A method for predicting the temperature of a silicon melt during the growth of a czochralski silicon single crystal

Abstract

The application provides a temperature prediction method for a silicon melt in a Czochralski silicon single crystal growth process, and belongs to the technical field of semiconductor silicon single crystal preparation. The method comprises the following steps: uniformly collecting temperature data of the silicon melt at all times during the Czochralski silicon single crystal growth process, constructing a silicon melt temperature matrix, and obtaining a first snapshot matrix and a second snapshot matrix with a time offset relationship; performing singular value decomposition on the first snapshot matrix, and determining a truncated rank to obtain a singular value decomposition result of the first snapshot matrix after the first snapshot matrix is truncated to the truncated rank; obtaining an approximate relationship of the first snapshot matrix and the second snapshot matrix, and projecting a high-dimensional matrix in the approximate relationship to obtain a low-rank matrix; performing eigenvalue decomposition on the low-rank matrix to construct a high-dimensional dynamic mode matrix; constructing a temperature prediction model; and performing adaptive temperature prediction on the silicon melt by using the temperature prediction model. The application can effectively improve the temperature prediction efficiency of the silicon melt and ensure the temperature prediction accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor silicon single crystal preparation, and in particular to a method for predicting the temperature of a silicon melt in a Czochralski silicon single crystal growth process. BACKGROUND

[0002] With the increasing scarcity of oil and coal resources and the increasingly serious problem of greenhouse gas emissions, solar photovoltaic power generation has become an ideal renewable energy source due to its safety, cleanliness, environmental protection and sustainability. Silicon single crystals can be used as a basic material for solar photovoltaic cells after processing, and solar photovoltaic cells produced using silicon single crystals can directly convert solar energy into electrical energy.

[0003] At present, the Czochralski method is the main method for preparing silicon single crystals. The Czochralski method is to melt raw materials such as polycrystalline silicon in a crucible by heating, insert a seed crystal into the silicon melt using a rotating seed crystal rod, and gradually grow a silicon single crystal by controlling the pulling speed, temperature and other parameters of the pulling device. The main control objective of this method is to stabilize the thermodynamic process of silicon single crystal growth, thereby growing a silicon single crystal with a constant diameter and low defects. The equipment used for preparing silicon single crystals by the Czochralski method is generally a Czochralski single crystal furnace, and the thermal field temperature in the Czochralski single crystal furnace is one of the key factors affecting the growth of silicon single crystals, which can directly affect the growth rate and quality of the silicon single crystal. The main factor closely related to the quality of the silicon single crystal is the temperature gradient of the silicon melt in the crucible, because the size of the temperature gradient determines the thermal convection of the silicon melt in the crucible, and significantly affects the concentration of the main impurity oxygen content in the silicon single crystal, as well as the integrity of the crystal lattice. In the process of controlling the constant pulling speed of the silicon single crystal, according to the rule representing the pulling speed, representing the axial temperature gradient of the silicon melt), it can be known that the temperature of the silicon melt is most closely related to the quality of the silicon single crystal. Therefore, predicting the temperature distribution of the silicon melt is of great significance for optimizing the growth process of the silicon single crystal and improving the quality of the silicon single crystal.

[0004] However, the thermal field space used for the growth of large-size silicon single crystals is large, and a larger thermal field space can result in slow response and lagging changes in the thermal field temperature, making it a challenging task to dynamically predict the temperature of the silicon melt in the Czochralski single crystal furnace and achieve precise control of the temperature. At present, the temperature prediction methods for the silicon melt mainly include two types: numerical simulation methods based on physical models and deep learning methods based on data-driven, but the existing temperature prediction methods have the following problems:

[0005] Firstly, the numerical simulation method based on the physical model, such as the current mainstream method using , and The existing software, which is based on the establishment of a physical model and uses a finite element method to perform numerical simulation calculation on the growth process of a silicon single crystal. However, this method is difficult to balance the prediction efficiency and prediction accuracy. Generally, a high-precision prediction simulation takes a long time and the efficiency is low. Meanwhile, due to the limitations of these software, users are difficult to flexibly adjust according to actual needs.

[0006] Secondly, a deep learning method based on data driving, such as a neural network using a long short-term memory network and a time convolution network, is used to learn the temperature data of the growth process of a silicon single crystal, so as to construct a deep learning model. This method is highly dependent on data. The larger the amount of data is, the better the performance of deep learning is. However, the increase of the amount of data will increase the calculation complexity, and the increase of the calculation complexity will bring about high computing power, resulting in high cost. On the other hand, the deep learning model is very complex, like a black box, and it is difficult to explain the results obtained.

[0007] Therefore, it is necessary to propose a scheme to improve one or more problems in the above-mentioned related technical solutions.

[0008] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those skilled in the art. SUMMARY

[0009] The present application provides a temperature prediction method for a silicon melt in a Czochralski silicon single crystal growth process, which comprises the following steps:

[0010] Uniformly collecting temperature data of the silicon melt at all times in the Czochralski silicon single crystal growth process, constructing a silicon melt temperature matrix, and obtaining a first snapshot matrix and a second snapshot matrix with a time offset relationship according to the silicon melt temperature matrix;

[0011] Performing singular value decomposition on the first snapshot matrix, determining a truncated rank by using the cumulative energy of all the singular values obtained, and obtaining the singular value decomposition result of the first snapshot matrix after the truncated rank;

[0012] Obtaining an approximate relationship between the first snapshot matrix and the second snapshot matrix, and projecting the high-dimensional matrix in the approximate relationship to obtain a low-rank matrix;

[0013] Performing eigenvalue decomposition on the low-rank matrix to obtain a plurality of eigenvectors and a corresponding eigenvalue of each eigenvector, and constructing a high-dimensional dynamic mode matrix by using all the eigenvectors;

[0014] A temperature prediction model is constructed using the high-dimensional dynamic mode matrix, all the eigenvalues, and the initial state of the first snapshot matrix.

[0015] The temperature prediction model is used to perform adaptive temperature prediction on the silicon melt.

[0016] Furthermore, the step of uniformly collecting temperature data of the silicon melt at all times during the Czochralski silicon single crystal growth process, constructing a silicon melt temperature matrix, and obtaining a first snapshot matrix and a second snapshot matrix with a time offset relationship based on the silicon melt temperature matrix includes:

[0017] A two-dimensional rectangular coordinate system is constructed with the center of the bottom of the crucible as the origin. The horizontal coordinate of the two-dimensional rectangular coordinate system represents the distance from the center of the circle, and the vertical coordinate of the two-dimensional rectangular coordinate system represents the height from the bottom of the crucible.

[0018] Multiple sampling points are uniformly set in the two-dimensional rectangular coordinate system. Temperature data is collected at each sampling point at the same time interval to obtain the temperature data of each sampling point at different times.

[0019] The temperature data at each sampling point are arranged in chronological order to obtain the time-temperature sequence corresponding to each sampling point. All the time-temperature sequences form the silicon melt temperature matrix.

[0020] Obtain from the silicon melt temperature matrix the temperature from the first... From the moment to the first The first snapshot matrix is ​​formed by taking all the time-temperature sequences at the nth time point; and the snapshot matrix is ​​obtained from the silicon melt temperature matrix from the nth time point. From the moment to the first The second snapshot matrix is ​​composed of all the time-temperature sequences at each time point.

[0021] Furthermore, the expression for the silicon melt temperature matrix is ​​as follows:

[0022] (1)

[0023] in, Represents the silicon melt temperature matrix. Indicates the first At the [time]th moment Temperature values ​​at each sampling point;

[0024] The expression for the first snapshot matrix is:

[0025] (2)

[0026] in, denotes a first snapshot matrix, denotes a second snapshot matrix, denotes a temperature value of a sample point at a first time instant,

[0027] The expression of the second snapshot matrix is:

[0028] (3)

[0029] wherein, denotes a second snapshot matrix.

[0030] Further, the step of performing singular value decomposition on the first snapshot matrix, determining a truncated rank by using the cumulative energy of all the singular values obtained, and obtaining the result of the singular value decomposition of the first snapshot matrix after the first snapshot matrix takes the truncated rank comprises:

[0031] performing the singular value decomposition on the first snapshot matrix to obtain a singular value spectrum of the first snapshot matrix, the singular value spectrum being a singular value sequence composed of a plurality of singular values;

[0032] setting an energy truncation threshold, starting from calculating the percentage of the cumulative energy of a first singular value in the total cumulative energy of all the singular values, increasing the number of singular values for calculation one by one until the percentage corresponding to a certain number of singular values reaches or exceeds the energy truncation threshold for the first time, obtaining the truncated rank, the truncated rank representing the first singular values to be retained;

[0033] obtaining the result of the singular value decomposition of the first snapshot matrix after the first snapshot matrix takes the truncated rank.

[0034] Further, the expression of performing the singular value decomposition on the first snapshot matrix is:

[0035] (4)

[0036] wherein, denotes a first snapshot matrix, , denotes a left singular vector matrix, , denotes a diagonal matrix, , denotes a right singular vector matrix, , denotes a transpose, denotes a real vector space of dimension n, denotes a real vector space of dimension n, denotes ​3D real vector space;

[0037] The energy cutoff threshold is used express, ;

[0038] forward The expression for the cumulative energy of the singular values ​​is:

[0039] (5)

[0040] in, Indicates the preceding The cumulative energy of a singular value This represents the number of all singular values. Indicates the first The size of the singular values;

[0041] The expression for the singular value decomposition of the first snapshot matrix after taking the truncated rank is:

[0042] (6)

[0043] This represents the left singular vector matrix after taking the truncated rank. , This represents the diagonal matrix after taking the truncated rank. , This represents the right singular vector matrix after taking the truncated rank. , and , express 3D real vector space, express 3D real vector space, express A real vector space.

[0044] Furthermore, the approximate relationship between the first snapshot matrix and the second snapshot matrix is ​​obtained, and the high-dimensional part of the approximate relationship is... Projecting the matrix yields a lower rank. The steps involved in the matrix process include:

[0045] Utilizing the aforementioned high dimension The matrix establishes the approximate relationship between the first snapshot matrix and the second snapshot matrix;

[0046] The high dimension Projecting the matrix onto the left singular vector matrix after taking the truncated rank, we obtain the low-rank matrix. matrix.

[0047] Further, the expression of the approximate relationship of the first snapshot matrix and the second snapshot matrix is:

[0048] (7)

[0049] wherein, denotes the first snapshot matrix, denotes the second snapshot matrix, denotes a high-dimensional matrix, , denotes the pseudo-inverse of the first snapshot matrix , , denotes the right singular vector matrix after taking the truncated rank, , denotes the inverse of the diagonal matrix after taking the truncated rank, , denotes the left singular vector matrix after taking the truncated rank, , denotes the transpose, denotes a real vector space of dimension, denotes a real vector space of dimension, denotes a real vector space of dimension.

[0050] The expression of the low-rank matrix is:

[0051] (8)

[0052] wherein, denotes the low-rank matrix.

[0053] Further, the expression of the eigen-decomposition of the low-rank matrix is:

[0054] (9)

[0055] wherein, denotes the low-rank matrix, denotes the eigenvector matrix, denotes the eigenvalue matrix, each diagonal element of the eigenvalue matrix is the eigenvalue corresponding to the corresponding eigenvector;

[0056] The expression of the high-dimensional dynamic modal matrix is:

[0057] (10)

[0058] wherein, represents a high-dimensional dynamic modal matrix, each column of which represents a modal, , represents a second snapshot matrix, represents a right singular vector matrix after taking a truncated rank, , represents a diagonal matrix after taking a truncated rank inverse, , represents a real vector space of dimension, represents a real vector space of dimension, represents a real vector space of dimension.

[0059] Further, the step of constructing a temperature prediction model using the high-dimensional dynamic modal matrix, all the eigenvalues, and an initial state of the first snapshot matrix comprises:

[0060] projecting the first snapshot matrix at the initial state onto the high-dimensional dynamic modal matrix to obtain an initial amplitude vector corresponding to the high-dimensional dynamic modal matrix;

[0061] The expression of the initial amplitude vector is:

[0062] (11)

[0063] wherein, represents an initial amplitude vector corresponding to the high-dimensional dynamic modal matrix, represents a pseudo-inverse of the high-dimensional dynamic modal matrix , represents a sequence of initial temperature values of the silicon melt in the silicon melt temperature matrix;

[0064] constructing the temperature prediction model using the initial amplitude vector and all the eigenvalues;

[0065] The expression of the temperature prediction model is:

[0066] (12)

[0067] wherein, represents a temperature value of the silicon melt at the th moment, represents a number of all the modes in the high-dimensional dynamic modal matrix, the number of all the modes in the high-dimensional dynamic modal matrix is equal to the number of retained first modes.the number of the singular values is equal, represents the first modality, represents the first modality, represents the first modality, represents the first modality, represents the first modality, represents the first modality,

[0068] further, the step of adaptively predicting the temperature of the silicon melt by using the temperature prediction model comprises:

[0069] setting a prediction duration, and starting from an initial prediction time, predicting the temperature of the silicon melt by using the temperature prediction model according to all historical temperature data to obtain a predicted temperature value at a corresponding time;

[0070] calculating a root mean square error of the predicted temperature value and a corresponding actual temperature value at the corresponding time respectively, and setting a root mean square error threshold, if the root mean square error is greater than the root mean square error threshold, updating the high-dimensional matrix; if the root mean square error is less than or equal to the root mean square error threshold, the predicted temperature value at the corresponding time is taken as a corresponding prediction result respectively;

[0071] the expression of the root mean square error is:

[0072] (13)

[0073] wherein, represents a root mean square error of a predicted temperature value and a corresponding actual temperature value of the silicon melt, represents the number of all sampling points, represents a predicted temperature value of the first sampling point, represents a corresponding actual temperature value of the first sampling point and the predicted temperature value .

[0074] The present application provides a temperature prediction method for a silicon melt in a Czochralski silicon single crystal growth process, which has at least the following beneficial effects:

[0075] (1) The present application constructs a silicon melt temperature matrix containing temperature data of the silicon melt at all times in the Czochralski silicon single crystal growth process, which not only retains the dynamic characteristics of the temperature change of the silicon melt in the silicon single crystal growth process, but also reduces the complexity of the traditional spatiotemporal high-dimensional matrix and improves the processing efficiency of matrix calculation;

[0076] (2) The present application can express the dynamic evolution process of the silicon melt temperature as a superposition of a group of dominant modes by singular value decomposition of the first snapshot matrix, that is, simulate the dynamic characteristics of the silicon melt temperature in a period of time and a certain range by using less characteristic data, thereby improving the prediction speed while ensuring the simulation accuracy;

[0077] (3) The present application constructs a temperature prediction model and performs self-adaptive temperature prediction on the silicon melt by using the temperature prediction model, thereby ensuring that the temperature prediction model can adapt to different stages of the Czochralski silicon single crystal growth process and effectively improving the temperature prediction efficiency and prediction accuracy of the silicon melt. BRIEF DESCRIPTION OF DRAWINGS

[0078] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application. It is apparent that the accompanying drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0079] Figure 1 A step schematic diagram of a temperature prediction method for a silicon melt in a Czochralski silicon single crystal growth process in an exemplary embodiment of the present application is shown;

[0080] Figure 2 A flowchart of a temperature prediction method for a silicon melt in a Czochralski silicon single crystal growth process in an exemplary embodiment of the present application is shown;

[0081] Figure 3 A structural schematic diagram of a single crystal furnace in an exemplary embodiment of the present application is shown;

[0082] Figure 4 A dominant mode schematic diagram of part of the temperature data in a simulation experiment in an exemplary embodiment of the present application is shown;

[0083] Figure 5 A comparison schematic diagram of the actual temperature value and the predicted temperature value of the silicon melt at the 61st minute in a simulation experiment in an exemplary embodiment of the present application is shown;

[0084] Figure 6 A schematic diagram of the root mean square error of the actual temperature value and the predicted temperature value of the silicon melt from the 61st minute to the 80th minute in a simulation experiment in an exemplary embodiment of the present application is shown. DETAILED DESCRIPTION

[0085] Example implementations are now described with reference to the drawings. Example implementations can, however, be implemented in many different forms and should not be construed as limited to the examples set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the example implementations to those skilled in the art. The described features, structures, or characteristics can be combined in one or more implementations.

[0086] In addition, the accompanying drawings are included to provide a further understanding of the present application and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the present application and, together with the description, serve to explain the principles of the present application. In the drawings:

[0087] In the following, a method for predicting the temperature of a silicon melt in a Czochralski silicon single crystal growth process according to the present example embodiment will be described in more detail.

[0088] The present example embodiment provides a method for predicting the temperature of a silicon melt in a Czochralski silicon single crystal growth process, which can include the following steps, as shown in Figure 1 and Figure 2

[0089] The present example embodiment provides a method for predicting the temperature of a silicon melt in a Czochralski silicon single crystal growth process, which can include the following steps, as shown in

[0090] The present example embodiment provides a method for predicting the temperature of a silicon melt in a Czochralski silicon single crystal growth process, which can include the following steps, as shown in Figure 3 Figure 3 As shown in FIG. 1, a two-dimensional rectangular coordinate system is constructed with the center of the crucible bottom as the origin, the horizontal coordinate of the two-dimensional rectangular coordinate system represents the distance from the center, and the vertical coordinate of the two-dimensional rectangular coordinate system represents the height from the bottom of the crucible.

[0091] ​​Sub-step S1012: Uniformly set multiple sampling points in a two-dimensional rectangular coordinate system, and perform temperature acquisition at each sampling point at the same interval time, respectively obtaining the temperature data of each sampling point at different moments.

[0092] Sub-step S1013: Arrange the temperature data at each sampling point in chronological order respectively to obtain the time-temperature sequence corresponding to each sampling point, and all the time-temperature sequences form the silicon melt temperature matrix.

[0093] Further, the expression of the silicon melt temperature matrix is:

[0094] (1)

[0095] Where, represents the silicon melt temperature matrix, represents the th moment and the th sampling point temperature value.

[0096] Sub-step S1014: Obtain all the time-temperature sequences from the th moment (i.e., the initial moment) to the th moment from the silicon melt temperature matrix to form the first snapshot matrix; and obtain all the time-temperature sequences from the th moment to the th moment from the silicon melt temperature matrix to form the second snapshot matrix.

[0097] Further, the expression of the first snapshot matrix is:

[0098] (2)

[0099] Where, represents the first snapshot matrix, represents the th moment and the th sampling point temperature value.

[0100] Further, the expression of the second snapshot matrix is:

[0101] (3)

[0102] Where, represents the second snapshot matrix.

[0103] In step S102 of this embodiment: Perform singular value decomposition on the first snapshot matrix, determine the truncation rank by using the cumulative energy of all the obtained singular values, and obtain the result of the singular value decomposition of the first snapshot matrix after taking the truncation rank. Step S102 of this embodiment may include the following sub-steps: <0000snapshot matrix after taking the truncation rank. Step S102 of this embodiment may include the following sub-steps:

[0104] Sub-step S1021: singular value decomposition is performed on the first snapshot matrix to obtain a singular value spectrum of the first snapshot matrix, the singular value spectrum being a singular value sequence composed of multiple singular values.

[0105] Further, the expression for singular value decomposition on the first snapshot matrix is:

[0106] (4)

[0107] wherein, denotes the first snapshot matrix, , denotes a left singular vector matrix, , denotes a diagonal matrix, , denotes a right singular vector matrix, , denotes a transpose, denotes a real vector space of dimension m, denotes a real vector space of dimension n, denotes a real vector space of dimension p.

[0108] Sub-step S1022: an energy cutoff threshold is set, starting from the percentage of the cumulative energy of the first singular value in the total cumulative energy of all singular values, the number of singular values is increased one by one for calculation until the percentage corresponding to a certain number of singular values first reaches or exceeds the energy cutoff threshold, obtaining a cutoff rank, the cutoff rank representing the first singular values to be retained.

[0109] Further, the energy cutoff threshold is denoted by . The value range of is .

[0110] Further, the expression for the cumulative energy of the first singular values is:

[0111] (5)

[0112] wherein, denotes the cumulative energy of the first singular values, denotes the number of all singular values, denotes the size of the singular value.

[0113] Sub-step S1023: the result of singular value decomposition of the first snapshot matrix after taking the cutoff rank is obtained.

[0114] Furthermore, the expression for the singular value decomposition of the first snapshot matrix after taking its truncated rank is:

[0115] (6)

[0116] This represents the left singular vector matrix after taking the truncated rank. , This represents the diagonal matrix after taking the truncated rank. , This represents the right singular vector matrix after taking the truncated rank. , and , express 3D real vector space, express 3D real vector space, express A real vector space.

[0117] Step S103 of this embodiment: Obtain the approximate relationship between the first snapshot matrix and the second snapshot matrix, and separate the high-dimensional elements in the approximate relationship. Projecting the matrix yields a lower rank. Matrix. Step S103 in this embodiment may include the following sub-steps:

[0118] Sub-step S1031: Utilizing high dimensions The matrix establishes an approximate relationship between the first snapshot matrix and the second snapshot matrix.

[0119] Furthermore, the approximate relationship between the first snapshot matrix and the second snapshot matrix is ​​expressed as follows:

[0120] (7)

[0121] in, This represents the first snapshot matrix. This represents the second snapshot matrix. Representing higher dimensions matrix, , Represents the first snapshot matrix The false rebellion, , This represents the right singular vector matrix after taking the truncated rank. , Represents the diagonal matrix after taking the truncated rank. Find the reverse. , This represents the left singular vector matrix after taking the truncated rank. , Indicates transpose. express 3D real vector space, express 3D real vector space, express A real vector space.

[0122] Sub-step S1032: Transform the high-dimensional... Projecting the matrix onto the left singular vector matrix after taking the truncated rank, we obtain the low-rank matrix. matrix.

[0123] Furthermore, low-rank The expression for a matrix is:

[0124] (8)

[0125] in, Indicates low rank matrix.

[0126] Step S104 of this embodiment: For low-rank... The matrix is ​​decomposed into eigenvectors to obtain multiple eigenvectors and the corresponding eigenvalues ​​of each eigenvector. A high-dimensional dynamic mode matrix is ​​then constructed using all the eigenvectors.

[0127] Furthermore, regarding low-rank The expression for eigenvalue decomposition of a matrix is:

[0128] (9)

[0129] in, Indicates low rank matrix, Represents the eigenvector matrix, Let represent the eigenvalue matrix, where each diagonal element of the eigenvalue matrix is ​​an eigenvalue corresponding to the eigenvector.

[0130] Furthermore, the expression for the high-dimensional dynamic mode matrix is:

[0131] (10)

[0132] in, This represents a high-dimensional dynamic mode matrix, where each column represents a mode. , This represents the second snapshot matrix. This represents the right singular vector matrix after taking the truncated rank. , Represents the diagonal matrix after taking the truncated rank. Find the reverse. , express 3D real vector space, express 3D real vector space, express A real vector space.

[0133] Step S105 of this embodiment: Construct a temperature prediction model using the high-dimensional dynamic mode matrix, all eigenvalues, and the initial state of the first snapshot matrix. Step S105 of this embodiment may include the following sub-steps:

[0134] Sub-step S1051: Project the first snapshot matrix at the initial state onto the high-dimensional dynamic mode matrix to obtain the initial amplitude vector corresponding to the high-dimensional dynamic mode matrix.

[0135] Furthermore, the expression for the initial amplitude vector is:

[0136] (11)

[0137] in, This represents the initial amplitude vector corresponding to the high-dimensional dynamic mode matrix. Representing high-dimensional dynamic mode matrix The false rebellion, This represents the sequence of initial temperature values ​​of the silicon melt in the silicon melt temperature matrix.

[0138] Sub-step S1052: Construct a temperature prediction model using the initial amplitude vector and all eigenvalues.

[0139] Furthermore, the expression for the temperature prediction model is:

[0140] (12)

[0141] in, Indicates the first The temperature value of the silicon melt at that moment. This represents the number of all modes in the high-dimensional dynamic mode matrix. With the retention of the former The number of singular values ​​is equal. Indicates the first One modality, Indicates the first Eigenvalues ​​corresponding to each mode Power of 1 Indicates the first The initial amplitude corresponding to each mode Representing the eigenvalue matrix Power of 1.

[0142] Step S106 of this embodiment: using the temperature prediction model to perform adaptive temperature prediction on the silicon melt. Step S106 of this embodiment can include the following steps:

[0143] Sub-step S1061: setting a prediction duration, and starting from an initial prediction time, using the temperature prediction model to perform temperature prediction on the silicon melt according to all historical temperature data, to obtain a predicted temperature value at each corresponding time.

[0144] Sub-step S1062: calculating the root mean square error of the predicted temperature value and the actual temperature value at each corresponding time, respectively, and setting a root mean square error threshold, if the root mean square error is greater than the root mean square error threshold, updating the high-dimensional matrix; if the root mean square error is less than or equal to the root mean square error threshold, respectively taking the predicted temperature value at each corresponding time as the corresponding prediction result.

[0145] Further, the expression of the root mean square error is:

[0146] (13)

[0147] wherein, represents the root mean square error of the predicted temperature value of the silicon melt and the corresponding actual temperature value, represents the number of all sampling points, represents the predicted temperature value of the i-th sampling point, represents the actual temperature value of the i-th sampling point.

[0148] In order to verify the excellent effect of the temperature prediction method for the silicon melt in the Czochralski silicon single crystal growth process proposed in this application, the following simulation experiment is performed.

[0149] The simulation experiment configures a plurality of physical fields, including a computational fluid dynamics module, a heat transfer module, weakly compressible flow and turbulent process of a simulation fluid (i.e. argon gas in the single crystal furnace), and simulates heat transfer processes such as conduction, convection and radiation of the temperature field.

[0150] The simulation experiment sets the structure parameters of the single crystal furnace model, including the rotation speed of the crucible containing the silicon melt, the rotation speed of the silicon single crystal rod, the heater power, the pressure in the single crystal furnace, the initial temperature of the single crystal furnace, the inlet flow rate of argon gas, the inlet area of argon gas, the inlet velocity of argon gas, the viscosity ratio of the silicon melt, the convective heat transfer coefficient between the solid surface and the silicon melt, and the thickness of the heat shield in the single crystal furnace. The values of all the structure parameters in the simulation experiment are shown in Table 1 as follows:

[0151] Table 1 Values of all structure parameters in the simulation experiment ​​​

[0152]

[0153] The simulation calculation of the single crystal furnace model takes approximately 20 minutes and is roughly divided into two steps: a steady-state flow field process and a transient full-field process. The average temperature of the growth interface (i.e., the interface between the solid and the silicon melt) stabilizes after 400 minutes.

[0154] The thermal field region inside the crucible was selected as the temperature data acquisition area. The temperature data sampling period was 1 minute, with temperature data collected at 961 sampling points per minute. After obtaining... [11 minutes ,60 minutes ] After collecting temperature data over a time interval, construct two datasets of size [missing data]. The silicon melt temperature matrix was obtained by collecting data from 961 sampling points over 49 minutes, constructing two snapshot matrices, and then processing and analyzing the temperature data to obtain the... [61 minutes ,80 minutes ] Predicted temperature values ​​over a time interval.

[0155] Figure 4 This demonstrates how dynamic mode decomposition (DynamD) is used to process snapshot matrices of temperature data, yielding the dominant modes of the temperature data. These dominant modes represent the temperature distribution at the current moment, retaining only the modes that have the greatest impact on the temperature data. One modality, Figure 4 In the diagram, a to g represent the 1st to 7th dominant modes, respectively. Figure 4 The energies of the dominant modes from a to g gradually decrease, and the predicted temperature value obtained by superimposing these dominant modes is very close to the corresponding actual temperature value. Figure 4 The x-coordinate represents the distance from the center of the circle at the bottom of the crucible, in mm, and the y-coordinate represents the height from the bottom of the crucible, in mm.

[0156] Here, the dominant mode is defined in formula (12). To express.

[0157] Figure 5 and Figure 6 The performance of the method proposed in this application in simulation experiments is shown. Figure 5 In this study, dynamic mode decomposition was used to predict the temperature value of a specified thermal field region at the 61st minute, at which point the furnace temperature was approximately 1000 Kelvin (abbreviated as Kelvin). )about.

[0158] Figure 5 a is an actual temperature value at the 61st minute, Figure 5 b is a predicted temperature value at the 61st minute. In Figure 5 In a and b, the x coordinate represents the distance from the center of the crucible bottom, in mm, and the y coordinate represents the height from the crucible bottom, in mm.

[0159] It can be seen that the root mean square error of the actual temperature value and the predicted temperature value of the silicon melt from the 61st minute to the 80th minute is within 2.5 Figure 6 , the prediction accuracy is high, and the calculation time is very short. This shows that compared with the numerical simulation method and the deep learning method, the temperature prediction method proposed in the present application requires a small amount of data, ensures the prediction accuracy and improves the operation efficiency, and the temperature prediction model of the present application has good interpretability and has obvious advantages in temperature prediction. Figure 6 The unit of the horizontal coordinate is minute, and the unit of the vertical coordinate is .

[0160] In addition, the terms "first", "second", "third", etc. are used only for descriptive purposes and should not be construed as indicating or implying relative importance or an indicated number of technical features. Therefore, the features defined as "first", "second", etc. can explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, the meaning of "a plurality of" is two or more, unless otherwise specifically limited.

[0161] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present application, the illustrative description of the above terms is not necessarily for the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the present application.

[0162] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present application, and these modifications or replacements should be included in the protection scope of the present application.

[0163] ​Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.

Claims

1. A method of temperature prediction of a silicon melt in a Czochralski silicon single crystal growth process, characterized by, The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: obtaining an approximate relationship of the first snapshot matrix and the second snapshot matrix, and projecting a high-dimensional matrix in the approximate relationship to obtain a low-rank matrix matrix​ For the low rank The matrix is ​​subjected to eigenvalue decomposition to obtain multiple eigenvectors and the eigenvalues ​​corresponding to each eigenvector, and a high-dimensional dynamic mode matrix is ​​constructed using all the eigenvectors. The method comprises the following steps: The method comprises the following steps:

2. The method of claim 1, wherein the temperature of the silicon melt is predicted based on the temperature of the silicon melt at the time of the start of the pulling of the single crystal of silicon. The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: Obtain from the silicon melt temperature matrix the temperature from the first... From the moment to the first The first snapshot matrix is ​​formed by taking all the time-temperature sequences at the nth time point; and the snapshot matrix is ​​obtained from the silicon melt temperature matrix from the nth time point. From the moment to the first The second snapshot matrix is ​​composed of all the time-temperature sequences at each time point.

3. The method of claim 1, wherein the temperature of the silicon melt is predicted based on the temperature of the silicon melt at the time of the start of the pulling of the single crystal of silicon. The method comprises the following steps: (1) in, Represents the silicon melt temperature matrix. Indicates the first At the [time]th moment Temperature values ​​at each sampling point; The method comprises the following steps: (2) in, This represents the first snapshot matrix. Indicates the first At the [time]th moment Temperature values ​​at each sampling point; The method comprises the following steps: (3) wherein, denotes the second snapshot matrix.

4. The method of claim 3, wherein the temperature of the silicon melt is predicted based on the temperature of the silicon melt at the time of the start of the pulling of the single crystal of silicon. The method comprises the following steps: The method comprises the following steps: setting an energy cutoff threshold, starting from calculating the percentage of the cumulative energy of the first singular value in the total cumulative energy of all the singular values, and increasing the number of singular values for calculation one by one until the percentage corresponding to a certain number of singular values first reaches or exceeds the energy cutoff threshold, obtaining the cutoff rank, the cutoff rank representing the number of singular values to be retained ​ The method comprises the following steps:

5. The method of claim 4, wherein the temperature of the silicon melt is predicted based on the temperature of the silicon melt at the time of the start of the pulling of the single crystal of silicon. The method comprises the following steps: (4) wherein, denotes a first snapshot matrix, , denotes a left singular vector matrix, , denotes a diagonal matrix, , denotes a right singular vector matrix, , denotes a transpose, denotes a real vector space of dimension denotes a real vector space of dimension denotes a real vector space of dimension The energy cut-off threshold is represented by , ; The expression of the cumulative energy of the singular values is: the singular values is: (5) wherein, denotes the cumulative energy of the first singular values, denotes the number of all singular values, denotes the size of the first singular value; The method comprises the following steps: (6) denotes the left singular vector matrix after taking the truncated rank, , denotes the diagonal matrix after taking the truncated rank, , denotes the right singular vector matrix after taking the truncated rank, , and , denotes a real vector space of dimension denotes a real vector space of dimension denotes a real vector space of dimension 6. The method of temperature prediction of a silicon melt during growth of a Czochralski silicon single crystal according to claim 5, characterized in that The step of obtaining the approximate relationship between the first snapshot matrix and the second snapshot matrix, and projecting the high-dimensional matrix in the approximate relationship to obtain a low-rank matrix includes: The high-dimensional matrix to establish the approximate relationship of the first snapshot matrix and the second snapshot matrix; projecting the high-dimensional matrix onto the left-singular vector matrix after taking the truncated rank, to obtain a low-rank matrix. matrix.​ 7. The method of claim 6, wherein the temperature of the silicon melt is predicted based on the temperature of the silicon melt at the time of the start of the pulling of the single crystal of silicon. The method comprises the following steps: (7) wherein, denotes the first snapshot matrix, denotes the second snapshot matrix, denotes the high-dimensional matrix, , denotes the pseudo-inverse of the first snapshot matrix , , denotes the right singular vector matrix after taking the truncated rank, , denotes the inversion of the diagonal matrix after taking the truncated rank , , denotes the left singular vector matrix after taking the truncated rank, , denotes the transpose, denotes a real vector space of dimension denotes a real vector space of dimension denotes a real vector space of dimension The low rank The expression of the matrix is: (8) wherein denotes a low-rank matrix.

8. The method of claim 4, wherein the temperature of the silicon melt is predicted by using a temperature model of the Czochralski silicon single crystal growth process. performing the eigen decomposition on the low-rank matrix is given by (9) wherein, denotes a low rank matrix, denotes a matrix of eigenvectors, denotes a matrix of eigenvalues, each diagonal element of which is the eigenvalue corresponding to the respective eigenvector, The method comprises the following steps: (10) wherein, represents a high-dimensional dynamic modal matrix, each column of which represents a modal, , represents a second snapshot matrix, represents a right singular vector matrix after taking a truncated rank, , represents a diagonal matrix after taking a truncated rank is inverted, , represents a real vector space of dimension represents a real vector space of dimension represents a real vector space of dimension 9. The method of claim 8, wherein the temperature of the silicon melt is predicted based on the temperature of the silicon melt at the time of the start of the pulling of the single crystal of silicon. The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: (11) wherein, represents an initial amplitude vector corresponding to the high-dimensional dynamic modal matrix, represents a pseudo-inverse of the high-dimensional dynamic modal matrix represents a sequence of initial temperature values of the silicon melt in the silicon melt temperature matrix;​ The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the 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10. The method of claim 9, wherein the temperature of the silicon melt is predicted based on the temperature of the silicon melt at the time of the start of the pulling of the single crystal of silicon. The step of adaptively predicting the temperature of the silicon melt by using the temperature prediction model comprises: a prediction duration is set, and starting from an initial prediction time, the temperature of the silicon melt is predicted by using the temperature prediction model according to all historical temperature data, and a predicted temperature value at a corresponding time is obtained respectively; respectively, and a root mean square error threshold is set, and if the root mean square error is greater than the root mean square error threshold, the high-dimensional matrix is updated; if the root mean square error is less than or equal to the root mean square error threshold, the predicted temperature value at the corresponding time is taken as the corresponding prediction result respectively. respectively, and a root mean square error threshold is set, and if the root mean square error is greater than the root mean square error threshold, the high-dimensional matrix is updated; if the root mean square error is less than or equal to the root mean square error threshold, the predicted temperature value at the corresponding time is taken as the corresponding prediction result respectively. an expression of the root mean square error is: (13) wherein, represents the root mean square error of the predicted temperature values of the silicon melt and the corresponding actual temperature values, represents the number of all sampling points, represents the predicted temperature value of the sampling point, represents the predicted temperature value of the sampling point, represents the actual temperature value of the sampling point corresponding to the predicted temperature value.

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