Estimation method, estimation device, and estimation program

Abstract

To provide an estimation method capable of accurately estimating temperature distribution of a silicon single crystal according to long-term deterioration of a furnace member.SOLUTION: The estimation method includes: a step of constructing a simulation model simulating a drawing furnace; a step of creating calculation results of temperature distribution in the drawing furnace respectively found from plural calculation conditions as training data by performing heat transmission simulation based on a simulation model regarding plural calculation conditions, to which a thermophysical property value of a furnace member constituting the drawing furnace is arbitrarily set; a step of constructing a regression model, in which inputs are used as temperature at a predetermined measuring position in the drawing furnace and outputs are used as temperature distribution of the silicon single crystal; and a step of estimating temperature distribution of the silicon single crystal being drawn by inputting the temperature measuring results at the predetermined measuring position found during drawing the silicon single crystal to the regression model.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to an estimation method, an estimation device, and an estimation program.

Background Art

[0002] In the manufacturing process of a silicon single crystal by the Chokralski (CZ) method, a silicon single crystal is grown by attaching a seed crystal to a silicon melt in a quartz crucible and then pulling it up. When the silicon single crystal grows, oxygen from the quartz crucible is mixed into the silicon melt. The oxygen mixed into the silicon melt becomes oxygen precipitates called BMD (Bulk Micro Defect) by heat treatment in the manufacturing process of a device using a silicon wafer.

[0003] Although BMD has an advantage of acting as a gettering source for capturing heavy metal impurities mixed in a silicon wafer and deteriorating device performance, it also has a disadvantage of reducing the mechanical strength of the silicon wafer. Therefore, a standard range is defined for the BMD density representing the amount of BMD in a silicon single crystal. It is known that the BMD density is determined by the thermal history (cooling conditions) of the silicon single crystal, the oxygen concentration, the nitrogen concentration, and the BMD precipitation heat treatment for precipitating BMD on a silicon wafer obtained from the silicon single crystal (see, for example, Patent Document 1 and Non-Patent Document 1).

Prior Art Documents

[0006] Of the above conditions that affect BMD density, the BMD precipitation heat treatment conditions are fixed for each product, and the oxygen and nitrogen concentrations can be controlled by the pulling conditions. However, although the thermal history is roughly determined during the design of the pulling furnace, it may change due to factors such as changes in thermophysical properties caused by the aging of furnace components.

[0007] The thermal history can be determined from the temperature distribution of the silicon single crystal. To directly measure the thermal history during pulling, it is sufficient to measure the temperature distribution of the silicon single crystal. Non-contact measurement using a thermal camera is a possible method for measuring temperature, but near the silicon melt, it is difficult to accurately measure the temperature distribution due to disturbances mainly caused by infrared radiation emitted from the high-temperature silicon melt. Therefore, it is also difficult to accurately estimate the BMD density during the pulling of the silicon single crystal.

[0008] The present invention aims to provide an estimation method, estimation apparatus, and estimation program that can accurately estimate the temperature distribution of a silicon single crystal in accordance with the aging degradation of a furnace component. [Means for solving the problem]

[0009] The estimation method of the present invention is an estimation method for estimating a silicon single crystal grown by the Czochralski method in a pulling furnace, and includes the steps of: constructing a simulation model that simulates the pulling furnace; performing a heat transfer simulation based on the simulation model for a plurality of calculation conditions in which the thermophysical properties of the furnace members constituting the pulling furnace are arbitrarily set, and generating training data for the calculation results of the temperature distribution in the pulling furnace obtained from each of the plurality of calculation conditions; constructing a regression model based on the training data, with the input being the temperature at a predetermined measurement position in the pulling furnace and the output being the temperature distribution of the silicon single crystal; and inputting the temperature measurement results at the predetermined measurement position obtained during the pulling of the silicon single crystal into the regression model to estimate the temperature distribution of the silicon single crystal during the pulling.

[0010] In the estimation method of the present invention, it is preferable to further include the step of estimating the thermal history of the silicon single crystal based on the estimated temperature distribution of the silicon single crystal and the pulling speed of the silicon single crystal.

[0011] In the estimation method of the present invention, it is preferable to further include the step of estimating the BMD density of the silicon single crystal based on the estimated thermal history, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions.

[0012] In the estimation method of the present invention, in the step of estimating the BMD density of the silicon single crystal, it is preferable to estimate the BMD density of the silicon single crystal based on the thermal history, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions.

[0013] In the estimation method of the present invention, it is preferable to further include the step of estimating the thermal stress near the solid-liquid interface in the silicon single crystal based on the estimated temperature distribution of the silicon single crystal.

[0014] In the estimation method of the present invention, in the step of constructing a simulation model that simulates the lifting furnace, it is preferable to construct the simulation model such that the temperature of the boundary between the silicon melt and the silicon crystal is the silicon melting point.

[0015] In the estimation method of the present invention, it is preferable that the furnace member for which the thermophysical property values ​​are set in the heat transfer simulation includes a cooling furnace member for cooling the silicon single crystal during pulling, and that the predetermined measurement position includes a position where the temperature is adjusted by the cooling furnace member.

[0016] In the estimation method of the present invention, it is preferable that the cooling furnace member includes a cylindrical cooler that cools the silicon single crystal as the silicon single crystal passes through it during the pulling process, and that the predetermined measurement position includes the outer circumferential surface of the silicon single crystal after it has passed through the cooler.

[0017] In the estimation method of the present invention, it is preferable that the furnace member for which the thermophysical property values ​​are set in the heat transfer simulation includes a temperature rise suppression furnace member for suppressing the temperature rise of the silicon single crystal during pulling, and that the predetermined measurement position includes a position on the temperature rise suppression furnace member.

[0018] The estimation device of the present invention is an estimation device for estimating a silicon single crystal grown by the Czochralski method in a pulling furnace, which constructs a simulation model simulating the pulling furnace, and for a plurality of calculation conditions in which the thermophysical property values of the furnace members constituting the pulling furnace are arbitrarily set, performs a heat transfer simulation based on the simulation model, and generates calculation results of the temperature distribution in the pulling furnace obtained from each of the plurality of calculation conditions as training data, a training data generation unit, a machine learning unit that constructs a regression model with an input being the temperature at a predetermined measurement position in the pulling furnace and an output being the temperature distribution of the silicon single crystal based on the training data, and a crystal temperature distribution estimation unit that inputs the temperature measurement result at the predetermined measurement position obtained during the pulling of the silicon single crystal into the regression model and estimates the temperature distribution of the silicon single crystal during the pulling.

[0019] In the estimation device of the present invention, it is preferable to further include a heat history estimation unit that estimates the heat history of the silicon single crystal based on the temperature distribution of the silicon single crystal estimated by the crystal temperature distribution estimation unit and the pulling speed of the silicon single crystal.

[0020] In the estimation device of the present invention, it is preferable to further include a BMD density estimation unit that estimates the BMD density of the silicon single crystal based on the heat history estimated by the heat history estimation unit, the oxygen concentration of the silicon single crystal, and the BMD precipitation heat treatment conditions.

[0021] In the estimation device of the present invention, it is preferable that the BMD density estimation unit estimates the BMD density of the silicon single crystal based on the heat history, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD precipitation heat treatment conditions.

[0022] In the estimation device of the present invention, it is preferable to further include a thermal stress estimation unit that estimates the thermal stress near the solid-liquid interface in the silicon single crystal based on the temperature distribution of the silicon single crystal estimated by the crystal temperature distribution estimation unit.

[0023] In the estimation device of the present invention, it is preferable that the training data generation unit constructs the simulation model such that the temperature at the boundary between the silicon melt and the silicon crystal becomes the silicon melting point.

[0024] The estimation program of the present invention causes a computer to function as the above-described estimation device.

Brief Description of the Drawings

[0025] [Figure 1] It is a schematic diagram showing a schematic configuration of a silicon single crystal manufacturing system in the first embodiment and the second embodiment. [Figure 2] It is a block diagram of an estimation device in the first embodiment. [Figure 3] It is a flowchart showing the estimation process of the BMD density in the first embodiment. [Figure 4] It is a block diagram of an estimation device in the second embodiment. [Figure 5] It is a flowchart showing the estimation process of the critical v / G in the second embodiment. [Figure 6] It is a graph showing the correlation between the measured BMD density and the estimated BMD density in Example 1.

Modes for Carrying Out the Invention

[0026] [First Embodiment] [Configuration of Silicon Single Crystal Manufacturing System]< First, the configuration of the silicon single crystal manufacturing system in the first embodiment of the present invention will be described. FIG. <![CDATA[1]]> is a schematic diagram showing a schematic configuration of a silicon single crystal manufacturing system in the first embodiment and the second embodiment. FIG. <![CDATA[2]]> is a block diagram of an estimation device in the first embodiment.

[0027] The silicon single crystal manufacturing system <![CDATA[1]]> shown in FIG. <![CDATA[1]]> includes a silicon single crystal manufacturing apparatus <![CDATA[2]]>, a temperature measurement unit <![CDATA[3]]>, and an estimation device <![CDATA[4]]>.

[0028] The silicon single crystal manufacturing apparatus 2 produces a silicon single crystal SM having a shoulder portion SM1, a straight body portion SM2, and a tail portion (not shown) using the Czochralski method. The silicon single crystal manufacturing apparatus 2 produces a silicon single crystal SM in which the diameter of the straight body portion SM2 is, for example, 200 mm or more and 450 mm or less. The silicon single crystal manufacturing apparatus 2 comprises a pulling furnace 20, a crystal pulling unit 27, a crucible drive unit 28, and a manufacturing apparatus control unit (not shown).

[0029] The lifting furnace 20 comprises a chamber 21, a crucible 22, a heater 23, a heat-insulating tube 24, a heat shield 25, and a cooler 26.

[0030] Chamber 21 comprises a main chamber 211, a top chamber 212, and a pull chamber 213. The main chamber 211, the top chamber 212, and the pull chamber 213 have a water-cooling structure.

[0031] The main chamber 211 is formed in a bottomed cylindrical shape. The main chamber 211 houses the crucible 22, heater 23, insulation tube 24, and heat shield 25.

[0032] The top chamber 212 is formed in a roughly frustoconical shape, with the diameter of its upper end being smaller than the diameter of its lower end. The lower end of the top chamber 212 is airtightly connected to the upper end of the main chamber 211, and it covers the top of the main chamber 211. The top chamber 212 is a cooling furnace component that cools the silicon single crystal SM during pulling.

[0033] The pull chamber 213 is formed in a cylindrical shape. The lower end of the pull chamber 213 is hermetically connected to the upper end of the top chamber 212. The pull chamber 213 temporarily houses the pulled-up silicon single crystal SM.

[0034] In this way, the main chamber 211, the top chamber 212, and the pull chamber 213 are each airtightly connected, thereby forming a sealed space within the chamber 21.

[0035] The upper part of the pull chamber 213 is provided with a gas inlet 213A for introducing an inert gas such as argon (Ar) gas into the chamber 21. The lower part of the main chamber 211 is provided with a gas outlet 211A for discharging the gas from the chamber 21 by driving a vacuum pump (not shown).

[0036] Crucible 22 is located within the main chamber 211 and stores the molten silicon MD to which the dopant has been added. Crucible 22 comprises a bottomed cylindrical quartz crucible 221 and a carbon material support crucible 222 that houses the quartz crucible 221. Note that if the resistivity of the silicon single crystal SM is very high, it is not necessary to add a dopant to the molten silicon MD.

[0037] The heater 23 is formed in a cylindrical shape. The heater 23 is positioned outside the crucible 22 at predetermined intervals and melts the silicon raw material inside the crucible 22.

[0038] The heat-insulating tube 24 is formed in a cylindrical shape. The heat-insulating tube 24 is arranged on the outside of the heater 23 at predetermined intervals.

[0039] The heat shield 25 is formed in a substantially cylindrical shape from a carbon material. The upper end of the heat shield 25 is supported by a plurality of heat shield support parts 214 that extend from the upper end of the main chamber 211 toward the center of the main chamber 211. The heat shield 25 is positioned to surround the silicon single crystal SM being pulled from the molten MD, and blocks radiant heat from the heater 23 to the silicon single crystal SM. In other words, the heat shield 25 is a furnace component for suppressing temperature rise, which suppresses the temperature rise of the silicon single crystal SM being pulled.

[0040] The cooler 26 is a cylindrical component used for crystal cooling. The cooler 26 extends downward from the lower end of the pull chamber 213 and is positioned to surround the silicon single crystal SM being pulled.

[0041] The crystal pulling unit 27 includes a cable 271 to which a seed crystal SC is attached at one end, and a pulling drive unit 272 positioned above the pulling furnace 20, which raises, lowers, and rotates the cable 271.

[0042] The crucible drive unit 28 includes a support shaft 281 that supports the crucible 22 from below. The crucible drive unit 28 is positioned below the lifting furnace 20 and rotates and raises the crucible 22 at a predetermined speed.

[0043] In the silicon single crystal manufacturing apparatus 2 described above, the manufacturing apparatus control unit controls the gas flow rate and furnace pressure in the chamber 21 to a predetermined state, and also starts water cooling of the chamber 21. The manufacturing apparatus control unit then controls the heater 23 to heat the crucible 22 to the melting point of silicon, thereby generating molten MD. This heating by the heater 23 results in a temperature distribution inside the lifting furnace 20 (hereinafter sometimes referred to as the "furnace temperature distribution") that corresponds to the thermal properties (e.g., thermal emissivity) of the furnace components constituting the lifting furnace 20 (e.g., the chamber 21, crucible 22, heater 23, heat-insulating cylinder 24, heat shield 25, and cooler 26).

[0044] Next, the manufacturing apparatus control unit controls the lifting drive unit 272 to lower the cable 271, thereby immersing the seed crystal SC in the molten MD. The manufacturing apparatus control unit then controls the crucible drive unit 28 and the lifting drive unit 272 to pull up the seed crystal SC while rotating the crucible 22 and cable 271 in a predetermined direction, thereby pulling up the silicon single crystal SM.

[0045] The silicon single crystal SM being pulled has a temperature distribution that corresponds to the temperature distribution inside the furnace, with the temperature decreasing in areas further away from the molten liquid MD. The temperature of the silicon single crystal SM is particularly affected by the water-cooled top chamber 212 and cooler 26, and the heat shield 25 that blocks radiant heat from the heater 23.

[0046] When the thermal properties of furnace components change due to aging or other factors, if the heater 23 is controlled under the same conditions as before the change in thermal properties, the internal furnace temperature distribution will be different from the distribution before the change in thermal properties. Along with this change in internal furnace temperature distribution, the temperature distribution of the silicon single crystal SM being pulled (hereinafter sometimes referred to as the "crystal temperature distribution") will be different from the distribution before the change in thermal properties. When the crystal temperature distribution changes, the thermal history (cooling conditions) of the silicon single crystal SM will be different from the history before the change in thermal properties. Along with this change in the thermal history of the silicon single crystal SM, the BMD density of the silicon single crystal SM will be different from the density before the change in thermal properties.

[0047] The temperature measuring unit 3 measures the temperature of a predetermined area inside the lifting furnace 20. The temperature measuring unit 3 comprises a first measuring unit 31 and a second measuring unit 32. The first measuring unit 31 and the second measuring unit 32 are composed of, for example, a thermal camera that measures the temperature inside the lifting furnace 20 in a non-contact manner.

[0048] The first measuring unit 31 measures the temperature of the region including the first measuring position Q1 and the second measuring position Q2 through the first viewing window 212A formed in the upper part of the top chamber 212, and outputs the measurement result to the estimation device 4.

[0049] The first measurement position Q1 is located on the inner circumferential surface of the portion surrounding the silicon single crystal SM in the heat shield 25. When the thermal properties of the heat shield 25, a furnace component, change due to aging, the performance of the heat shield 25 changes. When the performance of the heat shield 25 changes, the temperature at the first measurement position Q1 will be different from that before the performance change, even when the heater 23 is controlled under the same conditions as before the performance change. Thus, the temperature at the first measurement position Q1 corresponds to the performance (thermophysical properties) of the thermal shield 25, which affects the temperature of the silicon single crystal SM.

[0050] The second measurement position Q2 is located on the heat shield support portion 214. The second measurement position Q2 will be at a temperature corresponding to the temperature of the region between the heat shield support 214 and the water-cooled top chamber 212. When the thermophysical properties of the top chamber 212, which is a furnace component, change due to aging, the performance of the top chamber 212 changes. When the heater 23 is controlled under the same conditions as before the performance change, the region between the heat shield support 214 and the top chamber 212 (hereinafter sometimes referred to as the "cooling region by the top chamber 212") will be at a different temperature than before the performance change. As a result, the second measurement position Q2 will be at a different temperature than before the performance change of the top chamber 212. Thus, the temperature at the second measurement position Q2 is determined by the performance (thermophysical properties) of the top chamber 212, which affects the temperature of the silicon single crystal SM. In other words, the second measurement position Q2 is a position where the temperature is adjusted by the top chamber 212.

[0051] Here, we will explain the reason for positioning the second measurement position Q2 on the heat shield support portion 214. As mentioned above, the temperature at the second measurement position Q2 will be corresponding to the performance of the top chamber 212, so it is also possible to position the second measurement position Q2 on the inner surface of the top chamber 212. However, even if the temperature of the inner surface of the top chamber 212 is measured, there is a risk that the temperature measured may not reflect the performance of the top chamber 212. On the other hand, the heat shield support portion 214 reaches a temperature corresponding to the cooling region of the top chamber 212, that is, a temperature corresponding to the performance of the top chamber 212. For these reasons, in this first embodiment, the second measurement position Q2 is positioned on the heat shield support portion 214.

[0052] The second measuring unit 32 measures the temperature of the region including the third measuring position Q3 through the second viewing window 213B formed in the pull chamber 213, and outputs the measurement result to the estimation device 4.

[0053] The third measurement position Q3 is located on the outer surface of the silicon single crystal SM inside the pull chamber 213. As the thermophysical properties of the cooler 26, a furnace component, change due to aging, the performance of the cooler 26 changes. When the heater 23 is controlled under the same conditions as before the performance change, the silicon single crystal SM cooled by the cooler 26 reaches a different temperature than before the performance change. As a result, the temperature at the third measurement position Q3 is different from the temperature at the cooler 26 in the pull chamber 213 before the performance change. Thus, the temperature at the third measurement position Q3 corresponds to the performance (thermophysical properties) of the cooler 26, which affects the temperature of the silicon single crystal SM. In other words, the third measurement position Q3 is a position where the temperature has been adjusted by the cooler 26.

[0054] Here, we will explain why the third measurement position Q3 is located on the outer surface of the silicon single crystal SM inside the pull chamber 213. As mentioned above, the temperature at the third measurement position Q3 will be corresponding to the performance of the cooler 26, so it is also possible to position the third measurement position Q3 on the inner surface of the cooler 26. However, even if the temperature of the inner surface of the cooler 26 is measured, there is a risk that the temperature measured may not reflect the performance of the cooler 26. On the other hand, the silicon single crystal SM inside the pull chamber 213 reaches a temperature corresponding to the performance of the cooler 26. Furthermore, the region of the silicon single crystal SM located inside the pull chamber 213 is almost free from disturbances caused by the reflection of infrared radiation from the molten MD, allowing for accurate temperature measurement. For these reasons, in this first embodiment, the third measurement position Q3 is located on the outer surface of the silicon single crystal SM inside the pull chamber 213.

[0055] Estimation device 4 is a computer-based system that estimates the crystal temperature distribution of the silicon single crystal SM being pulled up by the silicon single crystal manufacturing apparatus 2. Based on the estimated crystal temperature distribution, estimation device 4 also estimates the thermal history of the silicon single crystal SM. Furthermore, based on the estimated thermal history, estimation device 4 estimates the BMD density of the silicon single crystal SM. As shown in Figure 2, the estimation device 4 is connected to a temperature measurement unit 3, an input unit 51, an output unit 52, a nitrogen concentration calculation unit 53, an oxygen concentration calculation unit 54, a BMD deposition heat treatment condition setting unit 55, and a storage unit 56, enabling them to send and receive various types of information.

[0056] The input unit 51 is configured, for example, as a touch panel or physical buttons. The input unit 51 is used for inputting various settings and outputs signals corresponding to the input operations to the estimation device 4.

[0057] The output unit 52 displays or outputs various information based on the control of the estimation device 4.

[0058] The nitrogen concentration calculation unit 53 calculates the nitrogen concentration during the pulling process in the silicon single crystal manufacturing apparatus 2 based on, for example, the amount of nitrogen added to the molten MD, and outputs the estimated result to the estimation device 4.

[0059] The oxygen concentration calculation unit 54 calculates the oxygen concentration during the pulling process in the silicon single crystal manufacturing apparatus 2 based on the pulling conditions, for example, the rotation speed of the crucible 22 and the silicon single crystal SM, and outputs the estimated result to the estimation device 4.

[0060] The BMD deposition heat treatment condition setting unit 55 sets the BMD deposition heat treatment conditions for depositing BMDs on a silicon wafer obtained from a silicon single crystal SM, based on setting input from the operator using the operator's input unit 51, for example, and outputs the setting details to the estimation device 4.

[0061] The storage unit 56 is composed of a well-known storage device such as an HDD (Hard Disk Drive). The storage unit 56 stores the estimation program P1 and various information necessary for estimating the crystal temperature distribution, thermal history, and BMD density.

[0062] Estimation program P1 is a program that causes the computer to function as estimation device 4. The estimated program P1 can be distributed, for example, through the sale, transfer, or lending of portable recording media such as Blu-ray®, DVD, and CD-ROM. Furthermore, the estimated program P1 can be distributed, for example, by being stored in the memory of a server on a network and transferred to other computers via the network.

[0063] The estimated program P1 stored in the memory unit 56 may be read by the computer from a portable recording medium, or it may be obtained from a server on a network. Alternatively, the estimated program P1 may not be stored in the memory unit 56, and the computer may sequentially obtain and execute the estimated program P1 from the server. Furthermore, the estimated program P1 may be stored in a separate memory unit provided within the computer.

[0064] The estimation device 4 is equipped with a CPU (Central Processing Unit). The estimation device 4 functions as a training data generation unit 41, a machine learning unit 42, a crystal temperature distribution estimation unit 43, a thermal history estimation unit 44, and a BMD density estimation unit 45 by having the CPU execute the estimation program P1 stored in the memory unit 56.

[0065] The training data generation unit 41 constructs a simulation model that simulates the lifting furnace 20. The training data generation unit 41 then performs heat transfer simulations under multiple calculation conditions in which the thermophysical properties of the furnace members in the lifting furnace 20 are arbitrarily set, and generates training data consisting of the calculation results of the furnace temperature distribution when a silicon single crystal is present in the lifting furnace under these multiple calculation conditions, and combinations of the parts being grown. The furnace temperature distribution that constitutes the training data may be the temperature distribution of at least one part of the straight body of the silicon single crystal, specifically the top part (the part on the upper end side in the lifting direction), the middle part (the part in the center in the lifting direction), and the bottom part (the part on the lower end side in the lifting direction).

[0066] The machine learning unit 42 constructs a regression model using a machine learning method, based on the training data generated by the training data generation unit 41. The input is the temperature of the first, second, and third measurement positions Q1, Q2, and Q3 inside the furnace 20, and the output is the crystal temperature distribution. Examples of machine learning methods include those using neural networks or genetic algorithms, but the machine learning method is not particularly limited, and well-known methods (such as support vector machines or sparse models) can be used.

[0067] The crystal temperature distribution estimation unit 43 inputs the temperature measurement results from the first, second, and third measurement positions Q1, Q2, and Q3 obtained from the temperature measurement unit 3 during the pulling of the silicon single crystal SM into a regression model constructed by the machine learning unit 42 to estimate the crystal temperature distribution. Here, since it is unlikely that the components of the pulling furnace 20 will rapidly deteriorate during the pulling of the silicon single crystal SM, the temperature distribution inside the furnace hardly changes. Therefore, if the temperature distribution inside the furnace can be estimated based on the temperature measurement results from the first, second, and third measurement positions Q1, Q2, and Q3, the crystal temperature distribution can be estimated.

[0068] The thermal history estimation unit 44 estimates the thermal history of the silicon single crystal SM based on the crystal temperature distribution estimated by the crystal temperature distribution estimation unit 43 and the pulling rate of the silicon single crystal SM.

[0069] The BMD density estimation unit 45 estimates the BMD density that can be deposited in the silicon single crystal SM based on the thermal history estimated by the thermal history estimation unit 44, the nitrogen and oxygen concentrations of the silicon single crystal SM, and the BMD deposition heat treatment conditions.

[0070] <Operation of a silicon single crystal manufacturing system> Next, we will describe the process of estimating the BMD density of the silicon single crystal SM during the pulling of the silicon single crystal SM as part of the operation of the silicon single crystal manufacturing system 1. Figure 3 is a flowchart showing the BMD density estimation process in the first embodiment.

[0071] First, as shown in Figure 3, the training data generation unit 41 of the estimation device 4 constructs a simulation model that mimics the lifting reactor 20 (step S1). When constructing a simulation model, the training data generation unit 41 sets the shape, size, placement, and thermophysical properties of the furnace members of the lifting furnace 20, the water cooling conditions for the water-cooled furnace members, the size of the silicon single crystal SM (for example, the lengths of the shoulder portion SM1, the straight body portion SM2, and the tail portion, and the diameter of the straight body portion SM2), and the temperature of the interface between the molten MD and the silicon single crystal SM as known values. The interface temperature is set to the melting point of silicon. As an example of the thermophysical properties of the furnace members, thermal emissivity can be used.

[0072] Next, the training data generation unit 41 performs a heat transfer simulation based on the simulation model to generate training data (step S2). When generating training data, the training data generation unit 41 sets a range of thermophysical properties for multiple furnace components based on the setting input using the operator's input unit 51, and then sets multiple calculation conditions by arbitrarily combining the thermophysical properties of each furnace component within the above range. Alternatively, the training data generation unit 41 may set a range of thermophysical properties for one furnace component and then set multiple calculation conditions by arbitrarily selecting thermophysical properties within the above range. Preferably, the furnace components for which thermophysical properties are set include the top chamber 212, the heat shield 25, and the cooler 26, which affect the temperature of the silicon single crystal SM during pulling. From the viewpoint of improving the accuracy of the regression model in the machine learning unit 42, it is preferable to set a large number of calculation conditions here. The training data generation unit 41 performs heat transfer simulations for each of the multiple calculation conditions and calculates the temperature distribution inside the furnace. The training data generation unit 41 outputs the calculation results of the temperature distribution inside the furnace obtained from each calculation condition as training data to the machine learning unit 42.

[0073] Next, the machine learning unit 42 uses the training data to construct a regression model in which the input is the temperatures of the first, second, and third measurement positions Q1, Q2, and Q3, and the output is the crystal temperature distribution (step S3). Then, the machine learning unit 42 outputs the constructed regression model to the crystal temperature distribution estimation unit 43.

[0074] After the processing in step S3, the manufacturing equipment control unit of the silicon single crystal manufacturing apparatus 2 pulls out a silicon single crystal SM of the size set during the construction of the simulation model from the molten MD, as shown in Figure 1. Then, as shown in Figure 3, the first and second measuring units 31 and 32 of the temperature measuring unit 3 measure the temperatures of the first, second, and third measuring positions Q1, Q2, and Q3 at the timing when the second measuring unit 32 can measure the temperature of the straight body SM2 located inside the pull chamber 213, and output the measurement results to the estimation device 4 (step S4). Note that the temperature measurement timings of the first measurement unit 31 and the second measurement unit 32 may be different.

[0075] Next, the crystal temperature distribution estimation unit 43 estimates the crystal temperature distribution of the silicon single crystal SM being pulled by inputting the temperature measurement results from the first, second, and third measurement positions Q1, Q2, and Q3 obtained from the temperature measurement unit 3 into the regression model obtained from the machine learning unit 42 (step S5). The crystal temperature distribution estimation unit 43 outputs the estimated crystal temperature distribution result to the thermal history estimation unit 44. The crystal temperature distribution estimation unit 43 may also display or output the estimated crystal temperature distribution results to the output unit 52.

[0076] Next, the thermal history estimation unit 44 estimates the thermal history of the silicon single crystal SM based on the crystal temperature distribution obtained from the crystal temperature distribution estimation unit 43 and the pulling rate of the silicon single crystal SM having said crystal temperature distribution (step S6). The thermal history estimation unit 44 outputs the thermal history estimation result to the BMD density estimation unit 45. The thermal history estimation unit 44 may also display or output the thermal history estimation results to the output unit 52. Furthermore, the thermal history estimation unit 44 may obtain the silicon single crystal SM pulling speed from the manufacturing equipment control unit, or it may obtain the value set by the operator using the input unit 51 as the silicon single crystal SM pulling speed.

[0077] Furthermore, the nitrogen concentration calculation unit 53 calculates the nitrogen concentration of the silicon single crystal SM and outputs the calculation result to the estimation device 4 (step S7). The oxygen concentration calculation unit 54 calculates the oxygen concentration of the silicon single crystal SM and outputs the calculation result to the estimation device 4 (step S8). The BMD deposition heat treatment condition setting unit 55 sets the BMD deposition heat treatment conditions and outputs the setting details to the estimation device 4 (step S9). Furthermore, the processes in steps S7 to S9 can be performed in any order and at any time.

[0078] Then, the BMD density estimation unit 45 estimates the BMD density of the silicon single crystal SM being pulled based on the thermal history obtained from the thermal history estimation unit 44, the nitrogen concentration, the oxygen concentration, and the BMD deposition heat treatment conditions (step S10). In this case, it is preferable for the BMD density estimation unit 45 to estimate the BMD density for each part with a different thermal history. The BMD density estimation unit 45 may display or output the estimated BMD density result to the output unit 52. The BMD density estimation unit 45 may also acquire the value set by the operator using the input unit 51 as the concentration of at least one of the nitrogen concentration and oxygen concentration.

[0079] <Effects of the First Embodiment> According to the estimation device 4 of the first embodiment, at least the following effects can be achieved. (1) The estimation device 4 performs heat transfer simulations under multiple calculation conditions in which the thermophysical properties of the furnace members constituting the pull-up furnace 20 are arbitrarily set, and generates training data from the calculation results of the furnace temperature distribution obtained from each calculation condition. Next, the estimation device 4 generates a regression model using machine learning, based on the training data, with the input being the temperatures of the first, second, and third measurement positions Q1, Q2, and Q3 inside the pull-up furnace 20, and the output being the crystal temperature distribution. Then, the estimation device 4 inputs the temperature measurement results of the first, second, and third measurement positions Q1, Q2, and Q3 obtained during the pull-up of the silicon single crystal SM into the regression model and estimates the crystal temperature distribution of the silicon single crystal SM during the pull-up. Therefore, the estimation device 4 can accurately estimate the crystal temperature distribution of the silicon single crystal SM in accordance with the aging degradation of the furnace members, based on the temperatures of the first, second, and third measurement positions Q1, Q2, and Q3 in the pulling furnace 20 and a regression model, without using the temperature of the silicon single crystal SM near the molten MD during pulling, which has poor measurement accuracy. In particular, by performing the crystal temperature distribution estimation process during the pulling of the silicon single crystal SM, the crystal temperature distribution can be estimated accurately in real time.

[0080] (2) The estimation device 4 estimates the thermal history of the silicon single crystal SM based on the accurately estimated crystal temperature distribution and the pulling rate of the silicon single crystal SM. Therefore, the estimation device 4 can accurately estimate the thermal history of silicon single crystal SM in accordance with the aging degradation of the reactor components. In particular, by performing the thermal history estimation process during the pulling of the silicon single crystal SM, the thermal history can be estimated accurately in real time.

[0081] (3) The estimation device 4 estimates the density of BMD that can precipitate in the silicon single crystal SM during pulling, based on the accurately estimated thermal history of the silicon single crystal SM, the oxygen and nitrogen concentrations of the silicon single crystal SM, and the pulling rate. Therefore, the estimation device 4 can accurately estimate the BMD density of silicon single crystal SM in accordance with the aging degradation of the reactor components. In particular, by taking nitrogen concentration into consideration in addition to oxygen concentration, the BMD density of silicon single crystal SM can be estimated with even greater accuracy. In particular, by performing the BMD density estimation process during the pulling of the silicon single crystal SM, the BMD density can be estimated accurately in real time. Therefore, adjustments to the pulling conditions to ensure that the BMD density of the silicon single crystal SM to be pulled next does not change, or preparations for replacing aged furnace components, can be started earlier. Examples of changes to the pulling conditions include changing the rotation speed of the crucible 22 or changing the power of the heater 23.

[0082] (4) The training data generation unit 41 constructs a simulation model such that the temperature at the boundary between the silicon melt and the silicon crystal is the silicon melting point. By using known silicon melting point values, the accuracy of estimating thermal history and BMD density can be improved.

[0083] (5) The furnace components for which thermal properties are set in the heat transfer simulation include a top chamber 212 that cools the silicon single crystal SM during pulling. The temperature measurement locations input to the regression model include a second measurement location Q2 on the heat shield support section 214, whose temperature is regulated by the top chamber 212. Thus, by measuring the temperature on the heat shield support section 214, which is adjusted to a temperature corresponding to the performance of the top chamber 212, rather than the top chamber 212 itself which has a water cooling function, an appropriate temperature corresponding to the aging degradation of the top chamber 212 can be input into the regression model. Therefore, the estimation device 4 can estimate the crystal temperature distribution of the silicon single crystal SM with greater accuracy.

[0084] (6) The furnace component for which thermal properties are set in the heat transfer simulation has the function of cooling the silicon single crystal SM during pulling and includes a cylindrical cooler 26 that cools the silicon single crystal SM as it passes through its interior. The temperature measurement positions input to the regression model include a third measurement position Q3 on the outer surface of the straight body SM2 cooled by the cooler 26. In this way, by measuring not the coolant 26 itself, but the straight body section SM2 which is adjusted to a temperature corresponding to the performance of the coolant 26, an appropriate temperature corresponding to the aging degradation of the coolant 26 can be input into the regression model. Furthermore, since the third measurement position Q3 is hardly affected by disturbances from infrared radiation generated from the molten MD, accurate temperature determination is possible. Therefore, the estimation device 4 can estimate the crystal temperature distribution of the silicon single crystal SM with greater accuracy.

[0085] (7) The furnace components for which thermal properties are set in the heat transfer simulation include a thermal shield 25 that suppresses the temperature rise of the silicon single crystal SM during pulling. The temperature measurement locations input to the regression model include a first measurement location Q1 on the thermal shield 25. In this way, by measuring on the heat shield 25, an appropriate temperature corresponding to the aging degradation of the heat shield 25 can be input into the regression model. Therefore, the estimation device 4 can estimate the crystal temperature distribution of the silicon single crystal SM with greater accuracy.

[0086] [Second Embodiment] <Configuration of a silicon single crystal manufacturing system> Next, the configuration of the silicon single crystal manufacturing system in the second embodiment of the present invention will be described based on Figures 1 and 4. Note that components identical to those in the first embodiment will be given the same names and reference numerals, and their descriptions will be simplified or omitted. Figure 4 is a block diagram of the estimation device in the second embodiment.

[0087] The silicon single crystal manufacturing system 1A shown in Figure 1 has the same configuration as the silicon single crystal manufacturing system 1 of the first embodiment, except that it includes an estimation device 6 instead of estimation device 4.

[0088] The estimation device 6 is computer-based and estimates the crystal temperature distribution of the silicon single crystal SM being pulled up in the silicon single crystal manufacturing apparatus 2. Based on the estimated crystal temperature distribution, the estimation device 6 also estimates the thermal stress of the silicon single crystal SM. Furthermore, based on the estimated thermal stress, the estimation device 6 estimates the critical value (hereinafter sometimes referred to as "critical v / G") of the ratio v / G between the silicon single crystal pulling speed v (mm / min) and the temperature gradient G near the solid-liquid interface. Here, critical v / G is a value that represents the boundary between the Pv region and the Pi region at the radial center of a silicon single crystal SM. The Pv region is a defect-free region where vacancy-type point defects are predominant. The Pv region contains oxygen precipitation nuclei in the as-grown state and is a region where BMD is likely to occur when BMD precipitation heat treatment is applied. The Pi region is a defect-free region where interstitial silicon-type point defects are predominant. The Pi region contains almost no oxygen precipitation nuclei in the as-grown state and is a region where BMD is unlikely to occur when BMD precipitation heat treatment is applied.

[0089] As shown in Figure 4, the estimation device 6 is connected to a temperature measuring unit 3, an input unit 51, an output unit 52, and a storage unit 56A, enabling them to send and receive various types of information.

[0090] The memory unit 56A is composed of a well-known storage device similar to the memory unit 56. The memory unit 56A stores the estimation program P2 and various information necessary for estimating the crystal temperature distribution, thermal stress, and boundary values.

[0091] Estimation program P2 is a program that causes the computer to function as estimation device 6. Estimated program P2 can be distributed in the same manner as estimated program P1. The estimated program P2 stored in the memory unit 56A may be read by the computer from a portable recording medium, or it may be obtained from a server on a network. Alternatively, the estimated program P2 may not be stored in the memory unit 56A, and the computer may sequentially obtain and execute the estimated program P2 from the server. Furthermore, the estimated program P2 may be stored in a separate memory unit provided within the computer.

[0092] The estimation device 6 is equipped with a CPU, and by executing the estimation program P2 stored in the memory unit 56A, the CPU functions as a training data generation unit 41, a machine learning unit 42, a crystal temperature distribution estimation unit 43, a thermal stress estimation unit 61, a defect distribution estimation unit 62, and a critical value estimation unit 63.

[0093] The thermal stress estimation unit 61 estimates the thermal stress near the solid-liquid interface with the molten silicon single crystal SM based on the crystal temperature distribution estimated by the crystal temperature distribution estimation unit 43.

[0094] The defect distribution estimation unit 62 estimates the defect distribution in the silicon single crystal SM based on the thermal stress estimated by the thermal stress estimation unit 61. In estimating this defect distribution, the defect distribution estimation unit 62 may use, for example, the method described in Japanese Patent Application Publication No. 2021-70593.

[0095] The critical value estimation unit 63 estimates the critical v / G in a silicon single crystal SM based on the defect distribution estimated by the defect distribution estimation unit 62. In estimating this critical v / G, the critical value estimation unit 63 can use, for example, the method described in Japanese Patent Application Publication No. 2021-70593.

[0096] <Operation of a silicon single crystal manufacturing system> Next, as part of the operation of the silicon single crystal manufacturing system 1A, the process for estimating the critical v / G of the silicon single crystal SM during the pulling of the silicon single crystal SM will be described. Note that processes identical to those in the first embodiment will be given the same names and reference numerals, and their explanations will be simplified or omitted. Figure 5 is a flowchart showing the estimation process for critical v / G in the second embodiment.

[0097] First, as shown in Figure 5, the training data generation unit 41 of the estimation device 6 constructs a simulation model that mimics the lifting reactor 20 (step S1). Next, the training data generation unit 41 generates training data by performing a heat transfer simulation based on the simulation model (step S2), and outputs the generated training data to the machine learning unit 42.

[0098] Next, the machine learning unit 42 uses the training data to construct a regression model in which the input is the temperatures of the first, second, and third measurement positions Q1, Q2, and Q3, and the output is the crystal temperature distribution (step S3), and outputs the constructed regression model to the crystal temperature distribution estimation unit 43. After the processing in step S3, the first and second measuring units 31 and 32 of the temperature measuring unit 3 measure the temperatures at the first, second, and third measuring positions Q1, Q2, and Q3, and output the measurement results to the estimation device 4 (step S4).

[0099] Subsequently, the crystal temperature distribution estimation unit 43 inputs the temperature measurement results from the first, second, and third measurement positions Q1, Q2, and Q3 obtained from the temperature measurement unit 3 into the regression model obtained from the machine learning unit 42, thereby estimating the crystal temperature distribution of the silicon single crystal SM being pulled (step S5), and outputs the estimated crystal temperature distribution result to the thermal stress estimation unit 61. The crystal temperature distribution estimation unit 43 may also display or output the estimated crystal temperature distribution result to the output unit 52.

[0100] Next, the thermal stress estimation unit 61 estimates the thermal stress of the silicon single crystal SM based on the crystal temperature distribution obtained from the crystal temperature distribution estimation unit 43 and the radial size of the silicon single crystal SM having said crystal temperature distribution (step S11). In this case, it is preferable for the thermal stress estimation unit 61 to estimate the thermal stress for each part with a different temperature distribution. The thermal stress estimation unit 61 outputs the thermal stress estimation result to the defect distribution estimation unit 62. The thermal stress estimation unit 61 may display or output the thermal stress estimation results to the output unit 52. Furthermore, the thermal stress estimation unit 61 may obtain the radial size of the silicon single crystal SM from the manufacturing equipment control unit, or it may obtain the value set by the operator using the input unit 51 as the radial size of the silicon single crystal SM.

[0101] Subsequently, the defect distribution estimation unit 62 estimates the defect distribution in the silicon single crystal SM based on the crystal temperature distribution obtained from the crystal temperature distribution estimation unit 43 and the thermal stress obtained from the thermal stress estimation unit 61 (step S12). The defect distribution estimation unit 62 outputs the estimated defect distribution result to the critical value estimation unit 63. The defect distribution estimation unit 62 may also display or output the defect distribution estimation results to the output unit 52.

[0102] Then, the critical value estimation unit 63 estimates the critical v / G in the silicon single crystal SM based on the defect distribution obtained from the defect distribution estimation unit 62 (step S13). The critical value estimation unit 63 may also display or output the estimated result of the critical value v / G to the output unit 52.

[0103] <Effects of the second embodiment> According to the estimation device 6 of the second embodiment, in addition to the effects similar to (1), (4) to (7) of the first embodiment, the following effects can be achieved. (8) The estimation device 6 estimates the thermal stress near the solid-liquid interface in the silicon single crystal SM based on the accurately estimated crystal temperature distribution. Because the estimation device 6 does not use the temperature of the silicon single crystal SM near the molten MD during pulling, which has poor measurement accuracy, it can accurately estimate the thermal stress of the silicon single crystal SM during pulling in accordance with the aging deterioration of the furnace components. In particular, by performing the thermal stress estimation process during the pulling of the silicon single crystal SM, the thermal stress can be estimated accurately in real time.

[0104] (9) The estimation device 6 estimates the defect distribution of the silicon single crystal SM based on the accurately estimated crystal temperature distribution and thermal stress. Therefore, the estimation device 6 can accurately estimate the defect distribution of silicon single crystals (SM) being pulled up in accordance with the aging deterioration of the reactor components. In particular, by performing the defect distribution estimation process during the pulling of the silicon single crystal SM, the defect distribution can be estimated accurately in real time.

[0105] (10) The estimation device 6 estimates the critical v / G of the silicon single crystal SM based on the accurately estimated defect distribution. Therefore, the estimation device 6 can accurately estimate the critical v / G of the silicon single crystal SM being pulled up in accordance with the aging deterioration of the reactor components. In particular, by performing the criticality v / G estimation process during the pulling of the silicon single crystal SM, the defect distribution can be estimated accurately in real time.

[0106] [Differentiation] Although embodiments of the present invention have been described in detail above with reference to the drawings, the specific configuration is not limited to these embodiments, and various improvements and design changes, etc., that do not depart from the spirit of the present invention are also included.

[0107] In the first embodiment, the estimation device 4 does not need to be provided with a thermal history estimation unit 44, nor does it need to be provided with a BMD density estimation unit 45. In the second embodiment, the estimation device 6 does not need to be provided with a defect distribution estimation unit 62, nor does it need to be provided with a critical value estimation unit 63.

[0108] In at least one of the first and second embodiments, the silicon single crystal to be used for estimating the crystal temperature distribution may be pulled from a silicon melt that is not doped with nitrogen. In the first embodiment, when a silicon single crystal is pulled from a silicon melt that is not doped with nitrogen, the BMD density estimation unit 45 may be configured to estimate the BMD density without relying on the nitrogen concentration. In this case, it becomes unnecessary to provide a nitrogen concentration calculation unit 53 in the silicon single crystal manufacturing apparatus 2.

[0109] The temperature measuring unit 3 may consist only of the first measuring unit 31 or the second measuring unit 32, or the first measuring unit 31 may measure the temperature only at the first measuring position Q1 or the second measuring position Q2, or a contact-type temperature measuring device may be used as the first measuring unit 31. Furthermore, the temperature measurement locations input to the regression model may be locations other than the first to third measurement locations Q1 to Q3, and may be on or near the furnace member where thermal properties are not set in the heat transfer simulation.

[0110] In the first embodiment, the processes from step S5 (estimated crystal temperature distribution), or from step S6 (estimated thermal history), or the process in step S10 (estimated BMD density) may be performed after the silicon single crystal SM to be used for crystal temperature distribution estimation has been pulled up. Similarly, in the second embodiment, the processes from step S5 (estimated crystal temperature distribution), or from step S11 (estimated thermal stress), or from step S12 (estimated defect distribution), or from step S13 (estimated critical v / G) may be performed after the pulling of the silicon single crystal SM to be estimated for crystal temperature distribution. [Examples]

[0111] Next, embodiments of the present invention will be described. However, the present invention is not limited to these embodiments.

[0112] [Example 1] The silicon single crystal manufacturing system 1 of the first embodiment was prepared as the silicon single crystal manufacturing system of Example 1. Then, the pulling process was performed on 50 silicon single crystal SMs, and the BMD density estimation process of the first embodiment shown in Figure 3 was performed in each pulling process. The main pulling conditions for silicon single crystal SM are as follows: Diameter of the straight section: 315mm Nitrogen concentration: 1.2 × 10⁻⁶ 18 / cm 3 Oxygen concentration: 3.2 × 10⁻⁶ 12 / cm 3

[0113] For each of the 50 silicon single crystal SMs, a sample wafer obtained from an arbitrary location in the straight body portion SM2 was subjected to the BMD deposition heat treatment set in the BMD deposition heat treatment condition setting unit 55, and the BMD density was measured. The method described in Patent Document 1 above was used to measure the BMD density. Then, we investigated the correlation between the measured BMD density of each sample wafer (hereinafter sometimes referred to as "measured BMD density") and the estimated BMD density of the area corresponding to the acquisition position of the sample wafer in each straight section SM2 (hereinafter sometimes referred to as "estimated BMD density"). The results are shown in Figure 6.

[0114] As shown in Figure 6, the absolute difference between the estimated BMD density and the measured BMD density for all sample wafers was within 10% of the measured BMD density. From this, it was confirmed that the BMD density can be estimated with high accuracy by the BMD density estimation process in the first embodiment of the present invention.

[0115] [Example 2] The silicon single crystal manufacturing system 1A of the second embodiment was prepared as the silicon single crystal manufacturing system of Example 1. Then, the three silicon single crystal SMs were subjected to pulling processes, and in each pulling process, the critical v / G estimation process of the second embodiment shown in Figure 5 was performed. The main pulling conditions for silicon single crystal SM are as follows: Diameter of the straight section: 315mm Nitrogen concentration: 1.2 × 10⁻⁶ 18 / cm 3 Oxygen concentration: 3.2 × 10⁻⁶ 12 / cm 3

[0116] Three silicon single crystal SMs were cut along the pulling direction, subjected to a Cu decoration treatment at 750°C for 5 minutes, and then selective etching (Wright etching) was performed. After this, the defect distribution of the silicon single crystal SMs was determined by identifying each defect region using a microscope. Then, the boundary between the Pv region and the Pi region was determined from the defect distribution, and the critical v / G (hereinafter sometimes referred to as "measured critical v / G") was determined based on the portion located at the radial center of the silicon single crystal SM at the determined boundary.

[0117] Furthermore, during the pulling of each silicon single crystal SM, the temperature gradient G near the solid-liquid interface was estimated based on the crystal temperature distribution estimated by the process in step S5. Then, as a comparison process between the measured critical v / G of each silicon single crystal SM and the critical v / G obtained by the estimation process for the critical v / G of each silicon single crystal SM (hereinafter sometimes referred to as "estimated critical v / G"), the measured critical v / G and the estimated critical v / G were each multiplied by the temperature gradient G estimated based on the crystal temperature distribution and compared.

[0118] The average absolute value of the difference between the measured criticality v, obtained by multiplying the measured criticality v / G by the temperature gradient G, and the estimated criticality v, obtained by multiplying the estimated criticality v / G by the temperature gradient G, was 1.3% of the measured criticality v. Generally, it is said that in order to pull a defect-free silicon single crystal (SM), the pulling speed v must be controlled so that the difference from the measured criticality v / G is within ±2%. As described above, the average value of the absolute difference between the measured critical v and the estimated critical v was 1.3% of the measured critical v. Therefore, it was confirmed that the critical v / G estimation process in the second embodiment of the present invention can estimate the critical v / G with high accuracy. [Explanation of symbols]

[0119] 20... Pulling furnace, 212... Top chamber (cooling furnace component), 25... Heat shield (furnace component for suppressing temperature rise), 26... Cooler (cooling furnace component), 4,6... Estimation device, 41... Training data generation unit, 42... Machine learning unit, 43... Crystal temperature distribution estimation unit, 44... Thermal history estimation unit, 45... BMD density estimation unit, 61... Thermal stress estimation unit, P1,P2... Estimation program, SM... Silicon single crystal.

Claims

1. An estimation method for making estimations regarding silicon single crystals grown by the Czochralski method in a pull-up reactor, The steps include constructing a simulation model that mimics the aforementioned lifting reactor, The steps include: performing a heat transfer simulation based on the simulation model for a plurality of calculation conditions in which the thermal properties of the furnace members constituting the lifting furnace are arbitrarily set, and generating training data from the calculation results of the temperature distribution inside the lifting furnace obtained from each of the plurality of calculation conditions; Based on the aforementioned training data, a regression model is constructed using machine learning, in which the input is the temperature at a temperature measurement location corresponding to the furnace member whose thermophysical properties change according to the aging deterioration inside the lifting furnace, and the output is the temperature distribution of a silicon single crystal. An estimation method comprising the step of inputting the temperature measurement results at the temperature measurement location obtained during the pulling of a silicon single crystal into the regression model to estimate the temperature distribution of the silicon single crystal during the pulling process.

2. In the estimation method described in claim 1, An estimation method further comprising the step of estimating the thermal history of the silicon single crystal based on the estimated temperature distribution of the silicon single crystal and the pulling rate of the silicon single crystal.

3. In the estimation method described in claim 2, An estimation method further comprising the step of estimating the BMD density of the silicon single crystal based on the estimated thermal history, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions.

4. In the estimation method described in claim 3, An estimation method for estimating the BMD density of a silicon single crystal, wherein the BMD density of the silicon single crystal is estimated based on the thermal history, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions.

5. In the estimation method described in claim 1, An estimation method further comprising the step of estimating thermal stress near the solid-liquid interface in the silicon single crystal based on the estimated temperature distribution of the silicon single crystal.

6. In the estimation method described in claim 1, The estimation method involves constructing a simulation model that simulates the aforementioned lifting furnace, such that the temperature at the boundary between the silicon molten liquid and the silicon crystal is the silicon melting point.

7. In the estimation method according to any one of claims 1 to 6, In the heat transfer simulation, the furnace member for which the thermal properties are set includes a cooling furnace member for cooling the silicon single crystal during the pulling process. The estimation method includes a temperature measurement position that is adjusted by the cooling furnace member.

8. In the estimation method described in claim 7, The cooling furnace member includes a cylindrical cooler that cools the silicon single crystal as it passes through it during the pulling process. The estimation method wherein the temperature measurement position includes the outer surface of the silicon single crystal after it has passed through the cooling body.

9. In the estimation method according to any one of claims 1 to 6, In the heat transfer simulation, the furnace member for which the thermophysical property values ​​are set includes a furnace member for suppressing temperature rise to suppress the temperature rise of the silicon single crystal during pulling, The estimation method includes determining the temperature measurement position as a position on the furnace member for suppressing temperature rise.

10. An estimation device for making estimations regarding silicon single crystals grown by the Czochralski method in a pull-up reactor, A training data generation unit constructs a simulation model that simulates the lifting furnace, performs heat transfer simulations based on the simulation model for multiple calculation conditions in which the thermal properties of the furnace members constituting the lifting furnace are arbitrarily set, and generates training data by generating the calculation results of the temperature distribution inside the lifting furnace obtained from each of the multiple calculation conditions. A machine learning unit constructs a regression model based on the aforementioned training data, where the input is the temperature at a temperature measurement location corresponding to the furnace member whose thermophysical properties change according to the aging deterioration inside the lifting furnace, and the output is the temperature distribution of a silicon single crystal. An estimation device comprising: a crystal temperature distribution estimation unit that inputs the temperature measurement results at the temperature measurement position obtained during the pulling of a silicon single crystal into the regression model to estimate the temperature distribution of the silicon single crystal during the pulling process.

11. In the estimation device according to claim 10, The estimation apparatus further comprises a thermal history estimation unit that estimates the thermal history of the silicon single crystal based on the temperature distribution of the silicon single crystal estimated by the crystal temperature distribution estimation unit and the pulling speed of the silicon single crystal.

12. In the estimation device according to claim 11, The estimation apparatus further comprises a BMD density estimation unit that estimates the BMD density of the silicon single crystal based on the thermal history estimated by the thermal history estimation unit, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions.

13. In the estimation device according to claim 12, The BMD density estimation unit is an estimation device that estimates the BMD density of the silicon single crystal based on the thermal history, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions.

14. In the estimation device according to claim 10, An estimation apparatus further comprising a thermal stress estimation unit that estimates the thermal stress near the solid-liquid interface in the silicon single crystal based on the temperature distribution of the silicon single crystal estimated by the crystal temperature distribution estimation unit.

15. In the estimation device according to claim 10, The aforementioned training data generation unit is an estimation device that constructs the simulation model such that the temperature at the boundary between the silicon melt and the silicon crystal is the silicon melting point.

16. An estimation program that causes a computer to function as an estimation device according to any one of claims 10 to 15.

Images