Temperature control method, device and equipment of semiconductor equipment and storage medium

Abstract

The invention relates to a temperature control method, device and equipment of semiconductor equipment and a storage medium. The method comprises the following steps: performing finite element mesh division and modal coordinate transformation on a plurality of temperature control areas of semiconductor equipment to obtain a temperature control area dynamic model; collecting measurement data of a temperature sensor and performing time-frequency domain transformation to generate a temperature prediction data sequence; gaussian mixture modeling is carried out to obtain prior distribution, and temperature parameter probability distribution is obtained; performing sub-domain division on the temperature control range to obtain a temperature inter-domain feature mapping matrix; and a temperature interval thermal coupling coefficient matrix is calculated based on the temperature control area dynamic model, a temperature control objective function is constructed in combination with the temperature prediction data sequence and the temperature inter-domain feature mapping matrix, and a temperature control quantity sequence is solved by adopting a model prediction control algorithm. According to the invention, the accuracy and dynamic response speed of temperature control are improved, and the stability of temperature control and the energy utilization efficiency are ensured.

Description

Technical Field

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

[0002] As semiconductor manufacturing processes develop towards smaller line widths and higher precision, higher requirements are placed on the accuracy, stability, and dynamic response characteristics of temperature control. Traditional semiconductor equipment temperature control methods mainly use single-zone PID control or simple multi-zone decoupling control strategies, which are difficult to effectively handle the thermal coupling effects between multiple temperature zones, resulting in insufficient temperature control accuracy and slow dynamic response.

[0003] Existing semiconductor equipment temperature control modeling methods mostly use simplified concentrated parameter models or empirical models, which cannot accurately describe the distribution characteristics and dynamic evolution of the temperature field. At the same time, due to the strong nonlinearity, multivariable coupling, and time-varying parameters of semiconductor equipment temperature control systems, traditional model predictive control methods have insufficient robustness when dealing with model uncertainties and external disturbances, making it difficult to ensure high precision and rapid response requirements 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 semiconductor equipment. The present invention 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 object, the present invention provides a temperature control method for semiconductor equipment, comprising the following steps: 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 a temperature parameter probability distribution; 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; Based on the temperature control area dynamic model, the temperature coupling coefficient matrix between temperature zones is calculated, 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 solving the temperature prediction control algorithm.

[0006] The present invention also provides a temperature control device for semiconductor equipment, comprising: 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 between temperature zones based on the dynamic model of the temperature control zone, construct a temperature control objective function by combining the temperature prediction data sequence with the temperature domain feature mapping matrix, and obtain a temperature control quantity sequence by using a model predictive control algorithm.

[0007] The present invention also provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any one of the above methods when executing the computer program.

[0008] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of any of the above-mentioned methods are implemented.

[0009] In summary, the technical solution provided by the present invention adopts the parameter global modal method to establish the dynamic model of the temperature control area. Through the dimensionality reduction processing of the first two dominant modes, the model complexity is effectively reduced, the calculation efficiency is improved, and the modeling accuracy is maintained at a high level. A dual-channel deep learning model structure is proposed to extract the spatial characteristics and time series characteristics of the temperature field and fuse them respectively, making full use of the spatiotemporal 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 probability modeling of temperature parameters, and the accurate estimation of the posterior probability is achieved by combining the double Gaussian process model, which enhances the model's adaptability to parameter uncertainty. A feature mapping method based on subdomain division is designed, and feature alignment under different working conditions is achieved by optimizing the inter-domain differences, thereby 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, and the coordinated control of multiple temperature zones is achieved through rolling time domain optimization and decoupling allocation, which improves the accuracy and dynamic response speed of temperature control. The adaptive control mechanism based on temperature state constraints realizes the reasonable allocation of heater and refrigerator power, and ensures the stability of temperature control and energy utilization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 1 is a schematic diagram of steps of a temperature control method for semiconductor equipment in one embodiment of the present invention; Figure 2 is a structural block diagram of a temperature control device for a semiconductor device in one embodiment of the present invention; Figure 3 It is a schematic block diagram of the structure of a computer device according to an embodiment of the present invention.

[0011] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0012] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 intended to limit the present invention.

[0013] Reference Figure 1 , this embodiment provides a temperature control method for a semiconductor device, comprising the following steps: S1, perform finite element meshing and modal coordinate transformation on multiple temperature control areas of semiconductor equipment, perform eigenvalue analysis on 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; 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.

[0014] 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; Specifically, real-time temperature measurement data is collected by temperature sensors arranged in each temperature control area of ​​the semiconductor device. Fast Fourier transform and wavelet transform are performed on the collected data. Fast Fourier transform is used to convert the original time series into frequency domain signals to reveal the spectral characteristics of the temperature change inside the temperature control area, while wavelet transform can simultaneously capture the characteristics of the local time domain and frequency domain, so as to obtain time-frequency features 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 to eliminate 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 to form a temperature distribution feature image. The temperature distribution law and its dynamic changes in the temperature control area are reflected. The temperature distribution feature image is input into the residual network channel of the dual-channel deep learning model. The architecture of the residual network channel includes 5 residual units, each of which is composed of two convolutional layers and an identity mapping path. The residual unit is designed to solve the problem of gradient vanishing or exploding in deep neural networks while retaining deeper feature information. Through continuous convolution operations and identity mapping, the residual network channel can extract 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 three-layer bidirectional long short-term memory network is constructed, each layer containing 64 memory units. The design of the bidirectional long short-term memory network extracts forward and backward time-dependent features from the time series of the data, solving the problem that traditional recurrent neural networks are insufficient in learning long sequence information. Through the gating operation of the memory unit on the data, the network channel can capture the dynamic time characteristics of the temperature change in the temperature control area and generate a time series feature vector. Feature fusion operations are performed on the spatial feature vector and the time series feature vector to obtain a high-dimensional fused feature vector. Through this process, the features extracted by different channels can complement each other at the semantic level, improving the prediction accuracy and generalization ability of the model. The fused feature vectors are subjected to sequence prediction operations, and the output layer of the deep learning model is used to generate prediction results to obtain a complete temperature prediction data sequence.

[0015] S3, Gaussian mixture modeling is performed on the temperature parameters of the dynamic model of the temperature control area 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 limit of evidence are calculated using the double Gaussian process model to obtain the probability distribution of the temperature parameters; It should be noted that a multi-component Gaussian mixture model is established for the key temperature parameters in the dynamic model of the temperature control area, including the temperature distribution coefficient and the heat conduction coefficient. The Gaussian mixture model is a probability density model that approximates complex probability distributions through multiple weighted Gaussian distributions. In order to optimally estimate the weights and parameters (mean, covariance matrix) 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 to the data given the current model parameters is calculated through the expectation step (E-step), 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 approached, and the prior probability distribution of the temperature parameters is obtained to describe 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 area, and the temperature response is calculated to capture the dynamic impact of the sensor data on the model output. The measurement likelihood function is constructed based on the measurement data to characterize the probability distribution characteristics of the observed data under given model parameters. The prior probability distribution of the temperature parameter 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 logarithmic posterior function. The logarithmic posterior function is input into a first Gaussian process model for probability regression calculation to fit the posterior probability distribution. Gaussian process is a non-parametric Bayesian model that can model 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 change law of the posterior probability in the entire parameter space. The posterior probability fitting function is used as input and passed to the second Gaussian process model for variational inference. The goal of variational inference is to approximate the posterior distribution by optimizing an evidence lower limit function. The evidence lower limit function ensures that the estimation of the posterior distribution not only satisfies the form of the logarithmic posterior function through a constrained optimization process, but also minimizes the uncertainty of the model prediction. After completing the variational inference of the a posteriori probability, a Bayesian optimization method is used to construct a composite objective function containing the posterior probability term and the evidence lower limit term. The construction of the composite objective function aims to comprehensively consider the accuracy (posterior probability) and complexity control (evidence lower bound) of the model. By numerically iterating and solving this objective function, the parameters of the variational posterior distribution are obtained, which reflect the best probability description of the temperature parameter under the current observation conditions. The variational posterior distribution parameters are stochastically optimized, 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 strikes a balance between model complexity and fitting of observed data. Based on the optimal posterior distribution parameters, the probability distribution of the temperature parameter is reconstructed.

[0016] S4, divide the temperature control range into sub-domains according to the probability distribution of temperature parameters, construct an optimization objective function including prediction error terms and inter-domain difference terms, and obtain the temperature inter-domain feature mapping matrix by solving the gradient descent method; Specifically, a probability density threshold analysis is performed on the probability distribution of temperature parameters. The temperature control range is reasonably divided according to the probability distribution characteristics. By setting a certain probability density threshold and combining the equal interval division method, the temperature control range is divided into multiple subdomains. Each subdomain represents a specific temperature control area or range. The temperature data in each temperature control subdomain is transformed by a kernel function. The subdomain data is mapped to a high-dimensional feature space by applying a nonlinear kernel function (such as a Gaussian kernel or a polynomial kernel) to generate subdomain feature data that can capture complex relationships. The subdomain feature data is divided 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, the two feature sets are standardized respectively to eliminate the differences in feature scale and dimension, and a normalized feature matrix is ​​generated. Based on the normalized feature matrix, the maximum mean difference statistic is calculated. This is a non-parametric method to measure the distance between two distributions. It quantifies the difference in feature distribution between subdomains by calculating the deviation of the feature mean in a high-dimensional space. According to the calculation results, the inter-domain feature distance measurement function is constructed to obtain the inter-subdomain feature difference matrix, which reflects the inconsistency of feature distribution between subdomains. The optimization objective function is established based on the feature difference matrix. The 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 average difference term, which is used to minimize the difference in feature distribution between subdomains. The back propagation algorithm is used to perform gradient descent calculation on the subdomain optimization objective function. In each iteration, the parameters are adjusted according to the gradient direction of the objective function so that the optimization process gradually approaches the global optimal solution, and the feature transformation parameter matrix is ​​obtained to capture the optimal mapping relationship between the source domain and the target domain features. The feature transformation parameter matrix is ​​input into a three-layer fully connected neural network for feature mapping. The design of the fully connected neural network uses rectified linear unit (ReLU) as the activation function of each layer to ensure that the model has good nonlinear fitting ability and gradient propagation stability. Through multi-layer feature combination and nonlinear transformation, the network can learn deeper mapping relationships from the input feature transformation parameter matrix and generate the final temperature domain feature mapping matrix.

[0017] S5, based on the dynamic model of the temperature control area, calculates the thermal coupling coefficient matrix between temperature zones, combines the temperature prediction data sequence with the temperature domain feature mapping matrix to construct the temperature control objective function, and uses the model predictive control algorithm to solve and obtain the temperature control quantity sequence.

[0018] Among them, the energy integral calculation of the coupled heat transfer equations in the dynamic model of the temperature control area is performed to extract the heat flux density and temperature gradient parameters between adjacent temperature zones, and quantify the heat transfer relationship between the temperature control zones. By combining the energy conservation and heat conduction equations, the heat flow interaction effect between the zones is accurately described. In the energy integral calculation, the directional distribution of the heat flux density and the coupling of convective heat transfer and heat conduction caused by the temperature gradient are calculated, and these parameters are organized into a thermal coupling coefficient matrix between the temperature zones. The thermal coupling coefficient matrix is ​​a multidimensional linear algebraic structure that reflects the thermodynamic interaction intensity between different temperature control zones in a numerical way. Based on the thermal coupling coefficient matrix between the temperature zones, the dynamic transfer relationship between the temperature field and the heat flow field is linearized, and the thermodynamic state equation between the temperature zones is established. This equation enables the model to simplify the computational complexity while ensuring accuracy by locally approximating the nonlinear transfer relationship into a linear form. The core of the thermodynamic state equation is to describe the thermal equilibrium relationship of each temperature control zone and the dynamic influence of the temperature of the adjacent zone on the zone under the action of thermal coupling. The temperature prediction data sequence obtained based on the dual-channel deep learning model is analyzed with the actual process set temperature to calculate the temperature prediction error sequence. Reflects the deviation between the current temperature control state and the target temperature control requirement. Based on the temperature prediction error sequence, the thermodynamic state equation between the temperature intervals is forward recursively calculated, and the temperature state constraints are gradually derived. At the same time, the temperature domain feature mapping matrix is ​​introduced into the above calculation process, and the temperature state constraints are processed through the inter-domain feature conversion. The function of the temperature domain feature mapping matrix is ​​to capture the feature correlation between different temperature control areas, 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, the temperature control objective function of the quadratic programming problem is constructed. The construction process of this objective function comprehensively considers the dual needs of minimizing temperature deviation and optimizing energy consumption, and embeds the thermal coupling effect and dynamic constraints between temperature intervals into the objective function. The rolling horizon optimization method is used to solve the temperature control objective function and obtain the control quantity optimization sequence. The rolling horizon optimization method is an optimization technology used 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 the optimal control strategy at each moment. The preliminary control quantity optimization sequence is decoupled and allocated to adapt to the specific implementation mechanism of independent heating or cooling of each temperature control area in actual semiconductor equipment, and finally a temperature control quantity sequence is generated.

[0019] By interpolating the temperature prediction data sequence and the process setting temperature curve, a temperature prediction deviation matrix with uniform 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 area. Based on the deviation matrix, the temperature change rate of each temperature control area is calculated to construct a temperature gradient vector. The temperature gradient vector captures the dynamic characteristics of heat transfer between regions by describing the rate of temperature change in the temperature control area. Combined with the thermodynamic state equation between temperature zones, the temperature gradient vector and the thermodynamic state equation are transformed in state space. The dynamic behavior of the system is represented by state variables so that the dynamic coupling characteristics of the system can be processed in a linear or nonlinear manner. Through transformation, a thermodynamic system state equation that can describe the evolution of the thermodynamic state of the entire system is constructed. In the specified prediction time domain, the thermodynamic system state equation is recursively operated to generate a temperature state prediction sequence. Recursive operation is an iterative process that realizes the step-by-step prediction of future temperature dynamics by deriving the state at the next moment based on the current state and the state equation. In order to ensure the actual execution capability of the temperature control equipment, the temperature state prediction sequence is combined with the physical constraints of the equipment. According to the temperature state prediction sequence, the output power limit conditions of the heater and the cooler are set to generate the actuator constraint vector. This vector reflects the maximum and minimum output range of the temperature control actuator under the current working conditions, ensuring that the temperature control operation will not exceed the tolerance of the equipment. The actuator constraint vector is combined with the temperature state prediction sequence to generate the temperature control area constraint matrix. The temperature control area constraint matrix is ​​divided into blocks according to the temperature zone, and the boundary temperature extreme values ​​in each temperature control zone are extracted. The boundary temperature extreme values ​​are the key indicators to ensure the safety and effectiveness of temperature control in each zone, and can reflect the minimum and maximum possible values ​​of temperature change in each zone. Based on these boundary extreme values, the temperature zone dynamic constraint equation is constructed to describe the dynamic behavior constraints of each temperature control zone in the specified prediction time domain. In order to improve the calculation efficiency and consistency, the constructed temperature zone dynamic constraint equation is normalized. By dimensionlessly processing the temperature state and constraint conditions of each zone, the temperature control standards of different zones are unified, and the final temperature state constraint conditions are generated.

[0020] In one example, finite element meshing and modal coordinate transformation are performed on multiple temperature control areas of a semiconductor device, 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, and a dynamic model of the temperature control area is obtained, 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; The temperature field discretization equations are Fourier transformed to construct the heat conduction equations including temperature distribution terms, heat source terms and boundary condition terms. The generalized coordinates of the temperature field are established by separation of variables method, and the modal dynamic equations are obtained by Lagrange transformation. Based on the modal dynamics equation, the eigenvalues ​​and eigenvectors are solved, the modal contribution analysis method is used to select the first two dominant modes, and the reduced-order temperature dynamics equation is constructed. The reduced-order temperature dynamics equation is processed by Euler discretization, and a coupled heat transfer equation group including heat conduction terms and convection heat transfer terms between temperature intervals is established. The temperature distribution coefficient and heat conduction coefficient in the coupled heat transfer equations are calibrated to obtain the calibration coefficient matrix. The temperature zone heat balance equation is established based on the calibration coefficient matrix. The heat flux density and temperature gradient of each temperature control area are numerically calculated to obtain the dynamic response characteristics of the temperature zone. The dynamic model of the temperature control area is constructed based on the dynamic response characteristics of the temperature range and the coupled heat transfer equations.

[0021] In this example, the temperature control areas of the semiconductor device are divided into several small units by tetrahedral mesh units. The nodes of each unit are interpolated by piecewise linear functions to obtain a discretized set of equations for the temperature field. For each tetrahedral unit, its node temperature is set to ( ), through the piecewise linear function Describes the temperature at any point in the cell : ; in, Nodes within the unit The corresponding shape function satisfies . By meshing the entire temperature control area and using the interpolation method, the temperature distribution of each point in the area is obtained. The temperature field discretization equations are Fourier transformed to construct a heat conduction equation group containing temperature distribution terms, heat source terms, and boundary condition terms. Fourier transform helps to convert from time domain analysis to frequency domain analysis to better capture the heat transfer characteristics of the system. In the frequency domain, the general form of the heat conduction equation is: ; in, 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 help analyze the thermal response of the system. The separation of variables method is used to establish the generalized coordinate system of the temperature field, and the modal dynamic equation is obtained through Lagrange transformation. The basic idea of ​​the separation of variables method is to transform the temperature field It is expressed as the product of the spatial component and the temporal component, that is: ; in, is the characteristic function of the spatial part, is a function of the time part. The Lagrange transformation is used to convert the coordinates and physical quantities in the equation, thereby transforming the equation into a modal dynamics equation: ; in, is the mass matrix, is the stiffness matrix, is the second-order time derivative of temperature, which represents the acceleration of temperature. By solving this equation, the eigenvalues ​​and eigenvectors of the temperature control area are obtained, reflecting the dominant modes of the system. In order to simplify the problem, the first two dominant modes are selected through modal contribution analysis. These two modes represent the most important heat transfer characteristics in the system. After selecting the dominant mode, a reduced-order temperature dynamics equation is constructed, which can reduce the amount of calculation and effectively capture the main thermal response behavior of the temperature control system. After the reduced-order temperature dynamics equation is subjected to Euler discretization, the numerical solution of the temperature control system is obtained. The form of the discrete equation is: ; in, is the time step The change in temperature, is the temperature at the next moment, and is the matrix obtained through modal analysis. This equation is used to numerically iterate and solve the dynamic temperature change of the temperature control system. After obtaining the reduced-order temperature dynamics equation, a coupled heat transfer equation group containing heat conduction terms and convection heat transfer terms between temperature intervals is established. The coupled heat transfer equation needs to consider both heat conduction and convection heat transfer effects, which jointly determine the temperature distribution in the temperature control area. The coupled heat transfer equation is in the form of: ; in, 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: ; 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.

[0022] 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: 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; 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. 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. 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.

[0023] 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 ,in represents the index of the region, Represents time. Each temperature sensor generates a temperature sequence that changes over time. These temperature sequences are subjected to fast Fourier transform and wavelet transform to extract the characteristics of the time-frequency domain. The form of Fourier transform is: ; in, is the temperature data in the frequency domain, is the frequency. Through Fourier transform, the spectrum of the temperature signal is obtained, revealing the changes of the temperature signal at different frequencies. Wavelet transform is used to further analyze the local changes of the signal in time and frequency. The formula of wavelet transform is: ; in, is the wavelet basis function, is the scale parameter, is the translation parameter, is the mother wavelet function. Wavelet transform helps the system capture the instantaneous frequency changes of temperature signals. The time-frequency feature matrix is ​​obtained by processing the data with Fourier transform and wavelet transform. , which contains the features analyzed in the time and frequency domains. The time-frequency feature matrix is ​​normalized and reconstructed. Normalization can eliminate the scale differences of the temperature sensor measurement data between different temperature control areas, so that the data can be processed at 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. The channel contains 5 residual units, each of which consists of two convolutional layers and an identity mapping. The basic structure of the residual network can effectively solve the gradient vanishing problem in deep neural networks. In each residual unit, the input After two convolutional layers, the output of the convolutional layer is Conv , then with the input Add and get the output ,Right now: ; in, and There are two convolutional layers, is the input, is the output. After residual learning, the model can learn the spatial feature vector of 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. The channel contains 3 layers of bidirectional long short-term memory network (Bi-LSTM), and each layer of Bi-LSTM contains 64 memory units. The characteristic of Bi-LSTM is that it can capture the forward and reverse information of time series data at the same time, so as to better model the temporal dependency. The basic calculation formula of Bi-LSTM is: ; in, is the hidden state at the current moment, is the input at the current moment, is the hidden state of the previous moment. In this way, the model can learn the time series characteristics from the historical temperature data and obtain the time series feature vector . The spatial eigenvector and the time series feature vector Perform feature fusion operation to obtain the fused feature vector The fused feature vector is input into the subsequent prediction network to predict the temperature series. Assuming the goal is to predict the future Temperature data at the moment , use the regression model to train the fusion features and finally get the temperature prediction sequence ,Right now: ; MLP is a multi-layer perceptron based on fusion feature vector Output temperature prediction results.

[0024] In one example, 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, including: A multi-component Gaussian mixture model is established for the temperature distribution coefficient and heat conduction coefficient in the dynamic model of the temperature control area. The weights and parameters of the Gaussian components are iteratively optimized through the expectation maximization algorithm to obtain the prior probability distribution of the temperature parameters. The temperature sensor measurement data of the semiconductor device is input into the dynamic model of the temperature control area to calculate the temperature response, a measurement likelihood function is constructed, and the product of the prior probability distribution of the temperature parameter and the measurement 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 the posterior probability fitting function, and the posterior probability fitting function is input into the second Gaussian process model for variational inference to obtain the evidence lower limit function; The Bayesian optimization method is used to construct a composite objective function including the posterior probability term and the evidence lower limit term, and the variational posterior distribution parameters are obtained through numerical iteration. The variational posterior distribution parameters are stochastically optimized, and the parameters are updated by maximizing the evidence lower bound function to obtain the optimal posterior distribution parameters. The temperature parameter probability distribution is reconstructed based on the optimal posterior distribution parameters.

[0025] In this example, the temperature distribution coefficient and thermal conductivity Modeling. 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: ; in, is the probability density function of the temperature distribution coefficient or the heat conductivity coefficient, is the number of mixture components, It is The weights of Gaussian components satisfy , and They are The mean vector and covariance matrix of the Gaussian components. The parameters of the Gaussian mixture model are optimized by 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, the posterior probability of each data point belonging to each Gaussian component is calculated, and in the M step, the model parameters are updated based on the posterior probability. For the prior probability distribution of the temperature parameter , and the optimal estimate is obtained through this process. The temperature sensor measurement data of the semiconductor device Input into the dynamic model of the temperature control area to calculate the temperature response , and construct the measurement likelihood function. Assume that the temperature measured by the sensor is and the temperature response predicted by the model There is some deviation between them, which is modeled by measurement error. The measurement likelihood function is expressed as: ; in, is a Gaussian distribution representing the temperature measurement With the model prediction value The difference between is the variance of the measurement error. The prior probability distribution of the temperature parameter The product of the measured likelihood function is logarithmically transformed to obtain the logarithmic posterior function: ; The logarithmic posterior function is used to estimate the posterior distribution of the temperature parameter. The logarithmic posterior function is input into the first Gaussian process model for probability 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 , the output is , then its joint distribution is: ; in, is the covariance matrix of the training data, is the covariance matrix between training data and test data, is the test data. Through the regression of the Gaussian process model, the posterior probability distribution of the temperature parameter is obtained. The posterior probability fitting function is input 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: ; in, is the variational distribution, is the posterior distribution, and the second term is the entropy term of the variational distribution. By maximizing the evidence lower limit function, the variational posterior distribution is obtained. After obtaining the variational posterior distribution, the temperature control model is optimized by 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 limit term. Assume that the optimization objective function is , the Bayesian optimization process will select the optimal input To maximize the objective function. In the optimization process, the numerical iteration method is used to solve the optimal variational posterior distribution parameters. Through the stochastic gradient descent algorithm, the update formula of stochastic gradient descent is: ; in, 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 parameter is obtained Based on the optimal posterior distribution parameters, the probability distribution of the temperature parameters is reconstructed, that is, the final estimate of the temperature parameters is obtained.

[0026] In one example, the temperature control range is divided into sub-domains according to the probability distribution of temperature parameters, and an optimization objective function including a prediction error term and an inter-domain difference term is constructed. The temperature inter-domain feature mapping matrix is ​​obtained by solving the gradient descent method, including: The probability density threshold analysis is performed on the probability distribution of the temperature parameters, and the temperature control range is divided into sub-domains using the equal interval division method to obtain multiple temperature control sub-domains; Perform kernel function transformation on the temperature data in each temperature control subdomain to generate subdomain feature data, divide the subdomain feature data into a source domain feature set and a target domain feature set, perform standardization on the source domain feature set and the target domain feature set to obtain a normalized feature matrix; Based on the normalized feature matrix, the maximum average difference statistic is calculated, the inter-domain feature distance measurement function is constructed, the inter-subdomain feature difference matrix is ​​obtained, and the sub-domain optimization objective function including the mean square error term and the maximum average difference term is established for the feature difference matrix; The back-propagation algorithm is used to perform gradient descent calculation on the subdomain optimization objective function to obtain the feature transformation parameter matrix, which is then input into a three-layer fully connected neural network for feature mapping to obtain the temperature domain feature mapping matrix. Each layer of the fully connected neural network uses a rectified linear function as the activation function.

[0027] In this example, a probability density threshold analysis is performed on the temperature parameter probability distribution. Assume that the temperature parameter The probability distribution of , set a threshold , so that when When , the temperature value is considered to be within the effective control range. Based on the threshold condition, the temperature control range is divided into multiple sub-domains using the equal interval division method. For example, the temperature control range is set to , by evenly spacing The range is divided into several sub-domains, and the interval of each sub-domain is: ; in is the number of subdomains after division, is the temperature interval for each subdomain. In this way, the temperature control range is refined into multiple subdomains, making the temperature change in each subdomain more controllable. The temperature data in each temperature subdomain is transformed by a kernel function to generate the characteristic data of the subdomain. By selecting an appropriate kernel function Map the input data to a high-dimensional feature space, in which the inner product of the data can better reflect its potential nonlinear relationship. For example, the Gaussian kernel function is: ; Under this transformation, the temperature data The transformed data is divided into the source domain feature set and the target domain feature set , which correspond to training data and test data respectively. These feature sets are standardized to obtain the normalized feature matrix: ; in, and are the mean and standard deviation of the source domain feature set, and is the mean and standard deviation of the target domain feature set. The purpose of the standardization operation is to make the data of different features on the same scale, thereby eliminating the impact of scale differences on subsequent processing. Based on the normalized feature matrix, the maximum average difference statistic is calculated, which is used to measure the distribution difference between the source domain and the target domain. The maximum average difference measures the difference between the source domain and the target domain by calculating the mean difference of two distributions in the feature space. The formula is: ; in, It is a mapping from kernel function to high-dimensional feature space. and are the number of samples in the source domain and the target domain, respectively. is the Hilbert space of the feature space. By calculating the MMD statistic, the feature difference matrix between subdomains is obtained, which reflects the difference between the source domain and the target domain. In order to optimize the feature mapping between subdomains, a subdomain optimization objective function containing a mean square error term and a maximum average difference term is established. The mean square error term is used to measure the gap between the model prediction value and the actual observation value, while the maximum average difference term is used to measure the distribution difference between the source domain and the target domain. The form of the objective function is: ; in, and is a hyperparameter used to balance the weights of the mean square error term and the maximum average difference term. By minimizing the objective function, the feature mapping can be optimized to minimize the feature differences between subdomains. The back propagation algorithm is used to perform gradient descent calculations on the subdomain optimization objective function. The back propagation algorithm calculates the gradient of the objective function relative to each parameter and updates the parameters based on the gradient. In each iteration, the back propagation algorithm calculates the gradient of each parameter and adjusts the weight parameters of the network by gradient descent. The update formula is as follows: ; in, 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 the 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: ; The activation function can effectively introduce nonlinear characteristics and avoid the gradient vanishing problem. Through the learning and training of the three-layer fully connected neural network, the feature mapping matrix between temperature domains is finally obtained.

[0028] In one example, the thermal coupling coefficient matrix between temperature zones is calculated based on the dynamic model of the temperature control zone, 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, including: Perform energy integration calculation on the coupled heat transfer equations in the dynamic model of the temperature control area, extract the heat flux density and temperature gradient parameters between adjacent temperature zones, and construct the thermal coupling coefficient matrix between temperature zones; Based on the thermal coupling coefficient matrix between temperature intervals, the dynamic transfer relationship between the temperature field and the heat flow field is linearized to construct the thermodynamic state equation between temperature intervals. The temperature prediction data sequence is calculated to have a deviation from the process set temperature to obtain a temperature prediction error sequence. Based on the temperature prediction error sequence, a forward recursive calculation is performed on the temperature interval thermodynamic state equation to obtain the temperature state constraint condition. The temperature state constraint conditions are converted between domains using the temperature domain feature mapping matrix to obtain a multi-temperature zone control parameter matrix. Based on the multi-temperature zone control parameter matrix, the temperature control objective function of the quadratic programming problem is constructed. The temperature control objective function is solved by the rolling time domain optimization method to obtain the control quantity optimization sequence. The control quantity optimization sequence is decoupled and distributed to obtain the temperature control quantity sequence.

[0029] In this example, the energy integration calculation is performed on the coupled heat transfer equations, the heat flux and temperature gradient parameters between adjacent temperature zones are extracted, and the thermal coupling coefficient matrix between temperature zones is constructed based on these parameters. The coupled heat transfer equations use the model of heat conduction and convection heat transfer, in which the heat conduction equation needs to be integrated in the case of multiple temperature zones to obtain the thermal coupling coefficient matrix between temperature zones. The form of the heat conduction equation in steady state is: ; in, is the temperature, is the thermal diffusivity, is the heat source term, is the density of the material, is the specific heat capacity, is the Laplace operator of temperature, which represents 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. and , whose coupling coefficient matrix elements are Calculated by the following formula: ; in, is the thermal conductivity, is the temperature gradient, is the unit normal vector, is the area of ​​the temperature zone boundary. By integrating the energy, the thermal coupling coefficients between adjacent regions are calculated, and the corresponding coupling matrix is ​​constructed. After obtaining the thermal coupling coefficient matrix between the temperature zones, the dynamic transfer relationship between the temperature field and the heat flow field is linearized to construct the thermodynamic state equation between the temperature zones. The nonlinear equation of the temperature field is approximated to a linear form for numerical calculation. For example, the temperature field is approximated by Taylor expansion or difference method. Through linearization, the temperature field Thermal flow field The relationship is expressed as a system of linear equations: ; in, is the temperature vector at the current moment, is the heat flux vector at the current moment, and are matrices representing the relationship between temperature and heat flow. After linearization, the thermodynamic state equation in the temperature range is simplified and used in the subsequent control algorithm. 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 that the temperature prediction data is , and the process setting temperature is , then the temperature prediction error series Calculated by the following formula: ; Based on the error sequence, the temperature state constraint condition is obtained by forward recursive calculation of the thermodynamic state equation in the temperature interval. 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 recursive process, the evolution of the temperature state is gradually promoted through numerical integration methods such as the Euler method or the Runge-Kutta method. Through recursion, the obtained temperature state constraint condition is expressed as: ; in, is the temperature prediction error sequence, which will affect the temperature state at the next moment. Through forward recursion, the temperature state constraints are dynamically calculated. The temperature state constraints are converted between domains using the temperature domain feature mapping matrix. The temperature domain feature mapping matrix is ​​a tool for converting and mapping temperature states between different temperature control areas, and is learned and trained through deep learning or machine learning models. For example, assuming that the temperature domain feature mapping matrix is , then the temperature state constraint is converted by the following formula: ; Map the temperature status of one area to another area to better integrate the control information of different areas and form a control parameter matrix of multiple temperature zones Based on these control parameters, a temperature control objective function of a quadratic programming problem is constructed. The temperature control objective function includes multiple target items, such as temperature deviation items, control power consumption items, etc. The objective function of the quadratic programming problem is expressed as: ; in, is the temperature deviation term, which indicates the difference between the actual temperature value and the set value. is the regularization coefficient for controlling power consumption. By optimizing the objective function, a suitable sequence of control quantities is obtained, thereby achieving precise temperature control. In order to optimize the objective function, a rolling horizon optimization method is used. By performing optimization calculations at each moment, the current control quantity is adjusted based on the prediction of the future moment. For example, in the 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 based on the current temperature state and prediction information, and adjusts it based on the new information at the next moment. This method can effectively handle the dynamics and uncertainties in the system. The optimal sequence of control quantities obtained by the rolling horizon optimization method Used for actual control of the temperature control system. After obtaining the control quantity sequence, decoupling distribution calculation is performed to ensure that the control quantities of each temperature control area are independent and coordinated, and finally the temperature control quantity sequence of each temperature control area is obtained. , thus completing the entire temperature control process.

[0030] In one example, the temperature prediction data sequence and the process set temperature are calculated for deviation to obtain a temperature prediction error sequence. Based on the temperature prediction error sequence, the temperature interval thermodynamic state equation is forward recursively calculated to obtain the temperature state constraint conditions, including: Interpolate the temperature prediction data sequence and the process setting temperature curve to obtain the temperature prediction deviation matrix. Calculate the temperature change rate of each temperature control area based on the temperature prediction deviation matrix and construct the temperature gradient vector. Perform state space transformation on the temperature gradient vector and the thermodynamic state equation between temperature intervals, construct the state equation of the thermodynamic system, perform recursive operation on the state equation of the thermodynamic system within the specified prediction time domain, and obtain the temperature state prediction sequence; 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; 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.

[0031] 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: ; 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: ; 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: ; in, is -direction temperature change rate, and so on. The thermodynamic state of the system is modeled by calculating the temperature gradient vector of the temperature control area. The state space transformation is performed based on the temperature gradient vector and the thermodynamic state equation between the temperature intervals to construct the state equation of the thermal system. The thermodynamic state equation describes the heat transfer and state change between the various regions in the temperature control system. The thermodynamic state equation includes terms such as heat conduction, convection heat transfer and radiation. Assume that the state equation of the temperature control area is: ; in, is the temperature vector at the current moment, is the heat flux vector, and is the system parameter matrix, which represents the relationship between temperature and heat flow. Through state space transformation, the dynamic evolution of temperature field is described by the above linear system equations. The state equations of the thermodynamic system are recursively calculated in the specified prediction time domain to obtain the temperature state prediction sequence. The recursive operation is implemented by numerical integration methods such as Euler method, Runge-Kutta method, etc. At each time step The temperature state will be updated according to the current temperature and heat flow input state to obtain the temperature value at the next moment. Based on the temperature state prediction sequence, the power output limit conditions of the heater and refrigerator are set. In order to ensure that the temperature control equipment will not be overloaded, the power output limit conditions are set for the heater and refrigerator. Assume that the power of the heater and refrigerator are and , then the limiting condition of power output is expressed as: ; The role of the power limit condition is to prevent the energy consumption of the control device from exceeding the maximum power limit of the system. On this basis, the actuator constraint vector is constructed , which is used to combine the actuator output with the temperature state prediction sequence to obtain the temperature control area constraint matrix. Assume that the temperature control area constraint matrix is , calculated based on the actuator constraints and the temperature prediction sequence. This matrix is ​​represented as follows: ; The constraint matrix combines the temperature prediction value and the actuator output limit to ensure that the temperature control system operates within the safety range at each moment. In order to handle the constraints of the temperature control area, the temperature control area constraint matrix is ​​processed in blocks. The temperature extremes in each temperature control area refer to the maximum and minimum values ​​of the temperature distribution in the area. These temperature extremes determine the thermodynamic boundary conditions of the area. In the dynamic constraint equation of the temperature control area, the temperature dynamic constraints of the temperature control area are calculated by considering the temperature extremes and actuator constraints. Assume that the boundary temperature extremes of the temperature control area are and , then the dynamic constraint equation is expressed as: ; Dynamic constraints ensure that the temperature of each temperature control zone remains within the set safety range, thereby avoiding overheating or overcooling of the equipment. In the temperature zone dynamic constraint equation, numerical optimization methods are used to normalize these constraints to obtain the final temperature state constraint conditions: ; Through normalization transformation, the constraints of the temperature control area are converted into a standard form to facilitate subsequent optimization and control.

[0032] Reference Figure 2 , this embodiment provides a temperature control device for semiconductor equipment, comprising: Transformation module 1 is used to perform finite element meshing and modal coordinate transformation on multiple temperature control areas of semiconductor equipment, perform eigenvalue analysis on 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; Extraction module 2, used to collect temperature sensor measurement data of semiconductor equipment and perform time-frequency domain transformation to generate a temperature distribution feature image, extract spatiotemporal features through a dual-channel deep learning model, and obtain a temperature prediction data sequence; Calculation module 3 is used to perform Gaussian mixture modeling on the temperature parameters of the dynamic model of the temperature control area 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 probability distribution of the temperature parameters; Building module 4, used for dividing the temperature control range into sub-domains according to the probability distribution of the temperature parameters, building an optimization objective function including a prediction error term and an inter-domain difference term, and obtaining a temperature inter-domain feature mapping matrix by solving the gradient descent method; Solving module 5 is used to calculate the thermal coupling coefficient matrix between temperature zones based on the dynamic model of the temperature control zone, construct the temperature control objective function by combining the temperature prediction data sequence with the temperature domain feature mapping matrix, and obtain the temperature control quantity sequence by using the model predictive control algorithm.

[0033] In this embodiment, for the specific implementation of each unit in the above device embodiment, please refer to the above method embodiment, which will not be repeated here.

[0034] Reference Figure 3 In an embodiment of the present invention, a computer device is also provided. The computer device may be a server, and its internal structure may be as follows: Figure 3 As 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 designed by the computer is used 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 used to store the corresponding data in this embodiment. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the above method is implemented.

[0035] Those skilled in the art will understand that Figure 3 The structure shown in the figure is merely a block diagram of a portion 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.

[0036] An embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the above method is implemented. It can be understood that the computer-readable storage medium in this embodiment can be a volatile readable storage medium or a non-volatile readable storage medium.

[0037] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and 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-mentioned methods. Among them, any reference to memory, storage, database or other media provided by the present invention and used in the embodiments may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double-speed data rate SDRAM (SSRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM.

[0038] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, device, article or method including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, device, article or method. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the presence of other identical elements in the process, device, article or method including the element.

[0039] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also 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 a temperature parameter probability distribution; 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; Based on the temperature control area dynamic model, the temperature coupling coefficient matrix between temperature zones is calculated, 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 solving the temperature prediction 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 between temperature intervals; 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 between temperature zones; A dynamic model of the temperature control area is constructed based on the dynamic response characteristics of the temperature 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 3, characterized in that: The temperature parameters of the temperature control area dynamic model are modeled using Gaussian mixture modeling to obtain a prior distribution, the product of the prior distribution and the measurement likelihood function is logarithmized, and the posterior probability and the lower limit of evidence are calculated using a double Gaussian process model to obtain a temperature parameter probability distribution, including: A multi-component Gaussian mixture model is established for the temperature distribution coefficient and the heat conduction coefficient in the temperature control area dynamic model, and the weights and parameters of the Gaussian components are iteratively optimized by an expectation maximization algorithm to obtain a priori probability distribution of the temperature parameters; Inputting the temperature sensor measurement data of the semiconductor device into the temperature control area dynamic model to calculate the temperature response, constructing a measurement likelihood function, performing a logarithmic transformation on the product of the temperature parameter prior probability distribution and the measurement likelihood function, and obtaining a logarithmic posterior function; Input the logarithmic posterior function into the first Gaussian process model for probability regression calculation to obtain a posterior probability fitting function, and input the posterior probability fitting function into the second Gaussian process model for variational inference to obtain an evidence lower limit function; The Bayesian optimization method is used to construct a composite objective function including the posterior probability term and the evidence lower limit term, and the variational posterior distribution parameters are obtained through numerical iteration. The variational posterior distribution parameters are subjected to stochastic gradient optimization, 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.

5. The temperature control method of semiconductor equipment according to claim 4, 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.

6. The temperature control method of semiconductor equipment according to claim 5, characterized in that: The method of calculating the thermal coupling coefficient matrix between temperature zones based on the temperature control zone dynamic model, building a temperature control objective function by combining the temperature prediction data sequence with 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 between adjacent temperature zones, and constructing a thermal coupling coefficient matrix between temperature zones; Based on the temperature interval thermal coupling coefficient matrix, the dynamic transfer relationship between the temperature field and the heat flow field is linearized to construct the temperature interval thermodynamic state equation; 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 temperature interval thermodynamic state equation 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.

7. The temperature control method of semiconductor equipment according to claim 6, characterized in that: The step of performing deviation calculation between the temperature prediction data sequence and the process setting temperature to obtain a temperature prediction error sequence, and performing forward recursive calculation on the temperature interval thermodynamic state equation based on the temperature prediction error sequence to obtain a temperature state constraint condition includes: 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 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.

8. A temperature control device for semiconductor equipment, characterized in that: For implementing the steps of the method according to any one of claims 1 to 7, the 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 between temperature zones based on the dynamic model of the temperature control zone, construct a temperature control objective function by combining the temperature prediction data sequence with the temperature domain feature mapping matrix, and obtain a temperature control quantity sequence by using a model predictive control algorithm.

9. 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 method according to any one of claims 1 to 7 are implemented.

10. 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 method according to any one of claims 1 to 7 are implemented.

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