JP7838464B2 - Estimation method, estimation device, and estimation program - Google Patents

Description

This invention relates to an estimation method, an estimation apparatus, and an estimation program.

In the Czochralski (CZ) method for manufacturing silicon single crystals, a seed crystal is attached to the silicon molten material in a quartz crucible and then pulled up to grow the silicon single crystal. During the growth of the silicon single crystal, oxygen is introduced into the silicon molten material from the quartz crucible. This oxygen, introduced into the silicon molten material, becomes oxygen precipitates called BMDs (Bulk Micro Defects) during the heat treatment process in the manufacturing of devices using silicon wafers.

While BMDs (Ballistic Metal Deposition) have the advantage of acting as a gettering source, capturing heavy metal impurities that degrade device performance when mixed into silicon wafers, they also have the disadvantage of reducing the mechanical strength of the silicon wafer. Therefore, a standard range is defined for the BMD density of silicon single crystals. 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 deposition heat treatment used to deposit BMDs on the silicon wafer obtained from the silicon single crystal (see, for example, Patent Document 1 and Non-Patent Document 1).

Japanese Patent Publication No. 2017-105675

The Science of Silicon, edited by the UCS Semiconductor Fundamental Technology Research Group (Publisher: Realize Co., Ltd.), Chapter 2, Section 5, Chapter 7, Section 3

Of the above conditions affecting BMD density, the BMD precipitation heat treatment conditions are fixed for each product, while 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.

The thermal history can be determined from the temperature distribution of the silicon single crystal. To directly measure the thermal history during crystal pulling, the temperature distribution of the silicon single crystal should be measured. While non-contact measurement using a thermal camera is a possible method, accurately measuring the temperature distribution near the silicon melt is difficult due to disturbances mainly caused by infrared radiation emitted from the high-temperature silicon melt. Therefore, accurately estimating the BMD density during silicon single crystal pulling is also difficult.

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 response to the aging degradation of a furnace component.

The present invention provides an estimation method for estimating a silicon single crystal grown in a pulling furnace by the Czochralski method, comprising the steps of: constructing a simulation model that mimics 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 from the calculation results of the temperature distribution inside 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 location inside 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 location 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 process.

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 rate of the silicon single crystal.

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.

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 and nitrogen concentrations of the silicon single crystal, and the BMD deposition heat treatment conditions.

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.

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 at the boundary between the silicon molten material and the silicon crystal is the silicon melting point.

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 regulated by the cooling furnace member.

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 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.

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.

The estimation device of the present invention is an estimation device for estimating silicon single crystals grown by the Czochralski method in a pulling furnace, and comprises: a training data generation unit that constructs a simulation model simulating the pulling furnace, performs heat transfer simulations 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 generates training data from the calculation results of the temperature distribution inside the pulling furnace obtained from each of the plurality of calculation conditions; a machine learning unit that constructs a regression model based on the training data, with the input being the temperature at a predetermined measurement position inside the pulling furnace and the output being the temperature distribution of the silicon single crystal; and a crystal temperature distribution estimation unit that inputs the temperature measurement results 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.

In the estimation apparatus of the present invention, it is preferable to further include 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.

In the estimation apparatus 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 thermal history estimated by the thermal history estimation unit, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions.

In the estimation apparatus 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 thermal history, the oxygen and nitrogen concentrations of the silicon single crystal, and the BMD deposition heat treatment conditions.

In the estimation apparatus 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.

In the estimation apparatus 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.

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

This is a schematic diagram showing the general configuration of the silicon single crystal manufacturing system in the first and second embodiments. This is a block diagram of the estimation device in the first embodiment. This is a flowchart showing the BMD density estimation process in the first embodiment. This is a block diagram of the estimation device in the second embodiment. This is a flowchart showing the estimation process for critical v/G in the second embodiment. This graph shows the correlation between the measured BMD density and the estimated BMD density in Example 1.

[First Embodiment]
<Configuration of a 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.
Figure 1 is a schematic diagram showing the general configuration of the silicon single crystal manufacturing system in the first and second embodiments. Figure 2 is a block diagram of the estimated apparatus in the first embodiment.

The silicon single crystal manufacturing system 1 shown in Figure 1 comprises a silicon single crystal manufacturing apparatus 2, a temperature measurement unit 3, and an estimation device 4.

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 with a straight body portion SM2 diameter of, for example, 200 mm to 450 mm. 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).

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

Chamber 21 comprises a main chamber 211, a top chamber 212, and a pull chamber 213. The main chamber 211, top chamber 212, and pull chamber 213 have a water-cooled structure.

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.

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 hermetically connected to the upper end of the main chamber 211, and it covers the upper part of the main chamber 211. The top chamber 212 is a cooling furnace component for cooling the silicon single crystal SM during pulling.

The pull chamber 213 is formed in a cylindrical shape. Its lower end 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.

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

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, driven by a vacuum pump (not shown).

Crucible 22 is located within the main chamber 211 and stores the molten silicon MD containing the dopant. Crucible 22 comprises a bottomed cylindrical quartz crucible 221 and a carbon-based support crucible 222 that houses the quartz crucible 221. Note that if the resistivity of the silicon single crystal SM is very high, dopant addition to the molten silicon MD may not be necessary.

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.

The heat-insulating tube 24 is formed in a cylindrical shape. The heat-insulating tube 24 is positioned outside the heater 23 at predetermined intervals.

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 portions 214 extending 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, blocking 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 in the silicon single crystal SM during pulling.

The cooler 26 is a cylindrical component 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.

The crystal pulling unit 27 comprises 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.

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.

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).

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.

The silicon single crystal SM being pulled has a temperature distribution corresponding to the furnace temperature distribution, 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.

When the thermal properties of furnace components change due to aging or other factors, controlling the heater 23 under the same conditions as before the change in thermal properties will result in a different internal furnace temperature distribution. This change in internal furnace temperature distribution will cause the temperature distribution of the silicon single crystal SM being pulled (hereinafter sometimes referred to as the "crystal temperature distribution") to differ from the distribution before the change in thermal properties. This change in crystal temperature distribution will result in a different thermal history (cooling conditions) for the silicon single crystal SM compared to the history before the change in thermal properties. Consequently, the BMD density of the silicon single crystal SM will differ from the density before the change in thermal properties.

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.

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.

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.

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.

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 in accordance with 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.

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.

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 is adjusted by the cooler 26.

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 in accordance with the performance of the cooler 26, so it is also possible to position the third measurement position Q3 on the inner circumferential 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 correspond to 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 coolant 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 rays generated from the molten MD, allowing for accurate temperature measurement.
For these reasons, in this first embodiment, the third measurement position Q3 is positioned on the outer surface of the silicon single crystal SM inside the pull chamber 213.

Estimation device 4 is a computer-based device that estimates the crystal temperature distribution of the silicon single crystal SM being pulled up by the silicon single crystal manufacturing apparatus 2. Furthermore, estimation device 4 estimates the thermal history of the silicon single crystal SM based on the estimated crystal temperature distribution. In addition, estimation device 4 estimates the BMD density of the silicon single crystal SM based on the estimated thermal history.
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.

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.

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

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

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.

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, for example, on setting input from the operator using the input unit 51, and outputs the setting details to the estimation device 4.

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.

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.

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 within the computer.

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.

The training data generation unit 41 constructs a simulation model that mimics the pull-up 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 pull-up furnace are arbitrarily set. It generates training data consisting of the calculated results of the furnace temperature distribution when a silicon single crystal is present in the pull-up furnace under these multiple calculation conditions, and combinations of the growing locations. The furnace temperature distribution constituting the training data may be the temperature distribution of at least one of the following locations in the straight body of the silicon single crystal: the top portion (the upper end in the pull-up direction), the middle portion (the center in the pull-up direction), and the bottom portion (the lower end in the pull-up direction).

The machine learning unit 42 constructs a regression model using machine learning methods, 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 neural networks or genetic algorithms, but the system is not particularly limited and well-known methods (such as support vector machines or sparse models) can be used.

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 furnace temperature distribution remains almost unchanged. Therefore, if the furnace temperature distribution 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.

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.

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.

<Operation of the 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.

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 furnace 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. Thermal emissivity can be used as an example of the thermophysical properties of the furnace members.

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.

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

After the processing in step S3, the manufacturing apparatus control unit of the silicon single crystal manufacturing apparatus 2 pulls up 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 portion 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.

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 of 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.

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 display or output the thermal history estimation results to the output unit 52. The thermal history estimation unit 44 may also obtain the silicon single crystal SM pulling speed from the manufacturing equipment control unit, or it may obtain the silicon single crystal SM pulling speed as a value set by the operator using the input unit 51.

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 timing.

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.

<Effects of the First Embodiment>
The estimation device 4 of the first embodiment can achieve at least the following effects.
(1) The estimation device 4 performs heat transfer simulations under multiple calculation conditions in which the thermophysical properties of the furnace members constituting the pulling 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 pulling 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 pulling of the silicon single crystal SM into the regression model and estimates the crystal temperature distribution of the silicon single crystal SM during the pulling.
Therefore, the estimation device 4 can accurately estimate the crystal temperature distribution of the silicon single crystal SM in accordance with the aging deterioration 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.

(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 speed of the silicon single crystal SM.
Therefore, the estimation device 4 can accurately estimate the thermal history of the silicon single crystal SM in accordance with the aging degradation of the furnace 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.

(3) The estimation device 4 estimates the density of BMDs that can precipitate on 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 speed.
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 while the silicon single crystal SM is being pulled, 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 time remains unchanged, 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.

(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.

(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 positions input to the regression model include a second measurement position Q2 on the heat shield support section 214, whose temperature is regulated by the top chamber 212.
In this way, 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.

(6) The furnace member 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. The temperature measurement position input to the regression model includes 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.

(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 positions input to the regression model include a first measurement position 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.

[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.

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.

The estimation device 6 is computer-based and estimates the crystal temperature distribution of the silicon single crystal SM being pulled in the silicon single crystal manufacturing apparatus 2. The estimation device 6 also estimates the thermal stress of the silicon single crystal SM based on the estimated crystal temperature distribution. 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 BMDs are 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 BMDs are unlikely to occur when BMD precipitation heat treatment is applied.

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

The memory unit 56A is composed of a well-known storage device similar to that of 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.

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.

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.

The thermal stress estimation unit 61 estimates the thermal stress near the solid-liquid interface between the silicon single crystal (SM) and the molten silicon (MD) based on the crystal temperature distribution estimated by the crystal temperature distribution estimation unit 43.

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. For this defect distribution estimation, the defect distribution estimation unit 62 can, for example, use the method described in Japanese Patent Application Publication No. 2021-70593.

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, for example, use the method described in Japanese Patent Application Publication No. 2021-70593.

<Operation of the silicon single crystal manufacturing system>
Next, as an 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.

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 furnace 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.

Next, the machine learning unit 42 uses the training data to construct a regression model in which the input is the temperature 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).

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. This estimates 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.

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 result 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.

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.

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.

<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.

(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 crystal SMs during the pulling process 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.

(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.

[Variations]
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.

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.

In at least one of the first and second embodiments, the silicon single crystal whose crystal temperature distribution is to be estimated may be pulled from a silicon melt that is not doped with nitrogen. In the first embodiment, when pulling a silicon single crystal 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. Furthermore, in this case, it becomes unnecessary to provide a nitrogen concentration calculation unit 53 in the silicon single crystal manufacturing apparatus 2.

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 location input to the regression model may be a location other than the first to third measurement locations Q1 to Q3, and may be on or near a furnace member where no thermal properties are set in the heat transfer simulation.

In the first embodiment, the processes from step S5 (estimated crystal temperature distribution) onwards, or from step S6 (estimated thermal history) onwards, or the process in step S10 (estimated BMD density) may be performed after the silicon single crystal SM to be estimated for crystal temperature distribution is 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 silicon single crystal SM to be estimated of the crystal temperature distribution.

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

[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: 315 mm
Nitrogen concentration: 1.2 × ^10¹⁸ / ^cm³
Oxygen concentration: 3.2 × ^10¹² / ^cm³

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 a 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 body section SM2 (hereinafter sometimes referred to as "estimated BMD density").
The results are shown in Figure 6.

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.

[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 pulling process was performed on three silicon single crystal SMs, 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: 315 mm
Nitrogen concentration: 1.2 × ^10¹⁸ / ^cm³
Oxygen concentration: 3.2 × ^10¹² / ^cm³

Three silicon single crystals (SMs) were cut along the pulling direction, subjected to 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 crystals (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.

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 of critical v/G for each silicon single crystal SM (hereinafter sometimes referred to as "estimated critical v/G"), the values obtained by multiplying the measured critical v/G and the estimated critical v/G by the temperature gradient G estimated based on the crystal temperature distribution were compared.

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.

20…Pulling furnace, 212…Top chamber (cooling furnace component), 25…Heat shield (temperature rise suppression furnace component), 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 (16)

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. 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. 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. 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. 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. 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. 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. 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 the interior 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. 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. An estimation device for making estimations regarding silicon single crystals grown by the Czochralski method in a pull-up furnace,
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. 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. 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. 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. 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. 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 becomes the silicon melting point. An estimation program that causes a computer to function as an estimation device according to any one of claims 10 to 15.