A method for controlling the temperature of a substrate before coating a photomask substrate

Abstract

The present application relates to the technical field of substrate temperature control, and particularly relates to a substrate temperature control method before film coating of a photomask substrate, which comprises the following steps: collecting a heating temperature of a film coating device, a surface temperature of the substrate and an ambient temperature in real time, and performing heat field calculation on a three-dimensional dynamic heat network model by combining with thermal physical parameters of the substrate to predict a target future temperature field distribution of the substrate under the influence of the heating of the film coating device; calculating a required heat compensation signal of each substrate sub-region on the substrate according to the target future temperature field distribution and a target substrate temperature; controlling a heat compensation array integrated on the substrate to perform partition heat compensation processing on the substrate according to the heat compensation signal, and obtaining control data of the partition heat compensation processing; and updating a mapping rule of the three-dimensional dynamic heat network model and the heat compensation signal based on the real-time heating temperature, the real-time surface temperature, the real-time ambient temperature and the control data obtained in the present collection, so that the problem of heat interference caused by the heating of the film coating device on the substrate is solved.

Description

Technical Field

[0001] This invention relates to the field of substrate temperature control technology, and more specifically to a method for controlling the substrate temperature before photomask substrate coating. Background Technology

[0002] In the photomask manufacturing process, precise and uniform temperature control of the glass substrate before coating is crucial. It directly determines the adhesion, internal stress, thickness uniformity and microstructure of the subsequently deposited thin film (such as chromium film), thus affecting the dimensional accuracy and service life of the photomask.

[0003] Currently, the industry mainly relies on precise air conditioning control of the cleanroom or local cavity environment of the coating equipment to control the temperature of the substrate before coating. This involves controlling the temperature of the air medium surrounding the substrate to bring it to and maintain the set process temperature. However, because the coating equipment itself generates continuous and uneven heat during operation, these heat sources create dynamically changing local microclimates around the substrate. Even if the ambient air temperature is stably controlled within a high precision range of ±0.1℃, the substrate itself, especially different areas of the substrate, is still in a non-uniform temperature field that is subject to real-time interference from the equipment's operating status. This results in unpredictable gradients and fluctuations in the actual substrate temperature, which cannot improve the quality and batch consistency of the photomask film. Summary of the Invention

[0004] To address the technical problem of thermal interference to the substrate caused by the heat source of the coating equipment itself, this application provides a method for controlling the substrate temperature before coating a photomask substrate.

[0005] This application provides a substrate temperature control method before coating a photomask substrate, which employs the following technical solution: A method for controlling the substrate temperature before coating a photomask substrate includes: By collecting the heating temperature of the coating equipment in real time, as well as the surface temperature of the substrate and the ambient temperature, and combining the thermal properties of the substrate, thermal field calculation is performed on a three-dimensional dynamic thermal network model to predict the target future temperature field distribution of the substrate under the influence of the heating of the coating equipment. Based on the target future temperature field distribution and the target substrate temperature, calculate the required thermal compensation signal for each substrate sub-region on the substrate. Based on the thermal compensation signal, the thermal compensation array integrated on the substrate is controlled to perform partitioned thermal compensation processing on the substrate, and control data for partitioned thermal compensation processing is obtained. Based on the currently acquired real-time heating temperature, real-time surface temperature, real-time ambient temperature, and control data, the mapping rules of the three-dimensional dynamic thermal network model and thermal compensation signal are updated.

[0006] Furthermore, by collecting real-time data on the heating temperature of the coating equipment, the surface temperature of the substrate, and the ambient temperature, and combining this data with the substrate's thermal properties, the thermal field is calculated on a three-dimensional dynamic thermal network model. The steps to predict the target future temperature field distribution of the substrate under the influence of the coating equipment's heating include: Based on the heating temperature, surface temperature and ambient temperature, combined with historical coating temperature change curves and material thermal property parameters retrieved from the process database, a three-dimensional dynamic thermal network model of the substrate in the coating equipment is constructed. In a three-dimensional dynamic thermal network model, the equivalent thermal load distribution of the equipment heat source corresponding to the operating power parameters of the coating equipment is loaded to obtain the initial future temperature field distribution. The first heating temperature, the first surface temperature, and the first ambient temperature are used as the boundary conditions and feedback inputs of the three-dimensional dynamic thermal network model to correct the initial future temperature field distribution in real time and predict the target future temperature field distribution.

[0007] Furthermore, the steps for loading the equivalent heat load distribution of the equipment heat source corresponding to the operating power parameters of the coating equipment into the three-dimensional dynamic thermal network model to obtain the initial future temperature field distribution include: Based on the current operating power parameters and the next operating power parameters, the total heat generation of each heat-generating component in the coating equipment can be obtained by querying the preset power-heating characteristic mapping table; Based on the thermal design layout information of the coating equipment, the total heat generation is distributed according to the relative geometric position and heat transfer path of each heat-generating component to the substrate, and the equivalent heat load distribution of the equipment heat source is obtained. The equivalent heat load distribution of the equipment's heat source is loaded as a time-varying endogenous heat source term into the network nodes of the three-dimensional dynamic thermal network model, and the initial future temperature field distribution is obtained by solving.

[0008] Furthermore, the steps of using the currently acquired first heating temperature, first surface temperature, and first ambient temperature as boundary conditions and feedback inputs for the three-dimensional dynamic thermal network model to real-time correct the initial future temperature field distribution and predict the target future temperature field distribution include: The first heating temperature and the first ambient temperature are input as boundary conditions into the three-dimensional dynamic thermal network model to update the thermal state of the three-dimensional dynamic thermal network model and calculate the updated initial future temperature field distribution. The initial predicted temperature distribution in the updated initial future temperature field distribution is compared with the first surface temperature to calculate the real-time prediction error of the three-dimensional dynamic thermal network model. Based on the real-time prediction error, the initial future temperature field distribution is weighted and corrected to obtain the target future temperature field distribution.

[0009] Furthermore, the step of calculating the required thermal compensation signal for each substrate sub-region on the substrate, based on the target future temperature field distribution and the target substrate temperature, includes: By comparing the predicted substrate temperature with the target substrate temperature for each substrate sub-region shown in the target future temperature field distribution, the temperature deviation value of each substrate sub-region is obtained. Based on each temperature deviation value, the heat flow compensation amount for each substrate sub-region is calculated by combining the thermal resistance and thermal capacity parameters of the corresponding substrate sub-region. In the heat flow-signal mapping table, the heat compensation signal for each substrate sub-region is obtained by querying the heat flow compensation amount.

[0010] Furthermore, the step of controlling the thermal compensation array integrated on the substrate to perform zoned thermal compensation processing on the substrate based on the thermal compensation signal, and acquiring control data for the zoned thermal compensation processing includes: Analyze each thermal compensation signal to obtain the drive current required to drive the corresponding thermal compensation device; After converting each driving current into a corresponding analog electrical signal, the corresponding thermal compensation device is driven to perform zoned thermal compensation processing based on each analog electrical signal. Record the actual drive current and actual power consumption of each thermal compensation device when performing zoned thermal compensation processing to obtain control data.

[0011] Furthermore, based on the currently acquired real-time heating temperature, real-time surface temperature, real-time ambient temperature, and control data, the steps for updating the mapping rules of the three-dimensional dynamic thermal network model and thermal compensation signal include: The temperature prediction error of the three-dimensional dynamic thermal network model is obtained by comparing the real-time heating temperature, real-time surface temperature, and real-time ambient temperature with the target future temperature field distribution. Backpropagation is performed based on temperature prediction errors to correct the heat transfer parameters in the three-dimensional dynamic heat network model, resulting in an updated three-dimensional dynamic heat network model; and, By comparing and analyzing the control data and heat flux compensation, the actual control error is calculated. Based on the actual control error, the mapping coefficients of the heat flow-signal mapping table are optimized to obtain an updated heat flow-signal mapping table.

[0012] Beneficial effects achieved: This application provides a method for controlling the substrate temperature before coating a photomask substrate, comprising: calculating the thermal field on a three-dimensional dynamic thermal network model by real-time acquisition of the heating temperature of the coating equipment, the surface temperature of the substrate, and the ambient temperature, combined with the thermal property parameters of the substrate, to predict the target future temperature field distribution of the substrate under the influence of the heating of the coating equipment; calculating the required thermal compensation signal for each sub-region of the substrate based on the target future temperature field distribution and the target substrate temperature; controlling the thermal compensation array integrated on the substrate to perform partitioned thermal compensation processing on the substrate according to the thermal compensation signal, and acquiring the control data of the partitioned thermal compensation processing; and updating the mapping rules of the three-dimensional dynamic thermal network model and the thermal compensation signal based on the currently acquired real-time heating temperature, real-time surface temperature, real-time ambient temperature, and control data.

[0013] In this application, by real-time acquisition of the heating temperature of the coating equipment, the surface temperature of the substrate, and the ambient temperature, and combining the thermal properties of the substrate to perform thermal field calculations on a three-dimensional dynamic thermal network model, the target future temperature field distribution of the substrate under the influence of the heating of the coating equipment can be accurately predicted, thereby directly quantifying the dynamic thermal interference caused by the heating source of the equipment to the substrate. Based on the target future temperature field distribution and the target substrate temperature, the required thermal compensation signal for each sub-region of the substrate is calculated, so that the compensation measures for thermal interference can be specified and zoned. According to the thermal compensation signal, the thermal compensation array integrated on the substrate is controlled to perform zoned thermal compensation processing on the substrate, and active heat is applied to offset the local temperature deviation caused by the heating of the equipment, so as to achieve uniform control of the substrate temperature. Based on the real-time acquisition of the heating temperature, real-time surface temperature, real-time ambient temperature, and control data of the zoned thermal compensation processing, the mapping rules of the three-dimensional dynamic thermal network model and the thermal compensation signal are updated, so that the entire system can adapt to the changes in the heating state of the equipment, continuously optimize the prediction and compensation accuracy, and finally form a closed-loop control process from prediction, compensation to feedback update, effectively overcoming the dynamic thermal interference caused by the heating source of the coating equipment itself to the substrate. Attached Figure Description

[0014] Figure 1 This is a schematic flowchart of a method for controlling substrate temperature before coating a photomask substrate according to this application. Figure 2 A schematic diagram of the steps to predict the target future temperature field distribution of a substrate under the influence of heat generation in the coating equipment. Figure 3 A flowchart illustrating the steps for calculating the thermal compensation signal required for each sub-region of the substrate. Figure 4 A flowchart illustrating the steps for performing zoned thermal compensation on a substrate and acquiring control data. Figure 5A flowchart illustrating the steps involved in updating the mapping rules for the three-dimensional dynamic thermal network model and thermal compensation signals. Detailed Implementation

[0015] The following combination Figures 1 to 5 This application will be described in further detail.

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0017] It should be noted that if the embodiments of the present invention involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative positional relationship and movement of the components in a specific posture. If the specific posture changes, the directional indications will also change accordingly.

[0018] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the use of "and / or" or "and / or" throughout the text includes three parallel solutions. For example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0019] This application discloses a method for controlling the substrate temperature before photomask substrate coating.

[0020] Please refer to Figure 1 The substrate temperature control method proposed in this embodiment before photomask substrate coating includes steps S10~S40: Step S10: By collecting the heating temperature of the coating equipment in real time, as well as the surface temperature of the substrate and the ambient temperature, and combining the thermal property parameters of the substrate, the thermal field is calculated on the three-dimensional dynamic thermal network model to predict the target future temperature field distribution of the substrate under the influence of the heating of the coating equipment.

[0021] This step constructs a three-dimensional dynamic thermal network model that can detect and quantify the dynamic and non-uniform thermal impact of the heat sources inherent in the coating equipment on the substrate in advance. It collects three types of data in real time: the heating temperature of the coating equipment, the surface temperature of the substrate, and the ambient temperature. These data, combined with the substrate's own thermal properties, are input into the three-dimensional dynamic thermal network model to perform thermal field calculations. This transforms the difficult-to-observe and analyze thermal interference from the equipment into a visualized prediction of the substrate's future temperature field—the target future temperature field distribution. This shifts the focus from passively responding to changes in ambient temperature to actively predicting the evolution of the substrate's temperature. It provides essential and highly reliable decision-making basis for subsequent accurate temperature compensation, enabling the entire control system to predict the substrate temperature distribution caused by the thermal interference from the coating equipment and plan compensation strategies in advance, rather than making delayed and limited adjustments after temperature deviations occur.

[0022] Step S20: Based on the target future temperature field distribution and the target substrate temperature, calculate the required thermal compensation signal for each substrate sub-region on the substrate.

[0023] The target future temperature field distribution obtained through the above steps is transformed into a series of thermal compensation signals for each sub-region of the substrate. This is based on comparing the predicted target future temperature field distribution with the preset target substrate temperature and calculating the required thermal compensation signal for each sub-region. This achieves spatial decoupling and precise quantification of the control strategy, decomposing the overall goal of "stabilizing the overall substrate temperature" into the control task of "how much heat or cold needs to be applied to each specific sub-region of the substrate". This effectively transforms the predicted target future temperature field distribution into an operable compensation plan, generating a set of thermal compensation signals to drive the subsequent thermal compensation array. This ensures that the subsequent physical compensation actions can accurately match the predicted thermal interference in terms of spatial distribution and intensity, providing a direct and quantitative input basis for implementing localized and differentiated real-time temperature compensation.

[0024] Step S30: Based on the thermal compensation signal, control the thermal compensation array integrated on the substrate to perform partitioned thermal compensation processing on the substrate, and obtain control data for partitioned thermal compensation processing.

[0025] By converting the thermal compensation signal output from the above steps into a partitioned thermal compensation process that can be directly applied to the substrate, the thermal compensation array integrated on the substrate is controlled to perform partitioned thermal compensation processing on the sub-regions of the substrate based on the thermal compensation signal.

[0026] By generating heating or cooling temperatures in corresponding substrate sub-regions using a thermal compensation array, the system offsets localized temperature deviations in the substrate caused by predicted equipment heating, achieving uniform temperature control of the substrate's overall temperature field. Simultaneously, it acquires control data for zoned thermal compensation processing, providing crucial action execution feedback and recording the relationship between the actual applied compensation energy and the thermal compensation signal. This dynamically alters the real-time thermal state of the substrate, putting the predictions and plans of the preceding steps into practice. This effectively suppresses equipment thermal interference, maintains the target substrate temperature, and provides control data on the actual response of the thermal compensation array for subsequent optimization of the mapping rules of the three-dimensional dynamic thermal network model and thermal compensation signal. This ensures the accuracy, reliability, and variability of the entire control process.

[0027] Step S40: Based on the currently acquired real-time heating temperature, real-time surface temperature, real-time ambient temperature, and control data, update the mapping rules of the three-dimensional dynamic thermal network model and thermal compensation signal.

[0028] This system enables self-learning and continuous optimization to address potential changes in equipment status, environmental conditions, or substrate characteristics during the process. Based on the currently acquired real-time heating temperature, real-time surface temperature, real-time ambient temperature, and control data from the partitioned thermal compensation processing obtained in the previous steps, it updates the mapping rules of the three-dimensional dynamic thermal network model and thermal compensation signals, forming a complete "perception-decision-execution-learning" closed loop. The latest control data is used to verify and correct the accuracy of the three-dimensional dynamic thermal network model, while the control data of the thermal compensation array is used to calibrate the mapping relationship of the thermal compensation signal output. This dynamically eliminates model errors and mapping errors, realizing the transformation from static open-loop control to dynamic adaptive closed-loop control. This allows the three-dimensional dynamic thermal network model to increasingly accurately reflect the real physical relationship between equipment heating and substrate temperature, and the mapping rules of the thermal compensation signal to increasingly accurately drive the thermal compensation array to produce the expected thermal effect. This ensures that the entire temperature control method maintains high accuracy and robustness even when facing long-term operational drift, individual differences between different equipment, or changes in process parameters. It effectively solves the fundamental problem that traditional methods cannot overcome dynamic thermal interference in the long term due to fixed models and lack of feedback.

[0029] In one feasible implementation, refer to Figure 2 As shown, step S10 may specifically include steps S11 to S13: Step S11: Based on the heating temperature, surface temperature, and ambient temperature, and combined with historical coating temperature change curves and material thermal property parameters retrieved from the process database, a three-dimensional dynamic thermal network model of the substrate within the coating equipment is constructed.

[0030] First, based on the solid three-dimensional geometry of the substrate, the substrate and the surrounding space of interest are divided into a series of continuous and non-overlapping control volume units. The mass or energy concentration point or its geometric center of each control volume unit is defined as a thermal network node of the model. After determining the specific positions of all thermal network nodes in three-dimensional space, based on the spatial adjacency relationship between thermal network nodes and the isotropic or anisotropic thermal properties (especially thermal conductivity) of the substrate material, thermal resistance connections representing heat conduction paths are established between adjacent thermal network nodes that have direct physical contact or significant heat exchange through a medium. At each thermal network node, node thermal capacity parameters representing thermal energy storage capacity are set according to the material density and specific heat capacity within its representative volume, thereby forming a three-dimensional network topology with thermal network nodes as points and thermal resistance connections as edges.

[0031] Then, the real-time collected heating temperature, surface temperature, and ambient temperature are used as known boundary conditions and initial state values ​​of some thermal network nodes, and assigned to the 3D network topology to align the thermal state of the 3D network topology at the initial moment of simulation with the current actual measured values. Using historical coating temperature change curves recorded under the same or similar process conditions retrieved from the process database as a target benchmark, the heating power time-series data of the coating equipment corresponding to the historical coating temperature change curve and the ambient temperature conditions are used as inputs in the simulation environment to drive the 3D network topology to perform dynamic heat conduction simulation calculations, obtaining its simulated temperature change curve output. Next, the simulated temperature change curve output is compared with the historical coating temperature change curve over the same time series to quantify the error between them. Based on this error, the thermal resistance and thermal capacity parameters in the 3D network topology are iteratively adjusted until the error between the simulated temperature change curve and the historical coating temperature change curve is within a preset tolerance range. Finally, another set of independent historical coating temperature change curves that were not involved in the above calibration process were used to verify the three-dimensional network topology with completed parameter adjustments. It was confirmed that the error between the simulation output and the new historical coating temperature change curve was within the preset tolerance range. It was then considered that the parameter calibration and verification in the three-dimensional network topology at this time were completed. This resulted in a three-dimensional dynamic thermal network model whose internal thermal resistance and thermal capacity parameters had been calibrated with historical data and could more accurately reflect the actual thermal behavior in this specific process and equipment.

[0032] This three-dimensional dynamic thermal network model not only inherently incorporates the thermophysical properties of the substrate material, but also initializes the current thermal state by integrating real-time measured heating temperature, surface temperature, and ambient temperature. Furthermore, it uses historical coating temperature change curves to correct the model's simulation accuracy for actual complex heat exchange processes, thus laying a reliable digital computational foundation for accurately predicting the impact of dynamic disturbances such as device heating on the substrate temperature field.

[0033] Step S12: Load the equivalent heat load distribution of the equipment heat source corresponding to the operating power parameters of the coating equipment into the three-dimensional dynamic thermal network model to obtain the initial future temperature field distribution.

[0034] By loading the equivalent heat load distribution of the equipment heat source corresponding to the operating power parameters of the coating equipment into the constructed three-dimensional dynamic thermal network model, the initial future temperature field distribution can be calculated. In this way, the equipment working command represented in the form of electrical power is transformed into a three-dimensional dynamic thermal network model with a clear three-dimensional spatial location and internal heat source item through a preset mapping relationship and spatial allocation rules. This yields the dynamic thermal disturbance process (i.e., temperature field distribution) caused by the equipment's heating on the substrate. The three-dimensional dynamic thermal network model can simulate in advance the spatiotemporal evolution of the temperature of the substrate due to the equipment's own heating without any active temperature compensation intervention, based on the process program that the equipment is about to execute or is currently executing. This provides a baseline prediction for the subsequent accurate calculation of the required compensation amount.

[0035] Furthermore, step S12 also includes steps S121 to S123: Step S121: Based on the current operating power parameters and the next operating power parameters, the total heat generation of each heat-generating component in the coating equipment is obtained by querying the preset power-heating characteristic mapping table.

[0036] It should be noted that the preset power-heating characteristic mapping table is a lookup table that stores the heat generation of each heat-generating component of the coating equipment (such as sputtering source, substrate heater, vacuum pump group, etc.) under different operating power parameters (such as current, voltage or power setting value) through experimental calibration or establishment.

[0037] First, the current operating power parameter value and the next operating power parameter, representing the current working status of each heat-generating component, are obtained in real time from the equipment control unit. Then, using these parameters as indexes, a matching query is performed in a preset power-heating characteristic mapping table to retrieve the real-time heat generation of each heat-generating component corresponding to the current operating power parameter, and the predicted heat generation of each heat-generating component corresponding to the next operating power parameter. Finally, these two sets of heat generation data are integrated along the time dimension according to the process sequence. Specifically, after retrieving the current total heat generation corresponding to the current operating power parameter... And the predicted total heat generation corresponding to the next operating power parameters. Then, first determine the time interval from the current time T0 to the future time T1 when the next operating power parameters are set. For scenarios requiring the generation of continuously changing curves, this time interval... Within this timeframe, linear interpolation or other pre-defined smoothing transition functions (such as exponential smoothing) are used, with time as the variable. and The weighted calculation is performed to determine the total heat generation at any intermediate time t (T0 < t < T1). ,in, It is a weighting function with values ​​ranging from 0 to 1, thus generating a curve of total calorific value change that transitions smoothly and continuously over time. .

[0038] Finally, the heat generated by all heating components during this period is summed to obtain the total heat generated by each heating component in the coating equipment.

[0039] The next step involves obtaining the operating power parameters from preset process recipes or equipment control programs in real time.

[0040] Step S122: Based on the thermal design layout information of the coating equipment, the total heat generation is distributed according to the spatial distribution based on the relative geometric position and heat transfer path of each heat-generating component to the substrate, thereby obtaining the equivalent heat load distribution of the equipment's heat source.

[0041] First, the thermal design layout information of the coating equipment is retrieved from the equipment design database. This information clearly defines the three-dimensional spatial coordinates, geometry, and dimensions of each heating component within the coating equipment cavity in the coating equipment coordinate system, as well as their relative orientation and distance to the substrate. After calculating the total heat generation of the coating equipment at a specific moment, the total heat generation is initially allocated to each heating component proportionally based on its rated power ratio or measured power ratio. After obtaining the heat generation of each heating component, for each component, based on its relative geometric position to each thermal network node on the substrate and a specific heat transfer path (such as direct radiation, convection through the cavity gas, or conduction through mechanical supports), the heat transfer coefficient calculated based on heat transfer formulas is used to calculate the heat distribution weight of the heat generated by the heating component to each thermal network node on the substrate. Specifically: ① For the radiative heat transfer path, the radiating surface of the heating element and the micro-element surfaces represented by each thermal network node of the substrate are approximated as diffuse gray surfaces. Based on the relative orientation and distance between them, the energy share of one surface directly radiated to another is determined by calculating the geometric viewing angle coefficient. This calculation is based on an analytical formula using the surface normal vector, the connecting distance, and the relative tilt angle. This is done after obtaining the surface of the heating element. To the substrate node surface Viewpoint coefficient Then, according to the Stefan-Boltzmann law, the net radiative heat transfer between the two surfaces... It is proportional to the difference of their fourth absolute temperatures, and can be expressed as ,in, It is the Stefan-Boltzmann constant. and These are the emissivity of the surface of the heat-generating component and the surface of the substrate node, respectively. and These are the temperatures of the surface of the heating element and the surface of the substrate node, respectively. By differentiating the Stefan-Boltzmann law with respect to temperature or performing a first-order Taylor expansion, an approximately linear relationship between radiative heat transfer and temperature difference can be obtained. Among them, the proportionality coefficient That is, radiative thermal conductivity, its expression is: ,in, It is the average temperature of the surface of the heating element and the surface of the substrate node; this linearized radiative thermal conductivity This is the reciprocal of the radiative heat transfer thermal resistance between the heating component and the specific thermal network node of the substrate, representing the heat transfer capability of the radiative path.

[0042] ② For convective heat transfer paths, clearly define the properties of the gas medium within the coating equipment cavity, including its type, density, specific heat capacity, thermal conductivity, and volumetric expansion coefficient. These parameters are typically determined by process conditions or gas composition. Simultaneously, determine the flow state based on the source of the driving force for gas flow within the coating equipment cavity. If the flow is driven solely by a density difference caused by temperature differences, it is natural convection; if driven by external forces such as fans or pumps, it is forced convection. Estimate or measure its characteristic flow velocity. Obtain the current temperature of the heating element surface and the average temperature of the gas medium in contact with it; the difference between the two is the driving temperature difference for convective heat transfer. Then, based on the determined flow state, select the appropriate empirical formula for convective heat transfer. For example, if it is natural convection, use the form: ,in, For Nusselt numbers, The Grashof number is calculated using the following formula: , The Prandtl number is calculated using the following formula: ,in, and As a constant that depends on the geometry and orientation of the heat exchange surface, It is the acceleration due to gravity. The coefficient of gas volume expansion. The temperature difference between the surface of the heating element and the contacting gas. The characteristic length of the surface of the heating element. The viscosity of the gas is kinematic. For gas thermal diffusivity; if it is forced convection, then the form is... The correlation, where, Let be the Reynolds number, and its formula is: ,in, , , As a constant that depends on the flow scenario and surface geometry, For gas density, Characteristic flow velocity, Let be the gas dynamic viscosity. After selecting a specific correlation, substitute the previously known gas physical properties, characteristic flow rate, and driving temperature difference into the corresponding calculation formulas for the Grashof number and Prandtl number or Reynolds number and Prandtl number to obtain the specific values ​​of these dimensionless numbers. Then, substitute these values ​​into the selected correlation to calculate the Nusselt number, which describes the intensity of that specific convective heat transfer. Then, according to Nusselt's numbers The definition of the convective heat transfer coefficient is used, combined with the gas thermal conductivity and the characteristic length of the heating element surface, to calculate the specific value of the convective heat transfer coefficient of the surface. Finally, the convective heat transfer coefficient is multiplied by the effective surface area of ​​the heating element participating in convection. The resulting product is the convective thermal conductance from the surface of the heating element to the surrounding gas medium, which characterizes the heat flow rate transferred through this convective path under a unit temperature difference. The convective heat transfer coefficient is... The Nusselt number is derived directly from its definition. ,in, It is the thermal conductivity of the gaseous medium.

[0043] ③ For the heat conduction path through the solid support structure, firstly, identify the solid connection structure between the heating component and the substrate for mechanical support and heat transfer, such as screws, thermal pads, or specially designed thermally conductive brackets, and determine its material composition. Next, obtain the thermal conductivity of this connection material at the corresponding operating temperature from a material property library or measured data. Simultaneously, based on the actual geometry of the solid support structure, measure the effective cross-sectional area along the heat transfer direction and the effective length along the transfer path from the heating component mounting point to the substrate support point. Then, calculate the thermal resistance of the solid support structure according to the basic form of the one-dimensional steady-state Fourier law of thermal conductivity, i.e., thermal resistance = effective length / (thermal conductivity × effective cross-sectional area). Finally, take the reciprocal of this thermal resistance to obtain the thermal conductivity. This thermal conductivity characterizes the heat flow rate conducted from the mounting point of the heating component to the substrate support point through the solid support structure under a unit temperature difference.

[0044] Then, for each identifiable heat transfer path from the heating component to a certain thermal network node on the substrate, the corresponding radiative thermal conductance, convective thermal conductance, and conductive thermal conductance are superimposed in parallel to obtain the total heat transfer thermal conductance from the heating component to the thermal network node. This total heat transfer thermal conductance is then divided by the sum of the total heat transfer thermal conductances from the heating component to all thermal network nodes on the substrate, resulting in a normalized value between 0 and 1. This value represents the heat distribution weight of the total heat generated by the heating component to the corresponding thermal network node on the substrate. This calculation is repeated for each thermal network node on the substrate to obtain the heat distribution weight describing the heat of the heating component to each corresponding thermal network node on the substrate. Next, the heat generated by each heating component is multiplied by its heat distribution weight to the corresponding thermal network node on the substrate to calculate the heat load contribution of the heating component to each thermal network node on the substrate. Finally, the heat load contributions of all heating components to the same thermal network node on the substrate are vector superimposed (when considering direction) or scalar accumulated to obtain a heat load field that defines how heat is distributed in the three-dimensional space of the substrate, i.e., the equivalent heat load distribution of the device's heat source.

[0045] Step S123: The equivalent heat load distribution of the equipment's heat source is loaded as a time-varying endogenous heat source term into the network nodes of the three-dimensional dynamic thermal network model, and the initial future temperature field distribution is obtained by solving.

[0046] As mentioned above, the equivalent heat load distribution of the equipment's heat source is a set of data that clearly defines the heat flux power values ​​applied to each node of the three-dimensional dynamic heat network model at each point in time within a future time sequence.

[0047] During loading, the heat flux power value corresponding to each discrete time point is used as the input of the endogenous heat source term driving the state change of the 3D dynamic thermal network model at that moment, and directly assigned to the corresponding thermal network node in the 3D dynamic thermal network model, in chronological order. Then, the simulation is advanced in one time step. Within each time step, the endogenous heat source term loaded at the current moment, the heat flux transferred between thermal network nodes through the thermal conductivity matrix, and the heat exchange between thermal network nodes and the environment are all substituted into the nodal energy balance equations based on the lumped heat capacity method:

[0048] This set of equations constitutes a set of ordinary differential equations describing the evolution of the system temperature over time, where, It is the heat capacity concentrated at the corresponding node; This corresponds to the temperature of the heat network node; It is time; This represents the rate of change of temperature at a thermal network node over time. It is the time-varying endogenous heat source power loaded onto the corresponding thermal network node, which is derived from the distribution of the equivalent heat load of the coating equipment's heat source. Indicates through thermal conduction With all other neighboring nodes The sum of heat flows that are transferred by conduction; This indicates that the thermal network node achieves equivalent thermal conductivity. With the environment (temperature is Convection and radiation heat transfer are carried out.

[0049] The process of solving the nodal energy balance equations based on the lumped heat capacity method using numerical integration is as follows: First, by left-multiplying the heat capacity matrix... The inverse (if) For a diagonal matrix, this simplifies to finding the reciprocals of each element, and can be rewritten in standard form. ,in, This comprehensively reflects the time-varying heat source Through thermal conductivity matrix Thermal network node conduction and interaction with ambient temperature Heat transfer contribution; at each time step Within, the temperature vector from the known current time ta Starting from this point, calculate the four intermediate slope vectors in sequence:

[0050]

[0051]

[0052]

[0053] The four slope vectors mentioned above are used to perform a weighted average to estimate the next time step. The node temperature vector is updated using the following formula: By iterating this time step process repeatedly until the calculation time covers the preset future simulation duration, the temperature vectors of all nodes corresponding to each time step from the current time to the future target time are arranged in chronological order to obtain the initial future temperature field distribution, which describes the predicted trajectory of the temperature state evolving from the current initial conditions under the equivalent thermal load driven by the time-varying device heat source.

[0054] Step S13: The first heating temperature, the first surface temperature, and the first ambient temperature currently collected are used as the boundary conditions and feedback inputs of the three-dimensional dynamic thermal network model to correct the initial future temperature field distribution in real time and predict the target future temperature field distribution.

[0055] This step, based on the goal of real-time correction and improved prediction accuracy, uses the currently acquired first heating temperature, first surface temperature, and first ambient temperature as boundary conditions and feedback inputs for the three-dimensional dynamic thermal network model. This allows for real-time correction of the initial future temperature field distribution. In other words, by dynamically updating the three-dimensional dynamic thermal network model using real-time measured data, the actual device state is tightly coupled with the predictions of the three-dimensional dynamic thermal network model. This compensates for initial prediction deviations caused by simplification of the three-dimensional dynamic thermal network model, parameter uncertainties, or external disturbances. It ensures that the three-dimensional dynamic thermal network model can track and reflect the real thermal dynamics, making the final target future temperature field distribution closer to the future thermal state evolution of the substrate in the actual operating environment. This provides timely and reliable decision-making basis for proactive thermal management, overheat warning, or performance optimization.

[0056] Furthermore, step S13 also includes steps S131 to S133: Step S131: Input the first heating temperature and the first ambient temperature as boundary conditions into the three-dimensional dynamic thermal network model to update the thermal state of the three-dimensional dynamic thermal network model and calculate the updated initial future temperature field distribution.

[0057] First, through preliminary experimental calibration or theoretical modeling, a function curve or data lookup table is established to describe the relationship between the temperature values ​​measured at key temperature measurement points of specific heat-generating components (such as sputtering targets, plasma sources, heaters, etc.) in the coating equipment and the actual heat generation power of the component, forming a preset power-temperature characteristic curve. The first heat generation temperature value collected by the temperature sensor installed at the key location of the heat-generating component is read in real time. Using this first heat generation temperature as input, the preset power-temperature characteristic curve is queried. After obtaining the actual heat generation power value corresponding to the heat-generating component at the current moment, the obtained actual heat generation power value is used as the updated time-varying endogenous heat source term and assigned to the corresponding heat network node representing the heat-generating component in the three-dimensional dynamic heat network model, thereby replacing the power value or theoretical value used in the previous prediction period.

[0058] Furthermore, the currently acquired first ambient temperature is directly assigned to the ambient temperature node in the 3D dynamic thermal network model, thereby updating the state of the ambient temperature node. Since all boundary nodes in the 3D dynamic thermal network model that exchange heat with the external environment through convection or radiation are connected to the ambient temperature node through an equivalent thermal conductivity, the amount of heat exchange with the environment is multiplied by the equivalent thermal conductivity by the first ambient temperature and the temperature value of the ambient temperature node before the update, thus synchronizing the heat exchange boundary conditions between the 3D dynamic thermal network model and the external environment with the current actual physical environment state.

[0059] After updating the heat source terms and environmental boundary conditions, the thermal state of the 3D dynamic thermal network model is refreshed. Using this corrected state as the new initial condition, the same heat conduction simulation process as in steps S12 and S123 is re-executed (i.e., loading the latest equivalent heat load distribution and performing time-progressive solution), thereby calculating an updated initial future temperature field distribution based on the latest measured state. By forcibly synchronizing the prediction baseline of the 3D dynamic thermal network model with the real-time operating thermal state of the real-world equipment, the prediction error caused by the drift accumulated over time between the model's initial state and the actual state is eliminated.

[0060] Step S132: Compare the initial predicted temperature distribution in the updated initial future temperature field distribution with the first surface temperature to calculate the real-time prediction error of the three-dimensional dynamic thermal network model.

[0061] From the updated initial future temperature field distribution, the predicted temperature values ​​of one or more thermal network nodes in the three-dimensional dynamic thermal network model that precisely correspond to the physical positions of the sensors installed on the substrate surface for collecting the first surface temperature are extracted at the current moment. This forms a set of predicted temperatures characterizing the predicted state of the substrate surface temperature. Then, the predicted temperature set is matched one-to-one with the set of measured values ​​of the first surface temperature collected in real time by the substrate surface temperature sensor. The difference between the predicted temperature value and the measured temperature value at each corresponding spatial position is calculated, and statistical methods (such as calculating the mean absolute error or root mean square error of these differences) are used to aggregate the deviations at all positions, thereby quantifying a real-time prediction error characterizing the overall prediction accuracy of the three-dimensional dynamic thermal network model for the substrate surface temperature.

[0062] Step S133: Based on the real-time prediction error, the initial future temperature field distribution is weighted and corrected to obtain the target future temperature field distribution.

[0063] The real-time prediction error is used as a correction factor and distributed across the entire prediction time axis of the initial future temperature field distribution according to a weighting function that decays over time.

[0064] For any predicted future time Its corrected target temperature field distribution From the initial predicted distribution at that moment Plus real-time prediction error With weight The product is obtained, where the weight function is... The model is typically designed to smoothly decay from a value close to 1.0 at the current time to a value close to 0 at some future time. This means that the impact of the current model error on future predictions will gradually weaken over time and as the model itself dynamically advances.

[0065] By using measured data, the purely theoretical predicted trajectory of the three-dimensional dynamic thermal network model was corrected. This made the final output of the target future temperature field distribution not only mathematically compensate for the systematic deviation of the three-dimensional dynamic thermal network model at the current moment, but also maintain a reasonable transition of the correction amount in the time dimension. This significantly improved the overall accuracy and reliability of the three-dimensional dynamic thermal network model in predicting the future temperature field, and provided a decision benchmark for real-time thermal compensation control based on this prediction.

[0066] In one feasible implementation, refer to Figure 3 As shown, step S20 may specifically include steps S21 to S23: Step S21: Compare the predicted substrate temperature of each substrate sub-region shown in the target future temperature field distribution with the target substrate temperature to obtain the temperature deviation value of each substrate sub-region.

[0067] Based on the pre-divided substrate sub-regions, the predicted substrate temperature corresponding to each substrate sub-region at the current or future specific control moment is extracted from the predicted target future temperature field distribution; at the same time, the preset target substrate temperature corresponding to the process requirements is called. This target substrate temperature is usually a globally constant setpoint, or a spatial distribution field predefined according to the process requirements of different substrate sub-regions.

[0068] Then, a subtraction operation is performed on each substrate sub-region, that is, the predicted substrate temperature of the corresponding substrate sub-region is subtracted from the corresponding target substrate temperature. The difference is the temperature deviation value of the corresponding substrate sub-region. This deviation value is a scalar with a positive or negative sign (indicating overheating or undercooling) and a specific value. By decoupling and quantifying the continuous future temperature field prediction information into a series of local control targets corresponding one-to-one with the thermal compensation device, the overall task of maintaining the uniform and stable temperature of the entire substrate is transformed into a quantitative task list for eliminating the specific temperature deviation of each independent substrate sub-region, providing the input basis for subsequent calculation of quantitative thermal compensation instructions.

[0069] Step S22: Based on each temperature deviation value, and combined with the thermal resistance and thermal capacity parameters of the corresponding substrate sub-region, calculate the heat flow compensation amount for each substrate sub-region.

[0070] Obtain the temperature deviation value of each substrate sub-region Simultaneously, from the stored substrate thermal characteristic parameters, pre-calibrated concentrated thermal resistance parameters corresponding to each substrate sub-region are retrieved. and lumped heat capacity parameters Then, for the set compensation response time constant Internal elimination of temperature deviation value Calculate the required amount of heat flux compensation. The specific calculation formula is as follows: The first term of the formula This represents the heat flux required to change the thermal state of the corresponding substrate sub-region, the magnitude of which is determined by the heat capacity of the substrate sub-region and the desired correction speed. (The second term...) This represents the heat flow that is continuously lost or introduced through thermal resistance during the correction process, ensuring that the net heat flow fully acts on the temperature change. This ensures that the calculated heat flow compensation not only meets the final temperature control target but also conforms to the physical laws and dynamic processes of heat conduction, laying a precise quantitative foundation for generating high-precision, dynamically responsive heat compensation signals.

[0071] Step S23: In the heat flow-signal mapping table, the heat compensation signal of each substrate sub-region is obtained by querying the heat flow compensation amount.

[0072] It should be noted that the heat flux-signal mapping table is a data comparison table established through experimental calibration. It defines the correspondence between heat flux compensation values ​​and heat compensation signals. That is, one column of the table is the predefined heat flux compensation value, which represents the heating or cooling power that needs to be applied to the corresponding substrate sub-region, and the other column is the corresponding heat compensation signal, which represents the control voltage or current required to drive the heat compensation device under the corresponding substrate sub-region.

[0073] The heat flux compensation amount of each substrate sub-region is used as a lookup key to search the heat flux-signal mapping table. If the heat flux compensation amount matches a predefined heat flux compensation value in the table, the corresponding heat compensation signal is read directly. If there is no exact match, the heat compensation signal corresponding to the predefined heat flux compensation value that is closest to the heat flux compensation value is extracted. This completes the conversion from physical energy demand to actual control command, ensuring that the calculated heat flux compensation amount can be accurately converted into the specific action of driving the heat compensation device to generate the required thermal effect.

[0074] In one feasible implementation, refer to Figure 4 As shown, step S30 may specifically include steps S31 to S33: Step S31: Analyze each thermal compensation signal to obtain the drive current required to drive the corresponding thermal compensation device.

[0075] If the thermal compensation signal itself is a digital quantity representing the magnitude of the target current, the parsing process directly reads this drive current. If the thermal compensation signal is given in other forms (such as an encoded value representing the target heat flow or a duty cycle parameter), the parsing process needs to map it to the corresponding drive current using a lookup table that matches the electrical characteristics of the thermal compensation device. This mapping relationship ensures the physical executability of the thermal compensation signal. By converting the control commands calculated by the upstream control algorithm into drive parameters that the power drive circuit of the thermal compensation device can directly recognize and execute, an input reference is provided for generating accurate analog electrical signals in subsequent steps, ensuring the accuracy and consistency of the entire thermal compensation execution chain.

[0076] Step S32: After converting each driving current into a corresponding analog electrical signal, drive the corresponding thermal compensation device to perform partitioned thermal compensation processing based on each analog electrical signal.

[0077] The drive current of each substrate sub-region is input to the corresponding digital-to-analog converter (DAC). Based on its built-in reference voltage and conversion resolution, the DAC converts the input drive current into an analog electrical signal with a corresponding voltage amplitude in a linear proportion. The analog voltage signal is then sent to a programmable current source drive circuit. The programmable current source drive circuit uses the analog voltage signal as a set reference to generate and output a pulse width modulated current that is stably proportional to the analog voltage signal and has sufficient driving capability. This pulse width modulated current is the actual drive current applied to both ends of the thermal compensation device.

[0078] Based on the actual driving current converted from analog electrical signals, each independently controllable thermal compensation device generates a corresponding Peltier heating effect to heat or cool its corresponding substrate sub-region, thereby performing zonal thermal compensation processing. This completes the signal conversion and power drive from the digital control domain to the physical execution domain, ensuring that the ideal control quantity calculated by the upper-level algorithm is converted into actual energy that can act on the physical world and change the local thermal state of the substrate without loss or distortion. This enables spatial selective adjustment of the entire substrate temperature field, offsetting the local microclimate caused by the heating of the coating equipment and achieving active and uniform control of the substrate temperature.

[0079] Step S33: Record the actual drive current and actual power consumption of each thermal compensation device when performing zoned thermal compensation processing to obtain control data.

[0080] By integrating a current sensor into the drive circuit of each thermal compensation device, the actual drive current value flowing through the thermal compensation device is sampled and measured in real time. At the same time, by measuring the actual operating voltage across the thermal compensation device, the real-time measured operating voltage value is multiplied by the actual drive current to calculate the actual power consumption of the corresponding thermal compensation device at the current moment. Then, at fixed time intervals or in response to specific events, the unique identifier of each thermal compensation device, the corresponding timestamp, and the associated actual drive current and actual power consumption are written as a complete execution record to a non-volatile storage medium or sent to a central data server, thereby forming structured control data.

[0081] By generating a feedback record of the actual working status of the thermal compensation device, it can not only be used to verify whether the preceding drive current is executed, but more importantly, by comparing the drive current with the actual drive current, the status of the drive link can be diagnosed. By analyzing the actual power consumption, the energy efficiency and health status of the thermal compensation device can be evaluated. This provides a closed-loop feedback data source for real-time calibration, performance evaluation, fault warning, and adaptive parameter updates of the three-dimensional dynamic thermal network model in subsequent steps, greatly enhancing the objectivity, reliability, and long-term operational stability of the control system.

[0082] In one feasible implementation, refer to Figure 5 As shown, step S40 may specifically include steps S41 to S44: Step S41: Compare the real-time heating temperature, real-time surface temperature, and real-time ambient temperature with the target future temperature field distribution to obtain the temperature prediction error of the three-dimensional dynamic thermal network model.

[0083] In the time dimension, the latest collected real-time heating temperature, real-time surface temperature, and real-time ambient temperature are aligned with the predicted temperature data corresponding to the same collection time in the target future temperature field distribution. In the spatial dimension, the location of each surface temperature sensor measurement point in the real-time surface temperature is matched with the predicted temperature value of the corresponding coordinate point in the target future temperature field distribution. Next, a point-by-point comparison is performed, that is, for each matched spatial point, the difference between the measured temperature value and the predicted temperature value is calculated, resulting in an instantaneous error distribution field composed of errors at numerous spatial points. The difference at each spatial point in the instantaneous error distribution field is squared, and then the average of all squares is calculated. Finally, the square root of the average is taken to obtain a scalar value, which is the temperature prediction error value. This temperature prediction error value not only directly reflects the degree of deviation between the prediction result of the three-dimensional dynamic thermal network model and reality under the current working conditions, but also provides numerical basis and optimization direction for targeted data-driven correction and optimization of the heat transfer parameters inside the three-dimensional dynamic thermal network model in subsequent steps.

[0084] Step S42: Backpropagation is performed based on the temperature prediction error to correct the heat transfer parameters in the three-dimensional dynamic heat network model, resulting in an updated three-dimensional dynamic heat network model.

[0085] The temperature prediction error is directly assigned or equivalently set as the loss function in the optimization algorithm. Therefore, the magnitude of the temperature prediction error is directly used as the only quantitative indicator to measure the prediction performance of the three-dimensional dynamic thermal network model. The smaller the value, the smaller the difference between the predicted output of the three-dimensional dynamic thermal network model and the actual measured value, that is, the higher the accuracy of the three-dimensional dynamic thermal network model. Therefore, the parameter correction process based on backpropagation is actually to iteratively adjust the heat transfer parameters inside the three-dimensional dynamic thermal network model so that the temperature prediction error of the loss function continues to decrease along the direction of gradient descent until it converges to a stable value that is as small as possible, thereby completing the optimization of the three-dimensional dynamic thermal network model.

[0086] A computational graph is constructed based on the differentiable mathematical representation of the 3D dynamic thermal network model. This computational graph encodes the entire data flow and computational relationship, starting from the heat transfer parameters as input, through the discretization of the heat conduction equation within the 3D dynamic thermal network model, the computation of thermal network nodes, and finally outputting the predicted temperature field distribution and aggregating it into the loss function value. Backpropagation is then performed, starting with the loss function and traversing the computational graph backwards, strictly applying the chain rule for gradient calculation layer by layer. Specifically, the partial derivative of the loss function with respect to each predicted temperature value in the target temperature field distribution output by the 3D dynamic thermal network model is first calculated. Then, based on the computational modules in the forward propagation of the 3D dynamic thermal network model... The local derivative rules of the blocks (for example, for linear thermal resistance relationships, the derivative of the output with respect to the thermal resistance parameter can be given by analogy with Ohm's law; for the dynamic equations of thermal capacity nodes, it involves the calculation of partial derivatives under time discretization) propagate the output gradient back to intermediate variables (such as heat flow and temperature change rate of each node) in turn, until it is traced back to each initial heat transfer parameter (such as thermal conductivity, heat capacity or thermal resistance coefficient). Finally, through this layer-by-layer gradient backpropagation, the partial derivative of the loss function with respect to each heat transfer parameter to be corrected in the three-dimensional dynamic thermal network model is calculated. These partial derivatives are the gradients, which quantify the direction and magnitude of the influence of small changes in each heat transfer parameter to be corrected on the overall prediction error.

[0087] Based on the calculated gradient and preset learning rate hyperparameters, all heat transfer parameters are updated synchronously. The update rule is to adjust parameter values ​​along the negative gradient direction to reduce the loss function. For example, for a parameter characterizing the thermal conductivity of a material in the 3D dynamic thermal network model, if gradient calculations show that increasing this value can reduce prediction errors, then the parameter value is increased proportionally during the update. After iterative parameter updates, the thermodynamic properties of the 3D dynamic thermal network model are corrected, resulting in a parameter-optimized 3D dynamic thermal network model, i.e., the updated 3D dynamic thermal network model. This achieves online parameter self-calibration of the 3D dynamic thermal network model. Through a data-driven feedback mechanism, the internal physical parameters of the model are adjusted, making its dynamic response characteristics continuously approximate the thermal behavior of the real controlled object. This significantly improves the temperature prediction accuracy of the 3D dynamic thermal network model under complex time-varying conditions, providing a reliable and adaptive prediction basis for the entire feedforward-feedback composite control system, and ensuring the accuracy and long-term effectiveness of zoned thermal compensation.

[0088] Step S43: Compare and analyze the control data and heat flux compensation amount to calculate the actual control error.

[0089] The actual power consumption of each thermal compensation device during the execution of zoned thermal compensation processing is extracted from the control data. Simultaneously, the expected heat flux compensation amount to be applied to the corresponding substrate sub-region, calculated by the preceding control, is obtained. The actual power consumption of each thermal compensation device is compared one-to-one with the heat flux compensation amount allocated to it. Specifically, the difference between the two values ​​within the same substrate sub-region is calculated: the actual power consumption minus the heat flux compensation amount. The resulting difference represents the actual control error of the corresponding substrate sub-region within the control cycle. This provides direct and accurate feedback for subsequent steps, ensuring that the entire thermal compensation control loop can self-correct based on the actual execution effect, gradually approaching the ideal control accuracy.

[0090] Step S44: Based on the actual control error, optimize the mapping coefficients of the heat flow-signal mapping table to obtain the updated heat flow-signal mapping table.

[0091] A heat flux-signal mapping table can be mathematically expressed as a set of thermal compensation signals (such as driving voltage) Mapped to predefined heat flux compensation values The coefficients, for example, in a simplified linear model, are related as follows: ,in, and This refers to the mapping coefficients to be optimized. By employing the least squares method, multiple sets of "heat compensation signal-heat flux compensation value" data pairs from all heat compensation devices within the current cycle are collected. With the objective of minimizing the sum of squared actual control errors of all data pairs, a new mapping coefficient is recalculated that makes the predefined heat flux compensation value closest to the actual heat flux compensation value. and Then, this set of optimized new mapping coefficients... and Replace the old coefficients stored in the original heat flow-signal mapping table. and This generates an updated heat flow-signal mapping table to compensate for execution errors caused by time-varying factors such as performance degradation of the heat compensation device, changes in contact thermal resistance, and changes in environmental heat dissipation conditions. This ensures that no matter how slowly the system state drifts, every heat compensation signal issued by the control algorithm can be continuously and accurately converted into the corresponding physical thermal effect, thereby maintaining the long-term stable operation and high-precision control of the entire partition heat compensation system.

[0092] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A method for controlling the substrate temperature before coating a photomask substrate, characterized in that, include: By collecting the heating temperature of the coating equipment in real time, as well as the surface temperature of the substrate and the ambient temperature, and combining the thermal property parameters of the substrate, thermal field calculation is performed on a three-dimensional dynamic thermal network model to predict the target future temperature field distribution of the substrate under the influence of the heating of the coating equipment. Based on the target future temperature field distribution and the target substrate temperature, calculate the required thermal compensation signal for each substrate sub-region on the substrate; Based on the thermal compensation signal, the thermal compensation array integrated on the substrate is controlled to perform partitioned thermal compensation processing on the substrate, and control data of the partitioned thermal compensation processing is obtained. Based on the currently acquired real-time heating temperature, real-time surface temperature, real-time ambient temperature, and the control data, the mapping rules of the three-dimensional dynamic thermal network model and the thermal compensation signal are updated. The thermal property parameters include historical coating temperature variation curves and material thermal property parameters. The step of predicting the target future temperature field distribution of the substrate under the influence of the coating equipment's heating temperature, substrate surface temperature, and ambient temperature obtained in real time, combined with the substrate's thermal property parameters, to perform thermal field calculations on a three-dimensional dynamic thermal network model includes: Based on the heating temperature, the surface temperature, and the ambient temperature, and combined with the historical coating temperature change curves retrieved from the process database and the material thermal property parameters, a three-dimensional dynamic thermal network model of the substrate within the coating equipment is constructed. In the three-dimensional dynamic thermal network model, the equivalent thermal load distribution of the equipment heat source corresponding to the operating power parameters of the coating equipment is loaded to obtain the initial future temperature field distribution. The first heating temperature, the first surface temperature, and the first ambient temperature currently collected are used as the boundary conditions and feedback inputs of the three-dimensional dynamic thermal network model to correct the initial future temperature field distribution in real time and predict the target future temperature field distribution.

2. The substrate temperature control method before coating of a photomask substrate according to claim 1, characterized in that, The operating power parameters include the current operating power parameters and the next operating power parameters. The step of loading the equivalent heat load distribution of the equipment heat source corresponding to the operating power parameters of the coating equipment into the three-dimensional dynamic thermal network model to obtain the initial future temperature field distribution includes: Based on the current operating power parameters and the next operating power parameters, the total heat generation of each heat-generating component in the coating equipment is obtained by querying the preset power-heating characteristic mapping table; Based on the thermal design layout information of the coating equipment, and according to the relative geometric position and heat transfer path of each heating component to the substrate, the total heat generation is distributed spatially to obtain the equivalent heat load distribution of the equipment's heat source. The equivalent heat load distribution of the device's heat source is loaded as a time-varying endogenous heat source term into the network nodes of the three-dimensional dynamic thermal network model, and the initial future temperature field distribution is obtained by solving.

3. The substrate temperature control method before coating of a photomask substrate according to claim 2, characterized in that, The step of using the currently acquired first heating temperature, first surface temperature, and first ambient temperature as boundary conditions and feedback inputs of the three-dimensional dynamic thermal network model to correct the initial future temperature field distribution in real time and predict the target future temperature field distribution includes: The first heating temperature and the first ambient temperature are used as boundary conditions and input into the three-dimensional dynamic thermal network model to update the thermal state of the three-dimensional dynamic thermal network model and calculate the updated initial future temperature field distribution. The initial predicted temperature distribution in the updated initial future temperature field distribution is compared with the first surface temperature to calculate the real-time prediction error of the three-dimensional dynamic thermal network model. Based on the real-time prediction error, the initial future temperature field distribution is weighted and corrected to obtain the target future temperature field distribution.

4. The substrate temperature control method before coating of a photomask substrate according to claim 1, characterized in that, The step of calculating the required thermal compensation signal for each substrate sub-region on the substrate based on the target future temperature field distribution and the target substrate temperature includes: By comparing the predicted substrate temperature of each substrate sub-region shown in the target future temperature field distribution with the target substrate temperature, a temperature deviation value for each substrate sub-region is obtained. Based on each temperature deviation value, the heat flow compensation amount for each substrate sub-region is calculated by combining the thermal resistance and thermal capacity parameters of the corresponding substrate sub-region. In the heat flow-signal mapping table, the heat compensation signal for each of the substrate sub-regions is obtained by querying based on the heat flow compensation amount.

5. The substrate temperature control method before coating of a photomask substrate according to claim 1, characterized in that, The thermal compensation array is composed of multiple thermal compensation devices arranged in a row, and each thermal compensation device corresponds one-to-one with a sub-region of the substrate. The step of controlling the thermal compensation array integrated on the substrate to perform zoned thermal compensation processing on the substrate according to the thermal compensation signal, and obtaining the control data of the zoned thermal compensation processing, includes: Analyze each of the thermal compensation signals to obtain the driving current required to drive the corresponding thermal compensation device; After each driving current is converted into a corresponding analog electrical signal, the corresponding thermal compensation device is driven to perform the partitioned thermal compensation process based on each analog electrical signal. The actual drive current and actual power consumption of each of the thermal compensation devices during the execution of the partition thermal compensation process are recorded to obtain the control data.

6. The substrate temperature control method before coating of a photomask substrate according to claim 4, characterized in that, The step of updating the mapping rules of the three-dimensional dynamic thermal network model and the thermal compensation signal based on the currently acquired real-time heating temperature, real-time surface temperature, real-time ambient temperature and the control data includes: The real-time heating temperature, the real-time surface temperature, and the real-time ambient temperature are compared with the target future temperature field distribution to obtain the temperature prediction error of the three-dimensional dynamic thermal network model. Backpropagation is performed based on the temperature prediction error to correct the heat transfer parameters in the three-dimensional dynamic heat network model, resulting in an updated three-dimensional dynamic heat network model; and, The actual control error is calculated by comparing and analyzing the control data and the heat flux compensation amount. Based on the actual control error, the mapping coefficients of the heat flow-signal mapping table are optimized to obtain an updated heat flow-signal mapping table.

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