BMD density estimation method, BMD density estimation device, and BMD density estimation program

Abstract

To provide an estimation method capable of accurately estimating a bulk micro defect (BMD) density of a silicon single crystal according to long-term deterioration of a furnace member.SOLUTION: In a bulk micro defect (BMD) density estimation method, heat transmission simulation is performed on the basis of a simulation model simulating a drawing furnace regarding plural calculation conditions, in which a thermophysical property value of a furnace member is arbitrarily set, so as to create calculation results of temperature distribution in the drawing furnace respectively found from plural calculation conditions as training data, and construct a regression model, in which inputs are used as temperature at a predetermined measuring position in the drawing furnace, an oxygen concentration of a silicon single crystal and a BMD precipitation heat treatment condition, and outputs are used a BMD density of the silicon single crystal. The temperature measuring results at a predetermined measuring position found during drawing the silicon single crystal, the oxygen concentration of the silicon single crystal and the BMD precipitation heat treatment are inputted to the regression model, so as to estimate the BMD density of the silicon single crystal being drawn.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to a BMD density estimation method, a BMD density estimation apparatus, and a BMD density estimation program.

Background Art

[0002] In the process of manufacturing a silicon single crystal by the Chochralski (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 the advantage of acting as a gettering source that captures heavy metal impurities mixed in a silicon wafer and deteriorates device performance, it also has the 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

Patent Documents

[0004]

Patent Document 1

Non-Patent Documents

[0005]

Non-Patent Document 1

Summary of the Invention

[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 a BMD density estimation method, a BMD density estimation device, and a BMD density estimation program that can accurately estimate the BMD density of silicon single crystals in accordance with the aging degradation of furnace components. [Means for solving the problem]

[0009] The present invention provides a BMD density estimation method for estimating the BMD density of a silicon single crystal grown by the Czochralski method in a pulling furnace, comprising 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 inputs being the temperature at a predetermined measurement location in the pulling furnace, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions, and outputting the BMD density of the silicon single crystal; and inputting the temperature measurement results at the predetermined measurement location, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions obtained during the pulling of the silicon single crystal into the regression model to estimate the BMD density of the silicon single crystal during the pulling.

[0010] In the BMD density estimation method of the present invention, it is preferable that in the step of constructing the regression model, the inputs are the temperature at a predetermined measurement position in the pulling furnace, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions, and in the step of estimating the BMD density of the silicon single crystal, the temperature measurement results at the predetermined measurement position obtained during the pulling of the silicon single crystal, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions are input to the regression model to estimate the BMD density.

[0011] In the BMD density estimation method of the present invention, in the step of constructing a simulation model that simulates the extraction 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.

[0012] In the BMD density 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.

[0013] In the BMD density 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 surface of the silicon single crystal after it has passed through the cooler.

[0014] In the BMD density 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.

[0015] The present invention provides a BMD density estimation device for estimating the BMD density of a silicon single crystal grown by the Czochralski method in a pulling furnace, comprising: a training data generation unit that constructs a simulation model that simulates the pulling furnace, performs a heat transfer simulation based on the simulation model under 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 for 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 inputs being the temperature at a predetermined measurement position inside the pulling furnace, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions, and outputting the BMD density of the silicon single crystal; and a BMD density estimation unit that inputs the temperature measurement results at the predetermined measurement position, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions obtained during the pulling of the silicon single crystal to the regression model and estimates the BMD density of the silicon single crystal during the pulling.

[0016] In the BMD density estimation device of the present invention, the machine learning unit constructs a regression model in which the output is the BMD density of the silicon single crystal based on the temperature at a predetermined measurement position in the pulling furnace, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD precipitation heat treatment conditions. The BMD density estimation unit inputs the temperature measurement result at the predetermined measurement position obtained during the pulling of the silicon single crystal, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD precipitation heat treatment conditions into the regression model to estimate the BMD density, which is preferable.

[0017] The BMD density estimation program of the present invention causes a computer to function as the above-described BMD density estimation device.

Brief Description of Drawings

[0018] [Figure 1] It is a schematic diagram showing a schematic configuration of a silicon single crystal manufacturing system in an embodiment. [Figure 2] It is a block diagram of a BMD density estimation device in an embodiment. [Figure 3] It is a flowchart showing an estimation process of BMD density in an embodiment. [Figure 4] It is a graph showing the correlation between the measured BMD density and the estimated BMD density in an example.

Embodiments for Carrying Out the Invention

[0019] [Embodiment] <Configuration of Silicon Single Crystal Manufacturing System> First, the configuration of the silicon single crystal manufacturing system in the embodiment of the present invention will be described. FIG. 1 is a schematic diagram showing a schematic configuration of a silicon single crystal manufacturing system in an embodiment. FIG. 2 is a block diagram of a BMD density estimation device in an embodiment.

[0020] The silicon single crystal manufacturing system 1 shown in FIG. 1 includes a silicon single crystal manufacturing device 2, a temperature measurement unit 3, and a BMD density estimation device 4.

[0021] 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).

[0022] 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.

[0023] 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.

[0024] 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.

[0025] 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.

[0026] 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.

[0027] 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.

[0028] 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).

[0029] 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.

[0030] 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.

[0031] 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.

[0032] 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.

[0033] 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.

[0034] 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.

[0035] 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.

[0036] 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).

[0037] 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.

[0038] 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.

[0039] 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.

[0040] 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.

[0041] 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 BMD density estimation device 4.

[0042] 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 or other factors, 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.

[0043] 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.

[0044] 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 embodiment, the second measurement position Q2 is positioned on the heat shield support portion 214.

[0045] The second measurement unit 32 measures the temperature of the region including the third measurement position Q3 through the second viewing window 213B formed in the pull chamber 213, and outputs the measurement result to the BMD density estimation device 4.

[0046] 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 higher temperature than before the performance change. As a result, the temperature at the third measurement position Q3 becomes different from that before the performance change of the cooler 26 in the pull chamber 213. 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.

[0047] 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 embodiment, the third measurement position Q3 is positioned on the outer surface of the silicon single crystal SM inside the pull chamber 213.

[0048] The BMD density estimation device 4 is computer-based and estimates the BMD density of silicon single crystals (SMs) being pulled up by the silicon single crystal manufacturing device 2. As shown in Figure 2, the BMD density 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.

[0049] 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 BMD density estimation device 4.

[0050] The output unit 52 displays or outputs various information based on the control of the BMD density estimation device 4.

[0051] 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 estimation result to the BMD density estimation device 4.

[0052] 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 BMD density estimation device 4.

[0053] 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 to the BMD density estimation device 4.

[0054] 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 BMD density estimation program P1 and various information necessary for estimating the BMD density.

[0055] The BMD density estimation program P1 is a program that makes the computer function as a BMD density estimation device 4. The BMD density estimation program P1 can be distributed, for example, through the sale, transfer, or rental of portable recording media such as Blu-ray®, DVD, and CD-ROM. Furthermore, the BMD density estimation 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.

[0056] The BMD density estimation program P1 stored in the memory unit 56 may be read by the computer from a portable recording medium or obtained from a server on a network. Alternatively, the BMD density estimation program P1 may not be stored in the memory unit 56, and the computer may sequentially obtain and execute the BMD density estimation program P1 from the server. Furthermore, the BMD density estimation program P1 may be stored in a separate memory unit provided within the computer.

[0057] The BMD density estimation device 4 is equipped with a CPU (Central Processing Unit). The BMD density estimation device 4 functions as a training data generation unit 41, a machine learning unit 42, and a BMD density estimation unit 43 by having the CPU execute the BMD density estimation program P1 stored in the memory unit 56.

[0058] 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).

[0059] The machine learning unit 42 constructs a regression model based on the training data generated by the training data generation unit 41. The inputs of the machine learning unit 42 are the temperatures of the first, second, and third measurement positions Q1, Q2, and Q3 in the lifting furnace 20, the oxygen and nitrogen concentrations of the silicon single crystal SM, and the BMD deposition heat treatment conditions. The output is the BMD density of the silicon single crystal SM. Examples of machine learning methods include neural networks and genetic algorithms, but the machine learning unit 42 is not particularly limited and well-known methods (such as support vector machines or sparse models) can be used.

[0060] The BMD density 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, the nitrogen and oxygen concentrations of the silicon single crystal SM, and the BMD deposition heat treatment conditions into a regression model constructed by the machine learning unit 42 to estimate the BMD density that can be deposited in the silicon single crystal SM.

[0061] <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 embodiment.

[0062] First, as shown in Figure 3, the training data generation unit 41 of the BMD density 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.

[0063] 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.

[0064] Next, the machine learning unit 42 uses the training data to construct a regression model in which the inputs are the temperatures of the first, second, and third measurement positions Q1, Q2, and Q3, the oxygen and nitrogen concentrations of the silicon single crystal SM, and the BMD deposition heat treatment conditions, and the output is the BMD density of the silicon single crystal SM (step S3). Then, the machine learning unit 42 outputs the constructed regression model to the BMD density estimation unit 43.

[0065] 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 BMD density 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.

[0066] Furthermore, the nitrogen concentration calculation unit 53 calculates the nitrogen concentration of the silicon single crystal SM and outputs the calculation result to the BMD density estimation device 4 (step S5). The oxygen concentration calculation unit 54 calculates the oxygen concentration of the silicon single crystal SM and outputs the calculation result to the BMD density estimation device 4 (step S6). The BMD precipitation heat treatment condition setting unit 55 sets the BMD precipitation heat treatment conditions and outputs the setting details to the BMD density estimation device 4 (step S7). Furthermore, the processes in steps S5 to S7 can be performed in any order and at any time.

[0067] Then, the BMD density estimation unit 43 estimates the BMD density 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, the nitrogen concentration, the oxygen concentration, and the BMD deposition heat treatment conditions into a regression model obtained from the machine learning unit 42 (step S8). In this case, it is preferable for the BMD density estimation unit 43 to estimate the BMD density for each part with a different thermal history. The BMD density estimation unit 43 may display or output the estimated BMD density result to the output unit 52. The BMD density estimation unit 43 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.

[0068] <Effects of the Embodiment> The BMD density estimation device 4 of this embodiment can achieve at least the following effects. (1) The BMD density estimation device 4 performs heat transfer simulations under multiple calculation conditions in which the thermophysical properties of the furnace members constituting the lifting furnace 20 are arbitrarily set, and generates training data from the calculation results of the furnace temperature distribution obtained from each calculation condition. Next, based on the training data, the BMD density estimation device 4 generates a regression model using machine learning, with the inputs being the temperatures of the first, second, and third measurement positions Q1, Q2, and Q3 inside the lifting furnace 20, the oxygen and nitrogen concentrations of the silicon single crystal SM, and the BMD deposition heat treatment conditions, and the output being the BMD density of the silicon single crystal SM. Then, the BMD density estimation device 4 inputs the temperature measurement results of the first, second, and third measurement positions Q1, Q2, and Q3 obtained during the lifting of the silicon single crystal SM, the oxygen and nitrogen concentrations of the silicon single crystal SM, and the BMD deposition heat treatment conditions into the regression model to estimate the BMD density of the silicon single crystal SM during the lifting. Therefore, the BMD density estimation device 4 can accurately estimate the BMD density of silicon single crystals 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 crystals SM near the molten MD during pulling, which has poor measurement 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, it is possible to start early on modifying the pulling conditions to keep the BMD density of the entire silicon single crystal SM to be pulled in the next batch nearly constant, or to prepare for the replacement of aged furnace components. Examples of modifications to the pulling conditions include changing the rotation speed of the crucible 22 or changing the power of the heater 23. Furthermore, by taking nitrogen concentration into account in addition to oxygen concentration, the BMD density of silicon single crystal SM can be estimated with greater accuracy, even for nitrogen-doped crystals.

[0069] (2) 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 the BMD density of silicon single crystal SM can be improved.

[0070] (3) 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 BMD density estimation device 4 can estimate the BMD density of silicon single crystal SM with greater accuracy.

[0071] (4) 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. 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 BMD density estimation device 4 can estimate the BMD density of silicon single crystal SM with greater accuracy.

[0072] (5) In the heat transfer simulation, the furnace components for which thermal properties are set 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 BMD density estimation device 4 can estimate the BMD density of silicon single crystal SM with greater accuracy.

[0073] [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.

[0074] The silicon single crystal to be used for BMD density estimation may be pulled from a silicon melt that is not doped with nitrogen. When pulling a silicon single crystal from a silicon melt that is not doped with nitrogen, the machine learning unit 42 and the BMD density estimation unit 43 should 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.

[0075] 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.

[0076] The processes from step S5 (estimation of nitrogen concentration) onward, or the process in step S8 (estimation of BMD density), may be performed after the pulling of the silicon single crystal SM for which the BMD density is to be estimated. [Examples]

[0077] Next, embodiments of the present invention will be described. However, the present invention is not limited to these embodiments.

[0078] The silicon single crystal manufacturing system 1 of the 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 according to the 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

[0079] 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 4.

[0080] As shown in Figure 4, 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 embodiment of the present invention. [Explanation of Symbols]

[0081] 20... Pulling furnace, 212... Top chamber (cooling furnace component), 25... Heat shield (furnace component for suppressing temperature rise), 26... Cooler (cooling furnace component), 4... BMD density estimation device, 41... Training data generation unit, 42... Machine learning unit, 43... BMD density estimation unit, P1... BMD density estimation program, SM... Silicon single crystal.

Claims

1. A method for estimating the BMD density of silicon single crystals grown by the Czochralski method in a pull-up furnace, 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, with inputs being the temperature at a predetermined measurement location in the pulling furnace, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions, and output being the BMD density of the silicon single crystal. A method for estimating BMD density, comprising the steps of inputting the temperature measurement results at a predetermined measurement position obtained during the pulling of a silicon single crystal, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions into the regression model to estimate the BMD density of the silicon single crystal during the pulling process.

2. In the BMD density estimation method according to claim 1, In the step of constructing the regression model, the inputs are the temperature at a predetermined measurement location in the pulling furnace, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions. A method for estimating BMD density, comprising the step of estimating the BMD density of the silicon single crystal, inputting the temperature measurement results at a predetermined measurement position obtained during the pulling of the silicon single crystal, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions into the regression model to estimate the BMD density.

3. In the BMD density estimation method according to claim 1, A BMD density estimation method comprising the step of constructing a simulation model that simulates the aforementioned lifting furnace, wherein the simulation model is constructed such that the temperature at the boundary between the silicon melt and the silicon crystal is the silicon melting point.

4. In the BMD density estimation method according to claim 1, 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. A BMD density estimation method wherein the predetermined measurement position includes a position where the temperature is adjusted by the cooling furnace member.

5. In the BMD density estimation method according to claim 4, The cooling furnace member includes a cylindrical cooler that cools the silicon single crystal as it passes through the interior during the pulling process. A BMD density estimation method wherein the predetermined measurement position includes the outer surface of the silicon single crystal after passing through the coolant.

6. In the BMD density estimation method according to claim 1, 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, A BMD density estimation method wherein the predetermined measurement position includes a position on the temperature rise suppression furnace member.

7. A BMD density estimation device for estimating the BMD density of 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 a heat transfer simulation based on the simulation model under 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, with inputs being the temperature at a predetermined measurement location in the lifting furnace, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions, and outputting the BMD density of the silicon single crystal. A BMD density estimation device comprising: a BMD density estimation unit that inputs the temperature measurement results at a predetermined measurement position obtained during the pulling of a silicon single crystal, the oxygen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions into the regression model to estimate the BMD density of the silicon single crystal during the pulling process.

8. In the BMD density estimation device according to claim 7, The machine learning unit constructs a regression model that takes the temperature at a predetermined measurement location in the pulling furnace, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions as inputs, and outputs the BMD density of the silicon single crystal. The BMD density estimation device is a BMD density estimation device that estimates the BMD density by inputting the temperature measurement results at a predetermined measurement position obtained during the pulling of the silicon single crystal, the oxygen concentration and nitrogen concentration of the silicon single crystal, and the BMD deposition heat treatment conditions into the regression model.

9. A BMD density estimation program that causes a computer to function as a BMD density estimation device according to claim 7 or claim 8.

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