TWI656247B - Method of manufacturing single-crystalline silicon - Google Patents

Abstract

Correctly determine the setting angle of the camera in the shooting chamber.

The present invention includes a camera installation angle measuring program (S21), which measures an installation angle of a camera provided on the outside of the reaction chamber in advance, and a crystal pulling program (S22) for drawing a melt from a crucible provided in the reaction chamber. crystallization. The camera sets the angle measurement program, and uses a camera to shoot the reaction chamber from obliquely above, and based on the estimated angle and focus distance of the camera, the projection image of the camera is projected onto the reference plane, and the furnace is displayed in the projected image after the projection conversion. The edge shape of the inner structure and the reference shape of the inner structure are shape-matched, and the estimated setting angle of the camera is changed as a variable parameter, and when the shape matching is performed, the estimation setting of the camera having the largest matching ratio is set. The angle is set to the actual set angle of the camera ( θ _c ). In the crystal pulling program (S22), the photographic image of the camera is projected and converted based on the actual setting angle of the camera.

Description

 Single crystal manufacturing method  

The present invention relates to a method for producing a single crystal according to the Czochralski (CZ) method, and more particularly to a method for accurately determining the installation angle of a camera in a shooting reaction chamber.

The single crystal of the substrate material of the semiconductor element is mostly produced by the CZ method. In the CZ method, the seed crystal is immersed in the crucible melt contained in the quartz crucible, and the seed crystal is gradually increased while rotating the seed crystal and the quartz crucible, thereby growing a single crystal having a large diameter at the lower end of the seed crystal. . By the CZ method, a large-diameter monocrystalline ingot having a diameter of 300 mm or more can be produced with high yield.

In order to control the crystal quality of the single crystal with high precision, it is necessary to control the liquid level of the molten metal with high precision, in particular, a cylindrical in-furnace structure called a heat insulating member disposed above the molten liquid. The distance from the lower end to the melt surface (gap). In order to control the liquid level of the mash liquid with high precision, for example, Patent Document 1 describes a method of accurately measuring the relative distance between the lower end of the thermal barrier tube disposed around the single crystal and the melt surface. In this method, the growth point of the single crystal which is the contact point of the single crystal and the melted surface and the lower end of the thermal barrier are taken from the outside of the furnace by the CCD camera, and the maximum growth point of the single crystal is detected from the image obtained therefrom. The position b and the position a of the inner diameter of the thermal barrier tube are the largest, and the difference between the position b at which the diameter of the single crystal has the largest growth point and the position a where the inner diameter of the thermal barrier tube is the largest is calculated. The difference between the obtained positions is taken as the difference x between the positions in the vertical direction on the image, and the difference between the position x in the vertical direction and the installation angle in the vertical direction of the CCD camera is used to calculate the melt surface and the lower end portion of the thermal barrier tube. The relative distance y.

Further, Patent Document 2 describes a method and system for obtaining a melting level and a position of a reflector in a Czochralski single crystal growth apparatus. The single crystal growth apparatus has a crucible that accommodates the crucible melt and heats it, and the crucible draws a single crystal. Similarly, the single crystal growth apparatus has a central opening, and has a reflector disposed in the crucible, and the single crystal is drawn through the central opening. The camera forms a part of the virtual image of a portion of the reflector and the reflector reflected by the liquid surface of the melt. The image processor processes the image as a function of the pixel value and detects the edge of the real image of the reflector and the edge of the virtual image. The control circuit determines the distance from the camera to the real image of the reflector and the distance from the camera to the virtual image of the reflector based on the relative position of the detected edge in the image. The control circuit obtains at least one parameter indicating the state of the single crystal growth device based on the obtained distance, and controls the single crystal growth device in accordance with the obtained parameters.

Patent Document 3 describes a method of accurately detecting the liquid surface position of the mash liquid and producing a single crystal having high quality crystal characteristics. In the manufacturing method, in the initial stage of the pulling, the first calculating unit sets the liquid level of the molten liquid based on the interval between the real image of the heat insulating member and the mirror image, and in the stage in which the single crystal migrates to the body portion, The second calculation unit sets the liquid level position of the molten liquid based on the image of the high luminance band (melting ring).

Further, Patent Document 4 describes a method for producing a single crystal in which the interval between the heat insulating member and the melt surface is controlled with higher precision. In this method, the differential information of the real image and the mirror image of the thermal insulation member photographed by the photographing device is used, and the contour of the real image and the mirror image is specified, and the melt liquid of the single crystal pulling is calculated from the specific contour line. The gap between the liquid level and the heat insulating member (gap). Further, in this method, the opening image of the heat insulating member having an elliptical appearance is circularly approximated, and the center position of the heat insulating member is calculated.

Patent Document 5 describes a method of adjusting the position of the camera and a camera position adjustment jig that can ensure the diameter detection accuracy at the stage before the start of the single crystal pulling. In this method, the display screen showing a circle having a known diameter is configured such that the display surface of the circle and the melt surface are at the same height position, and the camera is installed to detect the mounting position and the mounting angle of the circle by the diameter value of the circle detected by the camera. In order to make the detected diameter value coincide with the known diameter value, the camera is adjusted to an appropriate mounting position and mounting angle.

Advanced technical literature

Patent literature:

[Patent Document 1] Japanese Patent No. 4930487

[Patent Document 2] Japanese Patent Publication No. 2002-527341

[Patent Document 3] Japanese Patent No. 5678635

[Patent Document 4] Japanese Patent Laid-Open Publication No. 2013-216505

[Patent Document 5] Japanese Patent Laid-Open Publication No. 2015-129062

In the cultivation of a single crystal according to the CZ method, the type or distribution of defects contained in the single crystal is related to the ratio V/G of the drawing speed V of the single crystal and the temperature gradient G of the growth direction of the single crystal. In order to produce high-quality quinone crystals which do not contain a bit of defects or misaligned clusters and also take into account oxygen evolution after heat treatment, it is necessary to strictly control V/G.

The control of the V/G is performed by adjusting the pulling speed V. It is known that the distance between the melt face and the insulating member severely affects the temperature slope G. Therefore, in order to control the V/G in a very narrow variation allowable width, the distance between the melted surface and the heat insulating member must be kept constant. However, since the amount of melt is reduced as the crystal growth of the crucible is increased, in order to keep the distance between the melt surface and the heat insulating member constant, it is necessary to raise the crucible supporting the crucible, so it is necessary to accurately measure the liquid level. And precisely control the amount of rise of 坩埚 based on the measured value.

As described above, there are various methods for accurately measuring and precisely controlling the liquid level position. However, in recent years, the conditions for drawing high-quality single crystals have become very strict, and the measurement accuracy of the liquid surface position has to be further improved. In particular, it is not necessary to control the variation in the distance between the heat insulating member and the melt surface to be ±0.2 mm or less, and it is not necessary to improve the measurement accuracy of the liquid level position.

In order to correctly measure the position of the liquid surface, it is necessary to correctly project and convert the photographic image based on the correct setting angle of the camera. However, as described in Patent Document 5, in the method of physically adjusting the installation angle of the camera, it is difficult to accurately match the actual installation angle of the camera with the installation angle of the design, and therefore, based on the design deviation from the actual installation angle. When setting the angle for projection conversion, the photographic image cannot be correctly projected and converted on the reference plane. Therefore, the latter problem arises: the measurement accuracy of the liquid level position cannot be sufficiently improved due to the influence of the projection conversion error caused by the camera.

Therefore, an object of the present invention is to provide a method for producing a single crystal which accurately measures an installation angle of a camera in a shooting reaction chamber, and converts a captured image based on the installation angle, whereby the melt can be accurately measured and precisely controlled. Liquid level position.

In order to solve the above problem, the method for producing a single crystal according to the present invention is a method for producing a single crystal according to the Czochralski method, comprising: a camera setting angle measuring program, and measuring the reaction outside the reaction chamber in advance to photograph the reaction. a setting angle ( θ _c ) of the indoor camera; and a crystal pulling program for drawing a single crystal from the melt provided in the crucible in the reaction chamber; the camera is provided with an angle measuring program, and the above camera is used to photograph the above from obliquely above In the reaction chamber, based on the estimated installation angle ( θ ') and the focal length (f) of the camera, the photographic image of the camera is projected onto the reference plane; and the furnace structure appears in the photographic image after the projection conversion The edge shape and the reference shape of the above-described furnace structure are shape-matched; the estimated setting angle ( θ ') of the camera is used as a variable parameter to change within a predetermined range, and when the shape matching is performed, the matching ratio is maximized. The estimated setting angle ( θ ') of the above camera is set to the actual setting angle of the above camera ( θ _c ); the crystal pulling program, the above-mentioned melt in the reaction chamber is imaged obliquely from above by the camera; and the photographic image of the camera is based on the actual installation angle ( θ _c ) and the focal length (f) of the camera The projection is converted to the above reference plane.

According to the present invention, the installation angle of the camera can be accurately obtained, and the error of the projection conversion caused by the camera can be removed. Therefore, the liquid level position of the mash liquid can be accurately measured based on the photographic image of the camera, whereby the liquid level position can be precisely controlled.

In the present invention, it is preferable that the in-furnace structure is a heat insulating member disposed above the weir, and an edge shape of the in-furnace structure is a heat insulating member that penetrates the single crystal drawn from the melt The shape of the opening. Thereby, it is possible to accurately obtain the installation angle of the camera using the representative in-furnace structure appearing in the photographed image of the camera.

Preferably, in the present invention, the crystal pulling program is based on an opening of the real image of the heat insulating member which is projected in the converted photographic image based on the actual set angle ( θ _c ) and the focal length (f) of the camera. The shape and the opening shape of the heat insulating member of the above-mentioned heat insulating material appearing on the liquid surface of the melt are calculated, and the liquid level position of the melt is calculated. Thereby, the liquid level position in the single crystal pulling program can be accurately measured and controlled.

In the present invention, it is preferable that the reference shape of the opening of the heat insulating member is reduced according to a predetermined scale ratio, and the reduced reference shape and the shape of the opening shape of the solid image of the heat insulating member are matched, and based on the scale The ratio is the scale factor of the reference shape having the largest matching ratio when the shape matching is performed as the variable parameter, and the radius of the opening shape of the real image of the heat insulating member is calculated, and the reference shape of the opening of the heat insulating member is determined. The predetermined scale ratio is reduced, and the reduced reference shape is matched with the shape of the mirror-shaped opening shape of the heat insulating member, and the matching ratio is maximized when the shape matching is performed while changing the scale factor as a variable parameter. The scale ratio of the reference shape is calculated by calculating the radius of the opening shape of the heat insulating member in the mirror image. Thereby, the liquid level position in the single crystal pulling program can be correctly controlled.

In the method for producing a single crystal of the present invention, it is preferable that the radius from the installation position of the camera to the real image of the heat insulating member is calculated based on the radius of the opening shape of the real image of the heat insulating member and the actual installation angle of the camera. a distance from the installation position of the camera to a mirror image of the heat insulating member based on a radius of a mirror-shaped opening shape of the heat insulating member and an actual installation angle of the camera; the first distance and the first distance The second distance calculates the liquid level position of the melt. Thereby, the liquid level position in the single crystal pulling program can be correctly controlled.

In the method for producing a single crystal of the present invention, it is preferable that the distance between the heat insulating member and the liquid surface is calculated from a value of 1/2 of a difference between the first distance and the second distance. Thereby, the gap value can be calculated simply and accurately.

According to the present invention, the installation angle of the camera in the photographing reaction chamber is accurately measured, and the photographed image is projected and converted based on the set angle, whereby the liquid level position of the melt can be accurately measured and precisely controlled. Therefore, in the production of a single crystal, the manufacturing yield of a high-quality single crystal can be improved.

10‧‧‧矽Single crystal manufacturing equipment

11‧‧‧Quartz

12‧‧‧heater

13‧‧‧矽融液

13a‧‧‧ melt level

14‧‧ ‧ kinds of crystal

15‧‧‧矽Single crystal ingot

15a‧‧‧Neck

15b‧‧‧Shoulder

15c‧‧‧ Body Department

15d‧‧‧ tail

16‧‧‧坩埚Support

17‧‧‧Insulation members

17a‧‧‧ Opening

18‧‧‧ camera

18a‧‧‧Photographing device

18b‧‧‧ lens

19‧‧‧Reaction room

21‧‧‧坩埚 Lifting device

22‧‧‧ Pull drive

24‧‧ ‧ Calculation Department

26‧‧‧Control Department

C‧‧‧Center position of the camera

C ₀ ‧‧‧ coordinate origin of the reference plane

F‧‧‧Center position of the lens (main point)

f ₁ ‧‧‧Focus distance

L‧‧‧ optical axis

L _c ‧‧‧distance from the center of the camera to the origin of the coordinates of the reference plane

L _f ‧‧‧Distance from the center of the opening of the real image of the insulating member

L _m ‧‧‧Distance from the center of the mirrored opening of the insulating member

Ma‧‧‧ Real image of thermal insulation components

Mb‧‧ Mirror image of insulation

P‧‧‧any point on the camera 18a

P'‧‧‧ Projection point of any point on the imaging device 18a

r _f ‧‧‧ Radius of the real image opening of the insulating member

r _m ‧‧‧ Radius of the mirror opening of the insulating member

△a‧‧‧Change in working distance

△G‧‧‧ gap value

θ '‧‧‧ camera set angle

θ _c ‧‧‧The actual setting angle of the camera

Fig. 1 is a schematic cross-sectional view showing the configuration of a single crystal production apparatus in the present embodiment.

FIG. 2 is a flow chart for explaining a method of manufacturing a single crystal using the single crystal production apparatus 10.

Fig. 3 is a side view showing the shape of a single crystal ingot produced by the manufacturing method of Fig. 2;

Fig. 4 is a flow chart showing a control method of crystal pulling conditions.

Fig. 5 is a view showing a relationship between a real image and a mirror image of the heat insulating member 17 for a photographed image of the camera 18.

Fig. 6 is a schematic view for explaining a method of converting a quadratic coordinate projection of a photographic image into a coordinate of a real space.

Fig. 7 is a graph showing the luminance of the pixel sequence in the horizontal direction of the captured image and the differential value thereof.

FIG. 8 is a schematic view for explaining a method of calculating the gap value ΔG from the opening radii r _f and r _m of the real image Ma and the mirror image Mb of the heat insulating member 17 .

FIG. 9 is an explanatory view showing a change in the shape of the opening of the heat insulating member 17 in accordance with the change in the installation angle of the camera 18.

FIG. 10 is a view showing a result of matching the shape of the actual shape of the opening of the heat insulating member 17 and the shape of the reference shape when the installation angle of the camera 18 is changed, and (a) shows the left edge of the opening of the heat insulating member 17, (b) shows the right side edge of the opening of the heat insulating member 17.

FIG. 11 is a flowchart illustrating a method of measuring the installation angle θ _c of the camera 18.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In addition, the embodiments shown below are specifically described in order to enable a clearer understanding of the present invention, and are not intended to limit the present invention unless otherwise specified. In order to make the features of the present invention easier to understand, the drawings used in the following description may be enlarged and displayed as a part of an important portion, and the dimensional ratios and the like of the respective constituent elements are not necessarily the same as the actual ones.

Fig. 1 is a schematic cross-sectional view showing the configuration of a single crystal production apparatus in the present embodiment.

As shown in Fig. 1, a single crystal production apparatus 10 has a substantially cylindrical reaction chamber 19, and a quartz crucible 11 for storing a molten metal 13 is provided inside the reaction chamber 19. The reaction chamber 19 may be, for example, a double wall structure in which a certain gap is formed inside, and by allowing cooling water to flow into the gap, the reaction chamber 19 is prevented from being heated when the quartz crucible 11 is heated.

An inert gas such as argon is introduced into the inside of the reaction chamber 19 as described above before the start of the drawing of the single crystal. At the top of the reaction chamber 19, a pull drive unit 22 is provided. The driving device 22 is pulled so that the seed crystal 14 as the growth core of the single crystal ingot 15 and the single crystal ingot 15 grown therefrom are rotated while being pulled upward. On the above-described pulling drive device 22, a sensor (not shown) for sending the crystal length information of the single crystal ingot 15 based on the pulling amount of the single crystal ingot 15 can be formed.

Inside the reaction chamber 19, a heater 12 is provided which is arranged in a substantially cylindrical shape so as to surround the quartz crucible 11. The heater 12 heats the quartz crucible 11. The ruthenium support (graphite crucible) 16 and the quartz crucible 11 are housed inside the heater 12. The quartz crucible 11 is a substantially cylindrical container integrally formed of quartz and having an open surface formed above.

The quartz crucible 11 stores the molten thorium 13 after the solid crucible is melted. The ruthenium support 16 is, for example, formed entirely of graphite, and surrounds and closely supports the quartz crucible 11. The crucible support 16 maintains the shape of the quartz crucible 11 which has been softened when the crucible is melted, and realizes the task of supporting the quartz crucible 11.

A squat elevator device 21 is provided below the dam support 16. The crucible elevator device 21 supports the crucible support body 16 and the quartz crucible 11 from the lower side, and moves the quartz crucible 11 up and down so that the melted surface of the crucible melt 13 changes as the crucible single crystal ingot 15 is pulled. The liquid level of 13a is in the proper position. Thereby, the position of the melt surface 13a of the crucible melt 13 is controlled. The lifter device 21 is simultaneously provided with support so that the support body 16 and the quartz crucible 11 can be rotated according to a predetermined number of rotations during the drawing.

A heat insulating member (shield cylinder) 17 is formed on the upper surface of the quartz crucible 11 to cover the upper surface of the molten metal 13, that is, the melt surface 13a. The heat insulating member 17 is formed of a heat insulating plate having a stroke shape, for example, and has a circular opening 17a at its lower end. Further, the outer edge portion of the upper end of the heat insulating member 17 is fixed to the inner surface side of the reaction chamber 19.

As described above, the heat insulating member 17 prevents the unilateral crystal ingot 15 after the drawing from being subjected to the radiant heat from the mash liquid 13 in the quartz crucible 11 to change the heat history and deteriorate the quality. In addition, as the heat insulating member 17 described above, the pull-in ambient gas that has been introduced into the interior of the single crystal production apparatus 10 is induced from the side of the single crystal ingot 15 to the side of the melted liquid 13, thereby controlling the melting The residual oxygen amount in the vicinity of the melt surface 13a of the liquid 13, or the xenon vapor or SiO which is evaporated from the molten liquid 13 causes the single crystal ingot 15 to reach the target quality. The control of the pull-in ambient gas as described above depends on the flow velocity when passing through the furnace pressure and the gap between the lower end of the heat insulating member 17 and the melt surface 13a of the melted liquid 13. In order to achieve the target quality of the single crystal ingot 15, it is necessary to correctly set the distance (gap value) ΔG from the lower end of the heat insulating member 17 to the melt surface 13a of the mash 13 . Further, the pulling ambient gas may include hydrogen, nitrogen, or other predetermined gas as a dopant gas in an inert gas such as argon.

A camera 18 is provided outside the reaction chamber 19. The camera 18 is, for example, a CCD camera, and passes through an observation window formed in the reaction chamber 19 to capture the inside of the reaction chamber 19. The set angle θ _{c of the} camera 18 with respect to the drawing axis Z of the single crystal ingot 15 is first formed at a predetermined angle, and the camera 18 has an optical axis L inclined with respect to the vertical direction. That is, the camera 18 photographs the upper surface region of the quartz crucible 11 including the circular opening 17a of the heat insulating member 17 and the melt surface 13a from obliquely above.

The camera 18 is connected to the calculation unit 24 and the control unit 26. Further, the calculation unit 24 and the pull drive unit 22 are connected to the control unit 26. The control unit 26 controls the amount of movement (rise amount) of the quartz crucible 11 based on the crystal length data of the single crystal ingot 15 obtained from the sensor of the drawing drive device 22 and the crystal length data obtained from the camera 18.

In order to control the amount of movement of the quartz crucible 11, the control unit 26 performs position correction control of the quartz crucible 11 based on the position correction data of the quartz crucible 11 calculated by the calculation unit 24.

The calculation unit 24 calculates the liquid level position of the mash liquid 13 based on the image of the thermal image of the heat insulating member 17 that is imaged by the camera 18 and the image of the heat insulating member 17 that is reflected on the melt surface 13a of the mash. Therefore, the camera 18 captures the real image and the mirror image of the melt surface 13a of the mash 13 and the opening 17a of the heat insulating member 17 which are seen through the circular opening 17a at the lower end of the heat insulating member 17, and the calculation unit 24 measures the partition. The actual height position of the melt surface 13a is calculated from the interval between the real image and the mirror image of the heat member 17.

FIG. 2 is a flow chart for explaining a method of manufacturing monocrystalline crystals using the single crystal production apparatus 10. 3 is a side view showing the shape of a single crystal ingot produced by the manufacturing method of FIG. 2.

As shown in Fig. 2, in the production of a single crystal, first, a polycrystalline silicon of a raw material is introduced into a quartz crucible 11, and the polycrystalline crucible in the quartz crucible 11 is heated and melted by a heater 12 to produce a molten liquid 13 (step S11).

Next, the seed crystal 14 is lowered to bring it into contact with the mash liquid 13 (step S12). Then, the contact state with the mash liquid 13 is maintained, and a crystal pulling program for slowly pulling the seed crystal to grow the single crystal is carried out (steps S13 to S16).

In the crystal pulling process, the following steps are sequentially performed, and finally, the single crystal is detached from the melt surface: a neck forming process for forming the neck portion 15a which is reduced in thickness for thinning is formed (step S13), and formation is performed. The shoulder portion growing program of the shoulder portion 15b whose crystal diameter is gradually increased (step S14), and the main body portion growing program for forming the main body portion 15c having a crystal diameter maintained at a predetermined diameter (for example, about 300 mm) (step S15), forming a crystal diameter The tail breeding program of the tail portion 15d is gradually reduced (step S16). By the above, the single crystal ingot 15 having the neck portion 15a, the shoulder portion 15b, the body portion 15c, and the tail portion 15d as shown in Fig. 3 is completed.

In the crystal pulling program, the liquid level position of the mash liquid 13 is calculated from the image of the camera 18, and the gap value ΔG of the melt surface 13a of the mash 13 and the heat insulating member 17 is calculated. Then, based on the gap value ΔG, the temperature gradient next to the solid-liquid interface of the single crystal 15 and the flow rate of the ambient gas are respectively controlled. In this way, the melt surface 13a can be opposed to the furnace structure such as the heater 12 or the heat insulating member 17 regardless of the decrease in the mash liquid 13 from the start of the drawing of the single crystal to the end of the drawing. The position is kept constant, whereby the radiation distribution of heat with respect to the mash liquid 13 can be maintained constant. Therefore, the slope of the crystallization temperature next to the solid-liquid interface in the central portion of the crystal of the single crystal and the slope of the crystallization temperature next to the solid-liquid interface in the peripheral portion of the crystal are respectively controlled to the optimum values.

4 is a flow chart illustrating a control method of crystal pulling conditions.

As shown in FIG. 4, the control method of the crystal pulling condition includes an initial setting step (S21) including the installation angle measuring step of the camera 18, and a step of photographing the reaction chamber by the camera 18 in the crystal pulling program (S22) ( S23) A step of processing the image of the camera 18 to calculate the liquid level position of the mash (S24), and controlling the drawing condition so that the liquid level position (gap value ΔG) is constant (S25). The control conditions of the pulling conditions are the height of the quartz crucible 11, the crystal pulling speed, the heater output, and the like. In the crystal pulling program, control of the pulling condition using the photographic image of the camera 18 is performed. Specifically, the neck forming procedure (step S13) in Fig. 2 is executed to the tail breeding program (step S16).

Next, a method of calculating the liquid level position from the captured image of the camera 18 will be described in detail.

FIG. 5 is a photographic image of the camera 18 for explaining the relationship between the real image and the mirror image of the heat insulating member 17.

As shown in Fig. 5, the mash liquid 13 can be seen through the opening 17a of the heat insulating member 17, and the real image Ma of the heat insulating member 17 can be reflected on the photographic image. Further, since the inside of the opening 17a of the heat insulating member 17 is melted, the liquid 13 and the molten surface 13a of the molten metal 13 are mirror-finished, the mirror image Mb of the heat insulating member 17 is reflected on the melted surface 13a. Since the heat insulating member 17 is fixed to the reaction chamber 19 side, the position of the real image Ma of the heat insulating member 17 does not change and remains at the same position in the image.

On the other hand, the mirror image Mb of the heat insulating member 17 reflected on the melt surface 13a changes as the distance between the heat insulating member 17 and the melt surface 13a changes. Therefore, the interval D between the real image Ma of the heat insulating member 17 and the mirror image Mb reflected on the melt surface 13a, and the melt surface 13a caused by the consumption of the melt 13 or the rise and fall of the quartz crucible 11 as the crystal grows. Move up and down. Further, the position of the melt surface 13a is the midpoint of the interval D between the real image Ma and the mirror image Mb. For example, when the melt surface 13a and the lower end of the heat insulating member 17 are aligned, the interval between the real image Ma and the mirror image Mb of the heat insulating member 17 becomes zero, and when the melt surface 13a is gradually lowered, from the lower end of the heat insulating member 17 The distance (gap value) ΔG to the melt surface 13a is also gradually elongated. The gap value ΔG at this time can be calculated as a value of 1/2 of the interval D between the real image Ma and the mirror image Mb of the heat insulating member 17 (that is, D = ΔG × 2), and can be imaged by the camera 18. The pixel size and the prime number are calculated.

In the image method as described above (that is, the liquid level position is measured from the relationship between the real image Ma and the mirror image Mb of the heat insulating member 17), the image captured from the camera 18 detects the individual edges of the real image Ma and the mirror image Mb of the heat insulating member 17. The shape is calculated by recalculating the size of each opening, and the gap value ΔG is calculated from the two dimensions (the interval between the lower end of the heat insulating member 17 and the melt surface 13a: see Fig. 1). In detail, the distance (first distance) in the vertical direction from the camera 18 to the real image Ma is calculated based on the opening radius of the real image Ma of the heat insulating member 17, and the slave camera 18 is calculated based on the opening radius of the mirror image Mb of the heat insulating member 17. The distance ΔG is calculated from the difference between these distances by the distance (second distance) in the vertical direction of the mirror image Mb. This is because the position of the opening of the mirror image Mb of the heat insulating member 17 viewed from the camera 18 in the vertical direction is farther than the opening of the real image Ma of the heat insulating member 17 by 2 ΔG, and the mirror image Mb of the heat insulating member 17 The opening ratio of the opening with respect to the opening of the real image Ma of the heat insulating member 17 is proportional to the gap value ΔG, and the larger the ΔG is, the smaller the size of the opening of the mirror image Mb is.

However, since the camera 18 provided outside the reaction chamber 19 photographs the melt surface 13a from obliquely upward, the shape of the circular opening 17a of the heat insulating member 17 is not a perfect circular shape, and the captured image is distorted. In order to accurately calculate the opening size of each of the real image Ma and the mirror image Mb of the heat insulating member 17, it is necessary to correct the distortion of the image. Therefore, in the present embodiment, the opening of each of the real image Ma and the mirror image Mb of the heat insulating member 17 captured by the camera 18 is projected onto the reference plane, and the size of the opening 17a when viewed from directly above is obtained.

Further, the radius of the circle obtained by rounding the opening edge shape (sample value) in a minimum flat method can be used as the opening size (representative size) of each of the real image Ma and the mirror image Mb of the heat insulating member 17. The distance D = 2 ΔG between the real image Ma and the mirror image Mb is determined based on the size of the real image and the mirror image Mb of the heat insulating member 17 thus obtained.

The position of each of the real image Ma and the mirror image Mb of the heat insulating member 17 in the vertical direction is not necessarily obtained from the radius of the circular opening, and may be obtained by other dimensions. For example, in the case where a part of the opening 17a of the heat insulating member 17 is a straight line, the straight line approximation can be performed by the least square method, and the length of the straight line obtained by the approximation formula can be employed.

The position of the image of the heat insulating member 17 having an arbitrary opening shape in the vertical direction can be calculated by matching the opening shape of the heat insulating member 17 with the reference shape reduced by the predetermined reduction ratio. In other words, the reference shape of the opening shape of the heat insulating member 17 after changing the reduction ratio is prepared in accordance with the distance from the installation position of the camera 18, and the residual value when the edge shape of the image of the heat insulating member 17 is matched with the reference shape is used. The reduction ratio of the reference shape of the smallest (maximum matching ratio) is calculated as the actual distance from the installation position of the camera 18 to the image of the heat insulating member 17. In this way, the position of each of the real image and the mirror image of the heat insulating member 17 based on the installation position of the camera 18 can be obtained.

Fig. 6 is a schematic view for explaining a method of converting a quadratic coordinate projection of a photographic image to a coordinate of a real space.

As shown in the figure on the left side of Fig. 6, since the camera 18 is photographed from the obliquely upward direction in the reaction chamber 19, the shape of the opening 17a of the heat insulating member 17 in the photographed image is distorted, and becomes an image having a sense of distance. That is, the image on the lower side closer to the camera 18 is larger than the upper side. Therefore, in order to accurately calculate the opening size of each of the real image and the mirror image of the heat insulating member 17, it is necessary to correct the distortion of the image. Therefore, the coordinate projection of the photographic image of the camera 18 is converted into a coordinate set on the reference plane at the same height position as the lower end of the heat insulating member 17, to correct the distortion.

The graph on the right side of Fig. 6 shows the coordinate system when image correction is performed. In this coordinate system, the reference plane is the xy plane. Further, the origin C ₀ of the XY coordinates is a straight line drawn from the center position C of the imaging device 18a of the camera 18 and passing through the center position F (0, y _f , z _f ) of the lens 18b of the camera 18 (a little lock line) ) the intersection with the reference plane. This line is the optical axis of the camera 18.

Further, the drawing direction of the single crystal 15 is the positive direction of the z-axis, the center position C (0, y _c , z _c ) of the image pickup device 18a and the center position F (0, y _f , z _f ) of the lens 18b. Located in the yz plane. The coordinates (u, v) in the image shown on the left side of Fig. 6 are represented by the pixels of the imaging device 18a, and correspond to any point P (x _p , y) on the imaging device 18a shown by the following formula (1). _p , z _p ).

Here, α _u and α _v are the pixel sizes in the lateral direction and the longitudinal direction of the imaging device 18a, and y _c and z _c are the y coordinate and the z coordinate of the center position C of the imaging device 18a. Further, as shown in the right diagram of FIG. 6, θ _c is an angle between the optical axis of the camera 18 and the z-axis, which is the installation angle of the camera 18.

Further, the center position C (0, y _c , z _c ) of the imaging device 18a is such that the center position F (0, y _f , z _f ) of the lens 18b of the camera 18 and the focal length f _{1 of the} lens are used, Formula (2) is indicated.

Here, when Equation (2) is explained in detail, when L _c is the distance from the coordinate origin C ₀ on the reference plane to the center position C (0, y _c , z _c ) of the imaging device 18a, y _c , z _c are as shown in the following formula (3).

a is the distance from the coordinate origin C ₀ to the center position F of the lens 18b of the camera 18, and b is the distance from the center position F of the lens 18b to the center position C of the imaging device 18a, from the coordinate origin C ₀ to the shooting The distance L _c of the center position C of the device 18a is as shown in the following formula (4).

[Number 4] L _c = a + b (4)

Further, from the imaging formula of the lens, using the distances a, b, the focal length f _{1 is} expressed by the following formula (5).

When the distance b is removed from the equations (4) and (5) and L _c is expressed by the distance a and the focal length f _{1 , it is} expressed by the following formula (6).

The value of the distance a from the coordinate origin C ₀ to the center position F of the lens 18b of the camera 18 can be expressed by the following equation (7) by the center position F (0, y _f , z _f ) of the lens 18b of the camera 18.

Therefore, the above formula (2) is obtained from the equations (3), (6), and (7).

Considering that the lens 18b is a pinhole, an arbitrary point P(x _p , x _p , x _p ) on the imaging device 18a is projected on the reference plane by F(0, y _f , z _f ), and its projection point P' ( X, Y, 0) can be represented by the following formula (8).

Using the equations (1), (2), and (8), it is possible to obtain a real image or a mirror image of the circular opening 17a of the heat insulating member 17 projected on the reference plane.

The coordinate of the center position F of the lens 18b is known from the center position F(0, y _f , z _f ) of the lens 18b to the distance b of the center position C (0, y _c , z _c ) of the photographing device 18a. y _f , z _f , can be expressed by the following equation (9) using the distance b and the coordinates y _c , z _c of the center position C of the imaging device 18a.

Thus, in the case where the distance b (main point) from the center position F (main point) of the lens 18b to the center position C of the photographing device 18a is known, the projection point P' can be expressed by the value of the back distance ( X, Y, 0).

Next, a method of calculating the radius of the opening 17a of the heat insulating member 17 will be described. The least square method can be used as a method of calculating the coordinates (x ₀ , y ₀ ) and the radius r of the center position of the opening 17a from the coordinates of the real image and the mirror image projected on the reference plane. The opening 17a of the heat insulating member 17 is circular, and the image of the opening 17a satisfies the equation of the circle represented by the following formula (10).

[10] ( x - x ₀ ) ² + ( y - y ₀ ) ² = r ² (10)

Here, the calculation of (x ₀ , y ₀ ) and r in the equation (10) uses the least squares method. In order to easily perform the calculation in the least square method, the deformation shown in the following formula (11) is performed.

The variables a, b, and c in the equation (11) are obtained by the least squares method. This is a condition for obtaining the sum of the squares of the difference between the equation (11) and the measured point, which is obtained by solving the partial differential equation shown by the following formula (12).

Further, the solution of the formula (12) can be calculated by the simultaneous equation shown by the following formula (13).

In this manner, the radius r _f and r _m of the openings of the real image Ma and the mirror image Mb of the heat insulating member 17 projected on the reference plane can be calculated using the least square method.

When the gap value ΔG is measured in the present embodiment, stable detection of the real image Ma and the mirror image Mb of the heat insulating member 17 is necessary. In general, the method of detecting the position of a predetermined image from the image data is a method of setting a threshold value based on the luminance value of the image and binarizing the image. However, when the edge detection of the image of the heat insulating member 17 in the reaction chamber 19 is performed by the binarization processing, the detection position may be deviated due to the change in luminance accompanying the change in the temperature inside the furnace.

In order to eliminate this effect, in the present embodiment, instead of the general binarization method, the following method is employed: the luminance distribution in the lateral direction of the photographic image is differentiated to obtain the luminance change amount, and the thermal insulation is detected based on the luminance change amount. The edge of the image of member 17. That is, in the detection of the edge (contour) of the heat insulating member 17, a differential image indicating the amount of change in luminance of the original image is used. The data of the differential image has a maximum value at the edge portion of the real image Ma of the heat insulating member 17 and the mirror image Mb thereof, regardless of the luminance of the original image. Therefore, the position of the maximum value of the differential image is used as the detection edge, thereby reducing the measurement error caused by the influence of the luminance change, and the accurate size of the real image of the heat insulating member 17 and the mirror opening 17a can be stably detected.

Fig. 7 is a graph showing the luminance of the pixel sequence in the horizontal direction of the photographic image and the differential value thereof.

As shown in Fig. 7, it can be seen that when the luminance of the melted portion of the central portion changes with respect to the real image portion of the heat insulating member on both sides of the pattern, the differential value of the luminance does not change, and the mirror image corresponding to the heat insulating member is clearly determined. The boundaries of the parts.

The differential value of the luminance is calculated by the difference in luminance in the horizontal direction of the image, and in this case, it is greatly affected by the noise included in the image. Therefore, in the present embodiment, the average value of the nine-pixel component of the calculated differential value of the luminance is calculated, thereby removing the influence of the noise. By detecting the peak position of the calculated luminance differential data as described above, the position of the real image of the heat insulating member 17 and the edge position of the mirror image can be determined.

FIG. 8 is a schematic view for explaining a method of calculating the gap value ΔG from the opening radii r _f and r _m of the real image Ma and the mirror image Mb of the heat insulating member 17 .

As shown in Fig. 8, in the case where the heat insulating member 17 (F) is horizontally disposed, the center coordinates (X _hc , Y _hc , 0) of the lower end of the real image of the heat insulating member 17 and the center coordinates of the mirrored lower end of the heat insulating member 17 are shown. (X _hc , Y _hc , 0) exists with the melt surface 13a interposed therebetween, and the straight line connecting these two points passes (X _hc , Y _hc , 0) and becomes a straight line parallel to the Z axis. On the other hand, the central coordinates (X _mc , Y _mc , 0) of the mirror image of the heat insulating member 17 on the reference plane are such that the central coordinates (X _mc , Y _mc , Z _gap ) of the mirror image of the heat insulating member 17 are projected. The coordinates on the reference plane, therefore, the central coordinates (X _mc , Y _mc , Z _gap ) of the mirror image of the heat insulating member 17 are located at the center coordinates of the mirror image of the heat insulating member 17 passing through the reference plane (X _mc , Y _mc , 0 And on the line of the center position F(0, y _f , z _f ) of the lens 18b.

Therefore, the distance from the center position F of the lens 18b of the photographing device to the mirror-image opening of the heat insulating member 17 is the distance L _m from the center position F of the lens 18b of the photographing device to the center of the mirror image of the heat insulating member 17 In the case of L _f , the distances L _m and L _f represent the following formula (14).

[Number 14] L _m = L _f +2 △ G /cos θ _c (14)

According to this formula, the gap value ΔG can be expressed as in the formula (15).

[Number 15] 2 △ G = ( L _m - L _f ) cos θ _c (15)

Thus, it can be understood that the gap value ΔG can be calculated by obtaining the distances L _f and L _m .

The mirror image of the heat insulating member 17 reflected on the melt surface 13a is further 2 ΔG away from the actual heat insulating member 17, and therefore, the radius r _m of the mirror image of the heat insulating member 17 appears to be smaller than the radius r _{f of the} real image. Moreover, it has been known that in the furnace temperature environment in the drawing, the opening radius thereof is smaller than the design size (the size at normal temperature) due to the thermal expansion of the heat insulating member 17. Therefore, considering that the opening radius (theoretical value) of the thermal expansion is r _actual , the measured radius of the opening radius of the real image of the heat insulating member 17 is r _f , and the measured value of the opening radius of the mirror image of the heat insulating member 17 is r _m , then Equation (16) calculates the distances L _f , L _m .

From the above equations (15) and (16), the gap value ΔG can be calculated as in the following equation (17).

[Number 17] 2 △ G = L _c ( r _actual / r _m - r _actual / r _f ) cos θ _c (17)

In this manner, the gap value ΔG can be obtained from the opening radius measurement values r _f and r _m of the real image and the mirror image of the heat insulating member 17 .

As a method of calculating the gap value ΔG, a method of calculating the gap value ΔG from the difference between the Y coordinate values of the center positions of the openings of the real image Ma and the mirror image Mb of the heat insulating member 17 is known. However, in this calculation method, the range in which the approximate circle is obtained in the vertical direction of the image is narrow, and the restriction in the Y coordinate direction (longitudinal direction of the image) is large. Therefore, there is a problem described later: the influence of the detected change of the edge is affected. On the other hand, the calculation error of the gap value ΔG is increased. On the other hand, when the gap value ΔG is calculated from the radius of the circular opening of the heat insulating member 17, the approximate circle is calculated in addition to the Y coordinate of the center position of the approximate circle for the calculation of the gap value ΔG. The X coordinate of the center position and the radius of the approximate circle, especially the value of the radius of the approximate circle in the X coordinate direction (longitudinal direction of the image), can reduce the influence of the edge detection variation because the data of the left and right ends can be obtained.

Next, a method of setting the installation angle of the camera 18 will be described.

As described above, in order to improve the measurement accuracy of the liquid level position and the gap value ΔG of the mash liquid 13, it is necessary to accurately grasp the actual installation angle of the camera 18. This is because the error in the setting angle of the camera 18 has a large influence on the measurement accuracy of the liquid level position. Therefore, the value of the installation angle of the camera 18 for projection conversion is not a design value, but an accurate value of the installation angle of the camera 18 obtained by actual measurement. The error of the set angle of the calculation for the projection conversion with respect to the actual set angle of the camera 18 is preferably controlled within ±0.1°.

In the present embodiment, the camera 18 is actually photographed in the reaction chamber 19, and the captured image is projected and converted at the estimated installation angle θ ', and the edge shape of the opening of the heat insulating member 17 is detected by the projection-converted image to be grasped in advance. The shape of the opening 17a of the heat insulating member 17 and the shape of the shape (measured shape) obtained by the image captured by the camera 18 are matched. Then, when the estimated setting angle θ ' of the camera 18 used for the calculation of the projection conversion is used as a variable parameter so as to vary within a certain range, it is calculated by calculation how much the measured shape of the heat insulating member 17 is different from the reference shape. The estimated setting angle θ ' of the smallest error (maximum matching ratio) is set as the actual set angle θ _c of the camera 18. For example, in a range of ±2° centering on the installation angle of the design of the camera 18, θ ' is changed by 0.1° scale to perform shape matching. According to this adaptive residual method, the actual setting angle θ _{c of} the camera 18 can be accurately obtained by the high-definition photographing capability of the camera 18 itself, and based on the set angle θ _c , the liquid of the mash 13 can be accurately obtained. Surface position and gap value ΔG.

In the case where the set angle of the camera 18 used for the calculation of the projection conversion deviates from the set angle of the actual camera 18, since the shape after the projection conversion is distorted, the error with respect to the actual shape becomes large. The calculation of the projection conversion uses a set angle close to the actual set angle, and the error gradually becomes smaller. In an ideal situation, the error once becomes zero and then becomes larger again. Therefore, the installation angle of the camera 18 is scanned within a certain range, and the shape matching process between the reference shape of the heat insulating member 17 and the actual shape is performed, whereby the actual installation angle θ _{c of} the camera 18 can be accurately obtained.

Fig. 9 is an explanatory view showing a change in the shape of the opening of the heat insulating member 17 in accordance with the change in the installation angle of the camera 18. In addition, FIG. 10 is a view showing a result of matching the shape of the actual shape of the opening of the heat insulating member 17 and the shape of the reference shape when the installation angle of the camera 18 is changed, and (a) shows the left edge of the opening of the heat insulating member 17, ( b) indicates the right side edge of the opening of the heat insulating member 17. The horizontal axis of the graphs of Figs. 10(a) and (b) indicates the vertical direction pixel of the captured image, and the vertical axis indicates the design value of the detected edge and the residual value (error) of the measured value, that is, the matching ratio.

As shown in FIG. 9, when the setting angle of the camera 18 used for the calculation of the projection conversion is changed, the edge shape 17s (dashed line) of the opening 17a of the heat insulating member 17 is changed little by little. Therefore, there is a calculated opening shape closest to the actual edge shape 17r (solid line) of the opening 17a of the heat insulating member 17. In addition, FIG. 9 shows that the change in the edge shape 17s is very large.

As shown in Figs. 10(a) and (b), the setting angle θ _{c of the} camera 18 is changed by 1 degree from, for example, 25° to 30°, and the pattern of the residual is also changed. When the installation angle θ _c of the camera 18 is 25°, the graph of the residual is a curve having a peak on the positive side, and the maximum value of the residual is about 0.2 mm. When the set angle θ _{c of the} camera 18 is gradually increased, the peak gradually becomes smaller (the residual gradually becomes smaller), and the residual pattern when the angle is set to 27° is almost a straight line. When the installation angle θ _{c is} further increased to 28°, the direction of the peak of the residual pattern is reversed to have a peak having a peak on the negative side, and the maximum value of the residual is about 0.15 mm (about -0.15 mm). Then, while the set angle θ _{c is} increased, the maximum value of the residual is gradually increased, and the maximum value of the residual when the angle θ _c is set to 30° is about 3.5 mm (about -3.5 mm). Further, it can be seen that the installation angle θ _c of the camera having the smallest residual is 26.9°.

In this manner, the edge shape of the opening 17a of the heat insulating member detected from the image obtained by projecting the converted angle θ ' (estimated setting angle) using the camera 18 is detected, and the detected image is detected from the projected converted image. When the shape is compared with the reference shape, it is calculated by calculating how much error there is between the two, and finding the condition that the error is the smallest (the matching ratio is the largest) when the estimated setting angle θ ' of the camera 18 is changed, thereby being able to The high accuracy measures the actual set angle θ _c of the camera 18.

FIG. 11 is a flowchart illustrating a method of measuring the installation angle θ _c of the camera 18.

As shown in FIG. 11, in the measurement of the installation angle θ _c of the camera 18, the camera 18 is first placed outside the observation window of the reaction chamber 19 at a predetermined angle (step S31). The new setting or angle adjustment of the camera 18 is performed at the time of the new installation of the single crystal manufacturing apparatus 10 or at the time of the maintenance inspection, and does not need to be performed in each of the pull-out batches of the single crystal. The camera 18 is provided so that the installation angle of the mash 13 in the quartz crucible 11 can be imaged through the opening 17a of the heat insulating member 17. At this time, although the approximate setting angle of the camera 18 is known, the correct setting angle is not known.

Then, the inside of the reaction chamber 19 is photographed by the camera 18 (step S32), and the photographic image is projected onto the reference plane based on the estimated angle θ ' of the camera 18 in the scanning range (step S33), and the projection is converted from the projection. The image detects the edge shape (measured shape) of the opening 17a of the heat insulating member 17 (step S34).

Then, the shape matching processing of the actual shape and the reference shape of the opening 17a of the heat insulating member 17 detected from the projected image after the projection conversion is performed (step S35), and the predetermined setting angle θ ' is changed within the predetermined scanning range. The estimated setting angle θ ' of the camera 18 having the largest matching ratio (steps S36 and S37) sets the estimated setting angle θ ' of the camera 18 to the actual setting angle (step S38). Whether or not the matching rate is the largest can be determined by the following method: when the estimated setting angle θ ' is scanned from one direction, it is confirmed that the matching rate is peaked and then decreased, and the matching ratio at which the matching ratio is maximum can be set to the angle θ 'Set the angle θ _c of the actual camera 18 . When the matching ratio is not the maximum, after the estimated installation angle of the camera 18 is changed to the next value in the scanning range (step S37), the above-described shape matching is repeated (steps S33 to S36).

The camera installation angle measuring step according to the present embodiment is preferably performed at a normal temperature in which the single crystal production apparatus 10 is not operated, but may be performed at any time before the crystal pulling procedure. Therefore, it is also possible to carry out in a hot environment in which the crucible 13 is contained in the quartz crucible 11. When the camera setting angle calculation step is executed at normal temperature, it is necessary to perform photographing while illuminating the inside of the reaction chamber 19, so that the edge of the opening 17a of the heat insulating member 17 is clearly captured in the photographed image.

On the other hand, in the case where the camera setting angle calculation step is performed in a hot environment, since the heater 12 or the mash liquid 13 emits radiation, it is not necessary to illuminate the inside of the reaction chamber 19, but it is necessary to take into consideration the heat insulating member 17 The effect of thermal expansion. This is because the heat insulating member 17 in the thermal environment is thermally expanded, so that the actual size (diameter) of the opening 17a of the heat insulating member 17 is smaller than the design size (the size at normal temperature). Therefore, the reference shape in which thermal expansion has been considered is used, whereby the accuracy of the shape matching can be improved, and the installation angle of the camera 18 can be accurately obtained. Further, as described above, when the camera setting angle calculation step is executed in a hot environment, it is preferable to detect the edge of the heat insulating member 17 using the luminance differential value of the captured image.

As described above, the method for producing a single crystal according to the present embodiment includes measuring a camera installation angle measuring step provided on the outside of the reaction chamber to photograph the installation angle of the camera in the reaction chamber, and using a camera in the crystal pulling program. Shooting the reaction chamber obliquely above, and converting the photographic image projection onto the reference plane based on the set angle of the camera; controlling the crystallization pull condition based on the processing result of the photographic image after the projection conversion; the camera setting angle measuring step, The setting angle of the camera is changed as a variable parameter, and the shape of the reference structure of the furnace structure and the shape of the measured shape of the furnace structure in the photographic image are matched, and the value of the camera setting angle having the largest matching ratio is taken as the actual value. The camera sets the angle, so the camera's setting angle can be measured correctly. Therefore, in the crystal pulling program, the liquid surface position of the mash liquid can be accurately measured and controlled, whereby high-quality singular crystals can be produced.

The preferred embodiments of the present invention have been described above, but the present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the spirit and scope of the invention.

For example, in the above embodiment, the camera installation angle is calculated based on the shape of the circular opening 17a of the real image of the heat insulating member 17 appearing in the captured image. However, the present invention is not limited to a circular shape, and may be, for example, an elliptical shape. Or any shape such as a rectangle as an object. In addition, the in-furnace structure to be subjected to the dimension measurement is not limited to the heat insulating member 17, and may be another in-furnace structure.

In addition, in the above-described embodiment, the production method of the simple crystals is described. However, the present invention is not limited thereto, and various single crystal production methods can be used.

Claims (6)

A method for producing a single crystal, which is a method for producing a single crystal according to the Czochralski method, comprising: a camera setting angle measuring program, and measuring a setting angle of a camera disposed in the reaction chamber in advance in the reaction chamber side ( θ _c ); and a crystal pulling program for drawing a single crystal from a melt provided in the crucible in the reaction chamber; the camera is provided with an angle measuring program, and the above reaction chamber is photographed obliquely from above by the camera; Estimating the set angle (θ') and the focus distance (f) to project the projected image of the camera onto the reference plane; the edge shape of the furnace structure appearing in the projected image after the projection conversion and the above-described furnace structure The reference shape of the object is subjected to shape matching; when the estimated setting angle (θ') of the camera is used as a variable parameter to change within a predetermined range, and the shape matching is performed, the estimated setting angle of the camera having the largest matching ratio is set. (θ') is set to the actual setting angle ( θ _c ) of the above camera; the above crystal pulling program is used The camera captures the melt in the reaction chamber from obliquely above; the projected image of the camera is projected onto the reference plane based on an actual installation angle ( θ _c ) of the camera and a focal length; wherein the furnace structure It is a heat insulating member disposed above the above-mentioned crucible. The method for producing a single crystal according to the first aspect of the invention, wherein the edge shape of the furnace structure is the single sheet drawn from the melt The opening shape of the above-mentioned heat insulating member through which crystals pass. The method for producing a single crystal according to the second aspect of the invention, wherein the crystal pulling program is based on the heat insulation which is displayed in a projected image which is projected and converted according to an actual installation angle ( θ _c ) of the camera and a focal length. The opening shape of the real image of the member and the opening shape of the mirror image of the heat insulating member appearing on the liquid surface of the melt are calculated, and the liquid level position of the melt is calculated. The method for producing a single crystal according to the third aspect of the invention, comprising: reducing a reference shape of an opening of the heat insulating member to a predetermined scale ratio, and opening the reduced reference shape and a real image of the heat insulating member; The shape of the shape is matched, and the radius of the opening shape of the real image of the heat insulating member is calculated based on the scale factor of the reference shape having the largest matching ratio when the scale matching is performed as the variable parameter; The reference shape of the opening of the heat insulating member is reduced according to a predetermined scale ratio, and the reduced reference shape and the shape of the mirror shape of the heat insulating member are matched, and the scale factor is changed as a variable parameter. At the same time, the scale ratio of the reference shape having the largest matching ratio at the time of the shape matching is performed, and the radius of the opening shape of the mirror image of the heat insulating member is calculated. The method for producing a single crystal according to the fourth aspect of the invention, comprising: calculating a position from the installation position of the camera to the heat insulation based on a radius of an opening shape of a real image of the heat insulating member and an actual installation angle of the camera a first distance of the real image of the member; a radius from the mirror opening shape of the heat insulating member and an actual installation angle of the camera, and calculation from the installation position of the camera to the above a second distance of the mirror image of the heat insulating member; and a liquid level position of the melt is calculated from the first distance and the second distance. In the method for producing a single crystal according to the fifth aspect of the invention, the distance between the heat insulating member and the liquid surface is calculated from a value of 1/2 of a difference between the first distance and the second distance.