Temperature Control Method, Device, Equipment and Storage Medium of Semiconductor Equipment

Abstract

The present invention relates to a temperature control method, device, equipment and storage medium for semiconductor equipment. The method includes: performing finite element mesh division and modal coordinate transformation on multiple temperature control regions of the semiconductor equipment to obtain a temperature control region dynamic model; collecting measurement data of temperature sensors and performing time-frequency domain transformation to generate a temperature prediction data sequence; performing Gaussian mixture modeling to obtain a prior distribution and obtain a temperature parameter probability distribution; performing sub-domain division on the temperature control range to obtain a feature mapping matrix between temperature domains; calculating a thermal coupling coefficient matrix between temperature ranges based on the temperature control region dynamic model, constructing a temperature control objective function in combination with the temperature prediction data sequence and the feature mapping matrix between temperature domains, and solving using a model predictive control algorithm to obtain a temperature control quantity sequence. The present invention improves the accuracy and dynamic response speed of temperature control, and ensures the stability of temperature control and the energy utilization efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of semiconductor equipment, and particularly to a temperature control method, device, equipment and storage medium for a semiconductor equipment. Background Art

[0002] With the development of semiconductor manufacturing processes towards smaller line widths and higher precision, higher requirements are put forward for the accuracy, stability and dynamic response characteristics of temperature control. Traditional temperature control methods for semiconductor equipment mainly adopt single-region PID control or simple multi-region decoupling control strategies, which are difficult to effectively handle the thermal coupling effect between multiple temperature zones, resulting in problems such as insufficient temperature control accuracy and slow dynamic response.

[0003] Existing temperature control modeling methods for semiconductor equipment mostly adopt simplified lumped parameter models or empirical models, which cannot accurately describe the distribution characteristics and dynamic evolution process of the temperature field. At the same time, due to the characteristics of strong nonlinearity, multi-variable coupling and time-varying parameters in the semiconductor equipment temperature control system, traditional model predictive control methods have problems of insufficient robustness in dealing with model uncertainties and external disturbances, and it is difficult to meet the requirements of high-precision and fast response for temperature control. Summary of the Invention

[0004] The main purpose of the present invention is to provide a temperature control method, device, equipment and storage medium for a semiconductor equipment, which improves the accuracy and dynamic response speed of temperature control, and ensures the stability of temperature control and energy utilization efficiency.

[0005] To achieve the above purpose, the present invention provides a temperature control method for a semiconductor equipment, including the following steps:

[0006] Perform finite element mesh division and modal coordinate transformation on multiple temperature control regions of the semiconductor equipment, perform eigenvalue analysis on the modal equation and select the first two modes to establish a multi-temperature zone coupled heat transfer equation set, and obtain a temperature control region dynamic model;

[0007] Collect the measurement data of the temperature sensors of the semiconductor equipment and perform time-frequency domain transformation to generate a temperature distribution characteristic image, extract spatio-temporal characteristics through a dual-channel deep learning model, and obtain a temperature prediction data sequence;

[0008] Perform Gaussian mixture modeling on the temperature parameters of the temperature control region dynamic model to obtain a prior distribution, take the logarithm of the product of the prior distribution and the measurement likelihood function, and use a double Gaussian process model to calculate the posterior probability and the evidence lower bound to obtain a temperature parameter probability distribution;

[0009] According to the temperature parameter probability distribution, divide the temperature control range into sub-domains, construct an optimization objective function including a prediction error term and an inter-domain difference term, and solve it by the gradient descent method to obtain a temperature inter-domain feature mapping matrix;

[0010] Calculate the thermal coupling coefficient matrix between temperature zones based on the temperature control region dynamic model, construct a temperature control objective function by combining the temperature prediction data sequence and the temperature domain feature mapping matrix, and solve to obtain a temperature control quantity sequence using a model predictive control algorithm.

[0011] The present invention also provides a temperature control device for a semiconductor device, including:

[0012] A transformation module for performing finite element mesh division and modal coordinate transformation on multiple temperature control regions of the semiconductor device, performing eigenvalue analysis on the modal equation, and selecting the first two modes to establish a multi-temperature zone coupled heat transfer equation set to obtain a temperature control region dynamic model;

[0013] An extraction module for collecting the measurement data of the temperature sensors of the semiconductor device and performing time-frequency domain transformation to generate a temperature distribution feature image, and extracting spatio-temporal features through a dual-channel deep learning model to obtain a temperature prediction data sequence;

[0014] A calculation module for performing Gaussian mixture modeling on the temperature parameters of the temperature control region dynamic model to obtain a prior distribution, taking the logarithm of the product of the prior distribution and the measurement likelihood function, and calculating the posterior probability and the evidence lower bound using a dual Gaussian process model to obtain a temperature parameter probability distribution;

[0015] A construction module for sub-region dividing the temperature control range according to the temperature parameter probability distribution, constructing an optimization objective function including a prediction error term and an inter-domain difference term, and solving to obtain a temperature domain feature mapping matrix through the gradient descent method;

[0016] A solution module for calculating the thermal coupling coefficient matrix between temperature zones based on the temperature control region dynamic model, constructing a temperature control objective function by combining the temperature prediction data sequence and the temperature domain feature mapping matrix, and solving to obtain a temperature control quantity sequence using a model predictive control algorithm.

[0017] The present invention also provides a computer device, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the steps of the method described in any one of the above are implemented.

[0018] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method described in any one of the above are implemented.

[0019] In summary, the technical solution provided by the present invention uses the parametric global modal method to establish a dynamic model of the temperature control region. Through the dimensionality reduction processing of the first two dominant modes, the model complexity is effectively reduced, the calculation efficiency is improved, and a high modeling accuracy is maintained. A dual-channel deep learning model structure is proposed to extract and fuse the spatial and temporal features of the temperature field respectively, making full use of the spatio-temporal information of the temperature data and improving the accuracy and real-time performance of temperature prediction. The variational Bayesian inference method is introduced to perform probabilistic modeling on the temperature parameters, and the posterior probability is accurately estimated in combination with the double Gaussian process model, enhancing the model's adaptability to parameter uncertainties. A feature mapping method based on sub-domain division is designed to achieve feature alignment under different working conditions by optimizing the inter-domain differences, improving the generalization performance of the temperature control system under multiple working conditions. A model predictive control strategy considering the thermal coupling effect is constructed to achieve coordinated control of multiple temperature zones through rolling horizon optimization and decoupling allocation, improving the accuracy and dynamic response speed of temperature control. An adaptive control mechanism based on temperature state constraints realizes the reasonable allocation of the power of heaters and coolers, ensuring the stability of temperature control and the energy utilization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a schematic diagram of the steps of the temperature control method for a semiconductor device in an embodiment of the present invention;

[0021] Figure 2 is a block diagram of the structure of the temperature control device for a semiconductor device in an embodiment of the present invention;

[0022] Figure 3 is a schematic block diagram of the structure of a computer device in an embodiment of the present invention.

[0023] The implementation, functional features and advantages of the objectives of the present invention will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0025] Referring to Figure 1 , this embodiment provides a temperature control method for a semiconductor device, including the following steps:

[0026] S1, perform finite element mesh division and modal coordinate transformation on multiple temperature control regions of the semiconductor device, perform eigenvalue analysis on the modal equation, and select the first two modes to establish a multi-temperature zone coupled heat transfer equation set to obtain a dynamic model of the temperature control region;

[0027] Among them, finite element meshing is performed on multiple temperature control areas of semiconductor equipment, and tetrahedral mesh units are used to divide the temperature control area. The temperature field is interpolated by piecewise linear functions, and the continuous temperature distribution field is discretized to form a discretized set of equations for the temperature field. The discretized set of equations is Fourier transformed, and the different heat conduction characteristics in the temperature field are separated by frequency domain analysis. At the same time, the temperature distribution term, heat source term and boundary condition term are explicitly added to the heat conduction equation to fully describe the heat conduction behavior in the temperature control area. The temperature field is extended to a generalized coordinate representation using the separation variable method. The Lagrange transform is used to transform from physical space to modal space, and the modal dynamics equation is constructed. The dynamic characteristics of the temperature field are represented as a set of orthogonal modal functions, which describe the heat transfer behavior at different orders. Based on the modal dynamics equation, the eigenvalues ​​and eigenvectors are solved to obtain the solution space structure of the modal equation. In order to reduce the complexity of the model and highlight the main characteristics, the modal contribution analysis method is used to evaluate the importance of each mode. Only the first two modes are selected as the dominant modes, and the secondary effects of the higher-order modes are ignored. Based on this, the reduced-order temperature dynamics equation is constructed. The reduced-order temperature dynamics equation is processed by Euler discretization, and the time continuous model is converted into a discrete time model to obtain a coupled heat transfer equation group containing heat conduction terms and convective heat transfer terms between temperature zones. This equation group can effectively describe the heat exchange between each temperature control zone and the temperature change within the zone. The temperature distribution coefficient and heat conduction coefficient in the coupled heat transfer equation group are calibrated. The parameter calibration is completed through experimental data or numerical simulation to generate a calibrated coefficient matrix. Based on the calibrated coefficient matrix, the temperature zone heat balance equation is established to clarify the thermodynamic relationship between each temperature control zone, and the balance equation is used to numerically calculate the heat flux and temperature gradient of each zone. Through numerical calculation, the internal temperature distribution of each temperature control zone is obtained, and the thermal coupling behavior between each temperature control zone is analyzed to obtain the dynamic response characteristics of the temperature zone. The response characteristics include important information such as heat transfer efficiency, response speed and stability between temperature control areas. Based on the dynamic response characteristics of the temperature interval and the established coupled heat transfer equations, a complete dynamic model of the temperature control area is constructed.

[0028] S2, collects temperature sensor measurement data of semiconductor devices and performs time-frequency domain transformation to generate temperature distribution feature images, extracts spatiotemporal features through a dual-channel deep learning model, and obtains a temperature prediction data sequence;

[0029] Specifically, real-time temperature measurement data is collected by temperature sensors arranged in each temperature control area of the semiconductor device. The collected data is processed by fast Fourier transform and wavelet transform. The fast Fourier transform is used to convert the original time series into a frequency-domain signal, revealing the spectral characteristics of the temperature change inside the temperature control area, while the wavelet transform can capture the characteristics of the local time domain and frequency domain simultaneously, so as to obtain the time-frequency characteristics with time resolution and frequency resolution. Through these two processing methods, a time-frequency feature matrix containing multi-dimensional features is constructed. The time-frequency feature matrix is normalized to map the data values to a fixed range, eliminating the influence of different dimensions and scales on model training. Through matrix reconstruction operation, the normalized time-frequency feature matrix is converted into structured two-dimensional image data, forming a temperature distribution feature image, which reflects the temperature distribution law and its dynamic changes in the temperature control area. The temperature distribution feature image is input into the residual network channel of the dual-channel deep learning model. The architecture of this residual network channel contains 5 residual units, and each residual unit consists of two convolutional layers and an identity mapping path. The design of the residual unit aims to solve the problem of gradient disappearance or explosion in deep neural networks while retaining the feature information of deeper layers. Through continuous convolutional operations and identity mapping, the residual network channel can extract the spatial features in the temperature distribution image layer by layer and form a high-dimensional spatial feature vector to describe the distribution pattern of temperature inside the device and the correlation between regions. At the same time, the original temperature sensor measurement data is directly input into the recurrent neural network channel of the dual-channel deep learning model. In this channel, a 3-layer bidirectional long short-term memory network is constructed, with 64 memory units in each layer. The design of the bidirectional long short-term memory network extracts the forward and backward time-dependent features from the time series of data, solving the problem of insufficient learning of long sequence information by traditional recurrent neural networks. Through the gating operation of the memory unit on the data, this network channel can capture the dynamic time characteristics of the temperature change in the temperature control area and generate a time series feature vector. The spatial feature vector and the time series feature vector are subjected to feature fusion operation to obtain a high-dimensional fusion feature vector. Through this process, the features extracted by different channels can be complementary at the semantic level, improving the prediction accuracy and generalization ability of the model. The fused feature vector is subjected to sequence prediction operation, and the output layer of the deep learning model is used to generate the prediction result, obtaining a complete temperature prediction data sequence.

[0030] S3. Perform Gaussian mixture modeling on the temperature parameters of the dynamic model of the temperature control area to obtain the prior distribution, take the logarithm of the product of the prior distribution and the measurement likelihood function, and use the double Gaussian process model to calculate the posterior probability and the lower bound of the evidence to obtain the temperature parameter probability distribution;

[0031] It should be noted that for the key temperature parameters in the dynamic model of the temperature control region, including the temperature distribution coefficient and the heat conduction coefficient, a multi-component Gaussian mixture model is established. The Gaussian mixture model is a probability density model that approximates complex probability distributions through multiple weighted Gaussian distributions. To perform optimal estimation of the weights and parameters (means, covariance matrices) of the Gaussian components, the Expectation-Maximization (EM) algorithm is used to optimize the model. In the EM algorithm, the posterior probability of each Gaussian component for the data is calculated through the Expectation step (E-step) given the current model parameters, and then the model parameters are updated through the Maximization step (M-step) to maximize the log-likelihood value of the model. By repeatedly iterating this process, the global optimal solution is gradually approximated to obtain the prior probability distribution of the temperature parameters, which describes the initial uncertainty of the temperature parameters in the system. The temperature sensor measurement data of the semiconductor device is input into the dynamic model of the temperature control region to calculate the temperature response, so as to capture the dynamic impact of the sensor data on the model output. A measurement likelihood function is constructed based on the measurement data to characterize the probability distribution characteristics of the observed data given the model parameters. The prior probability distribution of the temperature parameters is combined with the measurement likelihood function, the product of the two is calculated, and the logarithm of the product is taken to obtain the log-posterior function. The log-posterior function is input into a first Gaussian process model for probability regression calculation to fit the posterior probability distribution. The Gaussian process is a non-parametric Bayesian model that can model the uncertainty in the function space and is suitable for approximating complex probability distributions. Through Gaussian process regression, a fitting function of the posterior probability is obtained, which describes the variation law of the posterior probability in the entire parameter space. This posterior probability fitting function is used as input and passed to a second Gaussian process model for variational inference. The goal of variational inference is to approximately model the posterior distribution by optimizing an evidence lower bound function. The evidence lower bound function ensures through the constrained optimization process that the estimation of the posterior distribution not only satisfies the form of the log-posterior function but also minimizes the uncertainty of the model prediction as much as possible. After completing the variational inference of the posterior probability, a Bayesian optimization method is used to construct a composite objective function that includes the posterior probability term and the evidence lower bound term. The construction of the composite objective function aims to comprehensively consider the accuracy of the model (posterior probability) and complexity control (evidence lower bound). By numerically iteratively solving this objective function, the parameters of the variational posterior distribution are obtained, which reflect the best probability description of the temperature parameters under the current observation conditions. Stochastic gradient optimization is performed on the parameters of the variational posterior distribution, and the model parameters are continuously updated by maximizing the evidence lower bound function. Stochastic gradient optimization is an efficient iterative optimization method that can achieve fast convergence in large-scale data and complex models. Through this process, the optimal posterior distribution parameters are finally obtained, which achieve a balance between model complexity and fitting to the observed data. Based on the optimal posterior distribution parameters, the probability distribution of the temperature parameters is reconstructed.

[0032] S4. Subdivide the temperature control range into sub-domains according to the probability distribution of temperature parameters, construct an optimization objective function that includes a prediction error term and an inter-domain difference term, and solve it by the gradient descent method to obtain the temperature inter-domain feature mapping matrix;

[0033] Specifically, perform probability density threshold analysis on the probability distribution of temperature parameters. Reasonably divide the temperature control range according to the characteristics of the probability distribution. By setting a certain probability density threshold and combining the equal-interval division method, divide the temperature control range into multiple sub-domains. Each sub-domain represents a specific temperature control area or range. Perform kernel function transformation on the temperature data within each temperature control sub-domain. Map the sub-domain data to a high-dimensional feature space by applying a non-linear kernel function (such as a Gaussian kernel or a polynomial kernel) to generate sub-domain feature data that can capture complex relationships. Divide the sub-domain feature data into a source domain feature set and a target domain feature set. The source domain feature set represents the original feature distribution, while the target domain feature set represents the feature distribution that needs to be aligned or mapped. On this basis, perform standardization processing on these two feature sets respectively to eliminate the differences in feature scale and dimension, and generate a normalized feature matrix. Based on the normalized feature matrix, calculate the maximum mean discrepancy statistic. This is a non-parametric method for measuring the distance between two distributions. By calculating the deviation of the feature means in the high-dimensional space, quantify the feature distribution differences between sub-domains. According to the calculation results, construct an inter-domain feature distance metric function to obtain an inter-sub-domain feature difference matrix, which reflects the inconsistency of feature distributions between sub-domains. Establish an optimization objective function based on the feature difference matrix. This objective function consists of two parts: one is the mean square error term, which is used to measure the prediction error after feature mapping; the other is the maximum mean difference term, which is used to minimize the difference in feature distributions between sub-domains. Use the backpropagation algorithm to perform gradient descent calculation on the sub-domain optimization objective function. In each iteration, adjust the parameters according to the gradient direction of the objective function to make the optimization process gradually approach the global optimal solution, and obtain a feature transformation parameter matrix to capture the best mapping relationship between the source domain and target domain features. Input the feature transformation parameter matrix into a three-layer fully connected neural network for feature mapping. The design of the fully connected neural network uses the rectified linear unit (ReLU) as the activation function for each layer to ensure that the model has good non-linear fitting ability and gradient propagation stability. Through multi-layer feature combination and non-linear transformation, the network can learn deeper mapping relationships from the input feature transformation parameter matrix and generate the final temperature inter-domain feature mapping matrix.

[0034] S5. Calculate the thermal coupling coefficient matrix between temperature intervals based on the temperature control region dynamic model, construct a temperature control objective function by combining the temperature prediction data sequence and the temperature inter-domain feature mapping matrix, and use the model predictive control algorithm to solve for the temperature control quantity sequence.

[0035] Among them, energy integration calculation is carried out on the coupled heat transfer equation set in the dynamic model of the temperature control region, the heat flux density and temperature gradient parameters between adjacent temperature intervals are extracted, and the heat transfer relationship between temperature control regions is quantified. By combining the law of conservation of energy and the heat conduction equation, the heat flux interaction effect between regions is accurately described. In the energy integration calculation, the directional distribution of the heat flux density and the coupled convection heat transfer and heat conduction effects caused by the temperature gradient are calculated, and these parameters are organized into a heat coupling coefficient matrix between temperature intervals. The heat coupling coefficient matrix is a multi-dimensional linear algebraic structure that numerically reflects the thermodynamic interaction intensity between different temperature control regions. Based on the heat coupling coefficient matrix between temperature intervals, the dynamic transfer relationship between the temperature field and the heat flux field is linearized, and the thermodynamic state equation between temperature intervals is established. This equation locally approximates the non-linear transfer relationship as a linear form, enabling the model to simplify the computational complexity while ensuring accuracy. The core of the thermodynamic state equation is to describe the heat balance relationship of each temperature control region and the dynamic temperature influence of adjacent regions on this region under the action of heat coupling. The difference analysis is carried out between the temperature prediction data sequence obtained based on the dual-channel deep learning model and the actual process set temperature, and the temperature prediction error sequence is calculated. It reflects the deviation between the current temperature control state and the target temperature control requirements. Based on the temperature prediction error sequence, forward recursive calculation is carried out on the thermodynamic state equation between temperature intervals, and the temperature state constraint conditions are gradually deduced. At the same time, the inter-domain feature mapping matrix of the temperature domain is introduced into the above calculation process, and the temperature state constraint conditions are processed through inter-domain feature conversion. The role of the inter-domain feature mapping matrix of the temperature domain is to capture the feature correlation between different temperature control regions, project the regional characteristics into a unified control parameter space, and generate a multi-temperature zone control parameter matrix. Based on the multi-temperature zone control parameter matrix, a temperature control objective function for the quadratic programming problem is constructed. The construction process of this objective function comprehensively considers the dual requirements of minimizing temperature deviation and optimizing energy consumption, and at the same time embeds the heat coupling effect and dynamic constraint conditions between temperature intervals into the objective function. The rolling horizon optimization method is used to solve the temperature control objective function, and an optimized sequence of control quantities is obtained. The rolling horizon optimization method is an optimization technique for model predictive control. By dynamically adjusting the optimization time window, the system state and prediction error are updated in real time, so as to generate an optimal control strategy at each moment. Decoupling and distribution calculation is carried out on the preliminary optimized sequence of control quantities to adapt to the specific implementation mechanism of independent heating or cooling of each temperature control region in the actual semiconductor device, and finally a temperature control quantity sequence is generated.

[0036] By performing interpolation calculations on the temperature prediction data sequence and the process-set temperature curve, a temperature prediction deviation matrix with a unified time resolution is generated, which reflects the difference between the predicted temperature and the target temperature at each time point and in each temperature control region. Based on this deviation matrix, the temperature change rate of each temperature control region is calculated, and a temperature gradient vector is constructed. The temperature gradient vector captures the dynamic characteristics of heat transfer between regions by describing the rate of temperature change within the temperature control region. Combining with the thermodynamic state equation between temperature intervals, a state space transformation is performed on the temperature gradient vector and the thermodynamic state equation. The dynamic behavior of the system is represented by state variables to facilitate the treatment of the dynamic coupling characteristics of the system in a linear or non-linear manner. Through the transformation, a thermodynamic system state equation that can describe the evolution of the thermodynamic state of the entire system is constructed. Within the specified prediction time domain, a recursive operation is performed on this thermodynamic system state equation to generate a temperature state prediction sequence. The recursive operation is an iterative process that gradually predicts the future temperature dynamics by deriving the state at the next moment based on the state at the current moment and the state equation. To ensure the actual execution ability of the temperature control device, the temperature state prediction sequence is combined with the physical limit conditions of the device. According to the temperature state prediction sequence, the output power limit conditions of the heater and the cooler are set to generate an actuator constraint vector. This vector reflects the maximum and minimum output ranges of the temperature control actuator under the current working conditions, ensuring that the temperature control operation does not exceed the bearing capacity of the device. The actuator constraint vector and the temperature state prediction sequence are combined and calculated to generate a temperature control region constraint matrix. The temperature control region constraint matrix is block-processed according to the temperature zones to extract the extreme boundary temperatures within each temperature control region. The extreme boundary temperatures are key indicators to ensure the safety and effectiveness of temperature control in each region, and can reflect the minimum and maximum possible values of temperature changes within each region. Based on these boundary extremes, a temperature zone dynamic constraint equation is constructed to describe the dynamic behavior constraints of each temperature control region within the specified prediction time domain. To improve the calculation efficiency and consistency, a normalization transformation is performed on the constructed temperature zone dynamic constraint equation. By performing non-dimensional processing on the temperature states and constraint conditions of each region, the temperature control standards of different regions are unified to generate the final temperature state constraint conditions.

[0037] In an example, finite element mesh division and modal coordinate transformation are performed on multiple temperature control regions of a semiconductor device, eigenvalue analysis is performed on the modal equation, and the first two modes are selected to establish a multi-temperature zone coupled heat transfer equation set to obtain a temperature control region dynamic model, including:

[0038] Tetrahedral mesh element division is performed on multiple temperature control regions of the semiconductor device, and piecewise linear functions are used for nodal interpolation calculation of the temperature field to obtain a discretized temperature field equation set;

[0039] Perform Fourier transform on the discretized equations of the temperature field, construct the heat conduction equations including temperature distribution terms, heat source terms and boundary condition terms, establish the generalized coordinates of the temperature field using the method of separation of variables, and obtain the modal dynamic equations through Lagrangian transformation;

[0040] Solve the eigenvalues and eigenvectors based on the modal dynamic equations, select the first two dominant modes using the modal contribution rate analysis method, construct the reduced-order temperature dynamic equations, perform Euler discretization on the reduced-order temperature dynamic equations, and establish the coupled heat transfer equations including heat conduction terms and convective heat transfer terms in the temperature intervals;

[0041] Calibrate the parameters of the temperature distribution coefficients and thermal conductivity coefficients in the coupled heat transfer equations to obtain the calibrated coefficient matrix, establish the heat balance equations in the temperature zones based on the calibrated coefficient matrix, perform numerical calculations on the heat flux density and temperature gradient in each temperature control region, and obtain the dynamic response characteristics between the temperature zones;

[0042] Construct the dynamic model of the temperature control region based on the dynamic response characteristics between the temperature zones and the coupled heat transfer equations.

[0043] In this example, tetrahedral mesh element division is performed on multiple temperature control regions of the semiconductor device, the temperature control regions are divided into several small elements, and the nodes of each element are interpolated through piecewise linear functions to obtain the discretized equations of the temperature field. For each tetrahedral element, set its node temperature as ( ) and describe the temperature at any point within the element through the piecewise linear function : :

[0044] ;

[0045] where is the shape function corresponding to node within the element and satisfies . By performing mesh division on the entire temperature control region and using the interpolation method, the temperature distribution at each point within the region is obtained. Perform Fourier transform on the discretized equations of the temperature field to construct the heat conduction equations including temperature distribution terms, heat source terms and boundary condition terms. Fourier transform helps to transform the analysis from the time domain to the frequency domain, better capturing the heat transfer characteristics of the system. In the frequency domain, the general form of the heat conduction equation is:

[0046] ;

[0047] where is the density of the material, is the specific heat capacity, is the temperature, is the thermal conductivity, is the heat source term per unit volume, represents the gradient operator. Through Fourier transform, the time term is transformed into a frequency-domain transformation to assist in analyzing the thermal response of the system. The method of separation of variables is used to establish a generalized coordinate system for the temperature field, and the modal dynamics equation is obtained through Lagrangian transformation. The basic idea of the method of separation of variables is to express the temperature field as the product of a spatial component and a time component, i.e.:

[0048] ;

[0049] where, is the eigenfunction of the spatial part, is the function of the time part. Lagrangian transformation is used to transform the coordinates and physical quantities in the equation, thus transforming the equation into a modal dynamics equation:

[0050] ;

[0051] where, is the mass matrix, is the stiffness matrix, is the second-order time derivative of temperature, representing the acceleration of temperature. By solving this equation, the eigenvalues and eigenvectors of the temperature control region are obtained, reflecting the dominant modes of the system. To simplify the problem, the first two dominant modes are selected through modal contribution rate analysis, and these two modes represent the most important heat transfer characteristics in the system. After selecting the dominant modes, a reduced-order temperature dynamics equation is constructed, which can reduce the computational amount and effectively capture the main heat response behavior of the temperature control system. After Euler discretization of the reduced-order temperature dynamics equation, the numerical solution of the temperature control system is obtained, and the form of the discrete equation is:

[0052] ;

[0053] where, is the time step is the change in temperature at is the temperature at the next moment, and are matrices obtained through modal analysis. This equation is used for numerical iterative solution of the dynamic temperature change of the temperature control system. After obtaining the reduced-order temperature dynamics equation, a coupled heat transfer equation set including the heat conduction term and the convective heat transfer term in the temperature range is established. The coupled heat transfer equation needs to consider both the heat conduction and convective heat transfer effects simultaneously, and these two effects jointly determine the temperature distribution in the temperature control region. The form of the coupled heat transfer equation is:

[0054] ;

[0055] where, is the fluid velocity field, which represents the influence of heat convection. By solving this equation, the dynamic response of the temperature in the temperature control area is obtained. Based on the coupled heat transfer equations, the parameters are calibrated to obtain the calibration coefficient matrix of the temperature control area. By comparing with experimental data or measurement data, the thermal conductivity coefficient, specific heat capacity and other parameters are adjusted to make the numerical model more consistent with the actual system. After parameter calibration, the heat balance equation of the temperature zone is established:

[0056] ;

[0057] in, Indicates temperature control area The heat balance equation is used to calculate the heat exchange and temperature gradient between each temperature control zone to obtain the dynamic response characteristics of the system. The dynamic response characteristics of the temperature interval are obtained by numerically calculating the heat flux and temperature gradient of each temperature control zone. These response characteristics reflect the degree of thermal coupling between different temperature control zones and the contribution of each zone to the overall temperature change. Based on the response characteristics and the coupled heat transfer equations, a dynamic model of the temperature control zone is constructed.

[0058] In one example, the temperature sensor measurement data of the semiconductor device is collected and transformed in the time-frequency domain to generate a temperature distribution feature image. The spatiotemporal features are extracted through a dual-channel deep learning model to obtain a temperature prediction data sequence, including:

[0059] Collect the temperature sensor measurement data of each temperature control area of ​​the semiconductor equipment, perform fast Fourier transform and wavelet transform on the temperature sensor measurement data, and obtain the time-frequency feature matrix;

[0060] The time-frequency feature matrix is ​​normalized and reconstructed to generate a temperature distribution feature image, which is then input into the residual network channel of the dual-channel deep learning model. The residual network channel contains five residual units, each of which consists of two convolutional layers and an identity mapping to obtain a spatial feature vector.

[0061] The temperature sensor measurement data is input into the recurrent neural network channel of the dual-channel deep learning model. The recurrent neural network channel contains three layers of bidirectional long short-term memory networks. Each layer of the bidirectional long short-term memory network contains 64 memory units to obtain a time series feature vector.

[0062] A feature fusion operation is performed on the spatial feature vector and the time series feature vector to obtain a fused feature vector, and a sequence prediction is performed on the fused feature vector to obtain a temperature prediction data sequence.

[0063] In this example, the temperature sensor data of each area is collected and preprocessed by various time-frequency analysis methods. Assume that each temperature control area of ​​the device has a temperature sensor, and the data measured by the temperature sensor is , where represents the index of the region, represents time. Each temperature sensor generates a temperature sequence that varies with time. Fast Fourier transform and wavelet transform are performed on these temperature sequences to extract the time-frequency domain features. The form of the Fourier transform is:

[0064] ;

[0065] where is the temperature data in the frequency domain, is the frequency. Through the Fourier transform, the spectrum of the temperature signal is obtained, revealing the changes of the temperature signal at different frequencies. The wavelet transform is used to further analyze the local changes of the signal in time and frequency. The formula of the wavelet transform is:

[0066] ;

[0067] where is the wavelet basis function, is the scale parameter, is the translation parameter, is the mother wavelet function. The wavelet transform helps the system capture the instantaneous frequency changes of the temperature signal. Through the data processed by the Fourier transform and the wavelet transform, the time-frequency feature matrix is obtained. This matrix contains the features analyzed in the time and frequency domains. Normalization and matrix reconstruction operations are performed on the time-frequency feature matrix. Normalization can eliminate the scale differences in the measurement data of temperature sensors between different temperature control regions, enabling the data to be processed on the same scale. Based on the normalized feature matrix, matrix reconstruction is performed to generate the temperature distribution feature image , which reflects the temperature distribution at different time and frequency scales. The temperature distribution feature image is input into the residual network channel of the dual-channel deep learning model. This channel contains 5 residual units, and each residual unit consists of two convolutional layers and an identity mapping. The basic structure of the residual network can effectively solve the problem of gradient disappearance in deep neural networks. In each residual unit, the input is processed through two convolutional layers, and the output of the convolutional layer is Conv , and then added to the input to obtain the output , that is:

[0068] ;

[0069] where and are the two convolutional layers respectively, is the input, Is the output. Through residual learning, the model can learn the spatial feature vector of the temperature distribution , which reflects the spatial temperature distribution pattern of different regions. At the same time, the original measurement data of the temperature sensor is input into the recurrent neural network (RNN) channel of the dual-channel deep learning model. This channel contains 3 layers of bidirectional long short-term memory networks (Bi-LSTM), and each layer of Bi-LSTM contains 64 memory units. The characteristic of Bi-LSTM is that it can capture both the forward and backward information of time series data, so as to better model the temporal dependence relationship. The basic calculation formula of Bi-LSTM is:

[0070] ;

[0071] where, is the hidden state at the current moment, is the input at the current moment, is the hidden state at the previous moment. In this way, the model can learn the time series features from the historical temperature data and obtain the temporal feature vector . The spatial feature vector and the temporal feature vector are subjected to feature fusion operation to obtain the fused feature vector . The fused feature vector is input into the subsequent prediction network for predicting the temperature sequence. Assuming the goal is to predict the temperature data at the future moment, a regression model is used to train the fused features, and finally the temperature prediction sequence is obtained, that is:

[0072] ;

[0073] MLP is a multi-layer perceptron, which outputs the temperature prediction result based on the fused feature vector .

[0074] In one example, a Gaussian mixture model is built for the temperature parameters of the temperature control region dynamic model to obtain the prior distribution. The logarithm of the product of the prior distribution and the measurement likelihood function is taken, and the posterior probability and the lower bound of the evidence are calculated using a dual Gaussian process model to obtain the temperature parameter probability distribution, including:

[0075] A multi-component Gaussian mixture model is established for the temperature distribution coefficient and the heat conduction coefficient in the temperature control region dynamic model. The weights and parameters of the Gaussian components are iteratively optimized by the expectation maximization algorithm to obtain the prior probability distribution of the temperature parameters;

[0076] Input the temperature sensor measurement data of the semiconductor device into the temperature control region dynamic model to calculate the temperature response, construct the measurement likelihood function, perform a logarithmic transformation on the product of the prior probability distribution of the temperature parameter and the measurement likelihood function to obtain the logarithmic posterior function;

[0077] Input the logarithmic posterior function into the first Gaussian process model for probability regression calculation to obtain the posterior probability fitting function, and input the posterior probability fitting function into the second Gaussian process model for variational inference to obtain the evidence lower bound function;

[0078] Adopt the Bayesian optimization method to construct a composite objective function containing the posterior probability term and the evidence lower bound term, and obtain the variational posterior distribution parameters through numerical iteration;

[0079] Perform stochastic gradient optimization on the variational posterior distribution parameters, update the parameters by maximizing the evidence lower bound function to obtain the optimal posterior distribution parameters, and reconstruct the temperature parameter probability distribution based on the optimal posterior distribution parameters.

[0080] In this example, model the temperature distribution coefficient and the heat conduction coefficient . Assume that these parameters follow a multi-component Gaussian mixture model, that is, each coefficient is a mixture model composed of multiple Gaussian distributions. A multi-component Gaussian mixture model is expressed as:

[0081] ;

[0082] where, is the probability density function of the temperature distribution coefficient or the heat conduction coefficient, is the number of mixture components, is the weight of the -th Gaussian component, and satisfies , and are the mean vector and covariance matrix of the -th Gaussian component respectively. Optimize the parameters of the Gaussian mixture model through the expectation maximization (EM) algorithm to estimate the weights and parameters of each Gaussian component. The core idea of the EM algorithm is to alternately execute the expectation step (E-step) and the maximization step (M-step). In the E-step, calculate the posterior probability that each data point belongs to each Gaussian component, and in the M-step, update the model parameters based on the posterior probability. For the prior probability distribution of the temperature parameter, its optimal estimate is obtained through this process. Input the temperature sensor measurement data of the semiconductor device into the temperature control region dynamic model to calculate the temperature response , and construct the measurement likelihood function. Assume that the temperature measured by the sensor and the temperature response There is a certain deviation between them, and this deviation is modeled by measurement error. The measurement likelihood function is expressed as:

[0083] ;

[0084] where, is a Gaussian distribution, representing the difference between the temperature measurement value and the model prediction value , is the variance of the measurement error. Taking the logarithm of the product of the prior probability distribution of the temperature parameter and the measurement likelihood function, the log posterior function is obtained:

[0085] ;

[0086] The log posterior function is used to estimate the posterior distribution of the temperature parameter. Input the log posterior function into the first Gaussian process model for probabilistic regression calculation. Gaussian process is a non-parametric Bayesian method, suitable for dealing with regression problems with uncertainty. The core of Gaussian process regression is to model the relationship between input and output through a covariance function (kernel function). Suppose there is a Gaussian process model, with input , and output , then its joint distribution is:

[0087] ;

[0088] where, is the covariance matrix of the training data, is the covariance matrix between the training data and the test data, is the test data. Through the regression of the Gaussian process model, the posterior probability distribution of the temperature parameter is obtained. Input the posterior probability fitting function into the second Gaussian process model for variational inference. Variational inference infers a complex posterior distribution by optimizing an approximate posterior distribution. The core idea of variational inference is to obtain an approximate posterior distribution by optimizing the evidence lower bound function. The optimized evidence lower bound function is defined as:

[0089] ;

[0090] where, is the variational distribution, is the posterior distribution, and the second term is the entropy term of the variational distribution. By maximizing the optimized evidence lower bound function, the variational posterior distribution is obtained. After obtaining the variational posterior distribution, optimize the temperature control model through the Bayesian optimization method. Bayesian optimization is a method for global optimization by sampling uncertainty. The goal of Bayesian optimization is to maximize the composite objective function of the posterior probability term and the evidence lower bound term. Suppose the optimization objective function is , the Bayesian optimization process will select the optimal input to maximize the objective function. During the optimization process, a numerical iterative method is used to solve for the optimal variational posterior distribution parameters. Through the stochastic gradient descent algorithm, the update formula for stochastic gradient descent is:

[0091] ;

[0092] where is the learning rate, is the gradient of the objective function, is the current parameter, is the updated parameter. Through multiple iterations, the optimal variational posterior distribution parameters are obtained. Based on the optimal posterior distribution parameters, the probability distribution of the temperature parameter is reconstructed, that is, the final estimate of the temperature parameter is obtained.

[0093] In one example, according to the probability distribution of the temperature parameter, the temperature control range is divided into sub-domains, an optimization objective function including a prediction error term and an inter-domain difference term is constructed, and the temperature inter-domain feature mapping matrix is obtained by solving through the gradient descent method, including:

[0094] Perform probability density threshold analysis on the probability distribution of the temperature parameter, and use the equal-interval division method to divide the temperature control range into sub-domains to obtain multiple temperature control sub-domains;

[0095] Perform kernel function transformation on the temperature data in each temperature control sub-domain to generate sub-domain feature data, divide the sub-domain feature data into a source domain feature set and a target domain feature set, and perform standardization processing on the source domain feature set and the target domain feature set to obtain a normalized feature matrix;

[0096] Calculate the maximum mean discrepancy statistic based on the normalized feature matrix, construct an inter-domain feature distance metric function to obtain an inter-sub-domain feature difference matrix, and establish a sub-domain optimization objective function including a mean squared error term and a maximum mean difference term for the feature difference matrix;

[0097] Use the backpropagation algorithm to perform gradient descent calculation on the sub-domain optimization objective function to obtain a feature transformation parameter matrix, input the feature transformation parameter matrix into a three-layer fully connected neural network for feature mapping to obtain a temperature inter-domain feature mapping matrix, and each layer of the fully connected neural network uses the rectified linear function as the activation function.

[0098] In this example, probability density threshold analysis is performed on the probability distribution of the temperature parameter. Assume that the probability distribution of the temperature parameter is , and a threshold is set such that when When it is determined that the temperature value is within the effective control range. Based on the threshold condition, the temperature control range is divided into multiple sub-domains using an equal-interval partitioning method. For example, assume the temperature control range is , and through a uniform interval this range is divided into several sub-domains, and the interval of each sub-domain is:

[0099] ;

[0100] where is the number of sub-domains after partitioning, and is the temperature interval of each sub-domain. Through this method, the temperature control range is refined into multiple sub-domains, making the temperature change within each sub-domain more controllable. The temperature data within each temperature sub-domain is subjected to a kernel function transformation to generate the characteristic data of the sub-domain. By selecting an appropriate kernel function the input data is mapped to a high-dimensional feature space, where the inner product of the data can better reflect its underlying non-linear relationship. For example, the Gaussian kernel function has the form:

[0101] ;

[0102] Under this transformation, the temperature data will be mapped into the new feature space, thus more effectively capturing the complex relationship between temperature and other control parameters. The transformed data is divided into a source domain feature set and a target domain feature set , which correspond to the training data and the test data respectively. These feature sets are normalized to obtain the normalized feature matrix:

[0103] ;

[0104] where and are the mean and standard deviation of the source domain feature set respectively, and and are the mean and standard deviation of the target domain feature set. The purpose of the normalization operation is to make the data of different features on the same scale, thus eliminating the influence of scale differences on subsequent processing. Based on the normalized feature matrix, the maximum mean discrepancy statistic is calculated, and this statistic is used to measure the distribution difference between the source domain and the target domain. The maximum mean discrepancy measures the difference between the source domain and the target domain by calculating the mean difference between the two distributions in the feature space, and its formula is:

[0105] ;

[0106] where is the mapping to the high-dimensional feature space through the kernel function, and are the numbers of source domain and target domain samples respectively, is the Hilbert space of the feature space. By calculating the MMD statistic, a feature difference matrix between subdomains is obtained, which reflects the difference between the source domain and the target domain. To optimize the feature mapping between subdomains, a subdomain optimization objective function containing a mean squared error term and a maximum mean discrepancy term is established. The mean squared error term is used to measure the gap between the model prediction value and the actual observed value, while the maximum mean discrepancy term is used to measure the distribution difference between the source domain and the target domain. The form of the objective function is:

[0107] ;

[0108] where, and are hyperparameters used to balance the weights of the mean squared error term and the maximum mean discrepancy term. By minimizing the objective function, the feature mapping can be optimized to minimize the feature difference between subdomains. The backpropagation algorithm is used to perform gradient descent calculation on the subdomain optimization objective function. The backpropagation algorithm calculates the gradient of the objective function with respect to each parameter and updates the parameters according to the gradient. In each iteration, the backpropagation algorithm calculates the gradient of each parameter and adjusts the weight parameters of the network through gradient descent. The update formula is as follows:

[0109] ;

[0110] where, is the learning rate, is the gradient of the objective function, and are the current and updated network parameters respectively. Through multiple iterations, the algorithm will continuously optimize the feature transformation parameter matrix. The feature transformation parameter matrix is input into a three-layer fully connected neural network for feature mapping to obtain the feature mapping matrix between temperature domains. Each layer of the fully connected neural network uses the rectified linear unit (ReLU) as the activation function. The form of the ReLU activation function is:

[0111] ;

[0112] The activation function can effectively introduce non-linear characteristics and avoid the problem of gradient vanishing. Through the learning and training of the three-layer fully connected neural network, the feature mapping matrix between temperature domains is finally obtained.

[0113] In an example, based on the temperature control region dynamic model, the thermal coupling coefficient matrix between temperature intervals is calculated. Combining the temperature prediction data sequence and the feature mapping matrix between temperature domains, a temperature control objective function is constructed. The model predictive control algorithm is used to solve and obtain the temperature control quantity sequence, including:

[0114] Perform energy integration calculations on the coupled heat transfer equations in the dynamic model of the temperature control region, extract the heat flux density and temperature gradient parameters between adjacent temperature zones, and construct the thermal coupling coefficient matrix between temperature zones;

[0115] Based on the thermal coupling coefficient matrix between temperature zones, linearize the dynamic transfer relationship between the temperature field and the heat flux field, and construct the thermodynamic state equation between temperature zones;

[0116] Calculate the deviation between the temperature prediction data sequence and the process set temperature to obtain the temperature prediction error sequence, and perform forward recursive calculations on the thermodynamic state equation between temperature zones based on the temperature prediction error sequence to obtain the temperature state constraint conditions;

[0117] Use the characteristic mapping matrix between temperature domains to perform inter-domain conversion on the temperature state constraint conditions to obtain the multi-temperature zone control parameter matrix, and construct the temperature control objective function of the quadratic programming problem based on the multi-temperature zone control parameter matrix;

[0118] Adopt the rolling horizon optimization method to solve the temperature control objective function to obtain the optimized control quantity sequence, and perform decoupling distribution calculations on the optimized control quantity sequence to obtain the temperature control quantity sequence.

[0119] In this example, perform energy integration calculations on the coupled heat transfer equations, extract the heat flux density and temperature gradient parameters between adjacent temperature zones, and construct the thermal coupling coefficient matrix between temperature zones according to these parameters. The coupled heat transfer equations adopt the models of heat conduction and convective heat transfer, where the heat conduction equation needs to be integrated in the case of multi-temperature zones to obtain the thermal coupling coefficient matrix between temperature zones. The form of the heat conduction equation under steady state is:

[0120] ;

[0121] where, is the temperature, is the thermal diffusivity, is the heat source term, is the material density, is the specific heat capacity, is the Laplace operator of the temperature, representing the diffusion of the temperature field. By integrating the above equation, the relationship between the heat flux density and the temperature gradient between adjacent temperature zones is obtained, and then the thermal coupling coefficient matrix is constructed. For adjacent temperature zones and , the element of its coupling coefficient matrix is calculated by the following formula:

[0122] ;

[0123] where, is the thermal conductivity, is the temperature gradient, is the unit normal vector, is the area of the temperature zone boundary. Through energy integration, the thermal coupling coefficient between adjacent regions is calculated, and the corresponding coupling matrix is constructed. After obtaining the thermal coupling coefficient matrix between temperature zones, the dynamic transfer relationship between the temperature field and the heat flux field is linearized to construct the thermodynamic state equation between temperature zones. The nonlinear equation of the temperature field is approximated as a linear form for numerical calculation. For example, the temperature field is approximated by Taylor expansion or the difference method. Through linearization, the temperature field and the heat flux field are expressed as a system of linear equations:

[0124] ;

[0125] where is the temperature vector at the current moment, is the heat flux density vector at the current moment, and are matrices representing the relationship between temperature and heat flux respectively. After linearization, the thermodynamic state equation between temperature zones is simplified and used in subsequent control algorithms. In the use of temperature prediction data, the deviation between the temperature prediction data sequence and the process set temperature is calculated to obtain the temperature prediction error sequence. Assume the temperature prediction data is , and the process set temperature is , then the temperature prediction error sequence is calculated by the following formula:

[0126] ;

[0127] Based on this error sequence, the temperature state constraint conditions are obtained by forward recursive calculation of the thermodynamic state equation between temperature zones. The basic principle of forward recursion is to use the state at the current moment to predict the temperature state at the next moment. In the recursion process, through numerical integration methods such as the Euler method or the Runge-Kutta method, the evolution of the temperature state is gradually advanced. Through recursion, the obtained temperature state constraint conditions are expressed as:

[0128] ;

[0129] where is the temperature prediction error sequence, which affects the temperature state at the next moment. Through forward recursion, the temperature state constraint conditions are dynamically calculated. The temperature state constraint conditions are transformed between domains using the temperature domain inter-feature mapping matrix. The temperature domain inter-feature mapping matrix is a tool for transforming and mapping temperature states between different temperature control regions, and is learned and trained through deep learning or machine learning models. For example, assume the temperature domain inter-feature mapping matrix is , then the temperature state constraint conditions are transformed by the following formula:

[0130] ;

[0131] Map the temperature state of one region to another region to better integrate the control information of different regions and form a control parameter matrix for multiple temperature zones. . Based on these control parameters, construct a temperature control objective function for a quadratic programming problem. The temperature control objective function includes multiple objective terms, such as temperature deviation term, control power consumption term, etc. The objective function of the quadratic programming problem is expressed as:

[0132] ;

[0133] where is the temperature deviation term, representing the difference between the actual temperature value and the set value, is the regularization coefficient of the control power consumption. By optimizing the objective function, a suitable control quantity sequence is obtained, and then precise temperature control is achieved. To optimize this objective function, a rolling horizon optimization method is adopted. By performing optimization calculations at each moment and adjusting the current control quantity based on the prediction of future moments. For example, in rolling horizon optimization, the temperature control objective function is optimized within a sliding time window. At each moment, the optimization algorithm calculates the optimal control quantity according to the current temperature state and prediction information, and adjusts it again at the next moment according to the new information. This method can effectively handle the dynamics and uncertainties in the system. The optimized control quantity sequence is used for the actual control of the temperature control system. After obtaining the control quantity sequence, decoupling and distribution calculations are performed to ensure that the control quantities of each temperature control region are independent and coordinated with each other, and finally the temperature control quantity sequence of each temperature control region is obtained, thus completing the entire temperature control process.

[0134] In an example, the deviation calculation is performed between the temperature prediction data sequence and the process set temperature to obtain the temperature prediction error sequence. Based on the temperature prediction error sequence, the forward recurrence calculation of the thermodynamic state equation between temperature zones is performed to obtain the temperature state constraint conditions, including:

[0135] Perform interpolation calculation on the temperature prediction data sequence and the process set temperature curve to obtain the temperature prediction deviation matrix. Based on the temperature prediction deviation matrix, calculate the temperature change rate of each temperature control region and construct a temperature gradient vector;

[0136] Perform state space transformation on the temperature gradient vector and the thermodynamic state equation between temperature zones to construct the thermodynamic system state equation, and perform recurrence operation on the thermodynamic system state equation within the specified prediction time domain to obtain the temperature state prediction sequence;

[0137] According to the temperature state prediction sequence, the output limit conditions of the heater power and the refrigerator power are set, the actuator constraint vector is constructed, and the actuator constraint vector is combined with the temperature state prediction sequence to obtain the temperature control area constraint matrix;

[0138] The temperature control area constraint matrix is ​​divided into blocks according to the temperature zones, the boundary temperature extremes of each temperature control zone are calculated, the temperature zone dynamic constraint equation is constructed, the temperature zone dynamic constraint equation is normalized and transformed, and the temperature state constraint conditions are obtained.

[0139] In this example, the temperature prediction data sequence and the process setting temperature curve are interpolated to obtain the temperature prediction deviation matrix, and then the temperature change rate of the temperature control area is calculated, and the temperature gradient vector is constructed. In this process, the temperature prediction data sequence is the historical data provided by the temperature sensor, and the process setting temperature curve is the temperature control target curve predetermined by the equipment. In order to perform precise control, the difference between the two is calculated, that is, the temperature prediction deviation matrix. Assume that the set temperature curve is , and the temperature prediction data series is , then the temperature prediction deviation matrix Calculated by the following formula:

[0140] ;

[0141] The deviation matrix reflects the difference between the predicted temperature and the set temperature, which affects the adjustment of the temperature control area. Based on the deviation matrix, the temperature change rate of each temperature control area is calculated, and the temperature gradient vector is constructed. The temperature difference between adjacent moments is calculated, and the specific temperature change rate is It is expressed as:

[0142] ;

[0143] in, is the time step. These temperature change rates will appear as temperature gradients in space, and the temperature gradient vector needs to be calculated in each temperature control area. Assume that the temperature gradient of the temperature control area is , then the temperature gradient vector is expressed as:

[0144] ;

[0145] in, is The temperature change rate in the - direction, and so on. By calculating the temperature gradient vector in the temperature control region, the thermodynamic state of the system is modeled. Based on the temperature gradient vector and the thermodynamic state equation between temperature intervals, a state - space transformation is performed to construct the state equation of the thermal system. The thermodynamic state equation describes the heat transfer and state changes between regions in the temperature control system. The thermodynamic state equation includes terms such as heat conduction, convective heat transfer, and radiation. Assume the state equation of the temperature control region is:

[0146] ;

[0147] where, is the temperature vector at the current moment, is the heat flux density vector, and are system parameter matrices, representing the relationship between temperature and heat flux respectively. Through state - space transformation, the dynamic evolution of the temperature field is described by the above linear system equation. A recursive operation is performed on the state equation of the thermal system within the specified prediction time domain to obtain the temperature state prediction sequence. The recursive operation is implemented through numerical integration methods such as the Euler method, the Runge - Kutta method, etc. At each time step , the state of the temperature will be updated according to the input states of the current temperature and heat flux to obtain the temperature value at the next moment. Based on the temperature state prediction sequence, power output limit conditions for the heater and cooler are set. To ensure that the temperature control equipment does not operate over - load, power output limit conditions are set for the heater and cooler. Assume the powers of the heater and cooler are and respectively, then the power output limit conditions are expressed as:

[0148] ;

[0149] The role of the power limit condition is to prevent the energy consumption of the control equipment from exceeding the maximum power limit of the system. On this basis, an actuator constraint vector is constructed to combine the actuator output with the temperature state prediction sequence to obtain the temperature control region constraint matrix. Assume the temperature control region constraint matrix is , calculated according to the actuator constraints and the temperature prediction sequence. This matrix is represented as follows:

[0150] ;

[0151] This constraint matrix combines the temperature prediction values and the limits of the actuator outputs to ensure that the operation of the temperature control system is within the safe range at all times. To handle the constraint conditions of the temperature control regions, the constraint matrix of the temperature control regions is block-processed. The temperature extreme values within each temperature control region refer to the maximum and minimum values of the temperature distribution within that region, and these temperature extreme values determine the thermodynamic boundary conditions of the region. In the dynamic constraint equation of the temperature control region, the temperature dynamic constraints of the temperature control region are calculated by considering the temperature extreme values and the actuator constraints. Assume that the boundary temperature extreme values of the temperature control region are and , then the dynamic constraint equation is expressed as:

[0152] ;

[0153] The dynamic constraint conditions ensure that the temperature in each temperature control region remains within the set safe range, thus avoiding the situation of overheating or overcooling of the equipment. In the dynamic constraint equation of the temperature zone, numerical optimization methods are used to normalize these constraints to obtain the final temperature state constraint conditions:

[0154] ;

[0155] Through the normalization transformation, the constraint conditions of the temperature control region are converted into a standard form for subsequent optimization and control.

[0156] Referring to Figure 2 , this embodiment provides a temperature control device for a semiconductor device, including:

[0157] Transformation module 1, which is used to perform finite element mesh division and modal coordinate transformation on multiple temperature control regions of the semiconductor device, perform eigenvalue analysis on the modal equation, select the first two modes to establish a multi-temperature zone coupled heat transfer equation set, and obtain the dynamic model of the temperature control region;

[0158] Extraction module 2, which is used to collect the measurement data of the temperature sensors of the semiconductor device and perform time-frequency domain transformation, generate a temperature distribution characteristic image, and extract spatio-temporal characteristics through a two-channel deep learning model to obtain a temperature prediction data sequence;

[0159] Calculation module 3, which is used to perform Gaussian mixture modeling on the temperature parameters of the dynamic model of the temperature control region to obtain a prior distribution, take the logarithm of the product of the prior distribution and the measurement likelihood function, and use a double Gaussian process model to calculate the posterior probability and the lower bound of the evidence to obtain the temperature parameter probability distribution;

[0160] Construction module 4, which is used to perform subdomain division on the temperature control range according to the temperature parameter probability distribution, construct an optimization objective function including a prediction error term and an inter-domain difference term, and solve it by the gradient descent method to obtain a temperature inter-domain feature mapping matrix;

[0161] A solution module 5 is configured to calculate a thermal coupling coefficient matrix between temperature ranges based on a temperature control region dynamic model, construct a temperature control objective function by combining a temperature prediction data sequence and a feature mapping matrix between temperature domains, and solve for a temperature control quantity sequence by using a model predictive control algorithm.

[0162] In this embodiment, for the specific implementation of each unit in the above device embodiment, please refer to the description in the above method embodiment, and details are not described herein again.

[0163] Refer to Figure 3 , in an embodiment of the present invention, a computer device is further provided. The computer device may be a server, and its internal structure may be as Figure 3 shown. The computer device includes a processor, a memory, a display screen, an input device, a network interface, and a database connected through a system bus. Among them, the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is configured to store corresponding data in this embodiment. The network interface of the computer device is configured to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the above method is implemented.

[0164] Those skilled in the art can understand that Figure 3 the structure shown in

[0165] is only a block diagram of a part of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied.

[0166] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium provided by the present invention and used in the embodiments can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (SSRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM, etc.

[0167] It should be noted that in this article, the terms "including", "comprising", or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, apparatus, article, or method that includes a series of elements includes not only those elements but also other elements not expressly listed, or elements that are inherent to such process, apparatus, article, or method. Without further limitation, an element defined by the statement "including one..." does not exclude the presence of another identical element in the process, apparatus, article, or method that includes such element.

[0168] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present invention.

Claims

1. A temperature control method for semiconductor equipment, characterized in that: The following steps are involved: Finite element meshing and modal coordinate transformation are performed on multiple temperature control areas of semiconductor equipment, eigenvalue analysis is performed on the modal equations, and the first two modes are selected to establish a multi-temperature zone coupled heat transfer equation group to obtain a dynamic model of the temperature control area; Collecting the temperature sensor measurement data of the semiconductor device and performing time-frequency domain transformation to generate a temperature distribution feature image, extracting the spatiotemporal features through a dual-channel deep learning model, and obtaining a temperature prediction data sequence; Gaussian mixture modeling is performed on the temperature parameters of the temperature control area dynamic model to obtain a prior distribution, the logarithm of the product of the prior distribution and the measurement likelihood function is taken, and the posterior probability and the lower limit of evidence are calculated using a double Gaussian process model to obtain the temperature parameter probability distribution; specifically, the following steps are performed: a multi-component Gaussian mixture model is established for the temperature distribution coefficient and the thermal conductivity coefficient in the temperature control area dynamic model, and the weights and parameters of the Gaussian components are iteratively optimized through an expectation maximization algorithm to obtain the temperature parameter prior probability distribution; the temperature sensor measurement data of the semiconductor device is input into the temperature control area dynamic model to calculate the temperature response, a measurement likelihood function is constructed, and the temperature parameter prior probability distribution and the thermal conductivity coefficient are calculated. The product of the measured likelihood function is logarithmically transformed to obtain a logarithmic posterior function; the logarithmic posterior function is input into the first Gaussian process model for probability regression calculation to obtain a posterior probability fitting function, and the posterior probability fitting function is input into the second Gaussian process model for variational inference to obtain an evidence lower limit function; a composite objective function including a posterior probability term and an evidence lower limit term is constructed using a Bayesian optimization method, and variational posterior distribution parameters are obtained through numerical iterative solution; the variational posterior distribution parameters are stochastically gradient optimized, and the parameters are updated by maximizing the evidence lower limit function to obtain optimal posterior distribution parameters, and the temperature parameter probability distribution is reconstructed based on the optimal posterior distribution parameters; The temperature control range is divided into sub-domains according to the temperature parameter probability distribution, an optimization objective function including a prediction error term and an inter-domain difference term is constructed, and a temperature inter-domain feature mapping matrix is ​​obtained by solving the problem through a gradient descent method; The thermal coupling coefficient matrix of the temperature control interval is calculated based on the dynamic model of the temperature control area, the temperature control objective function is constructed by combining the temperature prediction data sequence and the temperature domain feature mapping matrix, and the temperature control quantity sequence is obtained by using the model predictive control algorithm.

2. The temperature control method of semiconductor equipment according to claim 1, characterized in that: The finite element meshing and modal coordinate transformation are performed on multiple temperature control areas of the semiconductor device, the eigenvalue analysis is performed on the modal equation, and the first two order modes are selected to establish a multi-temperature zone coupled heat transfer equation group to obtain a dynamic model of the temperature control area, including: Divide multiple temperature control areas of semiconductor equipment into tetrahedral grid units, use piecewise linear functions to perform node interpolation calculations on the temperature field, and obtain a set of discretized equations for the temperature field; Performing Fourier transformation on the temperature field discretization equation group, constructing a heat conduction equation group including temperature distribution terms, heat source terms and boundary condition terms, establishing generalized coordinates of the temperature field by separation of variables method, and obtaining modal dynamic equations by Lagrange transformation; Solving the eigenvalues ​​and eigenvectors based on the modal dynamics equation, selecting the first two dominant modes by using the modal contribution analysis method, constructing a reduced-order temperature dynamics equation, performing Euler discretization on the reduced-order temperature dynamics equation, and establishing a coupled heat transfer equation group including heat conduction terms and convection heat transfer terms in the temperature control interval; Calibrate the temperature distribution coefficient and the heat conduction coefficient in the coupled heat transfer equations to obtain a calibration coefficient matrix, establish a temperature zone heat balance equation based on the calibration coefficient matrix, numerically calculate the heat flux density and temperature gradient of each temperature control area, and obtain the dynamic response characteristics of the temperature control interval; A dynamic model of the temperature control area is constructed based on the dynamic response characteristics of the temperature control interval and the coupled heat transfer equations.

3. The temperature control method of semiconductor equipment according to claim 2, characterized in that: The method collects the temperature sensor measurement data of the semiconductor device and performs time-frequency domain transformation to generate a temperature distribution feature image, extracts the time-space features through a dual-channel deep learning model, and obtains a temperature prediction data sequence, including: Collecting temperature sensor measurement data of each temperature control area of ​​the semiconductor device, performing fast Fourier transform and wavelet transform processing on the temperature sensor measurement data to obtain a time-frequency feature matrix; Normalizing and reconstructing the time-frequency feature matrix to generate a temperature distribution feature image, inputting the temperature distribution feature image into a residual network channel of a dual-channel deep learning model, wherein the residual network channel includes five residual units, each of which is composed of two convolutional layers and an identity mapping, to obtain a spatial feature vector; Input the temperature sensor measurement data into the recurrent neural network channel of the dual-channel deep learning model, wherein the recurrent neural network channel includes three layers of bidirectional long short-term memory networks, and each layer of the bidirectional long short-term memory network includes 64 memory units, to obtain a time series feature vector; A feature fusion operation is performed on the spatial feature vector and the temporal feature vector to obtain a fused feature vector, and sequence prediction is performed on the fused feature vector to obtain a temperature prediction data sequence.

4. The temperature control method of semiconductor equipment according to claim 1, characterized in that: The temperature control range is divided into sub-domains according to the temperature parameter probability distribution, an optimization objective function including a prediction error term and an inter-domain difference term is constructed, and a temperature inter-domain feature mapping matrix is ​​obtained by solving the gradient descent method, including: Performing probability density threshold analysis on the temperature parameter probability distribution, and dividing the temperature control range into sub-domains using an equal interval division method to obtain a plurality of temperature control sub-domains; Performing kernel function transformation on the temperature data in each temperature control subdomain to generate subdomain feature data, dividing the subdomain feature data into a source domain feature set and a target domain feature set, and performing standardization processing on the source domain feature set and the target domain feature set to obtain a normalized feature matrix; Calculating the maximum average difference statistic based on the normalized feature matrix, constructing an inter-domain feature distance measurement function, obtaining an inter-subdomain feature difference matrix, and establishing a sub-domain optimization objective function including a mean square error term and a maximum average difference term for the feature difference matrix; The back propagation algorithm is used to perform gradient descent calculation on the subdomain optimization objective function to obtain a feature transformation parameter matrix, and the feature transformation parameter matrix is ​​input into a three-layer fully connected neural network for feature mapping to obtain a temperature domain feature mapping matrix. Each layer of the fully connected neural network uses a rectified linear function as an activation function.

5. The temperature control method of semiconductor equipment according to claim 4, characterized in that: The method of calculating the thermal coupling coefficient matrix of the temperature control interval based on the temperature control area dynamic model, building a temperature control objective function by combining the temperature prediction data sequence and the temperature domain feature mapping matrix, and using a model predictive control algorithm to solve and obtain a temperature control quantity sequence includes: Performing energy integration calculation on the coupled heat transfer equations in the temperature control area dynamic model, extracting heat flux density and temperature gradient parameters of adjacent temperature control intervals, and constructing a thermal coupling coefficient matrix of the temperature control intervals; Based on the thermal coupling coefficient matrix of the temperature control interval, the dynamic transfer relationship between the temperature field and the heat flow field is linearized to construct a thermodynamic state equation of the temperature control interval; Calculate the deviation between the temperature prediction data sequence and the process setting temperature to obtain a temperature prediction error sequence, and perform forward recursive calculation on the thermodynamic state equation of the temperature control interval based on the temperature prediction error sequence to obtain a temperature state constraint condition; Using the temperature inter-domain feature mapping matrix to perform inter-domain conversion on the temperature state constraint condition to obtain a multi-temperature zone control parameter matrix, and constructing a temperature control objective function of a quadratic programming problem based on the multi-temperature zone control parameter matrix; The temperature control objective function is solved by a rolling time domain optimization method to obtain a control quantity optimization sequence, and a decoupling distribution calculation is performed on the control quantity optimization sequence to obtain a temperature control quantity sequence.

6. The temperature control method of semiconductor equipment according to claim 5, characterized in that: The temperature prediction data sequence is subjected to deviation calculation with respect to the process setting temperature to obtain a temperature prediction error sequence, and the temperature control interval thermodynamic state equation is subjected to forward recursive calculation based on the temperature prediction error sequence to obtain a temperature state constraint condition, including: Performing interpolation calculation on the temperature prediction data sequence and the process setting temperature curve to obtain a temperature prediction deviation matrix, calculating the temperature change rate of each temperature control area based on the temperature prediction deviation matrix, and constructing a temperature gradient vector; Performing state space transformation on the temperature gradient vector and the temperature control interval thermodynamic state equation, constructing a thermodynamic system state equation, and performing recursive operation on the thermodynamic system state equation within a specified prediction time domain to obtain a temperature state prediction sequence; According to the temperature state prediction sequence, output limiting conditions of heater power and refrigerator power are set, an actuator constraint vector is constructed, and the actuator constraint vector is combined with the temperature state prediction sequence to obtain a temperature control area constraint matrix; The temperature control area constraint matrix is ​​divided into blocks according to the temperature zones, the boundary temperature extreme value of each temperature control zone is calculated, the temperature zone dynamic constraint equation is constructed, the temperature zone dynamic constraint equation is normalized and transformed, and the temperature state constraint condition is obtained.

7. A temperature control device for semiconductor equipment, characterized in that: Steps for implementing the temperature control method of a semiconductor device according to any one of claims 1 to 6, wherein the temperature control device of the semiconductor device comprises: The transformation module is used to perform finite element meshing and modal coordinate transformation on multiple temperature control areas of semiconductor equipment, perform eigenvalue analysis on the modal equations and select the first two modes to establish a multi-temperature zone coupled heat transfer equation group to obtain a dynamic model of the temperature control area; An extraction module is used to collect the temperature sensor measurement data of the semiconductor device and perform time-frequency domain transformation to generate a temperature distribution feature image, extract the time-space features through a dual-channel deep learning model, and obtain a temperature prediction data sequence; A calculation module, used to perform Gaussian mixture modeling on the temperature parameters of the temperature control area dynamic model to obtain a prior distribution, take the logarithm of the product of the prior distribution and the measurement likelihood function, and use a double Gaussian process model to calculate the posterior probability and the lower limit of evidence to obtain the temperature parameter probability distribution; A construction module is used to divide the temperature control range into sub-domains according to the temperature parameter probability distribution, construct an optimization objective function including a prediction error term and an inter-domain difference term, and obtain a temperature inter-domain feature mapping matrix by solving the gradient descent method; A solution module is used to calculate the thermal coupling coefficient matrix of the temperature control interval based on the dynamic model of the temperature control area, construct a temperature control objective function by combining the temperature prediction data sequence and the temperature domain feature mapping matrix, and use a model predictive control algorithm to solve and obtain a temperature control quantity sequence.

8. A computer device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the computer program, the steps of the temperature control method of the semiconductor device according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the temperature control method of a semiconductor device according to any one of claims 1 to 6 are implemented.

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