JP2015107898A - Method of raising silicon single crystal - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of raising a silicon single crystal in which effects of stress acting in a single crystal during raising of the single crystal are taken into consideration and a large-diameter defective-free crystal can be precisely raised.SOLUTION: A single crystal raising device is used which has a water cooling body arranged to surround a single crystal being raised, and also has a heat shield body arranged to enclose an outer peripheral surface and a lower end surface of the water cooling body, and during raising of the single crystal having a diameter R(mm), the single crystal is lifted nearby the solid-liquid interface of the single crystal under a condition where an expression (A) of |G(R)-G(R)|/G(R)<0.08 holds for a temperature gradient G(R) in an axial direction of actual lifting at a position of a radius R (mm) from the center of the single crystal and an optimum temperature gradient G(R) within a range of 0<R<R-35 (mm).

Description

  The present invention relates to a method for growing a silicon single crystal by the Czochralski method (hereinafter referred to as “CZ method”). The present invention relates to a method for growing defect-free crystals that do not generate point defects such as infrared scatterer defects and dislocation clusters such as LD (Interstitial-type Large Dislocation).

  In the CZ method using a single crystal growth apparatus, a seed crystal is immersed in a silicon raw material melt stored in a quartz crucible in a chamber maintained in an inert gas atmosphere under reduced pressure, and the immersed seed crystal is gradually added. Pull up. Thereby, a silicon single crystal is grown continuously with the lower end of the seed crystal.

  FIG. 1 is a schematic diagram for explaining a situation in which various defects occur based on the Boronkov theory. As shown in the figure, in the Boronkov theory, the pulling speed is V (mm / min), and the temperature gradient in the pulling axis direction near the solid-liquid interface between the raw material melt in the crucible and the ingot (silicon single crystal) is G. (° C./mm), the ratio V / G is taken on the horizontal axis, and the concentration of vacancy-type point defects and the density of interstitial silicon type point defects are taken on the same vertical axis. The relationship with the defect concentration is schematically represented. It is explained that there is a boundary between a region where a vacancy type point defect occurs and a region where an interstitial silicon type point defect occurs, and that boundary is determined by V / G.

  The vacancy-type point defects originate from vacancies lacking silicon atoms that constitute the crystal lattice, and a representative example of the aggregate of the vacancy-type point defects is COP. Interstitial silicon type point defects originate from interstitial silicon in which silicon atoms enter between crystal lattices, and LD is a representative example of an aggregate of interstitial silicon type point defects.

As shown in FIG. 1, when V / G exceeds the critical point, a single crystal having a dominant vacancy point defect concentration is grown. On the other hand, when V / G falls below the critical point, a single crystal having a dominant interstitial silicon type point defect concentration is grown. For this reason, in the range where V / G is smaller than the critical point (V / G) ₁ , interstitial silicon type point defects are dominant in the single crystal, and aggregates of interstitial silicon point defects exist. Region [I] appears and LD occurs. In the range where V / G exceeds the critical point (V / G) ₂ , the vacancy-type point defects are dominant in the single crystal, and the region where the vacancy-type point defect aggregates exist [V] Appears and COP occurs.

When V / G is in the range of (V / G) ₁ to (V / G) ₂ , a defect-free region in which neither a vacancy-type point defect nor an interstitial silicon-type point defect exists as an aggregate in a single crystal [ P] appears and neither COP nor LD defect including OSF occurs. In the region [V] (V / G is in the range of (V / G) ₂ to (V / G) ₃ ) adjacent to the defect-free region [P], there is an OSF region that forms an OSF nucleus.

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], when V / G is in the range of the critical point to (V / G) ₂ , a region [P _V ] in which vacant point defects that do not become aggregates predominately appear. In the range of V / G from (V / G) ₁ to the critical point, a region [P _I ] in which interstitial silicon point defects that do not become aggregates predominately appears.

  FIG. 2 is a schematic diagram showing the relationship between the pulling rate and the defect distribution during single crystal growth. In the defect distribution shown in the figure, a silicon single crystal is grown while gradually lowering the pulling speed V, and the grown single crystal is cut along the central axis (pulling axis) to form a plate-shaped specimen. The result of having observed the plate-shaped test piece by the X-ray topograph method after making Cu adhere and heat-treating is shown.

As shown in FIG. 2, when growth is performed at a high pulling speed, a region where agglomerates of vacancy-type point defects (COP) exist over the entire in-plane region perpendicular to the pulling axis direction of the single crystal [V ] Occurs. When the pulling speed is decreased, the OSF region appears in a ring shape from the outer peripheral portion of the single crystal. The diameter of the OSF region gradually decreases as the pulling speed decreases, and disappears when the pulling speed becomes V ₁ . Accordingly, a defect-free region [P] (region [P _V ]) appears instead of the OSF region, and the entire in-plane area of the single crystal is occupied by the defect-free region [P]. Then, when the pulling rate is reduced to V ₂ , a region [I] where an interstitial silicon type point defect aggregate (LD) exists appears, and finally a defect-free region [P] (region [P _I ]). Instead, the entire in-plane area of the single crystal is occupied by the region [I].

  In recent years, the quality required for silicon wafers has been increasing due to the development of miniaturization of semiconductor devices. In addition, in order to improve the yield, there is an increasing demand for increasing the diameter of silicon wafers. For this reason, in the manufacture of silicon single crystal, which is a material for silicon wafers, various point defects such as OSF, COP, and LD are eliminated, and a defect-free region [P] is distributed over the entire surface. A technique for growing crystals is strongly desired.

In order to meet this demand, when pulling up the silicon single crystal, as shown in FIGS. 1 and 2, V / G is generated in the hot zone, and aggregates of interstitial silicon type point defects are generated over the entire surface. The first critical point (V / G) _{1 is not} higher than ₁ and the second critical point (V / G) _{2 is} not higher than the second critical point (V / G) ₂ where no agglomeration of vacancy-type point defects occurs. . In actual operation, manages the aim of the pulling speed as set between V ₁ and V ₂ (e.g., the median of the two), within the range of V ₁ ~V ₂ even if changing the pulling speed during growth To do.

Further, the temperature gradient G in the pulling axis direction in the vicinity of the solid-liquid interface depends on the size of the hot zone in the vicinity of the solid-liquid interface, so that the hot zone is appropriately designed in advance prior to single crystal growth. Generally, the hot zone is composed of a water-cooled body arranged so as to surround the growing single crystal and a heat shield arranged so as to surround the outer peripheral surface and the lower end surface of the water-cooled body. Here, the management indicators in designing the hot zone, and the temperature gradient G _c of the pulling axis direction of the center portion of the single crystal, the temperature gradient G _e in the pulling axis direction of the outer peripheral portion of the single crystal is used. In order to grow defect-free crystals, for example, in the technique disclosed in Patent Document 1, the difference ΔG (= G _e −) between the temperature gradient G _{c at the} center of the single crystal and the temperature gradient G _e at the outer periphery of the single crystal. G _c ) is within 0.5 ° C./mm.

  Incidentally, in recent years, it has been found that the V / G that should be aimed at growing defect-free crystals varies depending on the stress acting on the single crystal during single crystal growth. For this reason, since the technique disclosed in Patent Document 1 does not consider the effect of the stress at all, there are many situations in which a complete defect-free crystal cannot be obtained.

In this regard, for example, in Patent Document 2, a single crystal having a diameter of 300 mm or more is targeted for growth, and the temperature gradient G _{c in} the pulling axis direction at the center of the single crystal and the single crystal are considered in consideration of the effect of stress in the single crystal. A technique is disclosed in which a ratio (hereinafter also referred to as “temperature gradient ratio”) G _c / G _e with the temperature gradient G _{e in} the pulling axis direction of the crystal outer peripheral portion is larger than 1.8. However, the technique disclosed in Patent Document 2 does not always provide a perfect defect-free crystal even though the effect of stress in the single crystal is taken into consideration. This is considered to be due to the influence of the stress distribution in the plane perpendicular to the pulling axis direction in the single crystal.

JP 11-79889 A Japanese Patent No. 4819833

  The present invention has been made in view of the above problems, and in consideration of the in-plane distribution of stress acting on a single crystal during single crystal growth, grows defect-free crystals including large diameters with high accuracy. An object of the present invention is to provide a method for growing a silicon single crystal.

  In order to achieve the above-mentioned object, the present inventors paid attention to the stress acting on the single crystal during single crystal growth, and conducted a numerical analysis in consideration of this stress, and conducted extensive studies. As a result, the following knowledge was obtained.

Figure 3 is a diagram showing the relationship between stress sigma _mean and the critical V / G acting in the single crystal. As a result of investigating the relationship between the critical V / G and the average stress σ _mean by comprehensive heat transfer analysis with various hot zone conditions changed, as shown in FIG. 3, (critical V / G) = 0.17989 + 0.0012 Xσ _mean was found.

The stress distribution in the plane perpendicular to the pulling axis direction of the single crystal has regularity. If the stress in the center of the single crystal is determined, the stress distribution in the plane is the distance R in the radial direction from the center of the single crystal. Can be expressed as a function of Furthermore, by determining the stress at the center of the single crystal and determining the size of 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, From the stress distribution, it is possible to grasp the optimum temperature gradient distribution G _ideal (R) for growing defect-free crystals. Then, by using the optimum temperature gradient distribution G _ideal (R) as a management index, it becomes possible to perform appropriate dimensional design of the hot zone, and based on the optimum temperature gradient distribution G _ideal (R) as a reference. By setting the management range of the actual temperature gradient distribution G _real (R), it becomes possible to grow a defect-free crystal with high accuracy.

The present invention has been completed based on the above findings, and the gist thereof is the following method for growing a silicon single crystal. That is, the method for growing a silicon single crystal of the present invention includes:
A method of pulling up and growing a silicon single crystal from a raw material melt in a crucible placed in a chamber by a CZ method,
Using a single crystal growth apparatus in which a water-cooled body surrounding the single crystal being grown is arranged, and a heat shield surrounding the outer peripheral surface and the lower end surface of the water-cooled body is arranged,
When a single crystal having a radius of R _max (mm) is grown, an actual temperature gradient in the pulling axis direction at the position of the radius R (mm) from the center of the single crystal in the vicinity of the solid-liquid interface of the single crystal is expressed as G _real (R ), Where G _ideal (R) is the optimum temperature gradient in the pulling axis direction at the radius R from the center of the single crystal, the following equation (A) is satisfied within the range of 0 <R <R _max −35 (mm). The single crystal is pulled under satisfying conditions.
| G _real (R) −G _ideal (R) | / G _real (R) <0.08 (A)
In the formula (A), G _ideal (R) is represented 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 formula (a), x = R / _Rmax , and σ _mean (0) and σ _mean (x) are represented by the following formulas (b) and (c), respectively.
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, and σ _mean (0.75) and n (x) are represented by the following formula (d) and formula (e), respectively.
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 the distance (mm) between the lower end of the heat shield and the liquid surface of the raw material melt.

In the growth method described above, it is preferable to pull up the single crystal under the condition that satisfies the following formula (B).
| G _real (R) −G _ideal (R) | / G _real (R) <0.05 (B)

In the above growth method, when a single crystal having a diameter of 300 mm is grown, b ₁ = 17.2 and b ₂ = 40.8 in the above formula (b), and d ₁ = 0 in the above formula (d). 108, d ₂ = 11.3.

In the above growth method, when growing a single crystal having a diameter of 450 mm, b ₁ = 27.5 and b ₂ = 44.7 in the above formula (b), and d ₁ = 0 in the above formula (d). .081, d ₂ = 11.2.

According to the method for growing a silicon single crystal of the present invention, the control range of the temperature gradient distribution G _real (R) is appropriately set in consideration of the effect of stress in the single crystal, so that the defect-free crystal is accurately measured. It becomes possible to train well.

It is a schematic diagram explaining the condition where various defects generate | occur | produce based on the Boronkov theory. It is a schematic diagram which shows the relationship between the pulling speed at the time of single crystal growth, and defect distribution. It is a figure which shows the relationship between the average stress (sigma) _mean which acts in a single crystal, and critical V / G. It is a figure which shows the relationship between the in-plane average stress (sigma) _mean (0) of a single crystal center part, and the temperature gradient G (0) of a single crystal center part, The figure (a) is a single crystal of diameter 300mm, the figure ( b) shows the case of a single crystal having a diameter of 450 mm. When growing a single crystal with a diameter of 300 mm, it is a figure which shows the relationship between the relative radius r from the center of a single crystal, and in-plane average stress (sigma) _mean (r), The figure (a) is the magnitude | size of liquid level Gap. (B) shows the case where the size of the liquid surface gap is 70 mm, and (c) shows the case where the size of the liquid surface gap is 90 mm. When growing a single crystal with a diameter of 450 mm, it is a figure which shows the relationship between the relative radius r from the center of a single crystal, and in-plane average stress (sigma) _mean (r), The figure (a) is the magnitude | size of liquid level Gap. (B) shows the case where the liquid level gap is 90 mm, and (c) shows the case where the liquid level gap is 120 mm. It is a figure which shows the relationship between the magnitude | size of liquid level Gap, and average stress (sigma) _mean (0.75), The figure (a) shows the case of a single crystal with a diameter of 300 mm, The figure (b) shows the single crystal with a diameter of 450 mm. Each case is shown. It is a figure which shows the relationship between the relative radius r from the center of a single crystal, and the normalization average stress n (r). It is a figure which shows the relationship between the relative radius r from the center of a single crystal, and the optimal temperature gradient G _ideal , the figure (a) shows the case of a single crystal with a diameter of 300 mm, and the figure (b) shows the single crystal with a diameter of 450 mm. Each case is shown. It is a figure which shows typically the structure of the single crystal growth apparatus which can apply the growth method of the silicon single crystal of this invention.

  Below, the embodiment is explained in full detail about the growth method of the silicon single crystal of the present invention.

1. Expression of critical V / G in which stress effect is introduced V is the pulling speed when growing a single crystal (unit: mm / min), and G is the temperature gradient in the pulling axis direction near the solid-liquid interface of the single crystal (unit: ° C). / Mm), and the ratio of V to G (hereinafter also referred to as “critical V / G”) from which defect-free crystals are obtained is ξ. The critical V / G can be defined by the following equation (1) if the effect of stress acting on the single crystal during single crystal growth is introduced. Here, the vicinity of the solid-liquid interface of the single crystal means that the temperature of the single crystal is in the range from the melting point to 1350 ° C.
ξ _σmean = ξ ₀ + α × σ _mean (1)

In the equation, xi] _Shigumamean the stress in the crystal represents the critical V / G when the sigma _mean. ξ ₀ is a constant indicating the critical V / G when the stress in the crystal is zero. α is a stress coefficient, and σ _mean is an average stress (unit: MPa) in a single crystal. For example, ξ ₀ is 0.1789 and α is 0.0012. These values are the same regardless of whether a single crystal having a diameter of 300 mm is a growth target or a single crystal having a diameter of 450 mm. This is because these values do not depend on the diameter of the single crystal to be grown. The single crystal having a diameter of 300 mm herein refers to a product (silicon wafer) having a diameter of 300 mm, specifically, a single crystal having a diameter of 300.5 to 330 mm when grown. Similarly, a single crystal having a diameter of 450 mm refers to a product (silicon wafer) having a diameter of 450 mm, specifically, a single crystal having a diameter of 450.5 to 480 mm when grown.

Here, the average stress σ _mean corresponds to the stress that causes the volume change of the single crystal at the time of growth, and can be grasped by numerical analysis. In the surface along the radial direction in the minute part in the single crystal, the circumferential direction The vertical components σ _rr , σ _θθ , and σ _zz of the stress acting on each of the three planes, the plane along the plane and the plane perpendicular to the pulling-up axis direction, are extracted, and these are totaled and divided by three. Further, positive of the average stress σ _mean means tensile stress, and negative means a compressive stress.

The above equation (1) represents the relationship between the critical V / G in one dimension and the average stress σ _{mean. In} order to grow a defect-free crystal, an in-plane perpendicular to the pulling axis direction of the single crystal is used. It is necessary to think in.

2. Extension of the critical V / G formula introducing the stress effect to the in-plane distribution of the single crystal The pulling speed when growing the single crystal is V (unit: mm / min). Also, the radius of the single crystal to be grown is R _max (unit: mm), and the temperature gradient in the pulling axis direction near the solid-liquid interface at the radius R (unit: mm) from the center of the single crystal is G (r). (Unit: ° C./mm). Here, r = R / R _max and r is referred to as a relative radius. r = 0 means the center of the single crystal, r = 1 means the outer periphery of the single crystal for a R = R _max.

The ratio of V to G (r) from which a defect-free crystal can be obtained (hereinafter also referred to as “critical V / G (r)”, expressed by mathematical expression “(V / G (r)) _cri ”) is a stress effect. Can be defined by the following formula (2) according to the above formula (1). Again, ξ ₀ is 0.1789 and α is 0.0012. These values are the same regardless of whether a single crystal having a diameter of 300 mm is a growth target or a single crystal having a diameter of 450 mm. This is because these values do not depend on the diameter of the single crystal to be grown.
(V / G (r)) _cri = ξ ₀ + α × σ _mean (r) (2)

In the formula, σ _mean (r) is the average stress (unit: MPa) at the position of the relative radius r from the center of the single crystal, and the distribution of the average stress in the plane orthogonal to the pulling axis direction of the single crystal. Indicates.

Here, since the temperature gradient G (r) indicates the distribution of the temperature gradient in a plane orthogonal to the pulling axis direction of the single crystal, the distribution of the optimal temperature gradient G (r) for growing a defect-free crystal. I want to ask. However, there is a problem that the regularity of the distribution of the average stress σ _mean (r) in the plane is unknown. In addition, when there is no correlation between the distribution of the in-plane average stress σ _mean (r) and the temperature gradient G (r) under the conditions for growing defect-free crystals, the control condition cannot be determined. Become.

Therefore, the presence or absence of correlation between the in-plane average stress σ _mean (r) and the temperature gradient G (r) and the regularity of the in-plane average stress σ _mean (r) were examined.

2-1. Relationship between temperature gradient of single crystal center and average stress The relationship between the temperature gradient G (0) of the single crystal center and the in-plane average stress σ _mean (0) of the single crystal center was investigated. This examination was performed as follows. Based on the assumption that a single crystal with a diameter of 300 mm or a single crystal with a diameter of 450 mm is grown, first, the radiant heat of the surface of the single crystal under each hot zone condition is calculated by comprehensive heat transfer analysis with various changes in the hot zone conditions. Next, the temperature in the single crystal under each boundary condition was recalculated using the calculated radiant heat under each hot zone condition and variously changed solid-liquid interface shapes as boundary conditions. Here, as the hot zone condition change, the size of the gap (hereinafter also referred to as “liquid level gap”) between the lower end of the heat shield surrounding the single crystal and the liquid level of the raw material melt in the quartz crucible is set. changed. In addition, as a change in the condition of the solid-liquid interface shape, the height in the pulling axis direction from the liquid surface of the raw material melt to the center of the solid-liquid interface (hereinafter also referred to as “interface height”) was changed. And about each condition, based on the distribution of the temperature in a single crystal obtained by recalculation, the average stress was calculated.

FIG. 4 is a diagram showing the relationship between the in-plane average stress σ _mean (0) at the center of the single crystal and the temperature gradient G (0) at the center of the single crystal. FIG. 4 (a) shows a single crystal having a diameter of 300 mm. FIG. 5B shows the case of a single crystal having a diameter of 450 mm. This figure is obtained from the above analysis results. From the figure, the average stress σ _mean (0) at the center of the single crystal is proportional to the temperature gradient G (0) at the center of the single crystal regardless of the interface height, and the following equation (3) It was found that there was a correlation expressed.
σ _mean (0) = − b ₁ × G (0) + b ₂ (3)
Here, b ₁ and b ₂ are constants obtained by linear 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, respectively. In a single crystal having a diameter of 300 mm, b ₁ = 17.2 and b ₂ = 40.8, and 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, and strictly speaking, b ₁ = 27.548 and b ₂ = 44.713.

2-2. Regularity of in-plane average stress σ _mean (r) (1)
Subsequently, the regularity of the in-plane average stress σ _mean (r) was examined by the above numerical analysis. For a single crystal with a diameter of 300 mm, the size of the liquid level gap is set to three values of 40 mm, 70 mm, and 90 mm, and in each case, the height of the interface is 6 types at intervals of 5 mm at 0 to 25 mm. The in-plane average stress σ _mean (r) at the position of the relative radius r from the center of the single crystal was calculated. For single crystals with a diameter of 450 mm, the size of the liquid level gap is set to three values of 60 mm, 90 mm, and 120 mm, and in each case, the height of the interface is 8 types at intervals of 5 mm at 0 to 35 mm. The in-plane average stress σ _mean (r) at the position of the relative radius r from the center of the single crystal was calculated.

FIG. 5 is a diagram showing the relationship between the relative radius r from the center of the single crystal and the in-plane average stress σ _mean (r) in the case of growing a single crystal having a diameter of 300 mm. When the size of the surface gap is 40 mm, FIG. 7B shows the case where the size of the liquid surface gap is 70 mm, and FIG. 7C shows the case where the size of the liquid surface gap is 90 mm.

FIG. 6 is a diagram 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 a single crystal having a diameter of 450 mm is grown. When the size of the surface gap is 60 mm, FIG. 5B shows the case where the size of the liquid surface gap is 90 mm, and FIG. 5C shows the case where the size of the liquid surface gap is 120 mm.

5 and 6, if the size of the liquid level Gap is constant, the average stress σ _mean (0.75) at the position of the relative radius r = 0.75 from the center of the single crystal regardless of the interface height. Was a constant value. Based on this finding, the relationship between the size of the liquid surface gap and the average stress σ _mean (0.75) was examined, and FIG. 7 was obtained.

FIG. 7 is a diagram showing the relationship between the size of the liquid level Gap and the average stress σ _mean (0.75). FIG. 7A shows the case of a single crystal having a diameter of 300 mm, and FIG. The case of a single crystal of 450 mm is shown. From the figure, it was found that the relationship between the size of the liquid level gap (GAP, unit: mm) and the average stress σ _mean (0.75) (unit: MPa) is expressed by the following equation (4). . That is, it was found that σ _mean (0.75) is determined if the size of the liquid level Gap is determined.
σ _mean (0.75) = d ₁ × GAP−d ₂ (4)
Here, d ₁ and d ₂ are first-order approximations from the calculated values of the average stress σ _mean (0.75) at the position of each liquid level Gap and the relative radius r = 0.75 from the center of the single crystal. Is a constant obtained by In a single crystal having a diameter of 300 mm, d ₁ = 0.108 and d ₂ = 11.3, and 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, and strictly speaking, d ₁ = 0.0808 and d ₂ = 11233.

2-3. Regularity of in-plane average stress σ _mean (r) (2)
Furthermore, the regularity of the in-plane average stress σ _mean (r) was examined. Here, it was examined whether the shape of the in-plane average stress σ _mean (r) depends on the size of the liquid surface gap or the interface height.

The in-plane average stress σ _mean (r) described above was standardized as n (r) in the following equation (5). In equation (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 at the outer periphery of the single crystal.
n (r) = [σ _mean (r) −σ _mean (1)] / [σ _mean (0) −σ _mean (1)] (5)

FIG. 8 is a diagram showing the relationship between the relative radius r from the center of the single crystal and the standardized average stress n (r). In the figure, when the diameter of the single crystal is 300 mm and 450 mm, the size of the liquid level Gap and the interface height are variously changed and calculated from the in-plane average stress σ _mean (r) under each change condition. Normalized mean stress n (r) was plotted. From the figure, it was found that the standardized 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. n (r) can be expressed by the following equation (6) from the results shown in FIG.
n (r) = 0.959r ³ -2.0014r ² + 0.0393r + 1 (6)

That is, the in-plane average stress σ _mean (r) has regularity, and if the in-plane average stress σ _mean (0) at the center of the single crystal and the in-plane average stress σ _mean (1) at the outer periphery of the single crystal are known. From the above equation (5), the distribution of the in-plane average stress σ _mean (r) can be grasped.

3. Derivation of distribution of optimum temperature gradient G _ideal (r) By the above examination, the following formulas (3), (4) and (6) to be reprinted were obtained. In the study, 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 + 0.0393r + 1 (6)
n (r) = [σ _mean (r) −σ _mean (1)] / [σ _mean (0) −σ _mean (1)] (5)
Here, when growing a single crystal having a diameter of 300 mm, b ₁ = 17.2 and b ₂ = 40.8 in the above formula (3), and d ₁ = 0.108 in the above formula (4). , D ₂ = 11.3. When a single crystal having a diameter of 450 mm is grown, in the above formula (3), b ₁ = 27.5 and b ₂ = 44.7, and in the above formula (4), d ₁ = 0.081, d ₂ = 11.2.

From equation (6), n (0.75) can be calculated as a constant N (= 0.30827). By using this constant N and substituting r = 0.75 into the equation (5), the following equation (7) is obtained as an equation representing P (1).
σ _mean (1) = [σ _mean (0.75) −N × σ _mean (0)] / [1-N] (7)

Furthermore, by modifying the above equation (5), σ _mean (r) can be obtained as σ _mean (1) in the above equation (3) and σ _mean (0.75) in the above equation (4). And n (r) in the above formula (6) 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, if G (0) in the above equation (3) and GAP in the above equation (4) are determined, the in-plane average stress distribution σ _mean (r) can be obtained from the above equation (8).

Incidentally, as described above, the critical V / G (r) is expressed by the following equation (2).
(V / G (r)) _cri = ξ ₀ + α × σ _mean (r) (2)

V can be regarded as a constant. Therefore, the optimum temperature gradient G _ideal (r) for growing defect-free crystals can be expressed by the following equation (9) using G (0) in which r = 0 in equation (2).
G _ideal (r) = [(ξ ₀ + α × σ _mean (0)) / (ξ ₀ + α × σ _mean (r))] × G (0) (9)

4). Condition of temperature gradient during single crystal growth When a single crystal having a diameter of 300 mm or 450 mm is to be grown, ξ ₀ is 0.1789 and α is 0.0012. Substituting into 9), the optimum temperature gradient G _ideal (R) (unit: MPa) in the pulling axis direction at a radius R (unit: mm) from the center of the single crystal is expressed by the following equation (a).
G _ideal (R) = [(0.1789 + 0.0012 × σ _mean (0)) / (0.1789 + 0.0012 × σ _mean (x))] × G _real (0) (a)
(A) In the formula, x = R / R _max and G _real (0) is the actual temperature gradient in the pulling axis direction at the center of the single crystal. σ _mean (0) and σ _mean (x) are expressed by the following formulas (b) and (c). The expressions (b) and (c) are the same as the expressions (3) and (8), respectively. σ _mean (0) is an average stress at the center of the single crystal, and may be a value obtained by equation (b) or may 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 growing a single crystal having a diameter of 300 mm, b ₁ = 17.2 and b ₂ = 40.8 in the above formula (b). When a single crystal having a diameter of 450 mm is grown, b ₁ = 27.5 and b ₂ = 44.7 in the above formula (b). 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 expressions (d) and (e) are the same as the expressions (4) and (6), respectively.
σ _mean (0.75) = d ₁ × GAP−d ₂ (d)
n (x) = 0.959x ³ -2.0014x ² + 0.0393x + 1 (e)
In the formula (d), GAP is the size (unit: mm) of the liquid level Gap. When growing a single crystal having a diameter of 300 mm, d ₁ = 0.108 and d ₂ = 11.3. When a single crystal having a diameter of 450 mm is grown, d ₁ = 0.081 and d ₂ = 11.2.

FIG. 9 is a diagram showing the relationship between the relative radius r from the center of the single crystal and the optimum temperature gradient G _ideal , where FIG. 9A shows a single crystal having a diameter of 300 mm, and FIG. 9B shows a 450 mm diameter. The cases of single crystals are shown respectively. 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 1.5 ° C / mm, 2.0 ° C / mm, 2.5 ° C / mm, 3.0 ° C / mm and 3.5 ° C. / Mm and the size of the liquid level gap is 60 mm, 80 mm and 100 mm. As shown in the figure, the optimum temperature gradient can be grasped by determining the temperature gradient G _real (0) and the size of the liquid level Gap.

When growing a single crystal having a radius R _max (mm), the following equation (A) is satisfied within the range of 35 mm or more from the outer periphery, that is, in the range of 0 <R <R _max −35 (mm). The single crystal is pulled up. Thereby, it becomes possible to grow a defect-free single crystal with high accuracy.
| G _real (R) −G _ideal (R) | / G _real (R) <0.08 (A)
Here, G _real (R) is an actual temperature gradient in the pulling axis direction at a position of radius R (mm) from the center of the single crystal.

Moreover, in order to grow a single crystal without defect single crystals with higher accuracy, it is preferable to pull up the single crystal under conditions that satisfy the following formula (B).
| G _real (R) −G _ideal (R) | / G _real (R) <0.05 (B)

Thus, the distribution of the average stress σ _mean (r) in the plane orthogonal to the pulling axis direction of the single crystal is regular, and the distribution of the in-plane average stress σ _mean (r) is in the center of the single crystal. Can be grasped by the stress σ _mean (0) or the temperature gradient G _real (0) limited to. As a result, the temperature gradient G _real (0) of the single crystal central portion or the stress σ _mean (0) of the single crystal central portion and the liquid level Gap are determined in consideration of the effect of stress that affects the occurrence of point defects. This makes it possible to grasp the distribution of the temperature gradient G _ideal (R) that is optimal for growing defect-free crystals. Then, by using the distribution of the optimum temperature gradient G _ideal (R) as a management index, it becomes possible to perform an appropriate dimensional design of the hot zone, and the distribution of the optimum temperature gradient G _ideal (R) is used as a reference. By setting the management range, it is possible to grow a defect-free crystal with high accuracy.

5. Silicon Single Crystal Growth FIG. 8 is a diagram schematically showing a configuration of a single crystal growth apparatus to which the silicon single crystal growth method of the present invention can be applied. As shown in the figure, the single crystal growing apparatus is configured with a chamber 1 as an outer shell, and a crucible 2 is disposed at the center thereof. The crucible 2 has a double structure composed of an inner quartz crucible 2a and an outer graphite crucible 2b, and is fixed to the upper end of a support shaft 3 that can be rotated and lifted.

  A resistance heating type heater 4 surrounding the crucible 2 is disposed outside the crucible 2, and a heat insulating material 5 is disposed outside the crucible 2 along the inner surface of the chamber 1. Above the crucible 2, a pulling shaft 6 such as a wire that is coaxial with the support shaft 3 and rotates in a reverse direction or the same direction at a predetermined speed is disposed. A seed crystal 7 is attached to the lower end of the pulling shaft 6.

  In the chamber 1, a cylindrical water-cooled body 11 is disposed surrounding the silicon single crystal 8 being grown above the raw material melt 9 in the crucible 2. The water-cooled body 11 is made of, for example, a metal having good thermal conductivity such as copper, and is forcibly cooled by cooling water that is circulated inside. This water-cooled body 11 plays a role of accelerating the cooling of the growing single crystal 8 and controlling the temperature gradient in the pulling axis direction of the single crystal central portion and the single crystal outer peripheral portion.

  Furthermore, a cylindrical heat shield 10 is arranged so as to surround the outer peripheral surface and the lower end surface of the water-cooled body 11. The heat shield 10 shields high temperature radiant heat from the raw material melt 9 in the crucible 2, the heater 4, and the side wall of the crucible 2 from the growing single crystal 8, and a solid-liquid interface that is a crystal growth interface. In the vicinity of, the diffusion of heat to the low-temperature water-cooled body 11 is suppressed, and the temperature gradient in the pulling axis direction of the single crystal central part and the single crystal outer peripheral part is controlled together with the water-cooled body 11.

  A gas inlet 12 for introducing an inert gas such as Ar gas into the chamber 1 is provided at the upper portion of the chamber 1. An exhaust port 13 for sucking and discharging the gas in the chamber 1 by driving a vacuum pump (not shown) is provided below the chamber 1. The inert gas introduced into the chamber 1 from the gas inlet 12 descends between the growing single crystal 8 and the water-cooled body 11, and the lower end of the heat shield 10 and the liquid level of the raw material melt 9 are reduced. After passing through the gap (liquid level gap), it flows toward the outside of the heat shield 10 and further to the outside of the crucible 2, and then descends outside the crucible 2 and is discharged from the exhaust port 13.

  When growing the silicon single crystal 8 using such a growth apparatus, solid material such as polycrystalline silicon filled in the crucible 2 is used for the heater 4 while the chamber 1 is maintained in an inert gas atmosphere under reduced pressure. The raw material melt 9 is formed by melting by heating. When the raw material melt 9 is formed in the crucible 2, the pulling shaft 6 is lowered, the seed crystal 7 is immersed in the raw material melt 9, and the crucible 2 and the pulling shaft 6 are rotated in a predetermined direction while the pulling shaft 6 is gradually pulled up to grow a single crystal 8 connected to the seed crystal 7.

When growing a single crystal having a diameter of 450 mm, in order to grow a defect-free crystal, an actual pulling axis at a distance R (mm) from the center of the single crystal to the outer periphery in the vicinity of the solid-liquid interface of the single crystal. When the temperature gradient in the direction is G _real (R), the single crystal pulling speed is adjusted so as to satisfy the above formula (A) in the range of 0 <R <190 mm, and the single crystal is pulled. Prior to the growth of the single crystal, the dimensional shape of the hot zone (thermal shield and water-cooled body) is designed so as to satisfy the above formula (A), and this hot zone is used. Thereby, a large-diameter defect-free crystal having a diameter of 450 mm can be grown with high accuracy.

  The method for growing a silicon single crystal of the present invention is extremely useful for growing a large-diameter defect-free crystal in which various point defects such as OSF, COP, and LD do not occur.

1: chamber, 2: crucible, 2a: quartz crucible, 2b: graphite crucible,
3: support shaft, 4: heater, 5: heat insulating material, 6: lifting shaft,
7: seed crystal, 8: silicon single crystal, 9: raw material melt, 10: heat shield,
11: Water-cooled body, 12: Gas introduction port, 13: Exhaust port

Claims (4)

A method for growing a silicon single crystal from a raw material melt in a crucible placed in a chamber by the Czochralski method,
Using a single crystal growth apparatus in which a water-cooled body surrounding the single crystal being grown is arranged, and a heat shield surrounding the outer peripheral surface and the lower end surface of the water-cooled body is arranged,
When a single crystal having a radius of R _max (mm) is grown, an actual temperature gradient in the pulling axis direction at the position of the radius R (mm) from the center of the single crystal in the vicinity of the solid-liquid interface of the single crystal is expressed as G _real (R ), Where G _ideal (R) is the optimum temperature gradient in the pulling axis direction at the radius R from the center of the single crystal, the following equation (A) is satisfied within the range of 0 <R <R _max −35 (mm). A method for growing a silicon single crystal, comprising pulling the single crystal under satisfying conditions.
| G _real (R) −G _ideal (R) | / G _real (R) <0.08 (A)
In the formula (A), G _ideal (R) is represented 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 formula (a), x = R / _Rmax , and σ _mean (0) and σ _mean (x) are represented by the following formulas (b) and (c), respectively.
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, and σ _mean (0.75) and n (x) are represented by the following formula (d) and formula (e), respectively.
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 the distance (mm) between the lower end of the heat shield and the liquid surface of the raw material melt. 2. The method for growing a silicon single crystal according to claim 1, wherein the single crystal is pulled up under a condition satisfying the following formula (B).
| G _real (R) −G _ideal (R) | / G _real (R) <0.05 (B) When growing a single crystal having a diameter of 300 mm, in the above formula (b), b ₁ = 17.2, b ₂ = 40.8, in the above formula (d), d ₁ = 0.108, d ₂ = 11 3. The method for growing a silicon single crystal according to claim 1, wherein the growth method is .3. When growing a single crystal with a diameter of 450 mm, in the above formula (b), b ₁ = 27.5, b ₂ = 44.7, in the above formula (d), d ₁ = 0.081, d ₂ = 11 The method for growing a silicon single crystal according to claim 1 or 2, wherein: