TWI568897B - Cultivation method of silicon single crystal - Google Patents

Description

Method for cultivating single crystal

The present invention relates to a method for cultivating singular crystals by the Czochralski method (hereinafter referred to as "CZ method"), and more particularly to an OCT (Oxidation Induced Stacking Fault). In the case of accumulation defects, or infrared scattering defects such as COP (Crystal Originated Particle), or defect defects such as LD (Interstitial-type Large Dislocation) Method of cultivating crystals.

In the CZ method using a single crystal growth apparatus, the seed crystal is immersed in a raw material melt stored in a crucible of quartz crucible in a chamber maintained under an inert gas atmosphere under reduced pressure, and is impregnated. The seed crystal is slowly pulled. Thereby, a single crystal is grown in connection with the lower end of the seed crystal.

Fig. 1 is a schematic diagram showing the state of various defects generated according to Voronkov's theory. As shown in the figure, in the Voronkov theory, the drawing speed is set to V (mm/min), and the raw material melt in the crucible and the solid of the ingot (single crystal) When the temperature gradient in the direction of the pull axis near the liquid interface is G (°C/mm), the ratio of V/G is taken as the horizontal axis, and the concentration of the hole type defect and the inter-lattice type point are The concentration of defects is taken to be the same vertical axis, and the relationship between V/G and point defect concentration is schematically shown. Then, the boundary where the region where the void type defect is generated and the region where the lattice defect is generated between the lattices is described, and the boundary is determined by V/G.

The cavity type defect is rooted in a cavity lacking a germanium atom which should constitute a crystal lattice, and the representative lattice of the aggregate of the cavity type defect is COP. The inter-lattice-type point defect is based on the inter-lattice enthalpy between the argon atoms entering the crystal lattice, and the representative lattice of the condensate of the 矽-type point defect is LD.

As shown in Fig. 1, when V/G exceeds the critical point, a single crystal having a hole type defect concentration advantage is developed. Conversely, when V/G is below the critical point, a single crystal having an advantageous lattice point defect concentration concentration is developed. Therefore, in the range where V/G is lower than (V/G) ₁ which is smaller than the critical point, it is most advantageous in the case of inter-lattice-type point defects in a single crystal, and there is a lattice-type point defect. The area of the aggregate [I], which produces LD. When V/G exceeds the range of (V/G) ₂ larger than the critical point, the void point defect is the most advantageous in the single crystal, and the region [V] of the aggregate having the void type defect occurs, and Produce COP.

In the range where V/G is (V/G) ₁ to (V/G) ₂ , either single-crystal void point defects and inter-lattice-type point defects are not present in aggregate form. The defect-free area [P], including the OSF, does not occur in any of the COP and LD defects. In the region [V] adjacent to the defect-free region [P] (V/G is in the range of (V/G) ₂ to (V/G) ₃ ), there is an OSF region in which the OSF core is formed.

Further, the defect-free region [P] is divided into a region [P _V ] adjacent to the OSF region and a region [P I ] adjacent to the region [ _I ]. That is, in the defect-free region [P], in the range where the V/G is from the critical point to (V/G) ₂ , there is a region [P _V ] in which a void type defect which does not become an aggregate exists. However, in the range where V/G is from (V/G) ₁ to the critical point, there is a region where there is an advantage in the lattice-type point defect which does not become an aggregate [P _I ].

Fig. 2 is a schematic view showing the relationship between the drawing speed and the defect distribution at the time of single crystal growth. The defect distribution shown in the figure shows that while the drawing speed V is gradually lowered, the single crystal is grown while the single crystal to be grown is cut along the central axis (the pulling axis) to form a plate-like test piece. And Cu was attached to the surface thereof, and after the heat treatment was performed, the results of the plate-like test piece were observed by an x-ray topograph method.

As shown in Fig. 2, when the pulling speed is set to high speed, the entire area in the plane orthogonal to the direction of the drawing axis of the single crystal is covered, and a cluster of void-type point defects (COP) is generated. Area [V]. When the pulling speed is continuously lowered, the OSF region appears in a ring shape from the outer peripheral portion of the single crystal. The diameter of the OSF region will decrease as the pulling speed is gradually reduced, and when the pulling speed V ₁ becomes i.e. disappears. Along with this, the defect-free region [P] (region [P _V ]) appears instead of the OSF region, and the entire in-plane region of the single crystal is occupied by the defect-free region [P]. Furthermore, when the pulling speed is lowered to V ₂ , the region [I] of the aggregate (LD) where there is a lattice point defect occurs, and the entire area of the single crystal in the end will be the region [I]. Occupy replaces the defect-free area [P] (area [P _I ]).

Nowadays, due to the development of the miniaturization of semiconductor devices, the quality required for silicon wafers is increasing. In addition, in order to increase the yield, the requirements for the diameter of the silicon wafer are becoming higher and higher. Therefore, in the manufacture of single crystals belonging to the material of germanium wafers, it is strongly desired to exclude OSF. Or a variety of point defects such as COP or LD, and a technique of absorbing large-diameter defect-free crystals covering the entire area in the plane and distributing the defect-free area [P].

In order to meet this requirement, when drawing a single crystal, as shown in the above first and second figures, management must be performed to ensure that the V/G in the hot zone does not crystallize over the entire area of the covered surface. The first critical point (V/G) of the aggregate of the lattice defect of the lattice type is ₁ or more, and the second critical point (V/G) _{2 of the} aggregate of the void type defect is not generated. In actual operation, the target of the pulling speed is set between V ₁ and V ₂ (for example, the central value of both), and even if the pulling speed is changed during the cultivation, it falls within the range of V ₁ to V ₂ . The way to manage.

Further, the temperature gradient G in the direction of the drawing axis near the interface of the solid liquid depends on the size of the hot zone near the interface of the solid liquid, so that the hot zone is appropriately designed in advance before the single crystal is grown. In general, the hot zone is composed of a water-cooling body disposed so as to surround a single crystal in the cultivation, and a heat shielding body disposed to surround the outer circumferential surface and the lower end surface of the water-cooling body. Here, in the management index at the time of designing the hot zone, the temperature gradient G _{C in} the drawing axis direction of the center portion of the single crystal and the temperature gradient G _{e in} the drawing axis direction of the outer peripheral portion of the single crystal are used. Further, in order to cultivate a defect-free crystal, for example, in the technique disclosed in Patent Document 1, the difference ΔG (=G _e -G) between the temperature gradient G _C of the single crystal center portion and the temperature gradient G _e of the single crystal outer peripheral portion is set. _C ) is within 0.5 ° C / mm.

However, in recent years, it has become clear that the V/G which should be targeted in the cultivation of defect-free crystals fluctuates due to the stress acting on the single crystal during single crystal growth. Therefore, in the technique disclosed in the aforementioned Patent Document 1, since the effect of the stress is not considered at all, many cases in which complete defect-free crystallization cannot be obtained occur.

In this regard, for example, in Patent Document 2, it has been revealed that a single crystal having a diameter of 300 mm or more is a target for cultivation, and considering the effect of stress in a single crystal, the temperature gradient in the direction of the axial direction of the single crystal center portion is taken. The ratio of G _C to the temperature gradient G _e of the drawing axis direction of the outer peripheral portion of the single crystal (hereinafter also referred to as "temperature gradient ratio" G _C /G _{e is} increased to be larger than 1.8. However, Patent Document 2 In the disclosed technique, even if the effect of the stress in the single crystal is considered, it is not necessarily possible to obtain a complete defect-free crystal. It is presumed that the stress distribution in the plane orthogonal to the direction of the pull axis in the single crystal is affected. .

[Previous Technical Literature] [Patent Literature]

[Patent Document 1] Japanese Patent Laid-Open No. Hei 11-79889

[Patent Document 2] Japanese Patent No. 4819833

The present invention has been made in view of the above problems, and an object thereof is to provide an in-plane distribution in which stress acting on a single crystal during single crystal growth is considered, and a defect-free crystal can be accurately cultivated, including a large diameter. The method of cultivating single crystals.

In order to achieve the above object, the inventors of the present invention have focused on the stress acting on a single crystal at the time of single crystal growth, and have performed a numerical analysis in which the stress is incorporated, and have been carefully reviewed. As a result, the following wisdom is obtained.

Fig. 3 is a graph showing the relationship between the stress σ _mean acting on a single crystal and the critical V/G. The relationship between the critical V/G and the average stress σ _{mean was} investigated by comprehensive heat transfer analysis in which the conditions of the hot zone were variously changed. As a result, as shown in Fig. 3, (critical V/G) = 0.1789 was found. +0.0012 × σ _mean .

It has regularity in the stress distribution in the plane orthogonal to the direction of the pull-axis of the single crystal. As long as the stress at the center of the single crystal is specified, the in-plane stress distribution can be expressed as the radius from the center of the single crystal. The function of the direction distance R. Further, as long as the stress in the center portion of the single crystal is specified, and the gap between the lower end of the heat shielding body surrounding the single crystal and the liquid surface of the raw material melt in the quartz crucible is specified, the in-plane stress from the single crystal can be obtained. Distribution, mastering the distribution G _ideal (R) that is best suited to the temperature gradient of non-defective crystallization. Furthermore, by using the distribution G _ideal (R) of the optimum temperature gradient as a management index, an appropriate size design of the hot zone can be performed, and by setting the distribution of the optimal temperature gradient G _ideal (R As a basis for the management of the distribution of the actual temperature gradient G _real (R), the defect-free crystallization can be cultivated with good precision.

The present invention has been accomplished in light of the above-mentioned wisdom, and is intended to be a method of cultivating a single crystal as described below. That is, the method for cultivating the single crystal of the present invention is a method of cultivating a single crystal by a CZ method from a raw material melt disposed in a crucible in a chamber, characterized in that the use is arranged to surround the cultivation. a single crystal water-cooling body in which a single crystal growth device surrounding the outer surface and the lower end surface of the water-cooling body is disposed; in the case of cultivating a single crystal having a radius of R _max (mm), it will be in a single crystal In the vicinity of the solid liquid interface, the temperature gradient in the direction of the actual pull axis from the center of the single crystal from the radius R (mm) is set to G _real (R), and the pull axis from the center of the single crystal from the center of the radius R When the optimum temperature gradient of the direction is G _ideal (R), in the range of 0 < R < R _{max -} 35 (mm), single crystal pulling is performed to satisfy the condition of the following formula (A); |G _Real (R)-G _ideal (R)|/G _real (R)<0.08 ^· (A); in the above formula (A), G _ideal (R) is expressed by the following formula (a); G _ideal (R)=[(0.1789+0.0012×σ _mean (0))/(0.1789+0.0012×σ _mean (x))]×G _real (0) ^··· (a)

In the above formula (a), x = R / R _max , σ _mean (0) and σ _mean (X) are expressed by the following formulas (b) and (c); σ _mean (0) = -b ₁ ×G _real (0)+b ₂ ^··· (b)

σ _mean (X)[n(x)×(σ _mean (0)-σ _mean (0.75))-(N×σ _mean (0)-σ _mean (0.75))]/(1-N) ^··· (c)

In the above formula (c), N = 0.30827, σ _mean (0.75) and n(x) are expressed by the following formulas (d) and (e); σ _mean (0.75) = d ₁ × GAP-d ₂ ^··· (d)

n(x)=0.959x ³ -2.0014x ² +0.0393x+1 ^··· (e)

In the above formula (d), GAP is a distance (mm) between the lower end of the heat shielding body and the liquid surface of the raw material melt.

In the above-described cultivation method, it is preferred to carry out the drawing of the single crystal to satisfy the conditions of the following formula (B).

|G _real (R)-G _ideal (R)|/G _real (R)<0.05 ^··· (B)

In the above cultivation method, in the case of cultivating a single crystal having a diameter of 300 mm, in the above formula (b), b ₁ = 17.2 and b ₂ = 40.8, and in the above (d), d ₁ = 0.108 and d ₂ = 11.3.

In the above cultivation method, in the case of cultivating a single crystal having a diameter of 450 mm, in the above formula (b), b ₁ = 27.5 and b ₂ = 44.7, and in the above (d), d ₁ = 0.081 and d ₂ = 11.2.

According to the method for cultivating the single crystal of the present invention, since the effect of the stress in the single crystal is considered, the management range of the temperature gradient distribution G _real (R) is appropriately set, so that the defect-free crystal can be cultivated with high precision.

1‧‧‧ chamber

2‧‧‧坩埚

2a‧‧‧Quartz

2b‧‧‧Graphite

3‧‧‧Support shaft

4‧‧‧heater

5‧‧‧Insulation

6‧‧‧ Pulling shaft

7‧‧‧ seed crystal

8‧‧‧矽Single crystal

9‧‧‧Material melt

10‧‧‧Hot shield

11‧‧‧Water-cooled body

12‧‧‧ gas inlet

13‧‧‧Exhaust port

G, G(0), GC, Ge, G(r) ‧ ‧ temperature gradient

R‧‧‧relative radius

n(r)‧‧‧Standardized average stress

V‧‧‧ pull speed

Fig. 1 is a schematic diagram showing the state of occurrence of various defects according to the Voronkov theory.

Fig. 2 is a schematic view showing the relationship between the drawing speed and the defect distribution at the time of single crystal growth.

Fig. 3 is a graph showing the relationship between the average stress σ _mean acting on a single crystal and the critical V/G.

Fig. 4 is a graph showing the relationship between the in-plane average stress σ _mean (0) of the central portion of the single crystal and the temperature gradient G(0) of the central portion of the single crystal, and the figure (a) shows a single crystal having a diameter of 300 mm, and Figure (b) shows the case of a single crystal having a diameter of 450 mm.

Fig. 5 is a graph showing the relationship between the relative radius r from the center of the single crystal and the in-plane average stress σ _mean (r) when cultivating a single crystal having a diameter of 300 mm, and Fig. 5(a) shows the liquid surface Gap. In the case of a size of 40 mm, the figure (b) shows a case where the size of the liquid surface Gap is 70 mm, and the figure (c) shows a case where the size of the liquid surface Gap is 90 mm.

Fig. 6 is a graph showing the relationship between the relative radius r and the in-plane average stress σ _mean (r) from the center of the single crystal when a single crystal having a diameter of 450 mm is grown, and the figure (a) shows the liquid surface Gap. In the case of a size of 60 mm, the figure (b) shows a case where the size of the liquid surface Gap is 90 mm, and the figure (c) shows a case where the size of the liquid surface Gap is 120 mm.

Fig. 7 is a graph showing the relationship between the size of the liquid surface Gap and the average stress σ _mean (0.75), which shows the case of a single crystal having a diameter of 300 mm, and the figure (b) shows a single crystal having a diameter of 450 mm. The situation.

Figure 8 is a graph showing the relationship between the relative radius r and the normalized average stress n(r) from the center of the single crystal.

Figure 9 is a graph showing the relationship between the relative radius r from the center of the single crystal and the optimum temperature gradient G _ideal , which shows the case of a single crystal having a diameter of 300 mm, and the figure (b) shows the diameter. The case of a single crystal of 450 mm.

Fig. 10 is a schematic view showing the constitution of a single crystal growth apparatus to which the single crystal growth method of the present invention can be applied.

Hereinafter, the embodiment of the method for cultivating the single crystal of the present invention will be described in detail.

1. Formula for introducing critical V/G after stress effect

The drawing speed at the time of cultivating a single crystal is set to V (unit: mm/min), and the temperature gradient in the direction of the drawing axis near the interface of the solid liquid of the single crystal is set to G (unit: ° C/mm) to obtain no defect. The ratio of V to G (hereinafter also referred to as "critical V/G") of the crystal is set to ξ. The critical V/G can be defined by the following formula (1) as long as the effect of the stress acting on the single crystal at the time of single crystal growth is introduced. In the vicinity of the interface of the single crystal solid liquid referred to herein, it means the temperature of the single crystal from the melting Melting point to the range of 1350 °C.

Ξσ _mean =ξo+α×σ _mean ^··· (1)

In the same formula, ξσ _mean is the critical V/G when the stress in the crystal is σ _mean . Ξo is a constant indicating the critical V/G when the stress in the crystal is zero. The α-type stress coefficient, σ _mean is the average stress in a single crystal (unit: MPa). For example, ξo is 0.1789 and α is 0.0012. These values are not different when the single crystal having a diameter of 300 mm is used as a culture target or when a single crystal of 450 mm is used as a culture target. This is because the value of these values does not depend on the diameter of the single crystal to be cultivated. The single crystal having a diameter of 300 mm as used herein refers to a single crystal having a diameter of 300 mm as a product (矽 wafer), specifically, a diameter of 300.5 to 330 mm at the time of cultivation. Similarly, the single crystal having a diameter of 450 mm means that the diameter of the product (矽 wafer) is 450 mm, specifically, a single crystal having a diameter of 450.5 to 480 mm at the time of cultivation.

Here, the average stress σ _mean corresponds to the stress caused by the volume change of the single crystal during the incubation, and is graspable by numerical analysis, and is a radial direction acting on a minute portion of the single crystal. The vertical components σ _rr , σ _θθ , and σ _zz of the stresses of the surface, the surface along the circumferential direction, and the three faces orthogonal to the direction of the _{drawing axis} are extracted, and these are collectively _summarized and 3 In addition to the income. In addition, a positive value of the average stress σ _mean refers to tensile stress, and a negative value refers to compressive stress.

Although the above formula (1) shows the relationship between the critical V/G and the average stress σ _mean in one dimension, in order to cultivate a defect-free crystal, it is considered in a plane orthogonal to the direction of the drawing axis of the single crystal.

2. The formula of the critical V/G after the introduction of the stress effect is expanded to the single crystal in-plane distribution.

The drawing speed at the time of cultivating a single crystal is set to V (unit: mm/min). Further, the temperature gradient of the single-crystal to be cultivated is set to R _max (unit: mm), and the temperature gradient in the direction of the drawing axis near the interface of the solid liquid at the position of the radius R (unit: mm) from the center of the single crystal is set to G. (r) (unit: °C/mm). Here, r = R / R _max , and r is called a relative radius. r=0 means the center of a single crystal, and since r=1 is R=R _max , it means the outer periphery of a single crystal.

The ratio of V to G(r) in the defect-free crystal can be obtained (hereinafter also referred to as "critical V/G(r)"), and the formula is expressed by "(V/G(r) _cri )" as long as the stress effect is introduced. According to the above formula (1), it can be defined by the following formula (2). In this case, ξo is 0.1789 and α is 0.0012. The values are the same as the single crystal having a diameter of 300 mm. There is no difference in the time when the single crystal of 450 mm is used as the object of cultivation. This is because the value of these is not dependent on the diameter of the single crystal to be cultivated.

(V/G(r)) _cri =ξo+α×σ _mean (r) ^··· (2)

In the same formula, σ _mean (r) is the average stress (unit: MPa) from the center of the single crystal from the center of the radius r, which is the average stress in the plane orthogonal to the direction of the pull axis of the single crystal. distributed.

Here, since the temperature gradient G(r) shows the distribution of the temperature gradient in the plane orthogonal to the direction of the pull axis of the single crystal, an optimum temperature gradient G(r) is sought in order to cultivate the defect-free crystal. Distribution. However, the regularity of the distribution of the average stress σ _mean (r) in the plane is not clear, and this point becomes a problem. Further, when the distribution of the in-plane average stress σ _mean (r) and the temperature gradient G(r) have no correlation with the condition of cultivating the defect-free crystallization, the control condition cannot be determined to be a problem.

Therefore, it is reviewed whether the in-plane average stress σ _mean (r) has a correlation with the temperature gradient G(r) and the regularity of the in-plane average stress σ _mean (r).

2-1. Relationship between temperature gradient and average stress at the center of single crystal

The relationship between the temperature gradient G(0) at the center of the single crystal and the in-plane average stress σ _mean (0) at the center of the single crystal is reviewed. The review is conducted as follows. On the premise of cultivating a single crystal having a diameter of 300 mm or a single crystal of 450 mm, first, the surface of a single crystal under the conditions of each hot zone is calculated by comprehensive heat transfer analysis of various conditions of the hot zone. Radiation heat, and then the calculated radiant heat under the conditions of each hot zone and the shape of the interface of the solid liquid after various changes are used as boundary conditions, and the temperature in the single crystal under each boundary condition is calculated again. Here, in the change of the conditions of the hot zone, the gap between the lower end of the heat shield surrounding the single crystal and the liquid surface of the raw material melt in the quartz crucible (hereinafter also referred to as "liquid surface gap") is changed. Further, in the change of the condition of the solid liquid interface shape, the height from the liquid surface of the raw material melt to the center of the solid liquid interface in the direction of the drawing axis (hereinafter also referred to as "interface height") is changed. Further, for each condition, the calculation of the average stress was carried out based on the distribution of the temperature in the single crystal obtained by the recalculation.

Fig. 4 is a graph showing the relationship between the in-plane average stress σ _mean (0) of the central portion of the single crystal and the temperature gradient G(0) at the center of the single crystal, and Fig. 4(a) shows the case of a single crystal having a diameter of 300 mm. And Figure (b) shows the case of a single crystal having a diameter of 450 mm. This figure is obtained from the above analysis results. It can be understood from the figure that the average stress σ _mean (0) at the center of the single crystal is not dependent on the interface height, but is proportional to the temperature gradient G(0) of the central portion of the single crystal, and has the following (3) The correlation expressed by the formula.

σ _mean (0)=-b ₁ ×G(0)+b ₂ ^··· (3)

Here, b ₁ and b ₂ are constants obtained by a first approximation from the calculated value of the in-plane average stress σ _mean (0) and the calculated value of the temperature gradient G(0) at the center of the single crystal. In a single crystal having a diameter of 300 mm, b ₁ = 17.2 and b ₂ = 40.8. Strictly speaking, b ₁ = 17.211 and b ₂ = 40.826. In a single crystal having a diameter of 450 mm, b ₁ = 27.5 and b ₂ = 44.7. Strictly speaking, b ₁ = 27.548 and b ₂ = 44.713.

2-2. Regularity of the in-plane average stress σ _mean (r) (Part 1)

Next, the regularity of the in-plane average stress σ _mean (r) is reviewed by the numerical analysis described above. Regarding the single crystal having a diameter of 300 mm, the liquid level Gap is set to three values of 40 mm, 70 mm, and 90 mm, and in each case, the interface height is set to 6 heights at intervals of 5 mm from 0 to 25 mm, and The in-plane average stress σ _mean (r) from the center of the single crystal from the position of the radius r. For a single crystal having a diameter of 450 mm, the liquid level Gap is set to three values of 60 mm, 90 mm, and 120 mm, and in each case, the interface height is set to 8 heights at intervals of 5 mm from 0 to 35 mm, and The in-plane average stress σ _mean (r) from the center of the single crystal from the position of the radius r.

Fig. 5 is a graph showing the relationship between the relative radius r from the center of the single crystal and the in-plane average stress σ _mean (r) when cultivating a single crystal having a diameter of 300 mm, and Fig. 5(a) shows the liquid surface Gap. In the case of a size of 40 mm, the figure (b) shows a case where the size of the liquid surface Gap is 70 mm, and the figure (c) shows a case where the size of the liquid surface Gap is 90 mm.

Fig. 6 is a graph showing the relationship between the relative radius r from the center of the single crystal and the in-plane average stress σ _mean (r) when cultivating a single crystal having a diameter of 450 mm, and the graph (a) shows the liquid surface Gap. In the case of a size of 60 mm, the figure (b) shows a case where the size of the liquid surface Gap is 90 mm, and the figure (c) shows a case where the size of the liquid surface Gap is 120 mm.

As can be seen from Fig. 5 and Fig. 6, as long as the size of the liquid surface gap is constant, the average stress σ _mean (0.75) in the position of the relative radius r = 0.75 from the center of the single crystal becomes a constant value. It does not depend on the height of the interface. Based on this wisdom, the relationship between the size of the liquid surface gap and the average stress σ _mean (0.75) was reviewed. The result is shown in Fig. 7.

Fig. 7 is a graph showing the relationship between the size of the liquid surface Gap and the average stress σ _mean (0.75), which shows the case of a single crystal having a diameter of 300 mm, and the figure (b) shows a single diameter of 450 mm. The case of crystallization. As is clear from the figure, the relationship between the size of the liquid surface gap (GAP, unit: mm) and the average stress σ _mean (0.75) (unit: MPa) is expressed by the following formula (4). That is, as long as the size of the liquid surface Gap is determined, σ _mean (0.75) can be determined.

σ _mean (0.75)=d ₁ ×GAP-d ₂ ^··· (4)

Here, d ₁ and d ₂ are calculated from the calculated values of the average stress σ _mean (0.75) from the position of each liquid surface Gap and the relative radius r=0.75 from the center of the single crystal, respectively, in a first approximation manner. Constant. In a single crystal having a diameter of 300 mm, d ₁ = 0.108, d ₂ = 11.3, strictly speaking, d ₁ = 0.1084, and d ₂ = 11.333. In a single crystal having a diameter of 450 mm, d ₁ = 0.081 and d ₂ = 11.2, strictly speaking, d ₁ = 0.0808 and d ₂ = 11.233.

2-3. Regularity of in-plane average stress σ _mean (r) (2)

Further, the regularity of the in-plane average stress σ _mean (r) is reviewed. Here, whether or not the shape of the in-plane average stress σ _mean (r) depends on the size of the liquid surface gap or the interface height is examined.

The above-described in-plane average stress σ _mean (r) is normalized to n(r) by the following formula (5). In the formula (5), σ _mean (0) is the in-plane average stress at the center of the single crystal, and σ _mean (1) is the in-plane average stress outside the single crystal.

n(r)=[σ _mean (r)-σ _mean (1)]/[σ _mean (0)-σ _mean (1)] ^··· (5)

Fig. 8 is a graph showing the relationship between the relative radius r from the center of the single crystal and the normalized average stress n(r). In the figure, for the case where the single crystal diameter is 300 mm and the case of 450 mm, the size of the liquid surface gap and the height of the interface are variously changed, and the in-plane average stress σ _mean (r) under each changing condition is plotted. The calculated normalized average stress n(r). As can be seen from the figure, the normalized average stress n(r) does not depend on the diameter of the single crystal, the size of the liquid surface gap, and the interface height. The result of n(r) shown in the figure can be expressed by the following formula (6).

n(r)=0.959r ³ -2.0014r ² +0.393r+1 ^··· (6)

That is, the in-plane average stress σ _mean (r) has regularity, as long as the in-plane average stress σ _mean (0) of the center of the single crystal and the in-plane average stress σ _mean (1) of the outer periphery of the single crystal are known, that is, The distribution of the in-plane average stress σ _mean (r) can be grasped from the above formula (5).

3. Derivation of the distribution of the optimal temperature gradient G _ideal (r)

Through the above review, the following (3) and (4) are re-disclosed. Formula and (6). In addition, in the review, the following formula (5) was used.

σ _mean (0)=-b ₁ ×G(0)+b ₂ ^··· (3)

σ _mean (0.75)=d ₁ ×GAP-d ₂ ^··· (4)

n(r)=0.959r ³ -2.0014r ² +0.393r+1 ^··· (6)

n(r)=[σ _mean (r)-σ _mean (1)]/[σ _mean (0)-σ _mean (1)] ^··· (5)

Here, in the case of cultivating a single crystal having a diameter of 300 mm, in the above formula (3), b ₁ = 17.2 and b ₂ = 40.8, and in the above formula (4), d ₁ = 0.88 and d ₂ = 11.3. Further, in the case of cultivating a single crystal having a diameter of 450 mm, in the above formula (3), b ₁ = 27.5 and b ₂ = 44.7, and in the above formula (4), d ₁ = 0.081 and d ₂ = 11.2.

From the formula (6), n (0.75) can be calculated as a constant N (=0.30827). Using the constant N, r=0.75 is brought to the formula (5), and as the formula representing P(1), the following formula (7) can be obtained.

σ _mean (1)=[σ _mean (0.75)-N×σ _mean (0)]/[1-N] ^··· (7)

Further, the above formula (5) is modified, and σ _mean (r) is obtained by using σ _mean (1) of the above formula (3), σ _mean (0.75) of the above formula (4), and n of the above formula (6). (r) and the constant N can be expressed by the following formula (8).

σ _mean (r)=n(r)[σ _mean (0)-σ _mean (1)]+σ _mean (1)=[n(r)×(σ _mean (0)-σ _mean (0.75))- (N×σ _mean (0)-σ _mean (0.75))]/(1-N) ^··· (8)

Therefore, as long as the G(0) in the above formula (3) and the GAP in the above formula (4) are defined, the in-plane average stress distribution σ _mean (r) can be obtained from the above formula (8).

However, as described above, the critical V/G(r) is expressed by the following formula (2).

(V/G(r)) _cri =ξo+α×σ _mean (r) ^··· (2)

In addition, V can be regarded as a constant. Therefore, the temperature gradient G _ideal (r) which is most suitable for cultivating the defect-free crystal is G(0) which is set to r=0 in the formula (2), and can be expressed by the following formula (9).

G _ideal (r)=[(ξo+α×σ _mean (0))/(ξo+α×σ _mean (r))]×G(0) ^··· (9)

4. Conditions for temperature gradient in single crystal cultivation

When a single crystal having a diameter of 300 mm or 450 mm is used as the object of cultivation, ξo is 0.1789 and α is 0.0012. Therefore, the value is brought to the above formula (9), and the radius R (unit: mm) is obtained from the center of the single crystal. The optimum temperature gradient G _ideal (R) (unit: MPa) in the direction of the pull axis of the position is expressed by the following formula (a).

Gi _deal (R)=[(0.1789+0.0012×σ _mean (0))/(0.1789+0.0012×σ _mean (x))]×G _real (0) ^··· (a)

In the formula (a), x = R / R _max , and G _real (0) is a temperature gradient in the actual drawing axis direction of the center of the single crystal. σ _mean (0) and σ _mean (x) are expressed by the following formulas (b) and (c). The formulae (b) and (c) are the same formulas as the above formulas (3) and (8). σ _mean (0) is an average stress at the center of a single crystal, and can be a value obtained by the formula (b), and can also be a value obtained by another method.

σ _mean (0)=-b ₁ ×G _real (0)+b ₂ ^··· (b)

σ _mean (x)=[n(x)×(σ _mean (0)-σ _mean (0.75))-(N×σ _mean (0)-σ _mean (0.75))]/(1-N) ^{·· ·} (c)

When cultivating a single crystal having a diameter of 300 mm, in the above formula (b), b ₁ = 17.2 and b ₂ = 40.8. Further, in the case of cultivating a single crystal having a diameter of 450 mm, in the above formula (b), b ₁ = 27.5 and b ₂ = 44.7. In the formula (c), N = 0.30827, and σ _mean (0.75) and n (x) are represented by the following formulas (d) and (e). The formulas (d) and (e) are the same formulas as the above formulas (4) and (6).

σ _mean (0.75)=d ₁ ×GAP-d ₂ ^··· (d)

n(x)=0.959x ³ -2.0014x ² +0.0393x+1 ^··· (e)

In the above formula (d), the size (unit: mm) of the GAP liquid level Gap. When cultivating a single crystal having a diameter of 300 mm, d ₁ = 0.108 and d ₂ = 11.3. Further, when a single crystal having a diameter of 450 mm was grown, d ₁ = 0.081 and d ₂ = 11.2.

Figure 9 is a graph showing the relationship between the relative radius r from the center of the single crystal and the optimum temperature gradient G _ideal , which shows the case of a single crystal having a diameter of 300 mm, and the figure (b) shows the diameter. The case of a single crystal of 450 mm. In the figure, the horizontal axis is r (R/R _max ). In the figure, the temperature gradient G _real (0) at the center of the single crystal is set to 1.5 ° C / mm, 2.0 ° C / mm, 2.5 ° C / mm, 3.0 ° C / mm, and 3.5 ° C / mm, liquid level Gap The size is set to 60mm, 80mm and 100mm. As shown in the figure, the optimum temperature gradient can be grasped by specifying the magnitude of the temperature gradient G _real (0) and the liquid surface Gap.

When cultivating a single crystal having a radius R _max (mm), it is within a range of 35 mm or more from the outer circumference, that is, in a range of 0 < R < R _{max -} 35 (mm), to satisfy the following formula (A). Conditions for single crystal pulling. Thereby, the defect-free crystallization can be cultivated with good precision.

|G _real (R)-G _ideal (R)|G _real (R)<0.08 ^... (A)

Here, G _real (R) is a temperature gradient in the direction of the actual drawing axis from the center of the single crystal from the position of the radius R (mm).

Further, in order to further develop the defect-free single crystal with higher precision, it is preferred to carry out the drawing of the single crystal to satisfy the conditions of the following formula (B).

|G _real (R)-G _ideal (R)|G _real (R)<0.05 ^... (B)

Thus, there is regularity in the distribution of the average stress σ _mean (r) in the plane orthogonal to the direction of the pull axis of the single crystal, and the distribution of the in-plane average stress σ _mean (r) can be obtained by the single crystal center The stress σ _mean (0) or the temperature gradient G _real (0) defined by the part is grasped. As a result, the effect of stress which affects the generation of the point defect is incorporated, and the temperature gradient G _real (0) of the central portion of the single crystal or the stress σ _mean (0) of the central portion of the single crystal, and the liquid surface Gap are defined. It is possible to grasp the distribution of the temperature gradient G _ideal (R) which is most suitable for cultivating defect-free crystals. Furthermore, by using the distribution of the optimal temperature gradient G _ideal (R) as a management index, an appropriate size design of the hot zone can be performed, and by setting the optimal temperature gradient G _ideal (R) Distribution-based management allows for the development of defect-free crystals with precision.

5. Cultivation of single crystals

Fig. 8 is a view showing the constitution of a single crystal growth apparatus which can be applied to the cultivation method of the single crystal of the present invention. As shown in the figure, the single crystal growth apparatus has its outer periphery formed by the chamber 1, and has a crucible 2 disposed at the center thereof. The 坩埚 2 is a double structure composed of an inner quartz crucible 2a and an outer graphite crucible 2b, and is fixed to an upper end portion of the support shaft 3 that can be rotated and raised and lowered.

On the outside of the 坩埚2, there is a resistance added around 坩埚2 A heat type heater 4 is disposed on the outer side of the chamber 1 and a heat insulating material 5 is disposed along the inner surface of the chamber 1. Above the crucible 2, a pulling shaft 6 such as a wire that rotates in the opposite direction or the same direction at a predetermined speed coaxially with the support shaft 3 is disposed. A seed crystal 7 is attached to the lower end of the drawing shaft 6.

In the chamber 1, a cylindrical water-cooling body 11 surrounding the single crystal 8 in the growth is disposed above the raw material melt 9 in the crucible 2. The water-cooling body 11 is made of, for example, a metal having good thermal conductivity such as copper, and is forcibly cooled by cooling water flowing inside. The water-cooling body 11 serves to promote the cooling of the single crystal 8 in the cultivation, and controls the temperature gradient in the direction of the drawing axis of the single crystal center portion and the single crystal outer peripheral portion.

Further, a cylindrical heat shield 10 is disposed so as to surround the outer circumferential surface and the lower end surface of the water-cooling body 11. The heat shielding body 10 is responsible for blocking the high temperature radiant heat from the raw material melt 9 or the side wall of the heater 4 or the crucible 2 in the single crystal 8 in the cultivation, and is a solid liquid interface belonging to the crystal growth interface. In the vicinity, the water-cooling body 11 which is thermally diffused to a low temperature is suppressed, and the temperature gradient of the direction of the drawing axis of the single crystal center portion and the single crystal outer peripheral portion is controlled together with the water-cooling body 11.

A gas introduction port 12 for introducing an inert gas such as Ar gas into the chamber 1 is provided in an upper portion of the chamber 1. In the lower portion of the chamber 1, an exhaust port 13 for sucking and discharging the gas in the chamber 1 by driving of a vacuum pump (not shown) is provided. The inert gas introduced into the chamber 1 from the gas introduction port 12 is lowered between the single crystal 8 and the water-cooling body 11 during the incubation, and passes through the gap between the lower end of the heat shield 10 and the liquid surface of the raw material melt 9. (liquid level Gap), facing the outer side of the heat shielding body 10, and further toward the outer side of the crucible 2 After flowing, it descends to the outside of the crucible 2 and is discharged from the exhaust port 13.

When the single crystal 8 is grown by using such a growing device, the solid crystal filled in the crucible 2 is solidified by the heating of the heater 4 while maintaining the atmosphere in the chamber 1 under an inert gas atmosphere under reduced pressure. The raw material is melted to form a raw material melt 9. When the raw material melt 9 is formed in the crucible 2, the drawing shaft 6 is lowered to immerse the seed crystal 7 in the raw material melt 9, and the crucible 2 and the drawing shaft 6 are rotated in a predetermined direction while slowly pulling. The shaft 6 is pulled, thereby cultivating the single crystal 8 connected to the seed crystal 7.

In the case of cultivating a single crystal having a diameter of 450 mm, in order to cultivate a defect-free crystal, the position of the distance R (mm) from the center of the single crystal toward the outer peripheral direction in the vicinity of the solid liquid interface of the single crystal is actually in the direction of the pull axis. When the temperature gradient is G _real (R), in the range of 0 < R < 190 mm, the pulling speed of the single crystal is adjusted to satisfy the above formula (A), and the drawing of the single crystal is performed. Further, before cultivating the single crystal, the size and shape of the hot zone (heat shield and water-cooled body) are designed in such a manner as to satisfy the above formula (A), and the hot zone is used. Thereby, a large-diameter defect-free crystal having a diameter of 450 mm can be cultivated with high precision.

[Industrial availability]

The method for cultivating the single crystal of the present invention is extremely useful for cultivating large diameter non-defective crystals which do not cause various point defects such as OSF or COP or LD.

R‧‧‧relative radius

n(r)‧‧‧Standardized average stress

Claims (5)

A method for cultivating a single crystal by cultivating a single crystal having a radius of R _max (mm) by drawing a single crystal from a raw material melt disposed in a crucible disposed in a chamber by a Chalcola method, wherein a single crystal growth device surrounding the single crystal water-cooling body in the cultivation, and disposed with a heat shielding body surrounding the outer peripheral surface and the lower end surface of the water-cooling body; at this time, from the single crystal solid liquid interface, from the single crystal The temperature gradient in the actual pull axis direction of the center R from the position of the radius R (mm) is G _real (R); the central portion, the outer peripheral portion, the center portion, and the outer circumference including the single crystal are calculated by the integrated heat transfer analysis. in-plane stress distribution of the position between the portions, and σ _mean (x) is a single crystal plane stress distribution, where σ _mean (x) from the center line of the single crystal from the relative radial position x of the mean stress (unit: MPa), x = R / R _max , x = 0 refers to the center of the single crystal; calculates the in-plane temperature gradient distribution of the optimum single crystal for the purpose of cultivating the defect-free crystal in consideration of the aforementioned stress distribution, which is self-single crystal The center of the radius R is located in the direction of the pull axis The optimal temperature gradient G _ideal (R) is expressed by the following formula (a): G _ideal (R) = [(0.1789 + 0.0012 × σ _mean (0)) / (0.1789 + 0.0012 × σ _mean (x))] × ^{_{G real (0) ... (a}} ); the difference between the single crystal pulling axis direction of the temperature gradient of the distribution of the optimum temperature gradient above the actual set within a predetermined range, at 0 <R <R _max -35 inner (mm) in the range to satisfy the following conditions (a) of formula is a single crystal _{pulling: | G real (R) -G} ideal (R) | / G real (R) <0.08 ... (a); In the above formula (a), σ _mean (0) and σ _mean (X) are expressed by the following formulas (b) and (c); σ _mean (0) = -b ₁ × G _real (0) + b ₂ ^... (b) σ _mean (x)=[n(x)×(σ _mean (O)-σ _mean (0.75))-(N×σ _mean (0)-σ _mean (0.75))]/( 1-N) ^... (c) (c) above _{equation, N = 0.30827, σ mean (} 0.75) and n (x) lines were the following (D) of formula and (e) be represented; σ _mean (0.75) _{= d 1 × GAP-d 2} ... (d) n (x) = 0.959x 3 -2.0014x 2 + 0.0393x + 1 ... (e) (d) above wherein, GAP system of the body and the lower heat shield The interval (mm) of the liquid level of the raw material melt. According to the method for cultivating a single crystal according to the first aspect of the patent application, wherein the heat transfer analysis is performed, according to the temperature gradient of the central portion of the single crystal or the stress at the center of the single crystal, and the lower end of the heat shield and the raw material melt The gap between the liquid levels is used to calculate the temperature gradient distribution in the above-described optimum single crystal. According to the method of cultivating a single crystal according to the first item of the patent application, the drawing of a single crystal is carried out to satisfy the condition of the following formula (B): |G _real (R)-G _ideal (R)|/G _real ( R) < 0.05 ^... (B). According to the method for cultivating a single crystal according to the first or third aspect of the patent application, in the case of cultivating a single crystal having a diameter of 300 mm, in the above formula (b), b ₁ = 17.2 and b ₂ = 40.8, in the above (d), d ₁ =0.108, d ₂ = 11.3. According to the method for cultivating a single crystal according to the first or third aspect of the patent application, in the case of cultivating a single crystal having a diameter of 450 mm, in the above formula (b), b ₁ = 27.5 and b ₂ = 44.7, in the above (d), d ₁ = 0.081, d ₂ = 11.2.