Event-triggered learning-based method for predicting V / G values ​​in semiconductor silicon single crystal growth

Abstract

This application proposes a method for predicting the growth value of semiconductor silicon single crystals based on event-triggered learning, belonging to the field of silicon single crystal growth prediction technology. The method includes the following steps: constructing a value state-space model based on the silicon single crystal growth mechanism; embedding the value state-space model into a long short-term memory network to construct a network model; introducing an attention mechanism into the network model, and sequentially performing weighted fusion processing and physical constraint mapping processing to construct the network model; training and adjusting the network model based on the event-triggered learning mechanism and using historical time-series data of semiconductor silicon single crystal growth values ​​to obtain a trained network model; inputting the current process parameters into the trained network model and predicting the semiconductor silicon single crystal growth value for the next time step. This application can improve the accuracy, real-time performance, and adaptive update capability of predicting the growth value of semiconductor silicon single crystals.

Description

Technical Field

[0001] This application relates to the field of silicon single crystal growth prediction technology, and in particular to a semiconductor silicon single crystal growth method based on event-triggered learning. Value prediction method. Background Technology

[0002] Silicon single crystals are a crucial basic material for the fabrication of integrated circuit chips, and their quality directly affects the electrical performance, yield, and reliability of these chips. Currently, the Czochralski method is the mainstream method for preparing silicon single crystals. Theoretically, during the growth of silicon single crystals, Value (where, This indicates the growth rate of silicon crystals, measured in units of... , This represents the temperature gradient at the silicon crystal growth interface, measured in units of... The point defect type (including vacancy defects and self-interstitial defects) is closely related to the point defect type of silicon crystal, and it is a key parameter determining the quality of silicon single crystals. This can be achieved by adjusting... By adjusting the point defect concentration using a specific value, the bonding of interstitial atoms and atomic vacancies can be promoted, thereby altering the defect types within the silicon crystal and even obtaining low-defect or defect-free silicon single crystals. Therefore, for... Accurate prediction and effective control of values ​​play a crucial role in the quality control of silicon single crystals.

[0003] However, in actual production, the complex structure of the single crystal furnace, the limited sensor placement, and the influence of the high-temperature enclosed environment lead to... The value cannot be directly detected. Existing... The methods for predicting values ​​have the following problems:

[0004] First, a numerical simulation method based on multiphysics coupling is used to indirectly infer the distribution of thermal, flow, and stress fields by calculating them. The variation pattern of the value. Although this method has good physical interpretability and helps to reveal the causal relationship between process parameters and silicon crystal defects, it generally suffers from problems such as high computational complexity, long modeling cycle, and difficulty in adapting to online control. In particular, when facing different furnace types and dynamic operating conditions, the model lacks versatility and real-time performance.

[0005] Secondly, a soft-sensor modeling method based on process data is adopted, by establishing a relationship between measurable process variables (such as heating power, pulling speed, rotation speed, temperature signals, etc.) and... Value mapping models enable online estimation. While this method has advantages such as simplicity and ease of deployment, it generally relies heavily on data quality, is susceptible to noise interference, and lacks constraints on physical mechanisms in complex scenarios. This results in problems such as weak model generalization ability and limited accuracy and stability of prediction results.

[0006] Finally, as the semiconductor industry moves towards larger sizes, higher uniformity, and lower defect densities, the time-varying nonlinear characteristics, furnace structure differences, and unsteady-state operation in the silicon single crystal growth process become increasingly prominent, making the adaptability of single-mechanism simulation or pure data-driven methods under complex operating conditions more and more serious.

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

[0008] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0009] This application provides a semiconductor silicon single crystal growth method based on event-triggered learning. Value prediction method, which includes the following steps:

[0010] Constructed based on silicon single crystal growth mechanism Value state-space model;

[0011] Will The value state-space model is embedded in the long short-term memory network to construct... Network model;

[0012] exist An attention mechanism is introduced into the network model, followed by weighted fusion processing and physical constraint mapping processing to construct... Network model;

[0013] Based on an event-triggered learning mechanism, and utilizing semiconductor silicon single crystal growth Historical time series data of values The network model is trained and adjusted to obtain a well-trained model. Network model;

[0014] Input the current process parameters into the trained... In the network model, and for the next time step of semiconductor silicon single crystal growth. The value is used for prediction.

[0015] Furthermore, based on the silicon single crystal growth mechanism, a structure was constructed... The steps of a value state-space model include:

[0016] By utilizing the temperature gradient at the silicon crystal growth interface and the silicon crystal growth rate, a structure can be constructed. Value parameter model;

[0017] Using the energy conservation equation of silicon melt temperature changing with time and the heat transport equation of silicon crystal growth interface, a system is constructed. Value dynamic heat transfer model;

[0018] according to Value parameter model and Value dynamic heat transfer model, construction Value state-space model.

[0019] Furthermore, The expression for the value parameter model is:

[0020] (1)

[0021] in, Indicates the growth rate of silicon crystals. , Indicates the lifting speed. This indicates the tilt angle between the silicon melt and the silicon crystal at the silicon crystal growth interface. This represents the temperature gradient at the silicon crystal growth interface. , This represents the physical direction in which the temperature at the silicon crystal growth interface decreases along the silicon crystal growth direction, in the growth of semiconductor silicon single crystals. The absolute value of the temperature gradient is used in the value criterion. This represents the heat flux density at the silicon crystal growth interface. , Represents the Stefan-Boltzmann constant. This represents the effective emissivity of the silicon crystal surface. Indicates the temperature of the silicon melt. Indicates the temperature of the silicon crystal. This represents the convective heat transfer coefficient at the silicon crystal growth interface. This indicates the thermal conductivity of silicon crystals;

[0022] The expression for the dynamic heat transfer model is:

[0023] d Q crystal dk = π r 2 m crystal c crystal [a Q melt - Q crystal -λ Q crystal - Q 0 l -2εσ l r Q crystal 4 - Q env 4 -ρ v p L] (2)

[0024] in, Represents the radius of a silicon crystal. Indicates the quality of silicon crystals. This indicates the specific heat capacity of silicon crystals. This indicates the temperature at the top of the silicon crystal. This represents the effective length of the temperature gradient in a silicon crystal. This indicates the ambient temperature inside the single crystal furnace. This indicates the density of silicon crystals. This represents the latent heat of melting of silicon crystals. Indicates the first time;

[0025] The expression for the value state-space model is:

[0026] (3)

[0027] in, Indicates the first time The system state in the value state-space model. x k+1 = [ Q melt , Q crystal ] k+1 T , Indicates the first The state transition matrix at time t, Indicates the first time The system state in the value state-space model. x k = [ Q melt , Q crystal ] k T , Indicates the first The input matrix at time step, Indicates the first time External inputs to the value state-space model u k = [ P host , v p ] k T , This indicates the heating power of the main heater in the single crystal furnace. Indicates transpose. Indicates the first time The output of the state-space model. Indicates the first The output matrix at time 10:00. Indicates the first The direct transfer matrix at time step, express Bias terms in the state-space model.

[0028] Furthermore, the expression for the state transition matrix is:

[0029] (4)

[0030] in, Indicates the first Time and the The time interval of time, Indicates the first The quality of the silicon melt at any given time, Indicates the first The specific heat capacity of the silicon melt at any given time;

[0031] The expression for the input matrix is:

[0032] (5)

[0033] in, Indicates the first The quality of silicon crystals at any given time Indicates the first The specific heat capacity of silicon crystal at any given time;

[0034] The expression for the output matrix is:

[0035] D k =[ -4λcosθ v p k-1 Q melt k-1 3 σε ( Q melt k-1 4 - Q crystal k-1 4 ) 2 4λcosθ v p k-1 Q crystal k-1 3 σε ( Q melt k-1 4 - Q crystal k-1 4 ) 2 ] (6)

[0036] in, Indicates the first The speed of lifting at any moment, Indicates the first The temperature of the silicon crystal at any given time, Indicates the first The temperature of the silicon melt at any given time;

[0037] The expression for the direct transfer matrix is:

[0038] E k =[ β D 1,k λcosθ σε ( Q melt k-1 4 - Q crystal k-1 4 ) 2 ] (7)

[0039] in, Indicates the effect of heating power on the growth of semiconductor silicon single crystals. The influence coefficient of the value , Indicates the first The temperature of the silicon melt at any given time, Indicates the first The heating power of the main heater in the single crystal furnace at any given time. Indicates the first The heating power of the main heater in the single crystal furnace at any given time. Indicates the first The first element of the output matrix at time step 1.

[0040] Furthermore, The value state-space model is embedded in the long short-term memory network to construct... The steps involved in building a network model include:

[0041] Long Short-Term Memory (LSTM) networks consist of cell states. The process of updating cell states involves forgetting old information through a forget gate, inputting new information through an input gate, and outputting the updated cell state through an output gate.

[0042] Replace the weight matrix of the forget gate with the state transition matrix. ;

[0043] The input gate contains activation vectors and candidate value vectors. The weight matrices of both the activation vectors and candidate value vectors are replaced with the input matrix. ;

[0044] Update the cell state;

[0045] The output gate consists of a first variable and a second variable; the weight matrix of the first variable is replaced with the output matrix. The second variable is used as a physical constraint for the Long Short-Term Memory network, and a direct transfer matrix is ​​embedded in the second variable. ,get Network model.

[0046] Furthermore, the expression for the replaced forget gate is:

[0047] (8)

[0048] in, Indicates the first The Forgotten Gate after Time Replacement , express The dimensionality of physical parameters in a network model. Corresponding to silicon melt, Corresponding to silicon crystal, Corresponding to external input, express Activation function Indicates the first The hidden states of the Long Short-Term Memory network at all times. Indicates the first The process parameters are input at all times. This represents the bias term corresponding to the replaced forget gate;

[0049] The expression for the replaced activation vector is:

[0050] (9)

[0051] in, Indicates the first The activation vector after the time step replacement, This represents the bias term corresponding to the replaced activation vector;

[0052] The expression for the replaced candidate value vector is:

[0053] (10)

[0054] in, Indicates the first The candidate value vector after the time-replacement, This represents the hyperbolic tangent activation function. This represents the bias term corresponding to the replaced candidate value vector;

[0055] The updated expression for the cell state is:

[0056] (11)

[0057] in, Indicates the first The constantly updated state of the cell. Indicates the first Cellular state at any given moment;

[0058] The expression for the first variable after the substitution is:

[0059] (12)

[0060] in, Indicates the first The first variable after the time-replacement, This represents the bias term corresponding to the first variable after the replacement;

[0061] The expression for the second variable after the substitution is:

[0062] (13)

[0063] in, Indicates the first The second variable after the time-space replacement;

[0064] The updated cell state is output through the output gate as the following expression:

[0065] (14)

[0066] in, Indicates the first The result of the constantly updated cell state output through the output gate;

[0067] The expression for the network model is:

[0068] (15)

[0069] in, M k = [ M 1,k , M 2,k ] T , Indicates the first The constantly updated cellular state of the silicon melt. Indicates the first The constantly updated cell state of the silicon crystal Indicates the first Cellular state at any given moment Indicates the first time The output of the network model, express The bias term corresponding to the network model.

[0070] Furthermore, in An attention mechanism is introduced into the network model, followed by weighted fusion processing and physical constraint mapping processing to construct... The steps involved in building a network model include:

[0071] initialization Network model;

[0072] An attention layer is introduced, which uses a feedforward neural network to calculate the unnormalized attention score at each time step, and then... The function normalizes each unnormalized attention score to obtain the attention weight at the corresponding time step;

[0073] The expression for the unnormalized attention score is:

[0074] (16)

[0075] in, Indicates the first The unnormalized attention score at each moment, This represents the first linear transformation weight matrix of the attention layer. This represents the hyperbolic tangent activation function. This represents the weight matrix of the second linear transformation of the attention layer. Indicates the first The hidden states of the Long Short-Term Memory network at all times. This represents the bias term corresponding to the weight matrix of the first linear transformation;

[0076] The expression for attention weights is:

[0077] (17)

[0078] in, Indicates the first Attention weight at any moment Indicates the total time;

[0079] The attention weights at each time step are weighted with the hidden state at the corresponding time step to obtain the context vector at the corresponding time step. The context vectors at all time steps are then fused to obtain the global context vector.

[0080] The expression for the global context vector is:

[0081] (18)

[0082] in, Represents the global context vector;

[0083] Perform physical constraint mapping on the global context vector to obtain Predicted value;

[0084] The expression for physical constraint mapping is:

[0085] (19)

[0086] in, express Predicted value Represents the physical constraint parameters of the attention layer. This represents the bias term corresponding to the physical constraint parameters of the attention layer.

[0087] Furthermore, based on an event-triggered learning mechanism, and utilizing semiconductor silicon single crystal growth... Historical time series data of values The network model is trained and adjusted to obtain a well-trained model. The steps involved in building a network model include:

[0088] Loading semiconductor silicon single crystal growth Historical time-series data of values, and The relevant physical matrices of the network model include the state transition matrix. Input matrix Output matrix and direct transmission matrix ;

[0089] Semiconductor silicon single crystals are grown according to a fixed timing length. The historical time-series data of the values ​​are transformed into a sequence sample set, and the sequence sample set is divided into a training set and a test set.

[0090] The sequence sample set contains multiple sequence samples, each containing multiple consecutive feature segments. The next time step is obtained by taking the feature segment from the end of each time step. The measured values ​​serve as labels for the feature segments at that moment;

[0091] initialization The network model should include at least a loss function, an optimizer, and an event-triggered learning mechanism.

[0092] Use the training set to initialize The network model is trained iteratively, based on all the results obtained in each round of training. Predicted value and corresponding The training error between the measured values, The network weights of the network model are adjusted.

[0093] If the training error does not trigger the learning mechanism, training is complete, and the trained data is obtained. Network model;

[0094] If a training error triggers the learning mechanism, the adjustment process is optimized until training is complete and a well-trained system is obtained. Network model.

[0095] Furthermore, the training set is used to initialize the... The network model is trained iteratively, based on all the results obtained in each round of training. Predicted value and corresponding The training error between the measured values, The steps for adjusting the network weights of a network model include:

[0096] Utilize each moment separately Measured values ​​and Predicted value, calculated at the corresponding time. Value-weighted average absolute error; using each time step... The weighted average absolute error is used to calculate the value at the corresponding time. Value error gradient; using the error gradient at each time step. Value error gradient calculation corresponding to the time step Value dynamic threshold; based on all Value-weighted average absolute error, and the corresponding time interval Set dynamic threshold values ​​and design event triggering conditions;

[0097] Using event triggering conditions The parameters of the network model are adjusted to obtain a well-trained network. Network model;

[0098] The performance of the trained A-PI-LSTM network model was evaluated using mean square error, root mean square error, mean absolute percentage error, and coefficient of determination, respectively.

[0099] Furthermore, utilize event triggering conditions to... The parameters of the network model are adjusted to obtain a well-trained network. The steps involved in building a network model include:

[0100] The expression for the event trigger condition is:

[0101] (20)

[0102] in, Indicates the first The event triggering conditions at any given time. Indicates the first Moment Value weighted average absolute error , Indicates the first Weighting coefficients at time points, Indicates the first Moment Measured value Indicates the first Moment Predicted value Indicates the first Moment Value dynamic threshold, , Represents an empirical constant. Indicates an adjustable parameter. Indicates the first Moment Value error gradient, , Indicates the first Moment Value-weighted average absolute error;

[0103] When the event triggering condition is met, extract sequence samples from multiple time points prior to the triggering time;

[0104] Set the total length of the sliding window to And update all sequence samples extracted from before the trigger time in the sliding window respectively to obtain multiple updated sequence samples;

[0105] Keep training time All network weights of the network model are input in batches from all updated sequence samples. In the network model, and utilizing The network model predicts all input update sequence samples and generates corresponding time steps. Predicted value;

[0106] Each moment Predicted values ​​and corresponding The measured values ​​are compared and substituted into the loss function to calculate the prediction error at the corresponding time.

[0107] Using the prediction error at each time step to... The parameters of the network model are adjusted to obtain a well-trained network. Network model.

[0108] This application provides a semiconductor silicon single crystal growth method based on event-triggered learning. Value prediction methods have at least the following beneficial effects:

[0109] (1) This application is constructed based on the silicon single crystal growth mechanism. Value state-space model, and The value-space model is embedded in a long short-term memory network to obtain a physically consistent and mechanistically enhanced result. Network model;

[0110] (2) This application is approved by An attention mechanism is introduced into the network model, followed by weighted fusion processing and physical constraint mapping processing to construct... The network model can adaptively focus on features at key moments, improving the ability to characterize and predict complex time-series data.

[0111] (3) This application is designed to utilize The strategy of using dynamic thresholds for event-triggered learning mechanisms can only... The weighted average absolute error exceeds When the dynamic threshold is reached, the event trigger condition is met, and adjustments are made as needed. The parameters of the network model are updated, thereby achieving a dynamic balance between prediction accuracy and efficiency. Attached Figure Description

[0112] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0113] Figure 1 This application illustrates an event-triggered learning-based semiconductor silicon single crystal growth method in an exemplary embodiment. A schematic diagram illustrating the steps of the value prediction method;

[0114] Figure 2 In the exemplary embodiments shown in this application A schematic diagram of the network model structure;

[0115] Figure 3 In the exemplary embodiments shown in this application A schematic diagram of the network model structure;

[0116] Figure 4 This application demonstrates the use of simulation experiments. Network model Frequency distribution of the error for predicting values;

[0117] Figure 5 This application demonstrates the use of simulation experiments. Network model Frequency distribution of the error for predicting values;

[0118] Figure 6 This application demonstrates the simulation experiment using the method proposed in this application. Network model compared with other network models Comparison of error distribution frequencies in value prediction;

[0119] Figure 7 This application demonstrates the simulation experiment using the method proposed in this application. Network models and other network models, utilizing A sequence sample pair A comparative diagram showing the prediction results obtained by predicting values;

[0120] Figure 8 This application demonstrates the simulation experiment using the method proposed in this application. Network models and other network models, utilizing A sequence sample pair A comparative diagram showing how the prediction error obtained by predicting values ​​changes over time;

[0121] Figure 9 This demonstrates the simulation experiment of the application proposed in this application. A diagram showing the comparison of performance evaluation results between the network model and other network models. Detailed Implementation

[0122] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided to make this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0123] Furthermore, the accompanying drawings are merely illustrative of this application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0124] The following section will discuss an event-triggered learning-based semiconductor silicon single crystal growth method proposed in this example embodiment. The value prediction method will be explained in more detail.

[0125] This example implementation provides a semiconductor silicon single crystal growth method based on event-triggered learning. Value prediction methods, such as Figure 1 As shown, the method may include the following steps:

[0126] Step S101 of this embodiment: Constructing based on the silicon single crystal growth mechanism Value state-space model. Step S101 in this embodiment may include the following sub-steps:

[0127] Sub-step S1011: Utilizing the temperature gradient at the silicon crystal growth interface and the silicon crystal growth rate, construct... Value parameter model.

[0128] In this embodiment, based on the silicon single crystal growth mechanism and according to the heat conduction equation, the temperature gradient at the silicon crystal growth interface can be obtained, and its expression is as follows: ,here This refers to the temperature gradient at the silicon crystal growth interface. .

[0129] In the Czochralski process for preparing silicon single crystals, heat near the silicon crystal growth interface is mainly transferred through conduction and radiation. The expression for the heat flux density at the silicon crystal growth interface is: .

[0130] The growth rate of silicon crystals is determined by the pulling speed. The expression for the growth rate of silicon crystals is: .

[0131] Combining the temperature gradient at the silicon crystal growth interface and the silicon crystal growth rate, we can obtain: ,Will After directly substituting, we get .

[0132] Furthermore, in practice, to simplify the expression, a temperature gradient at the silicon crystal growth interface is usually assumed. It exhibits a linear distribution, and the heat flux density at the silicon crystal growth interface... It is determined by the main parameters of the lifting system. Based on these assumptions, it can be... This can be expressed as a simplified formula related to process parameters: ,in, It is a comprehensive parameter that includes , and wait. This represents the temperature difference between the silicon melt and the silicon crystal at the silicon crystal growth interface. From this, we can obtain... The expression for the value parameter model. The expression for the value parameter model is:

[0133] (1)

[0134] in, Indicates the growth rate of silicon crystals. , Indicates the lifting speed. This indicates the tilt angle between the silicon melt and the silicon crystal at the silicon crystal growth interface. This represents the temperature gradient at the silicon crystal growth interface. , This represents the physical direction in which the temperature at the silicon crystal growth interface decreases along the silicon crystal growth direction, in the growth of semiconductor silicon single crystals. The absolute value of the temperature gradient is used in the value criterion. This represents the heat flux density at the silicon crystal growth interface. , Represents the Stefan-Boltzmann constant. This represents the effective emissivity of the silicon crystal surface. Indicates the temperature of the silicon melt. Indicates the temperature of the silicon crystal. This represents the convective heat transfer coefficient at the silicon crystal growth interface. This indicates the thermal conductivity of silicon crystals.

[0135] use The expression of the value parameter model can quickly evaluate the growth of semiconductor silicon single crystals under different pulling speeds and temperature gradients at the silicon crystal growth interface. This value provides strong guidance for optimizing the silicon crystal growth process.

[0136] Sub-step S1012: Using the energy conservation equation of silicon melt temperature changing with time and the heat transport equation of silicon crystal growth interface, construct... Value dynamic heat transfer model.

[0137] The energy conservation equation for the temperature change of the silicon melt over time is: ,in, This indicates the input power of the heater in the single crystal furnace. This represents the thermal power transferred from the silicon melt to the silicon crystal.

[0138] The heat transfer equation at the silicon crystal growth interface, simulated using Newton's law of cooling, is as follows: ,in, This represents the area of ​​the contact surface between the silicon crystal and the silicon melt. This represents the radius of the silicon crystal.

[0139] Combining the energy conservation equation for the temperature change of the silicon melt over time and the heat transport equation for the silicon crystal growth interface, we can obtain: Further analysis revealed the following: d Q melt dt = 1 m melt c melt [ P in -aπ r 2 ( Q melt - Q crystal )] .

[0140] Silicon crystals receive heat from the molten silicon and dissipate it through conduction and radiation, while simultaneously releasing latent heat of phase transition. Therefore, the total energy conservation equation is:

[0141]

[0142] in, This indicates the internal thermal conductivity of silicon crystals. , This represents the surface radiation of a silicon crystal. , This indicates the release of latent heat during silicon crystal growth. .

[0143] Will , , and Substituting into the total energy conservation equation, we get:

[0144] .

[0145] Therefore, we can conclude that: The expression for the dynamic heat transfer model is:

[0146] d Q crystal dk = π r 2 m crystal c crystal [a Q melt - Q crystal -λ Q crystal - Q 0 l -2εσ l r Q crystal 4 - Q env 4 -ρ v p L] (2)

[0147] in, Represents the radius of a silicon crystal. Indicates the quality of silicon crystals. This indicates the specific heat capacity of silicon crystals. This indicates the temperature at the top of the silicon crystal. This represents the effective length of the temperature gradient in a silicon crystal. This indicates the ambient temperature inside the single crystal furnace. This indicates the density of silicon crystals. This represents the latent heat of melting of silicon crystals. Indicates the first At this moment, the position of the top of the silicon crystal is the height of the silicon crystal above the silicon crystal growth interface. The location.

[0148] Sub-step S1013: According to Value parameter model and Value dynamic heat transfer model, construction Value state-space model.

[0149] Furthermore, this is combined with the approximate processing. Value parameter model and Value dynamic heat transfer model, construction Value state-space model.

[0150] Using the temperatures of the silicon crystal and silicon melt in formula (2) to model energy conservation, a nonlinear temperature state equation can be obtained; using formula (1) to grow semiconductor silicon single crystals The relationship between the temperature of the silicon melt and silicon crystal, and the pulling speed, is expressed as an output equation. The nonlinear temperature equation of state is expanded using a first-order Taylor series and discretized under a fixed period to obtain a linear time-varying equation. Value state-space model.

[0151] The expression for the value state-space model is:

[0152] (3)

[0153] in, Indicates the first time The system state in the value state-space model. x k+1 = [ Q melt , Q crystal ] k+1 T , Indicates the first The state transition matrix at time t, Indicates the first time The system state in the value state-space model. x k = [ Q melt , Q crystal ] k T , Indicates the first The input matrix at time step, Indicates the first time External inputs to the value state-space model u k = [ P host , v p ] k T , This indicates the heating power of the main heater in the single crystal furnace. Indicates transpose. Indicates the first time The output of the state-space model. Indicates the first The output matrix at time 10:00. Indicates the first The direct transfer matrix at time step, express Bias terms in the state-space model.

[0154] Furthermore, the expression for the state transition matrix is:

[0155] (4)

[0156] in, Indicates the first Time and the The time interval of time, Indicates the first The quality of the silicon melt at any given time, Indicates the first The specific heat capacity of the silicon melt at any given time.

[0157] Furthermore, the expression for the input matrix is:

[0158] (5)

[0159] in, Indicates the first The quality of silicon crystals at any given time Indicates the first The specific heat capacity of silicon crystal at any given time.

[0160] Furthermore, the expression for the output matrix is:

[0161] D k =[ -4λcosθ v p k-1 Q melt k-1 3 σε ( Q melt k-1 4 - Q crystal k-1 4 ) 2 4λcosθ v p k-1 Q crystal k-1 3 σε ( Q melt k-1 4 - Q crystal k-1 4 ) 2 ] (6)

[0162] in, Indicates the first The speed of lifting at any moment, Indicates the first The temperature of the silicon crystal at any given time, Indicates the first The temperature of the silicon melt at any given time.

[0163] Furthermore, the expression for the direct transfer matrix is:

[0164] E k =[ β D 1,k λcosθ σε ( Q melt k-1 4 - Q crystal k-1 4 ) 2 ] (7)

[0165] in, Indicates the effect of heating power on the growth of semiconductor silicon single crystals. The influence coefficient of the value , Indicates the first The temperature of the silicon melt at any given time, Indicates the first The heating power of the main heater in the single crystal furnace at any given time. Indicates the first The heating power of the main heater in the single crystal furnace at any given time. Indicates the first The first element of the output matrix at time step 1.

[0166] Step S102 of this embodiment: as follows Figure 2 As shown, The value state-space model is embedded in the long short-term memory network to construct... Network model. Step S102 in this embodiment may include the following sub-steps:

[0167] Long Short-Term Memory (LSTM) networks are a special type of recurrent neural network architecture. Their core advantage lies in effectively addressing the gradient vanishing and gradient exploding problems that traditional recurrent neural networks encounter when processing long sequences of data. LSTM networks utilize a series of gating mechanisms, such as input gates, forget gates, and output gates, to control the flow of information within units. The main advantage of LSTM networks is their ability to effectively capture long-term dependencies in long sequences of data; through gating mechanisms, they can flexibly control the flow of information. However, LSTM networks are entirely data-driven and do not consider the manufacturing processes involved in the Czochralski method for preparing silicon single crystals. The physical properties of the value. In practical industrial applications, physical models can provide crucial prior knowledge, but traditional Long Short-Term Memory (LSTM) networks cannot fully utilize this prior knowledge, resulting in insufficient generalization ability and interpretability of physical models.

[0168] The core of a Long Short-Term Memory (LSTM) network is the cell state, which permeates the entire network and serves to store long-term information. Cell state updates are controlled by three gating mechanisms: the forget gate, the input gate, and the output gate. Specifically: the forget gate determines which information in the cell state needs to be forgotten; its output is a value between 0 and 1, representing the degree to which information is retained. The input gate determines which new information needs to be written into the cell state; it consists of two parts: an activation vector and a candidate value vector. The output gate determines which information in the cell state needs to be output.

[0169] Sub-step S1021: The long short-term memory network includes cell states. The process of updating cell states involves forgetting old information through the forget gate and inputting new information through the input gate. The updated cell state is then output through the output gate.

[0170] Sub-step S1022: Replace the weight matrix of the forget gate with the state transition matrix. .

[0171] Furthermore, the expression for the replaced forget gate is:

[0172] (8)

[0173] in, Indicates the first The Forgotten Gate after Time Replacement , express The dimensionality of physical parameters in a network model. Corresponding to silicon melt, Corresponding to silicon crystal, Corresponding to external input, express Activation function Indicates the first The hidden states of the Long Short-Term Memory network at all times. Indicates the first The process parameters are input at all times. This represents the bias term corresponding to the replaced forget gate.

[0174] Sub-step S1023: The input gate contains activation vectors and candidate value vectors. Replace the weight matrix of the activation vectors and the weight matrix of the candidate value vectors with the input matrix. .

[0175] Furthermore, the expression for the replaced activation vector is:

[0176] (9)

[0177] in, Indicates the first The activation vector after the time step replacement, This represents the bias term corresponding to the replaced activation vector.

[0178] Furthermore, the expression for the replaced candidate value vector is:

[0179] (10)

[0180] in, Indicates the first The candidate value vector after the time-replacement, This represents the hyperbolic tangent activation function. This represents the bias term corresponding to the candidate value vector after replacement.

[0181] Sub-step S1024: Update the cell state.

[0182] Furthermore, the updated expression for the cell state is:

[0183] (11)

[0184] in, Indicates the first The constantly updated state of the cell. Indicates the first The state of a cell at any given moment.

[0185] Sub-step S1025: The output gate includes a first variable and a second variable. Replace the weight matrix of the first variable with the output matrix. The second variable is used as a physical constraint for the Long Short-Term Memory network, and a direct transfer matrix is ​​embedded in the second variable. ,get Network model.

[0186] Furthermore, the expression for the first variable after the substitution is:

[0187] (12)

[0188] in, Indicates the first The first variable after the time-replacement, This represents the bias term corresponding to the first variable after the replacement.

[0189] Furthermore, the expression for the second variable after the substitution is:

[0190] (13)

[0191] in, Indicates the first The second variable after the time-replacement.

[0192] Furthermore, the expression for the updated cell state output through the output gate is:

[0193] (14)

[0194] in, Indicates the first The updated cell state is output through the output gate.

[0195] Furthermore, during silicon crystal growth, the evolution at the silicon crystal growth interface follows specific dynamic laws, which can be utilized using the state transition matrix. Replace the weight matrix of the forget gate; utilize the input matrix. The weight matrices of the activation vector and the candidate value vector are replaced respectively to ensure that the fusion process of the new input information satisfies the fundamental laws of thermodynamics; simultaneously, the output matrix is ​​used... Replace the weight matrix of the first variable of the output gate to achieve state output under physical constraints; to further enhance... The network model's adaptability to the prediction process is assessed by treating the second variable as a physical constraint layer variable and incorporating the direct transfer matrix. The second variable is embedded in the output gate, thereby enabling dynamic adjustment of the silicon single crystal growth rate prediction based on real-time sensor data.

[0196] The expression for the network model is:

[0197] (15)

[0198] in, M k = [ M 1,k , M 2,k ] T , Indicates the first The constantly updated cellular state of the silicon melt. Indicates the first The constantly updated cell state of the silicon crystal Indicates the first Cellular state at any given moment Indicates the first time The output of the network model, express The bias term corresponding to the network model.

[0199] Step S103 of this embodiment: as follows Figure 3 As shown, in An attention mechanism is introduced into the network model, followed by weighted fusion processing and physical constraint mapping processing to construct... Network model. Step S103 in this embodiment may include the following sub-steps:

[0200] Sub-step S1031: Initialization Network model. Utilizing the state transition matrix. Input matrix and output matrix Guided initialization is performed to ensure that the Long Short-Term Memory (LSTM) network structure itself contains prior physical knowledge. The LSM network outputs the hidden states at each time step, which contain multi-scale temporal dependencies of the input sequence.

[0201] Sub-step S1032: Introduce an attention layer. The attention layer uses a feedforward neural network to calculate the unnormalized attention score at each time step, and then... The function normalizes each unnormalized attention score to obtain the attention weight at the corresponding time step.

[0202] Here, the attention layer performs fine-grained weighting on the hidden state sequence output by the Long Short-Term Memory network. The feedforward neural network includes a first linear transformation, a hyperbolic tangent activation function, and a second linear transformation.

[0203] Furthermore, the expression for the unnormalized attention score is:

[0204] (16)

[0205] in, Indicates the first The unnormalized attention score at each moment, This represents the first linear transformation weight matrix of the attention layer. This represents the hyperbolic tangent activation function. This represents the weight matrix of the second linear transformation of the attention layer. Indicates the first The hidden states of the Long Short-Term Memory network at all times. This represents the bias term corresponding to the weight matrix of the first linear transformation.

[0206] Furthermore, the expression for attention weights is:

[0207] (17)

[0208] in, Indicates the first Attention weight at any moment Indicates the total time.

[0209] Sub-step S1033: Weight the attention weights at each time step with the corresponding hidden state to obtain the context vector at that time step. Then, fuse the context vectors from all time steps to obtain the global context vector. This serves to balance long-term dependencies and short-term dynamics.

[0210] Furthermore, the expression for the global context vector is:

[0211] (18)

[0212] in, This represents the global context vector.

[0213] Sub-step S1034: Perform physical constraint mapping on the global context vector to obtain... Predicted values. This mapping is achieved through a linear transformation, whose weight matrix can be derived from the direct transfer matrix. Initialization is performed to deeply integrate prior physical knowledge. Within the network model.

[0214] Furthermore, the expression for physical constraint mapping processing is:

[0215] (19)

[0216] in, express Predicted value Represents the physical constraint parameters of the attention layer. This represents the bias term corresponding to the physical constraint parameters of the attention layer.

[0217] Step S104 of this embodiment: Based on the event-triggered learning mechanism, and utilizing semiconductor silicon single crystal growth Historical time series data of values The network model is trained and adjusted to obtain a well-trained model. Network model. In this embodiment, semiconductor silicon single crystal growth... Value can be abbreviated as Value. Step S104 in this embodiment may include the following sub-steps:

[0218] Sub-step S1041: Loading semiconductor silicon single crystal growth Historical time-series data of values, and The relevant physical matrix of the network model.

[0219] Furthermore, the relevant physical matrices include the state transition matrix. Input matrix Output matrix and direct transmission matrix .

[0220] Sub-step S1042: Growing semiconductor silicon single crystals according to a fixed timing length The historical time-series data of the values ​​are converted into a sequence sample set, which is then divided into a training set and a test set.

[0221] Furthermore, the sequence sample set includes multiple sequence samples, each containing multiple consecutive feature segments. The next time step is obtained by taking the feature segment from each time step. The measured value serves as the label for the feature segment at that moment.

[0222] Sub-step S1043: Initialization The network model includes setting the loss function, optimizer, and event-triggered learning mechanism.

[0223] Sub-step S1044: Use the training set to initialize the... The network model is trained iteratively, based on all the results obtained in each round of training. Predicted value and corresponding The training error between the measured values, The network weights of the network model are adjusted.

[0224] If the training error does not trigger the learning mechanism, training is complete, and the trained data is obtained. Network model;

[0225] If a training error triggers the learning mechanism, the adjustment process is optimized until training is complete and a well-trained system is obtained. Network model.

[0226] Furthermore, the specific process of sub-step S1044 is as follows:

[0227] First, utilize each moment separately. Measured values ​​and Predicted value, calculated at the corresponding time. Value-weighted average absolute error; using each time step... The weighted average absolute error is used to calculate the value at the corresponding time. Value error gradient; using the error gradient at each time step. Value error gradient calculation corresponding to the time step Value dynamic threshold; based on all Value-weighted average absolute error, and the corresponding time interval Use dynamic threshold values ​​to design event triggering conditions.

[0228] Secondly, utilize event triggering conditions to The parameters of the network model are adjusted to obtain a well-trained network. Network model.

[0229] Here, the expression for the event triggering condition is:

[0230] (20)

[0231] in, Indicates the first The event triggering conditions at any given time. Indicates the first Moment Value weighted average absolute error , Indicates the first Weighting coefficients at time points, Indicates the first Moment Measured value Indicates the first Moment Predicted value Indicates the first Moment Value dynamic threshold, , Represents an empirical constant. Indicates an adjustable parameter. Indicates the first Moment Value error gradient, , Indicates the first Moment Value-weighted average absolute error.

[0232] When the event triggering condition is met, extract sequence samples from multiple time points prior to the triggering time;

[0233] Set the total length of the sliding window to And update all sequence samples extracted from before the trigger time in the sliding window respectively to obtain multiple updated sequence samples;

[0234] Keep training time All network weights of the network model are input in batches from all updated sequence samples. In the network model, and utilizing The network model predicts all input update sequence samples and generates corresponding time steps. Predicted value;

[0235] Each moment Predicted values ​​and corresponding The measured values ​​are compared and substituted into the loss function to calculate the prediction error at the corresponding time.

[0236] Using the prediction error at each time step to... The parameters of the network model are adjusted to obtain a well-trained network. Network model.

[0237] Sub-step S1045: Utilize the mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²) respectively. 2 The performance of the adjusted A-PI-LSTM network model was evaluated.

[0238] Step S105 of this embodiment: Input the current process parameters into the trained... In the network model, and for the next time step of semiconductor silicon single crystal growth. The value is used for prediction.

[0239] To verify the event-triggered learning-based semiconductor silicon single crystal growth proposed in this application... To demonstrate the superiority of the value prediction method, the following simulation experiment was conducted.

[0240] The data source for this simulation experiment is the equal-diameter segment of a specific type of single-crystal furnace during the fabrication of 12-inch silicon single crystals. A total of 36,300 sets of sequence data were collected to form the sequence dataset, with a sampling interval of 2 seconds. Gaussian white noise with a mean of zero and a standard deviation of 0.0366 was added to the input sequence data. The level of this Gaussian white noise is approximately the same as that in the sequence dataset. The value is 10% of the mean. This simulation experiment simulates minute measurement errors and system disturbances in a real industrial environment. Due to limitations in online prediction conditions, the event-triggered learning mechanism simulates online data updates in the form of a sliding window, and then executes the entire process of the method proposed in this application.

[0241] In construction In the steps of the value state-space model, Approximately a constant value , without considering Specific heat capacity of silicon melt Values The specific heat capacity of silicon crystal Values The thermal conductivity of silicon crystals Values Stefan-Boltzmann constant Values .

[0242] In construction In the steps of network modeling, The network model serves as the basis for time series data extraction. The input is 10-dimensional process parameters, which are processed through a two-layer stacked structure. The dimension of each hidden layer is set to 64, and the Long Short-Term Memory network outputs the hidden state at each time step.

[0243] The attention layer processes the hidden state at each time step of the Long Short-Term Memory (LSTM) network output. It performs a weighted selection of features from all time steps of the LTM output: First, it generates an unnormalized attention score for each time step through a non-linear transformation, then normalizes it to obtain the weight distribution, ensuring that the sum of the weights at each time step is 1. Second, the weights are designed using an incremental strategy, with the weight sequence as follows: [0.05,0.06,0.07,0.08,0.09,0.10,0.11,0.12,0.13,0.15] This assigns higher weights to process parameters that are closer to the current time, and finally, the weighted sum is used to obtain a 64-dimensional global context vector.

[0244] To balance the global thermal trend with the process parameters closer to the current moment The dual influence of values ​​triggers feature fusion operations: extraction The hidden state of the network model at the last moment is fused with the global context vector output by the attention layer in a fixed weighted ratio, with the global context vector accounting for... This is to adapt to the gradual changes in the thermal field and ensure long-term stability; the process parameters closest to the current moment account for... This is to highlight the immediate impact of parameters such as pull-up speed and power. After fusion, characteristic dimensions are maintained, preserving both the long-term control of temperature gradient by the global thermal field and the direct impact of process parameter adjustments closer to the current moment on the silicon single crystal growth rate.

[0245] The fusion features are mapped to conform to the growth laws of silicon single crystals through a physical constraint layer. Predicted values. The physical constraint layer adopts a linear transformation structure with an input dimension of 64 and an output dimension of 1, meaning it directly corresponds to... The predicted values, whose transformation weights are initialized through the direct transfer matrix.

[0246] In the In the training steps of the network model, based on the requirement of temporal continuity, a fixed time length is used. To construct a sequence sample set. And to sort the sequence sample set according to... The training and test sets are divided proportionally. Then, all sequence samples after the division are converted into adaptation samples. The tensor format computed by the network model is then used to sort all sequence samples in the training set according to the batch size. The data loading is encapsulated, and sequence samples are read in batches during training to balance computational efficiency and memory usage. During the loading process, the sequence samples in the training set are randomly shuffled to enhance the adaptability to feature segments of samples from different time series.

[0247] Four types of models were compared using simultaneous initialization: the traditional Recurrent Neural Network (RNN) model, the standard Long Short-Term Memory (LSTM) network model, and the model proposed in this application. Network models and Network model. And migrate all models to a specified computing device. Specifically, for the network model proposed in this application... Network models and All network models require the state transition matrix as input. Input matrix Output matrix and direct transmission matrix By guiding the initialization of gating parameters through a physical matrix, both models are ensured to incorporate the thermodynamic laws of silicon single crystal growth from the initial training stage. Traditional recurrent neural network models and standard long short-term memory network models both employ standard parameter initialization methods, serving as a benchmark without physical constraints.

[0248] Unified configuration of core training rules: Mean squared error loss is used as the loss function, adaptive momentum optimizer is used as the optimizer, and the learning rate is set according to the configuration. This approach balances the stability of parameter updates with convergence speed. An event-triggered learning mechanism is implemented to address the differences in characteristics between various models. Network models and Because network models incorporate physical constraints, they require a longer period to adapt to the fusion of data and physical laws; therefore, a longer timeframe is set. Network model set wheel, Network model set Rounds, and the loss reduction threshold is set to Traditional recurrent neural network models and standard long short-term memory network models both use relatively short periods. The standard descent threshold is set to [value]. This avoids the waste caused by overfitting and ineffective training.

[0249] The total number of training rounds is set according to the configuration. Initiate iterative training, with each round of training divided into a training segment and a testing phase. The specific process is as follows:

[0250] Training phase: Switch all models to training mode, read batches of training set data, and calculate the model's response to the input sequence through forward propagation. Forecast values, adjusted uniformly The predicted value and the shape of the label are then calculated using a loss function. Predicted values ​​and The deviation of the measured values. Backpropagation is performed based on the loss values ​​to solve for the gradients of the parameters of each layer, and the model parameters are updated through the optimizer. The average loss of the training set is calculated after each round.

[0251] Testing phase: Switch all models to evaluation mode, turn off gradient calculation to reduce resource consumption, perform forward propagation on the complete sequence data of the test set, calculate and record the overall loss of the test set; at the same time, compare the current test loss with the historical best loss. If the current test loss is lower than the historical best loss and the decrease exceeds the set threshold, update the best loss and save the parameters of the current model to ensure that the model state with the best generalization ability is retained.

[0252] After each training and testing round, an event trigger condition is determined: if no loss reduction meets the requirements during testing, the number of rounds without improvement is accumulated; when the count reaches the threshold of the number of rounds without improvement for the corresponding model, the training of the model is terminated immediately to avoid overfitting caused by continuous iteration.

[0253] After training, all sequence data from the training process of each model are systematically saved: the training loss and test loss of each model in each round are recorded, and the best test loss of each model is labeled, forming a result set containing the training trajectories of the four types of models. It is ensured that all saved optimal model parameter files are structurally complete and that the parameters are completely consistent with the optimal state during the training process, providing a directly loadable benchmark model for subsequent online prediction.

[0254] When determining event triggering conditions, set key parameters: the base threshold is set to... The sliding window length is set to The forced trigger time interval is set to At any given moment. In calculation When calculating the error gradient, it is necessary to... Value error gradient amplification This is multiplied to enhance signal sensitivity. In the calculation of dynamic threshold value, The value error gradient influence coefficient is set to Error weighting is adopted The linearly increasing weights, while... Dynamic threshold constraint on value In between, thus avoiding extremes. Value error gradient leads to The dynamic threshold value deviates from the physical range.

[0255] Event triggering conditions are determined according to The sampling interval is executed in seconds: First, collect the current time. Value weighted average absolute error and corresponding amplified Value error gradient, maintain sliding window length is When the sliding window is full, extract the one with the closest trigger time. indivual Calculated by the average value of the error gradient The value is a dynamic threshold, which is then calculated using incremental weights. The weighted average absolute error of the value, if The weighted average absolute error is greater than If the value is a dynamic threshold, it is determined that the event triggering condition has been updated and the triggering time is recorded, and the sliding window is cleared; if The weighted average absolute error is less than or equal to If the value is a dynamic threshold, then no update is needed. Furthermore, for each cumulative... An update is forcibly triggered at a specific time to prevent models from deviating from the process rules due to long periods without updates.

[0256] When performing incremental updates, if the event triggering condition is met or the cumulative threshold is reached... At any given moment, the system will immediately stop the current prediction process, switch to incremental update mode, and optimize the extraction and preprocessing of time series data to ensure that the updated time series data conforms to the actual process disturbances.

[0257] exist Figure 4 In the middle, the maximum can be obtained Predicted error not exceeding Approximately in the dataset The average value The average value is This indicates The network model has been precisely trained and can be used in practical applications, providing a guarantee for the preparation of silicon single crystals by the Czochralski method.

[0258] exist Figure 5 In the middle, the maximum can be obtained Predicted error not exceeding Approximately in the dataset The average value The average value is This indicates that in After adding an attention mechanism to the network model, we get The network model has superior performance.

[0259] from Figure 6 It can be seen that the traditional recurrent neural network model has the highest error distribution frequency, followed by the standard long short-term memory network model. The error frequency of the network model is lower than the previous two, while The network model has the lowest error frequency among the four models. (Explanation) Network model The value prediction effect is the best and the accuracy is the highest.

[0260] like Figure 7 and Figure 8 As shown, the time ending at the trigger time is used to extract the preceding time. Complete time-series data from the initial time point to the trigger time. A length of [length missing] is used. The sliding window for extraction The time series data is filtered as follows: data segments containing sensor outliers within the sliding window are removed, and small missing values ​​are filled with the mean of adjacent sliding windows to ensure that the time series data quality meets the model input requirements. Sliding window updates follow the principle of removing the oldest data segment. Add the latest time series data. Rules for time series data, initial sliding window used Filling in to maintain temporal continuity. Figure 7 and Figure 8 As can be seen, this application constructs The network model represents a significant improvement over other models. The results obtained from the network model are more consistent The measured values ​​are accurate, and the error fluctuations are small.

[0261] After cleaning Each time series data is categorized according to The input format of the network model is constructed by the input sequence and Measured value sample pairs: truncated continuous values At that moment The dimensional process features are used as the input sequence, and the 1st process feature is taken as the input sequence. At that moment The measured value is used as the prediction target, and finally generated Group of valid samples.

[0262] In Long Short-Term Memory (LSTM) networks, the core parameters initialized by the physical matrix are set to be fixed and non-updatable, including those determined by the state transition matrix. Embedded forget gate weights; derived from the input matrix Initialize the input gate weights; determined by the output matrix. The associated output gate weights. These parameters directly embody the thermodynamics of silicon single crystal growth, and their gradients are forcibly fixed during the update process, without participating in backpropagation.

[0263] Only parameters related to process fluctuation adaptation are set to be fine-tunable, including: linear transformation parameters of the attention layer; linear transformation weights and bias terms of the physical constraint layer; bias terms of cell gates in the long short-term memory network that are not covered by the physical matrix, and fine-tuning the intensity of local feature fusion.

[0264] The optimizer uses the training data. Adaptive optimizer, learning rate adjusted to offline stage This reduces the magnitude of parameter updates, preventing drastic parameter fluctuations caused by small increments of time-series data; the loss function used is the mean squared error loss function, consistent with the training loss function, and quantized. Predicted values ​​and The squared deviation of the measured values ​​ensures the consistency of loss calculation; the number of training rounds is fixed. wheel.

[0265] First, The network model switches from evaluation mode to training mode, enabling gradient calculation; subsequently... The incremental sequence samples are input into the model in single batches, and forward propagation is performed: the input sequence samples are processed by a long short-term memory network to extract temporal features, the attention layer focuses on the perturbation-related moments, and the output... 3D fusion features, then mapped through a physical constraint layer to Predicted values; comparison Predicted values ​​and After calculating the loss using the measured values, backpropagation is performed to solve for the gradient only for the finely tuned parameters. Finally, the non-zero gradient parameters are updated through the optimizer to complete one round of training. After each iteration, immediately switch the model to evaluation mode, disable gradient calculation, clear the temporary gradient cache from the training process, and restore online operation. Prediction process.

[0266] After the incremental update is completed, its effectiveness must be ensured through immediate verification, and the parameter retention method must be standardized to support subsequent process traceability and model iteration. The last sample in the incremental sequence should be selected. Using the time series data as the validation set, the updated [data] is calculated. The mean squared error loss and root mean square error of the network model are calculated and compared with the metrics before the update. If the mean squared error loss decreases... Or the root mean square error is reduced If the update is deemed valid, the updated parameters are retained; if there is no improvement, the update is deemed invalid, and the system is immediately switched back to the model parameters before the update to avoid affecting subsequent predictions.

[0267] Figure 9 of This is a bar chart comparing the performance of four models using mean squared error. The traditional recurrent neural network model... for The standard long short-term memory network model for , Network Model for , Network Model Reduce to .

[0268] Figure 9 of This is a bar chart comparing the performance of four models using root mean square error, with the traditional recurrent neural network model showing the best performance. for The standard long short-term memory network model for , Network Model for , Network Model Reduce to .

[0269] Figure 9 of This is a bar chart comparing the performance of four models using mean absolute percentage error (MASE). The traditional recurrent neural network model... for The standard long short-term memory network model for , Network Model for , Network Model Reduce to .

[0270] Figure 9 of This is a bar chart comparing the performance of four models using the coefficient of determination. The traditional recurrent neural network model... for The standard long short-term memory network model for , Network Model for , Network Model Rise to .

[0271] This indicates that the application made in this application The network model performs better.

[0272] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0273] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0274] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application.

[0275] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. An event-triggered learning-based semiconductor silicon single crystal growth method Value prediction method, characterized in that, The method includes the following steps: Constructed based on silicon single crystal growth mechanism Value state-space model, including: By utilizing the temperature gradient at the silicon crystal growth interface and the silicon crystal growth rate, a structure can be constructed. Value parameter model; Using the energy conservation equation for the temperature change of the silicon melt over time and the heat transport equation for the silicon crystal growth interface, a... Value dynamic heat transfer model; According to the above Value parameter model and the Value dynamic heat transfer model, construct the Value state-space model; The The value state-space model is embedded in the long short-term memory network to construct... Network model; In the An attention mechanism is introduced into the network model, followed by weighted fusion processing and physical constraint mapping processing to construct... Network model; Based on an event-triggered learning mechanism, and utilizing semiconductor silicon single crystal growth Historical time series data of the value for the The network model is trained and adjusted to obtain the trained version. Network model; Input the current process parameters into the trained... In the network model, and for the next time step of the semiconductor silicon single crystal growth... The value is used for prediction.

2. The semiconductor silicon single crystal growth based on event-triggered learning as described in claim 1 Value prediction method, characterized in that, The The expression for the value parameter model is: (1) in, Indicates the growth rate of silicon crystals. , Indicates the lifting speed. This indicates the tilt angle between the silicon melt and the silicon crystal at the silicon crystal growth interface. This represents the temperature gradient at the silicon crystal growth interface. , This represents the physical direction in which the temperature at the silicon crystal growth interface decreases along the silicon crystal growth direction, in the growth of semiconductor silicon single crystals. The absolute value of the temperature gradient is used in the value criterion. This represents the heat flux density at the silicon crystal growth interface. , Represents the Stefan-Boltzmann constant. This represents the effective emissivity of the silicon crystal surface. Indicates the temperature of the silicon melt. Indicates the temperature of the silicon crystal. This represents the convective heat transfer coefficient at the silicon crystal growth interface. This indicates the thermal conductivity of silicon crystals; The The expression for the dynamic heat transfer model is: (2) in, Represents the radius of a silicon crystal. Indicates the quality of silicon crystals. This indicates the specific heat capacity of silicon crystals. This indicates the temperature at the top of the silicon crystal. This represents the effective length of the temperature gradient in a silicon crystal. This indicates the ambient temperature inside the single crystal furnace. This indicates the density of silicon crystals. This represents the latent heat of melting of silicon crystals. Indicates the first time; The The expression for the value state-space model is: (3) in, Indicates the first time The system state in the value state-space model. , Indicates the first The state transition matrix at time t, Indicates the first time The system state in the value state-space model. , Indicates the first The input matrix at time step, Indicates the first time External inputs to the value state-space model , This indicates the heating power of the main heater in the single crystal furnace. Indicates transpose. Indicates the first time The output of the state-space model. Indicates the first The output matrix at time 10:

00. Indicates the first The direct transfer matrix at time step, express Bias terms in the state-space model.

3. Semiconductor silicon single crystal growth based on event-triggered learning as described in claim 2 Value prediction method, characterized in that, The expression for the state transition matrix is: (4) in, Indicates the first Time and the The time interval of time, Indicates the first The quality of the silicon melt at any given time, Indicates the first The specific heat capacity of the silicon melt at any given time; The expression for the input matrix is: (5) in, Indicates the first The quality of silicon crystals at any given time Indicates the first The specific heat capacity of silicon crystal at any given time; The expression for the output matrix is: (6) in, Indicates the first The speed of lifting at any moment, Indicates the first The temperature of the silicon crystal at any given time, Indicates the first The temperature of the silicon melt at any given time; The expression for the direct transmission matrix is: (7) in, Indicates the effect of heating power on the growth of semiconductor silicon single crystals. The influence coefficient of the value , Indicates the first The temperature of the silicon melt at any given time, Indicates the first The heating power of the main heater in the single crystal furnace at any given time. Indicates the first The heating power of the main heater in the single crystal furnace at any given time. Indicates the first The first element of the output matrix at time step 1.

4. Semiconductor silicon single crystal growth based on event-triggered learning as described in claim 2 Value prediction method, characterized in that, The The value state-space model is embedded in the long short-term memory network to construct... The steps involved in building a network model include: The long short-term memory network includes cell states. The cell state is updated by forgetting old information through a forget gate and inputting new information through an input gate. The updated cell state is then output through an output gate. Replace the weight matrix of the forget gate with the state transition matrix. ; The input gate includes an activation vector and a candidate value vector. The weight matrix of the activation vector and the weight matrix of the candidate value vector are both replaced with the input matrix. ; Update the cell state; The output gate includes a first variable and a second variable, and the weight matrix of the first variable is replaced with the output matrix. The second variable is used as a physical constraint of the Long Short-Term Memory network, and the direct transfer matrix is ​​embedded in the second variable. , to obtain the Network model.

5. Semiconductor silicon single crystal growth based on event-triggered learning according to claim 4 Value prediction method, characterized in that, The expression for the replaced forget gate is: (8) in, Indicates the first The Forgotten Gate after Time Replacement , express The dimensionality of physical parameters in a network model. Corresponding to silicon melt, Corresponding to silicon crystal, Corresponding to external input, express Activation function Indicates the first The hidden states of the Long Short-Term Memory network at all times. Indicates the first The process parameters are input at all times. This represents the bias term corresponding to the replaced forget gate; The expression for the replaced activation vector is: (9) in, Indicates the first The activation vector after the time step replacement, This represents the bias term corresponding to the replaced activation vector; The expression for the replaced candidate value vector is: (10) in, Indicates the first The candidate value vector after the time-replacement, This represents the hyperbolic tangent activation function. This represents the bias term corresponding to the replaced candidate value vector; The updated expression for the cell state is: (11) in, Indicates the first The constantly updated state of the cell. Indicates the first Cellular state at any given moment; The expression for the first variable after the replacement is: (12) in, Indicates the first The first variable after the time-replacement, This represents the bias term corresponding to the first variable after the replacement; The expression for the second variable after the substitution is: (13) in, Indicates the first The second variable after the time-time substitution; The updated cell state is expressed as follows through the output gate: (14) in, Indicates the first The result of the constantly updated cell state output through the output gate; The The expression for the network model is: (15) in, , Indicates the first The constantly updated cellular state of the silicon melt. Indicates the first The constantly updated cell state of the silicon crystal Indicates the first Cellular state at any given moment Indicates the first time The output of the network model, express The bias term corresponding to the network model.

6. Semiconductor silicon single crystal growth based on event-triggered learning as described in claim 1 Value prediction method, characterized in that, The above An attention mechanism is introduced into the network model, followed by weighted fusion processing and physical constraint mapping processing to construct... The steps involved in building a network model include: Initialize the Network model; An attention layer is introduced, which uses a feedforward neural network to calculate the unnormalized attention score at each time step, and then... The function normalizes each of the unnormalized attention scores to obtain the attention weights at the corresponding time points; The expression for the unnormalized attention score is: (16) in, Indicates the first The unnormalized attention score at each moment, This represents the first linear transformation weight matrix of the attention layer. This represents the hyperbolic tangent activation function. This represents the weight matrix of the second linear transformation of the attention layer. Indicates the first The hidden states of the Long Short-Term Memory network at all times. This represents the bias term corresponding to the weight matrix of the first linear transformation; The expression for the attention weight is: (17) in, Indicates the first Attention weight at any moment Indicates the total time; The attention weights at each time step are weighted together with the hidden state at the corresponding time step to obtain the context vector at the corresponding time step. The context vectors at all time steps are then fused to obtain the global context vector. The expression for the global context vector is: (18) in, Represents the global context vector; The global context vector is processed by the physical constraint mapping to obtain... Predicted value; The expression for the physical constraint mapping process is: (19) in, express Predicted value Represents the physical constraint parameters of the attention layer. This represents the bias term corresponding to the physical constraint parameters of the attention layer.

7. Semiconductor silicon single crystal growth based on event-triggered learning as described in claim 6 Value prediction method, characterized in that, The event-triggered learning mechanism, and the use of semiconductor silicon single crystal growth Historical time series data of the value for the The network model is trained and adjusted to obtain the trained version. The steps involved in building a network model include: Loading the semiconductor silicon single crystal growth Historical time-series data of the value, and the aforementioned The relevant physical matrix of the network model, the relevant physical matrix including the state transition matrix The input matrix The output matrix and the direct transmission matrix ; The semiconductor silicon single crystal is grown according to a fixed time sequence. The historical time-series data of the values ​​are transformed into a sequence sample set, and the sequence sample set is divided into a training set and a test set. The sequence sample set contains multiple sequence samples, and each sequence sample contains multiple consecutive feature segments. The sequence sample at each time step is used to obtain the sequence at the next time step after the completion of the feature segment at each time step. The measured value serves as the label for the feature segment at that moment; Initialize the The network model should include at least a loss function, an optimizer, and the event-triggered learning mechanism. Using the training set to initialize the The network model is trained iteratively, based on all the results obtained in each round of training. Predicted value and corresponding The training error between the measured values, for the The network weights of the network model are adjusted. If the training error does not trigger the event-triggered learning mechanism, training is complete, and the trained [learning mechanism] is obtained. Network model; If the training error triggers the event-triggered learning mechanism, the adjustment process is optimized until training is complete, resulting in a well-trained system. Network model.

8. Semiconductor silicon single crystal growth based on event-triggered learning according to claim 7 The method for predicting values ​​is characterized by, The training set is used to initialize the... The network model is trained iteratively, based on all the results obtained in each round of training. Predicted value and corresponding The training error between the measured values, for the The steps for adjusting the network weights of a network model include: Using the data at each time point Measured values ​​and the stated Predicted value, calculated at the corresponding time. Value-weighted average absolute error; using the values ​​at each time step... The weighted average absolute error is used to calculate the value at the corresponding time. Value error gradient; using the aforementioned values ​​at each time step Value error gradient calculation corresponding to the time step Value dynamic threshold; based on all stated Value-weighted average absolute error, and the corresponding time value. Set dynamic threshold values ​​and design event triggering conditions; Using the event triggering conditions to the The parameters of the network model are adjusted to obtain the trained model. Network model; The performance of the trained A-PI-LSTM network model was evaluated using mean square error, root mean square error, mean absolute percentage error, and coefficient of determination, respectively.

9. Semiconductor silicon single crystal growth based on event-triggered learning according to claim 8 The method for predicting values ​​is characterized by, The event triggering condition is used to... The parameters of the network model are adjusted to obtain the trained model. The steps involved in building a network model include: The expression for the event triggering condition is: (20) in, Indicates the first The event triggering conditions at any given time. Indicates the first Moment Value weighted average absolute error , Indicates the first Weighting coefficients at time points, Indicates the first Moment Measured value Indicates the first Moment Predicted value Indicates the first Moment Value dynamic threshold, , Represents an empirical constant. Indicates an adjustable parameter. Indicates the first Moment Value error gradient, , Indicates the first Moment Value-weighted average absolute error; When the event triggering condition is met, extract sequence samples from multiple time points prior to the triggering time; Set the total length of the sliding window to And update all the sequence samples extracted from before the trigger time in the sliding window respectively to obtain multiple updated sequence samples; Preserve the training time All network weights of the network model are input into the updated sequence samples in batches. In the network model, and utilizing the aforementioned The network model predicts all the input update sequence samples and generates the corresponding time steps. Predicted value; The statement at each time point Predicted values ​​and corresponding The measured values ​​are compared and substituted into the loss function to calculate the prediction error at the corresponding time. The prediction error at each time step is used to analyze the... The parameters of the network model are adjusted to obtain the trained model. Network model.

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