 114 hours (lower end forming step).

  When the rotation speed reached 35 rotations / minute, the single crystal ingot was separated and cooled for about 20 hours.

  By visual observation, no bubble defect was observed in most of the straight body portion of the obtained single crystal ingot. Even when a laser beam having a wavelength of 532 nm was irradiated so as to pass through the inside of the single crystal ingot, scattered light caused by minute bubble defects was not observed. Further, when this single crystal ingot was ground, no cracks occurred in the grinding process.

(Example 2)
A single crystal ingot was produced in the same manner as in Example 1 except that the content of the raw material titanium oxide and the conditions of the rotational speed and pulling speed of the pulling rod were changed. That is, in this example, a mixture of 2600 g of aluminum oxide having a purity of 99.99% by mass or more and 40 mg of titanium oxide having a purity of 99.99% by mass or more was used as a raw material. The ratio of the number of moles _{M T} of the titanium oxide to moles _{M A} of the aluminum oxide of the material _(M T / _{M A)} is 10 × ^{10 -6.} Further, in the straight body part forming step of this example, the rotation speed of the lifting rod was set to 70 rotations / minute and the lifting speed was set to 0.1 mm / hour, and the lifting was continued for 2 hours under these conditions. As a result, the portion immersed in the melt at the lower end of the single crystal ingot (the portion swelled on the melt side) was remelted.

  Thereafter, the single crystal ingot was pulled up under the conditions of a rotation speed of 70 rotations / minute and a pulling speed of 1.5 mm / hour, and a single crystal was grown in the c-axis direction until the length of the straight body portion reached 80 mm. Then, when the length of the straight body portion became 80 mm, the rotation speed was linearly decreased from 70 rotations / minute to 30 rotations / minute over 53 hours.

  When the rotation speed reached 35 rotations / minute, the single crystal ingot was separated and cooled for about 20 hours.

  By visual observation, no bubble defect was observed in most of the straight body portion of the obtained single crystal ingot. Even when a laser beam having a wavelength of 532 nm was irradiated so as to pass through the inside of the single crystal ingot, scattered light caused by minute bubble defects was not observed. Further, when this single crystal ingot was ground, no cracks occurred in the grinding process.

(Example 3)
A sapphire single crystal ingot was prepared in the same manner as in Example 2 except that a mixture of 2600 g of aluminum oxide having a purity of 99.99% by mass or more and 80 mg of titanium oxide having a purity of 99.99% by mass or more was used as a raw material. did. The ratio of the number of moles _{M T} of the titanium oxide to moles _{M A} of the aluminum oxide of the material _(M T / _{M A)} is 20 × ^{10 -6.}

  By visual observation, no bubble defect was observed in most of the straight body portion of the obtained single crystal ingot. However, when laser light having a wavelength of 532 nm was irradiated so as to pass through the inside of the single crystal ingot, scattered light due to minute bubble defects was observed in the upper half of the straight body portion of the single crystal ingot. When this single crystal ingot was ground, no cracks occurred in the grinding process.

Example 4
A single crystal ingot of sapphire was produced in the same manner as in Example 2 except that a melt of aluminum oxide containing titanium oxide having a content less than the measurement limit was used.

  By visual observation, no bubble defect was observed in most of the straight body portion of the obtained single crystal ingot. However, when laser light having a wavelength of 532 nm was irradiated so as to pass through the inside of the single crystal ingot, scattered light due to minute bubble defects was observed in the upper half of the straight body portion of the single crystal ingot. When this single crystal ingot was ground, no cracks occurred in the grinding process.

(Comparative Example 1)
A sapphire single crystal ingot was produced in the same manner as in Example 1 except that in the straight body portion forming step, the conditions of the rotational speed and pulling speed of the pulling rod were changed. That is, in the straight body part forming step of this comparative example, a single crystal is grown in the c-axis direction until the length of the straight body part becomes 80 mm under conditions of a rotation speed of 40 rotations / minute and a pulling speed of 0.7 mm / hour. did. And when the length of the straight body part became 80 mm, the single crystal ingot was cut off and cooled for about 20 hours.

  When the obtained single crystal ingot was visually observed, there were some bubble defects on the central axis of the single crystal ingot although there were regions where some bubble defects did not occur. Further, when this single crystal ingot was ground, cracks occurred in the shoulder portion of the ingot.

  Table 1 summarizes the growth conditions and evaluation results in Examples 1 to 4 and Comparative Example 1. Evaluation about the bubble defect in Table 1 and the growth time was performed based on the following criteria.

(Evaluation criteria for bubble defects)
A: There are almost no bubble defects in the straight body,
B: A bubble defect is visually recognized in a partial region of the straight body part.
C: Although no bubble defects are visually observed, scattered light is observed when irradiated with laser light.
D: A bubble defect is visually recognized in the most area | region of a straight trunk | drum.

(Evaluation criteria for training time)
A: Shorter than the time required for producing the ingot in Comparative Example 1,
B: The same level of time required to produce the ingot in Comparative Example 1,
C: Slightly longer than the time required to produce the ingot in Comparative Example 1,
D: It is longer than the time required to produce the ingot in Comparative Example 1.

It is a schematic cross section which shows an example of the pulling apparatus for manufacturing a sapphire single crystal. It is process drawing showing the suitable manufacturing process of the manufacturing method of the sapphire single crystal which concerns on this invention. It is a schematic cross section which shows the state which forms the straight body part of a single crystal using the pulling apparatus of FIG.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Single crystal ingot, 1a ... Shoulder part, 1b ... Straight body part, 2 ... Seed crystal, 10 ... Pulling device, 12 ... Lifting rod, 14 ... High frequency induction heating furnace, 15 ... High frequency induction coil, 17 ... Crucible, 18 ... melt.

Claims (5)

A method for producing a sapphire single crystal by crystal growth from a raw material melt,
Containing aluminum oxide and titanium oxide, melting and melting the ratio of the number of moles M _T of the titanium oxide to moles M _A of aluminum oxide (M T _{/ M A)} is 20 × 10 ^-6 or less material A melting step to obtain a liquid;
A shoulder forming step of forming a shoulder of the ingot of the sapphire single crystal by pulling up the sapphire single crystal while rotating it from the melt contained in the crucible,
A straight body part forming step of forming the straight body part of the ingot so that the sapphire single crystal is pulled up while rotating and extends below the shoulder part, and
With
In the straight body part forming step, the pulling speed and rotation speed of the sapphire single crystal are adjusted so that the lower end surface of the straight body part becomes a horizontal plane.   In the crucible, in the crucible, the melt flows upward from the lower part of the crucible on the horizontal center side in the crucible toward the lower end of the shoulder after the shoulder formation process, The rotational speed of the sapphire single crystal is adjusted so that convection flowing downward on the side wall surface side of the crucible is generated, and the sapphire is remelted so that the portion immersed in the melt at the lower end portion of the shoulder portion is remelted. The method according to claim 1, further comprising a remelting step of adjusting a pulling rate of the single crystal.   The straight body portion forming step includes a lower end portion forming step of pulling up the sapphire single crystal to form a lower end portion of the ingot while decelerating a rotation speed of the sapphire single crystal. Or the method of 2. The ratio of the number of moles _{M T} of the titanium oxide to moles _{M A} of aluminum oxide _(M T / _{M A),} characterized in that a ^{5 × 10 -6 ~20 × 10 -6} , according to claim 1 The method as described in any one of -3.   The production of the sapphire single crystal is performed by pulling up the sapphire single crystal in a direction within 10 ° with respect to the c-axis of the single crystal. The method according to one item.

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