Multi-zone multi-variable thermal disc high-precision temperature control method based on artificial intelligence and self-learning optimization

Abstract

This invention discloses a high-precision temperature control method for multi-zone, multi-variable hot plate based on artificial intelligence and self-learning optimization. Addressing the problems of insufficient temperature control accuracy, weak anti-interference capability, poor multi-variable coupling handling, and lack of self-learning ability in existing technologies, the core objective of this invention is to achieve high-precision (within ±0.1℃), high-uniformity (within ±0.2℃), and high-stability temperature control for each zone of a multi-zone hot plate; automatically resolve temperature control deviations caused by multi-zone thermal coupling and dynamic interference; possess self-learning optimization capabilities, eliminating the need for frequent manual adjustment of control parameters and adapting to changes in different process parameters and equipment states; and construct a customized hot plate technology system tailored to the unique characteristics of semiconductor multi-zone hot plate thin-plate structure, asymmetrical layout of heating elements, and predominantly radial heat conduction. Simultaneously, a three-loop timing coordination and dynamic weight control mechanism based on prediction, decoupling, and self-learning is designed to achieve full-process linkage optimization.

Description

Technical Field

[0001] This invention belongs to the field of temperature control technology and relates to a high-precision temperature control method for multi-zone, multi-variable hot plate based on artificial intelligence and self-learning optimization. Background Technology

[0002] In semiconductor manufacturing, multi-zone heating pads are key components in core processes such as wafer thermal processing and thin film deposition. Their temperature control accuracy, uniformity, and stability directly determine the wafer processing quality, yield, and device performance. As semiconductor devices iterate towards higher precision, higher density, and smaller size, extremely high requirements are placed on the temperature control of multi-zone heating pads: on the one hand, the widespread application of large-size wafers of 300mm and above requires the temperature uniformity error of each zone of the heating pad to be controlled within ±0.2℃, and the single-point temperature control accuracy to reach ±0.1℃; on the other hand, the diversity of semiconductor manufacturing processes (such as different temperature ranges, different heating rates, and different holding times), as well as the nonlinearity, large inertia, and thermal response hysteresis characteristics of the heating pad itself, make it difficult for traditional temperature control methods to adapt to complex operating conditions.

[0003] The core challenge of temperature control for multi-zone heating plates lies in "multivariable coupling" and "uncertainty of dynamic interference": the various zones of the heating plate have a strong coupling effect through heat conduction and heat radiation, and the temperature adjustment of one zone will affect the temperature stability of adjacent zones; at the same time, factors such as ambient temperature fluctuations, wafer material differences, heating element aging, and process parameter switching during the manufacturing process will continuously interfere with the temperature control system, causing the control accuracy and stability of traditional control methods to decline, and making it impossible to meet the stringent process requirements of semiconductor manufacturing in the long term.

[0004] Currently, temperature control of multi-zone hot plates in semiconductor manufacturing mainly relies on parameter tuning strategies, employing methods such as traditional PID control, piecewise PID control, or fuzzy PID control. However, this approach suffers from the following core problems:

[0005] Insufficient temperature control accuracy, weak anti-interference ability, and poor stability;

[0006] The multivariable coupling processing effect is poor, and the general decoupling model cannot adapt to the specific structural characteristics of the hot plate.

[0007] Manually determining PID parameters relies on the engineer's experience, and the debugging process is time-consuming and labor-intensive.

[0008] It lacks self-learning ability, has poor adaptability, and cannot cope with long-term changes in operating conditions caused by equipment aging and process switching.

[0009] The prediction, decoupling, and control modules operate independently without a coordination mechanism, which can easily lead to control conflicts. Summary of the Invention

[0010] To address the shortcomings of existing technologies, such as insufficient temperature control accuracy, weak anti-interference capability, poor handling of multi-variable coupling, and lack of self-learning ability, this invention provides a high-precision temperature control method for multi-zone, multi-variable hot plate based on artificial intelligence and self-learning optimization. The core objectives of this method are: to achieve high-precision (within ±0.1℃), high-uniformity (within ±0.2℃), and high-stability temperature control for each zone of the multi-zone hot plate; to automatically resolve temperature control deviations caused by multi-zone thermal coupling and dynamic interference; to possess self-learning optimization capabilities, eliminating the need for frequent manual adjustment of control parameters and adapting to changes in different process parameters and equipment states; and to construct a customized hot plate technology system tailored to the unique characteristics of semiconductor multi-zone hot plate thin-plate structure, asymmetrical layout of heating elements, and predominantly radial heat conduction. Simultaneously, a three-loop timing coordination and dynamic weight control mechanism based on prediction, decoupling, and self-learning is designed to achieve full-process linkage optimization.

[0011] This invention includes the following steps:

[0012] Real-time collection of temperature data, heating power data, operating parameters and health status parameters of each zone of the multi-zone hot plate; adaptive outlier removal, noise reduction and adaptive normalization of operating conditions are performed on the collected data to obtain a pre-processed dataset.

[0013] Feature parameters related to the temperature control target are extracted from the preprocessed dataset. A multivariate decoupling model based on the two-dimensional heat conduction equation of the hot plate is constructed. An asymmetric decoupling matrix is ​​used to eliminate inter-regional thermal coupling interference. The coupling coefficient is identified and updated online based on real-time operating conditions to obtain the decoupling equivalent control quantity of each region.

[0014] An LSTM temperature prediction model integrating the hot plate health status and Smith predictor is constructed. The decoupled temperature data, power data and health status parameters are input into the model to predict the temperature change trend in multiple sampling periods in the future and obtain the temperature prediction value.

[0015] A three-loop timing coordination mechanism of prediction-decoupling-self-learning is established, and the working weight of the three loops is dynamically adjusted according to the real-time temperature control status. When the decoupling residual or prediction error exceeds the set threshold, rapid iteration is triggered. The PPO reinforcement learning algorithm is used to construct a multi-objective optimization function that includes temperature control accuracy and temperature uniformity, and automatically tunes the PID control parameters of each zone.

[0016] Based on the thermal characteristics differences between the center and edge zones of the hot plate, a differentiated composite control strategy is executed. The power control quantity of each zone is calculated based on the optimized PID parameters and LSTM prediction feedforward compensation. Adjacent zones are coupled and compensated through a power coordination mechanism between zones, and the final heating power control signal is output to drive the heating element to work.

[0017] The system collects the actual temperature of each zone in real time, calculates the temperature control error, decoupling residual, and prediction error. When the error exceeds the preset threshold, it triggers corresponding decoupling coefficient correction, prediction model update, parameter optimization, or database rematching operations to form a closed-loop feedback control.

[0018] The beneficial effects of this invention are:

[0019] Compared with traditional PID control, this invention integrates artificial intelligence (LSTM prediction based on the health status of the hot plate and decoupling of two-dimensional heat conduction specific to the hot plate) and reinforcement learning self-learning optimization, eliminating the need for manual parameter tuning and enabling rapid and dynamic adaptation to changes in operating conditions. It designs a preprocessing algorithm with enhanced anti-interference robustness and a Smith predictor-fused compensation algorithm, effectively addressing the shortcomings of traditional PID control, such as fixed parameters, weak anti-interference capability, insufficient temperature control accuracy, and poor thermal hysteresis compensation. Temperature control accuracy reaches within ±0.1℃, and temperature uniformity reaches within ±0.2℃ (set temperature within 250℃, 12-inch wafer), while simultaneously reducing heating power fluctuation by more than 40%.

[0020] Compared with fuzzy PID and piecewise PID control, this invention designs a multivariable decoupling module specifically for hot plates, addressing the multi-zone thermal coupling problem. Combined with an asymmetric decoupling matrix and a real-time online identification mechanism, the decoupling error is reduced by more than 30%. A three-loop collaborative mechanism of prediction-decoupling-self-learning is constructed to achieve full-process linkage optimization and avoid control conflicts. It has complete multi-objective self-learning iteration capabilities, continuously optimizing parameters according to equipment status and process changes. Existing methods lack self-learning capabilities, cannot adapt to dynamic operating conditions, and do not fully consider the multi-zone coupling effect.

[0021] Compared with existing intelligent temperature control methods, this invention achieves a fully closed-loop integration and three-loop coordinated linkage of "prediction-decoupling-optimization-control-feedback", combining temperature control accuracy and temperature uniformity as multi-objective optimization goals, rather than solely pursuing temperature control accuracy; it adopts the PPO reinforcement learning algorithm to achieve multi-objective parameter optimization, which has higher self-learning efficiency and more accurate parameter optimization; it constructs a two-dimensional heat conduction decoupling model based on the unique structural characteristics of the hot plate, rather than the general MIMO decoupling method, so that the decoupling effect is more in line with the actual working conditions of semiconductor multi-zone hot plates; at the same time, it integrates the health status of the hot plate and process parameters to construct a multi-dimensional predictive feature system, which has higher prediction accuracy and stronger adaptability.

[0022] This invention designs a complete set of technical solutions for the unique characteristics of semiconductor multi-zone hot plates, such as thin plate structure, asymmetric layout, and radial heat conduction, which is fundamentally different from the heavy oil coupling control of steel plant heating furnaces and the general BP neural network PID control of diffusion furnaces. The proposed innovations, such as zone adaptive control, inter-zone power coordination, and three-dimensional classification parameter database, are fully adapted to the stringent requirements of large-size semiconductor wafer manufacturing.

[0023] Enhanced adaptability and practicality: This invention can be adapted to multi-zone hot disks with any number of partitions, and is especially optimized for manufacturing scenarios of large-size wafers of 300mm and above. It can be directly integrated into existing semiconductor manufacturing equipment without large-scale modification. Through a three-dimensional classification parameter database, it achieves rapid adaptation of working conditions, improves parameter calling efficiency by 80%, and has extremely high industrial application value. Attached Figure Description

[0024] Figure 1 This is a flowchart of the method in this application;

[0025] Figure 2 This is a schematic diagram of the hot disk and its corresponding partition in the embodiment;

[0026] Figure 3 This is a diagram showing the result of data noise reduction processing in the example;

[0027] Figure 4 The following is a graph showing the analysis results of some parameters in the example;

[0028] Figure 5 The result diagram of multi-zone hot plate thermal simulation;

[0029] Figure 6 This is a schematic diagram of the training loss curve;

[0030] Figure 7 This is a schematic diagram of the fitting results;

[0031] Figure 8 This is a temperature curve diagram for each zone of the hot plate;

[0032] Figure 9 To acquire temperature cloud maps for wafer sensors. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0034] This embodiment provides a high-precision temperature control method for multi-zone, multi-variable hot plate based on artificial intelligence and self-learning optimization, applicable to semiconductor manufacturing scenarios. The method is adaptable to multi-zone hot plates with any number of zones (e.g., 7 zones, 24 zones, etc.), and is particularly optimized for manufacturing large-size wafers of 300mm and above. It can achieve temperature uniformity error control within ±0.2℃ (for 12-inch wafers) across all zones of the hot plate, and single-point temperature control accuracy within ±0.1℃ (for set temperatures within 250℃), while simultaneously reducing heating power fluctuation by more than 40%.

[0035] like Figure 1 As shown, the method includes the following steps:

[0036] Step S1: Data acquisition and preprocessing with enhanced anti-interference robustness

[0037] A 7-zone hot plate (model: HL-00599(OV)-EO) was selected as the test verification object. Each zone is equipped with an independent heating element and a high-precision temperature sensor. The sensor is a PT1000 (accuracy ≥ 0.1℃, minimum temperature unit is 0.01℃). Temperature measurement points are evenly arranged radially in the blind holes of each zone and fixed with thermally conductive silicone. A wafer temperature sensor is placed on the front to ensure the accuracy of temperature acquisition. At the same time, a power acquisition module is deployed at the end of each heating element, and an ambient temperature sensor is deployed in the hot plate cavity to collect parameters related to the health status of the hot plate.

[0038] Multi-dimensional data collection: such as Figure 2 As shown, the system collects real-time temperature data, heating element power, ambient temperature, target temperature, heating rate, and wafer process parameters (material and process type) at each temperature measurement point in each zone. At the same time, it calculates the aging coefficient of the heating element, the thermal resistance coefficient of the hot plate fouling, and the drift coefficient of the temperature sensor, etc., through historical power-temperature response data, forming a multi-dimensional data collection dataset of "temperature + power + operating conditions + health status".

[0039] The following is a portion of the raw data collected:

[0040]

[0041] The collected datasets are preprocessed to enhance their robustness against interference, addressing data distortion issues caused by strong electromagnetic interference and large temperature fluctuations in semiconductor manufacturing workshops. The steps are as follows:

[0042] 1) Adaptive 3σ outlier removal

[0043] Abnormal temperature data caused by sensor malfunctions and electromagnetic interference are eliminated using the 3σ criterion. If the collected temperature data... satisfy:

[0044]

[0045] If it is an outlier, it will be removed.

[0046] in, Let be the average temperature of region i. The standard deviation is denoted as . For the sample size, This is an adaptive coefficient, which is adjusted adaptively according to ambient temperature fluctuations (when the ambient temperature fluctuation is ≤ ±1℃). When environmental fluctuations are greater than ±1℃ ).

[0047] 2) Noise reduction processing (wavelet transform + EMD composite noise reduction)

[0048] Using the db4 wavelet basis with a 3-level decomposition, wavelet transform is first applied to the temperature data to eliminate high-frequency electromagnetic interference, followed by empirical mode decomposition (EMD) to eliminate low-frequency ambient temperature drift interference. Compared to a single wavelet transform, the signal-to-noise ratio of the denoised data is improved by 35%. The reconstruction formula is:

[0049]

[0050] in This is a low-frequency approximation component. The high-frequency detail components (reconstructed after removing high-frequency noise components) are then decomposed using EMD to eliminate low-frequency drift components, resulting in clean temperature data. See [link to EMD]. Figure 3 .

[0051] 3) Adaptive Normalization of Operating Conditions

[0052] Different normalization formulas are used for different temperature ranges (low temperature ≤100℃, medium temperature 100-250℃, high temperature >250℃) to avoid accuracy loss after normalization of data in the low temperature range. Parameters of different magnitudes, such as temperature, power, ambient temperature, and health status parameters, are normalized to the [0,1] range to facilitate subsequent algorithm calculations. Specifically:

[0053] Low temperature range:

[0054] Medium / high temperature range:

[0055] 4) Data fusion

[0056] The temperature data from multiple temperature measurement points in each partition are weighted and fused to obtain the average temperature value of each partition, which serves as the real-time temperature representation of that partition. Simultaneously, the health status parameters of the heat exchanger are normalized and fused to form a health status feature vector. The preprocessed dataset is used for subsequent decoupling, prediction, and optimization.

[0057] Step S2: Feature Selection

[0058] Data mining was conducted based on the characteristics of the hot plate and its specific application conditions, combining the experience of process experts, mechanistic analysis, and equipment parameters. The initially selected characteristic parameters include:

[0059] Temperature characteristics (related to core temperature control targets): real-time temperature of each zone, mean / variance of temperature at each zone's temperature measurement point, real-time temperature of the wafer surface, ambient temperature, target temperature of each zone, and rate of temperature change;

[0060] Power characteristics (related to control input): Real-time power of heating elements in each zone, power change rate, power output limit, and historical power adjustment;

[0061] Operating characteristics (process and scenario related): various gas flow rates, heating rates, holding times, wafer materials / specifications, process types (heat treatment / thin film deposition), and workshop ambient humidity;

[0062] Health status characteristics (related to equipment aging): heating element aging coefficient, hot plate fouling thermal resistance coefficient, temperature sensor drift coefficient, and cumulative working time of heating element;

[0063] Coupling characteristics (related to thermal coupling effect): center distance of each zone, thermal coupling space attenuation coefficient, temperature difference between adjacent zones, and power regulation difference between adjacent zones.

[0064] Multidimensional correlation analysis was performed using Pearson correlation coefficient and Spearman rank correlation coefficient, see [link to relevant documentation]. Figure 4 The correlation coefficients between features are calculated. A threshold is set to remove highly redundant features (absolute correlation coefficient ≥ 0.85), retaining features with more direct physical meaning, higher acquisition accuracy, and stronger data stability. Features with an absolute correlation coefficient ≥ 0.3 with temperature control error (dependent variable) are also retained to ensure a strong correlation between features and the temperature control target.

[0065] After screening, weakly correlated or redundant features such as "workshop ambient humidity" (correlation coefficient with temperature control error is only 0.12) and "cumulative working time of heating elements" (correlation coefficient with "heating element aging coefficient" is 0.92, and the aging coefficient is a direct characterizing feature) were removed; core features such as "real-time temperature of each zone" (replacing the temperature variance of the temperature measurement point, the variance is a derived feature and is highly redundant with the real-time temperature) and "difference in power adjustment between adjacent zones" (directly characterizing the coupling strength and with a clearer physical meaning) were retained, optimizing the feature dimensions and reducing the computational complexity of the algorithm model.

[0066] Step S3: Decoupling of two-dimensional heat conduction for hot plate

[0067] To address the thermal coupling effect between different zones of a multi-zone hot plate, this paper abandons the decoupling method of general MIMO systems and designs a multivariate decoupling module based on the hot plate's proprietary two-dimensional heat conduction equation. Combining the characteristics of the hot plate's thin plate structure, asymmetric layout, and predominantly radial heat conduction, a spatial thermal coupling attenuation model and an asymmetric decoupling matrix are constructed to achieve real-time online identification of coupling coefficients and eliminate temperature interference between zones.

[0068] The core of the decoupling module is to construct a dedicated thermal coupling correlation model for the heat plate. Based on the laws of heat conduction and spatial heat distribution data from thermal simulation software, a two-dimensional thermal conduction and thermal coupling mathematical model of the multi-zone heat plate is established. The heating power of each zone is input, and the temperature response of each zone is output. The spatial thermal coupling coefficient between zones (characterizing the nonlinear correlation between zone distance and thermal coupling strength) is analyzed. Assuming that the multi-zone heat plate is divided into N independent control zones and secondary interference factors are ignored, a dynamic mathematical model of temperature for each zone is constructed to achieve precise decoupling.

[0069] 1) Dedicated two-dimensional heat conduction multi-zone thermal coupling dynamic model for hot plate

[0070] Based on the two-dimensional heat conduction equation of the hot plate thin-plate structure, combined with the spatial heat distribution data from thermal simulation, see... Figure 5 A spatial attenuation model for partitioned thermal coupling is established to quantify the nonlinear correlation between "partition distance and thermal coupling coefficient". The temperature dynamic characteristics of the i-th partition are expressed using a Laplace transform as follows:

[0071]

[0072] Symbol definition:

[0073] : Laplace transform of the temperature of the i-th partition (unit: °C);

[0074] : Laplace transform of the heating power control quantity of the i-th zone (unit: W);

[0075] The self-channel transfer function of the i-th partition, characterizing the effect of its own power on temperature, is of the form: ( This is the gain coefficient. It is a time constant. (This refers to the thermal response hysteresis time).

[0076] The coupling channel transfer function of the j-th partition to the i-th partition has the same form as the self-channel transfer function, but the gain coefficient is smaller than that of the self-channel.

[0077] : Thermal coupling space attenuation coefficient (determined by the material and structure of the heat plate, calibrated through simulation);

[0078] : The center distance between the i-th partition and the j-th partition (unit: mm);

[0079] : Laplace transform of the disturbance signal of the i-th partition (including ambient temperature fluctuations, wafer load changes, heating element aging, etc., unit: ℃).

[0080] 2) Design and decoupling of asymmetric decoupling matrices

[0081] Decoupling Objective: To design an asymmetric decoupling matrix for 7-zone / 24-zone heating plates with asymmetrical heating element layout. , offset coupling terms This makes the multivariable coupled system equivalent to N independent single-variable temperature control subsystems, enabling independent control of each zone. Differentiated decoupling weights are set for the central zone and the edge zone, as well as the adjacent zone and the non-adjacent zone, reducing the decoupling error by more than 30%.

[0082] Design formula for decoupling matrix:

[0083]

[0084] in:

[0085] : Power control vectors for each partition before decoupling;

[0086] : Equivalent power control vectors for each partition after decoupling;

[0087] : An N×N order asymmetric decoupling matrix, whose elements Based on the differentiated design of partition distance and thermal coupling spatial attenuation characteristics, and identified through a BP neural network, it meets the following requirements. (i≠k), ensuring that the coupling terms are completely canceled out.

[0088] Differentiated decoupling weights are applied to the central and edge partitions, as well as adjacent and non-adjacent partitions, reducing the decoupling error by more than 30%. After decoupling, the temperature dynamic model of the i-th partition is simplified to:

[0089]

[0090] in The amplitude of the decoupled disturbance signal is significantly reduced and can be eliminated through subsequent PID control.

[0091] 3) Real-time online identification of thermal coupling coefficient

[0092] Abandoning the traditional "offline identification, fixed use" model, a real-time online identification mechanism for thermal coupling coefficients is proposed. A BP neural network is used to identify the transfer function parameters of the self-channel and coupled channels. Based on the real-time temperature change rate and heating power increment of each partition, the coupling coefficient matrix is ​​dynamically updated to adapt to the coupling characteristic drift caused by heating element aging and wafer load changes.

[0093] The input to the neural network is the power of each partition. disturbance Real-time temperature change rate The output is the temperature of each zone. During training, gradient descent is used to optimize parameters, and the loss function formula is:

[0094]

[0095] in The number of training samples. Let i be the actual temperature of the i-th region of the m-th sample. To predict temperature using the model, train to The system stops at a certain time to obtain an accurate coupling coefficient; at the same time, the coupling coefficient is corrected every 10 sampling cycles based on real-time operating data to achieve online identification.

[0096] By decoupling, the multivariable coupled temperature control system is transformed into N independent single-variable temperature control subsystems. Each subsystem corresponds to a hot plate partition, enabling independent and precise temperature control of each partition and improving overall temperature uniformity.

[0097] Step S4: Artificial Intelligence Temperature Prediction

[0098] To address the temperature overshoot and oscillation issues caused by the nonlinearity, large inertia, and hysteresis characteristics of the hot plate, this paper abandons the common single-feature prediction model of "temperature + power" and constructs an LSTM (Long Short-Term Memory) temperature prediction model that integrates the health status of the hot plate and the Smith predictor. This model enables accurate prediction of temperature change trends, provides support for precise control, and solves the problem that traditional prediction models ignore equipment aging, leading to a decrease in prediction accuracy over time.

[0099] 1) Construction of a multi-dimensional predictive feature system

[0100] The preprocessed dataset is selected as training samples to construct a four-dimensional input feature system of "temperature + power + operating condition + health status," breaking through the limitations of traditional single features. Input features include: the uninterrupted temperature value of each partition after decoupling, real-time heating power, ambient temperature, heating rate, target temperature, wafer process parameters (material, process type), and hot plate health status feature vector (heating element aging coefficient, hot plate fouling thermal resistance coefficient, temperature sensor drift coefficient). Output features are: predicted temperature values ​​for each partition within the next 1-5 sampling periods.

[0101] 2) LSTM prediction model construction and training

[0102] An LSTM prediction model is constructed, consisting of an input layer, hidden layers, and an output layer. The hidden layers employ a two-layer structure, with the number of neurons adaptively adjusted based on the number of partitions N (ideally 64-128 neurons). The Adam optimizer is used to train the model, and overfitting is avoided by adjusting the learning rate and regularization parameters. The LSTM remembers historical temperature change patterns through the coordinated operation of forget gates, input gates, and output gates, preventing gradient vanishing. The formulas for each gate unit are as follows:

[0103] Forget Gate Formula:

[0104]

[0105] Input gate formula:

[0106]

[0107] Formula for current cell state candidate values:

[0108]

[0109] Cell state update formula:

[0110]

[0111] Output gate formula:

[0112]

[0113] Hidden layer output formula:

[0114]

[0115] Symbol definition:

[0116] The output of the forget gate determines whether to retain or forget historical cell state information, with a value range of [0,1].

[0117] : Input gate output, determines the retention ratio of the current input information, with a value range of [0,1];

[0118] : Candidate value for the current cell state, ranging from [-1, 1];

[0119] Cell state at time t, storing long-term characteristics of temperature changes;

[0120] : Output gate output, determines the output ratio of cell state, value range [0,1];

[0121] The hidden layer output at time t serves as the feature representation for the current time step.

[0122] The hidden layer output at time t-1;

[0123] : The model input feature vector at time t (temperature, power, ambient temperature, etc. after decoupling);

[0124] Weight matrix of each gate unit;

[0125] : The bias vector of each gating unit;

[0126] : sigmoid activation function Hyperbolic tangent activation function;

[0127] Element-wise multiplication operation.

[0128] 3) Fusion compensation algorithm of Smith predictor and LSTM

[0129] Instead of simply adding external components, the lag compensation Δτ of the Smith predictor is used as the hidden layer bias correction term of the LSTM model, allowing for a deep integration of lag compensation and time series prediction. Compared with the traditional linear combination of "prediction + compensation", the lag error compensation effect is improved by 40%, and the prediction error is stabilized within 0.03℃.

[0130] The multi-step lead prediction output formula of the LSTM model is:

[0131]

[0132] Symbol definition:

[0133] : The predicted temperature of the i-th partition in the next k steps (k=1~5) (unit: °C);

[0134] Historical data window length (preferably p=10~20, adjusted according to sampling frequency);

[0135] : The mapping function of the LSTM model;

[0136] : Feature vector of the health status of the hot plate in the i-th region;

[0137] The lag compensation for the Smith predictor is calculated using the following formula: ;

[0138] LSTM output gate bias correction factor (calibrated to 0.1-0.3 by simulation).

[0139] After model training, the prediction error is ≤0.05℃, the root mean square error (RMSE) is 0.034, the mean absolute error (MAE) is 0.021, and the coefficient of determination (R²) is 0.98. It can accurately predict future temperature change trends (such as whether overshoot or excessive bias will occur). The training loss curve is shown below. Figure 6 As shown, the fitting effect is as follows: Figure 7 As shown.

[0140] Step S5: Collaborative Prediction-Decoupling-Self-Learning Three-Ring Optimization and Multi-Objective Self-Learning Parameter Optimization

[0141] To address the control conflicts and low optimization efficiency caused by the independent operation of prediction, decoupling, and self-learning modules in traditional temperature control algorithms, a three-loop time-series collaborative and dynamic weight adjustment mechanism of prediction-decoupling-self-learning is designed. This mechanism allows the three core modules to work together on a time scale and adaptively adjust their weights according to the temperature control state. For multi-objective optimization, a PPO (Proximal Policy Optimization) reinforcement learning algorithm is adopted to construct an "accuracy + uniformity" objective optimization function, thereby realizing the PID control parameters (…). The system features online automatic tuning, enabling adaptive optimization without manual intervention, while balancing temperature control performance with industrial application requirements.

[0142] 1) Prediction-Decoupling-Self-Learning Three-Ring Timing Coordination Mechanism

[0143] Set time-scale matching rules for the three-loop operation to enable the three modules to work together on a time scale, avoiding control conflicts and adapting to the instantaneous, short-term, and long-term requirements of hot plate temperature control:

[0144] Decoupling module: Millisecond-level real-time decoupling (handles instantaneous interference from spatial thermal coupling, with a response time ≤100ms);

[0145] LSTM prediction model: Sampling period level advance prediction (1-5 sampling periods, handling thermal inertia lag, response time matched with sampling frequency);

[0146] PPO self-learning module: Operating condition-level iterative optimization (each batch of process / equipment status changes, handling long-term model mismatch, and the iteration cycle is adaptively adjusted according to the operating condition changes).

[0147] 2) Three-ring dynamic weight control mechanism

[0148] A three-ring collaborative weighting factor model is constructed. Based on the real-time temperature control status (heating stage / heat preservation stage, presence or absence of external interference, and magnitude of temperature control error), the weights of decoupling, prediction, and self-learning are adaptively adjusted. The total weight is 1, ensuring that each module functions as needed.

[0149] Heating Phase: Predictive Model Weights Decoupling module weights Self-learning module weights Prioritize suppressing overshoot;

[0150] Insulation Phase: Decoupling Module Weights Predictive model weights Self-learning module weights Prioritize ensuring temperature uniformity;

[0151] Weighting of self-learning modules during equipment aging / strong environmental interference Predictive model weights Decoupling module weights Quickly optimize PID parameters;

[0152] In steady-state, undisturbed condition: weights of the decoupling modules Predictive model weights Self-learning module weights Balanced optimization.

[0153] 3) Error-linked triggering mechanism

[0154] The decoupling residual and prediction error are used as the trigger threshold conditions for self-learning optimization. When the decoupling residual > 0.03℃ or the prediction error > 0.05℃, the rapid iteration of PPO self-learning is immediately triggered (the iteration step size is increased by 50%), realizing the linkage between "local error and global optimization". Compared with the traditional "fixed period optimization", the parameter adjustment response speed is increased by 50%.

[0155] 4) Multi-objective optimization function

[0156] The optimization objectives are to minimize temperature control error and improve temperature uniformity. A multi-objective optimization cost function is constructed, as shown in the following formula:

[0157]

[0158] Symbol definition:

[0159] : Target optimization cost function (the smaller the value, the better the overall performance of temperature control);

[0160] : The target process temperature for the i-th partition (unit: °C);

[0161] The weighting coefficients of each optimization objective are adaptively adjusted according to the semiconductor process requirements, prioritizing the constraint of temperature control uniformity, and are typically set to... , ;

[0162] Temperature difference across the entire disk surface, characterizing temperature uniformity (unit: °C).

[0163] 5) Update of multi-objective reinforcement learning strategies

[0164] The PPO algorithm adjusts the policy network parameters. (Corresponding PID parameters) Minimize the multi-objective optimization objective function The optimization logic adopts a hierarchical approach of "prioritizing the primary objective and constraining the secondary objective": the primary objective is temperature uniformity. The primary objective must meet the hard constraint of ±0.2℃; the secondary objective is temperature control accuracy, which is optimized under the premise that the primary objective is met, to avoid conflicts in the indicators of multi-objective optimization.

[0165] The strategy update formula is:

[0166]

[0167] Symbol definition:

[0168] Policy network parameter vectors before and after update ( );

[0169] Learning rate (preferred) Adjusted during rapid iteration );

[0170] : For parameters The gradient;

[0171] In strategy The following expectations;

[0172] The reward function is negatively correlated with the multi-objective optimization objective function. The better the temperature control performance, the higher the reward value;

[0173] KL divergence weights (used to limit the magnitude of policy updates and prevent instability caused by excessively rapid updates);

[0174] : KL divergence of the policy before and after the update, representing the magnitude of the policy change.

[0175] 6) Construction of a 3D classification parameter database

[0176] The self-learning module continuously iterates and updates strategy parameters, while recording the optimal PID parameter combination. It stores the parameters in a three-dimensional category of "process type + hot plate health status + wafer specification", forming a parameter database dedicated to semiconductor manufacturing. When encountering the same / similar working conditions, it can achieve parameter retrieval in seconds and local fine-tuning. Compared with the traditional "optimization from scratch", the parameter adaptation efficiency is improved by 80%, while avoiding frequent and large adjustments to heating power.

[0177] Step S6: Precise power control and closed-loop feedback correction with zone-adaptive technology

[0178] To address the thermal characteristic differences between the central and edge zones of the hot plate (the central zone has high thermal inertia, while the edge zone is more susceptible to environmental interference), a zone-adaptive composite control algorithm of "incremental PID + LSTM predictive feedforward" is adopted. Combined with PID parameters optimized by multi-objective self-learning, differentiated control logic is customized for different zones. At the same time, a power coordination mechanism between zones is designed to avoid temperature fluctuations in adjacent zones caused by power adjustments in a single zone. Finally, long-term stability of the temperature control system is achieved through closed-loop feedback correction and error linkage triggering.

[0179] 1) Partition Adaptive Composite Control Strategy

[0180] Based on the thermal characteristics of different partitions of the hot disk, design differentiated composite control logic:

[0181] Central zone: High thermal inertia and strong anti-interference ability. It adopts "LSTM feedforward + integral separation PID" control. Integral separation PID avoids integral saturation during the heating stage, and combined with LSTM feedforward, it suppresses overshoot caused by thermal inertia.

[0182] Edge partition: with low thermal inertia and susceptible to interference from ambient temperature fluctuations, it adopts "LSTM feedforward + derivative-first PID" control. The derivative-first PID prioritizes the differentiation of the temperature measurement value to suppress temperature fluctuations caused by environmental interference and improve anti-interference capability.

[0183] 2) Incremental PID control law

[0184] To avoid integral saturation and improve control stability, incremental PID control is used in the basic control, and the formula for the control increment is:

[0185]

[0186] The formula for the actual output control quantity is:

[0187]

[0188] Symbol definition:

[0189] : Control increment of the i-th partition at time t (unit: W);

[0190] : The PID parameters (proportional coefficient, integral coefficient, derivative coefficient) of the i-th partition obtained by multi-objective self-learning optimization;

[0191] Temperature control error of the i-th partition at time t (unit: °C);

[0192] : Control quantity of the i-th partition at time t-1 (unit: W);

[0193] LSTM prediction feedforward compensation (unit: W).

[0194] 3) LSTM predicts feedforward compensation amount

[0195] The feedforward compensation is calculated based on the LSTM temperature prediction value and is used to suppress temperature fluctuations in advance. The formula is as follows:

[0196]

[0197] in Forward gain coefficient (preferred) The center partition is set to 1.0. 1.2, edge partitioning is set to 0.8 (1.0) When the predicted temperature is higher than the target temperature, the feedforward compensation is negative, and the heating power is reduced in advance; when the predicted temperature is lower than the target temperature, the feedforward compensation is positive, and the heating power is increased in advance, thus achieving proactive control.

[0198] 4) Inter-regional power coordination mechanism

[0199] When a power adjustment is performed on a certain partition, micro-power compensation (≤0.5W) is applied to adjacent partitions based on the real-time coupling coefficient of the decoupling module. This avoids temperature fluctuations in adjacent partitions caused by power adjustments in a single partition, further improving overall temperature uniformity. The compensation power formula is:

[0200]

[0201] in These are the coupling compensation coefficients in the decoupling matrix. Let be the power adjustment amount for the i-th partition. This is the thermal coupling space attenuation coefficient. This represents the distance between the partition centers.

[0202] 5) Closed-loop feedback correction and error linkage triggering

[0203] A multi-level closed-loop feedback correction system is constructed to compare the actual temperature acquisition values ​​of each zone (after preprocessing and decoupling) with the target temperature in real time, calculate the temperature control error, decoupling residual, and prediction error, and realize multi-level feedback and linkage triggering.

[0204] First-level feedback: When the temperature control error is >0.05℃, the PID control quantity and feedforward compensation quantity are immediately adjusted to achieve real-time correction;

[0205] Secondary feedback: When the decoupling residual is >0.03℃, the online correction of the coupling coefficient of the decoupling module is triggered to improve the decoupling effect;

[0206] Three-level feedback: When the prediction error is >0.05℃, it triggers the rapid iteration of the bias correction and self-learning module of the LSTM prediction model, realizing the dual optimization of the model and parameters.

[0207] Level 4 feedback: When the temperature control error is >0.1℃ for 10 consecutive sampling cycles, the parameter database is re-matched and globally optimized to ensure that the temperature control accuracy always meets the requirements.

[0208] Based on actual temperature control test results, setting the temperature below 250℃ can achieve temperature uniformity control of each zone of the hot plate within ±0.2℃ (12-inch wafer). See [link / reference]. Figure 8 and Figure 9 The single-point temperature control accuracy reaches within ±0.1℃, while the heating power fluctuation rate is reduced by more than 40%.

[0209] Example 2: Algorithm Deployment and System Integration

[0210] This embodiment provides an integrated deployment scheme for the above-described temperature control method in existing semiconductor manufacturing equipment. The method can be directly integrated into the temperature control system of existing semiconductor manufacturing equipment without requiring large-scale equipment modifications, demonstrating strong compatibility.

[0211] 1. System Architecture Deployment

[0212] Edge computing layer: Deployed on the device control unit, responsible for real-time data acquisition, preprocessing, decoupled calculation and PID control output, with a response time of ≤100ms;

[0213] Model inference layer: Deployed on an industrial control computer or edge server, it is responsible for the inference calculation of the LSTM prediction model, and the prediction period is matched with the sampling frequency;

[0214] Optimization Learning Layer: Deployed in the cloud or on a local server, it is responsible for training and optimizing the parameters of the PPO self-learning algorithm, and regularly updates the model weights and PID parameter database.

[0215] 2. Communication and Synchronization Mechanism

[0216] The decoupling module communicates with the PID control via a real-time bus (such as EtherCAT) to ensure millisecond-level response;

[0217] The LSTM prediction model receives preprocessed feature data through a buffer queue and outputs a prediction value once per sampling period.

[0218] The PPO self-learning module receives historical batch data through asynchronous communication, updates the strategy in non-real-time, and distributes the updated parameters to the edge computing layer through the configuration file.

[0219] 3. Human-computer interaction interface

[0220] Real-time display of temperature curves, prediction curves, and power output curves for each zone;

[0221] Displays the working status and current weight allocation of the three rings;

[0222] It provides a process parameter configuration interface, supporting the setting of parameters such as process type, target temperature, and heating rate;

[0223] Displays the health status assessment results and maintenance recommendations for the hot plate.

[0224] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A high-precision temperature control method for multi-zone, multi-variable hot plate based on artificial intelligence and self-learning optimization, characterized in that: Includes the following steps: Real-time collection of temperature data, heating power data, operating parameters and health status parameters of each zone of the multi-zone hot plate; adaptive outlier removal, noise reduction and adaptive normalization of operating conditions are performed on the collected data to obtain a pre-processed dataset. Feature parameters related to the temperature control target are extracted from the preprocessed dataset. A multivariate decoupling model based on the two-dimensional heat conduction equation of the hot plate is constructed. An asymmetric decoupling matrix is ​​used to eliminate inter-regional thermal coupling interference. The coupling coefficient is identified and updated online based on real-time operating conditions to obtain the decoupling equivalent control quantity of each region. An LSTM temperature prediction model integrating the hot plate health status and Smith predictor is constructed. The decoupled temperature data, power data and health status parameters are input into the model to predict the temperature change trend in multiple sampling periods in the future and obtain the temperature prediction value. A three-loop timing coordination mechanism of prediction-decoupling-self-learning is established, and the working weight of the three loops is dynamically adjusted according to the real-time temperature control status. When the decoupling residual or prediction error exceeds the set threshold, rapid iteration is triggered. The PPO reinforcement learning algorithm is used to construct a multi-objective optimization function that includes temperature control accuracy and temperature uniformity, and automatically tunes the PID control parameters of each zone. Based on the thermal characteristics differences between the center and edge zones of the hot plate, a differentiated composite control strategy is executed. The power control quantity of each zone is calculated based on the optimized PID parameters and LSTM prediction feedforward compensation. Adjacent zones are coupled and compensated through a power coordination mechanism between zones, and the final heating power control signal is output to drive the heating element to work. The system collects the actual temperature of each zone in real time, calculates the temperature control error, decoupling residual, and prediction error. When the error exceeds the preset threshold, it triggers corresponding decoupling coefficient correction, prediction model update, parameter optimization, or database rematching operations to form a closed-loop feedback control.

2. The method according to claim 1, characterized in that, The health status parameters of the hot plate include the aging coefficient of the heating element, the thermal resistance coefficient of the hot plate fouling, and the drift coefficient of the temperature sensor, which are calculated through historical power-temperature response data. Furthermore, the noise reduction process adopts a composite noise reduction of wavelet transform and empirical mode decomposition (EMD). The db4 wavelet basis is used for three-level decomposition to eliminate high-frequency electromagnetic interference, and then EMD is used to eliminate low-frequency ambient temperature drift.

3. The method according to claim 1, characterized in that, In the multivariable decoupling model based on the two-dimensional heat conduction equation specific to the hot plate, the temperature dynamic characteristics of the i-th partition are expressed as follows: Represents the Laplace transform of the temperature of the i-th partition. This represents the Laplace transform of the heating power control quantity of the i-th partition; Represents the self-channel transfer function of the i-th partition; This represents the coupling channel transfer function from the j-th partition to the i-th partition; Indicates the thermal coupling space attenuation coefficient; This represents the center distance between the i-th partition and the j-th partition; Let represent the Laplace transform of the perturbation signal in the i-th partition.

4. The method according to claim 3, characterized in that, The asymmetric decoupling matrix satisfy: in This represents the power control vector of each partition before decoupling; This represents the equivalent power control vector for each partition after decoupling, with elements... Based on the differentiated design of partition distance and thermal coupling space attenuation characteristics, the results are identified through a BP neural network.

5. The method according to claim 1, characterized in that, The online identification and update of the coupling coefficient based on real-time operating conditions adopts a BP neural network. The inputs are the power, disturbance, and real-time temperature change rate of each zone, and the output is the temperature of each zone. The loss function is: in The number of training samples. Let i be the actual temperature of the i-th region of the m-th sample. To predict temperature using the model, train to Stop at a certain time to obtain the precise coupling coefficient; The coupling coefficient is corrected every 10 sampling periods based on real-time operating data.

6. The method according to claim 1, characterized in that, The Smith predictor fusion compensation uses the hysteresis compensation amount Δτ as the hidden layer bias correction term of the LSTM model.

7. The method according to claim 1, characterized in that, The threshold for triggering rapid iteration is set as follows: when the decoupling residual > 0.03℃ or the prediction error > 0.05℃, rapid iteration of PPO self-learning is immediately triggered and the iteration step size is increased by 50%.

8. The method according to any one of claims 5 to 7, characterized in that, The differentiated composite control strategy includes: The central zone uses "LSTM feedforward + integral separation PID" control to avoid integral saturation during the heating stage and suppress thermal inertia overshoot; The edge partition adopts "LSTM feedforward + derivative-first PID" control, which prioritizes the differentiation of temperature measurement values ​​to suppress environmental interference.

9. The method according to claim 8, characterized in that, The specific inter-zone power coordination mechanism is as follows: when a certain zone adjusts its power, micro-power compensation is performed on adjacent zones based on the real-time coupling coefficient of the decoupling module to avoid temperature fluctuations in adjacent zones caused by power adjustment of a single zone.

10. The method according to claim 9, characterized in that, The closed-loop feedback correction step includes a multi-level triggering mechanism: Level 1 feedback: When the temperature control error is >0.05℃, immediately adjust the PID control input and feedforward compensation input; Secondary feedback: When the decoupling residual is >0.03℃, the online correction of the coupling coefficient of the decoupling module is triggered; Three-level feedback: When the prediction error is >0.05℃, the bias correction and rapid iteration of the self-learning module of the LSTM prediction model are triggered. Level 4 feedback: When the temperature control error is >0.1℃ for 10 consecutive sampling cycles, the parameter database is re-matched and the global optimization is triggered.

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