JP2008184362A - Method for producing single crystal - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for producing a single crystal by conducting formation of a straight barrel part and a contracting diameter part by means of optimized control. <P>SOLUTION: This method for producing the single crystal is performed as follows: an average radius of liquid surface of a melt M within a predetermined time is measured; a variation in height of the liquid surface of the melt M within the predetermined time is measured; a variation in grown length of the single crystal C within the predetermined time is measured; a positional variation in height of a crucible 3a within the predetermined time is measured; weight reduction of the melt M is obtained based on the variation of the average radius of liquid surface, the variation in height of the liquid surface of the melt M and the positional variation in height of the crucible 3; weight increase of the grown single crystal C is obtained based on the variation in grown length of the single crystal C, the variation in height of the liquid surface of the melt M and a barrel radius parameter of the single crystal C; the barrel radius of the single crystal C is calculated provided that the obtained weight reduction of the melt M is equal to the weight increase of the grown single crystal C; and pulling up control of the single crystal C is conducted based on the calculated barrel radius of the single crystal. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for producing a single crystal that is pulled up while growing the single crystal by the Czochralski method (hereinafter referred to as “CZ method”).

  The CZ method is widely used for the growth of silicon single crystals. In this method, the seed crystal is brought into contact with the surface of the silicon melt contained in the crucible, the crucible is rotated, and the seed crystal is pulled upward while rotating in the opposite direction. In this way, a single crystal is formed.

As shown in FIG. 13, in the pulling method using the CZ method, first, raw silicon is loaded into a quartz glass crucible 52 provided in the chamber 51 and heated by a carbon heater 53 to obtain a silicon melt M. Thereafter, the seed crystal P attached to the tip of the pulling wire 54 is brought into contact with the silicon melt M to pull up the silicon crystal.
The crucible 52 and the wire 54 are provided so as to be rotatable about the pulling direction, respectively, but in the pulling process, the crucible 52 and the wire 54 are controlled to rotate in opposite directions.

  In general, prior to the start of pulling, after the temperature of the silicon melt M is stabilized, as shown in FIG. 13, necking is performed in which the seed crystal P is brought into contact with the silicon melt M to dissolve the tip of the seed crystal P. Necking is an indispensable process for removing dislocations generated in a silicon single crystal due to thermal shock generated by contact between the seed crystal P and the silicon melt M. By this necking, a neck portion P1 (small diameter portion) is formed. The neck portion P1 is generally required to have a diameter of 3 to 7 mm and a length of 30 to 40 mm or more.

When necking is completed, as shown in FIG. 14, the process proceeds to a diameter expanding process for expanding the crystal diameter to the straight body diameter. The enlarged diameter portion C1 is formed by this process.
After the formation of the enlarged diameter portion C1, as shown in FIG. 15, a straight body step of pulling up the single crystal C while maintaining the straight body portion diameter is performed. By this step, a straight body portion C2 (constant diameter portion) that is a product portion is formed.
Then, when ending the straight body process, as shown in FIG. 16, a diameter reducing process for gradually reducing the diameter of the single crystal C is performed. By this step, the reduced diameter portion C3 is formed, and finally the single crystal C is separated from the melt M.

In the pulling of the silicon single crystal by the CZ method, in order to manufacture a high-quality silicon single crystal, it is important to control the formation of the body diameter of the single crystal and the position of the liquid surface height of the silicon melt during the pulling process.
That is, with respect to the diameter of the single crystal, for example, in order to keep the diameter of the straight body portion constant, the diameter of the body is always measured, and this is fed back to the control of the pulling speed of the single crystal.
Conventionally, as a method of measuring the diameter of a single crystal, the interface between the solid single crystal and the liquid silicon melt (referred to as the solid-liquid interface) is optically measured by a measuring means such as a camera. Based on this, many optical methods for calculating the body diameter are used.

As for the control of the silicon melt liquid surface height, the silicon melt liquid surface in the crucible descends as the silicon single crystal grows. The relative position of the silicon melt liquid surface is made constant.
Conventionally, various methods have been proposed for measuring the liquid level necessary for controlling the liquid level height position of the silicon melt.
For example, Patent Document 1 discloses an apparatus that images a predetermined spot on a liquid surface with a laser and measures the melt surface height using an imaging signal.
JP 2002-80293 A

By the way, since the reduced diameter part C3 formed in the diameter reduction process after finishing the straight body process is not used in the product portion, it is desired that the diameter reduction process is completed in as short a time as possible.
This is because, if time is wasted in the diameter reduction process, the diameter-reduced portion becomes longer in the pulling direction and extra silicon melt M is used, resulting in a decrease in productivity.

However, in the method of measuring the barrel diameter of the single crystal, in the method of measuring the barrel diameter by an optical method, when the barrel diameter is rapidly reduced, measurement is performed following the change in the barrel diameter of the reduced diameter portion. There was a technical problem that it was difficult. For this reason, in order to maintain the measurement, it is necessary to form the reduced diameter portion long in the pulling direction.
Further, if the formation of the reduced diameter portion is performed rapidly without performing the diameter control of the single crystal, that is, without feeding back the measurement result of the diameter of the single crystal, the undesired melt from the unintended melt during the diameter reduction process. There is a high risk that the single crystal will be separated, and when this unintentional single crystal separation occurs, dislocation occurs in the single crystal or cracks occur.

  The present invention has been made under the circumstances as described above, and optimizes the formation of the straight body portion and the reduced diameter portion in the method of manufacturing a single crystal in which the silicon single crystal is pulled from the crucible by the Czochralski method. It is an object of the present invention to provide a method for producing a single crystal that can be executed by controlled control.

  In order to solve the above-described problems, a method for producing a single crystal according to the present invention is a method for producing a single crystal by pulling a single crystal from a melt melted in a crucible in a furnace body by a Czochralski method. Measuring an average liquid surface radius of the melt within a predetermined time, measuring a change in the liquid surface height of the melt within the predetermined time, and determining a change in growth length of the single crystal within the predetermined time. Based on the step of measuring and measuring the height position change amount of the crucible within the predetermined time, the average liquid surface radius and the liquid surface height change amount of the melt, and the height position change amount of the crucible Determining a decrease weight of the melt, and determining a growth increase weight of the single crystal based on a growth length change amount of the single crystal, a liquid surface height change amount of the melt, and a body radius variable of the single crystal The reduced weight of the melt obtained and the growth of the single crystal Calculating a cylinder radius of the single crystal based on the fact pressurized weight and are equal, characterized in that the run and performing a pulling control of the single crystal based on the single-crystal cylinder radius the calculated.

The average liquid surface radius of the melt is D, the liquid surface height change amount of the melt is N, the crucible height position change amount is H, the melt density is ρL, and the circularity is π. Then, in the step of obtaining the reduced weight of the melt, the reduced weight of the melt is obtained by π · ρL · D ² (HN), and the change amount of the growth length of the single crystal is g, cylinder radius variable d _pv crystal, when the a .rho.s the density of single crystal, in the step of obtaining the growth weight gain of the single crystal, the growth increase the weight of the single ^{_{crystal, π · ρS · d pv 2}} (g- obtained by N), in the step of calculating the cylinder radius d _pv of the single crystal, said cylinder radius d _pv ^{are, π · ρL · D 2 (} H-N) = π · ρS · d pv 2 (g-N ) Based on the relational expression
According to such a method, the diameter of the single crystal C can be measured by calculation regardless of the formation part of the straight body part or the reduced diameter part, and the value of the measured body diameter can be used for pulling control of the single crystal. You can give feedback.

Further, in the step of performing the pulling control of the single crystal, a step of setting a barrel radius of the single crystal as a target value before the pulling operation, and a single crystal so that the calculated barrel radius of the single crystal follows the target value. It is desirable to execute the step of controlling the pulling of the crystal.
Alternatively, in the step of performing the pulling control of the single crystal, a step of setting a cross-sectional area of the single crystal as a target value before the pulling operation, and a cutting of the single crystal obtained based on the calculated single crystal body radius. It is desirable to execute a step of performing pulling control of the single crystal so that the area follows the target value.
In this way, it is possible to form a straight body portion and a diameter-reduced portion having an optimal shape along the target value, and it is possible to prevent the occurrence of dislocation to single crystals, cracks, and the like.
In addition, since the length of the reduced diameter portion does not become redundant, a large amount of melt can be used for forming the straight body portion, and productivity can be improved.

  According to the present invention, in the method for producing a single crystal in which the single crystal is pulled from the crucible by the Czochralski method, the production of the single crystal that can execute the formation of the straight body portion and the reduced diameter portion by optimized control. A method and single crystal pulling apparatus can be obtained.

Embodiments of a method for producing a single crystal according to the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing an overall configuration of a single crystal pulling apparatus 1 to which a method for producing a single crystal according to the present invention is applied.
This single crystal pulling apparatus 1 includes a furnace body 2 formed by superposing a pull chamber 2b on a cylindrical main chamber 2a, a crucible 3 provided in the furnace body 2, and a semiconductor loaded in the crucible 3. And a carbon heater 4 for melting a raw material (raw material silicon) M. The crucible 3 has a double structure, and the inner side is constituted by a quartz glass crucible 3a and the outer side is constituted by a graphite crucible 3b.

  Further, a pulling mechanism 5 for pulling up the single crystal C is provided above the furnace body 2. The pulling mechanism 5 includes a winding mechanism 5a driven by a motor and a pulling wire 5b wound on the winding mechanism 5a. It consists of. A seed crystal P is attached to the tip of the wire 5b and pulled up while growing the single crystal C.

  Further, in the main chamber 2a, the surrounding of the single crystal C is surrounded above and in the vicinity of the crucible 3 in order not to give extra radiant heat from the carbon heater 4 or the like to the growing single crystal C. A radiation shield 6 having an opening at the top and bottom is provided.

  As shown in FIG. 1, the single crystal pulling apparatus 1 includes a heater controller 9 that controls the amount of power supplied to the heater 4 that controls the temperature of the silicon melt M, and a motor 10 that rotates the quartz glass crucible 3. And a motor control unit 10a for controlling the number of rotations of the motor 10. Furthermore, a lifting device 11 for controlling the height of the quartz glass crucible 3, a lifting device control unit 11a for controlling the lifting device 11, a wire reel rotating device control unit 12 for controlling the pulling speed and the number of rotations of the grown crystal, It has. These control units 9, 10a, 11a, 12 and the valve 14 and the exhaust pump 19 are connected to an arithmetic control device 8b of the computer 8.

Then, the manufacturing method of the single crystal C using such a single crystal pulling apparatus 1 is demonstrated.
In the raw material silicon melting step, first, raw material silicon is loaded into the quartz glass crucible 3 a of the crucible 3.
Next, based on the program stored in the storage device 8a of the computer 8, first, the heater control unit 9 is operated by the command of the arithmetic control device 8b to heat the heater 4, and the melting operation of the raw silicon in the crucible 3 is started. Is done.

When the silicon melt M is generated in the crucible 3, the single crystal pulling operation is started.
Specifically, the motor control unit 10a, the lifting / lowering device control unit 11a, and the wire reel rotation device control unit 12 are operated by the command of the arithmetic control device 8b, the crucible 3 is rotated, and the winding mechanism 5a is operated. Then the wire 5b is lowered. Then, the seed crystal P attached to the wire 5b is brought into contact with the silicon melt M, and necking for melting the tip of the seed crystal P is performed to form the neck portion P1.

Thereafter, the pulling conditions are adjusted by the command of the arithmetic control device 8b using the power supplied to the heater 4, the single crystal pulling speed (usually, a speed of several millimeters per minute) and the like as parameters, and first, the diameter-enlarged portion C1 is formed. A diameter expansion process is performed.
After the diameter expansion process, a straight cylinder process for forming the cylinder diameter constant is performed. In this straight body process, the operation control device 8b obtains a body diameter by arithmetic processing, and pulling up control is performed so as to maintain a predetermined body diameter.

また、微小単位時間ΔＴあたりの単結晶Ｃの成長増加重量は次式（２）により求められる。

尚、ρＬはシリコン融液Ｍの密度、ρＳは単結晶Ｃの密度、πは円周率である。また、ｇ、Ｈ、Ｎの各値については、上昇方向を正方向、下降方向を負方向と定義する。 The body diameter of the silicon single crystal C is calculated as follows. As shown in FIGS. 2 to 6, in a minute unit time ΔT (within a predetermined time), the cylinder radius (body radius variable) of the single crystal C is d _pv , and the average liquid surface radius of the silicon melt in the quartz glass crucible 3a. Where D is the single crystal growth length, G is the height position change amount of the crucible 3a, and N is the liquid surface height change amount of the silicon melt M, the decrease of the silicon melt M per minute unit time ΔT. A weight is calculated | required by following Formula (1).

Further, the growth increase weight of the single crystal C per minute unit time ΔT is obtained by the following equation (2).

Here, ρL is the density of the silicon melt M, ρS is the density of the single crystal C, and π is the circumference. For each value of g, H, and N, the upward direction is defined as a positive direction and the downward direction is defined as a negative direction.

ここで、シリコン融液Ｍの平均液面半径Ｄは、予め引上げ工程前において、この引上げ工程で使用されるルツボ形状に基づき、シリコン融液Ｍの液面高さに対応する値をコンピュータ８に入力設定しておくことにより求められる。
また、単結晶成長長さｇ、ルツボ３ａの高さ位置変化量Ｈ、シリコン融液Ｍの液面高さ変化量Ｎについては、公知の測定技術により求められる。 The following relational expression (3) is established based on the fact that the decrease weight of the silicon melt M per minute unit time ΔT and the growth increase weight of the single crystal C are equal.

Here, the average liquid surface radius D of the silicon melt M is preliminarily set to the computer 8 based on the crucible shape used in the pulling process before the pulling process. It is obtained by setting the input.
Further, the single crystal growth length g, the height position change amount H of the crucible 3a, and the liquid level change amount N of the silicon melt M can be obtained by a known measurement technique.

Therefore, the trunk radius (body radius variable) d _pv of the single crystal C is obtained from the following formula (4) from the formula (3).

2 is H> 0 and N = 0, FIG. 3 is H> 0 and N <0, FIG. 4 is H> 0 and N> 0, and FIG. 5 is H = 0 and N <0. In the case of 0, FIG. 6 is a case where H <0 and N <0, and shows a state change during a minute unit time ΔT, respectively. In any of these states, the trunk radius d _pv is obtained according to the equation (4) and fed back to the pulling up control by the computer 8.

Further, when the straight body process proceeds, the silicon melt M decreases from the crucible 3a, and as shown in FIG. 7 (when H> 0 and N = 0), during the minute unit time ΔT, the R at the bottom of the crucible. The average liquid surface radius D of the silicon melt M decreases to D ′ along the shape.
In this case, since the average liquid surface radius D of the melt M varies depending on the remaining amount of the silicon melt M, the remaining amount of the melt, the growth amount of the single crystal C, or the crucible height position is set as a variable x. By setting the average liquid surface radius D of the melt M corresponding to the change of the value of the variable x in the computer 8 in advance, the trunk radius d _pv of the single crystal C is obtained by the following equation (5).

When the straight body process is completed, the process proceeds to a diameter reducing process for forming the reduced diameter part C3. In this case, as shown in FIG. 8 (when H> 0 and N = 0), the body radius d _pv of the single crystal C is reduced to d _pv ′ and d _pv ″ during the minute unit times ΔT and ΔT ′. The average liquid surface radius D of the melt M is reduced to D ′ and D ″.
Here, if the height direction of the length of the reduced diameter portion C3 and g _t, cylinder radius d _pv monocrystalline C (g _t) is calculated by the following equation (6).

In the diameter reduction process, the following pulling control is performed.
First, as shown in the graph of FIG 9, the target value cylinder radius d _sp (g _t) is preset for the length g _t of the reduced diameter portion C3.
Then, as shown in the graph of FIG. 10, body diameter d _pv tapered segment C3 calculated for each minute unit time ΔT is, to be equal to the cylinder radius equal to the target value d _sp (g _t) single crystal pulling control The reduced diameter portion C3 is formed.

Alternatively, pulling up control may be performed as follows.
This pulling control, first, the target value d _sp (g _t) and d _sp-axis as shown in FIG. 11, g _t-axis area S _sp of the region formed by (or volume as a rotary body) is determined.
Further, at the time of the length dimension g _t is G _t of the reduced diameter portion C3 as shown in FIG. 12, the reduced diameter portion radius d _pv condensed in a micro unit time ΔT calculated for each small unit of time ΔT until then sum S _pv square area formed by multiplying the diameter growth length Delta] g _t (or, the sum of the cylinder volumes which are formed as a rotating body) and is determined.
The total area S _pv is pulled controlled to become equal to the obtained area S _sp from the target value d _sp (g _t) is performed.
The control method described with reference to FIGS. 9 to 12 is preferably used not only in the diameter-reduced portion C3 but also in the forming process of the straight body portion C2.

Further, in the above-described pulling control, in addition to the set value d _sp (g _t), it is preferable to set an ideal single crystal growth velocity V _sp at reduced diameter portion C3 formed.
This is due to the following reason. That is, when the silicon melt M decreases, the heat capacity of the melt M decreases, so the melt temperature tends to decrease. As a result, when the heating to the melt M by the heater is insufficient, there is a risk of inducing dislocation due to rapid solidification of the single crystal C or solidification of the raw material melt from the crucible inner wall.

Moreover, when the melt temperature is likely to decrease as the melt M decreases, the single crystal growth rate tends to increase gradually. This is because the solidification of the melt M is promoted as the temperature of the silicon melt M decreases.
Therefore, by setting the single crystal growth rate V _sp and increasing the heating amount of the melt M by the heater along the value, a rapid temperature change of the melt M is prevented, and the optimum single crystal pulling rate is achieved. It is possible to control, and the reduced diameter portion C3 can be reliably formed.

As described above, according to the embodiment of the present invention, the decrease weight of the silicon melt M and the growth increase weight of the single crystal are obtained by arithmetic processing, respectively, and the decrease weight of the silicon melt and the increase growth of the single crystal are obtained. Based on the equal weight, the body diameter (body radius) of the single crystal C is calculated.
In the pulling control, the pulling speed, the heater, and the like are controlled such that the calculated single crystal C has a barrel diameter equal to the target barrel diameter.
Therefore, according to this method, it is possible to measure the diameter of the single crystal C by calculation regardless of the location where the straight body portion or the reduced diameter portion is formed. There is no problem of not being able to follow.
That is, by feeding back the value of the measured body diameter, it is possible to form a straight body portion and a reduced diameter portion having an optimal shape according to the target value, and prevent the occurrence of dislocations, cracks, etc. to a single crystal. be able to.
Further, since the length of the reduced diameter portion does not become redundant, the silicon melt M can be used in a large amount for forming the straight body portion, and productivity can be improved.
In the above embodiment, the manufacturing method according to the present invention has been described as a means for solving the problems in the formation of the reduced diameter portion. However, in the method for manufacturing a single crystal of the present invention, as described above, only the reduced diameter portion is used. And can be applied to the formation of the straight body portion.
Moreover, in the said embodiment, although manufacture of the silicon single crystal was demonstrated to the example, in this invention, it can apply also to the manufacturing method of other single crystals other than the silicon | silicone pulled up by the Czochralski method. .

Then, the manufacturing method of the single crystal which concerns on this invention is further demonstrated based on an Example. In this example, the effect was verified by actually performing an experiment using the single crystal pulling apparatus having the configuration described in the above embodiment.
[Example 1]
In Example 1, a quartz glass crucible was filled with 300 kg of raw silicon, a single crystal having a diameter of 310 mm was pulled up, and a diameter reduction process was started to form a reduced diameter portion with a single crystal weight of 265 kg. Until the formation of the straight body part and the reduced diameter part, the single crystal diameter was controlled based on the production method according to the present invention.
In the final stage of the diameter reduction process, the diameter reduction part was formed based on the measurement value obtained by optical single crystal diameter measurement. This is because the change in the volume and weight of the single crystal grown per unit time due to the reduction in diameter (as well as the volume and weight changes in the melt raw material that decrease per unit time) is very small, and the calculated relative single crystal diameter This is because the error increases.
As a result, the length of the formed reduced diameter portion was about 370 mm and the weight was about 22 kg. The diameter reduction process was about 5 hours 30 minutes.
[Example 2]
In Example 2, a quartz glass crucible was filled with 300 kg of raw silicon, a single crystal having a diameter of 310 mm was pulled up, and a diameter reduction process was started to form a reduced diameter portion with a single crystal weight of 278 kg. In this experiment, the diameter-reduced portion was formed by the same method as in Example 1, and the amount of melt corresponding to the amount of melt remaining in the crucible after pulling up the single crystal in Example 1 Pulling up control was performed so that it might be used for part formation.
As a result of this experiment, it was possible to form a reduced diameter portion substantially the same as in Example 1. Furthermore, since the amount of silicon melt corresponding to the reduction of the reduced diameter portion contributed to the formation of the straight body portion, the length of the straight body portion increased by about 74 mm, which led to improvement in productivity and cost reduction.
[Comparative Example 1]
In Comparative Example 1, a quartz glass crucible was filled with 300 kg of raw silicon, a single crystal having a diameter of 310 mm was pulled up, and a diameter reduction process was started to form a reduced diameter portion with a single crystal weight of 265 kg.
In Comparative Example 1, a reduced diameter portion was formed in the reduced diameter portion process using a conventional optical single crystal diameter measurement method based on observation of a solid-liquid interface. And the solid-liquid interface was imaged with the camera which is a measurement means from the beginning of the diameter reduction part formation to the last, and diameter reduction part formation was performed.
As a result of this experiment, the length of the reduced diameter portion was about 500 mm and the weight was about 30 kg, and the time required for forming the reduced diameter portion was about 7 hours 30 minutes.

  From the experimental results of the above examples, it was confirmed that by using the method for producing a single crystal of the present invention, the production process can be shortened and the raw material melt can be used efficiently for producing a single crystal. That is, it was confirmed that the straight body part and the reduced diameter part formation after the straight body part formation can be executed by optimized control, and the productivity can be improved and the cost can be reduced.

  The present invention relates to a method for producing a single crystal by pulling the single crystal by the Czochralski method, and is suitably used in the semiconductor manufacturing industry and the like.

FIG. 1 is a block diagram showing the overall configuration of a single crystal pulling apparatus to which the method for producing a single crystal according to the present invention is applied. FIG. 2 is a diagram showing each dimensional position in a minute unit time necessary for calculating the straight body part diameter. FIG. 3 is another state diagram showing each dimensional position in a minute unit time necessary for calculating the straight body part diameter. FIG. 4 is another state diagram showing each dimensional position in a minute unit time necessary for calculating the straight body part diameter. FIG. 5 is another state diagram showing each dimensional position in a minute unit time necessary for calculating the straight body part diameter. FIG. 6 is another state diagram showing each dimensional position in a minute unit time required for calculating the straight body part diameter. FIG. 7 is another state diagram showing each dimensional position in a minute unit time necessary for calculating the straight body part diameter. FIG. 8 is a diagram showing each dimension position in a minute unit time necessary for calculating the diameter of the reduced diameter portion. FIG. 9 is a graph showing a trunk diameter as a target value of the reduced diameter portion. FIG. 10 is a graph illustrating an image for controlling the measured diameter value of the reduced diameter portion so as to follow the target value. FIG. 11 is a graph showing a cross-sectional area as a target value of the reduced diameter portion. FIG. 12 is a graph showing an image for controlling along the cross-sectional area with the cross-sectional area based on the measurement of the reduced diameter portion as a target value. FIG. 13 is a diagram for explaining a single crystal pulling step. FIG. 14 is a diagram for explaining a single crystal pulling step. FIG. 15 is a diagram for explaining a single crystal pulling step. FIG. 16 is a diagram for explaining a single crystal pulling step.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Single crystal pulling apparatus 2 Furnace body 2a Main chamber 2b Pull chamber 3 Crucible 3a Quartz glass crucible 4 Heater 5 Pulling mechanism 6 Radiation shield 8 Computer 8a Storage device 8b Arithmetic storage device C Single crystal M Raw material silicon, silicon melt P Seed crystal P1 neck

Claims (4)

A method for producing a single crystal by pulling a single crystal by a Czochralski method from a melt melted in a crucible in a furnace body,
Measure the average liquid surface radius of the melt within a predetermined time, measure the change in the liquid surface height of the melt within the predetermined time, and measure the change in the growth length of the single crystal within the predetermined time And measuring a height position change amount of the crucible within the predetermined time;
Based on the average liquid surface radius and liquid surface height change amount of the melt and the height position change amount of the crucible, the decrease weight of the melt is obtained, the growth length change amount of the single crystal, and the melt Determining the growth weight of the single crystal based on the change in the liquid level height and the body radius variable of the single crystal;
Calculating the radius of the single crystal based on the calculated reduced weight of the melt and the growth weight of the single crystal being equal;
Performing a pulling control of the single crystal based on the calculated single crystal body radius. When the average liquid surface radius of the melt is D, the liquid surface height change amount of the melt is N, the height position change amount of the crucible is H, the melt density is ρL, and the circumference is π. In the step of determining the reduced weight of the melt, the reduced weight of the melt is:
π · ρL · D ² (H−N),
In the step of determining the growth weight of the single crystal, where g is the amount of change in the growth length of the single crystal, d _pv is the body radius variable of the single crystal, and ρS is the density of the single crystal, Weight is
π · ρS · d _pv ² (g−N)
In the step of calculating the barrel radius d _pv of the single crystal, the barrel radius d _pv is:
π · ρL · D ² (H−N) = π · ρS · d _pv ² (g−N)
The method for producing a single crystal according to claim 1, wherein the single crystal is obtained based on the relational expression: In the step of performing pulling control of the single crystal,
Setting a barrel radius of the single crystal as a target value before the pulling operation;
The method for producing a single crystal according to claim 1, further comprising a step of performing pulling control of the single crystal so that the calculated body radius of the single crystal follows the target value. . In the step of performing pulling control of the single crystal,
Setting a cross-sectional area of the single crystal as a target value before the pulling operation;
The step of performing pull-up control of the single crystal so that a cross-sectional area of the single crystal obtained based on the calculated single crystal body radius is along the target value is executed. 2. A method for producing a single crystal described in 2.

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