Deep learning-based method, device, and product for estimating thermal field of single-crystal silicon using Czochralski method

Abstract

The present application provides a method, device, and product for estimating the thermal field of single-crystal silicon using the Czochralski method based on deep learning, and relates to the technical field of single-crystal silicon preparation. The method comprises: obtaining historical operating condition data during the process of preparing single-crystal silicon using the Czochralski method; training a thermal field estimation model based on shared parameters from a current round of training to obtain output results from the current round of training; updating the shared parameters for a next round of training based on the shared parameters from the current round of training and a momentum variable having a Gaussian distribution; optimizing the parameters of the thermal field estimation model based on a loss function value; and performing a next round of training on the thermal field estimation model based on the shared parameters from the next round of training until a preset number of training times is reached; determining the average value of temperature prediction values ​​in the output data obtained from the last S rounds of training as the temperature value of the corresponding position, and determining an uncertainty measurement value of the thermal field estimation model based on the standard deviation of the temperature prediction values ​​in the output data obtained from the last S rounds of training.

Description

Technical Field

[0001] The present application relates to the technical field of single crystal silicon preparation, and in particular to a method, device and product for estimating the thermal field of single crystal silicon using the Czochralski method based on deep learning. Background Art

[0002] In the process of preparing single crystal silicon using the Czochralski method, the internal thermal field of the single crystal silicon growth system is often at a high temperature of around 1800K, making it difficult to observe it and collect specific information.

[0003] In related technologies, experimental research is primarily used to obtain internal thermal field data. However, this method requires numerous repeated experiments, resulting in long and expensive experimental cycles, and the information directly measured is limited. Therefore, it is necessary to develop a deep learning-based method, device, and product for estimating the thermal field of single-crystal silicon grown using the Czochralski method to efficiently and accurately obtain temperature distribution data within the single-crystal silicon growth system. Summary of the Invention

[0004] In view of the above problems, the embodiments of the present application provide a method, device and product for estimating the thermal field of single crystal silicon produced by the Czochralski method based on deep learning, so as to overcome the above problems or at least partially solve the above problems.

[0005] A first aspect of an embodiment of the present application provides a method for estimating thermal field of single-crystal silicon using a Czochralski method based on deep learning, the method comprising:

[0006] Acquire historical operating condition data during the Czochralski process for preparing single crystal silicon, the historical operating condition data comprising at least: historical temperature monitoring data of multiple locations in the single crystal silicon growth system;

[0007] generating historical thermal field distribution information of the single crystal silicon growth system based on the historical temperature monitoring data;

[0008] Based on the shared parameters of this round of training, using the historical temperature monitoring data and the historical thermal field distribution information, training a thermal field estimation model to obtain output results of this round of training, the output results including: temperature prediction values ​​of various locations in the single crystal silicon growth system, and thermal field prediction values ​​of the single crystal silicon growth system;

[0009] According to the shared parameters of the current round of training and the momentum variable with Gaussian distribution, the shared parameters of the next round of training are updated;

[0010] Calculating a loss function value according to the output result, and performing parameter optimization on the thermal field estimation model according to the loss function value;

[0011] Based on the shared parameters of the next round of training, the historical temperature monitoring data and the historical thermal field distribution information are reused to perform the next round of training on the thermal field estimation model after parameter optimization until a preset number of training times is reached, thereby obtaining a trained thermal field estimation model and a shared parameter sequence; the shared parameter sequence represents a sequence of shared parameters and momentum variables obtained from the last S rounds of training, arranged in a training order; where S is less than the preset number of training times;

[0012] The average value of the temperature prediction values ​​in the output data obtained from the last S rounds of training is determined as the temperature value of the corresponding position point in the single crystal silicon growth system. The uncertainty measurement value of the trained thermal field estimation model is determined based on the standard deviation of the temperature prediction values ​​in the output data obtained from the last S rounds of training.

[0013] A second aspect of the embodiments of the present application further provides a device for estimating thermal fields of single-crystal silicon using a Czochralski method based on deep learning, the device comprising:

[0014] A historical operating condition data acquisition module is used to acquire historical operating condition data during the process of preparing single crystal silicon by the Czochralski method, wherein the historical operating condition data at least includes: historical temperature monitoring data of multiple positions in the single crystal silicon growth system;

[0015] a thermal field simulation module, configured to generate historical thermal field distribution information of the single crystal silicon growth system based on the historical temperature monitoring data;

[0016] a model training module for training a thermal field estimation model based on the shared parameters of this round of training and utilizing the historical temperature monitoring data and the historical thermal field distribution information to obtain output results of this round of training, wherein the output results include: temperature prediction values ​​of various locations in the single crystal silicon growth system and thermal field prediction values ​​of the single crystal silicon growth system;

[0017] A shared parameter updating module, configured to update the shared parameters for the next round of training based on the shared parameters of the current round of training and the momentum variable having a Gaussian distribution;

[0018] a parameter optimization module, configured to calculate a loss function value according to the output result, and perform parameter optimization on the thermal field estimation model according to the loss function value;

[0019] an iterative training module for reusing the historical temperature monitoring data and the historical thermal field distribution information based on the shared parameters of the next round of training to perform the next round of training on the thermal field estimation model after parameter optimization until a preset number of training times is reached, thereby obtaining a trained thermal field estimation model and a shared parameter sequence; the shared parameter sequence represents a sequence of shared parameters and momentum variables obtained from the last S rounds of training, arranged in a training order; where S is less than the preset number of training times;

[0020] The uncertainty calculation module is used to determine the average value of the temperature prediction value in the output data obtained from the last S rounds of training as the temperature value of the corresponding position point in the single crystal silicon growth system, and determine the uncertainty measurement value of the trained thermal field estimation model based on the standard deviation of the temperature prediction value in the output data obtained from the last S rounds of training.

[0021] The third aspect of the embodiments of the present application further provides an electronic device, comprising a memory, a processor, and a computer program stored on the memory, wherein the processor executes the computer program to implement the steps in the deep learning-based Czochralski single crystal silicon thermal field estimation method described in the first aspect of the embodiments of the present application.

[0022] The fourth aspect of the embodiment of the present application further provides a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps in the deep learning-based Czochralski single crystal silicon thermal field estimation method described in the first aspect of the embodiment of the present application are implemented.

[0023] The fifth aspect of the embodiments of the present application further provides a computer program product, which, when running on an electronic device, enables a processor to implement the steps in the deep learning-based Czochralski single crystal silicon thermal field estimation method as described in the first aspect of the embodiments of the present application.

[0024] An embodiment of the present application provides a method for estimating the thermal field of single-crystal silicon by a Czochralski method based on deep learning, the method comprising: obtaining historical operating condition data in a process of preparing single-crystal silicon by a Czochralski method, the historical operating condition data comprising at least historical temperature monitoring data of multiple positions in a single-crystal silicon growth system; generating historical thermal field distribution information of the single-crystal silicon growth system based on the historical temperature monitoring data; training a thermal field estimation model based on shared parameters of a current round of training using the historical temperature monitoring data and the historical thermal field distribution information to obtain output results of the current round of training, the output results comprising: temperature prediction values ​​of various positions in the single-crystal silicon growth system, and thermal field prediction values ​​of the single-crystal silicon growth system; updating the shared parameters of the next round of training based on the shared parameters of the current round of training and a momentum variable with a Gaussian distribution; and calculating, based on the output results, Loss function value, optimizing the parameters of the thermal field estimation model according to the loss function value; based on the shared parameters of the next round of training, reusing the historical temperature monitoring data and the historical thermal field distribution information, performing the next round of training on the thermal field estimation model after parameter optimization, until a preset number of training times is reached, and obtaining a trained thermal field estimation model and a shared parameter sequence; the shared parameter sequence represents a sequence in which the shared parameters and momentum variables obtained from the last S rounds of training are arranged in a training order; S is less than the preset number of training times; the average value of the temperature prediction values ​​in the output data obtained from the last S rounds of training is determined as the temperature value of the corresponding position point in the single crystal silicon growth system, and the uncertainty measurement value of the trained thermal field estimation model is determined according to the standard deviation of the temperature prediction values ​​in the output data obtained from the last S rounds of training.

[0025] The specific beneficial effects are as follows: Based on the actual operating conditions of single-crystal silicon grown by the Czochralski method (i.e., historical operating data), this application measures the temperature distribution at finite points within the thermal field (i.e., historical temperature monitoring data of multiple locations in the single-crystal silicon growth system). Using deep learning, this application trains a thermal field estimation model to predict continuous thermal field temperature distributions (i.e., the temperature values ​​at corresponding locations in the single-crystal silicon growth system). This enables simple and rapid estimation of the thermal field during single-crystal silicon growth, and can obtain specific temperature information for each location within the internal thermal field. Furthermore, by calculating the uncertainty of the model output results (the uncertainty measurement value of the trained thermal field estimation model), this solves the technical problem of difficulty in measuring the correctness of the model output prediction results, thereby improving the accuracy of the evaluated thermal field. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0027] Figure 1 This is a flowchart of the steps of a method for estimating the thermal field of single-crystal silicon using the Czochralski method based on deep learning provided in an embodiment of the present application;

[0028] Figure 2 1 is a schematic structural diagram of a device for estimating thermal field of single-crystal silicon using a Czochralski method, provided in an embodiment of the present application;

[0029] Figure 3 This is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0030] The exemplary embodiments of the present application will be described in more detail below in conjunction with the accompanying drawings in the embodiments of the present application. Although the accompanying drawings show exemplary embodiments of the present application, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present application and to fully convey the scope of the present application to those skilled in the art.

[0031] The Czochralski method is the mainstream method for producing single-crystal silicon. Currently, during the Czochralski method, the internal thermal field of the single-crystal silicon growth system is often at a high temperature of 1800K, making it difficult to observe and collect specific information.

[0032] In related technologies, experimental research is primarily used to obtain internal thermal field data. However, this method requires numerous repeated experiments, resulting in long and expensive experimental cycles. Furthermore, the information directly measured through these experiments is limited and has low accuracy. In contrast, numerical simulation can accurately simulate the temperature distribution within the entire system at a low cost and in a short cycle. However, conventional numerical simulation methods often have difficulty determining model accuracy and exhibit low robustness.

[0033] In response to the aforementioned issues, the present invention proposes a deep learning-based method, device, and product for estimating the thermal field of single-crystal silicon grown using the Czochralski method. These methods enable efficient and accurate acquisition of temperature distribution data within a single-crystal silicon growth system. The following, in conjunction with the accompanying drawings, describes in detail the deep learning-based method for estimating the thermal field of single-crystal silicon grown using the Czochralski method and its application scenarios.

[0034] The first aspect of the embodiment of the present application provides a method for estimating the thermal field of single crystal silicon by Czochralski method based on deep learning, referring to Figure 1 , Figure 1 A flowchart of a method for estimating thermal field of single crystal silicon using a Czochralski method based on deep learning is provided in an embodiment of the present application. Figure 1 As shown, the method includes:

[0035] Step S101 , obtaining historical operating condition data during the Czochralski method for preparing single crystal silicon, wherein the historical operating condition data at least includes historical temperature monitoring data of multiple locations in the single crystal silicon growth system.

[0036] In this embodiment, single crystal silicon is prepared by the Czochralski method, and during the preparation process of single crystal silicon, the temperature distribution of limited points inside the thermal field is measured according to the actual working conditions (i.e., historical working condition data collected in real time is obtained). Specifically, the historical working condition data represents the working condition data of the single crystal silicon growth system at a certain moment in the process of preparing single crystal silicon by the Czochralski method. Among them, the historical working condition data at least includes: the temperature values ​​of multiple positions in the single crystal silicon growth system at that moment (i.e., historical temperature monitoring data). The historical temperature monitoring data can be represented as a temperature data set {T(x)} with position information. In addition, the historical working condition data can also include the working condition parameters of the single crystal silicon growth system at that moment, such as: crystal length, crucible temperature, silicon melt loading, crystal rotation speed, crucible rotation speed, pulling speed, argon gas flow rate, crucible size, crystal size, etc.

[0037] In the embodiment of the present application, the single crystal silicon growth system can be any system that uses the Czochralski method to prepare single crystal silicon. In this embodiment, the specific structure, size, and process-related data of the single crystal silicon growth system are not limited.

[0038] Step S102: generating historical thermal field distribution information of the single crystal silicon growth system based on the historical temperature monitoring data.

[0039] Specifically, based on the historical temperature monitoring data (temperature data of multiple locations) of the single crystal silicon growth system collected, the corresponding thermal field distribution can be generated to obtain the historical thermal field distribution information {f(x)} that corresponds to the heat conduction equation. In this embodiment, according to the general numerical simulation method, based on the historical operating data collected in real time, boundary conditions, control equations, etc. can be set to simulate the corresponding thermal field distribution (historical thermal field distribution information) inside the single crystal silicon growth system at that moment. The embodiment of the present application does not impose specific restrictions on the simulation method of the thermal field. Therefore, the historical temperature monitoring data {T(x)} and the historical thermal field distribution information {f(x)} are used as a set of model training data D(x), where x∈R 3 , is the location information, where R 3Represents position information in three-dimensional space.

[0040] It should be noted that the monitoring data obtained in the above steps S101 and S102 may contain noise. This is because the internal thermal field of the single crystal silicon growth system is often at a high temperature of 1800K, which makes it difficult to observe and collect specific information. Therefore, the historical temperature monitoring data collected in real time is the temperature data of a limited number of location points, and there may be measurement errors, which may cause partial deviations in the generated historical thermal field distribution information. If there is noise in D(x), the corresponding thermal field estimation model obtained by training with this data set may not be able to make accurate temperature predictions, that is, the temperature prediction value finally output by the model may not be accurate. Since it is difficult to collect real and accurate temperature data inside the thermal field, it is also impossible to evaluate the accuracy of the thermal field estimation model. In order to solve the above problem, this application proposes a Czochralski single crystal silicon thermal field estimation method based on deep learning, so as to achieve the uncertainty of the model while training a thermal field estimation model that can predict the temperature values ​​of each location.

[0041] Step S103, based on the shared parameters of this round of training, using the historical temperature monitoring data and the historical thermal field distribution information, train the thermal field estimation model to obtain the output results of this round of training, and the output results include: the temperature prediction values ​​of each position point in the single crystal silicon growth system, and the thermal field prediction value of the single crystal silicon growth system.

[0042] Specifically, the thermal field estimation model can adopt the Bayesian-based physical information neural network B-PINNs. Specifically, the thermal field estimation model is a deep neural network, the input data is D(x), that is, the historical temperature monitoring data {T(x)} and the historical thermal field distribution information {f(x)}, and the output data is the temperature prediction value (the temperature of each position point in the single crystal silicon growth system) and the thermal field prediction value (the overall thermal field distribution of the single crystal silicon growth system). The temperature prediction value is expressed as T∈R. ​​The kth hidden layer of the thermal field estimation model can be expressed as ,in is the number of neurons in the kth hidden layer, k = 1, 2, ..., L. The forward propagation process of the thermal field estimation model is:

[0043] (Formula 1);

[0044] (Formula 2);

[0045] in, is the weight matrix, is the bias vector, L is the number of hidden layers, set to 10, is a nonlinear activation function, set to the hyperbolic tangent function, is the output of the k-th layer neuron, is the final output of the deep neural network, i.e., the output (prediction value) of the last layer of neurons, here the Lth layer. In this embodiment, using the historical temperature monitoring data and the historical thermal field distribution information, each time the thermal field estimation model is trained, the output result of this round of training is obtained, which means that the thermal field estimation model has executed a forward propagation process. The heat conduction equation f and boundary condition b in the thermal field estimation model can be expressed as:

[0046] (Formula 3);

[0047] (Formula 4);

[0048] in, is the thermal field control equation, which at least includes the heat conduction equation, is the thermal field boundary condition, It is a thermal field estimation model with a prior distribution The parameter vector of Represents the vector of all unknown parameters in the thermal field estimation model, that is, the shared parameters. When the thermal field estimation model is iteratively trained, the shared parameters of each round of training are If the values ​​are different, the following step S104 is required to determine the shared parameters used in this round of training. The value of .

[0049] Specifically, for:

[0050] (Formula 5);

[0051] in, is the heat source function. is the density, is the specific heat capacity, k is the thermal conductivity, and x, y, and z represent the position coordinate information in the single crystal silicon growth model.

[0052] Step S104 : updating the shared parameters for the next round of training based on the shared parameters of the current round of training and the momentum variable with Gaussian distribution.

[0053] In the embodiment of the present application, when the thermal field estimation model is iteratively trained, the shared parameters of each round of training are The values ​​are different, so after each forward propagation of the thermal field estimation model, it is necessary to determine the shared parameters used in the next round of model training. Specifically, The thermal field estimation model has The parameter vector of the prior distribution. The likelihood function is calculated as follows:

[0054] (Formula 6); where, Represents the prior distribution of historical temperature monitoring data T(x); Represents the prior distribution of historical thermal field distribution information f(x); Represents the prior distribution of the boundary conditions for the thermal field estimation model.

[0055] (Formula 7); where T is the historical temperature monitoring data, is the temperature prediction value of the thermal field estimation model, that is, the final output value, σ T is the uncertainty of the temperature prediction value of the thermal field estimation model, that is, the standard deviation, N T is the number of data in the training set.

[0056] (Formula 8); where f corresponds to Formula 3 above, which is the thermal field control equation, is the thermal field prediction value of the thermal field estimation model, σ f is the uncertainty of the thermal field prediction value of the thermal field estimation model, that is, the standard deviation, N f N is the number of data in the training set. f The number depends on the number of thermal field control equations. The control equation may not be 1 term. If there are n terms, it is n*N t , the same applies to the following.

[0057] (Formula 9); where b is the boundary condition, is the predicted value, σ b is the uncertainty of the thermal field estimation model for boundary conditions, that is, the standard deviation, N b is the number of data in the training set, N b The number of depends on the number of boundary conditions.

[0058] Based on the above formula, we get the posterior distribution:

[0059] (Formula 10);

[0060] Let, shared parameters The prior for follows an exponential distribution:

[0061] (Formula 11);

[0062] in, , is the normalization factor. To give T at any x, from

[0063] Sampling is performed, denoted as { }, then calculate the sample , the former is used to quantify the prediction accuracy, and the latter is used to express the prediction of T(x). The specific sampling process is as follows:

[0064] According to formula 11, The target posterior distribution of is defined as:

[0065] (Formula 12);

[0066] in, (Formula 13);

[0067] In the embodiment of the present application, the Hamiltonian Monte Carlo (HMC) algorithm is used to sample. The HMC algorithm uses the concept of dynamics in a physical system to calculate the future state of the Markov chain. HMC makes the Markov chain converge to a fixed distribution The embodiment of the present application is based on the Bayesian physical information neural network. Bayes is added to the physical information neural network and the HMC algorithm is used to update the network weight parameters. This can measure the uncertainty of the model calculation and has strong robustness.

[0068] In order to The HMC algorithm is used to construct the kinetic energy function from the auxiliary momentum variable r:

[0069] (Formula 14);

[0070] An auxiliary "momentum" variable r with an independent Gaussian distribution is introduced, which is distributed by the target Define a Hamiltonian function , let r be taken from a Gaussian distribution with mean 0 and standard deviation 1.

[0071] In a possible implementation, step S104, updating the shared parameters for the next round of training based on the shared parameters of the current round of training and the momentum variable with a Gaussian distribution, includes:

[0072] Step S1041 : generating candidate shared parameter states according to the shared parameter states of this round of training, wherein the shared parameter states include shared parameters and corresponding momentum variables.

[0073] Specifically, initialization and time step k=1,2,…,N. k is the number of network training times.

[0074] Using the Leapfrog method, let i = 0, 1, ..., M-1. M is the number of time steps set:

[0075] (Formula 15);

[0076] (Formula 16);

[0077] (Formula 17);

[0078] Cycle M times, based on the shared state of this round of training , get the candidate shared parameter state for the next round of training, the candidate shared parameter state includes the candidate shared parameter and the corresponding candidate momentum variables .

[0079] Step S1042: determining an acceptance rate based on the shared parameter status of the current round of training and the candidate shared parameter status.

[0080] In a possible implementation, determining the acceptance rate based on the shared parameter state of the current round of training and the candidate shared parameter state includes:

[0081] The acceptance rate is determined according to the shared parameter state of the current round of training and the candidate shared parameter state according to the following formula:

[0082] (Formula 18);

[0083] Where, α is the acceptance rate, represents the value of the candidate shared parameter state in the Hamiltonian function, represents the value of the shared parameter state of the current round of training in the Hamiltonian function, represents the shared parameters used in the k-1th round of training, represents the momentum variable used in the k-1th round of training, represents the candidate shared parameters in the candidate shared parameter state of the k-th round of training, represents the candidate momentum variable in the candidate shared parameter state of the kth round of training. Step S1043, randomly generate a random number p from the interval of uniform distribution [0, 1].

[0084] Step S1044: When the acceptance rate is less than or equal to the random number, the candidate shared parameter state is determined as the shared parameter state for the next round of training.

[0085] Step S1045 : When the acceptance rate is greater than the random number, the shared parameter state of the current round of training is determined as the shared parameter state of the next round of training.

[0086] Specifically, the Metropolis-Hastings (MH) method is used to select whether to accept the candidate shared parameter state: if p≤α, then let , if p>α, then let , and update k = k + 1. This embodiment simulates Hamiltonian dynamics to discretize Equation 14, alternately updating the variables of the system at the previous moment, and based on the Hamiltonian dynamics calculation trajectory, proposes a new state (a candidate shared parameter state). The MH algorithm is then used to determine whether to accept this state as the current state (i.e., the shared parameter state for the next round of training), thereby improving sampling efficiency.

[0087] Step S105: Calculate a loss function value based on the output result, and optimize the parameters of the thermal field estimation model based on the loss function value. Specifically, each time the thermal field estimation model performs forward propagation to obtain the output result of this round of training, the loss function is calculated based on the difference between the output result and the input data to perform model optimization.

[0088] In a possible implementation, step S105, calculating a loss function value based on the output result, includes:

[0089] Step S1051: Calculate the first loss function value based on the mean absolute error between the temperature prediction value in the output result and the historical temperature monitoring data. Specifically, the first loss function The specific formula for the mean absolute error between the temperature prediction value in the output result and the historical temperature monitoring data in the input data is:

[0090] (Formula 19);

[0091] in, represents the historical temperature monitoring data of the i-th location, Represents the temperature prediction value of the i-th position.

[0092] Step S1052: Calculate a second loss function value based on the mean absolute error between the thermal field prediction value in the output result and the historical thermal field distribution information. The specific calculation formula of the second loss function value is as follows:

[0093] (Formula 20);

[0094] in, represents the historical thermal field distribution information of the i-th position, Represents the thermal field prediction value in the output result of the i-th position.

[0095] Step S1053: Determine the sum of the first loss function value and the second loss function value as the loss function value.

[0096] That is, the final calculated loss function value is: .

[0097] In an embodiment of the present application, a deep neural network is used to approximate the input historical temperature monitoring data T(x). The shared parameters between T(x) and f(x) can optimize learning by minimizing the mean absolute error loss. represents the initial and boundary training data on T(x), Indicates the collocation point corresponding to Equation 5 for the specified f(x).

[0098] Step S106: Based on the shared parameters of the next round of training, the historical temperature monitoring data and the historical thermal field distribution information are reused to perform the next round of training on the thermal field estimation model after parameter optimization until the preset number of training times is reached, and a trained thermal field estimation model and a shared parameter sequence are obtained; the shared parameter sequence represents a sequence in which the shared parameters and momentum variables obtained from the last S rounds of training are arranged in the training order; and S is less than the preset number of training times.

[0099] Specifically, after determining the shared parameters for the next round of training, steps S103 through S106 are repeated. Based on the shared parameters from the next round of training, the thermal field estimation model is trained again using the historical temperature monitoring data and the historical thermal field distribution information (here, the same input data), yielding an output result. The thermal field estimation model is then iteratively trained until the number of training cycles reaches a preset number, resulting in a fully trained thermal field estimation model. In practical applications, the position information of the single crystal silicon growth system is input into the trained thermal field estimation model to obtain the temperature value at the corresponding location as output by the model.

[0100] Generate a Markov chain based on the corresponding shared parameter state and output results obtained from a total of N training times , select the last S items (i.e., the shared parameters obtained from the last S rounds of training) As a shared parameter sequence. In this embodiment, the value of S is much smaller than the preset number of training times.

[0101] Step S107, the average value of the temperature prediction values ​​in the output data obtained from the last S rounds of training is determined as the temperature value of the corresponding position in the single crystal silicon growth system, and the uncertainty measurement value of the trained thermal field estimation model is determined based on the standard deviation of the temperature prediction values ​​in the output data obtained from the last S rounds of training. Specifically, calculate The mean , as the final predicted temperature value at point x. For example, let S be 10. In the output results of the last 10 rounds of model training, the predicted temperature values ​​at point A are 100°C, 110°C, 105°C, 100°C, 100°C, 104°C, 100°C, 110°C, 105°C, and 104°C, respectively. The corresponding final predicted temperature value at point A is 103.8°C.

[0102] In one possible implementation, step S107, determining an uncertainty measure of the trained thermal field estimation model based on a standard deviation of temperature prediction values ​​in output data obtained from the last S rounds of training, includes:

[0103] Step S1071, for a plurality of positions in the single crystal silicon growth system, calculate the standard deviation of the temperature prediction value in the output data obtained from the last S rounds of training corresponding to each position point. For example, 1000 positions can be taken from the single crystal silicon growth system, and the standard deviation of the temperature prediction value of each of the 1000 positions can be calculated. .

[0104] Step S1072: Based on the standard deviations of the multiple position points, an uncertainty measurement value of the trained thermal field estimation model is calculated according to the following formula:

[0105] ;

[0106] in, represents the uncertainty measure of the trained thermal field estimation model, represents the total number of the plurality of location points, Indicates location point The uncertainty measurement value represents the accuracy of the temperature prediction of each location point by the trained thermal field estimation model.

[0107] In one possible implementation, the method further includes:

[0108] When the uncertainty measure value is less than or equal to a preset threshold, a continuous temperature distribution of the single crystal silicon growth system is generated according to the temperature values ​​at each location point.

[0109] When the uncertainty measurement value is greater than the preset threshold, the historical operating condition data is determined to be unqualified data, and new historical operating condition data is recollected to retrain the thermal field estimation model.

[0110] When the uncertainty measure value is less than or equal to a preset threshold (for example, the preset threshold value can be 1), it indicates that the prediction accuracy of the trained thermal field estimation model is sufficiently high, and the noise in the training data used (historical temperature monitoring data and historical thermal field distribution information) is relatively low. Therefore, the output results of the thermal field estimation model can be directly used to generate a continuous thermal field distribution (temperature values ​​at each location). When the uncertainty measure value is greater than the preset threshold, it indicates that the prediction accuracy of the trained thermal field estimation model is low, the model credibility is low, and the training data used contains excessive noise, resulting in poor model training results. In this case, new historical operating condition data can be recollected to retrain the thermal field estimation model and recalculate the model's uncertainty measure value until the uncertainty measure value meets the conditions (the uncertainty measure value is less than or equal to the preset threshold).

[0111] In one possible implementation, the method further includes:

[0112] According to the current process parameters, the solid-liquid interface temperature data of the central area of ​​the silicon melt in the single crystal silicon growth system is obtained.

[0113] The average value of the temperature prediction value of the solid-liquid interface position in the output data obtained from the last S rounds of training is determined as the interface temperature value of the solid-liquid interface position in the single crystal silicon growth system.

[0114] Calculating the temperature difference between the solid-liquid interface temperature data and the interface temperature value;

[0115] The accuracy of the trained thermal field estimation model is evaluated according to the uncertainty measurement value and the temperature difference to obtain an evaluation result.

[0116] Specifically, real-time data from the single crystal silicon growth system (solid-liquid interface temperature data in the center of the silicon melt) is collected. For single crystal silicon growth systems, the system's internal temperature is too high, often making it difficult to accurately measure the temperature values ​​at various locations within the system. However, the temperature of the silicon melt is relatively stable, and the temperature of the solid-liquid interface in the center of the silicon melt is typically 1685K, providing a certain reference value. Then, for the corresponding location (the solid-liquid interface in the center of the silicon melt), the trained thermal field estimation model is used to predict the corresponding temperature value (i.e., the interface temperature value) as the model output. For the same location within the single crystal silicon growth system (the solid-liquid interface in the center of the silicon melt), the collected real-world data (solid-liquid interface temperature data) is compared with the output of the thermal field estimation model (the interface temperature value) to determine the difference between the two. This allows the thermal field estimation model's temperature prediction accuracy for each location to be evaluated from two perspectives: the temperature difference and the uncertainty measure calculated in step S106, facilitating a more accurate evaluation result.

[0117] Based on the actual operating conditions of single-crystal silicon grown by the Czochralski method (i.e., historical operating data), the present application measures the temperature distribution at finite points within the thermal field (i.e., historical temperature monitoring data of multiple locations in the single-crystal silicon growth system). Using a deep learning approach, the present application trains a thermal field estimation model to predict a continuous thermal field temperature distribution (i.e., the temperature values ​​of corresponding locations in the single-crystal silicon growth system). This allows for simple and rapid estimation of the thermal field of single-crystal silicon growth, enabling the acquisition of specific temperature information for each location within the internal thermal field. Furthermore, to address the issue of excessively high internal temperatures in the single-crystal silicon growth system and the inability to determine the accuracy of the trained thermal field estimation model due to the presence of noise in the acquired training data (historical operating data), the present application solves the technical problem of difficulty in measuring the accuracy of the predicted results by calculating the uncertainty of the model output results (an uncertainty measure of the trained thermal field estimation model). This helps improve the accuracy of the evaluated thermal field estimation model and addresses the technical issues of high cost and long cycle times associated with thermal field estimation experiments for single-crystal silicon grown by the Czochralski method, as well as the difficulty in measuring the accuracy of the predicted results.

[0118] The second aspect of the embodiment of the present application further provides a Czochralski method single crystal silicon thermal field estimation device based on deep learning, referring to Figure 2 , Figure 2 A schematic diagram of the structure of a Czochralski single crystal silicon thermal field estimation device is shown. Figure 2 As shown, the device includes:

[0119] A historical operating condition data acquisition module is used to acquire historical operating condition data during the process of preparing single crystal silicon by the Czochralski method, wherein the historical operating condition data at least includes: historical temperature monitoring data of multiple positions in the single crystal silicon growth system;

[0120] a thermal field simulation module, configured to generate historical thermal field distribution information of the single crystal silicon growth system based on the historical temperature monitoring data;

[0121] a model training module for training a thermal field estimation model based on the shared parameters of this round of training and utilizing the historical temperature monitoring data and the historical thermal field distribution information to obtain output results of this round of training, wherein the output results include: temperature prediction values ​​of various locations in the single crystal silicon growth system and thermal field prediction values ​​of the single crystal silicon growth system;

[0122] A shared parameter updating module, configured to update the shared parameters for the next round of training based on the shared parameters of the current round of training and the momentum variable having a Gaussian distribution;

[0123] a parameter optimization module, configured to calculate a loss function value according to the output result, and perform parameter optimization on the thermal field estimation model according to the loss function value;

[0124] an iterative training module for reusing the historical temperature monitoring data and the historical thermal field distribution information based on the shared parameters of the next round of training to perform the next round of training on the thermal field estimation model after parameter optimization until a preset number of training times is reached, thereby obtaining a trained thermal field estimation model and a shared parameter sequence; the shared parameter sequence represents a sequence of shared parameters and momentum variables obtained from the last S rounds of training, arranged in a training order; where S is less than the preset number of training times;

[0125] The uncertainty calculation module is used to determine the average value of the temperature prediction value in the output data obtained from the last S rounds of training as the temperature value of the corresponding position point in the single crystal silicon growth system, and determine the uncertainty measurement value of the trained thermal field estimation model based on the standard deviation of the temperature prediction value in the output data obtained from the last S rounds of training.

[0126] In a possible implementation, the shared parameter updating module includes:

[0127] A candidate shared parameter state generation submodule is used to generate a candidate shared parameter state based on the shared parameter state of this round of training, wherein the shared parameter state includes the shared parameter and the corresponding momentum variable;

[0128] An acceptance rate determination submodule, configured to determine an acceptance rate based on the shared parameter state of the current round of training and the candidate shared parameter state; a random number generation submodule, configured to randomly generate a random number from a uniformly distributed interval of [0, 1];

[0129] A first determining submodule, configured to determine the candidate shared parameter state as the shared parameter state for the next round of training when the acceptance rate is less than or equal to the random number;

[0130] The second determining submodule is configured to determine the shared parameter state of the current round of training as the shared parameter state of the next round of training when the acceptance rate is greater than the random number.

[0131] In a possible implementation, the parameter optimization module includes:

[0132] A first loss function value calculation submodule, configured to calculate a first loss function value based on the mean absolute error between the temperature prediction value in the output result and the historical temperature monitoring data;

[0133] A second loss function value calculation submodule is configured to calculate a second loss function value based on the mean absolute error between the thermal field prediction value in the output result and the historical thermal field distribution information;

[0134] The loss function value calculation submodule is used to determine the sum of the first loss function value and the second loss function value as the loss function value.

[0135] In a possible implementation, the uncertainty calculation module includes:

[0136] a standard deviation calculation submodule, configured to calculate, for a plurality of positions in the single crystal silicon growth system, a standard deviation of a temperature prediction value in output data obtained from the last S rounds of training corresponding to each position point;

[0137] The uncertainty calculation submodule is used to calculate the uncertainty measurement value of the trained thermal field estimation model according to the standard deviation of the multiple position points according to the following formula:

[0138] ;

[0139] in, represents the uncertainty measure of the trained thermal field estimation model, represents the total number of the plurality of location points, Indicates location point The standard deviation at .

[0140] In a possible implementation, the device further includes:

[0141] a temperature distribution generating module, configured to generate a continuous temperature distribution of the single crystal silicon growth system according to the temperature values ​​at each location when the uncertainty measurement value is less than or equal to a preset threshold;

[0142] A retraining module is used to determine the historical operating condition data as unqualified data when the uncertainty measurement value is greater than the preset threshold, and to re-collect new historical operating condition data to retrain the thermal field estimation model.

[0143] In a possible implementation, the device further includes:

[0144] a solid-liquid interface temperature data acquisition module, configured to obtain solid-liquid interface temperature data of a central region of the silicon melt in the single crystal silicon growth system according to current process parameters;

[0145] an interface temperature value calculation module, configured to determine the average value of the temperature prediction values ​​of the solid-liquid interface position in the output data obtained from the last S rounds of training as the interface temperature value of the solid-liquid interface position in the single crystal silicon growth system;

[0146] a temperature difference calculation module, configured to calculate the temperature difference between the solid-liquid interface temperature data and the interface temperature value;

[0147] An evaluation module is used to evaluate the accuracy of the trained thermal field estimation model based on the uncertainty measurement value and the temperature difference to obtain an evaluation result.

[0148] In a possible implementation, the acceptance rate determination submodule includes:

[0149] The acceptance rate calculation unit is configured to determine the acceptance rate according to the shared parameter state of the current round of training and the candidate shared parameter state according to the following formula:

[0150] ;

[0151] Where, α is the acceptance rate, represents the value of the candidate shared parameter state in the Hamiltonian function, represents the value of the shared parameter state of the current round of training in the Hamiltonian function, represents the shared parameters used in the k-1th round of training, represents the momentum variable used in the k-1th round of training, represents the candidate shared parameters in the candidate shared parameter state of the k-th round of training, represents the candidate momentum variable in the candidate shared parameter state for the kth round of training.

[0152] The present application also provides an electronic device, Figure 3 , Figure 3 Schematic diagram of the structure of the electronic device proposed in the embodiment of this application. Figure 3As shown, the electronic device 100 includes: a memory 110 and a processor 120. The memory 110 and the processor 120 are connected via a bus communication. A computer program is stored in the memory 110. The computer program can be run on the processor 120, thereby implementing the steps in a deep learning-based Czochralski single crystal silicon thermal field estimation method disclosed in the first aspect of the embodiment of the present application.

[0153] An embodiment of the present application also provides a computer-readable storage medium having a computer program / instruction stored thereon. When the computer program / instruction is executed by a processor, the steps of a deep learning-based Czochralski single crystal silicon thermal field estimation method disclosed in the first aspect of the embodiment of the present application are implemented.

[0154] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0155] The embodiments of the present application are described with reference to the flowcharts and / or block diagrams of the methods, apparatuses, electronic devices, and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0156] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0157] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0158] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they become aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present invention.

[0159] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "includes," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or terminal device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or elements that are inherent to such process, method, article, or terminal device. In the absence of further restrictions, an element defined by the phrase "comprises a ..." does not exclude the presence of additional identical elements in the process, method, article, or terminal device that includes the element.

[0160] The above is a detailed introduction to the deep learning-based Czochralski single crystal silicon thermal field estimation method, device and product provided by this application. Specific examples are used in this article to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method of this application and its core idea; at the same time, for general technical personnel in this field, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on this application.

Claims

1. A method for estimating thermal field of single crystal silicon using Czochralski method based on deep learning, characterized in that: The method comprises: Acquire historical operating condition data during the Czochralski process for preparing single crystal silicon, the historical operating condition data comprising at least: historical temperature monitoring data of multiple locations in the single crystal silicon growth system; generating historical thermal field distribution information of the single crystal silicon growth system based on the historical temperature monitoring data; Based on the shared parameters of this round of training, using the historical temperature monitoring data and the historical thermal field distribution information, training a thermal field estimation model to obtain output results of this round of training, the output results including: temperature prediction values ​​of various locations in the single crystal silicon growth system, and thermal field prediction values ​​of the single crystal silicon growth system; According to the shared parameters of the current round of training and the momentum variable with Gaussian distribution, the shared parameters of the next round of training are updated; Calculating a loss function value according to the output result, and performing parameter optimization on the thermal field estimation model according to the loss function value; Based on the shared parameters of the next round of training, the historical temperature monitoring data and the historical thermal field distribution information are reused to perform the next round of training on the thermal field estimation model after parameter optimization until a preset number of training times is reached, thereby obtaining a trained thermal field estimation model and a shared parameter sequence; the shared parameter sequence represents a sequence of shared parameters and momentum variables obtained from the last S rounds of training, arranged in a training order; where S is less than the preset number of training times; Determining an average value of the temperature prediction values ​​in the output data obtained from the last S rounds of training as the temperature value of the corresponding position point in the single crystal silicon growth system, and determining an uncertainty measure value of the trained thermal field estimation model based on the standard deviation of the temperature prediction values ​​in the output data obtained from the last S rounds of training; Determining the uncertainty measurement value of the trained thermal field estimation model based on the standard deviation of the temperature prediction value in the output data obtained from the last S rounds of training includes: For a plurality of positions in the single crystal silicon growth system, calculating a standard deviation of a temperature prediction value in output data obtained from the last S rounds of training corresponding to each position; According to the standard deviation of the multiple position points, the uncertainty measurement value of the trained thermal field estimation model is calculated according to the following formula: ； in, represents the uncertainty measure of the trained thermal field estimation model, represents the total number of the plurality of location points, Indicates location point The standard deviation of The method further comprises: generating a continuous temperature distribution of the single crystal silicon growth system according to the temperature values ​​at each location when the uncertainty measure value is less than or equal to a preset threshold; When the uncertainty measurement value is greater than the preset threshold, the historical operating condition data is determined to be unqualified data, and new historical operating condition data is recollected to retrain the thermal field estimation model.

2. The method for estimating thermal field of single crystal silicon using Czochralski method based on deep learning according to claim 1, characterized in that: The updating of the shared parameters for the next round of training based on the shared parameters of the current round of training and the momentum variable with Gaussian distribution includes: Generate candidate shared parameter states based on the shared parameter states of this round of training, where the shared parameter states include shared parameters and corresponding momentum variables; Determine an acceptance rate based on the shared parameter state of the current round of training and the candidate shared parameter state; randomly generate a random number from a uniformly distributed interval of [0, 1]; When the acceptance rate is less than or equal to the random number, determining the candidate shared parameter state as the shared parameter state for the next round of training; When the acceptance rate is greater than the random number, the shared parameter state of the current round of training is determined as the shared parameter state of the next round of training.

3. The method for estimating thermal field of single crystal silicon using Czochralski method based on deep learning according to claim 1, characterized in that: Calculating the loss function value according to the output result includes: Calculating a first loss function value based on the mean absolute error between the temperature prediction value in the output result and the historical temperature monitoring data; Calculating a second loss function value according to the mean absolute error between the thermal field prediction value in the output result and the historical thermal field distribution information; The sum of the first loss function value and the second loss function value is determined as the loss function value.

4. The method for estimating thermal field of single crystal silicon using Czochralski method based on deep learning according to claim 1, characterized in that: The method further comprises: According to the current process parameters, the solid-liquid interface temperature data of the silicon melt center area in the single crystal silicon growth system is obtained; Determine the average value of the temperature prediction value of the solid-liquid interface position in the output data obtained from the last S rounds of training as the interface temperature value of the solid-liquid interface position in the single crystal silicon growth system; Calculating the temperature difference between the solid-liquid interface temperature data and the interface temperature value; The accuracy of the trained thermal field estimation model is evaluated according to the uncertainty measurement value and the temperature difference to obtain an evaluation result.

5. The method for estimating thermal field of single crystal silicon using Czochralski method based on deep learning according to claim 2, characterized in that: The determining of the acceptance rate according to the shared parameter state of the current round of training and the candidate shared parameter state includes: The acceptance rate is determined according to the shared parameter state of the current round of training and the candidate shared parameter state according to the following formula: ； Where, α is the acceptance rate, represents the value of the candidate shared parameter state in the Hamiltonian function, represents the value of the shared parameter state of the current round of training in the Hamiltonian function, represents the shared parameters used in the k-1th round of training, represents the momentum variable used in the k-1th round of training, represents the candidate shared parameters in the candidate shared parameter state of the k-th round of training, represents the candidate momentum variable in the candidate shared parameter state for the kth round of training.

6. A Czochralski single crystal silicon thermal field estimation device based on deep learning, characterized in that: The device is applied to perform the thermal field estimation method of Czochralski single crystal silicon according to any one of claims 1 to 5, comprising: A historical operating condition data acquisition module is used to acquire historical operating condition data during the process of preparing single crystal silicon by the Czochralski method, wherein the historical operating condition data at least includes: historical temperature monitoring data of multiple positions in the single crystal silicon growth system; a thermal field simulation module, configured to generate historical thermal field distribution information of the single crystal silicon growth system based on the historical temperature monitoring data; a model training module for training a thermal field estimation model based on the shared parameters of this round of training and utilizing the historical temperature monitoring data and the historical thermal field distribution information to obtain output results of this round of training, wherein the output results include: temperature prediction values ​​of various locations in the single crystal silicon growth system and thermal field prediction values ​​of the single crystal silicon growth system; A shared parameter updating module, configured to update the shared parameters for the next round of training based on the shared parameters of the current round of training and the momentum variable having a Gaussian distribution; a parameter optimization module, configured to calculate a loss function value according to the output result, and perform parameter optimization on the thermal field estimation model according to the loss function value; an iterative training module for reusing the historical temperature monitoring data and the historical thermal field distribution information based on the shared parameters of the next round of training to perform the next round of training on the thermal field estimation model after parameter optimization until a preset number of training times is reached, thereby obtaining a trained thermal field estimation model and a shared parameter sequence; the shared parameter sequence represents a sequence of shared parameters and momentum variables obtained from the last S rounds of training, arranged in a training order; where S is less than the preset number of training times; The uncertainty calculation module is used to determine the average value of the temperature prediction value in the output data obtained from the last S rounds of training as the temperature value of the corresponding position point in the single crystal silicon growth system, and determine the uncertainty measurement value of the trained thermal field estimation model based on the standard deviation of the temperature prediction value in the output data obtained from the last S rounds of training.

7. An electronic device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps in the method for estimating the thermal field of single crystal silicon using the Czochralski method based on deep learning are implemented.

8. A computer-readable storage medium, characterized in that A computer program / instruction is stored, and when the computer program / instruction is executed by a processor, the steps in the deep learning-based Czochralski single crystal silicon thermal field estimation method according to any one of claims 1 to 5 are implemented.

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