Oxygen concentration prediction system and oxygen concentration control system

Abstract

To improve the accuracy of controlling the oxygen concentration in a silicon ingot.SOLUTION: An oxygen concentration prediction system includes: manufacturing performance data composed of a set of a control parameter group that can be manipulated during crystal growth, a fixed-parameter group of which values are known before crystal growth begins, and a measured oxygen concentration measured on an evaluation sample from a specified portion of a silicon ingot; a prediction model that receives input of a control parameter group and a fixed-parameter group and outputs an oxygen concentration of a target silicon ingot; and a controller that inputs the control parameter group of the target silicon ingot and the fixed-parameter group into the prediction model to obtain a first oxygen concentration, calculates a correction value using a measured oxygen concentration of a reference ingot having characteristics similar to the target silicon ingot among the production performance data and the first oxygen concentration, and sets a second oxygen concentration obtained by correcting the first oxygen concentration with the correction value as a predicted value of the oxygen concentration of the target silicon ingot.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to an oxygen concentration prediction system and an oxygen concentration control system.

Background Art

[0002] The Czochralski method (hereinafter referred to as the CZ method) is a typical method for manufacturing a silicon single crystal (so-called silicon ingot) for semiconductor devices. In the growth of a silicon ingot by this CZ method, oxygen inevitably dissolves into the silicon melt from the quartz crucible, and as a result, oxygen is mixed into the silicon ingot. Oxygen in the silicon ingot affects device characteristics when oxygen precipitates are formed by a heat treatment process or the like during semiconductor device manufacturing, so various requirement specifications for oxygen concentration exist among each device manufacturer.

[0003] However, accurately predicting the oxygen concentration in a silicon ingot over the entire length of the ingot and freely controlling it is still a very difficult technique at present. In the growth of a silicon ingot by the CZ method, oxygen is dissolved from the contact interface between the quartz crucible and the silicon melt, and the dissolved oxygen is transported in the melt according to the behavior of the heat convection (natural convection, forced convection) of the silicon melt. In recent large-diameter silicon ingots, a pulling method in which a magnetic field is applied to the melt to precisely control the melt convection is the mainstream, and it is known that the behavior of oxygen in the melt is greatly affected by the type of magnetic field, the magnetic field strength, the amount of remaining melt, and the like.

[0004] On the free surface, the evaporation of oxygen from the melt occurs very actively, and it has also been found that the oxygen concentration in the melt (especially near the free surface) is greatly affected by the flow rate condition of argon (Ar) gas on the free surface. That is to say, the oxygen concentration incorporated into the crystal is determined by the complex interaction of many factors, such as the dissolution from the quartz crucible into the melt, the transport in the melt by convection, and the evaporation from the free surface. Also, in the actual manufacturing site, manufacturing variations occur due to various factors such as the change over time of the used members, the variation in the furnace internal environment caused by the setting variation of the furnace internal members between lots, the variation between members, the machine differences between devices, and the adjustment variation by the operator. Even if grown under the same operating conditions for each lot, it is not always possible to obtain silicon ingots with the same profile of oxygen concentration at present.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0006] By the way, the oxygen concentration in the silicon ingot is measured by the following procedure.

[0007] (1) After the single crystal pulling is completed, an evaluation sample is cut from a specified part of the single crystal ingot. (2) The evaluation sample is polished, etched, and cleaned. (3) The evaluation sample is measured by Fourier transform infrared spectroscopy (FT-IR).

[0008] Thus, there is a time lag from the completion of pulling a silicon ingot to the measurement of the oxygen concentration. This means that it takes time to reflect the actually measured oxygen concentration in the control of subsequent manufacturing processes of the silicon ingot. Naturally, this time lag will also have a great impact on the control accuracy of the oxygen concentration. Also, even if an evaluation sample is taken from a specified site, oxygen in samples from other sites, etc., is not measured, so the oxygen concentration cannot be known over the entire length of the silicon ingot.

[0009] Therefore, instead of directly measuring the oxygen concentration by obtaining a sample from the silicon ingot, various methods for predicting the oxygen concentration from manufacturing conditions have been proposed (see, for example, Patent Documents 1 to 3). However, as described above, the factors affecting the oxygen concentration in the silicon ingot are diverse, and it is still not easy to predict the oxygen concentration with sufficiently high accuracy. In particular, it is difficult to use monitor parameters reflecting the in-furnace situation during crystal growth for predicting the oxygen concentration of a silicon ingot to be manufactured now, which makes it difficult to determine a group of control parameters for the silicon ingot to be manufactured now.

[0010] An object of the present invention is to provide an oxygen concentration prediction system and an oxygen concentration control system that improve the control accuracy of the oxygen concentration of a silicon ingot.

Means for Solving the Problems

[0011] In order to solve the above problems, an oxygen concentration prediction system according to one aspect of the present invention is an oxygen concentration prediction system for predicting the oxygen concentration of a target silicon ingot, which includes a control parameter group that can be operated during crystal growth, a fixed parameter group whose values are known before the start of crystal growth, a monitor parameter group that reflects the furnace internal situation during crystal growth, and production result data composed of a set of a measured oxygen concentration measured by an evaluation sample from a specified part of the silicon ingot, a prediction model that inputs the control parameter group and the fixed parameter group and outputs the oxygen concentration of the target silicon ingot, and inputs the control parameter group and the fixed parameter group of the target silicon ingot into the prediction model to obtain a first oxygen concentration, calculates a correction value using the measured oxygen concentration of a reference ingot having characteristics similar to those of the target silicon ingot from among the production result data and the first oxygen concentration, and a controller that uses the correction value to correct the first oxygen concentration and uses the obtained second oxygen concentration as the predicted value of the oxygen concentration of the target silicon ingot.

[0012] Thus, when predicting the oxygen concentration of a target silicon ingot, the oxygen concentration prediction system according to one aspect of the present invention does not use a monitor parameter group that reflects the furnace internal situation during crystal growth, but calculates a correction value using the measured oxygen concentration of a reference ingot having characteristics similar to those of the target silicon ingot, and corrects the first oxygen concentration, which is the output of the prediction model, using this correction value, thereby improving the prediction accuracy of the oxygen concentration of the target silicon ingot.

[0013] Further, an oxygen concentration prediction system according to an aspect of the present invention is an oxygen concentration prediction system that predicts the oxygen concentration of a target silicon ingot, and includes a control parameter group that can be operated during crystal growth, a fixed parameter group whose values are known before the start of crystal growth, a monitor parameter group that reflects the furnace internal situation during crystal growth, production result data composed of a set of the measured oxygen concentration measured by an evaluation sample from a specified part of the silicon ingot, a prediction model that inputs the control parameter group and the fixed parameter group and outputs the oxygen concentration of the target silicon ingot, a controller that inputs the control parameter group and the fixed parameter group of the target silicon ingot into the prediction model to obtain a first oxygen concentration, inputs the control parameter group and the fixed parameter group of a reference ingot having characteristics similar to those of the target silicon ingot from among the production result data into the prediction model to obtain a third oxygen concentration, calculates a correction value using the measured oxygen concentration and the third oxygen concentration of the reference ingot, and uses the correction value to correct the first oxygen concentration to obtain a second oxygen concentration as the predicted value of the oxygen concentration of the target silicon ingot.

[0014] Thus, when calculating a correction value for correcting the first oxygen concentration, the oxygen concentration prediction system according to an aspect of the present invention inputs the control parameter group and the fixed parameter group of a reference ingot having characteristics similar to those of the target silicon ingot into the prediction model to obtain a third oxygen concentration, and calculates the correction value using the measured oxygen concentration and the third oxygen concentration of the reference ingot, thereby further improving the prediction accuracy of the oxygen concentration of the target silicon ingot.

[0015] Further, the controller in the oxygen concentration prediction system according to an aspect of the present invention calculates the correction value based on the formula correction value = amplitude C * wavelength λ + error Δ, and calculates the optimal solution after setting the lower limit of the wavelength to a range of 0.3 or more of the crystal length. Thus, the oxygen concentration prediction system according to an aspect of the present invention solves the problem by increasing the wavelength and fitting it gently, and improves the prediction accuracy of the oxygen concentration.

[0016] In addition, the correction value in the oxygen concentration prediction system according to one aspect of the present invention is preferably calculated by Gaussian process regression and is calculated based on data of crystal length, crystal radius, and oxygen concentration. Further, the kernel of the Gaussian process regression in the oxygen concentration prediction system according to one aspect of the present invention is preferably ConstantKernel * RBF + WhiteKernel.

[0017] Furthermore, an oxygen concentration control system according to one aspect of the present invention includes the oxygen concentration prediction system described above and a single crystal pulling apparatus that controls the control parameter group so that the oxygen concentration of the target silicon ingot predicted by the oxygen concentration prediction system is within a predetermined range.

[0018] Since the oxygen concentration prediction system described above does not use a monitor parameter group that reflects the furnace internal situation during crystal growth when predicting the oxygen concentration of the target silicon ingot, the oxygen concentration of the target silicon ingot can be made within a predetermined range by adjusting the control parameter group.

Effects of the Invention

[0019] According to the present invention, it is possible to provide an oxygen concentration prediction system and an oxygen concentration control system that improve the control accuracy of the oxygen concentration of a silicon ingot.

Brief Description of the Drawings

[0020]

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[0021] Hereinafter, embodiments of the present invention will be described with reference to the drawings. However, the present invention is not limited by the embodiments described below. In each drawing, the same or corresponding elements are appropriately denoted by the same reference numerals. Further, it should be noted that the drawings are schematic, and the dimensional relationships and ratios of the respective elements may be different from the actual ones. There may also be portions where the dimensional relationships and ratios are different between the drawings.

[0022] 〔Oxygen Concentration Control System〕 FIG. 1 is a diagram showing a schematic configuration of an oxygen concentration control system according to an embodiment of the present invention. As shown in the figure, the oxygen concentration control system 100 includes an oxygen concentration prediction system 10 and a single crystal pulling apparatus 20.

[0023] The single crystal pulling apparatus 20 is an apparatus for manufacturing a silicon ingot S using the CZ method. The single crystal pulling apparatus 20 includes a chamber furnace 21, a heater 22, a crucible 23, and a motor 24. The single crystal pulling apparatus 20 manufactures a silicon ingot S made of a single crystal of silicon by pulling up the silicon melt in the crucible 23 with the motor 24 while crystallizing it. As described above, in recent large-diameter silicon ingots, it is common to apply a magnetic field to the melt in order to precisely control the convection of the melt.

[0024] The single-crystal pulling apparatus 20 is provided with various sensors, and for each production of each silicon ingot S, production result data D is acquired. The production result data D is roughly divided into three types of parameter groups: a control parameter group, a fixed parameter group, and a monitor parameter group. Further, the production result data D includes measured values of the oxygen concentration in the silicon ingot S produced with the three types of parameter groups. Note that the measured value of the oxygen concentration is measured with an evaluation sample from a specified site of the silicon ingot.

[0025] The control parameter group is a parameter group that can be operated during crystal growth, and includes, for example, crucible rotation speed, magnetic field strength, and furnace internal pressure. The fixed parameter group is a parameter group whose values are known before the start of crystal growth, and includes, for example, the number of times the heater is used, the number of times the crucible is used, and the wall thickness of the quartz crucible. The monitor parameter group is a parameter group that reflects the furnace internal situation during crystal growth, and includes, for example, crystal diameter, the shape of the crown part, melt temperature, total energization time, integrated power consumption, and temperature measurement values at various locations in the furnace.

[0026] On the other hand, the oxygen concentration prediction system 10 is a system that inputs a control parameter group and a fixed parameter group for a target silicon ingot and predicts the oxygen concentration of the target silicon ingot to be produced.

[0027] The oxygen concentration prediction system 10 refers to the production result data D in order to predict the oxygen concentration of the target silicon ingot S. The data referred to in order to predict the oxygen concentration of the target silicon ingot S is the production result data of a silicon ingot (reference ingot) having characteristics and production conditions similar to those of the target silicon ingot. Note that the reference data includes a control parameter group that can be operated during crystal growth, a fixed parameter group whose values are known before the start of crystal growth, and a monitor parameter group that is a value reflecting the furnace internal situation during crystal growth.

[0028] In addition, the oxygen concentration prediction system 10 includes a neural network, and the neural network is trained using the production result data D. The methods of prediction and learning in the oxygen concentration prediction system 10 will be described in detail later.

[0029] The oxygen concentration control system 100 including the oxygen concentration prediction system 10 and the single crystal pulling apparatus 20 as described above controls the control parameter group so that the oxygen concentration of the target silicon ingot S predicted by the oxygen concentration prediction system 10 is within a predetermined range. That is, when the oxygen concentration of the target silicon ingot S predicted by the oxygen concentration prediction system 10 is within the predetermined range, the target silicon ingot S is manufactured using the control parameter group input to the oxygen concentration prediction system 10. On the other hand, when the oxygen concentration of the target silicon ingot S to be predicted is outside the predetermined range, the control parameter group is adjusted, and the oxygen concentration is predicted again using the adjusted control parameter group. Then, the adjustment of the control parameter group is repeated until the oxygen concentration of the target silicon ingot S to be predicted is within the predetermined range.

[0030] As described above, the oxygen concentration control system 100 includes the oxygen concentration prediction system 10 and the single crystal pulling apparatus 20, and controls the control parameter group so that the oxygen concentration of the target silicon ingot S predicted by the oxygen concentration prediction system 10 is within a predetermined range, thereby improving the control accuracy of the oxygen concentration of the target silicon ingot S. Conventionally, it has been difficult to use the monitor parameter group reflecting the furnace internal situation during crystal growth for predicting the oxygen concentration of the target silicon ingot S. However, the oxygen concentration control system 100 of Patent Document 3 adjusts the control parameter group that can be operated during crystal growth by referring to the monitor parameter group of the reference data, and controls so that the oxygen concentration of the target silicon ingot S is within a predetermined range. On the other hand, in the present invention, since the reference data for which oxygen has already been measured is used to correct the predicted value of the oxygen concentration of the target silicon ingot S based on the measured value, there is no need to consider the monitor parameter.

[0031] 〔Oxygen Concentration Prediction System According to the First Embodiment〕 The oxygen concentration prediction system according to the first embodiment is configured by an artificial intelligence technology including a neural network. FIG. 2 is a diagram showing a schematic configuration of the neural network in the prediction model.

[0032] As shown in FIG. 2, the neural network 11 in the prediction model inputs a control parameter group and a fixed parameter group, and outputs the oxygen concentration of the silicon ingot. Note that the neural network 11 shown in FIG. 2 is illustrated as having two nodes in the input layer, but the control parameter group and the fixed parameter group each include a plurality of parameters, and the number of nodes in the input layer has a number corresponding to the input of these plurality of parameters. Also, the configuration of the nodes in the intermediate layer is described by omitting it for convenience and does not show the actual configuration of the nodes.

[0033] (Learning phase) As shown in FIG. 3, the prediction model uses, as teacher data T1, two parameter groups, namely, the control parameter group and the fixed parameter group in the production result data, and the oxygen concentration of the silicon ingot manufactured using these two parameter groups, for learning.

[0034] For example, when learning using the production result data with ingot ID X, the control parameter group: a and the fixed parameter group: b are input to the input layer of the neural network 11 in the prediction model, and the difference between the value output from the output layer and the oxygen concentration: d is evaluated. Such evaluation is performed for all of the teacher data T1 recorded in the production result data. Optimization is performed so that the difference between the value output from the output layer and the oxygen concentration: d becomes minimum.

[0035] (Prediction phase) FIG. 4 is a diagram for explaining the prediction method in the oxygen concentration prediction system according to the first embodiment. The oxygen concentration prediction system according to the first embodiment includes the prediction model (neural network 11) learned as described above.

[0036] As shown in FIG. 4, in the prediction phase, the oxygen concentration prediction system according to the first embodiment inputs a control parameter group and a fixed parameter group of the lifted silicon ingot into a prediction model (neural network 11) to obtain a first oxygen concentration, and calculates a correction value using Gaussian process regression using the difference between the measured oxygen concentration of the production record data of the lifted silicon ingot and the first oxygen concentration. Next, the first oxygen concentration prediction value is corrected by the correction value, and the corrected second oxygen concentration prediction value is used as the prediction value of the oxygen concentration of the entire crystal length of the silicon ingot. Thereby, for a silicon ingot in which the oxygen concentration has been measured at only a few points, it is possible to accurately predict over the entire crystal length.

[0037] A method for calculating the correction value using Gaussian process regression will be described. Gaussian process regression is a technique of machine learning and is used to predict the output at any point in the input space. The Gaussian process is based on the assumption that the outputs for all inputs follow a joint normal distribution, and its covariance (correlation of function values) is defined by a kernel function.

[0038] Here, the kernel used in the present invention is "ConstantKernel * RBF + WhiteKernel", which is a combination of a plurality of kernel functions.

[0039] ConstantKernel is a kernel that controls the overall scale. That is, it is possible to adjust the overall scale of the variance of the output.

[0040] RBF (Radial Basis Function) is a very common kernel and is used to calculate the "similarity" between two inputs. Specifically, it is calculated based on the Euclidean distance between two inputs. With this kernel, the model can learn a smooth non-linear relationship between the inputs.

[0041] WhiteKernel is a kernel that models the noise contained in the observation data. That is, it is a kernel for expressing the noise and errors existing in the data, and by this, the reliability of the prediction can be improved.

[0042] Figure 5 is a graph of the oxygen concentration in the crystal longitudinal direction. The points indicate the measured values, the dashed line is the first oxygen concentration predicted value, and the solid line is the second oxygen concentration predicted value obtained by correcting the first oxygen concentration predicted value. In this embodiment, a silicon ingot with a diameter of about 305 mm and a crystal length of 1900 mm pulled up by the Czochralski method (CZ method) is used. The following parameters were adjusted to obtain the desired oxygen concentration. Furnace pressure 120 Torr, argon gas flow rate in the furnace 60 L / min, single crystal pulling speed 0.6 mm / min. The measured values indicated by the points are the actual measurements of the oxygen concentration at the center in the plane after slicing the silicon ingot into wafers. Also, the first oxygen concentration predicted value shown by the dashed line is the output of the oxygen concentration by inputting the above parameters into the neural network 11. As can be seen from Figure 5, the second oxygen concentration predicted value is closer to the measured value.

[0043] Figure 6 is a graph of the crystal length direction and the oxygen concentration correction value. The filled points represent the difference between the measured value and the predicted value of the first oxygen concentration, which is the deviation between the measured value and the predicted value of the first oxygen concentration at the site where the measurement was taken, indicating the necessary correction value. The hollow points are the points at the ends of the head and tail of the crystal added computationally. The same value as the point closest to the crystal length is entered. This prevents the correction values at both ends of the crystal length, which is an extrapolation, from having extreme movements. The solid line is the result of fitting the necessary correction value at each point using Gaussian process regression. The value of this solid line becomes the correction value. This fitting changes depending on the kernel parameters. If the fitting is too strong, the points will be connected by a wavy line so that they all pass through. Extreme cases would be like interpolating the measurement points while ignoring the predicted values. On the other hand, if it is too weak, it will not be corrected well. Thus, the parameters used for fitting become important. When there is variation in adjacent measured values, the predicted value does not necessarily have to match the measured value, so it is treated as noise with WhiteKernel.

[0044] The following is an excerpt of Python code related to Gaussian process regression. This code uses the GaussianProcessRegressor in the machine learning library scikit-learn to create a regression model that predicts a one-dimensional output ("error") from two-dimensional inputs ("Length" and "Radius"). If the radius is not required, it is done only with Length.

[0045] First, import the necessary libraries and modules. # Machine learning library Gaussian process regression from sklearn.gaussian_process import GaussianProcessRegressor # Kernel from sklearn.gaussian_process.kernels import RBF from sklearn.gaussian_process.kernels import ConstantKernel from sklearn.gaussian_process.kernels import WhiteKernel Here, GaussianProcessRegressor is a class for performing regression analysis using the Gaussian process, and RBF, ConstantKernel, and WhiteKernel represent the kernel functions used in the Gaussian process, respectively.

[0046] Next, set the kernel. # Create a regression model # Set the kernel # C: Amplitude (initial value of constant_value, range of constant_value) # RBF: Wavelength (initial value of length_scale, range of length_scale) # Wh: Noise (initial value of noise_level, range of noise_level) kernel = ConstantKernel(1, (1e - 6, 0.1)) * RBF(3000, (1200, 1e6)) + WhiteKernel(1e - 5, (1e - 5, 1e - 2)) reg = GaussianProcessRegressor(kernel = kernel, n_restarts_optimizer = 30) In this example, the constant kernel (ConstantKernel), the RBF kernel (the one with the Radial Basis Function as the basis function), and the white kernel (WhiteKernel) are combined. These correspond to the adjustment of the amplitude (constant_value), the adjustment of the wavelength (length_scale), and the adjustment of the noise (noise_level), respectively. The parameters of each kernel are optimized by specifying a range.

[0047] When creating an instance of GaussianProcessRegressor, specify the kernel you created. Also, the optional n_restarts_optimizer specifies the number of restarts for optimization. This reduces the risk of getting stuck in a local optimum and can yield better results.

[0048] Next, use the fit method to train the model using the input data ("Length" and "Radius") and the target output ("error") extracted from the data frame df. # Fitting to the regression model reg.fit(df[["Length", "Radius"]],df[["error"]])

[0049] Finally, make new predictions using the trained model and add the results as a new column "Correction value" to the data frame df. Here, use "Length" and "Radius" as inputs and set return_std=False to output only the predicted values. # Outputting the correction value from the regression model df["Correction value"] =reg.predict(df[["Length","Radius"]],return_std=False)

[0050] Setting the parameter range of the kernel here is important. It must be set so that the correction value does not become a wave with a large amplitude, a wave with a fine wavelength, or pick up measurement variations. Here, if the lower limit of the wavelength (RBF) is in the range of 0.3 times or more of the crystal length, it is preferable because it can prevent the correction value from becoming a wave with a large amplitude. Furthermore, if the lower limit of the wavelength (RBF) is in the range of 0.5 to 0.7 times the crystal length, a more accurate correction value will result.

[0051] By correcting the predicted value of the oxygen concentration of the target silicon ingot using the correction value calculated as described above, the oxygen concentration prediction system 10 according to the first embodiment can improve the control accuracy of the oxygen concentration of the silicon ingot. Further, an oxygen concentration control system 100 including the oxygen concentration prediction system 10 according to the first embodiment and the single crystal pulling apparatus 20 can improve the control accuracy of the oxygen concentration of the target silicon ingot S by controlling the control parameter group so that the oxygen concentration of the target silicon ingot S predicted by the oxygen concentration prediction system 10 falls within a predetermined range.

[0052] 〔Oxygen Concentration Prediction System According to the Second Embodiment〕 The oxygen concentration prediction system according to the second embodiment is an oxygen concentration prediction system that predicts the oxygen concentration of a target silicon ingot. It uses the correction value calculated in the first embodiment to accurately predict the oxygen concentration of the target ingot during pulling.

[0053] The oxygen concentration prediction system according to the second embodiment is an oxygen concentration prediction system that predicts the oxygen concentration of a target silicon ingot, and includes a control parameter group that can be operated during crystal growth, a fixed parameter group whose values are known before the start of crystal growth, a monitor parameter group that reflects the furnace internal situation during crystal growth, production result data composed of a set of the measured oxygen concentration measured with an evaluation sample from a specified part of the silicon ingot, a prediction model that inputs the control parameter group and the fixed parameter group and outputs the oxygen concentration of the target silicon ingot. It inputs the control parameter group and the fixed parameter group of the target silicon ingot into the prediction model to obtain a first oxygen concentration, inputs the control parameter group and the fixed parameter group of a reference ingot having characteristics close to those of the target silicon ingot from among the production result data into the prediction model to obtain a third oxygen concentration, calculates a correction value using the measured oxygen concentration of the reference ingot and the third oxygen concentration, and uses the second oxygen concentration obtained by correcting the first oxygen concentration with the correction value as the predicted value of the oxygen concentration of the target silicon ingot.

[0054] FIG. 7 is a diagram for explaining a prediction method in the oxygen concentration prediction system according to the second embodiment. As shown in FIG. 7, in the prediction method in the oxygen concentration prediction system according to the second embodiment, a control parameter group and a fixed parameter group of a target silicon ingot are input to a prediction model (neural network 11) to obtain a first oxygen concentration. On the other hand, a control parameter group and a fixed parameter group of a reference ingot having characteristics similar to those of the target silicon ingot are input from the manufacturing result data to the prediction model (neural network 11) to obtain a third oxygen concentration. Then, a correction value is calculated using the measured oxygen concentration and the third oxygen concentration of the reference ingot. Further, the second oxygen concentration obtained by correcting the first oxygen concentration using this correction value is used as the predicted value of the oxygen concentration of the target silicon ingot.

[0055] In the prediction method in the oxygen concentration prediction system according to the second embodiment as well as in the prediction method in the oxygen concentration prediction system according to the first embodiment, the method for calculating the correction value can use Gaussian process regression. Also, the oxygen concentration control system 100 including the oxygen concentration prediction system 10 according to the second embodiment and the single crystal pulling apparatus 20 can improve the control accuracy of the oxygen concentration of the target silicon ingot S by controlling the control parameter group so that the oxygen concentration of the target silicon ingot S predicted by the oxygen concentration prediction system 10 is within a predetermined range.

[0056] As described above, the present invention has been described based on the embodiments, but the present invention is not limited to the above embodiments. For example, although the oxygen concentration prediction system 10 according to the embodiment of the present invention can improve the prediction accuracy of the oxygen concentration of the silicon ingot without using the monitor parameter group, it may be configured to further improve the prediction accuracy by using the monitor parameter group for either one or both of the first oxygen concentration predicted value and the third oxygen concentration predicted value.

Description of Reference Numerals

[0057] 100 Oxygen concentration control system 10 Oxygen concentration prediction system 11 Neural network 20 Single crystal pulling apparatus 21 Chamber furnace 22 Heater 23 Crucible 24 Motor S Silicon ingot D Manufacturing performance data T1 Teacher data

Claims

1. An oxygen concentration prediction system for predicting the oxygen concentration of a target silicon ingot, comprising: manufacturing performance data composed of a set of control parameter groups that can be operated during crystal growth, fixed parameter groups whose values are known before the start of crystal growth, and measured oxygen concentrations measured from an evaluation sample at a specified site of the silicon ingot; a prediction model that inputs at least the control parameter group and the fixed parameter group and outputs the oxygen concentration of the target silicon ingot; a controller that inputs at least the control parameter group and the fixed parameter group of the target silicon ingot into the prediction model to obtain a first oxygen concentration, calculates a correction value using the measured oxygen concentration of a reference ingot with characteristics similar to those of the target silicon ingot among the manufacturing performance data and the first oxygen concentration, and uses the second oxygen concentration obtained by correcting the first oxygen concentration with the correction value as the predicted value of the oxygen concentration of the target silicon ingot; An oxygen concentration prediction system characterized by comprising the above.

2. An oxygen concentration prediction system for predicting the oxygen concentration of a target silicon ingot, comprising: manufacturing performance data composed of a set of control parameter groups that can be operated during crystal growth, fixed parameter groups whose values are known before the start of crystal growth, monitor parameter groups that reflect the furnace conditions during crystal growth, and measured oxygen concentrations measured from an evaluation sample at a specified site of the silicon ingot; a prediction model that inputs at least the control parameter group and the fixed parameter group and outputs the oxygen concentration of the target silicon ingot; a controller that inputs at least the control parameter group and the fixed parameter group of the target silicon ingot into the prediction model to obtain a first oxygen concentration, inputs the control parameter group and the fixed parameter group of a reference ingot with characteristics similar to those of the target silicon ingot among the manufacturing performance data into the prediction model to obtain a third oxygen concentration, calculates a correction value using the measured oxygen concentration of the reference ingot and the third oxygen concentration, and uses the second oxygen concentration obtained by correcting the first oxygen concentration with the correction value as the predicted value of the oxygen concentration of the target silicon ingot; An oxygen concentration prediction system characterized by comprising the above.

3. The controller calculates the correction value based on the formula correction value = amplitude C * wavelength λ + error Δ, and calculates the optimal solution with the lower limit of the wavelength in the range of 0.3 or more of the crystal length. The oxygen concentration prediction system according to claim 1 or claim 2.

4. The correction value is calculated by Gaussian process regression and is calculated based on data of crystal length, crystal radius, and oxygen concentration. The oxygen concentration prediction system according to claim 1 or claim 2.

5. The kernel of the Gaussian process regression is ConstantKernel * RBF + WhiteKernel The oxygen concentration prediction system according to claim 3, characterized in that it is as follows.

6. An oxygen concentration prediction system for predicting the oxygen concentration of a pulled silicon ingot, Composed of a set of control parameter groups that can be operated during crystal growth, a set of fixed parameter groups whose values are known before the start of crystal growth, and production performance data measured by an evaluation sample from a specified site of the silicon ingot, Comprising at least a prediction model that inputs the control parameter group and the fixed parameter group and outputs the oxygen concentration of the silicon ingot. At least the control parameter group and the fixed parameter group of the silicon ingot are input to the prediction model to obtain a first oxygen concentration, a correction value is calculated using the difference between the measured oxygen concentration and the first oxygen concentration of the silicon ingot, and the first oxygen concentration is corrected by the correction value to obtain a predicted value of the oxygen concentration of the silicon ingot An oxygen concentration prediction system characterized by the above.

7. The oxygen concentration prediction system according to claim 1 or claim 2, A single crystal pulling device that controls the control parameter group so that the oxygen concentration of the target silicon ingot predicted by the oxygen concentration prediction system is within a predetermined range. An oxygen concentration control system comprising the above.

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