WO2014148695A1

WO2014148695A1 - Method of interpreting sapphire single-crystal growth and method of growing sapphire single-crystal

Info

Publication number: WO2014148695A1
Application number: PCT/KR2013/006619
Authority: WO
Inventors: Do Won Song; Chang Youn Lee; Jun Hyuk Choi; Young Hee Mun
Original assignee: Lg Siltron Incorporated
Priority date: 2013-03-20
Filing date: 2013-07-24
Publication date: 2014-09-25
Also published as: KR101472351B1; TW201437441A; TWI476303B; KR20140115181A

Abstract

Disclosed is a method of interpreting sapphire single-crystal growth including preparing a crucible filled with an alumina melt, growing a single-crystal by bringing a seed crystal into contact with the alumina melt and dipping the seed crystal in the alumina melt, calculating at least one of an angle and a movement speed of an interface between the single-crystal and the alumina melt, measuring defects formed in the grown sapphire single-crystal, and calculating at least one of an angle and a movement speed of an interface between the single-crystal and the alumina melt in which defects are not formed by repeating the crucible preparation operation, the single-crystal growth operation, the operation of calculating at least one of the angle and the movement speed of the interface, and the defects measurement operation.

Description

METHOD OF INTERPRETING SAPPHIRE SINGLE-CRYSTAL GROWTH AND METHOD OF GROWING SAPPHIRE SINGLE-CRYSTAL

The present invention relates to a method of interpreting sapphire single-crystal growth and a method of growing a sapphire single-crystal.

More particularly, the present invention relates to a method of interpreting a crystallization front of a sapphire single-crystal, the method including bringing a seed crystal into contact with an upper portion of an alumina melt, to prevent formation of crystal defects in a single-crystal boule grown from the alumina melt, and a method of growing a sapphire single-crystal from which crystal defects are removed based on the method of interpreting sapphire single-crystal ingot growth.

Sapphire wafers are generally fabricated through several operations including a single-crystal growth process to produce a single-crystal ingot, a slicing process of slicing the single-crystal ingot into waters having a thin circular plate shape, a lapping process of removing damaged portions of the wafers caused by the mechanical process of slicing, a polishing process of improving mirror surface property, and a cleaning process of improving mirror surface property of the polished wafer and removing an abrasive attached to the wafer and contaminants.

Among the above-mentioned processes, the sapphire single-crystal growth process may be performed by use of various methods such as a Kyropoulos method (KY method), a Czochralski method (CZ method), an edge-defined film-fed growth (EFG) method, a heat exchange method, and a vertical horizontal gradient freezing method, after melting a high-purity alumina (Al₂O₃) raw material by heating in a furnace for growth of the single-crystal at 2100° or higher. The KY method and the CZ method, in which a seed crystal is brought into contact with an upper portion of an alumina melt to grow a single-crystal, may be applied to a method according to the present invention.

When a sapphire single-crystal is grown using the KY method or CZ method, an alumina raw material is added to a crucible and melted. A resistance heater is disposed to surround external walls and the bottom surface of the crucible to heat the crucible, and radiant heat generated therefrom is used. Generally, a single-crystal may grow up to about 1/2 to 2/3 the size of the crucible according to the CZ method. However, in accordance with the KY method, a single-crystal may grow up to about 8/10 to 9/10 the size of the crucible, thereby acquiring a large sapphire single-crystal.

According to the KY method or CZ method, the sapphire single-crystal may be grown by mounting a heat insulating structure (hot zone) in a chamber, filling a crucible with a raw material, i.e., alumina, and heating the crucible to a temperature greater than a melting point thereof. Then, a seed crystal disposed at an upper portion of the crucible is brought into contact with the alumina melt and is dipped in the alumina melt at a temperature suitable for contact and seeding to form a neck. Then, the sapphire single-crystal is grown while maintaining a temperature gradient required for growth thereof by reducing power. Diameter of the single-crystal grown in accordance with the KY method and the CZ method is dependent upon the size of the crucible.

However, such conventional methods of growing sapphire single-crystal have the following problems.

During growth of a sapphire single-crystal, a crystallization front of the single-crystal moves toward the bottom of the crucible in a state of being immersed in the alumina melt due to a thermal gradient of the heat insulating structure and rapid natural convection of the alumina melt in a sapphire single-crystal growing apparatus. However, the crystallization front can neither be measured nor predicted. That is, when the crystallization front, which is an interface between the alumina melt and the growing single-crystal, rapidly changes, crystal defects, such as bubbles, low angle block boundaries (LABBs), and lineage, may be generated in the single-crystal. At the LABB, polycrystallization is induced, so that fine grains are formed at the polycrystalline-single-crystal boundary. However, it is difficult to predict or control formation of such crystal defects.

In addition, the growing single-crystal may stick to the bottom surface and the inner wall of the crucible, thereby influencing the crystallization front. Thus, formation of bubbles and lineage may be induced, and cracks may occur due to thermal impact during a cooling process.

In order to prevent crystal defects such as bubbles, LABBs, lineage, and cracks, a growth rate of the sapphire single-crystal with time may be adjusted based on past experience. However, this cannot be regarded as a method for preventing defects, since factors causing various defects in the sapphire single-crystal during growth can be neither predicted nor controlled.

Furthermore, when a new sapphire single-crystal growth process is performed using the same apparatus, the same defects as described above may also be encountered.

Embodiments provide a method of growing a sapphire single-crystal in which crystal defects such as bubbles and low angle block boundaries (LABBs) are not formed by defining a crystallization front and predicting movement speed thereof during growth of the sapphire single-crystal according to a Kyropoulos Method (KY method) or a Czochralski Method (CZ method).

The objects of the present invention can be achieved by providing a method of interpreting sapphire single-crystal growth preparing a crucible filled with an alumina melt, growing a single-crystal by bringing a seed crystal into contact with the alumina melt and dipping the seed crystal in the alumina melt, calculating at least one of an angle and a movement speed of an interface between the single-crystal and the alumina melt, measuring defects formed in the grown sapphire single-crystal, and calculating at least one of an angle and a movement speed of an interface between the single-crystal and the alumina melt in which defects are not formed by repeating the crucible preparation operation, the single-crystal growth operation, the operation of calculating at least one of the angle and the movement speed of the interface, and the defects measurement operation.

The growing of the single-crystal may include growing a neck of the single-crystal from the seed crystal, growing a shoulder of the single-crystal from the neck, and growing a body of the single-crystal from the shoulder. The interface between the growing single-crystal and the alumina melt may have a lowest height at a region corresponding to the center of a bottom surface of the crucible.

The neck growth operation and the shoulder growth operations may be distinguished from each other by measuring weight of the single-crystal.

The weight of the single-crystal may be measured by a sensor connected to the seed crystal, and the growth of the shoulder may be completed when 8% to 10% of the alumina melt is solidified into the single-crystal.

The interface between the growing single-crystal and the alumina melt may have a turning point at a region corresponding to the center of a bottom surface of the crucible.

The angle of the interface between the single-crystal and the alumina melt may decrease as the single-crystal grows in some ranges.

The defects of the sapphire single-crystal may include at least one defect selected from the group consisting of bubbles, low angle black boundaries (LABBs), and lineage.

The bubbles may be formed in the shoulder and the body of the single-crystal.

The LABBs may be formed in a lengthwise direction on the surface of the single-crystal as stripe patterns

In accordance with another aspect of the present invention, there is provided a method of growing a sapphire single-crystal including preparing a crucible filled with an alumina melt, growing a neck of a single-crystal by bringing a seed crystal into contact with the alumina melt and dipping the seed crystal in the alumina melt, growing a shoulder of the single-crystal from the neck, and growing a body of the single-crystal from the shoulder. An angle of an interface between the single-crystal and the alumina melt may decrease in some ranges during the shoulder growth operation and the body growth operation.

The interface between the single-crystal and the alumina melt may have a turning point at a region corresponding to the center of a bottom surface of the crucible. The angle of the interface between the single-crystal and the alumina melt may be an angle of the turning point.

The interface between the growing single-crystal and the alumina melt may have a lowest height at a region corresponding to the center of a bottom surface of the crucible

The angle of the interface between the single-crystal and the alumina melt may increase in some ranges after the single-crystal contacts the bottom surface of the crucible during the body growth operation.

The seed crystal may be drawn up after the single-crystal contacts the bottom surface of the crucible, and a speed of drawing up the seed crystal may be 5 mm per hour or less.

When the body growth operation is initiated, the angle of the interface between the single-crystal and the alumina melt may be in the range of 60˚to 120˚.

When the single-crystal contacts the bottom surface of the crucible, the angle of the interface between the single-crystal and the alumina melt may be in the range of 40˚ to 60˚.

When the single-crystal contacts the bottom surface of the crucible, a solidification rate of the alumina melt to the single-crystal may be greater than 10%.

The angle of the interface between the single-crystal and the alumina melt may be in the range of 40˚to 120˚ in a range within which the angle of the interface between the single-crystal and the alumina melt decreases.

The interface between the single-crystal and the alumina melt may be defined an equation below:

h_i(t)={d_i(t)/2}×{cot(α_i(t)/2)}

In the equation, h_i(t) is a height of the single-crystal between a lowest point and a highest point of the single-crystal immersed in the alumina melt, d_i(t) is a maximum diameter of the growing single-crystal, and α_i(t) is an internal angle of the interface between the single-crystal and the alumina melt.

According to the method of interpreting a crystallization front of a sapphire single-crystal and the method of growing a sapphire single-crystal in accordance with embodiments of the present invention, formation of crystal defects may be prevented in the sapphire single-crystal by defining a crystallization front at which the sapphire single-crystal is grown from an alumina melt and measuring weight of the single-crystal, change of angle of the crystallization front, and movement speed of the crystallization front.

That is, formation of crystal defects such as bubbles, LABBs, lineage, and cracks may be prevented in the sapphire single-crystal by growing the sapphire single-crystal using the method according to embodiments of the present invention.

Arrangements and embodiments may be described in detail with reference to the following drawings in which like reference numerals refer to like elements and wherein:

FIG. 1 is a view illustrating a sapphire single-crystal manufacturing apparatus according to an embodiment of the present invention;

FIGs. 2 to 6 are views illustrating a sapphire single-crystal growth process;

FIG. 7 is a graph illustrating movement speed of a vertex of a crystallization front, change of internal angle thereof, and diameter of a single-crystal during growth of a shoulder and a body with respect to length from the shoulder of the single-crystal ingot;

FIG. 8 is a view for describing a method of interpreting a crystallization front of a sapphire single-crystal; and

FIGs. 9A to 9D are photographs of samples of single-crystal ingots grown under different conditions and cut at the center illustrating results of macroscopic examinations and polarization tests, crystallization fronts, and internal angles thereof.

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings in the best manner to improve understanding of the embodiments. However, various modifications of the embodiments are possible, and the technical sprit of the embodiments is not constructed as being limited to the embodiments. The embodiments of the present disclosure are provided to explain the disclosure to those skilled in the art.

In the drawings, the thickness or size of each layer is exaggerated, omitted, or schematically illustrated for convenience of description and clarity. In addition, the size or area of each constituent element does not entirely reflect the actual size thereof.

FIG. 1 is a view illustrating a sapphire single-crystal manufacturing apparatus according to an embodiment of the present invention. A Kyropoulos method may be applied thereto, but the present invention is not limited thereto.

A sapphire single-crystal-growing apparatus 100 according to the present embodiment may form a sapphire single-crystal by melting solid alumina into liquid alumina and re-crystallizing the alumina. The sapphire single-crystal-growing apparatus 100 includes a chamber 10, a crucible 30 disposed in the chamber 10 and accommodating an alumina melt 40, and a heater 80 mounted outside of the crucible 30 to heat the crucible 30.

The chamber 10 provides a space in which predetermined processes for growing a sapphire single-crystal boule from the alumina melt 40 are performed. The crucible 30 is disposed in the chamber 10 so as to accommodate the alumina melt 40 and may be formed of tungsten (W) or molybdenum (Mo). However, the present invention is not limited thereto.

In addition, according to the present embodiment, a radiant heat insulator may be disposed in the chamber 10 to prevent leakage of heat generated by the heater 80. The heat insulator may include upper heat insulators 92 disposed at upper portions of the crucible 30, side heat insulators 94 disposed at sides of the crucible 30, and lower heat insulators 96 disposed at lower portions of the crucible 30. However, the present invention is not limited thereto.

These heat insulators may be formed of suitable materials in desired shapes such that heat is uniformly distributed in the crucible 30 and energy loss thereof is minimized.

High-purity alumina raw materials having a variety of shapes and contained in the crucible 30 may be melted by the heater 80 to form an alumina melt M. The heater 80 may receive current from a current supply rod 70 disposed at an upper portion of the heater 80.

A support 20 is disposed at the center of the bottom of the crucible 30 to support the crucible 30. The alumina melt 40 is partially solidified by the seed crystal connection unit 62 disposed at an upper portion of the crucible 30 to grow a sapphire single-crystal, namely, a sapphire boule, 50.

The heater 80 may include a plurality of heater units that surround sides and the bottom surface of the crucible 30 and are aligned in a U-shape.

That is, the heater 80 may include a plurality of U-shaped heater units surrounding the crucible 30 at the sides and the bottom surface of the crucible 30. Alternatively, each of the heater units may be divided into a first heater 82, a second heater 84, and a third heater 86, which will be described later, in accordance with positions thereof.

The first heater 82 may be disposed at an edge of an upper portion, i.e., an upper side portion, of the crucible 30, the second heater 84 may be disposed at an edge of a lower portion, i.e., a lower side portion, of the crucible 30, and the third heater 86 may be disposed at a lower surface, i.e., the bottom surface, of the crucible 30.

The first heater 82, the second heater 84, and the third heater 86 may be formed integrally or independently. In this case, these heaters may be located in the crucible 30 at positions as described above.

The current supply rod 70 may supply current to the heater 80. The heater 80 may be formed of a material having high thermal conductivity and excellent resistance at a high temperature, for example, tungsten (W) and graphite.

Hereinafter, a method of interpreting sapphire single-crystal growth using the above-described sapphire single-crystal growing apparatus according to an embodiment of the present invention will be described.

In the KY method or CZ method, a single-crystal (boule) is drawn up while the single-crystal is not rotated or is rotated at a very low speed. Thus, the interface between the alumina melt and the single-crystal may be changed such that the interface has a conical shape due to natural convection. The present embodiment provides a method of growing a sapphire single-crystal to prevent crystal defects from being formed in the single-crystal by predicting the interface between the alumina melt and the single-crystal and changes of the interface.

First, the alumina melt is prepared in the crucible 30. Solid alumina having various shapes may be added to the crucible 30, and the crucible 30 is heated to a temperature greater than the melting point of alumina, that is, about 2030 C or greater, to prepare the alumina melt. The melting process and the single-crystal growth process are carried out in the chamber. These processes may be performed under a high vacuum condition by reducing the internal pressure of the chamber to 10^-6 torr or less, or under an inert gas atmosphere using argon or the like at atmospheric pressure.

Then, the seed crystal is brought into contact with the alumina melt and dipped in the alumina melt to grow the single-crystal. When solidification of the alumina melt is completed in the crucible, sapphire may be regarded as a boule.

According to the method of interpreting a crystallization front of the sapphire single-crystal in accordance with the present embodiment, weights of the alumina melt and the single-crystal boule solidified and grown therefrom are measured, an internal angle of a turning point of a crystallization front between the alumina melt and the single-crystal and a movement speed of the turning point are calculated, and then a diameter and crystal defects of the sapphire single-crystal boule in which growth is completed are measured. Then, ranges of the internal angle of the turning point and the movement speed of the turning point to prevent formation of crystal defects in the sapphire single-crystal are determined, and ranges of the solidification rate and the growth rate with time may be determined. Thus, a method of growing a sapphire single-crystal free of crystal defects may be provided.

FIGs. 2 to 6 are views illustrating a sapphire single-crystal growth process. Hereinafter, the sapphire single-crystal growth process will be described with reference to FIGs. 2 to 6.

Referring to FIG. 2, the crucible 30 is filled with the alumina melt 40, a seed crystal 62a connected to the seed crystal connection unit 62 is brought into contact with the alumina melt 40 and dipped in the alumina melt 40.

As illustrated in FIG. 3, when the seed crystal 62a is dipped in the high-temperature alumina melt 40, the seed crystal 62a may be partially melted. Simultaneously, the alumina melt 40 is partially solidified to continuously form seasons that are thicker than the seed crystal 62a, thereby growing a neck 50a.

The process of forming the neck 50a as described above may be referred to as a seasoning process. During the seasoning process, the diameter of the single-crystal may increase as a portion of the alumina melt 40 is solidified by the seed crystal 62a. Here, while the seed crystal 62a is drawn up, seasons may be formed. In a right diagram of FIG. 3, a, b, c, and d illustrate sequential shapes of the neck 50a while being drawn up.

In this regard, the interface between the growing single-crystal, particularly, the neck 50a and the alumina melt 40 may have a turning point (or vertex) at a region corresponding to the center of the bottom surface of the crucible 30. The neck 50a may have a smallest height at the region corresponding to the center of the bottom surface of the crucible 30, and the turning point may be disposed at the lowest region of the neck 50a. In FIG. 3, an internal angle of the turning point of the interface of the neck 50a is indicated as ₁. The internal angle ₁generally, but not always, increases during growth of the neck 50a.

FIG. 4 illustrates a shoulder growth process.

The single-crystal may be stably grown in the vertical direction since the center of the alumina melt has the lowest temperature at the center of the crucible referring to FIG. 1.

In the shoulder growth process, the alumina melt 40 is solidified to continuously grow the single-crystal from the lower portion of the neck 50a. A shoulder 50b grows in the radial and vertical directions, so that the diameter of the single-crystal increases and the single-crystal grows in a state of being immersed in the alumina melt 40. The shoulder 50b may grow to the diameter of the crucible 30. However, when the shoulder 50b contacts the inner wall of the crucible, the shoulder 50b sticks to the inner wall to cause physical stress during a crystal growth process and thermal stress during a cooling process leading to cracks. Thus, the shoulder 50b may be generally grown to have a diameter up to 75% to 90% of the diameter of the crucible according to the KY method and to have a diameter up to 50% to 70% of the diameter of the crucible according to the CZ method.

In this regard, the interface between the growing single-crystal, particularly, the shoulder 50b, and the alumina melt 40 may have a turning point at a region corresponding to the center of the bottom surface of the crucible 30. The turning point is a vertex of a cone shape where the growing shoulder 50b contacts the melted alumina.

The shoulder 50b may have a smallest height at the region corresponding to the center of the bottom surface of the crucible 30, and the turning point may be disposed at the lowest region of the shoulder 50b. In FIG. 4, an internal angle of the turning point of the interface of the shoulder 50b is indicated as ₂. The internal angle ₂ generally, but not always, increases during growth of the shoulder 50b.

The interface is also referred to as a crystallization front. The crystallization front may be an interface between the alumina melt 40 and the neck 50a, the shoulder 50b, or a body 50c, which is a portion of the solidified single-crystal.

FIGs. 5 and 6 illustrate a body growth process.

In the body growth process, the alumina melt 40 is solidified to continuously grow the single-crystal from the lower portion of the shoulder 50b. A body 50c may grow in the vertical direction. In general, however, the single-crystal of the body 50c grows in a direction perpendicular to the crystallization front.

As illustrated in FIG. 5, the interface between the growing single-crystal, particularly, the body 50c, and the alumina melt 40 moves downward of the crucible 30 to contact the bottom surface of the crucible 30.

In FIG. 5, the interface between the growing single-crystal, particularly, the body 50c, and the alumina melt 40, may have a turning point at a region corresponding to the center of the bottom surface of the crucible 30, i.e., the region where the interface and the crucible 30 contact each other. The body 50c may have a smallest height at the region corresponding to the center of the bottom surface of the crucible 30, and the turning point may be disposed at the contact region between the body 50c and the crucible 30. In FIG. 5, an internal angle of the turning point of the interface of the body 50c is indicated as ₃. The internal angle ₃ generally, but not always, increases during growth of the body 50c.

When the lowest point of the body 50c contacts the bottom surface of the crucible 30, the growth process of the body 50c may be continuously performed while the seed crystal connection unit 62 is pulled upward. FIG. 6 illustrates a single-crystal 50, growth of which is completed.

In the above-described processes, the angle of the interface between a portion of the single-crystal and the alumina melt, i.e., the angle of the crystallization front or the turning point, may increase or decrease during the neck growth process and the shoulder growth process and may gradually increase after the body growth process is initiated. The angle of the interface may also be constantly maintained for a predetermined time period after the body contacts the bottom surface of the crucible and may then increase.

In the single-crystal growth process, it is difficult to distinguish the neck, shoulder, and body growth processes from each other with the naked eye, and the neck, shoulder, and body growth processes may be distinguished from each other by measuring weight of the growing single-crystal. Although not shown in the drawings, weight of the single-crystal may be measured using a weighing sensor (not shown) connected to the seed crystal or the seed crystal connection unit. In this regard, mass of the growing single-crystal may be obtained in consideration of buoyancy by the alumina melt. In addition, linear velocity of the crystallization front may be calculated by use of the diameter and density of the growing single-crystal.

Then, the single-crystal 50 that is 100% solidified is separated from the crucible 30 and the single-crystal boule growth process is completed by gradually decreasing the internal temperature of the chamber. Differently from the CZ method, the grown sapphire single-crystal is cooled in the crucible according to the KY method. Thus, a separate annealing process is unnecessary.

Then, the diameter of the sapphire single-crystal (boule) separated from the crucible 30 is measured, and defects such as bubbles, LABBs, lineage, and cracks are detected. Impurities contained in the melt may be dissolved in the melt in a gaseous state at a high temperature, or the alumina melt (Al₂O₃) may be pyrolyzed into aluminum and oxygen at an elevated temperature. Such dissolved elements move near the crystallization front by natural convection and are gasified around the crystallization front due to a solubility difference, thereby forming such defects.

FIG. 7 is a graph illustrating movement speed of a vertex of a crystallization front, change of internal angle thereof, and diameter of a single-crystal during growth of a shoulder and a body with respect to length from the shoulder of the single-crystal.

In a range where the movement speed of the vertex of the crystallization front is not stably maintained, crystal defects such as bubbles, LABBs, and lineage may be formed at the crystallization front of the sapphire single-crystal due to latent heat of solidification and gasification.

By repeating the above process plural times, optimized weight of the sapphire single-crystal, angle of the crystallization front, and vertex movement speed to prevent formation of crystal defects are obtained and used as standards. Accordingly, the sapphire single-crystal may be stably grown.

FIG. 8 is a view for describing a method of interpreting a crystallization front of a sapphire single-crystal. The relation between the single-crystal and the alumina melt may be interpreted by equation 1 below.

Equation 1

h_i(t)={d_i(t)/2}×{cot(α_i(t)/2)}

In Equation 1, h_i(t) is a height of the growing sapphire single-crystal immersed in the melt, d_i(t) is a diameter of the growing single-crystal, and _i(t) is an internal angle of the interface between the single-crystal and the alumina melt. Here, i is an i^th value.

In addition, the relation between length of the single-crystal and weight of the single-crystal may be interpreted by Equation 2 below.

Equation 2

h_i(t)=A(W_i-W₀)-B(P₀-P_i)

In Equation 2, A and B are proportional constants obtained through experimentation, and P is a distance of movement of the seed crystal connection unit 62 upward during growth of the single-crystal.

The interface between the single-crystal 50 and the alumina melt 40 is not visible during growth of the single-crystal 50. After completion of the growth process, the diameter of the single-crystal boule may be measured.

Based on the diameter of the single-crystal 50 after growth of the single-crystal is completed, the weight of the single-crystal 50 measured during growth thereof, and the weight of the crucible containing the alumina melt, the position of the turning point (or vertex) of the single-crystal 50 and the internal angle of the crystallization front may be estimated using

Equations

1 and 2. The movement speed of the crystallization front may be calculated.

FIGs. 9A to 9D are photographs of samples of sapphire single-crystals grown under different conditions. The internal angle of the crystallization front of each of the neck, shoulder, and body of the single-crystal, the solidification rate when the turning point contacts the bottom surface of the crucible, bubbles and LABBs detected by macroscopic examination and polarization tests are calculated according to the above-described method and schematically illustrated in FIGs. 9A to 9D.

The LABB, which is one of the crystal defects marked at the surface of the grown single-crystal, is a planar defect formed in a direction perpendicular to the crystallization front in the single-crystal and is also referred to as a grain boundary or a block mark. The lineage is a planar defect formed in a direction parallel to the crystallization front. These defects may appear as stripe patterns in lengthwise directions on the surface of the single-crystals. FIGs. 9A and 9B illustrate polarization test results.

The samples of sapphire single-crystal illustrated in FIGs. 9A to 9D are plate-like samples prepared by cutting, at the center downward, the sapphire single-crystal boules grown in different apparatuses and under different growth conditions according to Examples 1 to 4. The angle of the turning point of the crystallization front and the movement speed of the turning point may be adjusted by controlling the growth rate of the sapphire single-crystal, the speed of drawing the sapphire single-crystal upward, power supplied to a heating element, and the structure of a hot zone aligned around the crucible.

Table 1 shows angle of the crystallization front, solidification rate, and crystal defects illustrated in FIGs. 9A to 9D.

Table 1

	Angle of crystallization front (°)			When contacting the bottom of the crucible		Weight at formation of crystal defects (kg)	Weight of raw material (kg)
	Neck	Shoulder	Body	Solidification rate (%)	Time(hour)	Weight at formation of crystal defects (kg)	Weight of raw material (kg)
Example 1	60	50	36	8	122	neck~1.2kg	85
Example 2	60	51	41	10	84	0~0.7kg	75
Example 3	60	105	54	20	41	free	27
Example 4	135	100	47	23	81	free	82

Based on Examples 1 to 4, crystal defects are formed the crystallization front has an angle of 41°or less, when the body of the single-crystal 50 contacts the bottom surface of the crucible 30 (Examples 1 and 2).

However, if the crystallization front has an angle of 47°and 54°(Examples 3 and 4) when the body of the sapphire single-crystal 50 contacts the bottom surface of the crucible 30, crystal defects were not formed.

While the sapphire single-crystal 50 is growing, the angle of the crystallization front may be changed. However, sapphire single-crystal (boules) having excellent characteristics without having crystal defects may be produced if the crystallization front has an angle of 40°to 60°when the crystallization front contacts the bottom surface of the crucible 30 based on the experiments including those illustrated in FIGs. 9A to 9D.

In addition, when the solidification rate from the alumina melt to the single-crystal is 10% or less at the time of contacting the bottom surface of the crucible 30, LABBs are formed. In addition, LABBs are not formed when the angle of the crystallization front is in the range of 60°to 120°during growth of the shoulder.

In accordance with the interpretation method as described above, conditions for preventing formation of crystal defects in the single-crystal during growth of the single-crystal from an alumina melt, such as the angle of the interface between the single-crystal and the alumina melt, the movement speed of the interface, and the solidification rate at the time of contacting the crucible, may be determined.

In addition, the crystal defects may be reduced in the single-crystal when the movement speed of the lowest point of the interface between the single-crystal and the alumina melt is constantly maintained, from the shoulder growth process until the lowest point of the single-crystal contacts the bottom surface of the crucible, that is, in a range within which the angle of the interface between the single-crystal and the alumina melt decreases. In other words, a seed crystal cable may be drawn up at a rate within the above-mentioned range.

In addition, during the body growth process after the single-crystal contacts the bottom surface of the crucible, the single-crystal may be drawn up at a constant speed by hoisting the seed crystal cable.

In this regard, when the speed of hoisting the seed crystal cable is 5 mm per hour or less, formation of the crystal defects may be minimized.

Conditions for growing the sapphire single-crystal not having crystal defects are determined according to the method of interpreting sapphire single-crystal growth. The sapphire single-crystal is then grown under the determined conditions.

Hereinafter, a method of growing a sapphire single-crystal according to an embodiment of the present invention will be described.

A crucible containing an aluminum melt is prepared.

Then, a seed crystal is brought into contact with an alumina melt and is dipped in the alumina melt to grow a neck of a single-crystal. In this regard, crystal defects may be minimized when the neck grows at a rate of 500 g per hour or less.

Then, a shoulder of the single-crystal is grown from the neck. In this regard, the shoulder and the body are distinguished from each other by a solidification rate of 8% to 10% as a reference.

Then, a body is grown from the shoulder. In this regard, in the shoulder and body growth processes, the angle of the interface between the single-crystal and the alumina melt may be reduced. That is, from the shoulder growth process until the single-crystal contacts the bottom surface of the crucible, the angle of the interface between the single-crystal and the alumina melt may be reduced.

Particularly, when the body growth process is initiated, the angle of the interface between the single-crystal and the alumina melt may be in the range of 60°to 120°. In addition, when the single-crystal contacts the bottom surface of the crucible, the internal angle of the interface between the single-crystal and the alumina melt may be in the range of 40°to 60°.

Thus, in the range within which the angle of the interface between the single-crystal and the alumina melt decreases, the angle of the interface between the single-crystal and the alumina melt may be in the range of 40°to 120°.

In addition, after the single-crystal contacts the bottom surface of the crucible, the angle of the interface between the single-crystal and the alumina melt may increase, for example, between the state illustrated in FIG. 5 and the state illustrated in FIG. 6.

While the single-crystal is growing, the interface between the single-crystal and the alumina melt may be defined by Equation 1 below, as described above.

Equation 1

h_i(t)={d_i(t)/2}×{cot(α_i(t)/2)}

The interface between the single-crystal and the alumina melt may have a turning point, as a vertex of a cone shape, at a region corresponding to the center of the bottom surface of the crucible 30. The internal angle of the interface between the single-crystal and the alumina melt may be an internal angle of the turning point. The interface between the growing single-crystal and the alumina melt may have a smallest height at the region corresponding to the center of the bottom surface of the crucible which may be identical to the position of the turning point.

The crystal defects may be reduced in the single-crystal when the movement speed of the lowest point of the interface between the single-crystal and the alumina melt is held constant, from the shoulder growth process until the lowest point of the single-crystal contacts the bottom surface of the crucible, that is, in the range within which the internal angle of the interface between the single-crystal and the alumina melt decreases. In other words, a seed crystal cable may be drawn up at a rate within the above-mentioned range.

Furthermore, the solidification rate of the alumina melt may be 10% or greater when the single-crystal contacts the bottom surface of the crucible.

Formation of crystal defects such as LABBs and bubbles may be prevented during growth of the single-crystal from the alumina melt contained in the crucible according to the above-described method.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.

Claims

A method of interpreting sapphire single-crystal growth, the method comprising:

preparing a crucible filled with an alumina melt;

growing a single-crystal by bringing a seed crystal into contact with the alumina melt and dipping the seed crystal in the alumina melt;

calculating at least one of an angle and a movement speed of an interface between the single-crystal and the alumina melt;

measuring defects formed in the grown sapphire single-crystal; and

calculating at least one of an angle and a movement speed of an interface between the single-crystal and the alumina melt in which defects are not formed by repeating the crucible preparation operation, the single-crystal growth operation, the operation of calculating at least one of the angle and the movement speed of the interface, and the defects measurement operation.
The method according to claim 1, wherein the growing of the single-crystal comprises:

growing a neck of the single-crystal from the seed crystal;

growing a shoulder of the single-crystal from the neck; and

growing a body of the single-crystal from the shoulder,

wherein the interface between the growing single-crystal and the alumina melt has a lowest height at a region corresponding to the center of a bottom surface of the crucible.
The method according to claim 2, wherein the neck growth operation and the shoulder growth operations are distinguished from each other by measuring weight of the single-crystal.
The method according to claim 3, wherein:

the weight of the single-crystal is measured by a sensor connected to the seed crystal; and

the growth of the shoulder is completed when 8% to 10% of the alumina melt is solidified into the single-crystal.
The method according to claim 1, wherein the interface between the growing single-crystal and the alumina melt has a turning point at a region corresponding to the center of a bottom surface of the crucible.
The method according to claim 1, wherein the angle of the interface between the single-crystal and the alumina melt decreases as the single-crystal grows in some ranges.
The method according to claim 1, wherein the defects of the sapphire single-crystal comprise at least one defect selected from the group consisting of bubbles, low angle black boundaries (LABBs), and lineage.
The method according to claim 7, wherein the bubbles are formed in the shoulder and the body of the single-crystal.
The method according to claim 7, wherein the LABBs are formed in a lengthwise direction on the surface of the single-crystal as stripe patterns.
A method of growing a sapphire single-crystal, the method comprising:

preparing a crucible filled with an alumina melt;

growing a neck of a single-crystal by bringing a seed crystal into contact with the alumina melt and dipping the seed crystal in the alumina melt;

growing a shoulder of the single-crystal from the neck; and

growing a body of the single-crystal from the shoulder,

wherein an angle of an interface between the single-crystal and the alumina melt decreases in some ranges during the shoulder growth operation and the body growth operation.
The method according to claim 10, wherein the interface between the single-crystal and the alumina melt has a turning point at a region corresponding to the center of a bottom surface of the crucible,

wherein the angle of the interface between the single-crystal and the alumina melt is an angle of the turning point.
The method according to claim 10, wherein the interface between the growing single-crystal and the alumina melt has a lowest height at a region corresponding to the center of a bottom surface of the crucible.
The method according to claim 10, wherein the angle of the interface between the single-crystal and the alumina melt increases in some ranges after the single-crystal contacts the bottom surface of the crucible during the body growth operation.
The method according to claim 10, wherein the seed crystal is drawn up after the single-crystal contacts the bottom surface of the crucible, and a speed of drawing up the seed crystal is 5 mm per hour or less.
The method according to claim 10, wherein when the body growth operation is initiated, the angle of the interface between the single-crystal and the alumina melt is in the range of 60°to 120°.
The method according to claim 10, wherein when the single-crystal contacts the bottom surface of the crucible, the angle of the interface between the single-crystal and the alumina melt is in the range of 40° to 60°.
The method according to claim 10, wherein when the single-crystal contacts the bottom surface of the crucible, a solidification rate of the alumina melt to the single-crystal is greater than 10%.
The method according to claim 10, wherein the angle of the interface between the single-crystal and the alumina melt is in the range of 40° to 120°in a range within which the angle of the interface between the single-crystal and the alumina melt decreases.
The method according to claim 10, wherein the interface between the single-crystal and the alumina melt is defined an equation below:

h_i(t)={d_i(t)/2}×{cot(α_i(t)/2}

where h_i(t) is a height of the single-crystal between a lowest point and a highest point of the single-crystal immersed in the alumina melt, d_i(t) is a maximum diameter of the growing single-crystal, and α_i(t) is an internal angle of the interface between the single-crystal and the alumina melt.
The method according to claim 10, wherein:

the neck growth operation, the shoulder growth operation, and the body growth operation are distinguished by measuring weight of the single-crystal;

wherein the weight of the single-crystal is measured by use of a sensor connected to the seed crystal; and

the growth of the shoulder is completed when 8% to 10% of the alumina melt is solidified into the single-crystal.